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Fundamentals of

Corporate Finance

Eighth EDITION

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Fundamentals of

Corporate Finance

Richard A. Brealey London Business School

Stewart C. Myers Sloan School of Management, Massachusetts Institute of Technology

Alan J. Marcus Carroll School of Management, Boston College

Eighth EDITION

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THE McGRAW-HILL/IRWIN SERIES IN FINANCE, INSURANCE, AND REAL ESTATE

Stephen A. Ross, Franco Modigliani Professor of Financial Economics Sloan School of Management, Massachusetts Institute of Technology Consulting Editor

Financial Management

Block, Hirt, and Danielsen Foundations of Financial Management Fifteenth Edition

Brealey, Myers, and Allen Principles of Corporate Finance Eleventh Edition

Brealey, Myers, and Allen Principles of Corporate Finance, Concise Second Edition

Brealey, Myers, and Marcus Fundamentals of Corporate Finance Eighth Edition

Brooks FinGame Online 5.0

Bruner Case Studies in Finance: Managing for Corporate Value Creation Seventh Edition

Cornett, Adair, and Nofsinger Finance: Applications and Theory Third Edition

Cornett, Adair, and Nofsinger M: Finance Second Edition

DeMello Cases in Finance Second Edition

Grinblatt (editor) Stephen A. Ross, Mentor: Influence through Generations

Grinblatt and Titman Financial Markets and Corporate Strategy Second Edition

Higgins Analysis for Financial Management Tenth Edition

Kellison Theory of Interest Third Edition

Ross, Westerfield, and Jaffe Corporate Finance Tenth Edition

Ross, Westerfield, Jaffe, and Jordan Corporate Finance: Core Principles and Applications Fourth Edition

Ross, Westerfield, and Jordan Essentials of Corporate Finance Eighth Edition

Ross, Westerfield, and Jordan Fundamentals of Corporate Finance Tenth Edition

Shefrin Behavioral Corporate Finance: Decisions That Create Value First Edition

White Financial Analysis with an Electronic Calculator Sixth Edition

Investments

Bodie, Kane, and Marcus Essentials of Investments Ninth Edition

Bodie, Kane, and Marcus Investments Tenth Edition

Hirt and Block Fundamentals of Investment Management Tenth Edition

Hirschey and Nofsinger Investments: Analysis and Behavior Second Edition

Jordan, Miller, and Dolvin Fundamentals of Investments: Valuation and Management Seventh Edition

Stewart, Piros, and Heisler Running Money: Professional Portfolio Management First Edition

Sundaram and Das Derivatives: Principles and Practice First Edition

Financial Institutions and Markets

Rose and Hudgins Bank Management and Financial Services Ninth Edition

Rose and Marquis Financial Institutions and Markets Eleventh Edition

Saunders and Cornett Financial Institutions Management: A Risk Management Approach Eighth Edition

Saunders and Cornett Financial Markets and Institutions Sixth Edition

International Finance

Eun and Resnick International Financial Management Seventh Edition

Real Estate

Brueggeman and Fisher Real Estate Finance and Investments Fourteenth Edition

Ling and Archer Real Estate Principles: A Value Approach Fourth Edition

Financial Planning and Insurance

Allen, Melone, Rosenbloom, and Mahoney Retirement Plans: 401(k)s, IRAs, and Other Deferred Compensation Approaches Eleventh Edition

Altfest Personal Financial Planning First Edition

Harrington and Niehaus Risk Management and Insurance Second Edition

Kapoor, Dlabay, and Hughes Focus on Personal Finance: An Active Approach to Help You Develop Successful Financial Skills Fourth Edition

Kapoor, Dlabay, and Hughes Personal Finance Eleventh Edition

Walker and Walker Personal Finance: Building Your Future First Edition

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Dedication To Our Wives

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FUNDAMENTALS OF CORPORATE FINANCE, EIGHTH EDITION

Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2015 by McGraw- Hill Education. All rights reserved. Printed in the United States of America. Previous editions © 2012, 2009, 2007, 2004, 2001, 1999, and 1995. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning.

Some ancillaries, including electronic and print components, may not be available to customers outside the United States.

This book is printed on acid-free paper.

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ISBN 978-0-07-786162-9 MHID 0-07-786162-0

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Library of Congress Cataloging-in-Publication Data

Brealey, Richard A. Fundamentals of corporate finance / Richard A. Brealey, London Business School; Stewart C. Myers,

Sloan School of Management, Massachusetts Institute of Technology; Alan J. Marcus, Carroll School of Management, Boston College.—Eighth edition.

pages cm.—(The McGraw-Hill/Irwin series in finance, insurance and real estate) Includes index. ISBN-13: 978-0-07-786162-9 (alk. paper) ISBN-10: 0-07-338230-2 (alk. paper) 1. Corporations–Finance. I. Myers, Stewart C. II. Marcus, Alan J. III. Title. HG4026.B6668 2014 658.15–dc23 2014018986

The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites.

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vi

the Authors About

Richard A. Brealey Professor of Finance at the London Business School He is the former president of the European Finance Association and a former director of the American Finance Association. He is a fellow of the British Academy and has served as a special adviser to the Governor of the Bank of England and as director of a number of financial institutions. Professor Brealey is also the author (with Professor Myers and Franklin Allen) of this book’s sister text, Principles of Corporate Finance.

Stewart C. Myers Gordon Y Billard Professor of Finance at MIT’s Sloan School of Management He is past president of the American Finance Association and a research associate of the National Bureau of Economic Research. His research has focused on financing decisions, valuation methods, the cost of capital, and financial aspects of government regulation of business. Dr. Myers is a director of The Brattle Group Inc. and is active as a financial consultant. He is also the author (with Professor Brealey and Franklin Allen) of this book’s sister text, Principles of Corporate Finance.

Alan J. Marcus Mario Gabelli Professor of Finance in the Carroll School of Management at Boston College His main research interests are in derivatives and securities markets. He is co-author (with Zvi Bodie and Alex Kane) of the texts Investments and Essentials of Invest- ments. Professor Marcus has served as a research fellow at the National Bureau of Economic Research. Professor Marcus also spent two years at Freddie Mac, where he helped to develop mortgage pricing and credit risk models. He currently serves on the Research Foundation Advisory Board of the CFA Institute.

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vii

Preface

This book is about corporate finance. It focuses on how companies invest in real assets, how they raise the money to pay for these investments, and how those assets ulti- mately affect the value of the firm. It also provides a broad introduction to the financial landscape, discussing, for example, the major players in financial markets, the role of financial institutions in the economy, and how securities are traded and valued by investors. The book offers a framework for systematically thinking about most of the important financial problems that both firms and individuals are likely to confront.

Financial management is important, interesting, and challenging. It is important because today’s capital investment decisions may determine the businesses that the firm is in 10, 20, or more years ahead. Also, a firm’s success or failure depends in large part on its ability to find the capital that it needs.

Finance is interesting for several reasons. Financial decisions often involve huge sums of money. Large investment projects or acquisitions may involve billions of dollars. Also, the financial community is international and fast-moving, with colorful heroes and a sprinkling of unpleasant villains.

Finance is challenging. Financial decisions are rarely cut and dried, and the finan- cial markets in which companies operate are changing rapidly. Good managers can cope with routine problems, but only the best managers can respond to change. To handle new problems, you need more than rules of thumb; you need to understand why companies and financial markets behave as they do and when common practice may not be best practice. Once you have a consistent framework for making financial decisions, complex problems become more manageable.

This book provides that framework. It is not an encyclopedia of finance. It focuses instead on setting out the basic principles of financial management and applying them to the main decisions faced by the financial manager. It explains why the firm’s own- ers would like the manager to increase firm value and shows how managers choose between investments that may pay off at different points of time or have different degrees of risk. It also describes the main features of financial markets and discusses why companies may prefer a particular source of finance.

We organize the book around the key concepts of modern finance. These concepts, properly explained, simplify the subject. They are also practical. The tools of financial management are easier to grasp and use effectively when presented in a consistent conceptual framework. This text provides that framework.

Modern financial management is not “rocket science.” It is a set of ideas that can be made clear by words, graphs, and numerical examples. The ideas provide the “why” behind the tools that good financial managers use to make investment and financing decisions.

We wrote this book to make financial management clear, useful, interesting, and fun for the beginning student. We set out to show that modern finance and good finan- cial practice go together, even for the financial novice.

Fundamentals and Principles of Corporate Finance This book is derived in part from its sister text Principles of Corporate Finance. The spirit of the two books is similar. Both apply modern finance to give students a work- ing ability to make financial decisions. However, there are also substantial differences between the two books.

First, we provide much more detailed discussion of the principles and mechanics of the time value of money. This material underlies almost all of this text, and we spend a lengthy chapter providing extensive practice with this key concept.

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viii Preface

Second, we use numerical examples in this text to a greater degree than in Prin- ciples. Each chapter presents several detailed numerical examples to help the reader become familiar and comfortable with the material.

Third, we have streamlined the treatment of most topics. Whereas Principles has 34 chapters, Fundamentals has only 25. The relative brevity of Fundamentals neces- sitates a broader-brush coverage of some topics, but we feel that this is an advantage for a beginning audience.

Fourth, we assume little in the way of background knowledge. While most users will have had an introductory accounting course, we review the concepts of account- ing that are important to the financial manager in Chapter 3.

Principles is known for its relaxed and informal writing style, and we continue this tradition in Fundamentals. In addition, we use as little mathematical notation as pos- sible. Even when we present an equation, we usually write it in words rather than sym- bols. This approach has two advantages. It is less intimidating, and it focuses attention on the underlying concept rather than the formula.

Organizational Design Fundamentals is organized in eight parts.

Part 1 (Introduction)  provides essential background material. In the first chapter we discuss how businesses are organized, the role of the financial manager, and the financial markets in which the manager operates. We explain how shareholders want managers to take actions that increase the value of their investment, and we introduce the concept of the opportunity cost of capital and the trade-off that the firm needs to make when assessing investment proposals. We also describe some of the mecha- nisms that help to align the interests of managers and shareholders. Of course, the task of increasing shareholder value does not justify corrupt and unscrupulous behavior. We therefore discuss some of the ethical issues that confront managers.

Chapter 2 surveys and sets out the functions of financial markets and institutions. This chapter also reviews the crisis of 2007–2009. The events of those years illustrate clearly why and how financial markets and institutions matter.

A large corporation is a team effort, and so the firm produces financial statements to help the players monitor its progress. Chapter 3 provides a brief overview of these finan- cial statements and introduces two key distinctions—between market and book values and between cash flows and profits. This chapter also discusses some of the shortcom- ings in accounting practice. The chapter concludes with a summary of federal taxes.

Chapter 4 provides an overview of financial statement analysis. In contrast to most introductions to this topic, our discussion is motivated by considerations of valuation and the insight that financial ratios can provide about how management has added to the firm’s value.

Part 2 (Value)  is concerned with valuation. In Chapter 5 we introduce the concept of the time value of money, and, since most readers will be more familiar with their own financial affairs than with the big leagues of finance, we motivate our discussion by looking first at some personal financial decisions. We show how to value long- lived streams of cash flows and work through the valuation of perpetuities and annui- ties. Chapter 5 also contains a short concluding section on inflation and the distinction between real and nominal returns.

Chapters 6 and 7 introduce the basic features of bonds and stocks and give students a chance to apply the ideas of Chapter 5 to the valuation of these securities. We show how to find the value of a bond given its yield, and we show how prices of bonds fluctuate as interest rates change. We look at what determines stock prices and how stock valuation formulas can be used to infer the return that investors expect. Finally, we see how investment opportunities are reflected in the stock price and why analysts focus on the price-earnings multiple. Chapter 7 also introduces the concept of market

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Preface ix

efficiency. This concept is crucial to interpreting a stock’s valuation; it also provides a framework for the later treatment of the issues that arise when firms issue securities or make decisions concerning dividends or capital structure.

The remaining chapters of Part 2 are concerned with the company’s investment decision. In Chapter 8 we introduce the concept of net present value and show how to calculate the NPV of a simple investment project. We then consider more com- plex investment proposals, including choices between alternative projects, machine replacement decisions, and decisions of when to invest. We also look at other mea- sures of an investment’s attractiveness—its internal rate of return, payback period, and profitability index. We show how the profitability index can be used to choose between investment projects when capital is scarce. The appendix to Chapter 8 shows how to sidestep some of the pitfalls of the IRR rule.

The first step in any NPV calculation is to decide what to discount. Therefore, in Chapter 9 we work through a realistic example of a capital budgeting analysis, show- ing how the manager needs to recognize the investment in working capital and how taxes and depreciation affect cash flows.

We start Chapter 10 by looking at how companies organize the investment process and ensure everyone works toward a common goal. We then go on to look at various techniques to help managers identify the key assumptions in their estimates, such as sensitivity analysis, scenario analysis, and break-even analysis. We explain the dis- tinction between accounting break-even and NPV break-even. We conclude the chap- ter by describing how managers try to build future flexibility into projects so that they can capitalize on good luck and mitigate the consequences of bad luck.

Part 3 (Risk)  is concerned with the cost of capital. Chapter 11 starts with a historical survey of returns on bonds and stocks and goes on to distinguish between the specific risk and market risk of individual stocks. Chapter 12 shows how to measure market risk and discusses the relationship between risk and expected return. Chapter 13 intro- duces the weighted-average cost of capital and provides a practical illustration of how to estimate it.

Part 4 (Financing)  begins our discussion of the financing decision. Chapter 14 pro- vides an overview of the securities that firms issue and their relative importance as sources of finance. In Chapter 15 we look at how firms issue securities, and we follow a firm from its first need for venture capital, through its initial public offering, to its continuing need to raise debt or equity.

Part 5 (Debt and Payout Policy)  focuses on the two classic long-term financing decisions. In Chapter 16 we ask how much the firm should borrow, and we summa- rize bankruptcy procedures that occur when firms can’t pay their debts. In Chapter 17 we study how firms should set dividend and payout policy. In each case we start with Modigliani and Miller’s (MM’s) observation that in well-functioning markets the decision should not matter, but we use this observation to help the reader understand why financial managers in practice do pay attention to these decisions.

Part 6 (Financial Analysis and Planning)  starts with long-term financial plan- ning in Chapter 18, where we look at how the financial manager considers the combined effects of investment and financing decisions on the firm as a whole. We also show how measures of internal and sustainable growth help managers check that the firm’s planned growth is consistent with its financing plans. Chapter 19 is an introduction to short-term financial planning. It shows how managers ensure that the firm will have enough cash to pay its bills over the coming year, and describes the principal sources of short-term borrowing. Chapter 20 addresses working capital management. It describes the basic steps of credit management, the principles of inventory management, and how firms handle payments efficiently and put cash to work as quickly as possible.

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x Preface

Part 7 (Special Topics)   covers several important but somewhat more advanced topics—mergers (Chapter 21), international financial management (Chapter 22), options (Chapter 23), and risk management (Chapter 24). Some of these topics are touched on in earlier chapters. For example, we introduce the idea of options in Chapter 10, when we show how companies build flexibility into capital projects. How- ever, Chapter 23 generalizes this material, explains at an elementary level how options are valued, and provides some examples of why the financial manager needs to be concerned about options. International finance is also not confined to Chapter 22. As one might expect from a book that is written by an international group of authors, examples from different countries and financial systems are scattered throughout the book. However, Chapter 22 tackles the specific problems that arise when a corpora- tion is confronted by different currencies.

Part 8 (Conclusion)   contains a concluding chapter (Chapter 25), in which we review the most important ideas covered in the text. We also introduce some interest- ing questions that either were unanswered in the text or are still puzzles to the finance profession. Thus the last chapter is an introduction to future finance courses as well as a conclusion to this one.

Routes through the Book There are about as many effective ways to organize a course in corporate finance as there are teachers. For this reason, we have ensured that the text is modular, so that topics can be introduced in different sequences.

We like to discuss the principles of valuation before plunging into financial plan- ning. Nevertheless, we recognize that many instructors will prefer to move directly from Chapter 4 (Measuring Corporate Performance) to Chapter 18 (Long-Term Finan- cial Planning) in order to provide a gentler transition from the typical prerequisite accounting course. We have made sure that Part 6 (Financial Analysis and Planning) can easily follow Part 1.

Similarly, we like to discuss working capital after the student is familiar with the basic principles of valuation and financing, but we recognize that here also many instructors prefer to reverse our order. There should be no difficulty in taking Chapter 20 out of order.

When we discuss project valuation in Part 2, we stress that the opportunity cost of capital depends on project risk. But we do not discuss how to measure risk or how return and risk are linked until Part 3. This ordering can easily be modified. For exam- ple, the chapters on risk and return can be introduced before, after, or midway through the material on project valuation.

Changes in the Eighth Edition Users of previous editions of this book will not find dramatic changes in either the material or the ordering of topics. But throughout we have made the book more up to date and easier to read. Here are some of the ways that we have done this.

Beyond the Page  The biggest change in this edition is the introduction of Beyond the Page digital extensions and applications. These digital extensions are not, as they may sound, false fingernails; they are additional examples, spreadsheet programs, and opportunities to explore topics in more depth. This material is very easily accessed on the web. For example, it is seamlessly available with a click on the e-versions of the book, but it is also readily accessible in the traditional hard copy of the text using either QR codes from a smartphone or shortcut URLs, both provided in the margins of relevant pages.

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Preface xi

Improving the Flow  A major part of our effort in revising this text was spent on improving the flow. Often this has meant a word change here or a redrawn diagram there, but sometimes we have made more substantial changes. Consider, for example, Chapter 1, where we have made three significant changes. First, we have included a completely rewritten section on corporate governance and agency issues. We empha- size that you need a good system of corporate governance to ensure that managers maximize value. Second, discussions of ethical issues often focus on the egregiously improper and illegal actions, but for honest financial managers the important problems are the gray areas. We have therefore addressed three topics for which there are no easy answers—the role of corporate raiders, short-selling, and tax avoidance. Finally, students tackling finance for the first time need some broad understanding of what the subject is all about. We therefore conclude Chapter 1 with a review of the big themes.

Updating  Of course, in each new edition we try to ensure that any statistics are as up to date as possible. For example, since the previous edition, we have available an extra 3 years of data on security returns. These show up in the figures in Chapter 11 of the long-run returns on stocks, bonds, and bills. Measures of EVA, data on security ownership, dividend payments, and stock repurchases are just a few of the other cases where data have been brought up to date.

Recent Events  We discussed the financial crisis of 2007–2009 in the previous edi- tion, but we have now been able to expand the discussion to include the spillover to the crisis in the eurozone and to introduce the Dodd-Frank Act. The eurozone crisis was also a reminder that government debt is not risk-free. We come back to that issue in Chapter 6 when we discuss default risk.

Concepts  There are several places where we have introduced new conceptual mate- rial. For example, students who have learned about the dividend discount model are often confused about how to value the many companies that also repurchase their stock. We introduce the issue in Chapter 13, and in Chapter 17 we explain how to value these companies. The growth in repurchases has also changed the way that we think about the dividend controversy. We have therefore substantially rewritten Chapter 17 to focus on the trade-off between dividends and repurchases. We have also added a final section that discusses how the payout decision changes over the life cycle of the firm.

New Illustrative Boxes  The text contains a number of boxes with illustrative real- world examples. Many of these are new. Look, for example, at the box in Chapter 15 that discusses the Facebook IPO or the box about how WobbleWorks used crowd- funding to finance its 3Doodler project.

More Worked Examples  We have added more worked examples in the text, many of them taken from real companies. For instance, when we discuss company valuation in Chapter 7, we show how to value the Cape Wind power project in Nantucket Sound.

New Calculator and Spreadsheet Boxes  We have reworked the explanations of how to use calculators or spreadsheets to solve financial problems. We now have separate subsections that show how they can be used to solve single-cash-flow and multiple-cash-flow problems. We think that this better integrates the material into the rest of the chapter and is easier for the student to follow.

Specific Chapter Changes in the Eighth Edition Chapter 1 contains an expanded discussion of agency issues, including additions

on corporate raiders, creative accounting, tax avoidance, and “say on pay.”

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xii Preface

Chapter 2 includes an additional discussion of the fi nancial crisis and its spillover to the sovereign debt crisis in the eurozone.

Chapter 3 introduces free cash fl ow in the discussion of accounting and fi nance and includes updated discussions of accounting malfeasance and the conver- gence of GAAP and IFRS accounting standards.

Chapter 5 has a reorganized and integrated discussion of calculators and spread- sheets.

Chapter 6 now includes an overview of the determinants of bond default risk in the discussion of credit spreads.

Chapter 7 contains an integrated discussion of sustainable growth in the develop- ment of the dividend growth model, includes a new box on Facebook’s IPO, and explains how to best deal with stock repurchases when using the dividend discount model.

Chapter 8 features an enhanced explanation of why mutually exclusive invest- ments are central to almost all real-life investment decisions and how that affects the capital budgeting decision.

Chapter 10 includes updated examples of real options and explains how those op- tions are integrated into a fi rm’s longer-term strategic considerations.

Chapter 11 introduces a simple derivation of the investment opportunity frontier and demonstrates the role of correlation in assessing the potential for an invest- ment to reduce risk through portfolio diversifi cation.

Chapter 12 contains a new discussion of how the index model can be used to measure and distinguish between systematic and diversifi able risks using an ex- tended example comparing the risks of mutual funds and individual stocks. The discussion also introduces key issues in performance evaluation, for example, the appropriate way to trade off average return versus risk.

Chapter 13 includes clarifi cations on real-world procedures used when computing the weighted-average cost of capital.

Chapter 14 features an extended treatment of corporate governance, particularly the composition of the board of directors.

Chapter 15 introduces alternative fundraising methods for start-ups, such as crowdsourcing.

Chapter 16 clarifi es the practical implications of Miller and Modigliani for debt policy and introduces new material on assessing the present value of tax shields associated with debt.

Chapter 17 contains a fully revamped treatment of the information content of div- idends as well the trade-offs governing the use of dividends versus repurchases.

Chapter 19 includes a closer integration of the analysis of sources and uses of funds with the fi rm’s statement of cash fl ows.

Chapter 21 features numerous updates to refl ect mergers that have taken place in recent years.

Chapter 23 presents a new treatment of the VIX contract and its use as a “fear index.”

Chapter 24 includes a new discussion of a practical issue in risk management— banks that have lost hundreds of millions after “rogue traders” made large but unauthorized trades.

Assurance of Learning Assurance of learning is an important element of many accreditation standards. Fun- damentals of Corporate Finance, Eighth Edition, is designed specifically to support your assurance-of-learning initiatives. Each chapter in the book begins with a list of numbered learning objectives, which are referred to in the end-of-chapter problems and exercises. Every test bank question is also linked to one of these objectives, in addition to level of difficulty, topic area, Bloom’s Taxonomy level, and AACSB skill area. Connect, McGraw-Hill’s online homework solution, and EZ Test, McGraw-Hill’s

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Preface xiii

easy-to-use test bank software, can search the test bank by these and other categories, providing an engine for targeted assurance-of-learning analysis and assessment.

AACSB Statement McGraw-Hill Education is a proud corporate member of AACSB International. Understanding the importance and value of AACSB accreditation, Fundamentals of Corporate Finance, Eighth Edition, has sought to recognize the curricula guidelines detailed in the AACSB standards for business accreditation by connecting selected questions in the test bank to the general knowledge and skill guidelines found in the AACSB standards.

The statements contained in Fundamentals of Corporate Finance, Eighth Edition, are provided only as a guide for the users of this text. The AACSB leaves content coverage and assessment within the purview of individual schools, the mission of the school, and the faculty. While Fundamentals of Corporate Finance, Eighth Edition, and the teaching package make no claim of any specific AACSB qualification or eval- uation, we have, within the test bank, labeled selected questions according to the six general knowledge and skills areas.

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O RG

A N

IZ A

TI O

N Key Features

New and Enhanced Pedagogy A great deal of effort has gone into expanding and enhancing the features in Fundamentals of Corporate Finance.

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Chapter Opener Each chapter begins with a chapter narrative to help set the tone for the material that follows. Learn- ing Objectives are also included to provide a quick introduction to the material students will learn and should understand fully before mov- ing to the next chapter.

Brealey / Myers / Marcus Your guide through the challenging landscape of corporate finance

The Time Value of Money 5 CHAPTE

R

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5.5 Level Cash Flows: Perpetuities and Annuities Frequently, you may need to value a stream of equal cash flows. For example, a home mortgage might require the homeowner to make equal monthly payments for the life of the loan. For a 30-year loan, this would result in 360 equal payments. A 4-year car loan might require 48 equal monthly payments. Any such sequence of equally spaced, level cash flows is called an annuity . If the payment stream lasts forever, it is called a perpetuity .

How to Value Perpetuities Some time ago the British government borrowed by issuing loans known as consols. Consols are perpetuities. In other words, instead of repaying these loans, the British government pays the investors a fixed annual payment in perpetuity (forever).

How might we value such a security? Suppose that you could invest $100 at an interest rate of 10%. You would earn annual interest of .10  ×  $100  =  $10 per year and

annuity Level stream of cash flows at regular intervals with a finite maturity.

perpetuity Stream of level cash payments that never ends.

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Key Terms in the Margin Key terms are presented in bold and defined in the margin as they are introduced. A glossary is also avail- able at the back of the book.

Example 5.8 Winning Big at the Lottery In May 2013 an 84-year-old Florida woman invested $10 in five Powerball lottery tickets and won a record $590.5 million. We suspect that she received unsolicited congratulations, good wishes, and requests for money from dozens of more or less worthy charities, relations, and newly devoted friends. In response, she could fairly point out that the prize wasn’t really worth $590.5 million. That sum was to be paid in 30 equal annual installments of $19.683 million each. Assuming that the first pay- ment occurred at the end of 1 year, what was the present value of the prize? The interest rate at the time was about 3.6%.

The present value of these payments is simply the sum of the present values of each annual payment. But rather than valuing the payments separately, it is much easier to treat them as a 30-year annuity. To value this annuity, we simply multiply $19.683 million by the 30-year annuity factor:

PV = 19.683 × 30-year annuity factor

= 19.683 × c1 r -

1 r (1 + r)30

d At an interest rate of 3.6%, the annuity factor is

c 1 .036

- 1

.036(1.036)30 d = 18.1638

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Numbered Examples Numbered and titled examples are integrated in each chapter. Students can learn how to solve specific problems step-by-step as well as gain insight into general principles by seeing how they are applied to answer concrete questions and scenarios.

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PE D

A G

O G

Y What makes Fundamentals of Corporate Finance such a powerful learning tool?

Spreadsheet Solutions Boxes These boxes provide the student with detailed examples of how to use Excel spreadsheets when applying financial con- cepts. The boxes include questions that apply to the spreadsheet, and their solutions are given at the end of the applicable chapter. Denoted by an icon, these spreadsheets are available in Connect.

The DATE function in Excel, which we use for both the settlement and maturity dates, uses the format DATE(year, month,day).

Notice that the coupon rate and yield to maturity are expressed as decimals, not percentages. In most cases, redemption value will be 100 (i.e., 100% of face value), and the resulting price will be expressed as a percent of face value. Occasionally, however, you may encounter bonds that pay off at a premium or discount to face value. One example would be callable bonds, which give the company the right to buy back the bonds at a premium before maturity.

The value of the bond assuming annual coupon payments is 120.556% of face value, or $1,205.56. If we wanted to assume semiannual coupon payments, as in Example 6.1, we would simply change the entry in cell B10 to 2 (see col- umn D), and the bond value would change to 120.574% of face value, as we found in that example.

Excel and most other spreadsheet programs provide built-in functions to compute bond values and yields. They typically ask you to input both the date you buy the bond (called the settlement date ) and the maturity date of the bond.

The Excel function for bond value is:

= PRICE(settlement date, maturity date, annual coupon rate, yield to maturity, redemption value as percent of face value, number of coupon payments per year)

(If you can’t remember the formula, just remember that you can go to the Formulas tab in Excel, and from the Financial tab pull down the PRICE function, which will prompt you for the necessary inputs.) For our 7.25% coupon bond, we would enter the values shown in the spreadsheet below. Alterna- tively, we could simply enter the following function in Excel:

= PRICE(DATE(2013,5,15),DATE(2016,5,15),.0725, .0035,100,1)

Solutions Spreadsheet Bond Valuation

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Finance in Practice Boxes These are excerpts that appear in most chapters, usually from the financial press, providing real-life illustrations of the chap- ter’s topics, such as ethi- cal choices in finance, disputes about stock valuation, financial plan- ning, and credit analysis.

But sometimes raids can enhance shareholder value. For example, in 2012 and 2013, Relational Investors teamed up with the California State Teachers’ Retirement System (CSTRS, a pension fund) to try to force Timken Co. to split into two separate companies, one for its steel business and one for its industrial bearings business. Relational and CSTRS believed that Timken’s combination of unrelated busi- nesses was unfocused and inefficient. Timken management responded that breakup would “deprive our shareholders of long-run value—all in an attempt to create illusory short-term gains through fi nancial engineering.” But Timken’s stock price rose at the prospect of a breakup, and a nonbinding share- holder vote on Relational’s proposal attracted a 53% majority.

How do you draw the ethical line in such examples? Was Relational Investors a “raider” (sounds bad) or an “activist investor” (sounds good)? Breaking up a portfolio of busi- nesses can create difficult adjustments and job losses. Some stakeholders lose. But shareholders and the overall economy

Short-Selling Investors who take short positions are betting that securities will fall in price. Usually they do this by borrowing the security, selling it for cash, and then waiting in the hope that they will be able to buy it back cheaply. * In 2007 hedge fund manager John Paulson took a huge short position in mortgage-backed securities. The bet paid off, and that year Paulson’s trade made a profi t of $1 billion for his fund. †

Was Paulson’s trade unethical? Some believe not only that he was profi ting from the misery that resulted from the crash in mortgage-backed securities but that his short trades accen- tuated the collapse. It is certainly true that short-sellers have never been popular. For example, following the crash of 1929, one commentator compared short-selling to the ghoulishness of “creatures who, at all great earthquakes and fi res, spring up to rob broken homes and injured and dead humans.”

Short-selling in the stock market is the Wall Street Walk on steroids. Not only do short-sellers sell all the shares they

Finance in Practice Ethical Disputes in Finance

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Excel Exhibits Selected exhibits are set as Excel spreadsheets. They are also available in Connect.

an example of how the function is used. Now let’s solve Example 5.2 in a spreadsheet. We can type the Excel function

= PV(rate, nper, pmt, FV)  =  PV(.08, 2, 0, 3000), or we can select the PV function from the pull-down menu of financial functions and fill in our inputs as shown in the dialog box below. Either way, you should get an answer of − $2,572. (Notice that you

SPREADSHEET 5.1 Using a spreadsheet to find the future value of $24

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0.08

388

0

-24

$223,166,175,426,958

BA C D F

Finding the future value of $24 using a spreadsheet

Formula in cell B8

=FV(B3,B4,B5,B6)

INPUTS

Interest rate

Periods

Payment

Present value (PV)

Future value

Notice that we enter the present value in cell B6 as a negative number,

since the "purchase price" is a cash outflow. The interest rate in cell B3

is entered as a decimal, not a percentage.

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bond is more sensitive to interest rate fluctuations than the 3 year bond. This should not surprise you. If you buy a 3-year bond and rates then rise, you will be stuck with a bad deal—you could have got a better interest rate if you had waited. However, think how much worse it would be if the loan had been for 30 years rather than 3 years. The longer the loan, the more income you have lost by accepting what turns out to be a low interest rate. This shows up in a bigger decline in the price of the longer-term bond. Of course, there is a flip side to this effect, which you can also see from Figure 6.5 . When interest rates fall, the longer-term bond responds with a greater increase in price.

Suppose that the market interest rate is 8% and then drops overnight to 4%. Calculate the present values of the 7.25%, 3-year bond and of the 7.25%, 30-year bond both before and after this change in interest rates. Assume annual coupon payments. Confirm that your answers correspond with Figure 6.5 . Use your financial calculator or a spreadsheet. You can find a box on b d i i i E l 176

Self-Test 6.4

y

Which is the longer term bond?

BEYOND THE PAGE

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Multiple Cash Flows Valuing multiple cash flows with a spreadsheet is no dif- ferent from valuing single cash flows. You simply find the present value of each flow and then add them up. Spreadsheet 5.3 shows how to find the solution to Example 5.7.

The time until each payment is listed in column A. This value is then used to set the number of periods (nper) in the formula in column C. The values for the cash flow in each future period are entered as negative numbers in the PV formula. The present val- ues (column C) therefore appear as positive numbers. Column E shows an alternative to the use of the PV function, where we calculate present values directly. This allows us to see exactly what we are doing.

Using Excel to solve time- value-of-money problems

BEYOND THE PAGE

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the €1,000 future payment by the 2-year discount factor:

PV = :1,000 × 1

(1.019)2

= :1,000 × .96306 = :963.06

Suppose that the Italian government had promised to pay € 1,000 at the end of 3 years. If the market interest rate was 2.5%, how much would you have been prepared to pay for a 3-year IOU of € 1,000?

Self-Test 5.3

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Calculator Financial You can use a fi nancial calculator to calculate the yield to maturity on our 7.25% Treasury bond. The inputs are:

Using a Financial Calculator to Compute Bond Yield

n i PV PMT FV

Inputs 3 –1205.56 72.5 1000 Compute .35

n i PV PMT FV

Inputs 6 –1205.56 36.25 1000 Compute .1777

Now compute i and you should get an answer of .35%. Let’s now redo this calculation but recognize that the cou-

pons are paid semiannually. Instead of three annual coupon payments of $72.5, the bond makes six semiannual payments

This yield to maturity, of course, is a 6-month yield, not an annual one. Bond dealers would typically annualize the semiannual rate by doubling it, so the yield to maturity would be quoted as .1777  ×  2  =  .3554%.

of $36.25. Therefore, we can fi nd the semiannual yield as follows:

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Calculator Boxes and Exercises In a continued effort to help students grasp the critical concept of the time value of money, many pedagogical tools have been added throughout the first section of the text. Financial Calculator boxes provide examples for solving a variety of problems, with directions for the three most popular financial calculators.

Self-Test Questions Provided in each chapter, these help- ful questions enable students to check their understanding as they read. Answers are worked out at the end of each chapter.

“Beyond the Page” Interactive Content and Applications New to this edition! Additional resources and hands-on applications are just a click away. Students can scan the in-text QR codes or use the direct web link to learn more about key concepts and try out calculations, tables, and figures when they go “Beyond the Page.”

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QUESTIONS AND PROBLEMS 1. Compound Interest. Old Time Savings Bank pays 4% interest on its savings accounts. If you

deposit $1,000 in the bank and leave it there: (LO5-1)

a. How much interest will you earn in the first year? b. How much interest will you earn in the second year? c. How much interest will you earn in the tenth year?

2. Compound Interest. New Savings Bank pays 4% interest on its deposits. If you deposit $1,000 in the bank and leave it there, will it take more or less than 25 years for your money to double? You should be able to answer this without a calculator or interest rate tables. (LO5-1)

3. Compound Interest. Investments in the stock market have increased at an average compound rate of about 5% since 1900. It is now 2013. (LO5-1)

a. If you invested $1,000 in the stock market in 1900, how much would that investment be worth today?

b. If your investment in 1900 has grown to $1 million, how much did you invest in 1900?

4. Future Values. Compute the future value of a $100 cash flow for the following combinations of

finance

®

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CHALLENGE PROBLEMS 66. Future Values. Your wealthy uncle established a $1,000 bank account for you when you were

born. For the first 8 years of your life, the interest rate earned on the account was 6%. Since then, rates have been only 4%. Now you are 21 years old and ready to cash in. How much is in your account? (LO5-1)

67. Present Values. If the interest rate this year is 8% and the interest rate next year will be 10%, what is the future value of $1 after 2 years? What is the present value of a payment of $1 to be received in 2 years? (LO5-2)

68. Perpetuities and Effective Interest Rate. What is the value of a perpetuity that pays $100 every 3 months forever? The interest rate quoted on an APR basis is 6%. (LO5-3)

69. Amortizing Loans and Inflation. Suppose you take out a $100,000, 20-year mortgage loan to buy a condo. The interest rate on the loan is 6%, and to keep things simple, we will assume you make payments on the loan annually at the end of each year. (LO5-3)

a. What is your annual payment on the loan? b. Construct a mortgage amortization table in Excel similar to Table 5.5 in which you compute

Templates can be found in Connect.

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L I S T I N G O F E Q UAT I O N S

5.1 Future value  =  present value  ×  (1  +   r ) t

5.2 Present value = future value after t periods

(1 + r)t

5.3 PV of perpetuity = C r =

cash payment

interest rate

5.4 Present value of t-year annuity = C c1 r -

1

r(1 + r)t d

5.5 Future value (FV) of annuity of $1 a year = present value of annuity of $1 a year × (1 + r)t

c1 1 d

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SUMMARY Investors and other stakeholders in the firm need regular financial information to help them monitor the firm’s progress. Accountants summarize this information in a balance sheet, income statement, and statement of cash flows.

The balance sheet provides a snapshot of the firm’s assets and liabilities. The assets consist of current assets that can be rapidly turned into cash and fixed assets such as plant and machinery. The liabilities consist of current liabilities that are due for payment within a year and long-term debts. The difference between the assets and the liabilities represents the amount of the shareholders’ equity.

The income statement measures the profitability of the company during the year. It shows the difference between revenues and expenses.

The statement of cash flows measures the sources and uses of cash during the year. The change in the company’s cash balance is the difference between sources and uses.

It is important to distinguish between the book values that are shown in the company accounts

What information is contained in the balance sheet, income statement, and statement of cash flows? (LO3-1)

What is the difference

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Summary This feature helps review the key points and learning objectives to provide closure to the chapter.

End-of-Chapter Material

Listing of Equations In selected chapters, the numbered equa- tions are summarized for quick and easy reference.

Questions and Problems The end-of-chapter questions and problems have been updated and reorganized by Learn- ing Objective and level of difficulty. Each question is labeled by topic, and Challenge Problems are listed in a separate section.

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c. Plot the values in columns D and E as a function of the interest rate. Which bond’s price is proportionally more sensitive to interest rate changes?

d. Can you explain the result you found in part (c)? Hint: Is there any sense in which a bond that pays a high coupon rate has lower “average” or “effective” maturity than a bond that pays a low coupon rate?

36. Yield Curve. In Figure 6.7, we saw a plot of the yield curve on stripped Treasury bonds and pointed out that bonds of different maturities may sell at different yields to maturity. In prin- ciple, when we are valuing a stream of cash flows, each cash flow should be discounted by the yield appropriate to its particular maturity. Suppose the yield curve on (zero-coupon) Treasury strips is as follows:

Years to Maturity Yield to Maturity

1 4.0% 2 5.0

3–5 5.5 6–10 6.0

You wish to value a 10-year bond with a coupon rate of 10%, paid annually. (LO6-4)

a. Set up an Excel spreadsheet to value each of the bond’s annual cash flows using this table of yields. Add up the present values of the bond’s 10 cash flows to obtain the bond price.

b. What is the bond’s yield to maturity? c. Compare the yield to maturity of the 10-year, 10% coupon bond with that of a 10-year

zero-coupon bond or Treasury strip. Which is higher? Why does this result make sense given this yield curve?

37. Credit Risk. Slush Corporation has two bonds outstanding, each with a face value of $2 mil- lion. Bond A is secured on the company’s head office building; bond B is unsecured. Slush has suffered a severe downturn in demand. Its head office building is worth $1 million, but its remaining assets are now worth only $2 million If the company defaults what payoff can the

Templates can be found in Connect.

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SOLUTIONS TO SPREADSHEET QUESTIONS 1. NPV = $4,515

2. NPV = $4,459

3. NPV = $5,741. NPV rises because the real value of depreciation allowances and the deprecia- tion tax shield is higher when the inflation rate is lower.

MINICASE Jack Tar, CFO of Sheetbend & Halyard Inc. opened the company confidential envelope. It contained a draft of a competitive bid for a contract to supply duffel canvas to the U.S. Navy. The cover memo from Sheetbend’s CEO asked Mr. Tar to review the bid before it was submitted.

The bid and its supporting documents had been prepared by Sheetbend’s sales staff. It called for Sheetbend to supply 100,000 yards of duffel canvas per year for 5 years. The proposed selling price was fixed at $30 per yard.

Mr. Tar was not usually involved in sales, but this bid was unusual in at least two respects. First, if accepted by the navy, it

would commit Sheetbend to a fixed-price, long-term contract. Sec- ond, producing the duffel canvas would require an investment of $1.5 million to purchase machinery and to refurbish Sheetbend’s plant in Pleasantboro, Maine.

Mr. Tar set to work and by the end of the week had collected the following facts and assumptions:

• The plant in Pleasantboro had been built in the early 1900s and is now idle. The plant was fully depreciated on Sheetbend’s books, except for the purchase cost of the land (in 1947) of $10,000.

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WEB EXERCISES 1. Log on to www.investopedia.com to find a simple calculator for working out bond prices.

Check whether a change in yield has a greater effect on the price of a long-term or a short-term bond.

2. When we plotted the yield curve in Figure 6.7, we used the prices of Treasury strips. You can find current prices of strips by logging on to the Wall Street Journal website (www.wsj.com) and clicking on Markets Data Center and then Bonds, Rates and Credit Markets. Try plotting the yields on stripped coupons against maturity. Do they currently increase or decline with maturity? Can you explain why? You can also use the Wall Street Journal site to compare the yields on nominal Treasury bonds with those on TIPS. Suppose that you are confident that infla- tion will be 3% per year. Which bonds are the better buy?

3. You can find the most recent bond rating for many companies by logging on to finance.yahoo. com and going to the Bond Center. Find the bond rating for some major companies. Were they investment-grade or below?

4. In Figure 6.9 we showed how bonds with greater credit risk have promised higher yields to maturity. This yield spread goes up when the economic outlook is particularly uncer- tain. You can check how much extra yield lower-grade bonds offer today by logging on to www.federalreserve.gov and comparing the yields on Aaa and Baa bonds. How does the spread in yields compare with the spread in November 2008 at the height of the financial crisis?

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Excel Problems Most chapters contain problems, denoted by an icon, specifically linked to Excel templates that are available in Connect.

Web Exercises Select chapters include Web Exer- cises that allow students to utilize the Internet to apply their knowl- edge and skills with real-world companies.

Minicases Integrated minicases allow students to apply their knowledge to rela- tively complex, practical problems and typical real-world scenarios.

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In addition to the overall refinement and improvement of the text material, considerable effort was put into develop- ing an exceptional supplement package to provide students and instructors with an abundance of teaching and learn- ing resources.

For the Instructor Instructor’s Manual This updated and enhanced manual includes a descriptive preface containing alternative course formats and case teach- ing methods, a chapter overview and out- line, key terms and concepts, a description of the PowerPoint slides, video teaching notes, related web links, and pedagogical ideas.

PowerPoint Presentations These visually stimulating slides have been fully updated by Matthew Will, University of Indianapolis, with colorful graphs, charts, and lists. The slides can be edited or manipulated to fit the needs of a particular course.

Print and Online Test Bank Kay Johnson has revised the test bank and added new questions and problems. Over 2,000 true/false, multiple-choice, and dis- cussion questions/problems are available to the instructor at varying levels of dif- ficulty and comprehension. All questions are tagged by learning objective, topic, AACSB category, and Bloom’s Taxonomy level. Complete answers are provided for all test questions and problems, and creat- ing computerized tests is easy with EZ Test Online!

Solutions Manual Matthew Will, University of Indianapolis, worked with the authors to prepare this resource containing detailed and thought- ful solutions to all the end-of-chapter problems.

grading to make classroom management more efficient than ever.

• Go paperless with the eBook and online submission and grading of student assignments.

Smart Grading    When it comes to studying, time is precious. Connect Finance helps students learn more effi- ciently by providing feedback and practice material when they need it, where they need it. When it comes to teaching, your time also is precious. The grading function enables you to:

• Have assignments scored automatically, giving students immediate feedback on their work and side-by-side comparisons with correct answers.

• Access and review each response and manually change grades or leave com- ments for students to review.

• Reinforce classroom concepts with prac- tice tests and instant quizzes.

Instructor Library    The Connect Finance Instructor Library is your reposi- tory for additional resources to improve student engagement in and out of class. You can select and use any asset that enhances your lecture. The Connect Finance Instructor Library includes all of the instructor supplements for this text.

Student Study Center    The Connect Finance Student Study Center is the place for students to access additional resources. The Student Study Center:

• Offers students quick access to lectures, eBooks, and more.

• Provides instant practice material and study questions, easily accessible on the go.

McGraw-Hill Connect Finance Less Managing. More Teaching. Greater Learning. McGraw-Hill Connect Finance is an online assignment and assessment solution that connects students with the tools and resources they’ll need to achieve success.

McGraw-Hill Connect Finance helps prepare students for their future by enabling faster learning, more effi- cient studying, and higher retention of knowledge.

McGraw-Hill Connect Finance  Features Connect Finance offers a number of powerful tools and features to make managing assignments easier, so faculty can spend more time teaching. With Connect Finance, students can engage with their coursework anytime and anywhere, making the learning process more accessible and efficient.

Simple Assignment Manage- ment    With Connect Finance, creating assignments is easier than ever, so you can spend more time teaching and less time managing. The assignment management function enables you to:

• Create and deliver assignments easily with selectable end-of-chapter questions and test bank items.

• Streamline lesson planning, student progress reporting, and assignment

Supplements

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Tegrity Campus: Lectures 24/7

Tegrity Campus is a service that makes class time available 24/7 by automatically capturing every lecture in a searchable for- mat for students to review when they study and complete assignments. With a simple one-click, start-and-stop process, you cap- ture all computer screens and correspond- ing audio. Students can replay any part of any class with easy-to-use, browser-based viewing on a PC or Mac.

Educators know that the more stu- dents can see, hear, and experience class resources, the better they learn. In fact, studies prove it. With Tegrity Campus, stu- dents quickly recall key moments by using Tegrity Campus’s unique search feature. This search helps students efficiently find what they need, when they need it, across an entire semester of class recordings. Help turn all your students’ study time into learning moments immediately supported by your lecture.

To learn more about Tegrity, watch a 2-minute Flash demo at http://tegritycam- pus.mhhe.com .

McGraw-Hill Customer Care Contact Information At McGraw-Hill, we understand that get- ting the most from new technology can be challenging. That’s why our services don’t stop after you purchase our products. You can e-mail our product specialists 24 hours a day to get product training online. Or you can search our knowledge bank of frequently asked questions on our support website. For customer support, call 800- 331-5094 or visit www.mhhe.com/sup- port . One of our technical support analysts will be able to assist you in a timely fashion.

• Access an instant view of student or class performance relative to learning objectives.

• Collect data and generate reports required by many accreditation organizations, such as AACSB and AICPA.

McGraw-Hill Connect Plus Finance    McGraw-Hill reinvents the textbook learning experience for the mod- ern student with Connect Plus Finance. A seamless integration of an eBook and Connect Finance, Connect Plus Finance provides all of the Connect Finance fea- tures plus the following:

• An integrated eBook, allowing for anytime, anywhere access to the textbook.

• Dynamic links between the problems or questions you assign to your students and the location in the eBook where that problem or question is covered.

• A powerful search function to pinpoint and connect key concepts in a snap.

Smartbook  Smartbook is an extension of LearnSmart—an adaptive eBook that helps students focus their study time more effectively. As students read, Smartbook assesses comprehension and dynamically highlights where they need to study more.

Connect Finance offers you and your students powerful tools and features that optimize your time and energies, enabling you to focus on course content, teaching, and student learning. Connect Finance also offers a wealth of content resources for both instructors and stu- dents. This state-of-the-art, thoroughly tested system supports you in preparing students for the world that awaits.

For more information about Connect, go to http://connect.mheducation.com , or contact your local McGraw-Hill sales representative.

Diagnostic and Adap- tive Learning of Concepts: LearnSmart    Students want to make the best use of their study time. The LearnSmart adaptive self-study technol- ogy within Connect Finance provides students with a seamless combination of practice, assessment, and remedia- tion for every concept in the textbook. LearnSmart’s intelligent software adapts to every student response and automati- cally delivers concepts that advance stu- dents’ understanding while reducing time devoted to the concepts already mastered. The result for every student is the fastest path to mastery of the chapter concepts. LearnSmart:

• Applies an intelligent concept engine to identify the relationships between concepts and to serve new concepts to each student only when he or she is ready.

• Adapts automatically to each student, so students spend less time on the topics they understand and practice more on those they have yet to master.

• Provides continual reinforcement and remediation, but gives only as much guidance as students need.

• Integrates diagnostics as part of the learning experience.

• Enables you to assess which concepts students have efficiently learned on their own, thus freeing class time for more applications and discussion.

Student Progress Tracking    Connect Finance keeps instructors informed about how each student, section, and class is performing, allowing for more productive use of lecture and office hours. The progress-tracking function enables you to:

• View scored work immediately and track individual or group performance with assignment and grade reports.

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McGraw-Hill Higher Education and Blackboard have teamed up. What does this mean for you?

1. Your life, simplified. Now you and your students can access McGraw- Hill’s Connect and Create right from within your Blackboard course—all

Blackboard? We thought so. When a student completes an integrated Connect assignment, the grade for that assignment automatically (and instantly) feeds your Blackboard grade center.

4. A solution for everyone. Whether your institution is already using Blackboard or you just want to try Blackboard on your own, we have a solution for you. McGraw-Hill and Blackboard can now offer you easy access to industry-lead- ing technology and content, whether your campus hosts it or we do. Be sure to ask your local McGraw-Hill repre- sentative for details.

with one single sign-on. Say goodbye to the days of logging in to multiple applications.

2. Deep integration of content and tools. Not only do you get single sign-on with Connect and Create; you also get deep integration of McGraw-Hill content and content engines right in Black- board. Whether you’re choosing a book for your course or building Connect assignments, all the tools you need are right where you want them—inside Blackboard.

3. Seamless Gradebooks. Are you tired of keeping multiple gradebooks and manually synchronizing grades into

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Marlena Akhbari Wright State University

Timothy Alzheimer Montana State University

Tom Arnold University of Richmond

Robert Balik Western Michigan University

Anindam Bandopadhyaya University of Massachusetts–Boston

Chenchu Bathala Cleveland State University

Deborah Bauer University of Oregon

Richard Bauer Saint Mary’s University

LaDoris Baugh Athens State University

John R. Becker Blease Washington State University–Vancouver

Theologos Bonitsis New Jersey Institute of Technology

Stephen Borde University of Central Florida

Edward Boyer Temple University

Stephen Buell Lehigh University

Deanne Butchey Florida International University

Shelley Canterbury George Mason University

Michael Casey University of Central Arkansas

Fan Chen University of Mississippi

Nicole Choi Washington State University–Pullman

Bruce Costa University of Montana

Kenneth Daniels Virginia Commonwealth University

Morris Danielson St. Joe’s University

Natalya Delcoure Sam Houston State University

Jared DeLisle Washington State University–Vancouver

Steven Dennis University of North Dakota

Robert Dubil University of Utah–Salt Lake City

Alan D. Eastman Indiana University of Pennsylvania

Michael Ehrlich New Jersey Institute of Technology

Richard Elliot University of Utah–Salt Lake City

Mike Evans Winthrop University

James Falter Franklin University

John Fay Santa Clara University

Richard Fedler Georgia State University

Michael Ferguson University of Cincinnati

Dov Fobar Brooklyn College

Eric Fricke California State University– East Bay

Steve Gallaher Southern New Hampshire University

Sharon Garrison University of Arizona

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We take this opportunity to thank all of the individuals who helped us prepare this Eighth Edition. We want to express our appreciation to those instructors whose insightful comments and suggestions were invaluable to us during this revision.

Acknowledgments

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Linda Lange Regis University

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In addition, we would like to thank our supplement authors, Kay Johnson, Mishal Rawaf, Matt Will, Steven Dennis, Peter Crabb, Deb Bauer, and Nicholas Racculia. Their efforts are much appreciated as they will help both students and instructors. We also appreciate help from Aleijda de Cazenove Balsan and Malcolm Taylor.

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Finally, as was the case with the last seven editions, we cannot overstate the thanks due to our wives, Diana, Maureen, and Sheryl.

Richard A. Brealey

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xxvi

1 Goals and Governance of the Corporation 2 2 Financial Markets and Institutions 32 3 Accounting and Finance 54 4 Measuring Corporate Performance 82

5 The Time Value of Money 116 6 Valuing Bonds 164 7 Valuing Stocks 192 8 Net Present Value and Other Investment Criteria 234 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 270 10 Project Analysis 298

11 Introduction to Risk, Return, and the Opportunity Cost of Capital 326 12 Risk, Return, and Capital Budgeting 356 13 The Weighted-Average Cost of Capital and Company Valuation 386

14 Introduction to Corporate Financing 414 15 How Corporations Raise Venture Capital and Issue Securities 436

16 Debt Policy 460 17 Payout Policy 496

18 Long-Term Financial Planning 520 19 Short-Term Financial Planning 544 20 Working Capital Management 576

21 Mergers, Acquisitions, and Corporate Control 606 22 International Financial Management 634 23 Options 660 24 Risk Management 686

25 What We Do and Do Not Know about Finance 706

Appendix: Present Value and Future Value Tables A-1 Glossary G-1 Global Index IND-1 Subject Index IND-5 Credits C-1

Part One Introduction

Part Two Value

Part Three Risk

Part Four Financing

Part Five Debt and Payout

Policy

Part Six Financial Analysis

and Planning

Part Seven Special Topics

Part Eight Conclusion

in Brief Contents

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xxvii

Contents Part One Introduction

Chapter 1 Goals and Governance of the Corporation 2 1.1 Investment and Financing Decisions 4

The Investment (Capital Budgeting) Decision 6

The Financing Decision 6

1.2 What Is a Corporation? 8

Other Forms of Business Organization 9

1.3 Who Is the Financial Manager? 10

1.4 Goals of the Corporation 12 Shareholders Want Managers to Maximize Market Value 12

1.5 Agency Problems, Executive Compensation, and Corporate Governance 15 Executive Compensation 16

Corporate Governance 17

1.6 The Ethics of Maximizing Value 18

1.7 Careers in Finance 20

1.8 Preview of Coming Attractions 22

1.9 Snippets of Financial History 23

Summary 25

Questions and Problems 26

Chapter 2 Financial Markets and Institutions 32 2.1 The Importance of Financial Markets

and Institutions 34

2.2 The Flow of Savings to Corporations 35 The Stock Market 37

Other Financial Markets 37

Financial Intermediaries 39

Financial Institutions 42

Total Financing of U.S. Corporations 43

2.3 Functions of Financial Markets and Intermediaries 44 Transporting Cash across Time 45

Risk Transfer and Diversification 45

Liquidity 46

The Payment Mechanism 46

Information Provided by Financial Markets 47

2.4 The Crisis of 2007–2009 49

Summary 50

Questions and Problems 51

Chapter 3 Accounting and Finance 54 3.1 The Balance Sheet 56

Book Values and Market Values 58

3.2 The Income Statement 61 Income versus Cash Flow 62

3.3 The Statement of Cash Flows 65 Free Cash Flow 67

3.4 Accounting Practice and Malpractice 68

3.5 Taxes 71 Corporate Tax 71

Personal Tax 72

Summary 74

Questions and Problems 74

Chapter 4 Measuring Corporate Performance 82 4.1 Value and Value Added 84

How Financial Ratios Help to Understand Value Added 84

4.2 Measuring Market Value and Market Value Added 85

4.3 Economic Value Added and Accounting Rates of Return 87 Accounting Rates of Return 89

Problems with EVA and Accounting Rates of Return 91

4.4 Measuring Efficiency 92

4.5 Analyzing the Return on Assets: The Du Pont System 93 The Du Pont System 94

4.6 Measuring Financial Leverage 96 Leverage and the Return on Equity 98

4.7 Measuring Liquidity 99

4.8 Interpreting Financial Ratios 100

4.9 The Role of Financial Ratios 104

Summary 105 Questions And Problems 107

Minicase 113

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Chapter 5 The Time Value of Money 116 5.1 Future Values and Compound Interest 118

5.2 Present Values 121 Finding the Interest Rate 125

5.3 Multiple Cash Flows 126 Future Value of Multiple Cash Flows 126

Present Value of Multiple Cash Flows 128

5.4 Reducing the Chore of the Calculations: Part 1 129 Using Financial Calculators to Solve Simple Time-Value- of-Money Problems 129

Using Spreadsheets to Solve Simple Time-Value-of- Money Problems 130

5.5 Level Cash Flows: Perpetuities and Annuities 133 How to Value Perpetuities 133

How to Value Annuities 134

Future Value of an Annuity 138

Annuities Due 141

5.6 Reducing the Chore of the Calculations: Part 2 143 Using Financial Calculators to Solve Annuity Problems 143

Using Spreadsheets to Solve Annuity Problems 143

5.7 Effective Annual Interest Rates 144

5.8 Inflation and the Time Value of Money 146 Real versus Nominal Cash Flows 146

Inflation and Interest Rates 148

Valuing Real Cash Payments 149

Real or Nominal? 151

Summary 151 Questions and Problems 152

Minicase 163

Chapter 6 Valuing Bonds 164 6.1 The Bond Market 166

Bond Characteristics 166

6.2 Interest Rates and Bond Prices 167 How Bond Prices Vary with Interest Rates 170

Interest Rate Risk 172

6.3 Yield to Maturity 172 Calculating the Yield to Maturity 174

6.4 Bond Rates of Return 174

6.5 The Yield Curve 177 Nominal and Real Rates of Interest 178

6.6 Corporate Bonds and the Risk of Default 180 Protecting against Default Risk 183 Not All Corporate Bonds Are Plain Vanilla 184

Summary 184 Questions and Problems 185

Chapter 7 Valuing Stocks 192 7.1 Stocks and the Stock Market 194

Reading Stock Market Listings 195

7.2 Market Values, Book Values, and Liquidation Values 197

7.3 Valuing Common Stocks 199 Valuation by Comparables 199 Price and Intrinsic Value 200 The Dividend Discount Model 202

7.4 Simplifying the Dividend Discount Model 205 The Dividend Discount Model with No Growth 205 The Constant-Growth Dividend Discount Model 205 Sustainable Growth 207 A Caveat 208 Estimating Expected Rates of Return 208 Nonconstant Growth 210 Repurchases and the Dividend Discount Model 212

7.5 Growth and Growth Opportunities 212 Valuing Growth Stocks 215 Market-Value Balance Sheets 215

7.6 There Are No Free Lunches on Wall Street 215 Method 1: Technical Analysis 216 Method 2: Fundamental Analysis 218 A Theory to Fit the Facts 219

7.7 Market Anomalies and Behavioral Finance 221 Market Anomalies 221 Bubbles and Market Efficiency 222 Behavioral Finance 223

Summary 225 Questions and Problems 226

Minicase 232

Chapter 8 Net Present Value and Other Investment Criteria 234 8.1 Net Present Value 236

A Comment on Risk and Present Value 237

Valuing Long-Lived Projects 238

Part Two Value

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Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 326 11.1 Rates of Return: A Review 328 11.2 A Century of Capital Market History 329

Market Indexes 329

The Historical Record 329

9.2 Calculating Cash Flow 279 Capital Investment 279

Operating Cash Flow 279

Changes in Working Capital 281

9.3 An Example: Blooper Industries 282 Cash-Flow Analysis 282

Calculating the NPV of Blooper’s Project 284

Further Notes and Wrinkles Arising from Blooper’s Project 285

Summary 289 Questions and Problems 290

Minicase 295

Chapter 10 Project Analysis 298 10.1 How Firms Organize the Investment Process 300

Stage 1: The Capital Budget 300

Stage 2: Project Authorizations 300

Problems and Some Solutions 301

10.2 Some “What-If” Questions 302 Sensitivity Analysis 303

Scenario Analysis 305

10.3 Break-Even Analysis 306 Accounting Break-Even Analysis 306

NPV Break-Even Analysis 308

Operating Leverage 311

10.4 Real Options and the Value of Flexibility 313 The Option to Expand 313

A Second Real Option: The Option to Abandon 315

A Third Real Option: The Timing Option 315

A Fourth Real Option: Flexible Production Facilities 316

Summary 316 Questions and Problems 317

Minicase 324

8.2 The Internal Rate of Return Rule 243 A Closer Look at the Rate of Return Rule 243

Calculating the Rate of Return for Long-Lived Projects 243

A Word of Caution 245

Some Pitfalls with the Internal Rate of Return Rule 245

8.3 The Profitability Index 250 Capital Rationing 250

Pitfalls of the Profitability Index 251

8.4 The Payback Rule 251 Discounted Payback 253

8.5 More Mutually Exclusive Projects 253 Problem 1: The Investment Timing Decision 254

Problem 2: The Choice between Long- and Short-Lived Equipment 255

Problem 3: When to Replace an Old Machine 257

8.6 A Last Look 258

Summary 259 Questions and Problems 260

Minicase 266

Appendix: More on the IRR Rule 267 Using the IRR to Choose between Mutually Exclusive Projects 267

Using the Modified Internal Rate of Return When There Are Multiple IRRs 268

Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 270 9.1 Identifying Cash Flows 272

Discount Cash Flows, Not Profits 272

Discount Incremental Cash Flows 274

Discount Nominal Cash Flows by the Nominal Cost of Capital 277

Separate Investment and Financing Decisions 278

Part Three Risk Using Historical Evidence to Estimate Today’s Cost of Capital 332

11.3 Measuring Risk 334

Variance and Standard Deviation 334

A Note on Calculating Variance 337

Measuring the Variation in Stock Returns 337

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xxx Contents

Chapter 13 The Weighted-Average Cost of Capital and Company Valuation 386 13.1 Geothermal’s Cost of Capital 388

13.2 The Weighted-Average Cost of Capital 389 Calculating Company Cost of Capital as a Weighted Average 390

Use Market Weights, Not Book Weights 392

Taxes and the Weighted-Average Cost of Capital 392

What If There Are Three (or More) Sources of Financing? 394

Wrapping Up Geothermal 394

Checking Our Logic 395

13.3 Measuring Capital Structure 396

13.4 Calculating the Weighted-Average Cost of Capital 398 The Expected Return on Bonds 398

The Expected Return on Common Stock 398

The Expected Return on Preferred Stock 400

Adding It All Up 400

Real-Company WACCs 400

13.5 Interpreting the Weighted-Average Cost of Capital 401 When You Can and Can’t Use WACC 401

Some Common Mistakes 401

How Changing Capital Structure Affects Expected Returns 402

What Happens When the Corporate Tax Rate Is Not Zero 403

13.6 Valuing Entire Businesses 403 Calculating the Value of the Concatenator Business 404

Summary 405 Questions and Problems 406

Minicase 411

11.4 Risk and Diversification 339 Diversification 339

Asset versus Portfolio Risk 340

Market Risk versus Specific Risk 346

11.5 Thinking about Risk 347 Message 1: Some Risks Look Big and Dangerous but Really Are Diversifiable 348

Message 2: Market Risks Are Macro Risks 349

Message 3: Risk Can Be Measured 349

Summary 350

Questions and Problems 351

Chapter 12 Risk, Return, and Capital Budgeting 356 12.1 Measuring Market Risk 358

Measuring Beta 358

Betas for Dow Chemical and Consolidated Edison 361

Total Risk and Market Risk 361

12.2 What Can You Learn from Beta? 363 Portfolio Betas 363

The Portfolio Beta Determines the Risk of a Diversified Portfolio 366

12.3 Risk and Return 367 Why the CAPM Makes Sense 369

The Security Market Line 370

Using the CAPM to Estimate Expected Returns 371

How Well Does the CAPM Work? 371

12.4 The CAPM and the Opportunity Cost of Capital 374 The Company Cost of Capital 376

What Determines Project Risk? 376

Don’t Add Fudge Factors to Discount Rates 377

Summary 377 Questions and Problems 378

Part Four Financing

Chapter 14 Introduction to Corporate Financing 414 14.1 Creating Value with Financing Decisions 416

14.2 Patterns of Corporate Financing 416 Are Firms Issuing Too Much Debt? 419

14.3 Common Stock 420 Ownership of the Corporation 422

Voting Procedures 423

Classes of Stock 424

14.4 Preferred Stock 424

14.5 Corporate Debt 425

Debt Comes in Many Forms 425

Innovation in the Debt Market 428

14.6 Convertible Securities 430

Summary 431 Questions and Problems 432

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15.3 General Cash Offers by Public Companies 446 General Cash Offers and Shelf Registration 447 Costs of the General Cash Offer 448 Market Reaction to Stock Issues 448

15.4 The Private Placement 449

Summary 450 Questions and Problems 451

Minicase 455 Appendix: Hotch Pot’s New-Issue Prospectus 456

Chapter 15 How Corporations Raise Venture Capital and Issue Securities 436 15.1 Venture Capital 438

Venture Capital Companies 439

15.2 The Initial Public Offering 440

Arranging a Public Issue 441

Other New-Issue Procedures 445

The Underwriters 445

Part Five Debt and Payout Policy

Chapter 16 Debt Policy 460 16.1 How Borrowing Affects Value in a Tax-Free

Economy 462

MM’s Argument—A Simple Example 463

How Borrowing Affects Earnings per Share 464

How Borrowing Affects Risk and Return 466

16.2 Debt and the Cost of Equity 467

No Magic in Financial Leverage 470

16.3 Debt, Taxes, and the Weighted-Average Cost of Capital 471

Debt and Taxes at River Cruises 472

How Interest Tax Shields Contribute to the Value of Stockholders’ Equity 473

Corporate Taxes and the Weighted-Average Cost of Capital 474

The Implications of Corporate Taxes for Capital Structure 475

16.4 Costs of Financial Distress 476

Bankruptcy Costs 476

Costs of Bankruptcy Vary with Type of Asset 478

Financial Distress without Bankruptcy 479

16.5 Explaining Financing Choices 481

The Trade-Off Theory 481

A Pecking Order Theory 482

The Two Faces of Financial Slack 483

Summary 484 Questions and Problems 485

Minicase 492

Appendix: Bankruptcy Procedures 493

Chapter 17 Payout Policy 496 17.1 How Corporations Pay Out

Cash to Shareholders 498

How Firms Pay Dividends 499

Limitations on Dividends 499

Stock Dividends and Stock Splits 500

Stock Repurchases 501

17.2 The Information Content of Dividends and Repurchases 501

17.3 Dividends or Repurchases? The Payout Controversy 503

Dividends or Repurchases? An Example 504

Repurchases and the Dividend Discount Model 505

Dividends and Share Issues 506

17.4 Why Dividends May Increase Value 507

17.5 Why Dividends May Reduce Value 509

Taxation of Dividends and Capital Gains under Current Tax Law 509

17.6 Payout Policy and the Life Cycle of the Firm 510

Summary 511 Questions and Problems 512

Minicase 517

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xxxii Contents

19.5 A Short-Term Financing Plan 561 Dynamic Mattress’s Financing Plan 562

Evaluating the Plan 563

19.6 Sources of Short-Term Financing 564 Bank Loans 564

Secured Loans 564

Commercial Paper 566

Summary 567 Questions and Problems 568

Minicase 574

Chapter 20 Working Capital Management 576 20.1 Accounts Receivable and Credit Policy 578

Terms of Sale 578

Credit Agreements 580

Credit Analysis 580

The Credit Decision 583

Collection Policy 587

20.2 Inventory Management 589

20.3 Cash Management 591 Check Handling and Float 592

Other Payment Systems 593

Electronic Funds Transfer 594

International Cash Management 595

20.4 Investing Idle Cash: The Money Market 596 Yields on Money Market Investments 597

The International Money Market 598

Summary 598 Questions and Problems 599

Minicase 605

Chapter 18 Long-Term Financial Planning 520 18.1 What Is Financial Planning? 522

Financial Planning Focuses on the Big Picture 522

Why Build Financial Plans? 523

18.2 Financial Planning Models 524 Components of a Financial Planning Model 524

Percentage of Sales Models 525

An Improved Model 526

18.3 Planners Beware 530 Pitfalls in Model Design 530

The Assumption in Percentage of Sales Models 531

The Role of Financial Planning Models 532

18.4 External Financing and Growth 533

Summary 537 Questions and Problems 538

Minicase 543

Chapter 19 Short-Term Financial Planning 544 19.1 Links between Long-Term

and Short-Term Financing 546

19.2 Working Capital 549 The Components of Working Capital 549

Working Capital and the Cash Conversion Cycle 551

The Working Capital Trade-Off 554

19.3 Tracing Changes in Cash and Working Capital 556

19.4 Cash Budgeting 557 Forecast Sources of Cash 558

Forecast Uses of Cash 559

The Cash Balance 559

Part Six Financial Analysis and Planning

Part Seven Special Topics

Chapter 21 Mergers, Acquisitions, and Corporate Control 606 21.1 Sensible Motives for Mergers 608

Economies of Scale 610

Economies of Vertical Integration 611

Combining Complementary Resources 611

Mergers as a Use for Surplus Funds 611

Eliminating Inefficiencies 612

Industry Consolidation 612

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The Cost of Capital for Foreign Investment 652

Avoiding Fudge Factors 652

Summary 653 Questions and Problems 654

Minicase 659

Chapter 23 Options 660 23.1 Calls and Puts 662

Selling Calls and Puts 664

Payoff Diagrams Are Not Profit Diagrams 665

Financial Alchemy with Options 666

Some More Option Magic 667

23.2 What Determines Option Values? 668 Upper and Lower Limits on Option Values 668

The Determinants of Option Value 669

Option-Valuation Models 671

23.3 Spotting the Option 674 Options on Real Assets 674

Options on Financial Assets 675

Summary 678

Questions and Problems 679

Chapter 24 Risk Management 686 24.1 Why Hedge? 688

The Evidence on Risk Management 689

24.2 Reducing Risk with Options 690

24.3 Futures Contracts 690 The Mechanics of Futures Trading 693

Commodity and Financial Futures 694

24.4 Forward Contracts 696

24.5 Swaps 696

24.6 Innovation in the Derivatives Market 699

24.7 Is “Derivative” a Four-Letter Word? 700

Summary 701

Questions and Problems 701

21.2 Dubious Reasons for Mergers 612 Diversification 613 The Bootstrap Game 613

21.3 The Mechanics of a Merger 614 The Form of Acquisition 614 Mergers, Antitrust Law, and Popular Opposition 615

21.4 Evaluating Mergers 615 Mergers Financed by Cash 615 Mergers Financed by Stock 617 A Warning 618 Another Warning 618

21.5 The Market for Corporate Control 619 21.6 Method 1: Proxy Contests 620 21.7 Method 2: Takeovers 620 21.8 Method 3: Leveraged Buyouts 623

Barbarians at the Gate? 624

21.9 Method 4: Divestitures, Spin-Offs, and Carve-Outs 625

21.10 The Benefits and Costs of Mergers 626 Merger Waves 626

Summary 628 Questions and Problems 629

Minicase 632

Chapter 22 International Financial Management 634 22.1 Foreign Exchange Markets 636

Spot Exchange Rates 636 Forward Exchange Rates 638

22.2 Some Basic Relationships 639 Exchange Rates and Inflation 639 Real and Nominal Exchange Rates 642 Inflation and Interest Rates 642 The Forward Exchange Rate and the Expected Spot Rate 645 Interest Rates and Exchange Rates 646

22.3 Hedging Exchange Rate Risk 647 Transaction Risk 647 Economic Risk 648

22.4 International Capital Budgeting 649 Net Present Values for Foreign Investments 649 Political Risk 651

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xxxiv Contents

Is Management an Off-Balance-Sheet Liability? 712

How Can We Explain Capital Structure? 713

How Can We Resolve the Payout Controversy? 713

How Can We Explain Merger Waves? 713

What Is the Value of Liquidity? 713

Why Are Financial Systems Prone to Crisis? 714

25.3 A Final Word 714

Questions and Problems 715

Appendix A A-1

Glossary G-1

Global Index IND-1

Subject Index IND-5

Credits C-1

Chapter 25 What We Do and Do Not Know about Finance 706 25.1 What We Do Know: The Six Most Important Ideas

in Finance 708 Net Present Value (Chapter 5) 708

Risk and Return (Chapters 11 and 12) 708

Efficient Capital Markets (Chapter 7) 708

MM’s Irrelevance Propositions (Chapters 16 and 17) 709

Option Theory (Chapter 23) 709

Agency Theory 710

25.2 What We Do Not Know: Nine Unsolved Problems in Finance 710 What Determines Project Risk and Present Value? 710

Risk and Return—Have We Missed Something? 711

Are There Important Exceptions to the Efficient-Market Theory? 711

Part Eight Conclusion

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2

Goals and Governance of the Corporation

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

1-1 Give examples of the investment and financing decisions that financial managers make.

1-2 Distinguish between real and financial assets.

1-3 Cite some of the advantages and disadvantages of organizing a business as a corporation.

1-4 Describe the responsibilities of the CFO, treasurer, and controller.

1-5 Explain why maximizing market value is the natural financial goal of the corporation.

1-6 Understand what is meant by “agency problems” and cite some of the ways that corporate governance helps mitigate agency problems.

1-7 Explain why unethical behavior does not maximize market value.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

1 CHAPTE R

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3

P A

R T

O N

E

T o carry on business, a corporation needs an almost endless variety of assets. Some are tan-gible assets such as plant and machinery, office buildings, and vehicles; others are intangible assets

such as brand names and patents. Corporations

finance these assets by borrowing, by reinvesting

profits back into the firm, and by selling additional

shares to the firm’s shareholders.

Financial managers therefore face two broad

questions. First, what investments should the corpo-

ration make? Second, how should it pay for these

investments? Investment decisions spend money.

Financing decisions raise money for investment.

We start this chapter with examples of recent

investment and financing decisions by major U.S.

and foreign corporations. We review what a corpo-

ration is and describe the roles of its top financial

managers. We then turn to the financial goal of the

corporation, which is usually expressed as maxi-

mizing value, or at least adding value. Financial

managers add value whenever the corporation can

invest to earn a higher return than its shareholders

can earn for themselves.

But managers are human beings; they cannot be

perfect servants who always and everywhere maxi-

mize value. We will consider the conflicts of interest

that arise in large corporations and how corporate

governance helps to align the interests of managers

and shareholders.

If we ask managers to maximize value, can the

corporation also be a good citizen? Won’t the man-

agers be tempted to try unethical or illegal financial

tricks? They may sometimes be tempted, but wise

managers realize that such tricks almost always

destroy value, not increase it. More challenging are

the gray areas where the line between ethical and

unethical financial actions is hard to draw.

Finally, we look ahead to the rest of this book and

look back to some entertaining snippets of financial

history.

In tr

o d

u c

tio n

To grow from small beginnings to a major corporation, FedEx needed to make good investment and financing decisions.

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4 Part One Introduction

1.1 Investment and Financing Decisions Fred Smith is best known today as the founder of FedEx. But in 1965 he was still a sophomore at Yale, where he wrote an economics term paper arguing that delivery systems were not keeping up with increasing needs for speed and dependability. 1 He later joined his stepfather at a struggling equipment and maintenance firm for air car- riers. He observed firsthand the difficulties of shipping spare parts on short notice. He saw the need for an integrated air and ground delivery system with a central hub that could connect a large number of points more efficiently than a point-to-point delivery system. In 1971, at the age of 27, Smith founded Federal Express.

Like many start-up firms, Federal Express flirted again and again with failure. Smith and his family had an inheritance of a few million dollars, but this was far from enough. The young company needed to purchase and retrofit a small fleet of aging Dassault Falcon jets, build a central-hub facility, and hire and train pilots, delivery, and office staff. The initial source of capital was short-term bank loans. Because of the company’s shaky financial position, the bank demanded that the planes be used as col- lateral and that Smith personally guarantee the loan with his own money.

In April 1973 the company went live with a fleet of 14 jets, servicing 25 U.S. cities out of its Memphis hub. By then, the company had spent $25 million and was effec- tively flat broke, without enough funds to pay for its weekly delivery of jet fuel. In desperation, it managed to acquire a bank loan for $23.7 million. This loan had to be backed by a guarantee from General Dynamics, which in return acquired an option to buy the company. (Today, General Dynamics must regret that it never exercised this option.)

In November of that year, the company finally achieved some financial stability when it raised $24.5 million from venture capitalists, investment firms that provide funds and advice to young companies in return for a partial ownership share. Eventu- ally, venture capitalists invested about $90 million in Federal Express.

In 1977 private firms were allowed for the first time to compete with the Postal Service in package delivery. Federal Express responded by expanding its operations. It acquired seven Boeing 727s, each with about seven times the capacity of the Falcon jets. To pay for these new investments, Federal Express raised about $19 million by selling shares of stock to the general public in an initial public offering (IPO). The new stockholders became part-owners of the company in proportion to the number of shares they purchased.

From this point on, success followed success, and the company invested heavily to expand its air fleet as well as its supporting infrastructure. It introduced an automated shipping system and a bar-coded tracking system. In 1994, it launched its fedex.com website for online package tracking. It opened several new hubs across the United States as well as in Canada, France, the Philippines, and China. In 2007 FedEx (as the company was now called) became the world’s largest airline measured by number of planes. FedEx also invested in other companies, capped by the acquisition of Kinko’s for $2.4 billion in 2004. By 2013, FedEx had over 300,000 employees, annual revenue of $43 billion, and a stock market value of $34 billion. Its name had become a verb— to “FedEx a package” was to ship it overnight.

Even in retrospect, FedEx’s success was hardly a sure thing. Fred Smith’s idea was inspired, but its implementation was complex and difficult. FedEx had to make good investment decisions. In the beginning, these decisions were constrained by lack of financing. For example, used Falcon jets were the only option, given the young com- pany’s precarious financial position. At first it could service only a short list of the major cities. As the company grew, its investment decisions became more complex. Which type of planes should it buy? When should it expand coverage to Europe and

1 Legend has it that Smith received a grade of C on this paper. In fact, he doesn’t remember the grade.

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Chapter 1 Goals and Governance of the Corporation 5

Asia? How many operations hubs should it build? What computer and tracking sys- tems were necessary to keep up with the increasing package volume and geographic coverage? Which companies should it acquire as it expanded its range of services?

FedEx also needed to make good financing decisions. For example, how should it raise the money it needed for investment? In the beginning, these choices were limited to family money and bank loans. As the company grew, its range of choices expanded. Eventually it was able to attract funding from venture capitalists, but this posed new questions. How much cash did the firm need to raise from the venture capitalists? How big a share in the firm would the venture capitalists demand in return? The initial public offering of stock prompted similar questions. How many shares should the company try to sell? At what price? As the company grew, it raised more funds by borrowing money from its banks and by selling publicly traded bonds to investors. At each point, it needed to decide on the proper form and terms of financing as well as the amounts to be raised.

In short, FedEx needed to be good at finance. It had a head start over potential competitors, but a series of bad financial decisions would have sunk the company. No two companies’ histories are the same, but, like FedEx, all successful companies must make good investment and financing decisions. And, as with FedEx, those decisions range from prosaic and obvious to difficult and strategically crucial.

Let’s widen our discussion. Table 1.1 gives an example of a recent investment and financing decision for 10 corporations. Six are U.S. corporations. Four are foreign: GlaxoSmithKline’s headquarters are in London, LVMH’s in Paris, 2 Volkswagen’s in Wolfsburg, and Vale’s in Rio de Janeiro. We have chosen very large public corpora- tions that you are likely to be familiar with. You may have flown with Southwest Air- lines, shopped at Walmart, and drooled over Bulgari’s watches and jewelry.

Take a look at the decisions now. We think you will agree that they appear sensible— at least there is nothing obviously wrong with them. But if you are new to finance, it may be difficult to think about why these companies made these decisions and not others.

TABLE 1.1 Examples of recent investment and financing decisions by major public corporations

Company Recent Investment Decisions Recent Financing Decisions

John Deere Opened a $250 million plant in China to produce agricultural machinery.

Returned cash to shareholders by buying back $1.6 billion of stock in 2012.

LVMH Acquired the jeweler Bulgari. Paid for the acquisition with a mixture of cash and shares.

Volkswagen Invested approximately $1 billion in an auto assembly plant in Chattanooga, Tennessee.

Issued a $2.5 billion eurobond that can be converted into the company’s shares.

Walmart Announced plans to open more than 200 new stores in the U.S. in 2013.

Raised its annual dividend to $1.88 a share.

GlaxoSmithKline Spent $6 billion in 2012 on research and development of new drugs.

Issued $2.3 billion of long-term bonds.

Southwest Airlines Placed orders for over 300 new narrow-bodied planes from Boeing.

Financed many of the aircraft by long-term leases.

Hess Announced plans to sell its gas stations and refi ning operations.

Reinvested $5.5 billion of profi ts.

Procter & Gamble Spent $9.3 billion per year on advertising. Spent $3.4 billion paying back short-term debt.

Vale Announced plans to expand its huge copper mine at Salobo in Brazil. Forecast cost is $1.7 billion.

Maintained credit lines with its banks that allow the company to borrow at any time up to $4.1 billion.

Facebook Spent $700 million to acquire Instagram, the privately owned photo-sharing company.

Raised $6.8 billion by issuing shares in an initial public offering (IPO).

2 LVMH (Moët Hennessy Louis Vuitton) markets perfumes and cosmetics, wines and spirits, leather goods, watches, and other luxury products. And, yes, we know what you are thinking, but “LVMH” really is short for “Moët Hennessy Louis Vuitton.”

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6 Part One Introduction

The Investment (Capital Budgeting) Decision Investment decisions, such as those shown in Table  1.1 , are also called capital budgeting or capital expenditure (CAPEX) decisions . Some of the investments in the table, such as Walmart’s new stores or Southwest Airlines’ new planes, involve tangible assets—assets that you can touch and kick. Others involve intangible assets, such as research and development (R&D), advertising, and the design of computer software. For example, GlaxoSmithKline and other major pharmaceutical manufactur- ers invest billions every year on R&D for new drugs.

Most of the investments in Table 1.1 have long-term consequences. For example, the planes acquired by Southwest Airlines may still be flying 20 or 30 years from now. Other investments may pay off in only a few months. For example, with the approach of the Christmas holidays, Walmart spends nearly $50 billion to stock up its ware- houses and retail stores. As the goods are sold over the following months, the company recovers its investment in these inventories.

The world of business can be intensely competitive, and corporations prosper only if they can keep launching new products or services. In some cases the costs and risks of doing so are amazingly large. For example, the cost of developing the Gorgon natu- ral gas field in Australia has been estimated at $46 billion. It’s not surprising that this cost is being shared among several major energy companies. But do not think of com- panies as making billion-dollar investments on a daily basis. Most investment deci- sions are smaller, such as the purchase of a truck, machine tool, or computer system. Corporations make thousands of such investments each year. The cumulative amount of these small expenditures can be just as large as the occasional jumbo investments, such as those shown in Table 1.1 .

Not all investments succeed. In October 2011 Hewlett-Packard (HP) paid $11.1 billion to acquire the British software company Autonomy. Just 13 months later, HP wrote down the value of this investment by $8.8 billion. HP claimed that it was misled by improper accounting at Autonomy. Nevertheless, the Autonomy acquisition was a disastrous investment for HP. HP’s CEO was fired in short order.

There are no free guarantees in finance. But you can tilt the odds in your favor if you learn the tools of investment analysis and apply them intelligently. We cover these tools in detail later in this book.

The Financing Decision The financial manager’s second main responsibility is to raise the money that the firm requires for its investments and operations. This is the financing decision . When a company needs to raise money, it can invite investors to put up cash in exchange for a share of future profits or it can promise to pay back the investors’ cash plus a fixed rate of interest. In the first case, the investors receive shares of stock and become shareholders, part-owners of the corporation. The investors in this case are referred to as equity investors, who contribute equity financing. In the second case, the investors are lenders, that is, debt investors, who one day must be repaid. The choice between debt and equity financing is often called the capital structure decision. Here “capital” refers to the firm’s sources of long-term financing. A firm that is seeking to raise long- term financing is said to be “raising capital.”

Notice the essential difference between the investment and financing decisions. When the firm invests, it acquires real assets , which are then used to produce the firm’s goods and services. The firm finances its investment in real assets by issuing financial assets to investors. A share of stock is a financial asset, which has value as a claim on the firm’s real assets and on the income that those assets will produce. A bank loan is a financial asset also. It gives the bank the right to get its money back plus inter- est. If the firm’s operations can’t generate enough income to repay the bank, the bank can force the firm into bankruptcy and stake a claim on its real assets. Financial assets

capital budgeting or capital expenditure (CAPEX) decision Decision to invest in tangible or intangible assets.

financing decision Decision on the sources and amounts of financing.

real assets Assets used to produce goods and services.

financial assets Financial claims to the income generated by the firm’s real assets.

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Are the following capital budgeting or financing decisions? ( Hint: In one case the answer is “both.”)

a. Intel decides to spend $1 billion to develop a new microprocessor. b. Volkswagen borrows 350 million euros (€350 million) from Deutsche Bank. c. Royal Dutch Shell constructs a pipeline to bring natural gas onshore from

a production platform in Australia. d. Avon spends €200 million to launch a new range of cosmetics in European

markets. e. Pfizer issues new shares to buy a small biotech company.

Self-Test1.1

Chapter 1 Goals and Governance of the Corporation 7

that can be purchased and traded by investors in public markets are called securities. The shares of stock issued by the public corporations in Table 1.1 are all securities. Volkswagen’s convertible eurobond in Table 1.1 is a security. But a bank loan from Deutsche Bank to Volkswagen is not called a security unless the bank resells the loan to public investors.

The firm can issue an almost endless variety of financial assets. Suppose it decides to borrow. It can issue debt to investors, or it can borrow from a bank. It can borrow for 1 year or 20 years. If it borrows for 20 years, it can reserve the right to pay off the debt early if interest rates fall. It can borrow in Paris, receiving and promising to repay euros, or it can borrow dollars in New York. (As Table 1.1 shows, Glaxo chose to bor- row U.S. dollars, but it could have borrowed euros or Japanese yen instead.)

In some ways financing decisions are less important than investment decisions. Financial managers say that “value comes mainly from the investment side of the balance sheet.” Also, the most successful corporations sometimes have the simplest financing strategies. Take Microsoft as an example. It is one of the world’s most valu- able corporations. In early 2013, Microsoft shares traded for $28 each. There were 8.4 billion shares outstanding. Therefore Microsoft’s market value—its market capi- talization or market cap —was 28  ×  8.4  =  $235 billion. Where did this market value come from? It came from Microsoft’s products, from its brand name and worldwide customer base, from its R&D, and from its ability to make profitable future invest- ments. It did not come from sophisticated financing. Microsoft’s financing strategy is very simple: It carries no debt to speak of and finances almost all investment by retain- ing and reinvesting cash flow.

Financing decisions may not add much value compared to good investment deci- sions, but they can destroy value if they are stupid or ambushed by bad news. For example, when a consortium of investment companies bought the energy giant TXU in 2007, the company took on an additional $40 billion in debt. This may not have been a stupid decision, but it did prove nearly fatal. The consortium did not foresee the expansion of shale gas production and the resulting sharp fall in natural gas and electricity prices, and by 2013 the company (renamed Energy Future Holdings) was barely servicing its debts and teetering on the brink of bankruptcy.

We have emphasized the financial manager’s responsibility for two decisions:

The investment decision = purchase of real assets The financing decision = sale of financial assets

But this is an oversimplification, for the financial manager is also involved in many other day-to-day activities that are essential to the smooth operation of a business. For

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Which of the following are financial assets, and which are real assets?

a. A patent. b. A share of stock issued by Wells Fargo Bank. c. A blast furnace in a steelmaking factory. d. A mortgage loan taken out to help pay for a new home. e. After a successful advertising campaign, potential customers trust FedEx

to deliver packages promptly and reliably. f. An IOU (“I owe you”) from your brother-in-law.

Self-Test 1.2

8 Part One Introduction

example, if the firm sells goods or services on credit, it needs to make sure that its cus- tomers pay on time. Corporations that operate internationally must constantly transfer cash from one currency to another. And the manager must keep an eye on the risks that the firm runs and ensure that they don’t land the firm in a pickle.

1.2 What Is a Corporation? We have been referring to “corporations.” But before going too far or too fast, we need to offer some basic definitions.

A corporation is a distinct, permanent legal entity. Suppose you decide to create a new corporation. 3 You would work with a lawyer to prepare articles of incorporation, which set out the purpose of the business and how it is to be financed, managed, and governed. These articles must conform to the laws of the state in which the business is incorporated. For many purposes, the corporation is considered a resident of its state. For example, it can enter into contracts, borrow or lend money, and sue or be sued. It pays its own taxes (but it cannot vote!).

A corporation’s owners are called shareholders or stockholders. 4 The shareholders do not directly own the business’s real assets (factories, oil wells, stores, etc.). Instead they have indirect ownership via financial assets (the shares of the corporation).

A corporation is legally distinct from the shareholders. Therefore, the shareholders have limited liability and cannot be held personally responsible for the corporation’s debts. When the U.S. financial corporation Lehman Brothers failed in 2008, no one demanded that its stockholders put up more money to cover Lehman’s massive debts. Shareholders can lose their entire investment in a corporation, but no more.

corporation A business organized as a separate legal entity owned by stockholders.

limited liability The owners of a corporation are not personally liable for its obligations.

3 In the United States, corporations are identified by the label “Corporation,” “Incorporated,” or “Inc.,” as in US Airways Group Inc. The United Kingdom identifies public corporations by “plc” (short for “Public Limited Corporation”). French corporations have the suffix “SA” (“Société Anonyme”). The corresponding labels in Germany are “GmbH” (“Gesellschaft mit beschränkter Haftung”) and “AG” (“Aktiengesellschaft”). 4 “Shareholder” and “stockholder” mean exactly the same thing and are used interchangeably.

Example 1.1 Business Organization Suppose you buy a building and open a restaurant. You have invested in the build- ing itself, kitchen equipment, dining-room furnishings, plus various other assets. If you do not incorporate, you own these assets personally, as the sole proprietor of the business. If you have borrowed money from a bank to start the business, then you are personally responsible for this debt. If the business loses money and can- not pay the bank, then the bank can demand that you raise cash by selling other

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Chapter 1 Goals and Governance of the Corporation 9

When a corporation is first established, its shares may be privately owned by a small group of investors, perhaps the company’s managers and a few backers. In this case the shares are not publicly traded and the company is closely held. Eventually, when the firm grows and new shares are issued to raise additional capital, its shares are traded in public markets such as the New York Stock Exchange. Such corpora- tions are known as public companies. Most well-known corporations in the United States are public companies with widely dispersed shareholdings. In other countries, it is more common for large corporations to remain in private hands, and many public companies may be controlled by just a handful of investors.

A large public corporation may have hundreds of thousands of shareholders, who together own the business. An individual may have 100 shares, receive 100 votes, and be entitled to a tiny fraction of the firm’s income and value. On the other hand, a pen- sion fund or insurance company may own millions of shares, receive millions of votes, and have a correspondingly large stake in the firm’s performance.

Public shareholders cannot possibly manage or control the corporation directly. Instead, they elect a board of directors, who in turn appoint the top managers and monitor their performance. This separation of ownership and control gives corpora- tions permanence. Even if managers quit or are dismissed, the corporation survives. Today’s stockholders can sell all their shares to new investors without disrupting the operations of the business. Corporations can, in principle, live forever, and in practice they may survive many human lifetimes. One of the oldest corporations is the Hud- son’s Bay Company, which was formed in 1670 to profit from the fur trade between northern Canada and England. The company still operates as one of Canada’s leading retail chains.

The separation of corporate ownership and control can also have a downside, for it can open the door for managers and directors to act in their own interests rather than in the stockholders’ interest. We return to this problem later in the chapter.

There are other disadvantages to being a corporation. One is the cost, in both time and money, of managing the corporation’s legal machinery. These costs are particu- larly burdensome for small businesses.

There is also an important tax drawback to corporations in the United States. Because the corporation is a separate legal entity, it is taxed separately. So corpora- tions pay tax on their profits, and shareholders are taxed again when they receive divi- dends from the company or sell their shares at a profit. By contrast, income generated by businesses that are not incorporated is taxed just once as personal income. 6

Other Forms of Business Organization Corporations do not have to be prominent, multinational businesses such as those listed in Table 1.1 . You can organize a local plumbing contractor or barber shop as a corporation if you want to take the trouble. But most corporations are larger businesses

assets—your car or house, for example—in order to repay the loan. But if you incor- porate the restaurant business, and then the corporation borrows from the bank, your other assets are shielded from the restaurant’s debts. Of course, incorpora- tion also means that the bank will be more cautious in lending, because the bank will have no recourse to your other assets. 5

Notice that if you incorporate your business, you exchange direct ownership of its real assets (the building, kitchen equipment, etc.) for indirect ownership via financial assets (the shares of the new corporation).

5 The bank may ask you to put up personal assets as collateral for the loan to your restaurant corporation. But it has to ask and get your agreement. It doesn’t have to ask if your business is a sole proprietorship. 6 The U.S. tax system is somewhat unusual in this respect. To avoid taxing the same income twice, many other countries give shareholders at least some credit for the taxes that the corporation has already paid.

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S-corporations

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10 Part One Introduction

or businesses that aspire to grow. Small “mom-and-pop” businesses are usually orga- nized as sole proprietorships.

What about the middle ground? What about businesses that grow too large for sole proprietorships but don’t want to reorganize as corporations? For example, suppose you wish to pool money and expertise with some friends or business associates. You can form a partnership and enter into a partnership agreement that sets out how deci- sions are to be made and how profits are to be split up. Partners, like sole proprietors, face unlimited liability. If the business runs into difficulties, each partner can be held responsible for all the business’s debts.

Partnerships have a tax advantage. Partnerships, unlike corporations, do not have to pay income taxes. The partners simply pay personal income taxes on their shares of the profits.

Some businesses are hybrids that combine the tax advantage of a partnership with the limited liability advantage of a corporation. In a limited partnership, partners are classified as general or limited. General partners manage the business and have unlim- ited personal liability for its debts. Limited partners are liable only for the money they invest and do not participate in management.

Many states allow limited liability partnerships (LLPs) or, equivalently, limited liability companies (LLCs). These are partnerships in which all partners have limited liability. Another variation on the theme is the professional corporation (PC), which is commonly used by doctors, lawyers, and accountants. In this case, the business has limited liability, but the professionals can still be sued personally, for example, for malpractice.

Most large investment banks such as Morgan Stanley and Goldman Sachs started life as partnerships. But eventually these companies and their financing requirements grew too large for them to continue as partnerships, and they reorganized as corpora- tions. The partnership form of organization does not work well when ownership is widespread and separation of ownership and management is essential.

1.3 Who Is the Financial Manager? What do financial managers do for a living? That simple question can be answered in several ways. We can start with financial managers’ job titles. Most large corporations have a chief financial officer (CFO) , who oversees the work of all financial staff. As you can see from Figure 1.1 , the CFO is deeply involved in financial policy and finan- cial planning and is in constant contact with the chief executive officer (CEO) and other top management. The CFO is the most important financial voice of the corpora- tion and explains earnings results and forecasts to investors and the media.

Below the CFO are usually a treasurer and a controller . The treasurer looks after the firm’s cash, raises new capital, and maintains relationships with banks and other

chief financial officer (CFO) Supervises all financial functions and sets overall financial strategy.

treasurer Responsible for financing, cash management, and relationships with banks and other financial institutions.

controller Responsible for budgeting, accounting, and taxes.

FIGURE 1.1 Financial managers in large corporations

Treasurer Responsible for: Cash management Raising capital Banking relationships

Controller Responsible for: Preparation of financial statements Accounting Taxes

Chief Financial Officer (CFO) Responsible for: Financial policy Corporate planning

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Fritz and Frieda went to business school together 10 years ago. They have just been hired by a midsize corporation that wants to bring in new financial managers. Fritz studied finance, with an emphasis on financial markets and institutions. Frieda majored in accounting and became a CPA 5 years ago. Who is more suited to be treasurer and who controller? Briefly explain.

Self-Test 1.3

Chapter 1 Goals and Governance of the Corporation 11

investors that hold the firm’s securities. The controller prepares the financial state- ments, manages the firm’s internal budgets and accounting, and looks after its tax affairs. Thus the treasurer’s main function is to obtain and manage the firm’s capital, whereas the controller ensures that the money is used efficiently.

In large corporations, financial managers are responsible for organizing and super- vising the capital budgeting process. However, major capital investment projects are so closely tied to plans for product development, production, and marketing that man- agers from these other areas are inevitably drawn into planning and analyzing the projects. If the firm has staff members specializing in corporate planning, they are naturally involved in capital budgeting too. For this reason we will use the term finan- cial manager to refer to anyone responsible for an investment or financing decision. Often we will use the term collectively for all the managers drawn into such decisions.

Now let’s go beyond job titles. What is the essential role of the financial manager? Figure 1.2 gives one answer. The figure traces how money flows from investors to the corporation and back again to investors. The flow starts when cash is raised from investors (arrow 1 in the figure). The cash could come from banks or from securi- ties sold to investors in financial markets. The cash is then used to pay for the real assets (investment projects) needed for the corporation’s business (arrow 2). Later, as the business operates, the assets generate cash inflows (arrow 3). That cash is either reinvested (arrow 4 a ) or returned to the investors who furnished the money in the first place (arrow 4 b ). Of course, the choice between arrows 4 a and 4 b is constrained by the promises made when cash was raised at arrow 1. For example, if the firm borrows money from a bank at arrow 1, it must repay this money plus interest at arrow 4 b.

You can see examples of arrows 4 a and 4 b in Table 1.1 . Hess financed its invest- ments by reinvesting earnings (arrow 4 a ). John Deere decided to return cash to share- holders by buying back its stock (arrow 4 b ) . It could have chosen instead to pay the money out as additional cash dividends.

Notice how the financial manager stands between the firm and outside investors. On the one hand, the financial manager is involved in the firm’s operations, particularly

FIGURE 1.2 Flow of cash between investors and the firm’s operations. Key: (1) Cash raised by selling financial assets to investors; (2) cash invested in the firm’s operations; (3) cash generated by the firm’s operations; (4 a ) cash reinvested; (4 b ) cash returned to investors.

(2)

(3)

(1)

(4b)

(4a)Financial manager

Firm’s operations

Real assets

Investors

Financial assets

(2)

(3)

(1)

(4b)

(4a)Financial Manager

Firm’s Operations

Real Assets

Investors

Financial Assets

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12 Part One Introduction

by helping to make good investment decisions. On the other hand, he or she deals with financial institutions and other investors and with financial markets such as the New York Stock Exchange. We say more about these financial institutions and markets in the next chapter.

1.4 Goals of the Corporation

Shareholders Want Managers to Maximize Market Value For small corporations, shareholders and management may be one and the same. But for large corporations, separation of ownership and management is a practical neces- sity. For example, Walmart has nearly 300,000 shareholders. There is no way that these shareholders can be actively involved in management; it would be like trying to run New York City by town meetings. Authority has to be delegated.

How can shareholders effectively delegate decision making when they all have dif- ferent tastes, wealth, time horizons, personal opportunities, and tolerance for risk? Delegation can work only if the shareholders have a common goal. Fortunately there is a natural financial objective on which almost all shareholders can agree: Maximize the current market value of shareholders’ investment in the firm.

This simple, unqualified goal makes sense when the shareholders have access to well-functioning financial markets and institutions. Access gives them the flexibility to manage their own savings and consumption plans, leaving the corporation’s financial managers with only one task, to increase market value. For example, a corporation’s roster of shareholders will usually include both risk-averse and risk-tolerant investors. You might expect the risk-averse to say, “Sure, maximize value, but don’t touch too many high-risk projects.” Instead, they say, “Risky projects are okay, provided that expected profits are more than enough to offset the risks. If this firm ends up too risky for my taste, I’ll adjust my investment portfolio to make it safer.” For example, the risk-averse shareholder can shift more of his or her portfolio to safe assets, such as U.S. government bonds. Shareholders can also just say good-bye, selling off shares of the risky firm and buying shares in a safer one. If the risky investments increase market value, the departing shareholders are better off than they would be if the risky investments were turned down.

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Foundations of the NPV rule

Example 1.2 Value Maximization Fast-Track Wireless shares trade for $20. It has just announced a “bet the com- pany” investment in a high-risk, but potentially revolutionary, WhyFi technology. Investors note the risk of failure but are even more impressed with the technology’s upside. They conclude that the possibility of very high future profits justifies a higher share price. The price goes up to $23.

Caspar Milquetoast, a thoughtful but timid shareholder, notes the downside risks and decides that it’s time for a change. He sells out to more risk-tolerant inves- tors. But he sells at $23 per share, not $20. Thus he captures the value added by the WhyFi project without having to bear the project’s risks. Those risks are trans- ferred to other investors, who are more risk-tolerant or more optimistic.

In a well-functioning stock market, there is always a pool of investors ready to bear downside risks if the upside potential is sufficiently attractive. We know that the upside potential was sufficient in this case, because Fast-Track stock attracted investors willing to pay $23 per share.

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Rhonda and Reggie Hotspur are working hard to save for their children’s col- lege education. They don’t need more cash for current consumption but will face big tuition bills in 2025. Should they therefore avoid investing in stocks that pay generous current cash dividends? ( Hint: Are they required to spend the dividends on current consumption?) Explain briefly.

Self-Test 1.4

Chapter 1 Goals and Governance of the Corporation 13

The same principles apply to the timing of a corporation’s cash flows, as the following Self-Test illustrates.

Sometimes you hear managers speak as if the corporation has other goals. For example, they may say that their job is to “maximize profits.” That sounds reasonable. After all, don’t shareholders want their company to be profitable? But taken literally, profit maximization is not a well-defined corporate objective. Here are two reasons:

1. Maximize profits? Which year’s profits? A corporation may be able to increase current profits by cutting back on outlays for maintenance or staff training, but that will not add value unless the outlays were wasteful in the first place. Shareholders will not welcome higher short-term profits if long-term profits are damaged.

2. A company may be able to increase future profits by cutting this year’s dividend and investing the freed-up cash in the firm. That is not in the shareholders’ best interest if the company earns only a very low rate of return on the extra investment.

Maximizing—or at least maintaining—value is necessary for the long-run survival of the corporation. Suppose, for example, that its managers forget about value and decide that the only goal is to increase the market share of its goods and services. So the managers cut prices aggressively to attract new customers, even when this leads to continuing losses. As losses mount, the corporation finds it more and more difficult to borrow money and sooner or later cannot pay existing debts. Nor can it raise new equity financing if shareholders see that new equity investment will follow previous investments down the drain.

This firm’s managers would probably pay the price for this business malpractice. For example, outside investors would see an opportunity for easy money. They could buy the firm from its current shareholders, toss out the managers, and reemphasize value rather than market share. The investors would profit from the increase in value under new management.

Managers who pursue goals that destroy value often end in early retirement— another reason that the natural financial goal of the corporation is to maximize market value.

The Investment Trade-Off Okay, let’s take the objective as maximizing mar- ket value, or at least adding market value. But why do some investments increase market value, while others reduce it? The answer is given by Figure 1.3 , which sets out the fundamental trade-off for corporate investment decisions. The corporation has a proposed investment project (the purchase of a real asset). Suppose it has sufficient cash on hand to finance the project. The financial manager is trying to decide whether to go ahead. If he or she decides not to invest, the corporation can pay out the cash to shareholders, say as an extra dividend. (The investment and dividend arrows in Figure 1.3 are arrows 2 and 4 b in Figure 1.2 .)

Assume that the financial manager is acting in the interests of the corporation’s owners, its stockholders. What do these stockholders want the financial manager to do? The answer depends on the rate of return on the investment project and on the

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14 Part One Introduction

rate of return that stockholders can earn by investing in financial markets. If the return offered by the investment project is higher than the rate of return that shareholders can get by investing on their own, then the shareholders would vote for the investment project. If the investment project offers a lower return than shareholders can achieve on their own, the shareholders would vote to cancel the project and take the cash instead.

Figure 1.3 could apply to Southwest Airlines’ decisions to invest in new aircraft. Suppose Southwest has cash set aside to buy new Boeing 737s. It could go ahead with the purchase, or it could choose to cancel the investment project and instead pay the cash out to its stockholders. If it pays out the cash, the stockholders could then invest for themselves.

Suppose that Southwest’s investment in new planes is just about as risky as the U.S. stock market and that investment in the stock market offers a 10% expected rate of return. If the new planes offer a superior rate of return, say 20%, then Southwest’s stock- holders would be happy to let the company keep the cash and invest it in the new planes. If the planes offer only a 5% return, then the stockholders are better off with the cash and without the new project; in that case, the financial manager should turn the project down.

As long as a corporation’s proposed investments offer higher rates of return than its shareholders can earn for themselves in the stock market (or in other financial markets), its shareholders will applaud the investments and the market value of the firm will increase. But if the company earns an inferior return, shareholders boo, market value falls, and stockholders clamor to get their money back so that they can invest on their own.

In our example, the minimum acceptable rate of return on Southwest Airlines’ new aircraft is 10%. This minimum rate of return is called the hurdle rate or opportunity cost of capital . It is called an opportunity cost of capital because it depends on the alternative investment opportunities available to shareholders in financial markets. Whenever a corporation invests cash in a new project, its shareholders lose the oppor- tunity to invest the cash on their own. Corporations increase value by accepting all investment projects that earn more than the opportunity cost of capital.

Figure 1.3 , which compares rates of return on investment projects with the oppor- tunity cost of capital, illustrates a general principle: A corporation should direct cash to investments that add market value, compared to the investments that shareholders could make on their own. 7

opportunity cost of capital The minimum acceptable rate of return on capital investment is set by the investment opportunities available to shareholders in financial markets.

Investment opportunity (real asset)

Invest Alternative: pay out cash

to shareholders

Shareholders invest for

themselves

Firm Shareholders Investment

opportunities (financial assets)

Cash

FIGURE 1.3 The firm can either keep and reinvest cash or return it to investors. (Arrows represent possible cash flows or transfers.) If cash is reinvested, the opportunity cost is the expected rate of return that shareholders could have obtained by investing in financial assets.

7 We have mentioned 5% or 20% as possible future rates of return on Southwest Airlines’ new planes. We will see in Chapter 8 that future rates of return are sometimes difficult to calculate and interpret. The general prin- ciple always holds, however. In Chapters 8 and 9 we show you how to apply the principle by calculating the net present value (NPV) of investment projects.

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Investing $100,000 in additional raw materials, mostly palladium, should allow Cryogenic Concepts to increase production and earn an additional $112,000 next year. This payoff could cover the investment, plus a 12% return. Pal- ladium is traded in commodity markets. The CFO has studied the history of returns from investments in palladium and believes that investors in the pre- cious metal can reasonably expect a 15% return. What is the opportunity cost of capital? Is Cryogenic’s proposed investment in palladium a good idea? Why or why not?

Self-Test 1.5

Chapter 1 Goals and Governance of the Corporation 15

Notice that the opportunity cost of capital depends on the risk of the proposed investment project. Why? It’s not just because shareholders are risk-averse. It’s also because shareholders have to trade off risk against return when they invest on their own. The safest investments, such as U.S. government debt, offer low rates of return. Investments with higher expected rates of return—the stock market, for example—are riskier and sometimes deliver painful losses. (The U.S. stock market fell 38% in 2008, for example.) Other investments are riskier still. For example, high-tech growth stocks offer the prospect of higher rates of return but are even more volatile than the stock market overall.

Managers look to the financial markets to measure the opportunity cost of capital for the firm’s investment projects. They can observe the opportunity cost of capital for safe investments by looking up current interest rates on safe debt securities. For risky investments, the opportunity cost of capital has to be estimated. We start to tackle this task in Chapter 11.

1.5 Agency Problems, Executive Compensation, and Corporate Governance Sole proprietors face no conflicts in financial management. They are both owners and managers, reaping the rewards of good decisions and hard work and suffering when they make bad decisions or slack off. Their personal wealth is tied to the value of their businesses.

In most large corporations the owners are mostly outside investors, and so the man- agers may be tempted to act in their own interests rather than maximize shareholder value. For example, they may shy away from valuable but risky investment proj- ects because they worry more about job security than maximizing value. They may build empires by overaggressive investment or overconfident acquisitions of other companies.

The temptation for such value-destroying actions arises because the managers are not the shareholders, but agents of the shareholders. Therefore the actions are called agency problems . Losses in value from agency problems—or from costs incurred to mitigate the problems—are called agency costs .

Agency problems sometimes lead to outrageous behavior. When Dennis Kozlowski, the former CEO of Tyco, threw a $2 million birthday bash for his wife, he charged half the cost to the company. Conrad Black, the former boss of Hollinger International, used the company jet for a trip with his wife to Bora Bora. These of course are extreme examples. The agency problems encountered in the ordinary course of business are often subtle and mundane. But agency problems do arise whenever managers think just a little less hard about spending money that is not their own.

agency problem Managers are agents for stockholders and are tempted to act in their own interests rather than maximizing value.

agency cost Value lost from agency problems or from the cost of mitigating agency problems.

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What are agency problems and agency costs? Give two or three examples of decisions by managers that lead to agency costs.

Self-Test 1.6

16 Part One Introduction

Think of the corporation’s value as a pie that is divided among several classes of claimants. These include managers and workers as well as shareholders and lenders. The government is a claimant too, because it taxes sales and profits. The claimants are called stakeholders because each has a stake in the firm. Agency problems arise whenever the stakeholders’ interests do not coincide.

stakeholder Anyone with a financial interest in the corporation.

Agency problems are controlled in practice in three ways. First, corporations set up internal controls and decision-making procedures to prevent wasteful spending and dis- courage careless investment. We discuss the controls and procedures in several later chap- ters. For example, Chapters 8 to 10 cover procedures for disciplined, value-maximizing capital investment decisions. Second, corporations try to design compensation schemes that align managers’ and shareholders’ interests. Third, the corporations are constrained by corporate governance. We comment on compensation and governance here.

Executive Compensation The compensation packages of top executives are almost always tied to the financial performance of their companies. The package typically includes a fixed base salary plus an annual award tied to earnings or other measures of financial performance. The more senior the manager, the smaller the base salary as a fraction of total compensa- tion. Also, compensation is not all in cash, but partly in shares. The shares are usually restricted stock, which the manager is required to hold onto while employed by the corporation. 8 Many corporations also include stock options in compensation packages. Stock options, which we cover in Chapter 23, give especially powerful incentives to maximize stock price per share.

The upside compensation potential for a few top managers is enormous. For exam- ple, Larry Ellison, CEO of the business software giant Oracle, received total compen- sation of $96 million for 2012. Only $1 of that amount was base salary. The rest came from grants of stock and options. The options will be worthless if Oracle’s stock price falls from its 2012 level but will pay off handsomely if the price rises. In addition, as a founder of Oracle, Ellison owns shares worth $35 billion. No one can say for certain how hard Ellison would have worked with a different compensation package, but one thing is clear: He has a huge personal stake in Oracle’s market value.

Well-designed compensation schemes alleviate agency problems by encouraging managers to maximize shareholder wealth. But some schemes are not well designed; they reward managers even when value is destroyed. For example, during Robert Nardelli’s 6-year tenure as CEO, Home Depot’s stock price fell by 20% while shares of its rival Lowe’s nearly doubled. When Nardelli was ousted in January 2007, he received a farewell package worth $210 million. Needless to say, many shareholders were livid.

In 2010 the Dodd-Frank financial reform law gave U.S. shareholders the right to express their opinion on executive compensation through nonbinding “say on pay” votes at 1- or 3-year intervals. (Shareholders of U.K. companies have a similar right.) Most votes have endorsed compensation policy, but occasionally shareholders refuse.

8 Most restricted stock does not “vest” immediately. Suppose the vesting period is 3 years. If the manager quits or is fired in year 2, the restricted stock stays behind. Vesting gives the managers an incentive to stay at the cor- poration, in this example, for at least 3 years.

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Chapter 1 Goals and Governance of the Corporation 17

For example, in 2011 Hewlett-Packard’s shareholders voted against a $40 million compensation package for its new CEO. When there is a “no” vote, the company gen- erally changes the pay package to make it less generous; other companies look anx- iously over their shoulders to check that their compensation package is not next in the spotlight.

Corporate Governance Financial markets and institutions are supposed to direct financing to firms that can invest to add value. But financing moves from investors to firms only if investors are protected and if agency problems within firms are absent or at least tolerable. Thus there is a need for a system of corporate governance so that money can flow to the right firms at the right times. “Corporate governance” refers to the laws, regulations, institutions, and corporate practices that protect shareholders and other investors. When scandals happen, we say that corporate governance has broken down. When corporations compete to deliver value to shareholders, we are comforted that corporate governance is working properly.

Good corporate governance relies in part on well-designed management compensa- tion packages. Other elements of good corporate governance include the following.

Legal Requirements Good governance requires laws and regulations that pro- tect investors from self-dealing by insiders. CEOs and financial managers have a fidu- ciary duty to stockholders. That is, they are required to act fairly and responsibly in the stockholders’ interests. If they don’t, they may end up like Tyco’s Dennis Kozlowski, who spent several years in jail.

Boards of Directors The board of directors appoints top managers, including the CEO and CFO, and must approve important financial decisions. For example, only the board has legal authority to approve a dividend or a public issue of securities. The board approves compensation schemes and awards to top management. Boards usu- ally delegate decision making for small and medium-size investments, but the author- ity to approve large investments is almost never delegated.

The board of directors is elected by shareholders and is supposed to represent their interests. Boards have been portrayed as passive supporters of top management, but the balance has tipped toward independence. The Sarbanes-Oxley Act of 2002 (SOX) requires that more directors be independent—that is, not affiliated with management. The majority of directors are now independent. Boards must also meet in executive sessions with the CEO not present. SOX also requires CEOs and CFOs to sign off personally on the corporation’s accounting procedures and results.

Activist Shareholders Institutional shareholders, including pension funds, have become more active in monitoring management and pushing for changes. CEOs have been forced out as a result, including the CEOs of JCPenney, Procter & Gamble, Barnes & Noble, Citigroup, Yahoo, and Carnival. Boards outside the United States, which have traditionally been more management-friendly, have also become more willing to replace underperformers. The list of companies with CEO departures includes Barclays, Carrefour, Siemens, Barrick, Research in Motion, and Rio Tinto.

Although U.S. corporations typically have thousands of individual shareholders, they often also have blockholders, that is, investors who own 5%, 10%, or more of out- standing shares. The blockholders may include wealthy individuals or families—for example, descendants of a founder. They may also include other corporations, pension funds, or foundations. 9 When a 5% blockholder calls, the CFO answers.

corporate governance The laws, regulations, institutions, and corporate practices that protect shareholders and other investors.

9 A large block of shares may give effective control even when there is no majority owner. For example, Larry Ellison’s billion-plus shares give him a 25% stake in Oracle. Barring some extreme catastrophe, this holding means that he can run the company as long as he wants to.

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18 Part One Introduction

Disgruntled shareholders can also take the “Wall Street Walk” by selling out and moving on to other investments. The Wall Street Walk can send a powerful message. If enough shareholders bail out, the stock price tumbles, which damages top managers’ compensation and reputation.

Takeovers The Wall Street Walk also opens the door for takeovers. The further the stock price falls, the easier it is for another company to buy up the majority of shares and take over. The old management team is then likely to find itself out on the street. We discuss takeovers in Chapter 21.

Information for Investors Corporate governance can’t work unless outside investors get detailed, up-to-date information. If a firm is transparent—if investors can see its true profitability and prospects—then problems will show up right away in a falling stock price. That in turn generates extra scrutiny from security analysts, bond rating agencies, and banks and other lenders, who keep an eagle eye on the progress of their borrowers.

The U.S. Securities and Exchange Commission (SEC) sets accounting and report- ing standards for public companies. We cover accounting and finance in Chapter 3.

Chapter 1 is not the right place for a worldwide tour of corporate governance. But be aware that governance laws, regulations, and practice vary. The differences are more dramatic in continental Europe and Japan than in Canada, the United King- dom, Australia, and other English-speaking countries. In Germany, for example, banks often control large blocks of stock and can push hard for changes in the management or strategy of poorly performing companies. (Banks in the United States are prohibited from large or permanent holdings of the stock of nonfinancial corporations.) Large German firms also have two boards of directors: the supervisory board (Aufsichtsrat) and the management board (Vorstand). Half of the supervisory board’s members are elected by employees. Some French firms also have two boards, one including employee representatives.

1.6 The Ethics of Maximizing Value Shareholders want managers to maximize the market value of their shares. But per- haps this begs the question: Is it desirable for managers to act in the narrow, selfish interest of their shareholders? Does a focus on shareholder value mean that the manag- ers must act as greedy mercenaries riding roughshod over widows and orphans?

Most of this book is devoted to financial policies that increase value. None of these policies requires galloping over widows and orphans. In most instances there is little conflict between doing well (maximizing value) and doing good. The first step in doing well is doing good by your customers. Here is how Adam Smith put the case in 1776:

It is not from the benevolence of the butcher, the brewer, or the baker, that we expect our din- ner, but from their regard to their own interest. We address ourselves, not to their humanity but to their self-love, and never talk to them of our own necessities but of their advantages. 10

Profitable firms are those with satisfied customers and loyal employees; firms with dissatisfied customers and a disgruntled workforce will probably end up with declin- ing profits and a low stock price. 11

10 Adam Smith, An Inquiry into the Nature and Causes of the Wealth of Nations (New York: Random House, 1937; first published 1776), p. 14. 11 Shareholders value integrity. Firms that are regarded as trustworthy by their employees and that are voted as good places to work tend to be more highly valued by investors and to perform better. See A. Edmans, “Does the Stock Market Fully Value Intangibles? Employee Satisfaction and Equity Prices,” Journal of Financial Economics 101(3) (September 2011), 621–640, and L. Guiso, P. Sapienza, and L. Zingales, “The Value of Corporate Culture,” Chicago Booth Research Paper No. 13-80, September 1, 2013, available at SSRN: http:// ssrn.com/abstract=2353486 or http://dx.doi.org/10.2139/ssrn.2353486 .

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Without knowing anything about the personal ethics of the owners, which company would you trust more to keep its word in a business deal?

a. Harry’s Hardware has been in business for 50 years. Harry’s grandchildren, now almost adults, plan to take over and operate the business. Successful hardware stores depend on long-term loyal customers.

b. Victor’s Videos just opened for business. It rents a storefront in a strip mall and has financed its inventory with a bank loan. Victor has little of his own money invested in the business. Video shops usually command little cus- tomer loyalty.

Self-Test 1.7

Chapter 1 Goals and Governance of the Corporation 19

Of course, ethical issues do arise in business as in other walks of life. When the stakes are high, it is often tempting for managers to cut corners. Laws and regulations seek to prevent managers from undertaking dishonest actions. But written rules and laws can help only so much. In business, as in other day-to-day affairs, there are also unwritten rules of behavior. They are reinforced because good managers know that their firm’s reputation is one of its most important assets, and therefore playing fair and keeping one’s word are simply good business practices. Thus huge financial deals are regularly completed on a handshake, and each side knows that the other will not renege later if things turn sour.

Reputation is particularly important in finance. If you buy a well-known brand in a supermarket, you can be fairly sure of what you are getting. But in financial transac- tions the other party often has more information than you, and it is less easy to be sure of the quality of what you are buying. Therefore, honest financial firms seek to build long-term relationships with their customers and to establish a name for fair dealing and financial integrity. Major banks and securities firms protect their reputations.

When something happens to undermine reputations, the costs can be enormous. Of course, trust is sometimes misplaced. Charlatans and swindlers are often able to hide behind booming markets, for it is only “when the tide goes out that you learn who’s been swimming naked.” 12 The tide went out in 2008 and a number of frauds were exposed. One notorious example was the Ponzi scheme run by the disgraced finan- cier Bernard Madoff (pronounced “Made-off”). 13 Individuals and institutions invested around $20 billion with Madoff and were told that their investments had grown to $65  billion. That figure turned out to be completely fictitious. (It’s not clear what Madoff did with all this money, but much of it was apparently paid out to early inves- tors in the scheme to create an impression of superior investment performance.) With hindsight, the investors should not have trusted Madoff or the financial advisers who steered money to him.

Madoff’s Ponzi scheme was (we hope) a once-in-a-lifetime event. (Ponzi schemes pop up frequently, but none has approached the scope and duration of Madoff’s.) It was astonishingly unethical and illegal and was bound to end in tears.

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Goldman Sachs causes a ruckus

12 The quotation is from Warren Buffett’s annual letter to the shareholders of Berkshire Hathaway, March 2008. 13 Ponzi schemes are named after Charles Ponzi, who founded an investment company in 1920 that promised investors unbelievably high returns. He was soon deluged with funds from investors in New England, taking in $1 million during one 3-hour period. Ponzi invested only about $30 of the money that he raised. But he used part of the cash provided by later investors to pay generous dividends to the original investors, thus promoting the illusion of high profits and quick payoffs. Within months the scheme collapsed and Ponzi started a 5-year prison sentence.

It is not always easy to know what is ethical behavior, and there can be many gray areas. The nearby box presents three ethical controversies in finance. Think about where you stand on these issues and where you would draw the ethical line.

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20

1.7 Careers in Finance Well over 1 million people work in the financial services industry in the United States, and many others work as financial managers in corporations. We can’t tell you what each one does all day, but we can give you some idea of the variety of careers in finance. The nearby box summarizes the experience of a small sample of recent graduates. 14

But sometimes raids can enhance shareholder value. For example, in 2012 and 2013, Relational Investors teamed up with the California State Teachers’ Retirement System (CSTRS, a pension fund) to try to force Timken Co. to split into two separate companies, one for its steel business and one for its industrial bearings business. Relational and CSTRS believed that Timken’s combination of unrelated busi- nesses was unfocused and inefficient. Timken management responded that breakup would “deprive our shareholders of long-run value—all in an attempt to create illusory short-term gains through fi nancial engineering.” But Timken’s stock price rose at the prospect of a breakup, and a nonbinding share- holder vote on Relational’s proposal attracted a 53% majority.

How do you draw the ethical line in such examples? Was Relational Investors a “raider” (sounds bad) or an “activist investor” (sounds good)? Breaking up a portfolio of busi- nesses can create difficult adjustments and job losses. Some stakeholders lose. But shareholders and the overall economy can gain if businesses are managed more efficiently.

Tax Avoidance In 2012 it was revealed that during the 14 years that Star- bucks had operated in the United Kingdom, it paid hardly any taxes. Public outrage led to a boycott of Starbucks shops, and the company responded by promising that it would voluntarily pay to the taxman about $16 million more than it was required to pay by law. Several months later, a U.S. Senate committee investigating tax avoidance by U.S. technology fi rms reported that Apple had used a “highly questionable” web of offshore entities to avoid billions of dollars of U.S. taxes.

Multinational companies, such as Starbucks and Apple, can reduce their tax bills using legal techniques with exotic names such as the “Dutch Sandwich,” “Double Irish,” and “Check-the-Box.” But the public outcry over the revelations suggested that many believed that use of these techniques, though legal, was unethical. If they were unethical, that leaves an awkward question: How do companies decide which tax schemes are ethical and which are not? Can a company act in shareholders’ interest if it voluntarily pays more taxes than it is legally obligated to pay?

Short-Selling Investors who take short positions are betting that securities will fall in price. Usually they do this by borrowing the security, selling it for cash, and then waiting in the hope that they will be able to buy it back cheaply. * In 2007 hedge fund manager John Paulson took a huge short position in mortgage-backed securities. The bet paid off, and that year Paulson’s trade made a profi t of $1 billion for his fund. †

Was Paulson’s trade unethical? Some believe not only that he was profi ting from the misery that resulted from the crash in mortgage-backed securities but that his short trades accen- tuated the collapse. It is certainly true that short-sellers have never been popular. For example, following the crash of 1929, one commentator compared short-selling to the ghoulishness of “creatures who, at all great earthquakes and fi res, spring up to rob broken homes and injured and dead humans.”

Short-selling in the stock market is the Wall Street Walk on steroids. Not only do short-sellers sell all the shares they may have previously owned, but they borrow more shares and sell them too, hoping to buy them back for less when the stock price falls. Poorly performing companies are natural targets for short-sellers, and the companies’ incumbent man- agers naturally complain, often bitterly. Governments some- times listen to such complaints. For example, in 2008 the U.S. government temporarily banned short sales of fi nancial stocks in an attempt to halt their decline.

But defendants of short-selling argue that selling secu- rities that one believes are overpriced is no less legitimate than buying those that appear underpriced. The object of a well-functioning market is to set the correct stock prices, not always higher prices. Why impede short-selling if it conveys truly bad news, puts pressure on poor performers, and helps corporate governance work?

Corporate Raiders In the movie Pretty Woman, Richard Gere plays the role of an asset stripper, Edward Lewis. He buys companies, takes them apart, and sells the bits for more than he paid for the total package. In the movie Wall Street, Gordon Gekko buys a failing airline, Blue Star, in order to break it up and sell the bits. Real corporate raiders may not be as ruthless as Edward Lewis or Gordon Gekko, but they do target companies whose assets can be profi tably split up and redeployed.

This has led some to complain that raiders seek to carve up established companies, often leaving them with heavy debt burdens, basically in order to get rich quick. One German politician has likened them to “swarms of locusts that fall on companies, devour all they can, and then move on.”

* We need not go into the mechanics of short sales here, but note that the seller is obligated to buy back the security, even if its price skyrockets far above what he or she sold it for. As the saying goes, “He who sells what isn’t his’n, buys it back or goes to prison.” † The story of Paulson’s trade is told in G. Zuckerman, The Greatest Trade Ever (Broadway Business, 2009). The trade was controversial for reasons beyond short-selling. Scan the nearby Beyond the Page icon “Goldman Sachs causes a ruckus” to learn more.

Finance in Practice Ethical Disputes in Finance

14 The careers are fictitious but based on the actual experiences of several of the authors’ students.

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Chapter 1 Goals and Governance of the Corporation 21

We explained earlier that corporations face two principal financial decisions: the investment decision and the financing decision. Therefore, as a newly recruited finan- cial analyst, you may help to analyze a major new investment project. Or you may instead help to raise the money to pay for it, perhaps by negotiating a bank loan or by arranging to lease the plant and equipment. Other financial analysts work on short- term finance, managing collection and investment of the company’s cash or checking whether customers are likely to pay their bills. Financial analysts are also involved in monitoring and controlling risk. For example, they may help to arrange insurance for the firm’s plant and equipment, or they may assist with the purchase and sale of options, futures, and other exotic tools for managing risk.

Instead of working in the finance department of a corporation, you may join a finan- cial institution. The largest employers are banks. Banks collect deposits and relend the cash to corporations and individuals. If you join a bank, you may start in a branch office, where individuals and small businesses come to deposit cash or to seek a loan. You could also work in the head office, helping to analyze a $500 million loan to a large corporation.

Banks do many things in addition to lending money, and they probably provide a greater variety of jobs than other financial institutions. For example, if you work in the cash management department of a large bank, you may help companies to transfer huge sums of money electronically as wages, taxes, and payments to suppliers. Banks also buy and sell foreign exchange, so you could find yourself working in front of one of those computer screens in a foreign exchange trading room. Another glamorous bank job is in the derivatives group, which helps companies to manage their risk by buying and selling options, futures, and so on. This is where the mathematicians and the computer buffs thrive.

Investment banks, such as Goldman Sachs or Morgan Stanley, help companies sell their securities to investors. They also have large corporate finance departments that assist firms in mergers and acquisitions. When firms issue securities or try to take over another firm, a lot of money is at stake and the firms may need to move fast. Thus, working for an investment bank can be a high-pressure activity with long hours. It can also pay very well.

The insurance industry is another large employer. Much of the insurance industry is involved in designing and selling insurance policies on people’s lives and property, but businesses are also major customers. So, if you work for an insurance company or a large insurance broker, you could find yourself arranging insurance on a Boeing 787 in the United States or an oil rig in Indonesia.

Life insurance companies are major lenders to corporations and to investors in com- mercial real estate. (Life insurance companies deploy the insurance premiums received from policyholders into medium- or long-term loans; banks specialize in shorter-term financing.) So you could end up negotiating a $50 million loan for construction of a new shopping center or investigating the creditworthiness of a family-owned manufac- turing company that has applied for a loan to expand production.

Then there is the business of “managing money,” that is, deciding which compa- nies’ shares to invest in or how to balance investment in shares with safer securities, such as the bonds (debt securities) issued by the U.S. Treasury. Take mutual funds, for example. A mutual fund collects money from individuals and invests in a port- folio of stocks or bonds. A financial analyst in a mutual fund analyzes the prospects for the securities and works with the investment manager to decide which should be bought and sold. Many other financial institutions also contain investment manage- ment departments. For example, you might work as a financial analyst in the invest- ment department of an insurance company. (Insurance companies also invest in traded securities.) Or you could be a financial analyst in the trust department of a bank that manages money for retirement funds, universities, and charities.

Stockbroking firms help investment management companies and private individu- als to invest in securities. They employ sales staff and dealers who make the trades.

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22

They also employ financial analysts to analyze the securities and help customers to decide which to buy or sell.

Investment banks and stockbroking firms are largely headquartered in New York, as are many of the large commercial banks. Insurance companies and investment manage- ment companies tend to be more scattered. For example, some of the largest insurance companies are headquartered in Hartford, Connecticut, and many investment manage- ment companies are located in Boston. Of course, some U.S. financial institutions have large businesses outside the United States. Finance is a global business. So you may spend some time working in a branch overseas or making the occasional trip to one of the other major financial centers, such as London, Tokyo, Hong Kong, or Singapore.

1.8 Preview of Coming Attractions This book covers investment decisions, then financing decisions, and finally a variety of planning issues that require an understanding of both investment and financing. But first there are three further introductory chapters that should be helpful to readers who are making a first acquaintance with financial management. Chapter 2 is an overview of financial markets and institutions. Chapter 3 reviews the basic concepts of account- ing, and Chapter 4 demonstrates the techniques of financial statement analysis.

We have said that the financial manager’s task is to make investment and financing decisions that add value for the firm’s shareholders. But that statement opens up a trea- sure chest of follow-up questions that will occupy us from Chapter 4 onward:

Finance in Practice Working in Finance builders, operators, suppliers, and so on, were all in place before we could arrange bank fi nancing for the project.

Albert Rodriguez, European Markets Group, Major New York Bank I joined the bank after majoring in fi nance. I spent the fi rst 6 months in the bank’s training program, rotating between departments. I was assigned to the European markets team just before the 2010 Greek crisis, when worries about a pos- sible default caused interest rates on Greek government debt to jump to more than 4% above the rate on comparable Ger- man government debt. There was a lot of activity, with every- one trying to fi gure out whether Greece might be forced to abandon the euro and how this would affect our business. My job is largely concerned with analyzing economies and assessing the prospects for bank business. There are plenty of opportunities to work abroad, and I hope to spend some time in Madrid or one of our other European offices.

Sherry Solera, Branch Manager, Regional Bank I took basic fi nance courses in college, but nothing specifi c for banking. I started here as a teller. I was able to learn about banking through the bank’s training program and also by eve- ning courses at a local college. Last year I was promoted to branch manager. I oversee the branch’s operations and help customers with a wide variety of problems. I’m also spending more time on credit analysis of business loan applications. I want to expand the branch’s business customers, but not by making loans to shaky companies.

Susan Webb, Research Analyst, Mutual Fund Group After majoring in biochemistry, I joined the research depart - ment of a large mutual fund group. Because of my background, I was assigned to work with the senior pharmaceuticals ana- lyst. I start the day by reading The Wall Street Journal and reviewing the analyses that come in each day from stockbrok- ing fi rms. Sometimes we need to revise our earnings forecasts and meet with the portfolio managers to discuss possible trades. The remainder of my day is spent mainly in analyzing companies and developing forecasts of revenues and earn- ings. I meet frequently with pharmaceutical analysts in stock- broking fi rms, and we regularly visit company management. In the evenings I study for the Chartered Financial Analyst (CFA) exam. Since I did not study fi nance at college, this is quite challenging. I hope eventually to move from a research role to become a portfolio manager.

Richard Gradley, Project Finance, Large Energy Company After leaving college, I joined the fi nance department of a large energy company. I spent my fi rst year helping to ana- lyze capital investment proposals. I then moved to the project fi nance group, which is responsible for analyzing indepen- dent power projects around the world. Recently, I have been involved in a proposal to set up a company that would build and operate a large new electricity plant in southeast Asia. We built a spreadsheet model of the project to make sure that it was viable. We had to check that the contracts with the

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Chapter 1 Goals and Governance of the Corporation 23

• How do I calculate the value of a stream of future cash flows? A dollar that you receive today is worth more than the promise of a dollar in 10 or 20 years’ time. So, when measuring the effect of a new project on firm value, the financial manager needs to recognize the timing of the cash flows. In Chapters 5 to 10 we show how to calculate the present value of an investment that produces a stream of future cash flows. We begin by calculating the present value of bonds and stocks and then look at how to value the cash flows resulting from capital investment projects. Present value is a workhorse concept of corporate finance that shows up in almost every chapter.

• How do I measure risk? In Chapters 5 to 10 we largely ignore the issue of risk. But risky cash flows are less valuable than certain ones. In Chapters 11 to 13 we look at how to measure risk and how it affects present values.

• Where does financing come from? Broadly speaking, it comes from borrowing or from cash invested or reinvested by stockholders. But financing can get compli- cated when you get down to specifics. Chapter 14 gives an overview of the sources of finance. Chapters 15 through 17 then look at how companies sell their securities to investors, the choice between debt and equity, and the decision to pay out cash to stockholders.

• How do I ensure that the firm’s financial decisions add up to a sensible whole? There are two parts to this question. The first is concerned with making sure that the firm can finance its future growth strategy. This is the role of long-term planning. The second is concerned with ensuring that the firm has a sensible plan for manag- ing and financing its short-term assets such as cash, inventories, and money due from customers. We cover long- and short-term planning in Chapters 18 to 20.

• What about some of those other responsibilities of the financial manager that you mentioned earlier? Not all of the financial manager’s responsibilities can be clas- sified simply as an investment decision or a financing decision. In Chapters 21 to 24 we review four such topics. First we look at mergers and acquisitions. Then we consider international financial management. All the financial problems of doing business at home are present overseas, but the international financial manager faces the additional complications created by multiple currencies, different tax systems, and special regulations imposed by foreign institutions and governments. Finally, we look at risk management and the specialized securities, including futures and options, which managers can use to hedge or lay off risks.

That’s enough questions to start, but as you reflect on this chapter, you can see cer- tain themes emerging that you will encounter again and again throughout this book:

1. Corporate finance is about adding value. 2. The opportunity cost of capital sets the standard for investments. 3. A safe dollar is worth more than a risky one. 4. Smart investment decisions create more value than smart financing decisions. 5. Good governance matters.

1.9 Snippets of Financial History Now let’s lighten up a little. In this book we are going to describe how financial deci- sions are made today. But financial markets also have an interesting history. Look at the nearby box, which lays out bits of this history, starting in prehistoric times, when the growth of bacteria anticipated the mathematics of compound interest, and continu- ing nearly to the present. We have keyed each of these episodes to the chapter of the book that discusses its topic.

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24

his way out of the country. Readers nearly two centuries later could only wonder at the naïve or foolhardy inves- tors in these ventures—that is, until they had a chance to participate in the follies unearthed by the fi nancial crisis of 2008–2009. (Chapter 2)

1792 Formation of the New York Stock Exchange The New York Stock Exchange (NYSE) was founded in 1792 when a group of brokers met under a buttonwood tree * and arranged to trade shares with one another at agreed rates of commission. Today the NYSE is the largest stock exchange in the world, trading on average over 3 billion shares a day. (Chapter 7)

1929 Stock Market Crashes Common stocks are risky investments. In September 1929 stock prices in the United States reached an all-time high, and the economist Irving Fisher forecast that they were at “a permanently high pla- teau.” Some 3 years later stock prices were almost 90% lower, and it was to be a quarter of a century before the prices of September 1929 were seen again. Eighty years later, history came close to repeating itself. After stock prices peaked in July 2007, they slumped over the next 20 months by 54%. (Chapter 11)

1960s Eurodollar Market In the 1950s the Soviet Union transferred its dollar holdings from the United States to a Russian-owned bank in Paris. This bank was best known by its telex address, eurobank, and consequently dollars held outside the United States came to be known as euro- dollars. In the 1960s U.S. taxes and regulation made it much cheaper to borrow and lend dollars in Europe than in the United States, and a huge market in eurodollars arose. (Chapter 14)

1971 Corporate Bankruptcies Every generation of investors is shocked and surprised by a major corporate bankruptcy. In 1971 the Penn Central Railroad, a pillar of American industry, suddenly collapsed. Penn Central showed assets of $4.6 billion, about $27 billion in today’s dollars. At that time it was the largest corporate bankruptcy in history. In 2008 the investment bank Lehman Brothers smashed Penn Central’s record. (Chapter 16)

1972 Financial Futures Financial futures allow companies to protect themselves against fl uctuations in interest rates, exchange rates, and so on. It is said that they originated from a remark by the economist Milton Friedman that he was unable to profi t from his view that sterling (the U.K. currency) was overpriced. The Chicago Mercantile Exchange founded the fi rst fi nancial futures market. Today futures exchanges trade 6 billion contracts a year of fi nan- cial futures. (Chapter 24)

1986 Capital Investment Decisions The largest investment project undertaken by a single private company was the construction of the tunnel under the English Channel. This started in 1986 and was completed in 1994 at a total cost of $15 billion. The cost of the Gorgon natural gas project in Australia is estimated at $46 billion. (Chapters 8, 9)

1988 Mergers The 1980s saw a wave of takeovers culmi- nating in the $25 billion takeover of RJR Nabisco. Over a period of 6 weeks three groups battled for control of the company. As one of the contestants put it, “We were charg- ing through the rice paddies, not stopping for anything and

Date unknown Compound Growth Bacteria start to propa- gate by subdividing. They thereby demonstrate the power of compound growth. (Chapter 5)

c. 1800 B.C. Interest Rates In Babylonia, Hammurabi’s Code established maximum interest rates on loans. Borrow- ers often mortgaged their property and sometimes their spouses, but lenders were obliged to return spouses in good condition within 3 years. (Chapter 6)

c. 1000 B.C. Options One of the earliest recorded options is described by Aristotle. The philosopher Thales knew by the stars that there would be a great olive harvest, so, having a little money, he bought options for the use of olive presses. When the harvest came, Thales was able to rent the presses at great profi t. Today fi nancial managers need to be able to evaluate options to buy or sell a wide variety of assets. (Chapter 23)

15th century International Banking Modern international banking had its origins in the great Florentine banking houses. But the entire European network of the Medici empire employed only 57 people in eight offices. Today the London-based bank HSBC has around 260,000 employ- ees in 85 different countries. (Chapter 14)

1650 Futures Futures markets allow companies to protect themselves against fl uctuations in commodity prices. During the Tokugawa era in Japan, feudal lords collected rents in the form of rice, but often they wished to trade their future rice deliveries. Rice futures therefore came to be traded on what was later known as the Dojima Rice Market. Rice futures are still traded, but now companies can also trade in futures on a range of items from pork bellies to stock market indexes. (Chapter 24)

17th century Joint Stock Corporations Although investors have for a long time combined together as joint owners of an enterprise, the modern corporation with a large number of stockholders originated with the formation in England of trading fi rms like the East India Company (est. 1599). (Chapter 15)

17th century Money America has been in the forefront in the development of new types of money. Early settlers often used a shell known as wampum. For example, Peter Stuyvesant raised a loan in wampum, and in Massachu- setts it was legal tender. Unfortunately, the enterprising settlers found that with a little dye the relatively common white wampum shells could be converted profi tably into the more valuable black ones, which confi rmed Gresham’s law that bad money drives out good. The fi rst issue of paper money in America was by the Massachusetts Bay Colony in 1690, and other colonies soon set their printing presses to producing money. In 1862 Congress agreed to an issue of paper money that would be legal tender. These notes, printed in green ink, immediately became known as “greenbacks.” (Chapters 19, 20)

1720 New-Issue Speculation From time to time investors have been tempted by speculative new issues. During the South Sea Bubble in England one company was launched to develop perpetual motion. Another enterprising individ- ual announced a company “for carrying on an undertaking of great advantage but nobody to know what it is.” Within 5 hours he had raised £2,000; within 6 hours he was on

Finance in Practice Finance through the Ages

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25

SUMMARY Financial management can be broken down into (1) the investment, or capital budgeting, decision and (2) the financing decision. The firm has to decide (1) which real assets to invest in and (2) how to raise the funds necessary to pay for those investments.

Real assets include all assets used in the production or sale of the firms’ products or ser- vices. They can be tangible (plant and equipment, for example) or intangible (patents or trademarks, for example). In contrast, financial assets (such as stocks or bonds) are claims on the income generated by real assets.

Corporations are distinct, permanent legal entities. They allow for separation of owner- ship and control, and they can continue operating without disruption even as ownership changes. They provide limited liability to their owners. On the other hand, managing the corporation’s legal machinery is costly. Also, corporations are subject to double taxation, because they pay taxes on their profits and the shareholders are taxed again when they receive dividends or sell their shares at a profit.

What are the two major decisions made by financial managers? ( LO1-1 )

What does “real asset” mean? ( LO1-2 )

What are the advantages and disadvantages of forming a corporation? ( LO1-3 )

different countries have agreed on a common currency. In 1865 France, Belgium, Switzerland, and Italy came together in the Latin Monetary Union, and they were joined by Greece and Romania the following year. Mem- bers of the European Monetary Union (EMU) hope that the euro will be a longer-lasting success than this earlier experiment. As we write this in 2014, the euro appears to have weathered the crisis caused by the Greek govern- ment’s debt default. (Chapter 23)

2002 Financial Scandals A seemingly endless series of fi nancial and accounting scandals climaxed in this year. Resulting bankruptcies included the icons Enron (and its accounting fi rm, Arthur Andersen), WorldCom, and the Italian food company Parmalat. Congress passed the Sarbanes-Oxley Act to increase the accountability of cor- porations and executives. (Chapters 1, 14)

2007–2009 Subprime Mortgages Subprime mortgages are housing loans made to homeowners with shaky credit standing. After a decade in which housing prices had con- sistently gone up, lenders became complacent about the risks of these home loans and progressively loosened lending standards. When housing prices stalled and inter- est rates increased in 2007, many of these loans went bad. Some large banks such as Lehman Brothers went to the wall, while others such as Wachovia and Merrill Lynch were rescued with the aid of government money. ( Chapters 2, 14)

2011 Defaults on Sovereign Debt By 2010 the Greek gov- ernment had amassed a huge $440 billion of debt. Other eurozone governments and the IMF rushed to Greece’s aid, but their assistance was insufficient and in 2011 the Greek government defaulted on $100 billion of debt. It was the largest-ever sovereign default. Investors nervously eyed other highly indebted eurozone countries.

taking no prisoners.” The takeover was the largest in his- tory and generated almost $1 billion in fees for the banks and advisers. (Chapter 21)

1993 Infl ation Financial managers need to recognize the effect of infl ation on interest rates and on the profi tability of the fi rm’s investments. In the United States infl ation has been relatively modest, but some countries have suffered from hyperinfl ation. In Hungary after World War II the gov- ernment issued banknotes worth 1,000 trillion pengoes. In Yugoslavia in October 1993 prices rose by nearly 2,000% and a dollar bought 105 million dinars. (Chapter 5)

1780 and 1997 Infl ation-Indexed Debt In 1780, Massachu- setts paid Revolutionary War soldiers with interest-bearing notes rather than its rapidly eroding currency. Interest and principal payments on the notes were tied to the rate of subsequent infl ation. After a 217-year hiatus, the U.S. Treasury issued infl ation-indexed notes called TIPS (Trea- sury Infl ation Protected Securities). Many other coun- tries, including Britain and Israel, had done so previously. (Chapter 6)

1993 Controlling Risk When a company fails to keep close tabs on the risks being taken by its employees, it can get into serious trouble. This was the fate of Barings, a 220-year-old British bank that numbered the queen among its clients. In 1993 it discovered that Nick Leeson, a trader in its Singapore office, had hidden losses of $1.3 billion (£869  million) from unauthorized bets on the Japanese equity market. The losses wiped out Barings and landed Leeson in jail, with a 6-year sentence. In 2008 a rogue trader at the French bank Societé Generale established a new record by losing $7 billion on unauthorized deals. (Chapter 24)

1999 The Euro Large corporations do business in many currencies. In 1999 a new currency came into existence when 11 European countries adopted the euro in place of their separate currencies. They have since been joined by seven other countries. This is not the fi rst time that * The American sycamore, Planatus occidentalis.

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26 Part One Introduction

QUESTIONS AND PROBLEMS 1. Vocabulary Check. Choose the term within the parentheses that best matches each of the

following descriptions. (LO1-1–LO1-7)

a. Expenditure on research and development (financing decision / investment decision) b. A bank loan (real asset / financial asset) c. Listed on a stock exchange (closely held corporation / public corporation) d. Has limited liability (partnership / corporation) e. Responsible for bank relationships (the treasurer / the controller) f. Agency cost (the cost resulting from conflicts of interest between managers and shareholders

/ the amount charged by a company’s agents such as the auditors and lawyers)

2. Financial Decisions. Which of the following are investment decisions, and which are financing decisions? (LO1-1)

a. Should we stock up with inventory ahead of the holiday season? b. Do we need a bank loan to help buy the inventory? c. Should we develop a new software package to manage our inventory? d. With a new automated inventory management system, it may be possible to sell off our Bird-

lip warehouse. e. With the savings we make from our new inventory system, it may be possible to increase our

dividend. f. Alternatively, we can use the savings to repay some of our long-term debt.

3. Financial Decisions. What is the difference between capital budgeting decisions and capital structure decisions? (LO1-1)

4. Real versus Financial Assets. Which of the following are real assets, and which are financial? (LO1-2)

a. A share of stock b. A personal IOU

Almost all managers are involved to some degree in investment decisions, but some man- agers specialize in finance, for example, the treasurer, controller, and CFO. The treasurer is most directly responsible for raising capital and maintaining relationships with banks and investors that hold the firm’s securities. The controller is responsible for preparing financial statements and managing budgets. In large firms, a chief financial officer over- sees both the treasurer and the controller and is involved in financial policymaking and corporate planning.

Value maximization is the natural financial goal of the firm. Shareholders can invest or con- sume the increased wealth as they wish, provided that they have access to well- functioning financial markets.

Companies either can invest in real assets or can return the cash to shareholders, who can invest it for themselves. The return that shareholders can earn for themselves is called the opportunity cost of capital. Companies increase shareholder wealth whenever they can earn a higher return on their investments than the opportunity cost of capital.

Shareholders do not want the maximum possible stock price; they want the maximum hon- est price. But there need be no conflict between value maximization and ethical behavior. The surest route to maximum value starts with products and services that satisfy custom- ers. A good reputation with customers, employees, and other stakeholders is important for the firm’s long-run profitability and value.

Conflicts of interest between managers and stockholders can lead to agency problems and agency costs. Agency problems are kept in check by financial controls, by well-designed compensation packages for managers, and by effective corporate governance.

Who are the principal financial managers in a corporation? ( LO1-4 )

Why does it make sense for corporations to maximize shareholder wealth? ( LO1-5 )

What is the fundamental trade-off in investment decisions? ( LO1-6 )

Is value maximization ethical? ( LO1-7 )

How do corporations ensure that managers act in the interest of stockholders? ( LO1-8 )

finance

®

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Chapter 1 Goals and Governance of the Corporation 27

c. A trademark d. A truck e. Undeveloped land f. The balance in the firm’s checking account g. An experienced and hardworking sales force h. A bank loan agreement

5. Real and Financial Assets. Read the following passage and fit each of the following terms into the most appropriate space: financing, real, bonds, investment, executive airplanes, financial, capital budgeting, brand names. (LO1-2)

Companies usually buy _____ assets. These include both tangible assets such as _____ and intangible assets such as _____ . To pay for these assets, they sell _____ assets such as _____ . The decision about which assets to buy is usually termed the _____ or _____ decision. The decision about how to raise the money is usually termed the _____ decision.

6. Corporations. Choose in each case the type of company that best fits the description. (LO1-3)

a. The business is owned by a small group of investors. (private corporation / public corporation)

b. The business does not pay income tax. (private corporation / partnership) c. The business has limited liability. (sole proprietorship / public corporation) d. The business is owned by its shareholders. (partnership / public corporation)

7. Corporations. What do we mean when we say that corporate income is subject to double taxa- tion? (LO1-3)

8. Corporations. Which of the following statements always apply to corporations? (LO1-3)

a. Unlimited liability b. Limited life c. Ownership can be transferred without affecting operations d. Managers can be fired with no effect on ownership

9. Corporations. What is limited liability, and who benefits from it? (LO1-3)

10. Corporations. Which of the following are advantages in separating ownership and manage- ment in large corporations? (LO1-3)

a. Managers no longer have the incentive to act in their own interests. b. The corporation survives even if managers are dismissed. c. Shareholders can sell their holdings without disrupting the business. d. Corporations, unlike sole proprietorships, do not pay tax; instead, shareholders are taxed on

any dividends they receive.

11. Corporations. Is limited liability always an advantage for a corporation and its shareholders? Hint: Could limited liability reduce a corporation’s access to financing? (LO1-3)

12. Financial Managers. Which of the following statements more accurately describes the trea- surer than the controller? (LO1-4)

a. Monitors capital expenditures to make sure that they are not misappropriated b. Responsible for investing the firm’s spare cash c. Responsible for arranging any issue of common stock d. Responsible for the company’s tax affairs

13. Financial Managers. Explain the differences between the CFO’s responsibilities and the trea- surer’s and controller’s responsibilities. (LO1-4)

14. Goals of the Firm. Give an example of an action that might increase short-run profits but at the same time reduce stock price and the market value of the firm. (LO1-5)

15. Cost of Capital. Why do financial managers refer to the opportunity cost of capital? How would you find the opportunity cost of capital for a safe investment? (LO1-5)

16. Goals of the Firm. You may have heard big business criticized for focusing on short-term performance at the expense of long-term results. Explain why a firm that strives to maximize stock price should be less subject to an overemphasis on short-term results than one that simply maximizes profits. (LO1-5)

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28 Part One Introduction

17. Goals of the Firm. Fritz is risk-averse and is content with a relatively low but safe return on his investments. Frieda is risk-tolerant and seeks a very high rate of return on her invested savings. Yet both shareholders will applaud a high-risk capital investment that nevertheless offers a superior rate of return. Why? What is meant by “superior”? (LO1-5)

18. Goals of the Firm. We claim that the goal of the firm is to maximize current market value. Could the following actions be consistent with that goal? (LO1-5)

a. The firm adds a cost-of-living adjustment to the pensions of its retired employees. b. The firm reduces its dividend payment, choosing to reinvest more earnings in the business. c. The firm buys a corporate jet for its executives. d. The firm drills for oil in a remote jungle. The chance of finding oil is only 1 in 5.

19. Goals of the Firm. Fill in the blanks in the following passage by choosing the most appropriate term from the following list (some of the terms may be used more than once or not used at all): expected return, financial assets, lower, market value, higher, opportunity cost of capital, real assets, dividend, shareholders. (LO1-5)

Shareholders want managers to maximize the _____ of their investments. The firm faces a trade-off. Either it can invest its cash in _____ or it can give the cash back to _____ in the form of a _____ and they can invest it in _____ . Shareholders want the company to invest in _____ only if the _____ is _____ than they could earn for themselves. The return that shareholders could earn for themselves is therefore the _____ for the firm.

20. Goals of the Firm. Explain why each of the following may not be appropriate corporate goals. (LO1-5)

a. Increase market share b. Minimize costs c. Underprice any competitors d. Expand profits

21. Goals of the Firm. We can imagine the financial manager doing several things on behalf of the firm’s stockholders. For example, the manager might do the following: (LO1-5)

a. Make shareholders as wealthy as possible by investing in real assets. b. Modify the firm’s investment plan to help shareholders achieve a particular time pattern of

consumption. c. Choose high- or low-risk assets to match shareholders’ risk preferences. d. Help balance shareholders’ checkbooks.

However, in well-functioning capital markets, shareholders will vote for only one of these goals. Which one will they choose?

22. Cost of Capital. British Quince comes across an average-risk investment project that offers a rate of return of 9.5%. This is less than the company’s normal rate of return, but one of Quince’s directors notes that the company can easily borrow the required investment at 7%. “It’s simple,” he says. “If the bank lends us money at 7%, then our cost of capital must be 7%. The project’s return is higher than the cost of capital, so let’s move ahead.” How would you respond? (LO1-5)

23. Cost of Capital. In a stroke of good luck, your company has uncovered an opportunity to invest for 10 years at a guaranteed 6% rate of return. How would you determine the opportunity cost of capital for this investment? (LO1-5)

24. Cost of Capital. Pollution Busters Inc. is considering a purchase of 10 additional carbon sequesters for $100,000 apiece. The sequesters last for only 1 year before becoming saturated. Then the carbon is sold to the government. (LO1-5)

a. Suppose the government guarantees the price of carbon. At this price, the payoff after 1 year is $115,000 for sure. How would you determine the opportunity cost of capital for this investment?

b. Suppose instead that the sequestered carbon has to be sold on the London Carbon Exchange. Carbon prices have been extremely volatile, but Pollution Busters’ CFO learns that average rates of return from investments on that exchange have been about 20%. She thinks this is a reasonable forecast for the future. What is the opportunity cost of capital in this case? Is the purchase of additional sequesters a worthwhile capital investment?

25. Ethics. Look at some of the practices described in the box on page 20. What, if any, do you believe are the ethical issues involved? (LO1-7)

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Chapter 1 Goals and Governance of the Corporation 29

CHALLENGE PROBLEM 38. Goals of the Firm. It is sometimes suggested that instead of seeking to maximize shareholder

value and, in the process, pursuing profit, the firm should seek to maximize the welfare of all its stakeholders, such as its employees, its customers, and the community in which it operates. How far would this objective conflict with one of maximizing shareholder value? Do you think such an objective is feasible or desirable? (LO1-5)

26. Agency Issues. Many firms have devised defenses that make it much more costly or difficult for other firms to take them over. How might such takeover defenses affect the firm’s agency problems? Are managers of firms with formidable takeover defenses more or less likely to act in the firm’s interest rather than their own? (LO1-6)

27. Agency Issues. Sometimes lawyers work on a contingency basis. They collect a percentage of their clients’ settlements instead of receiving fixed fees. Why might clients prefer this arrange- ment? Would the arrangement mitigate an agency problem? Explain. (LO1-6)

28. Agency Issues. One of the “Finance through the Ages” episodes that we cited is the 1993 col- lapse of Barings Bank, when one of its traders lost $1.3 billion. Traders are compensated in large part according to their trading profits. How might this practice have contributed to an agency problem? (LO1-6)

29. Agency Issues. When a company’s stock is widely held, it may not pay an individual share- holder to spend time monitoring managers’ performance and trying to replace poor performers. Explain why. Do you think that a bank that has made a large loan to the company is in a differ- ent position? (LO1-6)

30. Agency Issues. Company A pays its managers a fixed salary. Company B ties compensation to the performance of the stock. (LO1-6)

a. Which company’s compensation would most help to mitigate conflicts of interest between managers and shareholders?

b. Other things equal, which company would experience the greatest variation in earnings?

31. Corporate Governance. How do clear and comprehensive financial reports promote effective corporate governance? (LO1-6)

32. Corporate Governance. Some commentators have claimed that the U.S. system of corporate governance is “broken” and needs thorough reform. What do you think? Do you see systematic failures in corporate governance or just a few “bad apples”? (LO1-6)

33. Agency Issues. Which of the following forms of compensation is most likely to align the inter- ests of managers and shareholders? (LO1-6)

a. A fixed salary b. A salary linked to company profits c. A salary that is paid partly in the form of the company’s shares

34. Agency Costs. What are agency costs? List some ways by which agency costs are mitigated. (LO1-6)

35. Reputation. As you drive down a deserted highway, you are overcome with a sudden desire for a hamburger. Fortunately, just ahead are two hamburger outlets; one is owned by a national brand, and the other appears to be owned by “Joe.” Which outlet has the greater incentive to serve you cat meat? Why? (LO1-7)

36. Ethics. In some countries, such as Japan and Germany, corporations develop close long-term rela- tionships with one bank and rely on that bank for a large part of their financing needs. In the United States, companies are more likely to shop around for the best deal. Do you think that this practice is more or less likely to encourage ethical behavior on the part of the corporation? (LO1-7)

37. Ethics. Is there a conflict between “doing well” and “doing good”? In other words, are policies that increase the value of the firm (doing well) necessarily at odds with socially responsible policies (doing good)? When there are conflicts, how might government regulations or laws tilt the firm toward doing good? For example, how do taxes or fees charged on pollutants affect the firm’s decision to pollute? Can you cite other examples of “incentives” used by governments to align private interests with public ones? (LO1-7)

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30 Part One Introduction

SOLUTIONS TO SELF-TEST QUESTIONS 1.1 a. The development of a microprocessor is a capital budgeting decision. The investment of

$1 billion will purchase a real asset, the microprocessor design and production facilities. b. The bank loan is a financing decision. This is how Volkswagen will raise money for its

investment. c. Capital budgeting. d. Capital budgeting. The marketing campaign should generate a real, though intangible,

asset. e. Both. The acquisition is an investment decision. The decision to issue shares is a financing

decision.

1.2 a. A real asset. Real assets can be intangible assets. b. Financial. c. Real. d. Financial. e. Real. f. Financial.

1.3 Fritz would more likely be the treasurer and Frieda the controller. The treasurer raises money from the financial markets and requires a background in financial institutions. The controller requires a background in accounting.

1.4 There is no reason for the Hotspurs to avoid high-dividend stocks, even if they wish to invest for tuition bills in the distant future. Their concern should be with only the risk and expected return of the shares. If a particular stock pays a generous cash dividend, they always have the option of reinvesting the dividend in that stock or, for that matter, in other securities. The divi- dend payout does not affect their ability to redirect current investment income to their future needs as they plan for their anticipated tuition bills.

1.5 Because investors can reasonably expect a 15% return in other investments in palladium, the firm should take this as the opportunity cost of capital for its proposed investment. Although the project is expected to show an accounting profit, its expected return is only 12%. There- fore, the firm should reject the project: its expected return is less than the 15% expected return offered by equivalent-risk investments.

1.6 Agency problems arise when managers and shareholders have different objectives. Manag- ers may empire-build with excessive investment and growth. Managers may be unduly risk- averse, or they may try to take excessive salaries or perquisites.

1.7 Harry’s has a far bigger stake in the reputation of its business than Victor’s. The store has been in business for a long time. The owners have spent years establishing customer loyalty. In con- trast, Victor’s has just been established. The owner has little of his own money tied up in the firm, and so has little to lose if the business fails. In addition, the nature of the business results in little customer loyalty. Harry’s is probably more reliable.

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LEARNING OBJECTIVES

After studying this chapter, you should be able to:

2-1 Understand how financial markets and institutions channel savings to corporate investment.

2-2 Understand the basic structure of banks, insurance companies, mutual funds, and pension funds.

2-3 Explain the functions of financial markets and institutions.

2-4 Understand the main events behind the financial crisis of 2007–2009 and the subsequent eurozone crisis.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

32

Financial Markets and Institutions 2 CHAPTE

R

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33

P A

R T

O N

E

I f a corporation needs to issue more shares of stock, then its financial manager had better understand how the stock market works. If it wants to take out a bank loan, the financial manager had better

understand how banks and other financial institu-

tions work. If the firm contemplates a capital invest-

ment, such as a factory expansion or a new product

launch, the financial manager needs to think clearly

about the cost of the capital that the firm raises from

outside investors. As we pointed out in Chapter 1, the

opportunity cost of capital for the firm is the rate of

return that its stockholders expect to get by investing

on their own in financial markets. This means that the

financial manager must understand how prices are

determined in the financial markets in order to make

wise investment decisions.

Financial markets and institutions are the firm’s

financial environment. You don’t have to know every-

thing about that environment to begin the study of

financial management, but a general understand-

ing provides useful context for the work ahead. For

example, it will help you to understand why you are

calculating the yield to maturity of a bond in Chap-

ter 6, the net present value of a capital investment in

Chapter 9, or the weighted-average cost of capital

for a company in Chapter 13.

This chapter does three things. First, it surveys finan-

cial markets and institutions. We will cover the stock

and bond markets, banks and insurance companies,

and mutual and pension funds. Second, we will set

out the functions of financial markets and institu-

tions and look at how they help corporations and the

economy. Third, we will discuss the financial crisis of

2007–2009 and the eurozone crisis that followed. An

understanding of what happens when financial mar-

kets do not function well is important for understand-

ing why and how financial markets and institutions

matter.

In tr

o d

u c

tio n

Image: George Rex. Read this chapter before you visit the New York Stock Exchange.

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34 Part One Introduction

2.1 The Importance of Financial Markets and Institutions In the previous chapter we explained why corporations need to be good at finance in order to survive and prosper. All corporations face important investment and financing decisions. But of course those decisions are not made in a vacuum. They are made in a financial environment. That environment has two main segments: financial markets and financial institutions.

Businesses have to go to financial markets and institutions for the financing they need to grow. When they have a surplus of cash, and no need for immediate financing, they have to invest the cash, for example, in bank accounts or in securities. Let’s take Apple Computer Inc. as an example.

Table 2.1 presents a timeline for Apple and examples of the sources of financing tapped by Apple from its start-up in a California garage in 1976 to its cash-rich status in 2013. The initial investment in Apple stock was $250,000. Apple was also able to get short-term financing from parts suppliers who did not demand immediate pay- ment. Apple got the parts, assembled and sold the computers, and afterward paid off its accounts payable to the suppliers. (We discuss accounts payable in Chapter 19.) Then, as Apple grew, it was able to obtain several rounds of financing by selling Apple shares to private venture capital investors. (We discuss venture capital in Chapter 15.) In December 1980, it raised $91 million in an initial public offering (IPO) of its shares to public investors. There was also a follow-up share issue in May 1981. 1

1 Many of the shares sold in the 1981 issue were previously held by Apple employees. Sale of these shares allowed the employees to cash out and diversify some of their Apple holdings but did not raise additional financing for Apple.

April 1976: Apple Computer Inc. founded

Mike Makkula, Apple’s fi rst chairman, invests $250,000 in Apple shares.

1976: First 200 computers sold

Parts suppliers give Apple 30 days to pay. (Financing from accounts payable.)

1978–79 Apple raises $3.5 million from venture capital investors. December 1980: Initial public offering

Apple raises $91 million, after fees and expenses, by selling shares to public investors.

May 1981 Apple sells 2.6 million additional shares at $31.25 per share. April 1987 Apple pays its fi rst dividend at an annual rate of $.12 per share Early 1990s Apple carries out several share repurchase programs. 1994 Apple issues $300 million of debt at an interest rate of 6.5%. 1996–97: Apple reports a $740 million loss in the second quarter of 1996. Lays off 2,700 employees in 1997.

Dividend is suspended in February 1996. Apple sells $661 million of debt to private investors in June 1996. The borrowing provides “sufficient liquidity” to execute Apple’s strategic plans and to “return the company to profi tability.”

September 1997: Acquires assets of Power Computing Corp.

Acquisition is fi nanced with $100 million of Apple stock.

2004: Apple is healthy and profi table, thanks to iMac, iPod, and other products.

Apple pays off the $300 million in long-term debt issued in 1994, leaving the company with no long-term debt outstanding.

2005–13 Apple’s profi ts grow rapidly. It invests in marketable securities, which accumulate to $147 billion by June 2013.

2012–13 Apple announces plans to pay out $100 billion to shareholders over the next 3 years. It also borrows a record $17 billion.

From start-up to 2013 Apple stockholders reinvest $104.6 billion of earnings. Thus Apple’s balance sheet for June 2013 shows cumulative retained earnings of $104.6 billion.

TABLE 2.1 Examples of financing decisions by Apple Computer

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Chapter 2 Financial Markets and Institutions 35

Once Apple was a public company, it could raise financing from many sources, and it was able to pay for acquisitions by issuing more shares. We show a few examples in Table 2.1 .

Apple started paying cash dividends to shareholders in 1987, and it also distrib- uted cash to investors by stock repurchases in the early 1990s. But Apple hit a rough patch in 1996 and 1997, and regular dividends were eliminated. The company had to borrow $661 million from a group of private investors in order to cover its losses and finance its recovery plan. Apple was generally profitable, despite the rough years, and it financed growth by plowing back earnings into its operations. These retained earn- ings had cumulated to $104.6 billion by June 2013.

Apple is well known for its product innovations, including the Macintosh computer, the iPhone, and the iPad. Apple is not special because of financing. In fact, the story of its financing is not too different from that of many other successful companies. But access to financing was vital to Apple’s growth and profitability. Would we have iMac computers, iPhones, or iPads if Apple had been forced to operate in a country with a primitive financial system? Definitely not. A prosperous economy requires a well- functioning financial system.

A modern financial system offers financing in many different forms, depending on the company’s age, its growth rate, and the nature of its business. For example, Apple relied on venture capital financing in its early years and only later floated its shares in public stock markets. Still later, as the company matured, it turned to other forms of financing, including the examples given in Table 2.1 . But the table does not begin to cover the range of financing channels open to modern corporations. We will encounter many other channels later in the book, and new channels are opening up regularly. The nearby box describes one recent financial innovation, micro-lending funds that make small loans to businesspeople in the poorer parts of the world.

2.2 The Flow of Savings to Corporations The money that corporations invest in real assets comes ultimately from savings by investors. But there can be many stops on the road between savings and corporate investment. The road can pass through financial markets, financial intermediaries, or both.

Let’s start with the simplest case of a small, closely held corporation, like Apple in its earliest years. The orange arrows in Figure 2.1 show the flow of savings from shareholders in this simple setting. There are two possible paths: The firm can sell new shares, or it can reinvest cash back into the firm’s operations. Reinvestment means additional savings by existing shareholders. The reinvested cash could have been paid out to those shareholders and spent by them on personal consumption. By not taking and spending the cash, shareholders have reinvested their savings in the corporation. Cash retained and reinvested in the firm’s operations is cash saved and invested on behalf of the firm’s shareholders.

FIGURE 2.1 Flow of savings to investment in a closely held corporation. Investors use savings to buy additional shares. Investors also save when the corporation reinvests on their behalf. Investment

in real assets

Corporation Shareholders

in closely held corporation

InvestorsCash raised from share issues

Cash reinvested

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36

Of course, a small corporation has other financing choices. It could take out a bank loan, for example. The bank in turn may have raised money by attracting savings accounts. In this case investors’ savings flow through the bank to the firm.

Now consider a large, public corporation, for example, Apple Computer in June 2013. What’s different? Scale, for one thing: Apple’s annual revenues for the previous 12 months were $169 billion, and its balance sheet showed total assets of $200 billion. The scope of Apple’s activities has also expanded: It now has dozens of products and operates worldwide. Because of this scale and scope, Apple attracts investors’ savings by a variety of different routes. It can do so because it is a large, profitable, public firm.

The flow of savings to large public corporations is shown in Figure 2.2 . Notice two key differences from Figure 2.1 . First, public corporations can draw savings from investors worldwide. Second, the savings flow through financial markets, financial intermediaries, or both. Suppose, for example, that Bank of America raises $900 mil- lion by a new issue of shares. An Italian investor buys 4,000 of the new shares for

Finance in Practice Micro Loans, Solid Returns The interest rates on these micro loans are relatively

high; this is because the cost of writing and administering such small loans is high and the loans are made in nations with weak currencies. However, default rates on the loans run only about 4 percent. “There is a deep pride in keeping up with payments,” says Deidre Wagner, an executive vice president of Starbucks, who invested $100,000 in a microfi - nance fund in 2003. “In some instances, when an individual is behind on payments, others in the village may make up the difference.” Investors and borrowers know that when the micro loans are repaid, the money gets recycled into new loans, giving still more borrowers a chance to move up the economic ladder.

Source: Adapted from Eric Uhlfelder, “Micro Loans, Solid Returns,” Business- Week, May 9, 2005, pp. 100–102.

Vahid Hujdur had dreams of opening his own business. With about $200 of his own money and a $1,500 loan, he was able to rent space in the old section of Sarajevo, and he began repairing and selling discarded industrial sewing machines. After just eight years, Hujdur has 10 employees building, installing, and fi xing this industrial machinery. Hujdur didn’t get his initial loan from a local bank. “They were asking for guarantees that were impossible to get,” he recalls. Instead the capital came from LOKmicro, a local fi nancial institution specializing in microfi nance—the lending of small amounts to the poor in developing nations to help them launch small enterprises.

Microfi nance institutions get capital from individual and institutional investors via microfi nance funds, which collect the investors’ money, vet the local lenders, offer them man- agement assistance, and administer investors’ accounts.

FIGURE 2.2 Flow of savings to investment for a large, public corporation. Savings come from investors worldwide. The savings may flow through financial markets or financial intermediaries. The corporation also reinvests on shareholders’ behalf.

Stock markets Fixed-income markets Money markets

Financial Markets

Mutual Funds Pension funds

Financial Intermediaries

Banks Insurance companies

Financial Institutions

Investors WorldwideInvestment

in real assets

Corporation Reinvestment

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Chapter 2 Financial Markets and Institutions 37

$15 per share. Now Bank of America takes that $60,000, along with money raised by the rest of the issue, and makes a $300 million loan to Apple. The Italian investor’s savings end up flowing through financial markets (the stock market), to a financial intermediary (Bank of America), and finally to Apple.

Of course our Italian friend’s $60,000 doesn’t literally arrive at Apple in an envelope marked “From L. DaVinci.” Investments by the purchasers of the Bank of America’s stock issue are pooled, not segregated. Signor DaVinci would own a share of all of Bank of America’s assets, not just one loan to Apple. Nevertheless, investors’ sav- ings are flowing through the financial markets and the bank to finance Apple’s capital investments.

The Stock Market A financial market is a market where securities are issued and traded. A security is just a traded financial asset, such as a share of stock. For a corporation, the stock mar- ket is probably the most important financial market.

As corporations grow, their requirements for outside capital can expand dramati- cally. At some point the firm will decide to “go public” by issuing shares on an orga- nized exchange such as the New York Stock Exchange (NYSE) or NASDAQ; that first issue is called an initial public offering or IPO. The buyers of the IPO are helping to finance the firm’s investment in real assets. In return, the buyers become part-owners of the firm and participate in its future success or failure. (Most investors in the Inter- net IPOs of 1999 and 2000 are by now sorely disappointed, but many IPOs pay off handsomely. If only we had bought Apple shares on their IPO day in 1980 .  .  .) Of course a corporation’s IPO is not its last chance to issue shares. For example, Bank of America went public in the 1930s, but it could make a new issue of shares tomorrow.

A new issue of shares increases both the amount of cash held by the company and the number of shares held by the public. Such an issue is known as a primary issue, and it is sold in the primary market. But in addition to helping companies raise new cash, financial markets also allow investors to trade securities among themselves. For example, Smith might decide to raise some cash by selling her Apple stock at the same time that Jones invests his spare cash in Apple. The result is simply a transfer of own- ership from Smith to Jones, which has no effect on the company itself. Such purchases and sales of existing securities are known as secondary transactions, and they take place in the secondary market. Notice that Smith and Jones might be less happy for Apple to raise new capital and invest in long-term projects if they could not sell their stock in the secondary market when they needed the cash for personal use.

Stock markets are also called equity markets, since stockholders are said to own the common equity of the firm. You will hear financial managers refer to the capital structure decision as “the choice between debt and equity financing.”

Now may be a good time to stress that the financial manager plays on a global stage and needs to be familiar with markets around the world. For example, Apple’s stock is traded on the NASDAQ market and also in Germany on the Deutsche Börse. China Telecom, Deutsche Bank, Novartis, Petrobras (Brazil), Sony, Unilever, Manchester United football club, and over 500 other overseas firms have listed their shares on the NYSE. We return to the trading and pricing of shares in Chapter 7.

Other Financial Markets Debt securities as well as equities are traded in financial markets. The Apple bond issue in 1994 was sold publicly to investors (see Table 2.1 ). Table 1.1 in the previ- ous chapter also gives examples of debt issues, including issues by Volkswagen and GlaxoSmithKline.

A few corporate debt securities are traded on the NYSE and other exchanges, but most corporate debt securities are traded over the counter, through a network of banks and securities dealers. Government debt is also traded over the counter.

financial market Market where securities are issued and traded.

primary market Market for the sale of newly issued securities.

secondary market Market in which previously issued securities are traded among investors.

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Stock exchanges: From clubs to commercial

businesses

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38 Part One Introduction

A bond is a more complex security than a share of stock. A share is just a propor- tional ownership claim on the firm, with no definite maturity. Bonds and other debt securities can vary in maturity, in the degree of protection or collateral offered by the issuer, and in the level and timing of interest payments. Some bonds make “floating” interest payments tied to the future level of interest rates. Many can be “called” (repur- chased and retired) by the issuing company before the bonds’ stated maturity date. Some bonds can be converted into other securities, usually the stock of the issuing company. You don’t need to master these distinctions now; just be aware that the debt or fixed-income market is a complicated and challenging place. A corporation must not only decide between debt and equity finance. It must also consider the design of debt. We return to the trading and pricing of debt securities in Chapter 6.

The markets for long-term debt and equity are called capital markets. A firm’s cap- ital is its long-run financing. Short-term securities are traded in the money markets. “Short term” means less than 1 year. For example, large, creditworthy corporations raise short-term financing by issues of commercial paper, which are debt issues with maturities of no more than 270 days. Commercial paper is issued in the money market.

fixed-income market Market for debt securities.

capital market Market for long-term financing.

money market Market for short-term financing (less than 1 year).

The financial manager regularly encounters other financial markets. Here are three examples, with references to the chapters where they are discussed:

• Foreign exchange markets (Chapter 22). Any corporation engaged in international trade must be able to transfer money back and forth between dollars and other cur- rencies. Foreign exchange is traded over the counter through a network of the larg- est international banks.

• Commodities markets (Chapter 24). Dozens of commodities are traded on orga- nized exchanges, such as the Chicago Mercantile Exchange (CME) or the Inter- continental Exchange. You can buy or sell corn, wheat, cotton, fuel oil, natural gas, copper, silver, platinum, and so on.

• Markets for options and other derivatives (Chapters 23 and 24). Derivatives are securities whose payoffs depend on the prices of other securities or commodities. For example, you can buy an option to purchase IBM shares at a fixed price on a fixed future date. The option’s payoff depends on the price of IBM shares on that date. Commodities can be traded by a different kind of derivative security called a futures contract.

Commodity and derivative markets are not sources of financing but markets where the financial manager can adjust the firm’s exposure to various business risks. For example, an electric generating company may wish to lock in the future price of natu- ral gas by trading in commodity markets, thus eliminating the risk of a sudden jump in the price of its raw materials.

Wherever there is uncertainty, investors may be interested in trading, either to spec- ulate or to lay off their risks, and a market may arise to meet that trading demand. In recent years several smaller markets have been created that allow punters to bet on a single event. The nearby box discusses how prices in these markets can reveal people’s predictions about the future.

Do you understand the following distinctions? Briefly explain in each case.

a. Primary market vs. secondary market. b. Capital market vs. money market. c. Stock market vs. fixed-income market.

Self-Test 2.1

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Finance in Practice Prediction Markets Take a look at the accompanying fi gure from the Iowa

Electronic Markets. It shows the contract prices for the two contenders for the White House between April and Novem- ber 2012. In June, before the Republican convention, the price of a Republican candidate reached a maximum of $.47. From then on, apart from a brief wobble in October, the mar- ket suggested a steady rise in the probability of an Obama victory.

Participants in prediction markets are putting their money where their mouth is. So the forecasting accuracy of these markets compares favorably with that of major polls. Some businesses have formed internal prediction markets to sur- vey the views of their staff. For example, Google operates an internal market to forecast product launch dates, the number of Gmail users, and other strategic questions. *

* Google’s experience is analyzed in B. Cowgill, J. Wolfers, and E. Zitzewitz, “Using Prediction Markets to Track Information Flows: Evidence from Google,” working paper, Dartmouth College, January 2009.

Stock markets allow investors to bet on their favorite stocks. Prediction markets allow them to bet on almost anything else. These markets reveal the collective guess of traders on issues as diverse as New York City snowfall, an avian fl u out- break, and the occurrence of a major earthquake.

Prediction markets are conducted on the major futures exchanges and on a number of smaller online exchanges such as Intrade ( www.intrade.com ) and Iowa Electronic Markets ( www.biz.uiowa.edu/iem ). Take the 2012 presiden- tial race as an example. On the Iowa Electronic Markets you could have bet that Barack Obama would win by buying one of his contracts. Each Obama contract promised to pay $1 if he won the presidency and nothing if he lost. If you thought that the probability of an Obama victory was 55% (say), you would have been prepared to pay up to $.55 for his contract. Someone who was relatively pessimistic about Obama’s chances would have been happy to sell you such a contract, for that sale would turn a profi t if Obama were to lose. With many participants buying and selling, the market price of a contract revealed the collective wisdom of the crowd.

0

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

4/ 1/

12

5/ 1/

12

6/ 1/

12

7/ 1/

12

8/ 1/

12

9/ 1/

12

10 /1

/1 2

11 /1

/1 2

Obama Romney

P ric

e, $

Presidential futures prices, 2012 election

Source: Iowa Electronic Markets, www.biz.uiowa.edu/iem.

39

Financial Intermediaries A financial intermediary is an organization that raises money from investors and provides financing for individuals, companies, and other organizations. For corpora- tions, intermediaries are important sources of financing. Intermediaries are a stop on the road between savings and real investment.

Why is a financial intermediary different from a manufacturing corporation? First, it may raise money in different ways, for example, by taking deposits or selling insur- ance policies. Second, it invests that money in financial assets, for example, in stocks, bonds, or loans to businesses or individuals. In contrast, a manufacturing company’s main investments are in plant, equipment, or other real assets.

We will start with two important classes of intermediaries, mutual funds and pension funds.

financial intermediary An organization that raises money from investors and provides financing for individuals, corporations, or other organizations.

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40 Part One Introduction

Mutual funds raise money by selling shares to investors. The investors’ money is pooled and invested in a portfolio of securities. Investors can buy or sell shares in mutual funds as they please, and initial investments are often $3,000 or less. Van- guard’s Explorer Fund, for example, held a portfolio of over 600 stocks with a market value of about $13 billion in early 2014. An investor in Explorer can increase her stake in the fund’s portfolio by buying additional shares, and so gain a higher share of the portfolio’s subsequent dividends and price appreciation. 2 She can also sell her shares back to the fund if she decides to cash out of her investment. 3

The advantages of a mutual fund should be clear: Unless you are very wealthy, you cannot buy and manage a 600-stock portfolio on your own, at least not efficiently. Mutual funds offer investors low-cost diversification and professional manage- ment. For most investors, it’s more efficient to buy a mutual fund than to assem- ble a diversified portfolio of stocks and bonds.

Mutual fund managers also try their best to “beat the market,” that is, to generate superior performance by finding the stocks with better-than-average returns. Whether they can pick winners consistently is another question, which we address in Chapter 7.

In exchange for their services, the fund’s managers take out a management fee. There are also the expenses of running the fund. For Explorer, fees and expenses absorb about .5% of portfolio value each year. This seems reasonable, but watch out: The typical mutual fund charges more than Explorer does. In some cases fees and expenses add up to 2% per year. That’s a big bite out of your investment return.

Mutual funds are a stop on the road from savings to corporate investment. Suppose Explorer purchases part of the new issue of shares by Bank of America. Again we show the flow of savings to investment by orange arrows:

mutual fund An investment company that pools the savings of many investors and invests in a portfolio of securities.

2 Mutual funds are not corporations but investment companies. They pay no tax, providing that all income from dividends and price appreciation is passed on to the funds’ shareholders. The shareholders pay personal tax on this income. 3 Explorer, like most mutual funds, is an open-end fund. It stands ready to issue shares to new investors in the fund and to buy back existing shares when its shareholders decide to cash out. The purchase and sale prices depend on the fund’s net asset value (NAV) on the day of purchase or redemption. Closed-end funds have a fixed number of shares traded on an exchange. If you want to invest in a closed-end fund, you must buy shares from another stockholder in the fund.

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U.S. mutual funds

Bank of America Explorer Fund Sells shares

$

Investors Issues shares

$

There are nearly 8,700 mutual funds in the United States. In fact there are more mutual funds than public companies! The funds pursue a wide variety of investment strategies. Some funds specialize in safe stocks with generous dividend payouts. Some specialize in high-tech growth stocks. Some “balanced” funds offer mixtures of stocks and bonds. Some specialize in particular countries or regions. For example, the Fidel- ity Investments mutual fund group sponsors funds for Canada, Japan, China, Europe, and Latin America.

Like mutual funds, hedge funds also pool the savings of different investors and invest on their behalf. But they differ from mutual funds in at least two ways. First, because hedge funds usually follow complex, high-risk investment strategies, access

hedge fund Private investment fund that pursues complex, high-risk investment strategies.

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Chapter 2 Financial Markets and Institutions 41

is usually restricted to knowledgeable investors such as pension funds, endowment funds, and wealthy individuals. Don’t try to send a check for $3,000 or $5,000 to a hedge fund; most hedge funds are not in the “retail” investment business. Second, hedge funds try to attract the most talented managers by compensating them with potentially lucrative, performance-related fees. 4 In contrast, mutual funds usually charge a fixed percentage of assets under management.

Hedge funds follow many different investment strategies. Some try to make a profit by identifying over valued stocks or markets and selling short. (We will not go into procedures for short-selling here. Just remember that short-sellers profit when prices fall. ) 5 “Vulture funds” specialize in the securities of distressed corporations. Some hedge funds take bets on firms involved in merger negotiations, others look for mis- priced convertible bonds, and some take positions in currencies and interest rates. Hedge funds manage less money than mutual funds, but they sometimes take very big positions and have a large impact on the market.

There are other ways of pooling and investing savings. Consider a pension plan set up by a corporation or other organization on behalf of its employees. There are several types of pension plan. The most common type of plan is the defined-contribution plan. In this case, a percentage of the employee’s monthly paycheck is contributed to a pension fund. (The employer and employee may each contribute 5%, for example.) Contributions from all participating employees are pooled and invested in securities or mutual funds. (Usually the employees can choose from a menu of funds with different investment strategies.) Each employee’s balance in the plan grows over the years as contributions continue and investment income accumulates. The balance in the plan can be used to finance living expenses after retirement. The amount available for retirement depends on the accumulated contributions and on the rate of return earned on the investments. 6

Pension funds are designed for long-run investment. They provide professional management and diversification. They also have an important tax advantage: Contri- butions are tax-deductible, and investment returns inside the plan are not taxed until cash is finally withdrawn. 7

Pension plans are among the most important vehicles for savings. Private pension plans held $8.0 trillion in assets in 2013.

4 Sometimes these fees can be very large indeed. For example, Forbes estimated that the top hedge fund man- ager in 2012 earned $2.2 billion in fees. 5 A short-seller borrows a security from another investor and sells it. Of course, the seller must sooner or later buy the security back and return it to its original owner. The short-seller earns a profit if the security can be bought back at a lower price than it was sold for.

pension fund Fund set up by an employer to provide for employees’ retirement.

6 In a defined-benefit plan, the employer promises a certain level of retirement benefits (set by a formula) and the employer invests in the pension plan. The plan’s accumulated investment value has to be large enough to cover the promised benefits. If not, the employer must put in more money. Defined-benefit plans are gradually giving way to defined-contribution plans. 7 Defined-benefit pension plans share these same advantages, except that the employer invests rather than the employees. In a defined-benefit plan, the advantage of tax deferral on investment income accrues to the employer. This deferral reduces the cost of funding the plan.

Individual investors can buy bonds and stocks directly, or they can put their money in a mutual fund or a defined-contribution pension fund. What are the advantages of the second strategy?

Self-Test 2.2

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42 Part One Introduction

Financial Institutions Banks and insurance companies are financial institutions. 8 A financial institution is an intermediary that does more than just pool and invest savings. Institutions raise financing in special ways, for example, by accepting deposits or selling insurance poli- cies, and they provide additional financial services. Unlike a mutual fund, they not only invest in securities but also lend money directly to individuals, businesses, or other organizations.

Commercial Banks There are about 6,300 commercial banks in the United States. They vary from giants such as JPMorgan Chase with $2.4 trillion of assets to midgets like the Tightwad Bank with some $18 million.

Commercial banks are major sources of loans for corporations. (In the United States, they are generally not allowed to make equity investments in corporations, although banks in most other countries can do so.) Suppose that a local forest products company negotiates a 9-month bank loan for $2.5 million. The flow of savings is:

financial institution A bank, insurance company, or similar financial intermediary.

8 We may be drawing too fine a distinction between financial intermediaries and institutions. A mutual fund could be considered a financial institution. But “financial institution” usually suggests a more complicated intermediary, such as a bank.

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The world’s largest banks

Company Bank

(Institution) Issues debt to bank

$2.5 million Investors

(Depositors) Accepts deposits

$2.5 million

The bank provides debt financing for the company and, at the same time, provides a place for depositors to park their money safely and withdraw it as needed.

Investment Banks We have discussed commercial banks, which raise money from depositors and other investors and then make loans to businesses and individuals. Investment banks are different. 9 Investment banks do not generally take deposits or make loans to companies. Instead, they advise and assist companies in obtaining finance. For example, investment banks underwrite stock offerings by purchasing the new shares from the issuing company at a negotiated price and reselling the shares to investors. Thus the issuing company gets a fixed price for the new shares, and the investment bank takes responsibility for distributing the shares to thousands of inves- tors. We discuss share issues in more detail in Chapter 15.

Investment banks also advise on takeovers, mergers, and acquisitions. They offer investment advice and manage investment portfolios for individual and institutional investors. They run trading desks for foreign exchange, commodities, bonds, options, and derivatives.

Investment banks can invest their own money in start-ups and other ventures. For example, the Australian Macquarie Bank has invested in airports, toll highways, elec- tric transmission and generation, and other infrastructure projects around the world.

9 Banks that accept deposits and provide financing to businesses are called commercial banks. Savings banks accept deposits and savings accounts and lend the money out mostly to individuals, for example, as mortgage loans to home buyers. Investment banks do not take deposits and do not lend money to businesses or individu- als, except as bridge loans made as temporary financing for takeovers or other transactions. Investment banks are sometimes called merchant banks.

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Chapter 2 Financial Markets and Institutions 43

The largest investment banks are financial powerhouses. They include Goldman Sachs, Morgan Stanley, Lazard, Nomura (Japan), and Macquarie Bank. 10 In addition, the major commercial banks, including Bank of America and Citigroup, all have investment banking operations. 11

Insurance Companies Insurance companies are more important than banks for the long-term financing of business. They are massive investors in corporate stocks and bonds, and they often make long-term loans directly to corporations.

Suppose a company needs a loan of $2.5 million for 9 years, not 9 months. It could issue a bond directly to investors, or it could negotiate a 9-year loan with an insurance company:

10 The distinction between investment and commercial banks is not a legal one. Since 2008 both Goldman Sachs and Morgan Stanley have held banking licenses and are supervised by the Federal Reserve. However, they are not in the business of taking retail deposits or providing loans. 11 Bank of America owns Merrill Lynch, one of the largest investment banks. Merrill was rescued by Bank of America in 2009 after making huge losses from mortgage-related investments.

What are the key differences between a mutual fund and a bank or an insur- ance company?

Self-Test 2.3

Company Insurance company

(Institution) Issues debt

$2.5 million Investors

(Policyholders) Sells policies

$2.5 million

The money to make the loan comes mainly from the sale of insurance policies. Say you buy a fire insurance policy on your home. You pay cash to the insurance company and get a financial asset (the policy) in exchange. You receive no interest payments on this financial asset, but if a fire does strike, the company is obliged to cover the dam- ages up to the policy limit. This is the return on your investment. (Of course, a fire is a sad and dangerous event that you hope to avoid. But if a fire does occur, you are better off getting a payoff on your insurance policy than not having insurance at all.)

The company will issue not just one policy but thousands. Normally the incidence of fires “averages out,” leaving the company with a predictable obligation to its policy- holders as a group. Of course the insurance company must charge enough for its poli- cies to cover selling and administrative costs, pay policyholders’ claims, and generate a profit for its stockholders.

Total Financing of U.S. Corporations The pie chart in Figure 2.3 shows the investors in bonds and other debt securities. Notice the importance of institutional investors—mutual funds, pension funds, insur- ance companies, and banks. Households (individual investors) hold less than 20% of the debt pie. The other slices represent the rest of the world (investors from outside the United States) and various other categories.

The pie chart in Figure 2.4 shows holdings of the shares issued by U.S. corpora- tions. Here households make a stronger showing, with 39.5% of the total. Pension

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44 Part One Introduction

funds, insurance companies, and mutual funds add up to 47.2% of the total. Remem- ber, banks in the United States do not usually hold stock in other companies. The rest- of-the-world slice is 12.1%.

The aggregate amounts represented in these figures are enormous. There is $12.5 trillion of debt behind Figure 2.3 and $25.9 trillion of equity behind Figure 2.4 ($25,900,000,000,000). 12

Chapter 14 reviews corporate financing patterns in more detail.

2.3 Functions of Financial Markets and Intermediaries Financial markets and intermediaries provide financing for business. They channel savings to real investment. That much should be loud and clear from Sections 2.1 and 2.2 of this chapter. But there are other functions that may not be quite so obvious.

12 The total market value of shares issued by U.S. nonfinancial corporations is $16.2 trillion. “Nonfinancial” excludes financial institutions, such as banks and insurance companies.

FIGURE 2.3 Holdings of corporate and foreign bonds, December 31, 2012. The total amount is $12.5 trillion. Households

(19.2%)

Mutual funds, etc. (16.9%)

Pension funds (5.0%)

Rest of world (20.5%)

Banks & savings institutions

(6.0%)

Other (12.4%)

Insurance companies (20.1%)

Source: Board of Governors of the Federal Reserve System, Division of Research and Statistics, Flow of Funds Accounts, Table L.212 (www.federalreserve.gov).

FIGURE 2.4 Holdings of corporate equities, December 31, 2012. The total amount is $25.9 trillion. Pension funds

(16.3%)

Rest of world (12.1%)

Mutual funds, etc. (24.1%)

Insurance companies (6.8%)

Households (39.5%)

Other (1.1%)

Source: Board of Governors of the Federal Reserve System, Division of Research and Statistics, Flow of Funds Accounts, Table L.213 (www.federalreserve.gov).

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Chapter 2 Financial Markets and Institutions 45

Transporting Cash across Time Individuals need to transport expenditures in time. If you have money now that you wish to save for a rainy day, you can (for example) put the money in a savings account at a bank and withdraw it with interest later. If you don’t have money today, say to buy a car, you can borrow money from the bank and pay off the loan later. Modern finance provides a kind of time machine. Lenders transport money forward in time; borrow- ers transport it back. Both are happier than if they were forced to spend income as it arrives. Of course, individuals are not alone in needing to raise cash from time to time. Firms with good investment opportunities, but a shortage of internally generated cash, raise cash by borrowing or selling new shares. Many governments run deficits and finance current outlays by issuing debt.

Young people saving for retirement may transport their current earnings 30 or 40 years into the future by means of a pension fund. They can even transport income to their heirs by purchase of a life insurance policy.

In principle, individuals or firms with cash surpluses could take out newspaper advertisements or surf the web looking for counterparties with cash shortages. But it is usually cheaper and more convenient to use financial markets and intermediaries. It is not just a matter of avoiding the cost of searching for the right counterparty. Follow-up is needed. For example, banks don’t just lend money and walk away. They monitor the borrower to make sure that the loan is used for its intended purpose and that the bor- rower’s credit stays solid.

Risk Transfer and Diversification Financial markets and intermediaries allow investors and businesses to reduce and reallocate risk. Insurance companies are an obvious example. When you buy homeowner’s insurance, you greatly reduce the risk of loss from fire, theft, or acci- dents. But your policy is not a very risky bet for the insurance company. It diversi- fies by issuing thousands of policies, and it expects losses to average out over the policies. 13 The insurance company allows you to pool risk with thousands of other homeowners.

Investors should diversify too. For example, you can buy shares in a mutual fund that holds hundreds of stocks. In fact, you can buy index funds that invest in all the stocks in the popular market indexes. For example, the Vanguard 500 Index Fund holds the stocks in the Standard & Poor’s Composite stock market index. (The “S&P 500” tracks the performance of the largest U.S. stocks. It is the index most used by profes- sional investors.) If you buy this fund, you are insulated from the company-specific risks of the 500 companies in the index. These risks are averaged out by diversifica- tion. Of course you are still left with the risk that the level of the stock market as a whole will fall. In fact, we will see in Chapter 11 that investors are mostly concerned with market risk, not the specific risks of individual companies.

Index mutual funds are one way to invest in widely diversified portfolios at low cost. Another route is provided by exchange-traded funds (ETFs), which are portfolios of stocks that can be bought or sold in a single trade. For example, Standard & Poor’s Depositary Receipts (SPDRs, or “spiders”), invest in portfolios that match Standard & Poor’s stock market indexes. The total amount invested in the spider that tracks the benchmark S&P 500 index was $161 billion in early 2014.

ETFs are in some ways more efficient than mutual funds. To buy or sell an ETF, you simply make a trade, just as if you bought or sold shares of stock. 14 To invest in

13 Unfortunately for insurance companies, the losses don’t always average out. Hurricanes and earthquakes can damage thousands of homes at once. The potential losses are so great that property insurance companies buy reinsurance against such catastrophes. 14 ETFs are in this respect like closed-end mutual funds (see footnote 3 above). But ETFs do not have managers with the discretion to try to “pick winners.” ETF portfolios are tied down to indexes or fixed baskets of securi- ties. ETF issuers make sure that the ETF price tracks the price of the underlying index or basket.

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How ETFs work

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46 Part One Introduction

an open-end mutual fund, you have to send money to the fund in exchange for newly issued shares. If you want to withdraw the investment, you have to notify the fund, which redeems your shares and sends you a check or credits your account with the fund. Also, many of the larger ETFs charge lower fees than mutual funds. State Street Global Advisors charges just .06% a year for managing the Standard & Poor’s 500 Index Spider. For a $100,000 investment, the fee is only .0006  ×  100,000  =  $60.

Financial markets provide other mechanisms for sharing risks. For example, a wheat farmer and a baking company are each exposed to fluctuations in the price of wheat after the harvest. The farmer worries about low prices, the baker about high prices. They can both rest easier if the baker can agree with the farmer to buy wheat in the future at a fixed price. Of course, it would be difficult, to say the least, if the baker and the farmer had to contact an Internet dating service to get together to make a deal. Fortunately no dating service is needed: Each can trade in commodity markets, the farmer as a seller and the baker as a buyer.

Liquidity Markets and intermediaries also provide liquidity, that is, the ability to turn an invest- ment back into cash when needed. Suppose you deposit $5,000 in a savings bank on February 1. During that month, the bank uses your deposit and other new deposits to make a 6-month construction loan to a real estate developer. On March 1, you realize that you need your $5,000 back. The bank can give it to you. Because the bank has thousands of depositors, and other sources of financing if necessary, it can make an illiquid loan to the developer financed by liquid deposits made by you and other cus- tomers. If you lend your money for 6 months directly to the real estate developer, you will have a hard time retrieving it 1 month later. 15

The shares of public companies are liquid because they are traded more or less continuously in the stock market. An Italian investor who puts $60,000 into Bank of America shares can recover that money on short notice. (A $60,000 sell order is a drop in the bucket compared with the normal trading volume of Bank of America shares.) Mutual funds can redeem their shares for cash on short notice because the funds invest in traded securities, which can be sold as necessary.

Of course, liquidity is a matter of degree. Foreign exchange markets for major cur- rencies are exceptionally liquid. Bank of America or Deutsche Bank could buy $200 million worth of yen or euros in the blink of an eye, with hardly any effect on foreign exchange rates. U.S. Treasury securities are also very liquid, and the shares of the largest companies on the major international stock exchanges are only slightly less so.

Liquidity is most important when you’re in a hurry. If you try to sell $500,000 worth of the shares of a small, thinly traded company all at once, you will probably knock down the price to some extent. If you’re patient and don’t surprise other inves- tors with a large, sudden sell order, you may be able to unload your shares on better terms. It’s the same problem that you may face in selling real estate. A house or condo- minium is not a liquid asset in a panic sale. If you’re determined to sell in an afternoon, you’re not going to get full value.

The Payment Mechanism Think how inconvenient life would be if you had to pay for every purchase in cash or if Boeing had to ship truckloads of hundred-dollar bills around the country to pay its suppliers. Checking accounts, credit cards, and electronic transfers allow individuals

liquidity The ability to sell an asset on short notice at close to the market price.

15 Of course, the bank can’t repay all depositors simultaneously. To do so, it would have to sell off its loans to the real estate developer and other borrowers. These loans are not liquid. This raises the specter of bank runs, where doubts about a bank’s ability to pay off its depositors cause a rush of withdrawals, with each depositor trying to get his or her money out first. Bank runs are rare, because bank deposits are backed up by the U.S. Federal Deposit Insurance Corporation, which insures bank accounts up to $250,000 per account.

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Chapter 2 Financial Markets and Institutions 47

and firms to send and receive payments quickly and safely over long distances. Banks are the obvious providers of payment services, but they are not alone. For example, if you buy shares in a money market mutual fund, your money is pooled with that of other investors and used to buy safe, short-term securities. You can then write checks on this mutual fund investment, just as if you had a bank deposit.

Information Provided by Financial Markets In well-functioning financial markets, you can see what securities and commodities are worth, and you can see—or at least estimate—the rates of return that investors can expect on their savings. The information provided by financial markets is often essential to a financial manager’s job. Here are three examples of how this information can be used.

Commodity Prices Catalytic converters are used in the exhaust systems of cars and light trucks to reduce pollution. The catalysts include platinum, which is traded on the New York Mercantile Exchange (NYMEX).

In March a manufacturer of catalytic converters is planning production for October. How much per ounce should the company budget for purchases of platinum in that month? Easy: The company’s CFO looks up the market price of platinum on the New York Mercantile Exchange—$1,607 per ounce for delivery in October (this was the closing price for platinum in March 2013, for delivery in October). The CFO can lock in that price if she wishes. The details of such a trade are covered in Chapter 24.

Interest Rates The CFO of Catalytic Concepts has to raise $400 million in new financing. She considers an issue of 30-year bonds. What will the interest rate on the bonds be? To find out, the CFO looks up interest rates on existing bonds traded in financial markets.

The results are shown in Table 2.2 . Notice how the interest rate climbs as credit quality deteriorates: The largest, safest companies, which are rated AAA (“triple-A”), can raise long-term debt at a 3.35% interest rate. The interest rates for AA, A, and BBB climb to 3.93%, 4.28%, and 5.08%, respectively. BBB companies are still regarded as investment grade, that is, good quality, but the next step down takes the investor into junk bond territory. The interest rate for BB debt climbs to 5.27%. Single-B companies are riskier still, so investors demand 6.35%.

There will be more on bond ratings and interest rates in Chapter 6. But you can see how a financial manager can use information from fixed-income markets to forecast the interest rate on new debt financing. For example, if Catalytic Concepts can qualify as a BBB-rated company, and interest rates are as shown in Table 2.2 , it should be able to raise new debt financing for approximately 5.08%.

Company Values How much was Callaway Golf worth in March 2013? How about Alaska Air Group, Estée Lauder, Yum! Brands, or GE? Table 2.3 shows the mar- ket capitalization of each company. We simply multiply the number of shares out- standing by the price per share in the stock market. Investors valued Callaway Golf at $467 million and GE at $247 billion.

TABLE 2.2 Interest rates on long-term corporate bonds, July 2013. The interest rate is lowest for top-quality (AAA) issuers. The rate rises as credit quality declines.

Credit Rating Interest Rate

AAA 3.35% AA 3.93 A 4.28 BBB 5.08 BB 5.27 B 6.35

Source: Thomson Reuters.

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48 Part One Introduction

Stock prices and company values summarize investors’ collective assessment of how well a company is doing, both its current performance and its future pros- pects. Thus an increase in stock price sends a positive signal from investors to managers. 16 That is why top management’s compensation is linked to stock prices. A manager who owns shares in his or her company will be motivated to increase the company’s market value. This reduces agency costs by aligning the interests of man- agers and stockholders.

This is one important advantage of going public. A private company can’t use its stock price as a measure of performance. It can still compensate managers with shares, but the shares will not be valued in a financial market.

Cost of Capital Financial managers look to financial markets to measure, or at least estimate, the cost of capital for the firm’s investment projects. The cost of capital is the minimum acceptable rate of return on the project. Investment projects offering rates of return higher than their cost of capital are worthwhile, because they add value; they make both the firm and its shareholders better off financially. Projects offering rates of return less than the cost of capital subtract value and should not be undertaken. 17

Thus the hurdle rate for investments inside the corporation is actually set outside the corporation. The expected rate of return on investments in financial markets deter- mines the opportunity cost of capital.

The opportunity cost of capital is generally not the interest rate that the firm pays on a loan from a bank or insurance company. If the company is making a risky invest- ment, the opportunity cost of capital is the expected rate of return that investors can achieve in financial markets at the same level of risk. The expected rate of return on risky securities is normally well above the interest rate on corporate borrowing.

We introduced the cost of capital in Chapter 1, but this brief reminder may help to fix the idea. We cover the cost of capital in detail in Chapters 11 and 12.

16 We can’t claim that investors’ assessments of value are always correct. Finance can be a risky and danger- ous business—dangerous for your wealth, that is. With hindsight we see horrible mistakes by investors, for example, the gross overvaluation of Internet and telecom companies in 2000. On average, however, it appears that financial markets collect and assess information quickly and accurately. We’ll discuss this issue again in Chapter 7.

cost of capital Minimum acceptable rate of return on capital investment.

17 Of course, the firm may invest for other reasons. For example, it may invest in pollution control equipment for a factory. The equipment may not generate a cash return but may still be worth investing in to meet legal and ethical obligations.

TABLE 2.3 Calculating the market capitalization of Callaway Golf and other companies in March 2013. (Shares and market values in millions. Ticker symbols in parentheses.)

Which of the functions described in this section require financial markets? Explain briefly.

Self-Test 2.4

Number of Shares × Stock Price = Market Capitalization

Callaway Golf (ELY) 71.00 ×  $6.58 = $467 Alaska Air Group (ALK) 70.34 ×  $57.50 = $4,045 Estée Lauder (EL) 386.65 ×  $65.70 = $25,402 Yum! Brands (YUM) 450.73 ×  $67.72 = $30,523 General Electric (GE) 10,398.00 ×  $23.77 = $247,167

Source: Yahoo! Finance, fi nance.yahoo.com.

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Chapter 2 Financial Markets and Institutions 49

2.4 The Crisis of 2007–2009 The financial crisis of 2007–2009 raised many questions, but it settled one question conclusively: Yes, financial markets and institutions are important. When financial markets and institutions ceased to operate properly, the world was pushed into a global recession.

The financial crisis had its roots in the easy-money policies that were pursued by the U.S. Federal Reserve and other central banks following the collapse of the Inter- net and telecom stock bubble in 2000. At the same time, large balance-of-payments surpluses in Asian economies were invested back into U.S. debt securities. This also helped to push down interest rates and contribute to lax credit.

Banks took advantage of this cheap money to expand the supply of subprime mort- gages to low-income borrowers. Many banks tempted would-be homeowners with low initial payments, offset by significantly higher payments later. 18 (Some home buyers were betting on escalating housing prices so that they could resell or refinance before the higher payments kicked in.) One lender is even said to have advertised what it dubbed its “NINJA” loan— NINJA standing for “No Income, No Job and No Assets.” Most subprime mortgages were then packaged together into mortgage-backed securi- ties that could be resold. But, instead of selling these securities to investors who could best bear the risk, many banks kept large quantities of the loans on their own books or sold them to other banks.

The widespread availability of mortgage finance fueled a dramatic increase in house prices, which doubled in the 5 years ending June 2006. At that point prices started to slide and homeowners began to default on their mortgages. A year later Bear Stearns, a large investment bank, announced huge losses on the mortgage investments that were held in two of its hedge funds. By the spring of 2008 Bear Stearns was on the verge of bankruptcy, and the U.S. Federal Reserve arranged for it to be acquired by JPMorgan Chase.

The crisis peaked in September 2008, when the U.S. government was obliged to take over the giant federal mortgage agencies Fannie Mae and Freddie Mac, both of which had invested several hundred billion dollars in subprime mortgage-backed secu- rities. Over the next few days the financial system started to melt down. Both Merrill Lynch and Lehman Brothers were in danger of failing. On September 14, the govern- ment arranged for Bank of America to take over Merrill in return for financial guaran- tees. However, it did nothing to rescue Lehman Brothers, which filed for bankruptcy protection the next day. Two days later the government reluctantly lent $85 billion to the giant insurance company AIG, which had insured huge volumes of mortgage- backed securities and other bonds against default. The following day, the Treasury unveiled its first proposal to spend $700 billion to purchase “toxic” mortgage-backed securities.

Uncertainty about which domino would be next to fall made banks reluctant to lend to one another, and the interest rate that they charged for such loans rose to 4.6% above the rate on U.S. Treasury debt. (Normally this spread above Treasuries is less than .5%.) This had an immediate knock-on effect on the supply of credit to industry, and the economy suffered one of its worst setbacks since the Great Depression. Unem- ployment rose rapidly, and business bankruptcies tripled.

Who was responsible for the financial crisis? In part, the U.S. Federal Reserve for its policy of easy money. The U.S. government also must take some of the blame for encouraging banks to expand credit for low-income housing. The rating agencies were at fault for providing triple-A ratings for many mortgage bonds that shortly afterward went into default. Last but not least, the bankers themselves were guilty of promoting

18 With a so-called option ARM loan the minimum mortgage payment was often not even sufficient to cover that month’s interest on the loan. The unpaid interest was then added to the amount of the mortgage, so the home- owner was burdened by an ever-increasing mortgage that one day would need to be paid off.

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House prices in the financial crisis

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Time line of the financial crisis

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50 Part One Introduction

and reselling the subprime mortgages. As we suggested in the previous chapter, man- agers were probably aware that a strategy of originating massive amounts of subprime debt was likely to end badly. Perhaps they were trying to squeeze in one more fat bonus before the game ended. That is why we described the mess as largely an agency problem—a failure to incentivize managers to act in shareholders’ interests. Since the crisis abated, politicians and regulators have been arguing about the causes and casting around for ways to stop a repeat.

Few developed economies escaped the crisis. As well as suffering from a collapse in their own housing markets, a number of foreign banks had made large investments in U.S. subprime mortgages and had to be rescued by their governments. Many Euro- pean governments were already heavily in debt and, as the cost of the bank bailouts mounted, investors began to worry about the ability of the governments to repay their debts. Thus in Europe the banking crisis became entwined with a sovereign debt crisis.

Investor concerns focused on Greece, which had amassed a massive €350 billion (or about $460 billion) of government debt. Greece’s position was complicated by its membership in the single-currency euro club. Much of the country’s borrowing was in euros; the government had no control over its currency and could not simply print more euros to service the debt. In May 2010 other eurozone governments and the International Monetary Fund (IMF) rushed to help, but investors were unconvinced that their assistance would be sufficient. By November 2011 the yield on Greek gov- ernment debt had climbed to nearly 27%. After extensive meetings involving other eurozone members and the IMF, Greece agreed to default on €100 billion of debt in return for a further bailout package. It was the largest sovereign default in history.

Throughout much of Europe, governments’ actions to reduce their mountains of debt led to deep recession and severe unemployment. The default by Greece did not put an end to investors’ jitters. As we write this in September 2013, investors are pre- pared to hold German government debt yielding just 1.9%, but they demand 10.2% from Greek debt, 7.1% from Portugual, and 6.0% from Cyprus. These yields reflect concerns that other indebted eurozone governments may be forced to default. Inves- tors joke gloomily that, instead of offering a risk-free return, eurozone government bonds just offer a return-free risk.

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The Dodd-Frank Act

SUMMARY The ultimate source of financing is individuals’ savings. The savings may flow through financial markets and intermediaries. The intermediaries include mutual funds, pension funds, and financial institutions, such as banks and insurance companies.

It’s simple: Corporations need access to financing in order to innovate and grow. A mod- ern financial system offers different types of financing, depending on a corporation’s age and the nature of its business. A high-tech start-up will seek venture capital financing, for example. A mature firm will rely more on bond markets.

In that case, the corporation is saving on behalf of its shareholders.

Mutual and pension funds allow investors to diversify in professionally managed port- folios. Pension funds offer an additional tax advantage, because the returns on pension investments are not taxed until withdrawn from the plan.

Where does the financing for corporations come from? (LO2-1)

Why do nonfinancial corporations need modern financial markets and institutions? (LO2-1)

What if a corporation finances investment by retaining and reinvesting cash generated from its operations? (LO2-1)

What are the key advantages of mutual funds and pension funds? (LO2-2)

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Chapter 2 Financial Markets and Institutions 51

Financial markets help channel savings to corporate investment, and they help match up borrowers and lenders. They provide liquidity and diversification opportunities for inves- tors. Trading in financial markets provides a wealth of useful information for the financial manager.

Financial institutions carry out a number of similar functions but in different ways. They channel savings to corporate investment, and they serve as intermediaries between bor- rowers and lenders. Banks also provide liquidity for depositors and, of course, play a spe- cial role in the economy’s payment systems. Insurance companies allow policyholders to pool risks.

The financial crisis of 2007–2009 provided a dramatic illustration. The huge expansion in subprime mortgage lending in the United States led to a collapse of the banking system. The government was forced into a costly bailout of banks and other financial institutions. As the credit markets seized up, the country suffered a deep recession. In much of Europe the financial crisis did not end in 2009. As governments struggled to reduce their debt mountains and to strengthen their banking systems, many countries suffered sharp falls in economic activity and severe unemployment.

What are the functions of financial markets? (LO2-3)

Do financial institutions have different functions? (LO2-3)

What happens when financial markets and institutions no longer function well? (LO2-3)

QUESTIONS AND PROBLEMS 1. Corporate Financing. How can a small, private firm finance its capital investments? Give two

or three examples of financing sources. (LO2-1)

2. Financial Markets. The stock and bond markets are not the only financial markets. Give two or three additional examples. (LO2-1)

3. Financial Markets and Institutions. True or false? (LO2-1)

a. Financing for public corporations must flow through financial markets. b. Financing for private corporations must flow through financial intermediaries. c. Almost all foreign exchange trading occurs on the floors of the FOREX exchanges in

New York and London. d. Derivative markets are a major source of finance for many corporations. e. The opportunity cost of capital is the capital outlay required to undertake a real investment

opportunity. f. The cost of capital is the interest rate paid on borrowing from a bank or other financial

institution.

4. Corporate Financing. Financial markets and intermediaries channel savings from investors to corporate investment. The savings make this journey by many different routes. Give a specific example for each of the following routes: (LO2-1)

a. Investor to financial intermediary, to financial markets, and to the corporation b. Investor to financial markets, to a financial intermediary, and to the corporation c. Investor to financial markets, to a financial intermediary, back to financial markets, and to

the corporation

5. Financial Intermediaries. You are a beginning investor with only $5,000 in savings. How can you achieve a widely diversified portfolio at reasonable cost? (LO2-2)

6. Financial Intermediaries. Is an insurance company also a financial intermediary? How does the insurance company channel savings to corporate investment? (LO2-2)

7. Corporate Financing. Choose the most appropriate term to complete each sentence. (LO2-2)

a. Households hold a greater percentage of (corporate equities / corporate bonds). b. (Pension funds / Banks) are major investors in corporate equities. c. (Investment banks / Commercial banks) raise money from depositors and make loans to

individuals and businesses.

finance

®

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52 Part One Introduction

8. Financial Markets. Which of the following are financial markets? (LO2-2)

a. NASDAQ b. Vanguard Explorer Fund c. JPMorgan Chase d. Chicago Mercantile Exchange

9. Financial Intermediaries. True or false? (LO2-2)

a. Exchange traded funds are hedge funds that can be bought and sold on the stock exchange. b. Hedge funds provide small investors with low-cost diversification. c. The sale of policies is a source of financing for insurance companies. d. In defined-contribution pension plans, the pension pot depends on the rate of return earned

on the contributions by the employer and employee.

10. Liquidity. Securities traded in active financial markets are liquid assets. Explain why liquidity is important to individual investors and to mutual funds. (LO2-2)

11. Liquidity. Bank deposits are liquid; you can withdraw money on demand. How can the bank provide this liquidity and at the same time make illiquid loans to businesses? (LO2-2)

12. Financial Institutions. Summarize the differences between a commercial bank and an invest- ment bank. (LO2-2)

13. Mutual Funds. Why are mutual funds called financial intermediaries? Why does it make sense for an individual to invest her savings in a mutual fund rather than directly in financial markets? (LO2-2)

14. Functions of Financial Markets. Fill in the blanks in the following passage by choosing the most appropriate term from the following list: CFO, save, financial intermediaries, stock mar- ket, savings, real investment, bonds, commodity markets, mutual funds, shares, liquid, ETFs, banks. Each term should be used once only. (LO2-3)

Financial markets and _____ channel _____ to _____. They also channel money from individu- als who want to _____ for the future to those who need cash to spend today. A third function of financial markets is to allow individuals and businesses to adjust their risk. For example, _____, such as the Vanguard Index fund, and _____, such as SPDRs or “spiders,” allow individuals to spread their risk across a large number of stocks. Financial markets provide other mechanisms for sharing risks. For example, a wheat farmer and a baker may use the _____ to reduce their exposure to wheat prices. Financial markets and intermediaries allow investors to turn an invest- ment into cash when needed. For example, the _____ of public companies are _____ because they are traded in huge volumes on the _____. _____ are the main providers of payment ser- vices by offering checking accounts and electronic transfers. Finally, financial markets provide information. For example, the _____ of a company that is contemplating an issue of debt can look at the yields on existing _____ to gauge how much interest the company will need to pay.

15. Financial Markets and Intermediaries. List the major functions of financial markets and intermediaries in a modern financial system. (LO2-3)

16. Functions of Financial Markets. On a mountain trek, you discover a 6-ounce gold nugget. A friend offers to pay you $2,500 for it. How do you check whether this is a fair price? (LO2-3)

17. Functions of Financial Markets. What kinds of useful information can a financial manager obtain from financial markets? Give examples. (LO2-3)

18. Functions of Financial Markets. Look back at Section 2.3 and then answer the following questions: (LO2-3)

a. The price of Estée Lauder stock has risen to $90. What is the market value of the firm’s equity?

b. The rating agency has revised Catalytic Concept’s bond rating to A. What interest rate, approximately, would the company now need to pay on its bonds?

c. A farmer and a meatpacker use the commodity markets to reduce their risk. One agrees to buy live cattle in the future at a fixed price, and the other agrees to sell. Which one sells?

19. The Financial Crisis. True or false? (LO2-4)

a. The financial crisis was largely caused by banks taking large positions in the options and futures markets.

b. The prime cause of the financial crisis was an expansion in bank lending for the overheated commercial real estate market.

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Chapter 2 Financial Markets and Institutions 53

c. Many subprime mortgages were packaged together by banks for resale. d. The crisis could have been much more serious if the government had not stepped in to rescue

Merrill Lynch and Lehman Brothers. e. The crisis in the eurozone finally ended when other eurozone countries and the IMF pro-

vided a massive bailout package to stop Greece from defaulting on its debts.

20. The Financial Crisis. What were the causes of the financial crisis? We mentioned several. Can you suggest others that we have not identified? (LO2-4)

WEB EXERCISES 1. Log on to finance.yahoo.com and use the website to update Table 2.3. How have market values

of these companies changed?

2. Find the websites for the Vanguard Group, Fidelity Investments, and Putnam Investments. Pick three or four funds from these sites and compare their investment objectives, risks, past returns, fund fees, and so on. Read the prospectuses for each fund. Who do you think should, or should not, invest in each fund?

3. Morningstar provides data on mutual fund performance. Log on to its website. Which category of funds has performed unusually well or badly?

SOLUTIONS TO SELF-TEST QUESTIONS 2.1 a. Corporations sell securities in the primary market. The securities are later traded in the

secondary market. b. The capital market is for long-term financing; the money market, for short-term financing. c. The market for stocks versus the market for bonds and other debt securities.

2.2 Efficient diversification and professional management. Pension funds offer an additional advantage, because investment returns are not taxed until withdrawn from the fund.

2.3 Mutual funds pool investor savings and invest in portfolios of traded securities. Financial institutions such as banks or insurance companies raise money in special ways, for example, by accepting deposits or selling insurance policies. They not only invest in securities but also lend directly to businesses. They provide various other financial services.

2.4 Liquidity, risk reduction by investment in diversified portfolios of securities (through a mutual fund, for example), information provided by trading.

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54

Accounting and Finance

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

3-1 Interpret the information contained in the balance sheet, income statement, and  statement of cash flows.

3-2 Distinguish between market and book values.

3-3 Explain why income differs from cash flow.

3-4 Understand the essential features of the taxation of corporate and personal income.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

3 CHAPTE R

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55

P A

R T

O N

E

I n Chapter 1 we pointed out that a large corpo-ration is a team effort. All the players—the share-holders, lenders, directors, management, and employees—have a stake in the company’s success,

and all therefore need to monitor its progress. For

this reason the company prepares regular financial

accounts and arranges for an independent firm of

auditors to certify that these accounts present a “true

and fair view.”

Until the mid-nineteenth century most businesses

were owner-managed and seldom required out-

side capital beyond personal loans to the proprietor.

There was little need, therefore, for firms to produce

comprehensive accounting information. But with the

industrial revolution and the creation of large railroad

and canal companies, the shareholders and bank-

ers demanded information that would help them

gauge a firm’s financial strength. That was when the

accounting profession began to come of age.

We don’t want to get lost in the details of account-

ing practice. But because we will refer to financial state-

ments throughout this book, it may be useful to review

briefly their main features. In this chapter we introduce

the major financial statements: the balance sheet, the

income statement, and the statement of cash flows.

We discuss the important differences between income

and cash flow and between book values and market

values. We also discuss the federal tax system.

This chapter is our first look at financial statements

and is meant primarily to serve as a brief review of

your accounting class. It will be far from our last look.

For example, we will see in the next chapter how man-

agers use financial statements to analyze a firm’s per-

formance and assess its financial strength.

In tr

o d

u c

tio n

Accounting is not the same as finance, but the two are related.

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56 Part One Introduction

3.1 The Balance Sheet Public companies are obliged to file their financial statements with the SEC each quar- ter. These quarterly reports (or 10Qs) provide the investor with information about the company’s earnings during the quarter and its assets and liabilities at the end of the quarter. In addition, companies need to file annual financial statements (or 10Ks) that provide rather more detailed information about the outcome for the entire year.

The financial statements show the firm’s balance sheet, the income statement, and a statement of cash flows. We will review each in turn. 1

Firms need to raise cash to pay for the many assets used in their businesses. In the process of raising that cash, they also acquire obligations or “liabilities” to those who provide the funding. The balance sheet presents a snapshot of the firm’s assets and liabilities at one particular moment. The assets—representing the uses of the funds raised—are listed on the left-hand side of the balance sheet. The liabilities— representing the sources of that funding—are listed on the right.

Some assets can be turned more easily into cash than others; these are known as liquid assets. The accountant puts the most liquid assets at the top of the list and works down to the least liquid. Look, for example, at Table 3.1 , which shows the consolidated balance sheet for Home Depot (HD), at the end of its 2012 fiscal year. 2 (“Consolidated” simply means that the balance sheet shows the position of Home Depot and any companies it owns.) You can see that Home Depot had $2,494 million of cash and marketable securi- ties. In addition, it had sold goods worth $1,395 million but had not yet received payment. These payments are due soon, and therefore the balance sheet shows the unpaid bills or accounts receivable (or simply receivables ) as a current asset. The next asset consists of inventories. These may be (1) raw materials and ingredients that the firm bought from suppliers, (2) work in process, and (3) finished products waiting to be shipped from the warehouse. For Home Depot, inventories consist largely of goods in the warehouse or on the store shelves; for manufacturing companies, inventories would be more skewed toward raw materials and work in progress. Of course, there are always some items that don’t fit into neat categories. So there is a fourth entry, other current assets.

Up to this point all the assets in Home Depot’s balance sheet are likely to be used or turned into cash in the near future. They are therefore described as current assets. The next assets listed in the balance sheet are longer-lived or fixed assets and include items such as buildings, equipment, and vehicles.

The balance sheet shows that the gross value of Home Depot’s property, plant, and equipment is $38,491 million. This is what the assets originally cost. But they are unlikely to be worth that now. For example, suppose the company bought a delivery van 2 years ago; that van may be worth far less now than Home Depot paid for it. It might in principle be possible for the accountant to estimate separately the value today of the van, but this would be costly and somewhat subjective. Accountants rely instead on rules of thumb to estimate the depreciation in the value of assets, and with rare exceptions they stick to these rules. For example, in the case of that delivery van the accountant may deduct a third of the original cost each year to reflect its declining value. So if Home Depot bought the van 2 years ago for $15,000, the balance sheet would show that accumulated depreciation is 2  ×  $5,000  =  $10,000. Net of deprecia- tion the value is only $5,000. Table 3.1 shows that Home Depot’s total accumulated depreciation on fixed assets is $14,422 million. So while the assets cost $38,491 mil- lion, their net value in the accounts is only $38,491  −  $14,422  =  $24,069 million.

1 In addition, the company provides a statement of the shareholders’ equity, which shows how much of the firm’s earnings has been retained in the business rather than paid out as dividends and how much money has been raised by issuing new shares or spent by repurchasing stock. We will not review in detail the statement of shareholders’ equity.

balance sheet Financial statement that shows the firm's assets and liabilities at a particular time.

2 Home Depot’s fiscal 2012 ended February 3, 2013. The balance sheet in Table 3.1 therefore shows the firm’s assets and liabilities on this date. We have simplified and eliminated some of the detail in the company’s pub- lished financial statements.

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Chapter 3 Accounting and Finance 57

In addition to its tangible assets, Home Depot also has valuable intangible assets, such as its brand name, skilled management, and a well-trained labor force. Accoun- tants are generally reluctant to record these intangible assets in the balance sheet unless they can be readily identified and valued.

There is, however, one important exception. When Home Depot has acquired other businesses in the past, it has paid more for their assets than the value shown in the firms’ accounts. This difference is shown in Home Depot’s balance sheet as “good- will.” Most of the intangible assets on Home Depot’s balance sheet consist of goodwill.

Now look at the right-hand portion of Home Depot’s balance sheet, which shows where the money to buy its assets came from. The accountant starts by looking at the company’s liabilities—that is, the money owed by the company. First come those liabili- ties that are likely to be paid off most rapidly. For example, Home Depot has borrowed $1,321 million, due to be repaid shortly. It also owes its suppliers $8,871 million for goods that have been delivered but not yet paid for. These unpaid bills are shown as accounts payable (or payables ). Both the borrowings and the payables are debts that Home Depot must repay within the year. They are therefore classified as current liabilities.

Home Depot’s current assets total $15,372 million; its current liabilities amount to $11,462 million. Therefore the difference between the value of Home Depot’s current assets and its current liabilities is $15,372  −  $11,462  =  $3,910 million. This figure is known as Home Depot’s net current assets or net working capital. It roughly measures the company’s potential reservoir of cash.

Below the current liabilities Home Depot’s accountants have listed the firm’s long- term liabilities, such as debts that come due after the end of a year. You can see that banks and other investors have made long-term loans to Home Depot of $9,475 million.

Home Depot’s liabilities are financial obligations to various parties. For example, when Home Depot buys goods from its suppliers, it has a liability to pay for them; when it borrows from the bank, it has a liability to repay the loan. Thus the suppliers and the bank have first claim on the firm’s assets. What is left over after the liabilities have been paid off belongs to the shareholders. This figure is known as the

End of Fiscal End of Fiscal

Assets 2012 2011 Liabilities and Shareholders’ Equity 2012 2011

Current assets Current liabilities Cash and marketable securities 2,494 1,987 Debt due for repayment 1,321 30 Receivables 1,395 1,252 Accounts payable 8,871 8,173 Inventories 10,710 10,360 Other current liabilities 1,270 1,183 Other current assets 773 866 Total current liabilities 11,462 9,386 Total current assets 15,372 14,465

Fixed assets Long-term debt 9,475 10,798 Tangible fi xed assets Deferred income taxes 319 212 Property, plant, and equipment 38,491 37,059 Other long-term liabilities 2,051 2,161 Less accumulated depreciation 14,422 12,738 Net tangible fi xed assets 24,069 24,321 Total liabilities 23,307 22,557

Intangible asset (goodwill) 1,170 1,267 Shareholders’ equity Long-term investments 140 138 Common stock and other paid-in capital 8,433 7,649 Other assets 333 551 Retained earnings 20,038 17,246 Treasury stock -10,694 -6,710 Total assets 41,084 40,742 Total shareholders’ equity 17,777 18,185

Total liabilities and shareholders’ equity 41,084 40,742

TABLE 3.1 Home Depot’s balance sheet (figures in $ millions)

Note: Column sums subject to rounding error Source: Derived from Home Depot annual reports

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Suppose that Home Depot borrows $500 million by issuing new long-term bonds. It places $100 million of the proceeds in the bank and uses $400 mil- lion to buy new machinery. What items of the balance sheet would change? Would shareholders’ equity change?

Self-Test3.1

58 Part One Introduction

shareholders’ equity. For Home Depot the total value of shareholders’ equity amounts to $17,777 million. Table 3.1 shows that Home Depot’s equity is made up of three parts. One portion, $8,433 million, has resulted from the occasional sale of new shares to investors. A much larger amount, $20,038 million, has come from earnings that Home Depot has retained and reinvested in the business on the shareholders’ behalf. 3 Finally, treasury stock is a large negative number, − $10,694 million. This represents the amount that Home Depot has spent on buying back its shares. The money to repur- chase them has gone out of the firm and reduced shareholders’ equity.

Figure 3.1 shows how the separate items in the balance sheet link together. There are two classes of assets—current assets, which will soon be used or turned into cash, and long-term or “fixed” assets, which may be either tangible or intangible. There are also two classes of liability—current liabilities, which are due for payment shortly, and long-term liabilities.

The difference between the assets and the liabilities represents the amount of the shareholders’ equity. This is the basic balance sheet identity. Shareholders are some- times called “residual claimants” on the firm. We mean by this that shareholders’ equity is what is left over when the liabilities of the firm are subtracted from its assets:

Shareholders’ equity = net assets = total assets - total liabilities (3.1)

3 Here is an occasional source of confusion. You may be tempted to think of retained earnings as a pile of cash that the company has built up from its past operations. But there is absolutely no link between retained earn- ings and cash balances. The earnings that Home Depot has kept in the business may have been used to buy new equipment, trucks, warehouses, and so on. Typically only a small proportion will be kept in the bank. Notice that Home Depot’s balance sheet lists $20,038 in retained earnings but only $2,494 in cash and marketable securities.

When comparing financial statements, analysts often calculate a common- s ize balance sheet, which reexpresses all items as a percentage of total assets. Table 3.2 is Home Depot’s common-size balance sheet. The financial manager might look at this common-size balance sheet and notice right away that in 2012 cash and market- able securities accounted for a higher proportion of the firm’s assets than they did in the previous year. There may be good reasons for this, but the manager might wish to check that control of working capital has not become lax.

By the way, it is easy to obtain the financial statements of almost any publicly traded firm. Most firms make their annual reports available on the web. You also can find key financial statements of most firms at Yahoo! Finance ( finance.yahoo.com ) or Google Finance ( finance.google.com ).

Book Values and Market Values Throughout this book we will frequently make a distinction between the book values of the assets shown in the balance sheet and their market values.

Items in the balance sheet are valued according to generally accepted accounting principles, commonly called GAAP. These state that assets must be shown in the bal- ance sheet at their historical cost adjusted for depreciation. Book values are therefore “backward-looking” measures of value. They are based on the past cost of the asset, not its current market price or value to the firm. For example, suppose that 2 years ago

common-size balance sheet All items in the balance sheet are expressed as a percentage of total assets.

generally accepted accounting principles (GAAP) Procedures for preparing financial statements.

book value Value of assets or liabilities according to the balance sheet.

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Chapter 3 Accounting and Finance 59

FIGURE 3.1 Assets and liabilities on the balance sheet

Current assets • Cash & securities • Receivables • Inventories + Fixed assets • Tangible assets • Intangible assets

=

THE MAIN BALANCE SHEET ITEMS

Current liabilities • Payables • Short-term debt + Long-term liabilities + Shareholders’ equity

Home Depot built an office building for $30 million and that in today’s market the build- ing would sell for $40 million. The book value of the building would be less than its market value, and the balance sheet would understate the value of Home Depot’s asset.

Or consider a specialized plant that Intel develops for producing special-purpose computer chips at a cost of $800 million. The book value of the plant is $800 million less depreciation. But suppose that shortly after the plant is constructed, a new chip makes the existing one obsolete. The market value of Intel’s new plant could fall by 50% or more. In this case market value would be less than book value.

The difference between book value and market value is greater for some assets than for others. It is zero in the case of cash but potentially very large for fixed assets where the accountant starts with initial cost and then depreciates that figure according to a prespecified schedule. The purpose of depreciation is to allocate the original cost of the asset over its life, and the rules governing the depreciation of asset values do not reflect actual loss of market value. The market value of fixed assets usually is much higher than the book value, but sometimes it is less.

End of Fiscal End of Fiscal

Assets 2012 2011 Liabilities and Shareholders’ Equity 2012 2011

Current assets Current liabilities Cash and marketable securities 6.1% 4.9% Debt due for repayment 3.2% 0.1% Receivables 3.4 3.1 Accounts payable 21.6 20.1 Inventories 26.1 25.4 Other current liabilities 3.1 2.9 Other current assets 1.9 2.1 Total current liabilities 27.9 23.0 Total current assets 37.4 35.5 Fixed assets Long-term debt 23.1 26.5 Tangible fi xed assets Deferred income taxes 0.8 0.5 Property, plant, and equipment 93.7 91.0 Other long-term liabilities 5.0 5.3 Less accumulated depreciation 35.1 31.3 Net tangible fi xed assets 58.6 59.7 Total liabilities 56.7 55.4

Intangible asset (goodwill) 2.8 3.1 Shareholders’ equity: Long-term investments 0.3 0.3 Common stock and other paid-in capital 20.5 18.8 Other assets 0.8 1.4 Retained earnings 48.8 42.3 Treasury stock -26.0 -16.5 Total assets 100.0% 100.0% Total shareholders’ equity 43.3 44.6

Total liabilities and shareholders’ equity 100.0% 100.0%

TABLE 3.2 Common-size balance sheet of Home Depot (all items expressed as a percentage of total assets)

Note: Column sums subject to rounding error

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60 Part One Introduction

The same goes for the right-hand side of the balance sheet. In the case of liabili- ties the accountant simply records the amount of money that you have promised to pay. For short-term liabilities this figure is generally close to the market value of that promise. For example, if you owe the bank $1 million tomorrow, the accounts show a book liability of $1 million. As long as you are not bankrupt, that $1 million is also roughly the value to the bank of your promise. But now suppose that $1 million is not due to be repaid for several years. The accounts still show a liability of $1 million, but how much your debt is worth depends on what happens to interest rates. If interest rates rise after you have issued the debt, lenders may not be prepared to pay as much as $1 million for your debt; if interest rates fall, they may be prepared to pay more than $1 million. 4 Thus the market value of a long-term liability may be higher or lower than the book value. Market values of assets and liabilities do not generally equal their book values. Book values are based on historical or original values. Market values measure current values of assets and liabilities.

The difference between book value and market value is likely to be greatest for shareholders’ equity. The book value of equity measures the cash that shareholders have contributed in the past plus the cash that the company has retained and reinvested in the business on their behalf. But this often bears little resemblance to the total mar- ket value that investors place on the shares.

If the market price of the firm’s shares falls through the floor, don’t try telling the shareholders that the book value is satisfactory—they won’t want to hear. Sharehold- ers are concerned with the market value of their shares; market value, not book value, is the price at which they can sell their shares. Managers who wish to keep their share- holders happy will focus on market values.

We will often find it useful to think about the firm in terms of a market-value bal- ance sheet. Like a conventional balance sheet, a market-value balance sheet lists the firm’s assets, but it records each asset at its current market value rather than at histori- cal cost less depreciation. Similarly, each liability is shown at its market value. The difference between the market values of assets and liabilities is the market value of the shareholders’ equity claim. The stock price is simply the market value of shareholders’ equity divided by the number of outstanding shares.

4 We will show you how changing interest rates affect the market value of debt in Chapter 6.

Example 3.1 Market- versus Book-Value Balance Sheets Jupiter has developed a revolutionary auto production process that enables it to produce cars 20% more efficiently than any rival. It has invested $10 billion in pro- ducing its new plant. To finance the investment, Jupiter borrowed $4 billion and raised the remaining funds by selling new shares of stock in the firm. There are currently 100 million shares of stock outstanding. Investors are very excited about Jupiter’s prospects. They believe that the flow of profits from the new plant justifies a stock price of $75.

If these are Jupiter’s only assets, the book-value balance sheet immediately after it has made the investment is as follows:

BOOK-VALUE BALANCE SHEET FOR JUPITER MOTORS (Figures in $ billions)

Assets Liabilities and Shareholders’ Equity

Auto plant 10 Debt 4 Shareholders’ equity 6

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Chapter 3 Accounting and Finance 61

Is it surprising that market value generally exceeds book value? It shouldn’t be. Firms find it attractive to raise money to invest in various projects because they believe the projects will be worth more than they cost. Otherwise, why bother? You will usually find that shares of stock sell for more than the value shown in the company’s books.

3.2 The Income Statement If Home Depot’s balance sheet resembles a snapshot of the firm at a particular time, its income statement is like a video. It shows how profitable the firm has been during the past year.

Look at the summary income statement in Table 3.3 . You can see that during fiscal 2012 Home Depot sold goods worth $74,754 million and that the total expenses of acquiring and selling those goods were $48,912  +  $16,305  =  $65,217 million. The largest expense item, amounting to $48,912 million, consisted of the cost of goods sold, which included the acquisition cost of its products, the wages of its employees, and

income statement Financial statement that shows the revenues, expenses, and net income of a firm over a period of time.

a. What would be Jupiter’s price per share if the auto plant had a market value of $14 billion?

b. How would you reassess the value of the auto plant if the value of out- standing stock were $8 billion?

Self-Test 3.2

Investors are placing a market value on Jupiter’s equity of $7.5 billion ($75 per share times 100 million shares). We assume that the debt outstanding is worth $4  billion.5 Therefore, if you owned all Jupiter’s shares and all its debt, the value of your investment would be $7.5 + $4 = $11.5 billion. In this case you would own the company lock, stock, and barrel and would be entitled to all its cash flows. Because you can buy the entire company for $11.5 billion, the total value of Jupiter’s assets must also be $11.5 billion. In other words, the market value of the assets must be equal to the market value of the liabilities plus the market value of the share - holders’ equity.

We can now draw up the market-value balance sheet as follows:

MARKET-VALUE BALANCE SHEET FOR JUPITER MOTORS (Figures in $ billions)

Assets Liabilities and Shareholders’ Equity

Auto plant 11.5 Debt 4 Shareholders’ equity 7.5

Notice that the market value of Jupiter’s plant is $1.5 billion more than the plant cost to build. The difference is due to the superior profits that investors expect the plant to earn. Thus, in contrast to the balance sheet shown in the company’s books, the market-value balance sheet is forward-looking. It depends on the profits that investors expect the assets to provide.

5 Jupiter has borrowed $4 billion to finance its investment, but if the interest rate has changed in the meantime, the debt could be worth more or less than $4 billion.

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62 Part One Introduction

other expenses incurred to obtain and sell its wares. Almost all the remaining expenses were administrative expenses such as head office costs, advertising, and distribution.

In addition to these out-of-pocket expenses, Home Depot also made a deduction for the value of the plant and equipment used up in producing the goods. In 2012 this charge for depreciation was $1,684 million. Thus Home Depot’s earnings before inter- est and taxes (EBIT) were

EBIT = total revenues - costs - depreciation = 74,754 - (48,912 + 16,305) - 1,684 = $7,853 million

The remainder of the income statement shows where these earnings went. As we saw earlier, Home Depot has partly financed its investment in plant and equipment by borrowing. In 2012 it paid $632 million of interest on this borrowing. A further slice of the profit went to the government in the form of taxes. This amounted to $2,686 million. The $4,535 million that was left over after paying interest and taxes belonged to the shareholders. Of this sum Home Depot paid out $1,743 million in dividends and reinvested the remaining $2,792 million in the business. Presumably, these reinvested funds made the company more valuable.

The $2,792 of earnings that Home Depot retained and reinvested in the firm show up on its balance sheet as an increase in retained earnings. Notice that retained earnings in Table 3.1 increased by $2,792 million in 2012, from $17,246 million to $20,038 million. However, shareholders’ equity fell during the year because Home Depot repurchased some of its stock.

Just as it is sometimes useful to prepare a common-size balance sheet, we can also prepare a common-size income statement. In this case, all items are expressed as a percentage of revenues. The last column of Table 3.3 is Home Depot’s common-size income statement. You can see, for example, that the cost of goods sold consumes 65.4% of revenues and that selling, general, and administrative expenses absorb a fur- ther 21.9%.

Income versus Cash Flow It is important to distinguish between Home Depot’s income and the cash that the company generates. Here are two reasons why income and cash are not the same:

1. Depreciation. When Home Depot’s accountants prepare the income statement, they do not simply count the cash coming in and the cash going out. Instead, the accountant starts with the cash payments but then divides these payments into two

common-size income statement All items on the income statement are expressed as a percentage of revenues.

$ Million % of Sales

Net sales 74,754 100.0 Cost of goods sold 48,912 65.4 Selling, general, & administrative expenses 16,305 21.9 Depreciation 1,684 2.3 Earnings before interest and income taxes (EBIT) 7,853 10.5 Interest expense 632 0.8 Taxable income 7,221 9.7 Taxes 2,686 3.6 Net income 4,535 6.1 Allocation of net income Dividends 1,743 2.3 Addition to retained earnings 2,792 3.7

TABLE 3.3 Home Depot’s income statement

Source: Derived from Home Depot annual reports.

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Chapter 3 Accounting and Finance 63

groups—current expenditures (such as wages) and capital expenditures (such as the purchase of new machinery). Current expenditures are deducted from current profits. However, rather than deducting the cost of machinery in the year it is purchased, the accountant makes an annual charge for depreciation. So the cost of machinery is spread over its forecast life.

Thus, when calculating profits, the accountant does not deduct the expenditure on new equipment that year, even though cash is paid out. However, the accountant does deduct depreciation on assets previously purchased, even though no cash is currently paid out. For example, suppose a $100,000 investment is depreciated by $10,000 a year. 6 This depreciation is treated as an annual expense, although the cash actually went out of the door when the asset was first purchased. For this reason, the deduction for depreciation is classified as a noncash expense.

To calculate the cash produced by the business, it is necessary to add the depreciation charge (which is not a cash payment) back to accounting profits and to subtract the expenditure on new capital equipment (which is a cash payment).

2. Cash versus accrual accounting. Consider a manufacturer that spends $60 to produce goods in period 1. In period 2 it sells these goods for $100, but its customers do not pay their bills until period 3. The following diagram shows the firm’s cash flows. In period 1 there is a cash outflow of $60. Then, when customers pay their bills in period 3, there is an inflow of $100.

It would be misleading to say that the firm was running at a loss in period 1 (when cash flow was negative) or that it was extremely profitable in period 3 (when cash flow was positive). Therefore, to construct the income statement, the accountant looks at when the sale was made (period 2 in our example) and gathers together all the revenues and expenses associated with that sale. For our company the income statement would show:

6 We discuss depreciation rules in Chapter 9.

+$100 (collect payment)

-$60 (pay for goods)

1 2 3 Period

Revenue $100 Less cost of goods sold 60 Profi t $ 40

This practice of matching revenues and expenses is known as accrual accounting. Of course, the accountant cannot ignore the actual timing of the cash expenditures

and payments. So the cash outlay in the first period will be treated not as an expense but as an investment in inventories. Subsequently, in period 2, when the goods are taken out of inventory and sold, the accountant shows a reduction in inventories.

To go from the cost of goods sold in the income statement to the cash outflows, we need to subtract the investment in inventories that is shown in the balance sheet:

Period: 1 2

Cost of goods sold (income statement) 0 60 + Investment in inventories (balance sheet) 60 -60 = Cash paid out 60 0

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64 Part One Introduction

The accountant also does not ignore the fact that the firm has to wait until period  3 to collect its bills. When the sale is made in period 2, the figure for accounts receivable in the balance sheet is increased to show that the company’s customers owe an extra $100 in unpaid bills. Later, when the customers pay those bills in period 3, accounts receivable are reduced by $100. Therefore, to go from the sales shown in the income statement to the cash inflows, we need to subtract the investment in receivables:

Period: 2 3

Sales (income statement) 100 0 − Investment in receivables (balance sheet) 100 -100 = Cash received 0 +100

We will return to these issues in more detail in Chapter 9, but for now we summarize the key points as follows: Cash outflow is equal to the cost of goods sold, which is shown in the income statement, plus the change in inventories. The cash that the company receives is equal to the sales shown in the income statement less the change in uncollected bills.

Example 3.2 Profits versus Cash Flows Suppose our manufacturer spends a further $80 to produce goods in period 2. It sells these goods in period 3 for $120, but customers do not pay their bills until period 4.

The cash flows from these transactions are now as follows:

How do the new transactions affect the income statement and the balance sheet? The income statement will match costs with revenues and record the cost of goods sold when the sales are made in periods 1 and 2. The difference between the costs shown in the income statement and the cash flows is recorded as an investment (and later, disinvestment) in inventories. Thus, in period 1 the accoun- tant shows an investment in inventories of $60 just as before. In period 2 these goods are taken out of inventory and sold, but the firm also produces a further $80 of goods. Thus there is a net increase in inventories of $20. As these goods in turn are sold in period 3, inventories are reduced by $80. The following table con- firms that the cash outflow in each period is equal to the cost of goods sold that is shown in the income statement plus the change in inventories.

Period: 1 2 3

Cost of goods sold (income statement) 0 60 80 + Investment in inventories (balance sheet) 60 −60 + 80 = 20 −80 = Cash paid out 60 80 0

$100 (collect payment)

$120 (collect further payment)

-$60 (pay for goods) -$80

(pay for more goods)

1 2 3 4 Period

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Chapter 3 Accounting and Finance 65

3.3 The Statement of Cash Flows The firm requires cash when it buys new plant and machinery or when it pays interest to the bank and dividends to the shareholders. Therefore, the financial manager needs to keep track of the cash that is coming in and going out.

We have seen that the firm’s cash flow can be quite different from its net income. These differences can arise for at least two reasons:

1. The income statement does not recognize capital expenditures as expenses in the year that the capital goods are paid for. Instead, it spreads those expenses over time in the form of an annual deduction for depreciation.

2. The income statement uses the accrual method of accounting, which means that revenues and expenses are recognized when sales are made, rather than when the cash is received or paid out.

The statement of cash flows shows the firm’s cash inflows and outflows from oper- ations as well as from its investments and financing activities. Table 3.4 is the cash-flow statement for Home Depot. It contains three sections. The first shows the cash flow from operations. This is the cash generated from Home Depot’s normal business activi- ties. Next comes the cash that Home Depot has invested in plant and equipment or in the acquisition of new businesses. The final section reports cash flows from financing activities such as the sale of new debt or stock. We will look at these sections in turn.

The first section, cash flow from operations, starts with net income but adjusts that figure for those parts of the income statement that do not involve cash coming in or going out. Therefore, it adds back the allowance for depreciation because depreciation is not a cash outflow, even though it is treated as an expense in the income statement.

Any additions to current assets (other than cash itself) need to be subtracted from net income, since these absorb cash but do not show up in the income state- ment. Conversely, any additions to current liabilities need to be added to net income because these release cash. For example, you can see that the increase of $143 million

statement of cash flows Financial statement that shows the firm’s cash receipts and cash pay- ments over a period of time.

Consider a firm that spends $200 to produce goods in period 1. In period 2 it sells half of those goods for $150, but it doesn't collect payment until one period later. In period 3 it sells the other half of the goods for $150, and it col- lects payment on these sales in period 4. Calculate the profits and the cash flows for this firm in periods 1 to 4.

Self-Test3.3

The following table provides a similar reconciliation of the difference between the revenues shown in the income statement and the cash inflow:

Period: 2 3 4

Sales (income statement) 100 120 0 − Investment in receivables (balance sheet) 100 −100 + 120 = 20 −120 = Cash received 0 +100 +120

In the income statement the accountant records sales of $100 in period 1 and $120 in period 2. The fact that the firm has to wait for payment is recognized in the balance sheet as an investment in receivables. The cash that the company receives is equal to the sales shown in the income statement less the investment in receivables.

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66 Part One Introduction

in accounts receivable is deducted from income. In addition, Home Depot increased inventories by $350 million. This increase in inventory levels also absorbed cash and must be deducted from net income when calculating cash flows. On the other hand, Home Depot does not pay all its bills immediately. These delayed payments show up as payables. In 2012 Home Depot had much larger bills outstanding: Accounts pay- able increased by $698 million. Delaying these payments resulted in extra cash.

We have pointed out that depreciation is not a cash payment; it is simply the accountant’s allocation to the current year of the original cost of the capital equipment. However, cash does flow out the door when the firm actually buys and pays for new capital equipment. Therefore, these capital expenditures are set out in the second sec- tion of the cash-flow statement. You can see that Home Depot spent $1,432 million on new capital equipment. Notice that (gross) property, plant, and equipment on Home Depot’s balance sheet increased by precisely this amount. On the other hand, Home Depot freed up $313 million by selling off other investments (this amount shows up as the change in the sum of intangible fixed assets plus other assets). Total cash used by investments was $1,119 million.

Finally, the third section of the cash-flow statement shows the cash from financing activities. Home Depot used $1,323  −  $1,291  =  $32 million to retire debt. It also paid out $1,743 million to stockholders in the form of dividends and used $3,984 million to repurchase stock. These cash outflows were partly offset by an inflow of $784 million by the sale of additional shares. 7

7 You might think that interest payments also ought to be listed in this section. However, it is usual to include interest in the first section with cash flow from operations. This is because, unlike dividends, interest payments are not discretionary. The firm must pay interest when a payment comes due, so these payments are treated as a business expense rather than as a financing decision.

Cash provided by operations

Net income 4,535 Depreciation 1,684 Changes in working capital items Decrease (increase) in accounts receivable − 143 Decrease (increase) in inventories − 350 Decrease (increase) in other current assets 93 Increase (decrease) in accounts payable 698 Increase (decrease) in other current liabilities 87 Total decrease (increase) in working capital 385 Cash provided by operations 6,604

Cash fl ows from investments

Cash provided by (used for) disposal of (additions to) property, plant, and equipment − 1,432 Sales (acquisitions) of other long-term assets 313 Cash provided by (used for) investments − 1,119

Cash provided by (used for) fi nancing activities

Additions to (reduction in) short-term debt 1,291 Additions to (reduction in) long-term debt − 1,323 Dividends − 1,743 Issues of stock 784

Repurchases of stock − 3,984

Other − 3 Cash provided by (used for) fi nancing activities − 4,978

Net increase (decrease) in cash and cash equivalents 507

TABLE 3.4 Home Depot’s statement of cash flows, 2012 (figures in $ millions)

Source: Calculated from data in Tables 3.1 and 3.3.

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Chapter 3 Accounting and Finance 67

To summarize, the cash-flow statement tells us that Home Depot generated $6,604 million from operations, spent $1,119 million on new investments, and used $4,978 million in financing activities. Home Depot earned and raised more cash than it spent. Therefore, its cash balance increased by $507 million. To calculate this change in cash balance, we subtract the uses of cash from the sources:

In Millions

Cash fl ow from operations $6,604 − Cash fl ow for new investment −  1,119 + Cash provided by new fi nancing −  4,978 = Change in cash balance +     507

Look back at Table 3.1 and you will see that cash accounts on the balance sheet did indeed increase by this amount in 2012. 8

8 Home Depot’s published statement of cash flows differs from the cash-flow statement that we derived from the balance sheet and income statement. This is a common occurrence, particularly if the company has engaged in mergers or divestitures during the year.

Would the following activities increase or decrease the firm’s cash balance?

a. Inventories are increased. b. The firm reduces its accounts payable. c. The firm issues additional common stock. d. The firm buys new equipment.

Self-Test 3.4

Free Cash Flow The value of a company depends on how much cash it can generate for investors after it has paid for any new capital investments. This cash is called the company’s free cash flow. Free cash flow is available to be paid out to investors as interest or divi- dends or to repay debt or buy back stock.

free cash flow Cash available for distribution to investors after firm pays for new investments or additions to working capital.

Example 3.3 Free Cash Flow for Home Depot Let’s use Home Depot’s income and cash-flow statements to calculate its free cash flow in 2012. We start with the earnings produced by the firm’s ongoing operations. This is equal to

Net income + debt interest = $4,535 + $632 = $5,167 million

We need to make two adjustments to this figure for those parts of the income statement that do not involve cash coming in or going out. First, we must add back depreciation because depreciation is not a cash outflow, even though it is treated as an expense in the income statement. Second, accounting income is not cash in the bank. For example, the firm may need to lay out money to buy materi- als ahead of time, or its customers may not pay for their purchases immediately.

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68 Part One Introduction

11 J. R. Graham, C. R. Harvey, and S. Rajgopal, “The Economic Implications of Corporate Financial Reporting,” Journal of Accounting and Economics 40 (2005), pp. 3–73.

3.4 Accounting Practice and Malpractice Managers of public companies face constant scrutiny. Much of that scrutiny focuses on earnings. Security analysts forecast earnings per share, and investors then wait to see whether the company can meet or beat the forecasts. A shortfall, even if it is only a cent or two, can be a big disappointment. Investors might judge that if you could not find that extra cent or two of earnings, the firm must be in a really bad way.

Managers complain about this pressure, but do they do anything about it? Unfor- tunately, the answer appears to be yes, according to Graham, Harvey, and Rajgopal, who surveyed about 400 senior managers. 11 Most of the managers said that accounting

Therefore, to measure the cash from ongoing operations, we need to subtract any additions to net working capital. This gives us cash flow from operations:

Cash flow from operations = net income + interest + depreciation - additions to net working capital

= $5,167 + $1,684 + $385 = $7,236 million

This cash is not all available to be paid out to investors, for the company needs some of the cash for new capital expenditures. So the capital that is free for distribution is

Free cash flow = cash flow from operations - capital expenditures = $7,236 - $1,119 = $6,117 million

This free cash flow could be paid out as interest or dividends, or it could be used to pay back debt or repurchase stock. Of course, the company is not obliged to pay out all of its free cash flow. Some of it may be kept in the company and used to build up the cash reserves.

Notice that free cash flow differs from the addition-to-cash balances found in the statement of cash flows (Table 3.4). First, when we calculate free cash flow, we ignore altogether items in the last panel of Table 3.4, “Cash provided by financ- ing activities.”9 This is because free cash flow measures how much cash the com- pany’s operations generate for possible distribution to investors. The available amount should not be confused with the amount that the company actually raised by financing activities. Second, we add back interest payments when computing free cash flow, as those payments are part of the distributions made to investors.10

It is often useful to ask what Home Depot’s free cash flow would have been if the company had been financed entirely by equity. In that case, all the free cash flow would belong to the shareholders. However, if Home Depot no longer paid out $632 million as interest, pretax income would be increased by that amount, and the company would pay an additional .35 × 632 = $221 million in tax. Thus, if the company was financed solely by equity, free cash flow would have been $6,117 − $221 = $5,896 million.

9 For this reason, when we calculated cash flow from operations, we ignored the change in holdings of short-term debt, even though this short-term debt is listed under current liabilities. We were interested only in the items of working capital that arose from the firm’s operations. 10 We can check the logic linking free cash flow to the statement of cash flows as follows:

Increase in cash balance from Table 3.4 $507

+ Cash used for financing activities from Table 3.4 4,978

+ Interest payments 632

Free cash flow $6,117

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Chapter 3 Accounting and Finance 69

earnings were the single most important number reported to investors. Most admit- ted to adjusting their firms’ operations and investments to produce the earnings that investors were looking for. For example, 80% were prepared to decrease discretionary spending in R&D, advertising, or maintenance to meet earnings targets.

Of course, managers may not need to adjust the firm’s operations if they can instead adjust their accounting methods. U.S. accounting rules are spelled out by the Financial Accounting Standards Board (FASB) and its generally accepted accounting principles (GAAP). Yet, inevitably, rules and principles leave room for discretion, and manag- ers under pressure to perform are tempted to take advantage of this leeway to satisfy investors. Investors worry about the fact that some companies seem particularly prone to inflate their earnings by playing fast and loose with accounting practice. They refer to such companies as having “low-quality” earnings, and they place a correspondingly lower value on the firms’ stock.

Here are some examples of ambiguities in accounting rules that have been used by companies to conceal unflattering information:

• Revenue recognition. As we saw above, firms record a sale when it is made, not when the customer actually pays. But the date of sale is not always obvious. For example, suppose that you sell goods today but you give the customer the right to return them “if not fully satisfied.” Have you made the sale when the goods are delivered or only when you can be sure that they will not be returned? Some com- panies have used this ambiguity to deliberately inflate their profits. This process is termed channel stuffing. For example, between 1997 and 2001 Xerox took an overly optimistic view of its revenues. Whenever a customer signed a long-term lease of a copy machine, Xerox booked the entire stream of future rental payments in the period that the lease contract was signed instead of spreading them over the life of the contract. In so doing, it inflated profits by around $3 billion. In Chapter 1 we mentioned Hewlett-Packard’s disastrous acquisition of the British company Autonomy. Hewlett-Packard paid $11.1 billion for Autonomy. Just over a year later it wrote down the value of the company by $8.8 billion, alleging that it had greatly inflated its revenues.

• Cookie-jar reserves. The giant mortgage-pass-through firm Freddie Mac earned the Wall Street nickname “Steady Freddie” for its unusually smooth and predictable pattern of earnings growth, at least until 2008 when it suddenly collapsed in the wake of the meltdown in subprime mortgages. Unfortunately, it emerged in 2003 that Freddie achieved this predictability in part by misusing its reserve accounts. Normally, such accounts are intended to allow for the likely impact of events that might reduce earnings, such as the failure of customers to pay their bills. But Fred- die seemed to “overreserve” against such contingencies so that it could “release” those reserves and bolster income in a bad year. Its steady growth was largely a matter of earnings management.

• Lehman Brothers’ repurchase agreements. As the financial crisis of 2007–2009 worsened, Lehman Brothers desperately looked for a way to improve its appar- ent financial health. It did so using an arcane accounting trick that removed about $50 billion from its balance sheet. The trick was called Repo 105. Lehman sold $50 billion of bonds to several other investment banks with an agreement that it would repurchase those bonds at a slightly higher price within a week or so. This arrangement is called a repurchase or “repo” agreement. Everyone knows that a repurchase agreement is not really a sale of the bonds—it is for all intents and purposes a loan, with the higher repurchase price serving as an implicit interest payment. The bonds serve only to protect the lender—if Lehman defaults on the promised repurchase, it will not get its bonds back. Repurchase agreements are commonly, and properly, treated in U.S. law as loans. But in this case Lehman entered into the transaction through its European office and pledged bonds worth more than 105% of the cash it received. This loophole allowed it to obtain an

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70 Part One Introduction

opinion from a British law firm that the repo could qualify under British account- ing rules as a true sale of assets. Lehman’s plan was to use the money it received from selling the bonds to pay off some of its other debts. Then, after it had filed its quarterly financial reports, it would borrow the funds necessary to repurchase the bonds. But until that time it would look less indebted than it actually was. The firm (barely) followed the letter of the law but used the discretion provided by account- ing rules to paint a misleading picture of its actual condition.

• Off–balance sheet assets and liabilities. Before its bankruptcy in 2001, Enron had accumulated large debts and had also guaranteed the debts of other companies in which it had an ownership stake. To present a fair view of the firm, Enron should have recognized these potential liabilities on its balance sheet. But the firm created and placed paper firms—so-called special-purpose entities (SPEs)—in the middle of its transactions and excluded these liabilities from its financial statements.

The collapse of Enron illustrates how dishonest managers with creamy compensa- tion packages may be tempted to conceal the truth from investors. If the company had been more transparent to outsiders—that is, if they could have assessed its true profit- ability and prospects—its problems would have shown up right away in a falling stock price. This in turn would have generated extra scrutiny from security analysts, bond rating agencies, lenders, and investors.

With transparency, corporate troubles generally lead to corrective action. But the top management of a troubled and opaque company may be able to maintain its stock price and postpone the discipline of the market. Market discipline caught up with Enron only a month or two before bankruptcy.

Enron was not the only company to be mired in accounting scandals in the early years of the century. Firms such as Global Crossing, Qwest Communications, and WorldCom misstated profits by billions of dollars. Overseas, the Italian dairy com- pany Parmalat falsified the existence of a bank account to the tune of $5.5 billion, and the French media and entertainment company Vivendi came close to bankruptcy after it was accused of accounting fraud. In response to these scandals Congress passed the Sarbanes-Oxley Act, widely known as SOX. A major goal of SOX is to increase trans- parency and ensure that companies and their accountants provide directors, lenders, and shareholders with the information they need to monitor progress.

SOX created the Public Accounting Oversight Board to oversee the auditing of public companies; it banned accounting firms from offering their services to com- panies whose accounts they audit; it prohibited any individual from heading a firm’s audit for more than 5 years; and it required that the board’s audit committee consist of directors who are independent of the company’s management. Sarbanes-Oxley also required that management certify that the financial statements present a fair view of the firm’s financial position and demonstrate that the firm has adequate controls and procedures for financial reporting. All this has come at a price. Managers and inves- tors worry that the costs of SOX and the burden of meeting detailed, inflexible regula- tions are pushing some corporations to return from public to private ownership. Some blame SOX and onerous regulation in the United States for the fact that an increasing number of foreign companies have chosen to list their shares in London rather than New York.

There is also a vigorous debate over “rules-based” versus “principles-based” approaches to accounting standards. The United States follows a rules-based approach, with detailed rules governing virtually every circumstance that possibly can be antici- pated. In contrast, the European Union takes a principles-based approach to account- ing. Its International Financial Reporting Standards set out general approaches that financial statements should take to valuing assets. Europe and the United States have been engaged for years in attempts to coordinate their systems, and many in the United States have lobbied for the greater simplicity that principles-based accounting stan- dards might offer. The nearby box reports on these efforts.

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71

3.5 Taxes Taxes often have a major effect on financial decisions. Therefore, we should explain how corporations and investors are taxed.

Corporate Tax Companies pay tax on their income. Table 3.5 shows that there are special low rates of corporate tax for small companies, but for large companies (those with income over $18.33 million) the corporate tax rate is 35%. 12 Thus for every $100 that the firm earns it pays $35 in corporate tax.

When firms calculate taxable income, they are allowed to deduct expenses. These expenses include an allowance for depreciation. However, the Internal Revenue Service (IRS) specifies the rates of depreciation that the company can use for different types of equipment. The rates of depreciation used to calculate taxes are not the same as the rates used when the firm reports its profits to shareholders. 13

12 In addition, corporations pay state income taxes, which we ignore here for simplicity. 13 If the company assumes a slower rate of depreciation in its income statement than the Internal Revenue Ser- vice assumes, the tax charge shown in the income statement will be higher in the early years of a project’s life than the actual tax payment. This difference is recorded in the balance sheet as a liability for deferred tax. We will tell you more about depreciation allowances in Chapter 9.

Finance in Practice Farewell to GAAP? and when companies record revenue. This leaves less room for judgment, but detailed rules rapidly become out of date, and unscrupulous companies have been able to structure transactions so that they keep to the letter but not the spirit of the rules.

For some years the SEC has been working to bring the country’s standards more in line with international rules. In order to encourage foreign companies to list in the United States, it has allowed foreign issuers to use international standards. But a move to oblige U.S. companies to adopt IFRS would be a more costly and longer-term project. It is, however, supported by many large U.S. multinationals, which already use IFRS for their overseas subsidiaries.

Companies in the United States may soon face the big- gest change to their accounting methods since generally accepted accounting principles (GAAP) were introduced in the 1930s. The SEC has been debating whether U.S. com- panies should be obliged to follow International Financial Reporting Standards (IFRS) rather than GAAP, which com- panies currently use.

The International Financial Reporting Standards, which are set by the London-based International Accounting Stan- dards Board (IASB), aim to harmonize fi nancial reporting around the world. They are the basis for reporting throughout the European Union. Some 100 other countries, such as Aus- tralia, Canada, Brazil, India, and China, have adopted them or plan to do so.

A shift from GAAP to IFRS would involve a major change in the way that accountants in the United States approach their task. IFRS tend to be “principles-based,” which means that there are no hard-and-fast codes to follow. By contrast, in the United States, GAAP are accompanied by thousands of pages of prescriptive regulatory guidance and interpre- tations from auditors and accounting groups. For example, more than 160 pieces of authoritative literature relate to how

Taxable Income, $ Tax Rate, %

0–50,000 15 50,001–75,000 25 75,001–100,000 34 100,001–18,333,333 Varies between 39 and 34 Over 18,333,333 35

TABLE 3.5 Corporate tax rates, 2014

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Accounting acronyms

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72 Part One Introduction

The company is also allowed to deduct interest paid to debtholders when calculat- ing its taxable income, but dividends paid to shareholders are not deductible. These dividends are therefore paid out of after-tax income. Table 3.6 provides an example of how interest payments reduce corporate taxes. Although EBIT for both firms A and B is $100 million, firm A, which has $40 million of interest expense, has lower pretax income and therefore pays less taxes.

The bad news about taxes is that each extra dollar of revenue increases taxable income by $1 and results in 35 cents of extra taxes. The good news is that each extra dollar of expense reduces taxable income by $1 and therefore reduces taxes by 35 cents. For example, if the firm borrows money, every dollar of interest it pays on the loan reduces taxes by 35 cents. Therefore, after-tax income is reduced by only 65 cents.

TABLE 3.6 Firms A and B both have earnings before interest and taxes (EBIT) of $100 million, but A pays out part of its profits as debt interest. This reduces the corporate tax paid by A.

Firm A Firm B

EBIT 100 100 Interest 40 0 Pretax income 60 100 Tax (35% of pretax income) 21 35 Net income 39 65

Note: Figures in millions of dollars.

Recalculate the figures in Table 3.6 assuming that firm A now has to make interest payments of $60 million. What happens to taxes paid? Does net income fall by the additional $20 million interest payment compared with the case considered in Table 3.6 , where interest expense was only $40 million?

Self-Test 3.5

When firms make profits, they pay 35% of the profits to the Internal Revenue Ser- vice. But the process doesn’t work in reverse; if the firm suffers a loss, the IRS does not send it a check for 35% of the loss. However, the firm can carry the losses back, deduct them from taxable income in earlier years, and claim a refund of past taxes. Losses can also be carried forward and deducted from taxable income in the future. 14

Personal Tax Table 3.7 shows the U.S. rates of personal tax. Notice that as income increases, the tax rate also increases. Notice also that the top personal tax rate is higher than the top corporate rate.

14 Losses can be carried back for a maximum of 3 years and forward for up to 15 years.

Taxable Income (dollars)

Single Taxpayers Married Taxpayers Filing Joint Returns Tax Rate, %

0–9,075 0–18,150 10 9,076–36,900 18,151–73,800 15 36,901–89,350 73,801–148,350 25

89,351–186,350 148,351–226,850 28 186,351–405,100 226,851–405,100 33 405,101–406,750 405,101–457,600 35

406,751 and above 457,601 and above 39.6

TABLE 3.7 Personal tax rates, 2014

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Chapter 3 Accounting and Finance 73

The tax rates presented in Table  3.7 are marginal tax rates. The marginal tax rate is the tax that the individual pays on each extra dollar of income. For example, as a single taxpayer, you would pay 10 cents of tax on each extra dollar you earn when your income is below $9,075, but once income exceeds $9,075, you would pay 15 cents of tax on each extra dollar of income up to an income of $36,900. If your total income is $50,000, your tax bill is 10% of the first $9,075 of income, 15% of the next $27,825 (i.e., 36,900  −  9,075), and 25% of the remain- ing $13,100:

Tax = (.10 × $9,075) + (.15 × $27,825) + (.25 × $13,100) = $8,356.25

The average tax rate is simply the total tax bill divided by total income. In this example it is $8,356.25/$50,000  =   .167,  or  16.7%. Notice that the average rate is lower than the marginal rate. This is because of the lower rates on the first $34,500.

marginal tax rate Additional taxes owed per dollar of additional income.

average tax rate Total taxes owed divided by total income.

What are the average and marginal tax rates for a single taxpayer with a taxable income of $80,000? What are the average and marginal tax rates for married taxpayers filing joint returns if their joint taxable income is also $80,000?

Self-Test 3.6

The tax rates in Table 3.7 apply to “ordinary income,” primarily income earned as salary or wages. Interest earnings also are treated as ordinary income.

The treatment of dividend income in the United States leads to what is commonly dubbed the “double taxation” of corporate earnings. Each dollar the company earns is taxed at the corporate rate. Then, if the company pays a dividend out of this after-tax income, the shareholder pays personal income taxes on the distribution. The origi- nal earnings are taxed first as corporate income and again as dividend income. Sup- pose instead that the company earns a dollar which is paid out as interest. The dollar escapes corporate tax because the interest payment is considered a business expense that reduces the firm’s taxable income.

Capital gains are also taxed, but only when the gains are realized. Suppose that you bought Bio-technics stock when it was selling for 10 cents a share. Its market price today is $1 a share. As long as you hold on to your stock, there is no tax to pay on your gain. But if you sell, the 90 cents of capital gain is taxed. The marginal tax rate on capital gains for most shareholders is 15%.

Financial managers need to worry about the tax treatment of investment income because tax policy will affect the prices individuals are willing to pay for the com- pany’s stock or bonds. We will return to these issues in Part 5 of the text.

The tax rates in Table 3.7 apply to individuals. But financial institutions are major investors in corporate securities. These institutions often have special tax provisions. For example, pension funds are not taxed on interest or dividend income or on capi- tal gains.

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Average and marginal tax rates

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74 Part One Introduction

SUMMARY Investors and other stakeholders in the firm need regular financial information to help them monitor the firm’s progress. Accountants summarize this information in a balance sheet, income statement, and statement of cash flows.

The balance sheet provides a snapshot of the firm’s assets and liabilities. The assets consist of current assets that can be rapidly turned into cash and fixed assets such as plant and machinery. The liabilities consist of current liabilities that are due for payment within a year and long-term debts. The difference between the assets and the liabilities represents the amount of the shareholders’ equity.

The income statement measures the profitability of the company during the year. It shows the difference between revenues and expenses.

The statement of cash flows measures the sources and uses of cash during the year. The change in the company’s cash balance is the difference between sources and uses.

It is important to distinguish between the book values that are shown in the company accounts and the market values of the assets and liabilities. Book values are historical measures based on the original cost of an asset. For example, the assets in the balance sheet are shown at their historical cost less an allowance for depreciation. Similarly, the figure for shareholders’ equity measures the cash that shareholders have contributed in the past or that the company has rein- vested on their behalf. In contrast, market value is the current price of an asset or liability.

Income is not the same as cash flow. There are two reasons for this: (1) Investment in fixed assets is not deducted immediately from income but is instead spread (as charges for depre- ciation) over the expected life of the equipment, and (2) the accountant records revenues when the sale is made, rather than when the customer actually pays the bill, and at the same time deducts the production costs even though those costs may have been incurred earlier.

For large companies the marginal rate of tax on income is 35%. In calculating taxable income the company deducts an allowance for depreciation and interest payments. It can- not deduct dividend payments to the shareholders.

Individuals are also taxed on their income, which includes dividends and interest on their investments. Capital gains are taxed, but only when the investment is sold and the gain realized.

What information is contained in the balance sheet, income statement, and statement of cash flows? (LO3-1)

What is the difference between market and book values? (LO3-2)

Why does accounting income differ from cash flow? (LO3-3)

What are the essential features of the taxation of corporate and personal income? (LO3-4)

L I S T I N G O F E Q UAT I O N 3.1 Shareholders’ equity  =  net assets  =  total assets  −  total liabilities

QUESTIONS AND PROBLEMS 1. Financial Statements. Earlier in the chapter, we characterized the balance sheet as providing a

snapshot of the firm at one point in time and the income statement as providing a video. What did we mean by this? Is the statement of cash flow more like a snapshot or a video? (LO3-1)

2. Balance Sheet. Balance sheet items are usually entered in order of declining liquidity. Place each of the terms below in the appropriate place in the balance sheet. (LO3-1)

Accounts payable Total current assets

Net fixed assets Accounts receivable

Debt due for repayment Total current liabilities

Cash and marketable securities Inventories

Equity Long-term debt

finance

®

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Chapter 3 Accounting and Finance 75

Assets Liabilities and Equity

a. f. b. g. c. h. d. i. e. j. Total assets Total liabilities and equity

3. Balance Sheet. Construct a balance sheet for Sophie’s Sofas given the following data. What is shareholders’ equity? (LO3-1)

Cash balances  =  $10,000

Inventory of sofas  =  $200,000

Store and property  =  $100,000

Accounts receivable  =  $22,000

Accounts payable  =  $17,000

Long-term debt  =  $170,000

4. Income Statement. A firm’s income statement included the following data. The firm’s average tax rate was 20%. (LO3-1)

Cost of goods sold $8,000

Income taxes paid $2,000

Administrative expenses $3,000

Interest expense $1,000

Depreciation $1,000

a. What was the firm’s net income? b. What must have been the firm’s revenues? c. What was EBIT?

5. Balance Sheet/Income Statement. The year-end 2013 balance sheet of Brandex Inc. listed common stock and other paid-in capital at $1,100,000 and retained earnings at $3,400,000. The next year, retained earnings were listed at $3,700,000. The firm's net income in 2014 was $900,000. There were no stock repurchases during the year. What were the dividends paid by the firm in 2014? (LO3-1)

6. Financial Statements. South Sea Baubles has the following (incomplete) balance sheet and income statement. (LO3-1, LO3-4)

BALANCE SHEET AT END OF YEAR (Figures in $ millions)

Assets 2013 2014 Liabilities and Shareholders’ Equity 2013 2014

Current assets 90 140 Current liabilities 50 60 Net fi xed assets 800 900 Long-term debt 600 750

INCOME STATEMENT, 2014 (Figures in $ millions)

Revenue 1,950 Cost of goods sold 1,030 Depreciation 350 Interest expense 240

a. What is shareholders’ equity in 2013 and 2014? b. What is net working capital in 2013 and 2014? c. What are taxes paid in 2014? Assume the firm pays taxes equal to 35% of taxable income. d. What is cash provided by operations during 2014? Pay attention to changes in net working

capital, using Table 3.4 as a guide.

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76 Part One Introduction

e. Net fixed assets increased from $800 million to $900 million during 2014. What must have been South Sea’s gross investment in fixed assets during 2014?

f. If South Sea reduced its outstanding accounts payable by $35 million during the year, what must have happened to its other current liabilities?

7. Financial Statements. Here are the 2013 and 2014 (incomplete) balance sheets for Newble Oil Corp. (LO3-1)

BALANCE SHEET AT END OF YEAR (Figures in $ millions)

Assets 2013 2014 Liabilities and Shareholders’ Equity 2013 2014

Current assets 310 420 Current liabilities 210 240 Net fi xed assets 1,200 1,420 Long-term debt 830 920

a. What was owners’ equity at the end of 2013 and 2014? b. If Newble paid dividends of $100 in 2014 and made no stock issues, what must have been

net income during the year? c. If Newble purchased $300 in fixed assets during the year, what must have been the deprecia-

tion charge on the income statement? d. What was the change in net working capital between 2013 and 2014? e. If Newble issued $200 of new long-term debt, how much debt must have been paid off

during the year?

8. Financial Statements. Henry Josstick has just started his first accounting course and has prepared the following balance sheet and income statement for Omega Corp. Unfortunately, although the data for the individual items are correct, he is very confused as to whether an item should go in the balance sheet or income statement and whether it is an asset or liability. Help him by rearranging the items and filling in the blanks.

BALANCE SHEET

Payables 35 Inventories 50 Less accumulated depreciation 120 Receivables 35 Total current assets Total current liabilities Long-term debt 350 Interest expense 25 Property, plant, and equipment 520 Total liabilities Net fi xed assets Shareholders’ equity 90 Total assets Total liabilities and shareholders’

equity

INCOME STATEMENT

Net sales 700 Cost of goods sold 580 Selling, general, and administrative expenses 38 EBIT Debt due for repayment 25 Cash 15 Taxable income Taxes 15 Depreciation 12 Net income

What is the correct total for the following? (LO3-1)

a. Current assets b. Net fixed assets c. Total assets d. Current liabilities e. Total liabilities f. Total liabilities and shareholders’ equity g. EBIT h. Taxable income i. Net income

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Chapter 3 Accounting and Finance 77

9. Market versus Book Values. The founder of Alchemy Products Inc. discovered a way to turn gold into lead and patented this new technology. He then formed a corporation and invested $200,000 in setting up a production plant. He believes that he could sell his patent for $50 million. (LO3-2)

a. What are the book value and market value of the firm? b. If there are 2 million shares of stock in the new corporation, what would be the price per

share and the book value per share?

10. Market versus Book Values. State whether each of the following events would increase or decrease the ratio of market value to book value. (LO3-2)

a. Big Oil announces the discovery of a major new oil field in Costaguana. b. Big Autos increases its depreciation provision. c. Since Big Stores purchased its assets, inflation has risen sharply.

11. Market versus Book Values. (LO3-2)

a. In early 2013, the market values of the shares of many banks (e.g., Bank of America or Citi- group) were less than book value per share. How would you interpret this pattern?

b. At the same time, Google’s market value per share was more than three times its book value. Is this consistent with your analysis in part (a)?

12. Income versus Cash Flow. Explain why accounting income generally differs from a firm’s cash inflows. (LO3-3)

13. Cash Flows. Will the following actions increase or decrease the firm’s cash balance? (LO3-3)

a. The firm sells some goods from inventory. b. The firm sells some machinery to a bank and leases it back for a period of 20 years. c. The firm buys back 1 million shares of stock from existing shareholders.

14. Income versus Cash Flow. Butterfly Tractors had $14 million in sales last year. Cost of goods sold was $8 million, depreciation expense was $2 million, interest payment on outstanding debt was $1 million, and the firm’s tax rate was 35%. (LO3-3)

a. What were the firm’s net income and net cash flow? b. What would happen to net income and cash flow if depreciation were increased by

$1 million? c. Would you expect the change in income and cash flow to have a positive or negative impact

on the firm’s stock price? d. What would be the impact on net income if depreciation was $1 million and interest expense

was $2 million? e. What would be the impact on cash if depreciation was $1 million and interest expense was

$2 million?

15. Working Capital. QuickGrow is in an expanding market, and its sales are increasing by 25% per year. Would you expect its net working capital to be increasing or decreasing? (LO3-3)

16. Income Statement. Sheryl’s Shipping had sales last year of $10,000. The cost of goods sold was $6,500, general and administrative expenses were $1,000, interest expenses were $500, and depreciation was $1,000. The firm’s tax rate is 35%. (LO3-3)

a. What are earnings before interest and taxes? b. What is net income? c. What is cash flow from operations?

17. Income versus Cash Flow. Start-up firms typically have negative net cash flows for several years. (LO3-3)

a. Does this mean that they are failing? b. Accounting profits for these firms are also commonly negative. How would you interpret

this pattern? Is there a shortcoming in our accounting rules?

18. Income versus Cash Flow. Can cash flow from operations be positive if net income is nega- tive? Can it be negative if net income is positive? Give examples. (LO3-3)

19. Income versus Cash Flow. During the last year of operations, Theta’s accounts receivable increased by $10,000, accounts payable increased by $5,000, and inventories decreased by $2,000. What is the total impact of these changes on the difference between profits and cash flow? (LO3-3)

20. Income versus Cash Flow. Candy Canes Inc. spends $100,000 to buy sugar and peppermint in April. It produces its candy and sells it to distributors in May for $150,000, but it does not receive payment until June. For each month, find the firm’s sales, net income, and net cash flow. (LO3-3)

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78 Part One Introduction

21. Income versus Cash Flow. Ponzi Products produced 100 chain-letter kits this quarter, resulting in a total cash outlay of $10 per unit. It will sell 50 of the kits next quarter at a price of $11, and the other 50 kits in the third quarter at a price of $12. It takes a full quarter for Ponzi to collect its bills from its customers. (Ignore possible sales in earlier or later quarters.) (LO3-3)

a. What is the net income for Ponzi next quarter? b. What are the cash flows for the company this quarter? c. What are the cash flows for the company in the third quarter? d. What is Ponzi’s net working capital in the next quarter?

22. Income versus Cash Flow. Value Added Inc. buys $1 million of sow's ears at the beginning of January but doesn't pay immediately. Instead, it agrees to pay the bill in March. It processes the ears into silk purses, which it sells for $2 million in February. However, it will not collect pay- ment on the sales until April. (LO3-3)

a. What is the firm’s net income in February? b. What is its net income in March? c. What is the firm’s net new investment in working capital in January? d. What is its net new investment in working capital in April? e. What is the firm’s cash flow in January and April? f. What is the cash flow in February? g. What is the cash flow in April?

23. Free Cash Flow. Free cash flow measures the cash available for distribution to debtholders and shareholders. Look at Section 3.4 where we calculate free cash flow for Home Depot. Show how this cash was distributed to investors. How much was used to build up cash reserves? (LO3-3)

24. Free Cash Flow. The following table shows an abbreviated income statement and balance sheet for McDonald's Corporation for 2012.

INCOME STATEMENT OF MCDONALD’S CORP., 2012 (Figures in $ millions)

Net sales 27,567 Costs 17,569 Depreciation 1,402 Earnings before interest and taxes (EBIT) 8,596 Interest expense 517 Pretax income 8,079 Taxes 2,614 Net income 5,465

BALANCE SHEET OF MCDONALD’S CORP., 2012 (Figures in $ millions)

Assets 2012 2011 Liabilities and Shareholders’ Equity 2012 2011

Current assets Current liabilities Cash and marketable securities 2,336 2,336 Debt due for repayment — 367 Receivables 1,375 1,335 Accounts payable 3,403 3,143 Inventories 122 117 Total current liabilities 3,403 3,509 Other current assets 1,089 616 Total current assets 4,922 4,403 Fixed assets Long-term debt 13,633 12,134 Property, plant, and equipment 24,677 22,835 Other long-term liabilities 3,057 2,957 Intangible assets (goodwill) 2,804 2,653 Total liabilities 20,093 18,600 Other long-term assets 2,983 3,099 Total shareholders’ equity 15,294 14,390 Total assets 35,387 32,990 Total liabilities and shareholders’ equity 35,387 32,990

In 2012 McDonald’s had capital expenditures of $3,049. (LO3-3)

a. Calculate McDonald’s free cash flow in 2012. b. If McDonald’s was financed entirely by equity, how much more tax would the company

have paid? (Assume a tax rate of 35%.) c. What would the company’s free cash flow have been if it was all-equity financed?

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Chapter 3 Accounting and Finance 79

25. Tax Rates. What would be the marginal and average tax rates for a married couple with income of $90,000? For an unmarried taxpayer with the same income? (LO3-4)

26. Tax Rates. Using Table 3.7 , calculate the marginal and average tax rates for a single taxpayer with the following incomes: (LO3-4)

a. $20,000 b. $50,000 c. $300,000 d. $3,000,000

27. Taxes. A married couple earned $95,000 in 2014. How much did they pay in taxes? (LO3-4)

a. What was their marginal tax bracket? b. What was their average tax bracket?

28. Tax Rates. What would be the marginal and average tax rates for a corporation with an income level of $100,000? (LO3-4)

29. Tax Rates. Turn back to Table  3.7 , which shows marginal personal tax rates. Make a table in Excel that calculates taxes due for income levels ranging from $10,000 to $10 million. (LO3-4)

a. For each income, calculate the average tax rate of a single taxpayer. Plot the average tax rate as a function of income.

b. What happens to the difference between the average and top marginal tax rates as income becomes very large?

The table below contains data on Fincorp Inc. that you should use for Problems 30–37. The balance sheet items correspond to values at year-end of 2013 and 2014, while the income statement items correspond to revenues or expenses during the year ending in either 2013 or 2014. All values are in thousands of dollars.

2013 2014

Revenue $4,000 $4,100 Cost of goods sold 1,600 1,700 Depreciation 500 520 Inventories 300 350 Administrative expenses 500 550 Interest expense 150 150 Federal and state taxes * 400 420 Accounts payable 300 350 Accounts receivable 400 450 Net fi xed assets † 5,000 5,800 Long-term debt 2,000 2,400 Notes payable 1,000 600 Dividends paid 410 410

Cash and marketable securities 800 300

*Taxes are paid in their entirety in the year that the tax obligation is incurred. † Net fi xed assets are fi xed assets net of accumulated depreciation since the asset was installed.

30. Balance Sheet. Construct a balance sheet for Fincorp for 2013 and 2014. What is shareholders’ equity? (LO3-1)

31. Working Capital. What was the change in net working capital during the year? (LO3-1)

32. Income Statement. Construct an income statement for Fincorp for 2013 and 2014. What were reinvested earnings for 2014? (LO3-1)

33. Earnings per Share. Suppose that Fincorp has 500,000 shares outstanding. What were earn- ings per share? (LO3-1)

34. Balance Sheet. Examine the values for depreciation in 2014 and net fixed assets in 2013 and 2014. What was Fincorp’s gross investment in plant and equipment during 2014? (LO3-1)

Templates can be found in Connect.

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80 Part One Introduction

35. Book versus Market Value. Suppose that the market value (in thousands of dollars) of Fin- corp's fixed assets in 2014 is $6,000 and that the value of its long-term debt is only $2,200. In addition, the consensus among investors is that Fincorp’s past investments in developing the skills of its employees are worth $2,900. This investment of course does not show up on the balance sheet. What will be the price per share of Fincorp stock? (LO3-2)

36. Income versus Cash Flows. Construct a statement of cash flows for Fincorp for 2014. (LO3-3)

37. Tax Rates. (LO3-4)

a. What was the firm's average tax bracket for each year? b. Do you have enough information to determine the marginal tax bracket?

CHALLENGE PROBLEM 38. Tax Rates. You have set up your tax preparation firm as an incorporated business. You took

$70,000 from the firm as your salary. The firm's taxable income for the year (net of your sal- ary) was $30,000. How much tax must be paid to the federal government, including both your personal taxes and the firm’s taxes? Assume you pay personal taxes as an unmarried taxpayer. (LO3-4)

a. By how much will you reduce the total tax bill if you cut your salary to $50,000, thereby leaving the firm with taxable income of $50,000? Use the tax rates presented in Tables 3.5 and 3.7 .

b. What allocation will minimize the total tax bill? Hint: Think about marginal tax rates and the ability to shift income from a higher marginal bracket to a lower one.

WEB EXERCISES 1. Find Microsoft (MFST) and Ford (F) on finance.yahoo.com, and examine the financial state-

ments of each. Which firm uses more debt finance? Which firm has higher cash as a percentage of total assets? Which has higher EBIT per dollar of total assets? Which has higher profits per dollar of shareholders’ equity?

2. Now choose two highly profitable technology firms, such as Intel (INTC) and Microsoft (MSFT), and two electric utilities, such as American Electric Power (AEP) and Duke Energy (DUK). Which firms have the higher ratio of market value to book value of equity? Does this make sense to you? Which firms pay out a higher fraction of their profits as dividends to share- holders? Does this make sense?

3. Log on to the website of a large nonfinancial company and find its latest financial statements. Draw up a simplified balance sheet, income statement, and statement of cash flows as in Tables 3.1 , 3.3 , and 3.4 . Some companies’ financial statements can be extremely complex; try to find a relatively straightforward business. Also, as far as possible, use the same headings as in these tables, and don’t hesitate to group some items as “other current assets,” “other expenses,” and so on. Look first at your simplified balance sheet. How much was the company owed by its customers in the form of unpaid bills? What liabilities does the company need to meet within a year? What was the original cost of the company’s fixed assets? Now look at the income state- ment. What were the company’s earnings before interest and taxes (EBIT)? Finally, turn to the cash-flow statement. Did changes in working capital add to cash or use it up?

4. The schedule of tax rates for individuals changes frequently. Check the latest schedules on either www.irs.gov or moneycentral.msn.com. What is your marginal tax rate if you are single with a taxable income of $70,000? What is your average tax rate?

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Chapter 3 Accounting and Finance 81

SOLUTIONS TO SELF-TEST QUESTIONS 3.1 Cash and equivalents would increase by $100 million. Property, plant, and equipment would

increase by $400 million. Long-term debt would increase by $500 million. Shareholders’ equity would not increase: Assets and liabilities have increased equally, leaving shareholders’ equity unchanged.

3.2 a. If the auto plant were worth $14 billion, the equity in the firm would be worth $14  −  $4  = $10 billion. With 100 million shares outstanding, each share would be worth $100.

b. If the outstanding stock were worth $8 billion, we would infer that the market values the auto plant at $8  +  $4  =  $12 billion.

3.3 The profits for the firm are recognized in periods 2 and 3 when the sales take place. In both of those periods, profits are $150  −  $100  =  $50. Cash flows are derived as follows.

Period: 1 2 3 4

Sales $ 0 $ 150 $ 150 $ 0 − Change in accounts receivable 0 150 0 -150 − Cost of goods sold 0 100 100 0 − Change in inventories 200 -100 -100 0 = Net cash fl ow − 200 0 + 150 + 150

In period 2, half the units are sold for $150 but no cash is collected, so the entire $150 is treated as an increase in accounts receivable. Half the $200 cost of production is recognized, and a like amount is taken out of inventory. In period 3, the firm sells another $150 of product but collects $150 from its previous sales, so there is no change in outstanding accounts receivable. Net cash flow is the $150 collected in this period on the sale that occurred in period 2. In period 4, cash flow is again $150, as the accounts receivable from the sale in period 3 are collected.

3.4 a. An increase in inventories uses cash, reducing the firm’s net cash balance. b. A reduction in accounts payable uses cash, reducing the firm’s net cash balance. c. An issue of common stock is a source of cash. d. The purchase of new equipment is a use of cash, and it reduces the firm’s net cash balance.

3.5 Firm A Firm B

EBIT 100 100 Interest 60 0

Pretax income 40 100 Tax (35% of pretax income) 14 35

Net income 26 65

Taxes owed by firm A fall from $21 million to $14 million. The reduction in taxes is 35% of the extra $20 million of interest income. Net income does not fall by the full $20 million of extra interest expense. It instead falls by interest expense less the reduction in taxes, or $20 million  −  $7 million  =  $13 million.

3.6 For a single taxpayer with taxable income of $80,000, total taxes paid are

(.10 × 9,075) + [.15 × (36,900 - 9,075)] + [.25 × (80,000 - 36,900)] = $15,856.25

The marginal tax rate is 25%, but the average tax rate is only 15,856.25/80,000 = .198, or 19.8%. For the married taxpayers filing jointly with taxable income of $80,000, total taxes paid are

(.10 × 18,150) + [.15 × (73,800 - 18,150)] + [.25 × (80,000 - 73,800)] = $11,712.50

The marginal tax rate is 25%, and the average tax rate is 11,712.50/80,000 = .146, or 14.6%.

Note: Figures in millions of dollars.

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82

Measuring Corporate Performance

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

4-1 Calculate and interpret the market value and market value added of a public corporation.

4-2 Calculate and interpret key measures of financial performance, including economic value added (EVA) and rates of return on capital, assets, and equity.

4-3 Calculate and interpret key measures of operating efficiency, leverage, and liquidity.

4-4 Show how profitability depends on the efficient use of assets and on profits as a fraction of sales.

4-5 Compare a company’s financial standing with its competitors and its own position in previous years.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

4 CHAPTE R

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83

P A

R T

O N

E

I n Chapter 1 we introduced the basic objective of corporate finance: Maximize the current value of shareholders’ investment in the firm. For public corporations, this value is set in the stock market. It

equals market price per share multiplied by the num-

ber of shares outstanding. Of course, the fluctuations

in market value partly reflect events that are outside

the manager’s control. Nevertheless, good manag-

ers always strive to add value by superior investment

and financing decisions.

How can we judge whether managers are

doing a good job at adding value or where there

may be scope for improvement? We need mea-

sures of value added. We also need measures that

help explain where the value added comes from.

For example, value added depends on profitabil-

ity, so we need measures of profitability. Profitability

depends in turn on profit margins and on how effi-

ciently the firm uses its assets. We will describe the

standard measures of profitability and efficiency in

this chapter.

Value also depends on sound financing. Value is

destroyed if the firm is financed recklessly and can’t

pay its debts. Value is also destroyed if the firm does

not maintain adequate liquidity and therefore has

difficulty finding the cash to pay its bills. Therefore, we

will describe the measures that financial managers

and investors use to assess debt policy and liquidity.

These financial measures are mostly financial ratios

calculated from the firm’s income statement and bal-

ance sheet. Therefore, we will have to take care to

remember the limitations of these accounting data.

You have probably heard stories of whizzes who

can take a company’s accounts apart in minutes,

calculate a list of financial ratios, and divine the

company’s future. Such people are like abominable

snowmen: often spoken of but never truly seen. Finan-

cial ratios are no substitute for a crystal ball. They are

just a convenient way to summarize financial data

and to assess and compare financial performance.

The ratios help you to ask the right questions, but

they seldom answer them.

In tr

o d

u c

tio n

When managers need to judge a firm’s performance, they start with some key financial ratios.

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84 Part One Introduction

4.1 Value and Value Added

How Financial Ratios Help to Understand Value Added The good news about financial ratios is that they are usually easy to calculate. The bad news is that there are so many of them. To make it worse, the ratios are often presented in long lists that seem to require memorization first and understanding maybe later.

We can mitigate the bad news by taking a moment to preview what the ratios are measuring and how the ratios connect to the ultimate objective of value added for shareholders.

Shareholder value depends on good investment decisions. The financial manager evaluates investment decisions by asking several questions, including: How profitable are the investments relative to the cost of capital? How should profitability be mea- sured? What does profitability depend on? (We will see that it depends on efficient use of assets and on the bottom-line profits on each dollar of sales.)

Shareholder value also depends on good financing decisions. Again, there are obvious questions: Is the available financing sufficient? The firm cannot grow unless financing is available. Is the financing strategy prudent? The financial manager should not put the firm’s assets and operations at risk by operating at a dangerously high debt ratio, for example. Does the firm have sufficient liquidity (a cushion of cash or assets that can be readily sold for cash)? The firm has to be able to pay its bills and respond to unexpected setbacks.

Figure 4.1 summarizes these questions in somewhat more detail. The boxes on the left are for investment, the boxes on the right for financing. In each box we have posed a question and, where appropriate, given examples of financial ratios or other measures that the financial manager can use to answer the question. For example, the bottom box on the far left of Figure 4.1 asks about efficient use of assets. Three financial ratios that measure asset efficiency are turnover ratios for assets, inventory, and accounts receivable.

FIGURE 4.1 An organization chart for financial ratios. The figure shows how common financial ratios and other measures relate to shareholder value.

Shareholder Value How much value has been generated?

Turnover ratios for assets, inventory, and receivables

Efficient use of assets? Profits from sales?

Operating profit margin

Prudent financial leverage?

Sufficient liquidity for the coming year?

Current, quick, and cash ratios

Debt ratios Interest coverage ratios

Economic value added (EVA) Returns on capital, assets, and equity

How profitable? How can the firm safely finance future growth?

Investment Financing

Market value added Market-to-book ratio

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Chapter 4 Measuring Corporate Performance 85

The two bottom boxes on the right ask whether financial leverage (the amount of debt financing) is prudent and whether the firm has enough liquidity for the coming year. The ratios for tracking financial leverage include debt ratios, such as the ratio of debt to equity, and interest coverage ratios. The ratios for liquidity are the current, quick, and cash ratios.

We will explain how to calculate and interpret these and the other ratios in Figure 4.1 . For now you can read the figure as an organization chart that locates some important financial ratios and shows how they relate to the objective of shareholder value.

Now we start at the top of the figure. Our first task is to measure value. We will explain market capitalization, market value added, and the market-to-book ratio.

4.2 Measuring Market Value and Market Value Added Twenty years have passed since your introductory finance class. You are well into your career, and Home Depot is on your mind. Perhaps you are a mutual fund manager trying to decide whether to allocate $25 million of new money to Home Depot stock. Perhaps you are a major shareholder pondering a sellout. You could be an investment banker seeking business from Home Depot or a bondholder concerned with Home Depot’s credit standing. You could be the treasurer or CFO of Home Depot or of one of its competitors. You want to understand Home Depot’s value and financial perfor- mance. How would you start?

Home Depot’s common stock closed fiscal 2012 at a price of $67.30 per share. There were 1,754 million shares outstanding, so Home Depot’s market capitalization or “market cap” was $67.30  ×  1,754  =  $118,044 million, or nearly $120 billion. This is a big number, of course, but Home Depot is a big company. Home Depot’s share- holders have, over the years, invested billions in the company. Therefore, you decide to compare Home Depot’s market capitalization to the book value of Home Depot’s equity. The book value measures shareholders’ cumulative investment in the firm.

You turn to Home Depot’s income statement and balance sheet, which are repro- duced in Tables 4.1 and 4.2 . 1 At the end of 2012, the book value of Home Depot’s equity was $17,777 million. Therefore, Home Depot’s market value added, the dif- ference between the market value of the firm’s shares and the amount of money that shareholders have invested in the firm, was $118,044  −  $17,777  =  $100,267 million.

market capitalization Total market value of equity, equal to share price times number of shares outstanding.

market value added Market capitalization minus book value of equity.

1 For convenience the statements are repeated from Chapter 3. We are pretending that you actually had these statements on February 3, 2013, the close of Home Depot’s fiscal year. They were not published until March.

$ Millions

Net sales 74,754 Cost of goods sold 48,912 Selling, general, & administrative expenses 16,305 Depreciation 1,684 Earnings before interest and income taxes (EBIT) 7,853 Interest expense 632 Taxable income 7,221 Taxes 2,686 Net income 4,535 Allocation of net income Dividends 1,743 Addition to retained earnings 2,792

TABLE 4.1 Income statement for Home Depot, 2012

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86 Part One Introduction

In other words, Home Depot shareholders have contributed nearly $20 billion and ended up with shares worth $120 billion. They have accumulated $100 billion in market value added.

The consultancy firm EVA Dimensions calculates market value added for a large sample of U.S. companies. Table 4.3 shows a few of the firms from EVA’s list. They include some of the most and least successful companies as well as an old friend from Chapter 1, FedEx. Apple heads the group. It has created $237 billion of wealth for its shareholders. Bank of America is near the bottom of the class: The market value of its shares is $133 billion less than the amount of shareholders’ money invested in the firm.

The top-listed companies in Table 4.3 are large firms. Their managers have lots of assets to work with. A small firm could not hope to create so much extra value. There- fore, financial managers and analysts also like to calculate how much value has been added for each dollar that shareholders have invested. To do this, they compute the

End of Fiscal End of Fiscal

Assets 2012 2011 Liabilities and Shareholders’ Equity 2012 2011

Current assets Cash and marketable securities 2,494 1,987 Current liabilities Receivables 1,395 1,252 Debt due for repayment 1,321 30 Inventories 10,710 10,360 Accounts payable 8,871 8,173 Other current assets 773 866 Other current liabilities 1,270 1,183 Total current assets 15,372 14,465 Total current liabilities 11,462 9,386

Fixed assets Long-term debt 9,475 10,798 Tangible fi xed assets Deferred income taxes 319 212 Property, plant, and equipment 38,491 37,059 Other long-term liabilities 2,051 2,161 Less accumulated depreciation 14,422 12,738 Net tangible fi xed assets 24,069 24,321 Total liabilities 23,307 22,557

Intangible asset (goodwill) 1,170 1,267 Shareholders’ equity Long-term investments 140 138 Common stock and other

paid-in capital 8,433 7,649

Other assets 333 551 Retained earnings 20,038 17,246 Treasury stock - 10,694 - 6,710 Total assets   41,084 40,742 Total shareholders’ equity 17,777 18,185

Total liabilities and shareholders’ equity

41,084 40,742

Note: Column sums subject to rounding error.

TABLE 4.2 Home Depot’s balance sheet (figures in $ millions)

Market Value Added

Market-to- Book Ratio

Market Value Added

Market-to- Book Ratio

Apple $ 237,190 2.91 FedEx $8,634 1.21 Google 208,248 5.84 U.S. Steel − 9,680 0.32 ExxonMobil 194,548 1.66 Xerox − 12,230 0.66 Microsoft 180,808 5.31 Time Warner − 21,204 0.81 Walmart 173,285 2.15 Ford − 24,458 0.29 Coca-Cola 143,347 3.46 Bank of America − 133,278 0.51

Source: We are grateful to EVA Dimensions for providing these statistics.

TABLE 4.3 Stock market measures of company performance, June 2013. Companies are ranked by market value added (dollar values in millions).

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Chapter 4 Measuring Corporate Performance 87

ratio of market value to book value. For example, Home Depot’s market-to-book ratio at the end of its 2012 fiscal year was 2

Market-to-book ratio = market value of equity

book value of equity =

$118,044

$17,777 = 6.6

In other words, Home Depot has multiplied the value of its shareholders’ investment 6.6 times.

Table 4.3 also shows a sample of market-to-book ratios for June 2013. Notice that Microsoft has a much higher market-to-book ratio than Exxon. But Exxon’s market value added is higher because of its larger scale.

2 The market-to-book ratio can also be calculated by dividing stock price by book value per share.

market-to-book ratio Ratio of market value of equity to book value of equity.

Shares of Notung Cutlery Corp. closed 2013 at $75 per share. Notung had 14.5 million shares outstanding. The book value of equity was $610 million. Compute Notung’s market capitalization, market value added, and market- to-book ratio.

Self-Test 4.1

The market-value performance measures in Table 4.3 have three drawbacks. First, the market value of the company’s shares reflects investors’ expectations about future per- formance. Investors pay attention to current profits and investment, of course, but they also avidly forecast investment and growth. Second, market values fluctuate because of many risks and events that are outside the financial manager’s control. Thus, market values are noisy measures of how well the corporation’s management is performing. Third, you can’t look up the market value of privately owned companies whose shares are not traded. Nor can you observe the market value of divisions or plants that are parts of larger companies. You may use market values to satisfy yourself that Home Depot as a whole has performed well, but you can’t use them to drill down to compare the performance of the lumber and home improvement divisions. To do this, you need accounting measures of profitability. We start with economic value added (EVA).

4.3 Economic Value Added and Accounting Rates of Return When accountants draw up an income statement, they start with revenues and then deduct operating and other costs. But one important cost is not included: the cost of the capital the firm employs. Therefore, to see whether the firm has truly created value, we need to measure whether it has earned a profit after deducting all costs, including the cost of its capital.

Recall from Chapters 1 and 2 that the cost of capital is the minimum acceptable rate of return on capital investment. It is an opportunity cost of capital, because it equals the expected rate of return on opportunities open to investors in financial markets. The firm creates value only if it can earn more than its cost of capital, that is, more than its investors can earn by investing on their own.

The profit after deducting all costs, including the cost of capital, is called the company’s economic value added or EVA. The term “EVA” was coined by Stern Stewart & Co., which did much to develop and promote the concept. EVA is also called residual income.

economic value added (EVA) Net income minus a charge for the cost of capital employed. Also called residual income.

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88 Part One Introduction

In calculating EVA, it’s customary to take account of all the long-term capital contributed by investors in the corporation. That means including bonds and other long-term debt as well as equity capital. Total long-term capital, usually called total capitalization, is the sum of long-term debt and shareholders’ equity.

At the end of 2011 Home Depot’s total capitalization amounted to $28,983 million, the sum of $10,798 million of long-term debt and $18,185 million of shareholders’ equity. This was the cumulative amount that had been invested by Home Depot’s debt and equity investors. Home Depot’s cost of capital was about 8%. 3 So we can convert the cost of capital into dollars by multiplying total capitalization by 8%: .08  ×  $28,983  million  =  $2,319 million. To satisfy its debt and equity investors, Home Depot needed to earn total income of $2,319 million.

Now we can compare this figure with the income that Home Depot actually gener- ated for its debt and equity investors. In 2012 debt investors received interest income of $632 million. The after-tax equivalent, using Home Depot’s 35% tax rate, is (1  −   .35)  ×  632  =  $411 million. 4 Net income to shareholders was $4,535 million. Therefore, Home Depot’s after-tax interest and net income totaled 411  +   4,535  =  $4,946 million. If you deduct the dollar cost of capital from this figure, you can see that the company earned 4,946  −  2,319  =  $2,627 million more than investors required. This was Home Depot’s EVA or residual income:

EVA = after-tax interest + net income - (cost of capital × total capitalization)

= 411 + 4,535 - 2,319 = $2,627 million

The sum of Home Depot’s net income and after-tax interest is its after-tax operat- ing income. This is what Home Depot would earn if it had no debt and could not take interest as a tax-deductible expense. After-tax operating income is what the company would earn if it were all-equity-financed. In that case it would have no (after-tax) interest expense and all operating income would go to shareholders.

Thus EVA also equals:

EVA = after-tax operating income - (cost of capital × total capitalization)

= 4,946 - 2,319 = $2,627 million

Of course Home Depot and its competitors do use debt financing. Nevertheless, EVA comparisons are more useful if focused on operating income, which is not affected by interest tax deductions.

Table 4.4 shows estimates of EVA for our sample of large companies. ExxonMobil heads the list. It earned over $33 billion more than was needed to cover its cost of capital. By contrast, Bank of America was a laggard. Although it earned an accounting profit of $3.6 billion, this figure was calculated before deducting the cost of capital. After deducting the cost of capital, the company made an EVA loss of $13 billion.

Notice how the cost of capital differs across the 12 firms in Table 4.4 . The varia- tion is due to differences in business risk. Relatively safe companies like Walmart and Coca-Cola tend to have low costs of capital. Riskier companies like Xerox and espe- cially Google have high costs of capital.

EVA, or residual income, is a better measure of a company’s performance than is accounting income. Accounting income is calculated after deducting

3 This is an after-tax weighted-average cost of capital, or WACC. A company’s WACC depends on the risk of its business. The WACC is almost the same as the opportunity cost of capital, but with the cost of debt calculated after tax. We will explain WACC and how to calculate it in Chapter 13. 4 Why do we take interest after tax? Remember from Chapter 3 that when a firm pays interest, it reduces its taxable income and therefore its tax bill. This tax saving, or tax shield, will vary across firms depending on the amounts of debt financing. But we want to focus here on operating results. To put all firms on a common basis, we subtract the interest tax shield from reported income, or, equivalently, we look at after-tax interest payments. By ignoring the tax shield, we calculate each firm’s income as if it had no debt outstanding and shareholders got the (after-tax) interest. To be consistent, the cost of capital is defined as an after-tax weighted-average cost of capital (WACC). We have more to say about these issues in Chapters 13 and 16.

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Chapter 4 Measuring Corporate Performance 89

all costs except the cost of capital. By contrast, EVA recognizes that companies need to cover their opportunity costs before they add value.

EVA makes the cost of capital visible to operating managers. There is a clear target: Earn at least the cost of capital on assets employed. A plant or divisional manager can improve EVA by reducing assets that aren’t making an adequate contribution to prof- its. Evaluating performance by EVA pushes managers to flush out and dispose of such underutilized assets. Therefore, a growing number of firms now calculate EVA and tie managers’ compensation to it.

1. Operating Income *

2. Cost of Capital, %

3. Total Capitalization

4. EVA  =   1  −  (2  ×  3)

5. ROC, %  =  1  ÷  3

ExxonMobil $ 44,852 4.2 $ 280,152 33,086 16.0 Apple 35,458 8.7 115,425 25,463 30.7 Microsoft 21,728 8.9 40,037 18,165 54.3 Walmart 17,380 3.8 152,323 11,653 11.4 Google 12,140 10.3 41,935 7,812 29.0 Coca-Cola 8,614 3.9 57,853 6,352 14.9 Ford 3,865 5.2 32,755 2,149 11.8 FedEx 2,381 4.9 39,030 468 6.1 U.S. Steel 116 4.7 14,508 − 569 0.8 Xerox 1,375 6.4 36,076 − 927 3.8 Time Warner 3,874 5.7 113,954 − 2,667 3.4 Bank of America 3,643 5.9 280,194 − 13,001 1.3

*Net income plus after-tax interest. Source: We are grateful to EVA Dimensions for providing these statistics.

TABLE 4.4 EVA and ROC, June 2013. Companies are ranked by EVA (dollar values in millions).

Roman Holidays Inc. had operating income of $30 million on a start-of-year total capitalization of $188 million. Its cost of capital was 11.5%. What was its EVA?

Self-Test 4.2

Accounting Rates of Return EVA measures how many dollars a business is earning after deducting the cost of capital. Other things equal, the more assets the manager has to work with, the greater the opportunity to generate a large EVA. The manager of a small division may be highly competent, but if that division has few assets, she is unlikely to rank high in the EVA stakes. Therefore, when comparing managers, it can be helpful to mea- sure the firm’s profits per dollar of assets. Three common measures are the return on capital (ROC), the return on equity (ROE), and the return on assets (ROA). These are called book rates of return, because they are based on accounting information.

Return on Capital (ROC) The return on capital is equal to after-tax operat- ing income divided by total capitalization. In 2012 Home Depot’s operating income was $4,946 million. It started the year with total capitalization (long-term debt plus shareholders’ equity) of $28,983 million. Therefore its return on capital (ROC) was 5

5 The numerator of Home Depot’s ROC is again its after-tax operating income, calculated by adding back after- tax interest to net income. More often than not, financial analysts forget that interest is tax-deductible and use pretax interest to calculate operating income. This complicates comparisons of ROC for companies that use dif- ferent fractions of debt financing. It also muddies comparisons of ROC with the after-tax weighted-average cost of capital (WACC). We cover WACC in Chapter 13.

return on capital (ROC) Net income plus after-tax interest as a percentage of long-term capital.

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90 Part One Introduction

ROC = after-tax operating income

total capitalization =

4,946

28,983 = .171, or 17.1%

As we noted earlier, Home Depot’s cost of capital was about 8%. This was the return that investors could have expected to earn at the start of 2012 if they invested their money in other companies or securities with the same risk as Home Depot’s busi- ness. So in 2012 the company earned 17.1  −  8.0  =  9.1% more than investors required.

When we calculated ROC, we compared a flow measure (income earned over the year) with a snapshot measure (capital at the start of the year). We therefore ignored the company’s additional financing and investment during that year. If the additional investment contributed a significant part of the year’s operating income, it may be better to divide by the average of the total capitalization at the beginning and end of the year. In the case of Home Depot, the company repaid long-term debt in 2012 and repurchased some of its stock. So it actually ended the year with less capital than it had at the start. Therefore, if we divide operating income by average capitalization, Home Depot’s ROC for 2012 increases slightly to

ROC = after-tax operating income

average total capitalization =

4,946 (28,983 + 27,252)/2

= .176, or 17.6%

Is one measure better than another? It is difficult to generalize, but if you would like to know more about when one might prefer to use average rather than start-of-year figures to calculate a financial ratio, the icon in the margin provides a link to a short discussion of the issue. 6

The last column in Table 4.4 shows ROC for our sample of well-known companies. Notice that Microsoft’s return on capital was 54.3%, over 45 percentage points above its cost of capital. Although Microsoft had a higher return on capital than ExxonMobil, it had a lower EVA. This was partly because it was more risky than Exxon and so had a higher cost of capital, but also because it had far fewer dollars invested than Exxon.

The four companies in Table 4.4 with negative EVAs all have ROCs less than their cost of capital. The spread between ROC and the cost of capital is really the same thing as EVA but expressed as a percentage return rather than in dollars.

Return on Assets (ROA) Return on assets (ROA) measures after-tax oper- ating income as a fraction of the firm’s total assets. Total assets (which equal total liabilities plus shareholders’ equity) are greater than total capitalization because total capitalization does not include current liabilities. For Home Depot, ROA was

Return on assets = after-tax operating income

total assets =

4,946

40,742 = .121, or 12.1%

Using average total assets, ROA was almost identical:

ROA = after-tax operating income

average total assets =

4,946 (40,742 + 41,084)/2

= .121, or 12.1%

For both ROA and ROC, we use after-tax operating income, which is calculated by adding after-tax interest to net income. We are again asking how profitable the com- pany would have been if it were all-equity-financed. This what-if calculation is help- ful when comparing the profitability of firms with different capital structures. The tax deduction for interest is often ignored, however, and operating income is calculated using pretax interest. Some financial analysts take no account of interest payments and measure ROA as net income for shareholders divided by total assets. This calculation is really —we were about to say “stupid,” but don’t want to offend anyone. This calcula- tion ignores entirely the income that the firm’s assets have generated for debt investors.

6 Sometimes it’s convenient to use a snapshot figure at the end of the year, although this procedure is not strictly correct.

return on assets (ROA) Net income plus after-tax interest as a percentage of total assets.

BEYOND THE PAGE

brealey.mhhe.com/ch04-01

Average or start-of- year assets?

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Chapter 4 Measuring Corporate Performance 91

Return on Equity (ROE) We measure the return on equity (ROE) as the income to shareholders per dollar that they have invested. Home Depot had net income of $4,535 million in fiscal 2012 and shareholders’ equity of $18,185 million at the start of the year. So Home Depot’s ROE was

Return on equity = ROE = net income

equity =

4,535

18,185 = .249, or 24.9%

Using average equity, ROE was

ROE = net income

average equity =

4,535 (18,185 + 17,777)/2

= .252, or 25.2%

return on equity (ROE) Net income as a percentage of shareholders’ equity.

What is the difference between after-tax operating income and net income to shareholders? How is after-tax operating income calculated? Why is it useful in calculating EVA, ROC, and ROA?

Self-Test 4.3

Explain the differences between ROE, ROC, and ROA.

Self-Test 4.4

Problems with EVA and Accounting Rates of Return Rates of return and economic value added have some obvious attractions as measures of performance. Unlike market-value-based measures, they show current performance and are not affected by all the other things that move stock market prices. Also, they can be calculated for an entire company or for a particular plant or division. However, remember that both EVA and accounting rates of return are based on book (balance sheet) values for assets. Debt and equity are also book values. As we noted in the pre- vious chapter, accountants do not show every asset on the balance sheet, yet our calcu- lations take accounting data at face value. For example, we ignored the fact that Home Depot has invested large sums in marketing in order to establish its brand name. This brand name is an important asset, but its value is not shown on the balance sheet. If it were shown, the book values of assets, capital, and equity would increase, and Home Depot would not appear to earn such high returns.

EVA Dimensions, which produced the figures in Tables 4.3 and 4.4 , does make a number of adjustments to the accounting data. However, it is impossible to include the value of all assets or to judge how rapidly they depreciate. For example, did Microsoft really earn a return on capital of 54.3%? It’s difficult to say, because its investment over the years in operating systems and other software is not shown in the balance sheet and cannot be measured exactly.

Remember also that the balance sheet does not show the current market values of the firm’s assets. The assets in a company’s books are valued at their original cost less any depreciation. Older assets may be grossly undervalued in today’s market condi- tions and prices. So a high return on assets indicates that the business has performed well by making profitable investments in the past, but it does not necessarily mean that you could buy the same assets today at their reported book values. Conversely a low return suggests some poor decisions in the past, but it does not always mean that today the assets could be employed better elsewhere.

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92 Part One Introduction

4.4 Measuring Efficiency We began our analysis of Home Depot by calculating how much value that company has added for its shareholders and how much profit the company is earning after deducting the cost of the capital that it employs. We examined its rates of return on equity, capital, and total assets, which were all impressively high. Our next task is to probe a little deeper to understand the reasons for Home Depot’s success. What factors contribute to this firm’s overall profitability? One is the efficiency with which it uses its many types of assets.

Asset Turnover Ratio The asset turnover, or sales-to-assets, ratio shows how much sales are generated by each dollar of total assets, and therefore it measures how hard the firm’s assets are working. For Home Depot, each dollar of assets produced $1.83 of sales:

Asset turnover = sales

total assets at start of year =

74,754

40,742 = 1.83

Like some of our profitability ratios, the sales-to-assets ratio compares a flow mea- sure (sales over the entire year) to a snapshot measure (assets on one day). Therefore, financial managers and analysts often calculate the ratio of sales over the entire year to the average level of assets over the same period. In this case, the value is about the same:

Asset turnover = sales

average total assets =

74,754 (40,742 + 41,084)/2

= 1.83

The asset turnover ratio measures how efficiently the business is using its entire asset base. But you also might be interested in how hard particular types of assets are being put to use. Below are a couple of examples.

Inventory Turnover Efficient firms don’t tie up more capital than they need in raw materials and finished goods. They hold only a relatively small level of inventories of raw materials and finished goods, and they turn over those inventories rapidly.

The balance sheet shows the cost of inventories rather than the amount that the fin- ished goods will eventually sell for. So it is usual to compare the level of inventories with the cost of goods sold rather than with sales. In Home Depot’s case,

Inventory turnover = cost of goods sold

inventory at start of year =

48,912

10,360 = 4.7

Another way to express this measure is to look at how many days of output are represented by inventories. This is equal to the level of inventories divided by the daily cost of goods sold:

Average days in inventory = inventory at start of year

daily cost of goods sold =

10,360

48,912/365 = 77 days

You could say that on average Home Depot has sufficient inventories to maintain oper- ations for 77 days.

In Chapter 20 we will see that many firms have managed to increase their inventory turnover in recent years. Toyota has been the pioneer in this endeavor. Its just-in-time inventory system ensures that auto parts are delivered exactly when they are needed. Toyota now keeps only about one month’s supply of parts and finished cars in inven- tory and turns over its inventory about 11 times a year.

Receivables Turnover Receivables are sales for which you have not yet been paid. The receivables turnover ratio measures the firm’s sales as a multiple of its receivables. For Home Depot,

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Chapter 4 Measuring Corporate Performance 93

Receivables turnover = sales

receivables at start of year =

74,754

1,252 = 60

If customers are quick to pay, unpaid bills will be a relatively small proportion of sales and the receivables turnover will be high. Therefore, a high ratio often indicates an efficient credit department that is quick to follow up on late payers. Sometimes, however, a high ratio may indicate that the firm has an unduly restrictive credit policy and offers credit only to customers who can be relied on to pay promptly. 7

Another way to measure the efficiency of the credit operation is by calculating the average length of time for customers to pay their bills. The faster the firm turns over its receivables, the shorter the collection period. On average, Home Depot’s customers pay their bills in about 6.1 days:

Average collection period = receivables at start of year

average daily sales =

1,252

74,754/365 = 6.1 days

7 Where possible, it makes sense to look only at credit sales. Otherwise, a high receivables turnover ratio (or, equivalently, a low average collection period) might simply indicate that a small proportion of sales are made on credit. For example, if a retail customer pays cash for a purchase at Home Depot, that transaction will have a collection period of zero, regardless of any policies of the firm’s credit department.

The average collection period measures the number of days it takes Home Depot to collect its bills. But Home Depot also delays paying its own bills. Use the information in Tables 4.1 and 4.2 to calculate the average number of days that it takes Home Depot to pay its bills.

Self-Test 4.5

The receivables turnover ratio and the inventory turnover ratio may help to highlight particular areas of inefficiency, but they are not the only possible indicators. For exam- ple, a retail chain might compare its sales per square foot with those of its competitors, an airline might look at revenues per passenger-mile, and a law firm might look at rev- enues per partner. A little thought and common sense should suggest which measures are likely to produce the most helpful insights into your company’s efficiency.

4.5 Analyzing the Return on Assets: The Du Pont System We have seen that every dollar of Home Depot’s assets generates $1.83 of sales. But Home Depot’s success depends not only on the efficiency with which it uses its assets to generate sales but also on how profitable those sales are. This is measured by Home Depot’s profit margin.

Profit Margin The profit margin measures the proportion of sales that finds its way into profits. It is sometimes defined as

Profit margin = net income

sales =

4,535

74,754 = .061, or 6.1%

This definition can be misleading. When companies are partly financed by debt, a portion of the revenue produced by sales must be paid as interest to the firm’s lend- ers. So profits from the firm’s operations are divided between the debtholders and the shareholders. We would not want to say that a firm is less profitable than its rivals

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94 Part One Introduction

simply because it employs debt finance and pays out part of its income as interest. Therefore, when we are calculating the profit margin, it makes sense to add back the after-tax debt interest to net income. This leads us again to after-tax operating income and to the operating profit margin:

Operating profit margin = after-tax operating income

sales

= 4,535 + (1 - .35) × 632

74,754 = .066, or 6.6%

The Du Pont System We calculated earlier that Home Depot has earned a return of 12.1% on its assets. The following equation shows that this return depends on two factors—the sales that Home Depot generates from its assets (asset turnover) and the profit that it earns on each dollar of sales (operating profit margin):

Return on assets = after-tax operating income

assets (4.1)

=

sales

assets ×

after-tax operating income

sales

c c asset turnover operating profit margin

This breakdown of ROA into the product of turnover and margin is often called the Du Pont formula, after the chemical company that popularized the procedure. In Home Depot’s case the formula gives the following breakdown of ROA:

ROA = asset turnover × operating profit margin = 1.83 × .066 = .121

The Du Pont formula is a useful way to think about a company’s strategy. For example, a retailer may strive for high turnover at the expense of a low profit margin (a “Walmart strategy”), or it may seek a high profit margin even if that results in low turnover (a “Bloomingdales strategy”). You would naturally prefer both high profit margin and high turnover, but life isn’t that easy. A high-price and high-margin strat- egy will typically result in lower sales per dollar of assets, so firms must make trade- offs between these goals. The Du Pont formula can help sort out which strategy the firm is pursuing.

All firms would like to earn a higher return on their assets, but their ability to do so is limited by competition. The Du Pont formula helps to identify the constraints that firms face. Fast-food chains, which have high asset turnover, tend to operate on low margins. Classy hotels have relatively low turnover ratios but tend to compensate with higher margins.

operating profit margin After-tax operating income as a percentage of sales.

Du Pont formula ROA equals the product of asset turnover and operating profit margin.

Example 4.1 Turnover versus Margin Firms often seek to improve their profit margins by acquiring a supplier. The idea is to capture the supplier’s profit as well as their own. Unfortunately, unless they have some special skill in running the new business, they are likely to find that any gain in profit margin is offset by a decline in asset turnover.

A few numbers may help to illustrate this point. Table 4.5 shows the sales, profits, and assets of Admiral Motors and its components supplier, Diana Corporation. Both earn a 10% return on assets, though Admiral has a lower operating profit mar- gin (20% versus Diana’s 25%). Since all of Diana’s output goes to Admiral, Admi- ral’s management reasons that it would be better to merge the two companies.

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Chapter 4 Measuring Corporate Performance 95

Millions of Dollars

Sales Profi ts Assets Asset

Turnover Profi t

Margin ROA

Admiral Motors $20 $4 $40 0 .50 20% 10% Diana Corp. 8 2 20 0 .40 25 10 Diana Motors (the merged fi rm) 20 6 60 0 .33 30 10

TABLE 4.5 Merging with suppliers or customers will generally increase the profit margin, but this will be offset by a reduction in asset turnover

That way, the merged company would capture the profit margin on both the auto components and the assembled car.

The bottom row of Table 4.5 shows the effect of the merger. The merged firm does indeed earn the combined profits. Total sales remain at $20 million, however, because all the components produced by Diana are used within the company. With higher profits and unchanged sales, the profit margin increases. Unfortu- nately, the asset turnover is reduced by the merger since the merged firm has more assets. This exactly offsets the benefit of the higher profit margin. The return on assets is unchanged.

Figure 4.2 shows evidence of the trade-off between turnover and profit margin. You can see that industries with high average turnover ratios tend to have lower average profit margins. Conversely, high margins are typically associated with low turnover. The classic examples here are electric or water utilities, which have enormous capital requirements and therefore low asset turnover ratios. However, they have extremely low marginal costs for each unit of additional output and therefore earn high markups. The two curved lines in the figure trace out the combinations of profit margin and turnover that result in an ROA of either 3% or 10%. Despite the enormous dispersion across industries in both margin and turnover, that variation tends to be offsetting, so for most industries the return on assets lies between 3% and 10%.

FIGURE 4.2 Profit margin and asset turnover for 43 industries for year ending March 2013

Source: U.S. Census Bureau, Quarterly Report for Manufacturing and Trade Corporations, First Quarter 2013 ( www.census.gov/econ/qfr ). This is an updated version of a fi gure that fi rst appeared in Thomas I. Selling and Clyde P. Stickney, “The Effects of Business Environments and Strategy on a Firm’s Rate of Return on Assets.” Financial Analysts Journal, January–February 1989, pp. 43–52.

ROA = 3%

Asset turnover 0.100 0.600 1.100 1.600 2.100 2.600 3.6003.100 0

50

100

150

200

250

300

Pharmaceuticals

ROA = 10%

Wholesalers—nondurable

P ro

fi t

m ar

g in

( %

)

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96 Part One Introduction

4.6 Measuring Financial Leverage As Figure 4.1 indicates, shareholder value depends not only on good investment deci- sions and profitable operations but also on sound financing decisions. We look first at measures of financial leverage and then at measures of liquidity.

When a firm borrows money, it promises to make a series of interest payments and then to repay the amount that it has borrowed. If profits rise, the debtholders continue to receive only the fixed interest payment, so all the gains go to the shareholders. Of course, the reverse happens if profits fall. In this case shareholders bear most of the pain. If times are sufficiently hard, a firm that has borrowed heavily may not be able to pay its debts. The firm is then bankrupt, and shareholders lose most or all of their entire investment.

Because debt increases returns to shareholders in good times and reduces them in bad times, it is said to create financial leverage. Leverage ratios measure how much financial leverage the firm has taken on. CFOs keep an eye on leverage ratios to ensure that lenders are happy to continue to take on the firm’s debt.

Debt Ratio Financial leverage is usually measured by the ratio of long-term debt to total long-term capital (that is, to total capitalization). Here long-term debt should include not just bonds or other borrowing but also financing from long-term leases. 8 For Home Depot,

Long-term debt ratio = long-term debt

long-term debt + equity =

9,475

9,475 + 17,777 = .35, or 35%

This means that 35 cents of every dollar of long-term capital is in the form of debt. Leverage may also be measured by the debt-equity ratio. For Home Depot,

Long-term debt-equity ratio = long-term debt

equity =

9,475

17,777 = .53, or 53%

For highly leveraged companies the difference between these two ratios is large. For example, a company financed two-thirds with debt and one-third with equity has a long-term debt ratio of 67% (2/3) and a debt-equity ratio of 2. Sometimes you see projects such as oil pipelines financed with 90% debt and 10% equity. In that case the debt-equity ratio is 90/10  =  9.

The long-term debt ratio for the average U.S. manufacturing company is about 30%, but some companies deliberately operate at much higher debt levels. For exam- ple, in Chapter 21 we will look at leveraged buyouts (LBOs). Firms that are acquired in a leveraged buyout usually issue large amounts of debt. When LBOs first became popular in the 1990s, these companies had average debt ratios of about 90%. Many of them flourished and paid back their debtholders in full; others were not so fortunate.

8 A finance lease is a long-term rental agreement that commits the firm to make regular payments. This commit- ment is just like the obligation to make payments on an outstanding loan.

The Du Pont formula (Equation 4.1) seems to suggest that companies with above-average asset turnover ratios generally will have above-average ROAs. Why may this not be so?

Self-Test 4.6

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Chapter 4 Measuring Corporate Performance 97

Notice that debt ratios make use of book (accounting) values rather than market values. 9 In principle, lenders should be more interested in the market value of the com- pany, which reflects the actual value of the company’s assets and the actual cash flows those assets will produce. If the market value of the company covers its debts, then lenders should get their money back. Thus you would expect to see the debt ratio com- puted using the market values of debt and equity. Yet book debt ratios are used almost universally.

Does use of book rather than market leverage ratios matter much? Perhaps not; after all, the market value of the firm includes the value of intangible assets generated by research and development, advertising, staff training, and so on. These assets are not easy to sell, and if the company falls on hard times, their value may disappear altogether. Thus, when banks demand that a borrower keep within a maximum debt ratio, they usually define that ratio in terms of book values and they ignore the intan- gible assets that contribute to the market value of the firm but are not shown on the balance sheet.

Notice also that these measures of leverage ignore short-term debt. That probably makes sense if the short-term debt is temporary or is matched by similar holdings of cash, but if the company is a regular short-term borrower, it may be preferable to widen the definition of debt to include all liabilities. In this case,

Total debt ratio = total liabilities

total assets =

23,307

41,084 = .57, or 57%

Therefore, Home Depot is financed 57% with long- and short-term debt and 43% with equity. 10 We could also say that its ratio of total debt to equity is 23,307/17,777  =  1.31.

Managers sometimes refer loosely to a company’s debt ratio, but we have just seen that the debt ratio may be measured in several different ways. For example, Home Depot has a debt ratio of .35 (the long-term debt ratio) and also .57 (the total debt ratio). This is not the first time we have come across several ways to define a financial ratio. There is no law stating how a ratio should be defined. So be warned: Do not use a ratio without understanding how it has been calculated.

Times Interest Earned Ratio Another measure of financial leverage is the extent to which interest obligations are covered by earnings. Banks prefer to lend to firms with earnings that cover interest payments with room to spare. Interest coverage is measured by the ratio of earnings before interest and taxes (EBIT) to interest pay- ments. For Home Depot,

Times interest earned = EBIT

interest payments =

7,853

632 = 12.4

By this measure, Home Depot is conservatively financed. Sometimes lenders are con- tent with coverage ratios as low as 2 or 3.

The regular interest payment is a hurdle that companies must keep jumping if they are to avoid default. The interest coverage ratio measures how much clear air there is between hurdle and hurdler. The ratio is only part of the story, however. For example, it doesn’t tell us whether Home Depot is generating enough cash to repay its debt as it becomes due.

Cash Coverage Ratio As we explained in Chapter 3, depreciation is not a cash expense. Depreciation is deducted when calculating the firm’s earnings, even though

9 In the case of leased assets, accountants estimate the value of the lease commitments. In the case of long-term debt, they simply show the face value, which can be very different from market value. 10 In this case, the 57% of debt includes other liabilities, including accounts payable and other current liabilities.

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98 Part One Introduction

no cash goes out the door. Suppose we add back depreciation to EBIT in order to cal- culate operating cash flow. We then calculate a cash coverage ratio. 11 For Home Depot,

Cash coverage ratio = EBIT + depreciation

interest payments =

7,853 + 1,684

632 = 15.1

11 Depreciation of intangible assets is called amortization and is therefore also added back to EBIT. This gives EBIT  +  depreciation  +  amortization  =  EBITDA. EBITDA coverage ratios are common. You may also encoun- ter still other ratios, in addition to the standard ratios covered here. You will see some examples in Table 4.7 .

A firm repays $10 million face value of outstanding debt and issues $10 mil- lion of new debt with a lower rate of interest. What happens to its long-term debt ratio? What happens to its times interest earned and cash coverage ratios?

Self-Test 4.7

Leverage and the Return on Equity When the firm raises cash by borrowing, it must make interest payments to its lenders. This reduces net profits. On the other hand, if a firm borrows instead of issuing equity, it has fewer equityholders to share the remaining profits. Which effect dominates? An extended version of the Du Pont formula helps us answer this question. It breaks down the return on equity (ROE) into four parts:

ROE = net income

equity =

assets

equity ×

sales

assets ×

after-tax operating income

sales ×

net income

after-tax

c c c operating income

leverage asset operating c ratio turnover profit margin “debt burden”

(4.2)

Notice that the product of the two middle terms in Equation 4.2 is the return on assets. It depends on the firm’s production and marketing skills and is unaffected by the firm’s financing mix. 12 However, the first and fourth terms do depend on the debt- equity mix. The first term, assets/equity, which we call the leverage ratio, can be expressed as (equity  +  liabilities)/equity, which equals 1  +  total-debt-to-equity ratio. The last term, which we call the “debt burden,” measures the proportion by which interest expense reduces profits.

Suppose that the firm is financed entirely by equity. In this case, both the lever- age ratio and the debt burden are equal to 1, and the return on equity is identical to the return on assets. If the firm borrows, however, the leverage ratio is greater than 1 (assets are greater than equity) and the debt burden is less than 1 (part of the profits is absorbed by interest). Thus leverage can either increase or reduce return on equity. In fact, we will see in Chapter 16 that leverage increases ROE when the firm’s return on assets is higher than the interest rate it pays on its debt. Since Home Depot’s return on capital exceeds the interest rate on its debt, return on equity is higher than return on capital.

12 Again, we use after-tax operating income, which is the sum of net income and after-tax interest.

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Chapter 4 Measuring Corporate Performance 99

4.7 Measuring Liquidity If you are extending credit to a customer or making a short-term bank loan, you are interested in more than the borrower’s financial leverage. You want to know whether the company can lay its hands on the cash to repay you. That is why credit analysts and bankers look at several measures of liquidity. Liquid assets can be converted into cash quickly and cheaply.

Think, for example, what you would do to meet a large unexpected bill. You might have some money in the bank or some investments that are easily sold, but you would not find it so easy to turn your old sweaters into cash. Companies, likewise, own assets with different degrees of liquidity. For example, accounts receivable and inventories of finished goods are generally quite liquid. As inventories are sold off and custom- ers pay their bills, money flows into the firm. At the other extreme, real estate may be quite illiquid. It can be hard to find a buyer, negotiate a fair price, and close a deal at short notice.

There is another reason to focus on liquid assets: Their book (balance sheet) values are usually reliable. The book value of a catalytic cracker may be a poor guide to its true value, but at least you know what cash in the bank is worth.

Liquidity ratios also have some less desirable characteristics. Because short-term assets and liabilities are easily changed, measures of liquidity can rapidly become outdated. You might not know what the catalytic cracker is worth, but you can be fairly sure that it won’t disappear overnight. Cash in the bank can disappear in seconds.

Also, assets that seem liquid sometimes have a nasty habit of becoming illiquid. This happened during the subprime mortgage crisis in 2008. Some financial insti- tutions had set up funds known as structured investment vehicles (SIVs) that issued short-term debt backed by residential mortgages. As mortgage default rates began to climb, the market in this debt dried up and dealers became very reluctant to quote a price.

Bankers and other short-term lenders applaud firms that have plenty of liquid assets. They know that when they are due to be repaid, the firm will be able to get its hands on the cash. But more liquidity is not always a good thing. For example, efficient firms do not leave excess cash in their bank accounts. They don’t allow customers to postpone paying their bills, and they don’t leave stocks of raw materials and finished goods lit- tering the warehouse floor. In other words, high levels of liquidity may indicate sloppy use of capital. Here, EVA can highlight the problem, because it penalizes managers who keep more liquid assets than they really need.

Net Working Capital to Total Assets Ratio Current assets include cash, marketable securities, inventories, and accounts receivable. Current assets are mostly liquid. The difference between current assets and current liabilities is known as net working capital. It roughly measures the company’s potential net reservoir of cash. Since current assets usually exceed current liabilities, net working capital is usually positive. For Home Depot,

Net working capital = 15,372 - 11,462 = $3,910 million

liquidity Access to cash or assets that can be turned into cash on short notice.

a. Sappy Syrup has a profit margin below the industry average, but its ROA equals the industry average. How is this possible?

b. Sappy Syrup’s ROA equals the industry average, but its ROE exceeds the industry average. How is this possible?

Self-Test 4.8

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100 Part One Introduction

Home Depot’s net working capital was 10% of total assets:

Net working capital

Total assets =

3,910

41,084 = .10, or 10%

Current Ratio The current ratio is just the ratio of current assets to current liabilities:

Current ratio = current assets

current liabilities =

15,372

11,462 = 1.34

Home Depot has $1.34 in current assets for every dollar in current liabilities. Changes in the current ratio can be misleading. For example, suppose that a com-

pany borrows a large sum from the bank and invests it in marketable securities. Current liabilities rise and so do current assets. If nothing else changes, net working capital is unaffected but the current ratio changes. For this reason it is sometimes preferable to net short-term investments against short-term debt when calculating the current ratio.

Quick (Acid-Test) Ratio Some current assets are closer to cash than others. If trouble comes, inventory may not sell at anything above fire-sale prices. (Trouble typically comes because the firm can’t sell its inventory of finished products for more than production cost.) Thus managers often exclude inventories and other less liq- uid components of current assets when comparing current assets to current liabilities. They focus instead on cash, marketable securities, and bills that customers have not yet paid. This results in the quick ratio:

Quick ratio = cash + marketable securities + receivables

current liabilities =

2,494 + 1,395

11,462 = .34

Cash Ratio A company’s most liquid assets are its holdings of cash and market- able securities. That is why analysts also look at the cash ratio:

Cash ratio = cash + marketable securities

current liabilities =

2,494

11,462 = .22

A low cash ratio may not matter if the firm can borrow on short notice. Who cares whether the firm has actually borrowed from the bank or whether it has a guaranteed line of credit that lets it borrow whenever it chooses? None of the standard measures of liquidity takes the firm’s “reserve borrowing power” into account.

a. A firm has $1.2 million in current assets and $1 million in current liabilities. If it uses $.5 million of cash to pay off some of its accounts payable, what will happen to the current ratio? What happens to net working capital?

b. A firm uses cash on hand to pay for additional inventories. What will hap- pen to the current ratio? To the quick ratio?

Self-Test 4.9

4.8 Interpreting Financial Ratios We have shown how to calculate some common summary measures of Home Depot’s performance and financial condition. These are summarized in Table 4.6 .

Now that you have calculated these measures, you need some way to judge whether they are a matter for concern or congratulation. In some cases there may be a natural

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Chapter 4 Measuring Corporate Performance 101

benchmark. For example, if a firm has negative value added or a return on capital that is less than the cost of that capital, it is not creating wealth for its shareholders.

But what about some of our other measures? There is no right level for, say, the asset turnover or profit margin, and if there were, it would almost certainly vary from year to year and industry to industry. When assessing company performance, manag- ers usually look first at how the financial ratios have changed over time, and then they look at how their measures stack up in comparison with companies in the same line of business.

We will first compare Home Depot’s position in 2012 with its performance in ear- lier years. For example, Figure 4.3 plots Home Depot’s return on assets since 2000. Between 2000 and 2008, Home Depot’s return on assets slumped from 15.5% to just over 6% before recovering. We know that ROA  =  asset turnover  ×  operating profit margin. So what accounted for the changes in ROA? Figure 4.3 shows that both the company’s ability to generate sales from its assets and its profit margin contributed to the fluctuations in ROA, but much of the recovery in the company’s fortune has been due to an increase in margins. Perhaps Home Depot has got a better grip on its costs, perhaps there has been less price pressure from competitors, or perhaps the company has moved into higher-margin products. You will need to dig deeper to fully under- stand the reasons for the recovery.

Performance Measures Market value added ($ millions) market value of equity  −  book value of equity $ 100,267 Market-to-book ratio market value of equity  ÷  book value of equity 6.6 Profi tability Measures Return on assets (ROA) after-tax operating income/total assets 12.1% Return on capital (ROC) after-tax operating income/(long-term debt  +  equity) 17.1% Return on equity (ROE) net income/equity 24.9% EVA * ($ millions) after-tax operating income  −  cost of capital  ×  capital $ 2,627 Operating profi t margin after-tax operating income/sales 6.6% Efficiency Measures Asset turnover sales/total assets at start of year 1.83 Receivables turnover sales/receivables at start of year 60 Average collection period (days) receivables at start of year/daily sales 6.1 Inventory turnover cost of goods sold/inventory at start of year 4.7 Days in inventory inventories at start of year/daily cost of goods sold 77 Leverage Measures Long-term debt ratio long-term debt/(long-term debt  +  equity) 35% Long-term debt-equity ratio long-term debt/equity 53% Total debt ratio total liabilities/total assets 57% Times interest earned EBIT/interest payments 12.4 Cash coverage ratio (EBIT  +  depreciation)/interest payments 15.1 Liquidity Measures Net working capital to assets net working capital/total assets 0.10 Current ratio current assets/current liabilities 1.34 Quick ratio (cash  +  marketable securities  +  receivables)/current liabilities 0.34 Cash ratio (cash  +  marketable securities)/current liabilities 0.22 Growth Measure Payout ratio dividends/earnings 0.38

*Authors’ calculation.

TABLE 4.6 Summary of Home Depot’s performance measures

You can find this spreadsheet in Connect.

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102 Part One Introduction

Managers also need to ask themselves how the company’s performance compares with that of its principal competitors. Table 4.7 sets out some key performance mea- sures for Home Depot and Lowe’s. Home Depot’s ROA is higher, due to its higher

FIGURE 4.3 Home Depot financial ratios over time

Home Depot Lowe’s

Performance Measures Market value added ($ millions) $ 100,267 $28,534 Market-to-book ratio 6.6 3.1

Profi tability Measures Return on assets (ROA) 12.1% 6.7% Return on capital (ROC) 17.1% 9.7% Return on equity (ROE) 24.9% 11.8% EVA* ($ millions) $ 2,627 $ 388 Operating profi t margin 6.6% 4.4%

Efficiency Measures Asset turnover 1.83 1.50 Receivables turnover 60 276 Average collection period (days) 6.1 1.3 Inventory turnover 4.7 4.0 Days in inventory 77 92

Leverage Measures Long-term debt ratio 35% 39% Long-term debt-equity ratio 53% 65% Total debt ratio 57% 58% Times interest earned 12.4 8.4 Cash coverage ratio 15.1 12.0

Liquidity Measures Net working capital to assets 0.10 0 .06 Current ratio 1.34 1.27 Quick ratio 0.34 0.11 Cash ratio 0.22 0.09

Growth Measure Payout ratio 0.38 0.38

TABLE 4.7 Selected financial measures for Home Depot and Lowe’s, 2012

20 00

20 01

20 02

20 03

20 04

20 05

20 06

20 07

20 08

20 09

20 10

20 11

20 12

0

2

4

6

8

10

12

14

16

18

ROA

P er

ce nt

Operating profit margin Asset turnover

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Chapter 4 Measuring Corporate Performance 103

BEYOND THE PAGE

brealey.mhhe.com/ch04-02

Financial ratios for U.S. companies

Food Beverage &

Tobacco Clothing Paper Chemicals Drugs Machinery

Computers &

Electronics Electrical Autos All

Manufacturing

ROA (%) 6.34 10.88 11.35 5.41 8.14 8.43 8.33 8.67 6.68 6.80 8.09 ROE (%) 13.22 22.85 19.44 11.64 17.05 16.75 17.80 14.48 11.64 18.11 16.38 Asset turnover 1.19 0.50 1.23 0.92 0.51 0.35 0.85 0.54 0.52 1.33 0.84 Operating profi t margin (%)

5.32 21.69 9.25 5.89 16.12 24.38 9.76 16.20 12.74 5.11 9.58

Receivables turnover

13.35 16.30 9.45 9.87 7.85 7.50 6.54 11.38 6.03 14.90 9.11

Inventory turnover

9.82 9.99 6.36 10.29 8.25 7.90 7.13 11.73 6.50 16.90 9.66

Long-term debt ratio

0.41 0.35 0.25 0.48 0.39 0.37 0.29 0.03 0.21 0.02 0.32

Times interest earned

4.28 5.34 6.60 2.77 3.59 3.22 6.25 5.82 4.53 4.99 4.71

Current ratio 1.41 1.04 2.37 1.54 1.03 0.89 1.34 1.61 1.14 1.39 1.36 Quick ratio 0.62 0.46 1.13 0.77 0.50 0.45 0.64 1.03 0.59 0.87 0.71 Payout ratio 0.38 0.48 0.35 0.51 0.51 0.52 0.32 0.31 0.58 0.19 0.38

Source: Authors’ calculations using data from U.S. Department of Commerce, Quarterly Financial Report for Manufacturing, Mining and Trade Corporations, March 2013. Available at www.census.gov/econ/qfr/current/qfr_pub.pdf .

TABLE 4.8 Financial ratios for major industry groups, 2012

asset turnover ratio and its better operating profit margin. The two companies have similar debt ratios, but, thanks to its greater profitability, Home Depot has the higher interest cover. Home Depot turns over its inventory more rapidly. However, its longer collection period seems to suggest that it is much less efficient in collecting its bills. This is actually an illusion. Lowe’s tends to sell its accounts receivable to other parties, and thus maintains lower receivables on its balance sheet. The lesson? Ratios can tip us off to differences in strategy as well as to emerging business strengths or problems, but you will generally have to probe further to fully understand the implications of the numbers.

Home Depot and Lowe’s are fairly close competitors, and it makes sense to com- pare their financial ratios. However, all financial ratios must be interpreted in the con- text of industry norms. For example, you would not expect a soft-drink manufacturer to have the same profit margin as a jeweler or the same leverage as a finance company. You can see this from Table 4.8 , which presents some financial ratios for a sample of industry groups.

Notice the large variation across industries. Some of these differences, particularly in profitability measures, may arise from chance; in 2012 the sun shone more kindly on some industries than others. But other differences may reflect more fundamen- tal factors. For example, notice the comparatively high debt ratios of paper and food product companies. In comparison, computer and electronic companies tend to borrow far less, and these differences persist in both good times and bad. We pointed out ear- lier that some businesses are able to generate a high level of sales from relatively few assets. Differences in turnover ratios also tend to be relatively stable. For example, you can see that the asset turnover ratio for food companies is more than double that for pharmaceutical companies. But competition ensures that food businesses earn a cor- respondingly lower margin on their sales. The net effect is that the return on assets in the two industries is broadly similar.

Now that you know how to interpret financial ratios, you can use the Beyond the Page feature shown in the margin to compare the ratios of other U.S. companies.

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104 Part One Introduction

4.9 The Role of Financial Ratios Whenever two managers get together to talk business and finance, it’s a good bet that they will refer to financial ratios. Let’s drop in on two conversations.

Conversation 1 The CEO was musing out loud: “How are we going to finance this expansion? Would the banks be happy to lend us the $30 million that we need?”

“I’ve been looking into that,” the financial manager replies. “Our current debt ratio is 30%. If we borrow the full cost of the project, the ratio would be about 45%. When we took out our last loan from the bank, we agreed that we would not allow our debt ratio to get above 50%. So if we borrow to finance this project, we wouldn’t have much leeway to respond to possible emergencies. Also, the rating agencies currently give our bonds an investment-grade rating. They too look at a company’s leverage when they rate its bonds. I have a table here ( Table 4.9 ), which shows that when firms are highly leveraged, their bonds receive a lower rating. I don’t know whether the rat- ing agencies would downgrade our bonds if our debt ratio increased to 45%, but they might. That wouldn’t please our existing bondholders, and it could raise the cost of any new borrowing.

Rating Category Return on Assets, %  a

Operating Margin, %  b

Interest Cover  c

Debt Ratio, % d

Retained Earnings/Net Debt

Aaa 15.2 17.9 18.6 22.2 201.3 Aa 20.0 21.0 13.3 35.3 46.7 A 14.5 15.5 8.4 42.2 35.7 Baa 10.8 13.2 5.2 44.5 28.0 Ba 9.2 11.1 3.3 51.3 21.5 B 7.1 8.4 1.4 74.0 10.2 C 2.9 1.8 0 .4 102.6 2.6

a Earnings before interest, tax, and amortization (EBITA)/average assets b Operating profi t/net revenues c Interest/EBITA d (Short-term  +  long-term debt)/earnings before interest, tax, depreciation, and amortization (EBITDA)

Source: Moody’s Financial Metrics, “Key Ratios by Rating and Industry for North American Non-Financial Corporations: 2008,” January 2009.

TABLE 4.9 Median financial ratios by rating class for nonfinancial North American corporations, 2008

Even within an industry, there can be a considerable difference in the type of business that companies do, and this shows up in their financial ratios. Here are some data on assets, sales, and income for two companies. Calculate for each company the asset turnover, the operating profit margin, and the return on assets. In each case the values are expressed as a percentage of sales. One of these two companies is Walmart. The other is Tiffany. Which one is which? Explain.

Self-Test 4.10

Company A Company B

Sales 100 100 Assets 41.2 109.6 Net income  +  after-tax interest 4.1 12.0

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Chapter 4 Measuring Corporate Performance 105

“We also need to think about our interest cover, which is beginning to look a bit thin. Debt interest is currently covered three times, and if we borrowed the entire $30  million, interest cover would fall to about two times. Sure, we expect to earn additional profits on the new investment, but it could be several years before they come through. If we run into a recession in the meantime, we could find ourselves short of cash.”

“Sounds to me as if we should be thinking about a possible equity issue,” concluded the CEO.

Conversation 2 The CEO was not in the best of moods after his humiliating defeat at the company golf tournament by the manager of the packaging division: “I see our stock was down again yesterday,” he growled. “It’s now selling below book value, and the stock price is only six times earnings. I work my socks off for this com- pany; you would think that our stockholders would show a little more gratitude.”

“I think I can understand a little of our shareholders’ worries,” the financial man- ager replies. “Just look at our book rate of return on assets. It’s only 6%, well below the cost of capital. Sure we are making a profit, but that profit does not cover the cost of the funds that investors provide. Our economic value added is actually negative. Of course, this doesn’t necessarily mean that the assets could be used better elsewhere, but we should certainly be looking carefully at whether any of our divisions should be sold off or the assets redeployed.

“In some ways we’re in good shape. We have very little short-term debt, and our current assets are three times our current liabilities. But that’s not altogether good news because it also suggests that we may have more working capital than we need. I’ve been looking at our main competitors. They turn over their inventory 12 times a year compared with our figure of just 8 times. Also, their customers take an average of 45 days to pay their bills. Ours take 67. If we could just match their performance on these two measures, we would release $300 million that could be paid out to shareholders.”

“Perhaps we could talk more about this tomorrow,” said the CEO. “In the mean- time I intend to have a word with the production manager about our inventory levels and with the credit manager about our collections policy. You’ve also got me thinking about whether we should sell off our packaging division. I’ve always worried about the divisional manager there. Spends too much time practicing his backswing and not enough worrying about his return on assets.”

SUMMARY For a public corporation, this is relatively easy. Start with market capitalization, which equals price per share times the number of shares outstanding. The difference between market capitalization and the book value of equity measures the market value added by the firm’s investments and operations. The book value of equity is the cumulative invest- ment (including reinvested earnings) by shareholders in the company. The ratio of market value to book value is another way of expressing value added.

For private corporations, financial managers and analysts have to turn to other perfor- mance measures, because stock prices are not available.

Financial managers and analysts track return on equity (ROE), which is the ratio of net income to shareholders’ equity. But net income is calculated after interest expense, so ROE depends on the debt ratio. The return on capital (ROC) and the return on assets (ROA) are better measures of operating performance. These are the ratios of after-tax operating income to total capitalization (long-term debt plus shareholders’ equity) and to total assets. ROC should be compared with the company’s cost of capital. EVA (economic value added

How do you measure whether a public corporation has delivered value for its shareholders? (LO4-1)

What measures are used to assess financial performance? (LO4-2)

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106 Part One Introduction

or residual income) deducts the cost of capital from operating income. If EVA is positive, then the firm’s current operations are adding value for shareholders.

Financial managers and analysts have to condense the enormous volume of information in a company’s financial statements. They rely on a handful of ratios to summarize financial performance, operating efficiency, and financial strength. Look back at Table 4.6 , which summarizes the most important ratios. Remember that the ratios sometimes appear under different names and may be calculated differently.

Profitability ratios measure return on investment. Leverage ratios measure how much the firm has borrowed and its obligations to pay interest. Efficiency ratios measure how intensively the firm uses its assets. Liquidity ratios measure how easily the firm can obtain cash.

Financial ratios crop up repeatedly in financial discussions and contracts. Banks and bondholders usually demand limits on debt ratios or interest coverage.

The Du Pont system links financial ratios together to explain the return on assets and equity. Return on assets is the product of asset turnover and operating profit margin. Return on equity is the product of the leverage ratio, asset turnover, operating profit margin, and debt burden.

Financial statement analysis will rarely be useful if done mechanically. Financial ratios do not provide final answers, although they should prompt the right questions. In addition, accounting entries do not always reflect current market values, and in rare cases account- ing is not transparent, because unscrupulous managers make up good news and hide bad news in financial statements.

You will need a benchmark to assess a company’s financial condition. Therefore, we usually compare financial ratios to the company’s ratios in earlier years and to ratios of other firms in the same business.

L I S T I N G O F E Q UAT I O N S

4.1 Return on assets = after-tax operating income

assets

= sales

assets

c asset turnover

×

after-tax operating income

sales

c operating profit margin

4.2

ROE = net income

equity =

assets

equity

c

leverage ratio

×

sales

assets

c

asset turnover

×

after-tax operating income

sales

c

operating profit margin

×

net income

after-tax operating income

c “debt burden”

What are the standard measures of profitability, efficiency, leverage, and liquidity? (LO4-3)

What determines the return on assets and equity? (LO4-4)

What are some potential pitfalls in financial statement analysis? (LO4-5)

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Chapter 4 Measuring Corporate Performance 107

Caterpillar has 657 million shares outstanding with a market price of $83 a share. (LO4-1)

a. Calculate the company’s market value added. b. Calculate the market-to-book ratio. c. Has the company created value for shareholders?

2. Market Value Added. Suppose the broad stock market falls 20% in a year and Home Depot’s stock price falls by 10%. (LO4-1)

a. Will the company’s market value added rise or fall? b. Should this change affect our assessment of the performance of Home Depot’s managers? c. Would you feel differently about Home Depot’s managers if the stock market were

unchanged and Home Depot’s stock fell by 10%?

3. Measuring Performance. Here are simplified financial statements for Watervan Corporation:

QUESTIONS AND PROBLEMS 1. Market Value Added. Here is a simplified balance sheet for Caterpillar Tractor:

finance

®

Current assets $42,524 Current liabilities $ 29,755 Long-term assets 46,832 Long-term debt 27,752 Other liabilities 14,317 Equity 17,532 Total $89,356 Total $ 89,356

INCOME STATEMENT (Figures in $ millions)

Net sales 881 Cost of goods sold 741 Depreciation 31 Earnings before interest and taxes (EBIT) 109 Interest expense 12 Income before tax 97 Taxes 34 Net income 63

BALANCE SHEET (Figures in $ millions)

End of Year Start of Year

Assets Current assets 369 312 Long-term assets 258 222 Total assets 627 534 Liabilities and shareholders’ equity Current liabilities 194 157 Long-term debt 108 121 Shareholders’ equity 325 256 Total liabilities and shareholders’ equity 627 534

The company’s cost of capital is 8.5%. (LO4-2)

a. Calculate Watervan’s economic value added (EVA). b. What is the company’s return on capital? (Use start-of-year rather than average capital.) c. What is its return on equity? (Use start-of-year rather than average equity.) d. Is the company creating value for its shareholders?

4. Measuring Performance. Recalculate Home Depot’s economic value added assuming its cost of capital is 10%. (LO4-2)

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108 Part One Introduction

5. Economic Value Added. EVA will be positive whenever ROC is positive and greater than the cost of capital. Explain why this is so. (LO4-2)

6. Return on Capital. Microlimp does not raise any new finance during the year, but it generates a lot of earnings, which are immediately reinvested. If you were calculating the company’s return on capital, would it make more sense to use capital at the start of the year or an average of the starting and ending capital? Would your answer change if Microlimp made a large issue of debt early in the year? Illustrate your answer with simple examples. (LO4-2)

7. Financial Ratios. Here are simplified financial statements for Phone Corporation in a recent year:

INCOME STATEMENT (Figures in $ millions)

Net sales 13,193 Cost of goods sold 4,060 Other expenses 4,049 Depreciation 2,518 Earnings before interest and taxes (EBIT) 2,566 Interest expense 685 Income before tax 1,881 Taxes (at 35%) 658 Net income 1,223 Dividends 856

BALANCE SHEET (Figures in $ millions)

End of Year Start of Year

Assets Cash and marketable securities $ 89 $ 158 Receivables 2,382 2,490 Inventories 187 238 Other current assets 867 932 Total current assets $ 3,525 $ 3,818 Net property, plant, and equipment 19,973 19,915 Other long-term assets 4,216 3,770 Total assets $ 27,714 $ 27,503 Liabilities and shareholders’ equity Payables $ 2,564 $ 3,040 Short-term debt 1,419 1,573 Other current liabilities 811 787 Total current liabilities $ 4,794 $ 5,400 Long-term debt and leases 7,018 6,833 Other long-term liabilities 6,178 6,149 Shareholders’ equity 9,724 9,121 Total liabilities and shareholders’ equity $ 27,714 $ 27,503

Calculate the following financial ratios for Phone Corporation: (LO4-3)

a. Return on equity b. Return on assets c. Return on capital d. Days in inventory e. Inventory turnover f. Average collection period g. Operating profit margin h. Long-term debt ratio i. Total debt ratio j. Times interest earned k. Cash coverage ratio

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Chapter 4 Measuring Corporate Performance 109

l. Current ratio m. Quick ratio

8. Financial Ratios. Consider this simplified balance sheet for Geomorph Trading: (LO4-3)

Current assets $100 Current liabilities $ 60 Long-term assets 500 Long-term debt 280 Other liabilities 70 Equity 190 $600 $600

a. What is the company’s debt-equity ratio? b. What is the ratio of total long-term debt to total long-term capital? c. What is its net working capital? d. What is its current ratio?

9. Receivables. Chik’s Chickens has average accounts receivable of $6,333. Sales for the year were $9,800. What is its average collection period? (LO4-3)

10. Inventory. Salad Daze maintains an inventory of produce worth $400. Its total bill for produce over the course of the year was $73,000. How old on average is the lettuce it serves its custom- ers? (LO4-3)

11. Times Interest Earned. In the past year, TVG had revenues of $3 million, cost of goods sold of $2.5 million, and depreciation expense of $200,000. The firm has a single issue of debt outstanding with book value of $1 million on which it pays an interest rate of 8%. What is the firm’s times interest earned ratio? (LO4-3)

12. Leverage Ratios. Lever Age pays an 8% rate of interest on $10 million of outstanding debt with face value $10 million. The firm’s EBIT was $1 million. (LO4-3)

a. What is its times interest earned? b. If depreciation is $200,000, what is its cash coverage?

13. Financial Ratios. There are no universally accepted definitions of financial ratios, but some of the following ratios make no sense at all. Substitute correct definitions. (LO4-3)

a. Debt-equity ratio  =  long-term debt/(long-term debt  +  equity) b. Return on equity  =  net income/average equity c. Operating profit margin  =  after-tax operating income/sales d. Inventory turnover  =  total sales/average inventory e. Current ratio  =  current liabilities/current assets f. Average collection period  =  sales/(average receivables/365) g. Quick ratio  =  (cash  +  marketable securities  +  receivables)/current liabilities)

14. Asset Turnover. In each case, choose the firm that you expect to have the higher asset turnover ratio. (LO4-3)

a. Economics Consulting Group or Home Depot b. Catalog Shopping Network or Neiman Marcus c. Electric Utility Co. or Standard Supermarkets

15. Inventory Turnover. If a firm’s inventory level of $10,000 represents 30 days’ sales, what is the annual cost of goods sold? What is the inventory turnover ratio? (LO4-3)

16. Leverage. A firm has a long-term debt-equity ratio of .4. Shareholders’ equity is $1 million. Current assets are $200,000, and the current ratio is 2. The only current liabilities are notes pay- able. What is the total debt ratio? (LO4-3)

17. Leverage Ratios. A firm has a debt-to-equity ratio of .5 and a market-to-book ratio of 2. What is the ratio of the book value of debt to the market value of equity? (LO4-3)

18. Liquidity Ratios. A firm uses $1 million in cash to purchase inventories. (LO4-3)

a. Will its current ratio rise or fall? b. Will its quick ratio rise or fall?

19. Current Ratio. Would the following events increase or decrease a firm’s current ratio? (LO4-3)

a. Inventory is sold. b. The firm takes out a bank loan to pay its suppliers.

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110 Part One Introduction

c. The firm arranges a line of credit with a bank that allows it to borrow at any time to pay its suppliers.

d. A customer pays its overdue bills. e. The firm uses cash to buy additional inventory.

20. Financial Ratios. True or false? (LO4-3)

a. A company’s debt-equity ratio is always less than 1. b. The quick ratio is always less than the current ratio. c. For a profitable company, the return on equity is always less than the return on assets.

21. Interpreting Financial Ratios. In each of the following cases, state which of the two compa- nies is likely to be characterized by the higher ratio. (LO4-3)

a. Debt-equity ratio: a shipping company or a computer software company b. Payout ratio: United Foods Inc. or Computer Graphics Inc. c. Ratio of sales to assets: an integrated pulp and paper manufacturer or a paper mill d. Average collection period: Regional Electric Power Company or Z-Mart Discount Outlets

22. Financial Ratios. As you can see, someone has spilled ink over some of the entries in the bal- ance sheet and income statement of Transylvania Railroad. Use the information from the tables to work out the following missing entries, and then calculate the company’s return on equity. Note: Inventory turnover, average collection period, and return on equity are calculated using start-of-year, not average, values. (LO4-3)

Long-term debt ratio 0.4 Times interest earned 8.0 Current ratio 1.4 Quick ratio 1.0 Cash ratio 0.2 Inventory turnover 5.0 Average collection period 73 days

INCOME STATEMENT (Figures in $ millions)

Net sales     Cost of goods sold     Selling, general, and administrative expenses 10 Depreciation 20 Earnings before interest and taxes (EBIT)     Interest expense     Income before tax     Tax (35% of income before tax)     Net income     

BALANCE SHEET (Figures in $ millions)

This Year Last Year

Assets Cash and marketable securities     20

Accounts receivable     34

Inventories     26

Total current assets     80

Net property, plant, and equipment     25

Total assets     105

Liabilities and shareholders’ equity Accounts payable 25 20 Notes payable 30 35 Total current liabilities     55

Long-term debt     20

Shareholders’ equity     30

Total liabilities and shareholders’ equity 115 105

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Chapter 4 Measuring Corporate Performance 111

a. Total assets b. Total current liabilities c. Total current assets d. Cash and marketable securities e. Accounts receivable f. Inventory g. Fixed assets h. Long-term debt i. Shareholders’ equity j. Net sales k. Cost of goods sold l. EBIT m. Interest expense n. Income before tax o. Tax p. Net income

23. Interpreting Financial Ratios. (LO4-3)

a. Turn back to Table 4.8 . For the sample of industries in that table, plot operating profit margin against asset turnover in a scatter diagram. What is the apparent relationship between these two variables? Does this make sense to you?

b. Now plot a scatter diagram of the cash ratio versus quick ratio. Do these two measures of liquidity tend to move together? Would you conclude that once you know one of these ratios, there is little to be gained by calculating the other?

24. Du Pont Analysis. In 2014 Electric Autos had sales of $100 million and assets at the start of the year of $150 million. If its return on start-of-year assets was 15%, what was its operating profit margin? (LO4-4)

25. Du Pont Analysis. Torrid Romance Publishers has total receivables of $3,000, which represents 20 days’ sales. Total assets are $75,000. The firm’s operating profit margin is 5%. Find the firm’s ROA and asset turnover ratio. (LO4-4)

26. Du Pont Analysis. Keller Cosmetics maintains an operating profit margin of 5% and asset turn- over ratio of 3. (LO4-4)

a. What is its ROA? b. If its debt-equity ratio is 1, its interest payments and taxes are each $8,000, and EBIT is

$20,000, what is its ROE?

27. Du Pont Analysis. CFA Corp. has a debt-equity ratio that is lower than the industry average, but its cash coverage ratio is also lower than the industry average. What might explain this seeming contradiction? (LO4-4)

28. Using Financial Ratios. For each category of financial ratios discussed in this chapter, give some examples of who would be likely to examine these ratios and why. (LO4-5)

WEB EXERCISE 1. Log on to finance.yahoo.com to find the latest simplified financial statements for Home Depot.

Recalculate HD’s financial ratios. What have been the main changes from the financial state- ments shown in this chapter? If you owned some of HD’s debt, would these changes make you feel more or less happy?

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112 Part One Introduction

Company A Company B

1. Asset turnover 2.4 0.91 2. Operating profi t margin, % 4.1 12.0 3. Return on assets, % (= 1 × 2) 10.0 10.9

Company A is Walmart; it generates a high volume of sales from its assets, but earns a rela- tively low profit margin on these sales. The reverse is true of Tiffany (company B). The two companies differ enormously in their asset turnover and profit margin, but much less in their return on assets.

SOLUTIONS TO SELF-TEST QUESTIONS 4.1 Market capitalization is $75  ×   14.5  million  =   $1,087.5  million. Market value added is

$1,087.5  −  $610  =  $477.5 million. Market to book is 1,087.5/610  =  1.78. You can also cal- culate book value per share at $610/14.5  =  $42.07, and use price per share to calculate market to book: $75/$42.07  =  1.78.

4.2 The cost of capital in dollars is .115  ×   $188  million  =   $21.62  million. EVA is $30  −  $21.62  =  $8.38 million.

4.3 After-tax operating income is calculated before interest expense. Net income is calculated after interest expense. Financial managers usually start with net income, so they add back after-tax interest to get after-tax operating income. After-tax operating income measures the profitability of the firm’s investment and operations. If properly calculated, it is not affected by financing.

4.4 ROE measures return to equity as net income divided by the book value of equity. ROC and ROA measure the return to all investors, including interest paid as well as net income to share- holders. ROC measures return versus long-term debt and equity. ROA measures return versus total assets.

4.5 Average daily expenses are (48,912  +   16,305)/365  =   $178.7  million. Accounts pay- able at the start of the year are $8,173 million. The average payment delay is therefore 8,173/178.7  =  45.7 days.

4.6 In industries with rapid asset turnover, competition forces prices down, reducing profit margins.

4.7 Nothing will happen to the long-term debt ratio computed using book values, since the face values of the old and new debt are equal. However, times interest earned and cash coverage will increase since the firm will reduce its interest expense.

4.8 a. The firm must compensate for its below-average profit margin with an above-average turn- over ratio. Remember that ROA is the product of operating margin  ×  turnover.

b. If ROA equals the industry average but ROE exceeds the industry average, the firm must have above-average leverage. As long as ROA exceeds the borrowing rate, leverage will increase ROE.

4.9 a. The current ratio starts at 1.2/1.0  =  1.2. The transaction will reduce current assets to $.7 million and current liabilities to $.5 million. The current ratio increases to .7/.5  =  1.4. Net working capital is unaffected: Current assets and current liabilities fall by equal amounts.

b. The current ratio is unaffected, since the firm merely exchanges one current asset (cash) for another (inventories). However, the quick ratio will fall since inventories are not included among the most liquid assets.

4.10

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Chapter 4 Measuring Corporate Performance 113

MINICASE Burchetts Green had enjoyed the bank training course, but it was good to be starting his first real job in the corporate lending group. Earlier that morning the boss had handed him a set of financial statements for The Hobby Horse Company Inc. (HH). “Hobby Horse,” she said, “has a $45 million loan from us due at the end of September, and it is likely to ask us to roll it over. The company seems to have run into some rough weather recently, and I have asked Furze Platt to go down there this afternoon and see what is happening. It might do you good to go along with her. Before you go, take a look at these financial statements and see what you think the problems are. Here’s a chance for you to use some of that stuff they taught you in the training course.”

Mr. Green was familiar with the HH story. Founded in 1990, it had rapidly built up a chain of discount stores selling materials for crafts and hobbies. However, last year a number of new store openings coinciding with a poor Christmas season had pushed the company into loss. Management had halted all new construction and put 15 of its existing stores up for sale.

Mr. Green decided to start with the 6-year summary of HH’s balance sheet and income statement ( Table 4.10 ). Then he turned to examine in more detail the latest position ( Tables 4.1 1 and 4.12 ).

What appear to be the problem areas in HH? Do the finan- cial ratios suggest questions that Ms. Platt and Mr. Green need to address?

2014 2013 2012 2011 2010 2009

Net sales 3,351 3,314 2,845 2,796 2,493 2,160 EBIT -9 312 256 243 212 156 Interest 37 63 65 58 48 46 Taxes 3 60 46 43 39 34 Net profi t -49 189 145 142 125 76 Earnings per share -0.15 0.55 0.44 0.42 0.37 0.25 Current assets 669 469 491 435 392 423 Net fi xed assets 923 780 753 680 610 536 Total assets 1,592 1,249 1,244 1,115 1,002 959 Current liabilities 680 365 348 302 276 320 Long-term debt 236 159 297 311 319 315 Stockholders’ equity 676 725 599 502 407 324 Number of stores 240 221 211 184 170 157 Employees 13,057 11,835 9,810 9,790 9,075 7,825

TABLE 4.10 Financial highlights for The Hobby Horse Company Inc., year ending March 31

TABLE 4.11 Income statement for The Hobby Horse Company Inc., year ending March 31, 2014 (figures in $ millions)

Net sales 3,351 Cost of goods sold 1,990 Selling, general, and administrative expenses 1,211 Depreciation expense 159 Earnings before interest and taxes (EBIT) -9 Net interest expense 37 Taxable income -46 Income taxes 3 Net income -49 Allocation of net income Addition to retained earnings -49 Dividends 0

Note: Column sums subject to rounding error.

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114 Part One Introduction

TABLE 4.12 Consolidated balance sheet for The Hobby Horse Company Inc. (figures in $ millions)

Assets Mar. 31, 2014 Mar. 31, 2013

Current assets Cash and marketable securities 14 72 Receivables 176 194 Inventories 479 203 Total current assets 669 469 Fixed assets Property, plant, and equipment 1,077 910 Less accumulated depreciation 154 130 Net fi xed assets 923 780 Total assets 1,592 1,249

Liabilities and Shareholders’ Equity Mar. 31, 2014 Mar. 31, 2013

Current liabilities Debt due for repayment 484 222 Accounts payable 94 58 Other current liabilities 102 85 Total current liabilities 680 365 Long-term debt 236 159 Stockholders’ equity Common stock and other paid-in capital 155 155 Retained earnings 521 570 Total stockholders’ equity 676 725 Total liabilities and stockholders’ equity 1,592 1,249

Note: Column sums subject to rounding error.

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116

The Time Value of Money

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

5-1 Calculate the future value of money that is invested at a particular interest rate.

5-2 Calculate the present value of a future payment.

5-3 Calculate present and future values of a level stream of cash payments.

5-4 Compare interest rates quoted over different time intervals—for example, monthly versus annual rates.

5-5 Understand the difference between real and nominal cash flows and between real and nominal interest rates.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

5 CHAPTE R

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117

P A

R T

TW O

C ompanies invest in lots of things. Some are tangible assets —that is, assets you can kick, like factories, machinery, and offices. Others are intangible assets, such as patents or trademarks.

In each case the company lays out some money

now in the hope of receiving even more money later.

Individuals also make investments. For example,

your college education may cost you $20,000 per

year. That is an investment you hope will pay off in

the form of a higher salary later in life. You are sowing

now and expecting to reap later.

Companies pay for their investments by raising

money and in the process assuming liabilities. For

example, they may borrow money from a bank and

promise to repay it with interest later. You also may

have financed your investment in a college educa-

tion by borrowing money that you plan to pay back

out of that fat salary.

All these financial decisions require comparisons

of cash payments at different dates. Will your future

salary be sufficient to justify the current expenditure

on college tuition? How much will you have to repay

the bank if you borrow to finance your education?

In this chapter we take the first steps toward under-

standing the time value of money, that is, the rela-

tionship between the values of dollars today and

dollars in the future. We start by looking at how funds

invested at a specific interest rate will grow over time.

We next ask how much you would need to invest

today to produce a specified future sum of money,

and we describe some shortcuts for working out the

value of a series of cash payments. Then we consider

how inflation affects these financial calculations.

There is nothing complicated about these calcu-

lations, but if they are to become second nature, you

should read the chapter thoroughly, work carefully

through the examples (we have provided plenty),

and make sure you tackle the self-test questions. We

are asking you to make an investment now in return

for a payoff later. One of the payoffs is that you will

understand what is going on behind the screen

when you value cash flows using a spreadsheet

Va lu

e

Time affects the value of a dollar.

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118

program or a financial calculator. We show how to

use spreadsheets and financial calculators later in

this chapter.

For simplicity, almost every example in this chapter

is set out in dollars, but the concepts and calculations

are identical in euros, yen, tugrik, or drams. 1

1 The tugrik is the currency of Mongolia, and the dram is the currency of Armenia.

5.1 Future Values and Compound Interest You have $100 invested in a bank account. Suppose banks are currently paying an interest rate of 6% per year on deposits. So after a year your account will earn interest of $6:

Interest = interest rate × initial investment

= .06 × $100 = $6

You start the year with $100 and you earn interest of $6, so the value of your invest- ment will grow to $106 by the end of the year:

Value of investment after 1 year = $100 + $6 = $106

Notice that the $100 invested grows by the factor (1  +  .06)  =  1.06. In general, for any interest rate r, the value of the investment at the end of 1 year is (1  +   r ) times the initial investment:

Value after 1 year = initial investment × (1 + r)

= $100 × (1.06) = $106

What if you leave this money in the bank for a second year? Your balance, now $106, will continue to earn interest of 6%. So

Interest in year 2 = .06 × $106 = $6.36

You start the second year with $106, on which you earn interest of $6.36. So by the end of the year the value of your account will grow to $106  +  $6.36  =  $112.36.

In the first year your investment of $100 increases by a factor of 1.06 to $106; in the second year the $106 again increases by a factor of 1.06 to $112.36. Thus the initial $100 investment grows twice by a factor 1.06:

Value of investment after 2 years = $100 × 1.06 × 1.06

= $100 × (1.06)2 = $112.36

If you keep your money invested for a third year, your investment multiplies by 1.06 each year for 3 years. By the end of the third year it will total $100  ×  (1.06) 3   =  $119.10, scarcely enough to put you in the millionaire class, but even millionaires have to start somewhere.

Clearly, if you invest your $100 for t years, it will grow to $100  ×  (1.06) t . For an interest rate of r and a horizon of t years, the future value (FV) of your investment will be

Future value (FV) of $100 = $100 × (1 + r)t (5.1)

Notice in our example that your interest income in the first year is $6 (6% of $100) and in the second year is $6.36 (6% of $106). Your income in the second year is higher because you now earn interest on both the original $100 investment and the $6 of interest earned in the previous year. Earning interest on interest is called compound- ing or compound interest . In contrast, if the bank calculated the interest only on your original investment, you would be paid simple interest . With simple interest the value of your investment would grow each year by .06  ×  $100  =  $6.

future value (FV) Amount to which an investment will grow after earning interest.

compound interest Interest earned on interest.

simple interest Interest earned only on the original investment; no interest is earned on interest.

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Chapter 5 The Time Value of Money 119

Table 5.1 and Figure 5.1 illustrate the mechanics of compound interest. Table 5.1 shows that in each year, you start with a greater balance in your account—your sav- ings have been increased by the previous year’s interest. As a result, your interest income also is higher.

Obviously, the higher the rate of interest, the faster your savings will grow. Figure 5.2 shows the balance in your savings account after a given number of years

Year Balance at

Start of Year Interest Earned

during Year Balance at End of Year

1 $100.00 0.06  ×  $100.00  =  $6.00 $106.00 2 $106.00 0.06  ×  $106.00  =  $6.36 $112.36 3 $112.36 0 .06  ×  $112.36  =  $6.74 $119.10 4 $119.10 0 .06  ×  $119.10  =  $7.15 $126.25 5 $126.25 0 .06  ×  $126.25  =  $7.57 $133.82

TABLE 5.1 How your savings grow; the future value of $100 invested to earn 6% with compound interest

FIGURE 5.1 A plot of the data in Table 5.1 , showing the future values of an investment of $100 earning 6% with compound interest

Year

V al

u e

in y

o u

r ac

co u

n t

($ )

140

120

100

80

60

40

20

0 1 2 3 4 5

This year’s interest

Interest from previous years

Original investment

FIGURE 5.2 How an investment of $100 grows with compound interest at different interest rates

2 4 6 8 10 12 14 16 18 20

Number of years

r = 0

r = 5%

r = 10%

r = 15%

Fu tu

re v

al u

e o

f $1

0 0

($ )

1,800

1,600

1,400

1,200

1,000

800

600

400

200

0

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120 Part Two Value

for several interest rates. Even a few percentage points added to the (compound) inter- est rate can dramatically affect the future balance. For example, after 10 years $100 invested at 10% will grow to $100  ×   (1.10) 10   =  $259.37. If invested at 5%, it will grow to only $100  ×  (1.05) 10   =  $162.89.

Calculating future values is easy using almost any calculator. If you have the patience, you can multiply your initial investment by 1  +   r (1.06 in our example) once for each year of your investment. A simpler procedure is to use the power key (the y x key) on your calculator. For example, to compute (1.06) 10 , enter 1.06, press the y x key, enter 10, press = , and discover that the answer is 1.7908. (Try this!)

If you don’t have a calculator, you can use a table of future values such as Table 5.2 . Let’s use it to work out the future value of a 10-year investment at 6%. First find the row corresponding to 10 years. Now work along that row until you reach the column for a 6% interest rate. The entry shows that $1 invested for 10 years at 6% grows to $1.7908.

Notice that as you move across each row in Table  5.2 , the future value of a $1 investment increases, as your funds compound at a higher interest rate. As you move down any column, the future value also increases, as your funds compound for a lon- ger period.

Now try one more example. If you invest $1 for 20 years at 10% and do not with- draw any money, what will you have at the end? Your answer should be $6.7275.

Table 5.2 gives future values for only a small selection of years and interest rates. Table A.1 at the end of the book is a bigger version of Table 5.2 . It presents the future value of a $1 investment for a wide range of time periods and interest rates.

Future value tables are tedious, and as Table 5.2 demonstrates, they show future values only for a limited set of interest rates and time periods. For example, suppose that you want to calculate future values using an interest rate of 7.835%. The power key on your calculator will be faster and easier than future value tables.

Example 5.1 Manhattan Island Almost everyone’s favorite example of the power of compound interest is the pur- chase of Manhattan Island for $24 in 1626 by Peter Minuit. Based on New York real estate prices today, it seems that Minuit got a great deal. But did he? Consider the future value of that $24 if it had been invested for 388 years (2014 minus 1626) at an interest rate of 8% per year:

$24 × (1.08)388 = $223,166,175,426,958

= $223 trillion

Perhaps the deal wasn’t as good as it appeared. The total value of land on Man- hattan today is only a fraction of $223 trillion.

TABLE 5.2 An example of a future value table, showing how an investment of $1 grows with compound interest

Number of Years

Interest Rate per Year

5% 6% 7% 8% 9% 10%

1 1.0500 1.0600 1.0700 1.0800 1.0900 1.1000 2 1.1025 1.1236 1.1449 1.1664 1.1881 1.2100 3 1.1576 1.1910 1.2250 1.2597 1.2950 1.3310 4 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641 5 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105

10 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937 20 2.6533 3.2071 3.8697 4.6610 5.6044 6.7275 30 4.3219 5.7435 7.6123 10.0627 13.2677 17.4494

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Chapter 5 The Time Value of Money 121

Suppose that Peter Minuit did not become the first New York real estate tycoon but instead had invested his $24 at a 5% interest rate in New Amster- dam Savings Bank. What would have been the balance in his account after 5 years? 50 years?

Self-Test 5.1

In 1973 Gordon Moore, one of Intel’s founders, predicted that the number of transistors that could be placed on a single silicon chip would double every 18 months, equivalent to an annual growth of 59% (i.e., 1.59 1.5   =  2.0). The first microprocessor was built in 1971 and had 2,250 transistors. By 2010 Intel chips contained 2.3 billion transistors, over 1 million times the number of transistors 39 years earlier. What has been the annual compound rate of growth in processing power? How does it compare with the prediction of Moore’s law?

Self-Test 5.2

The power of compounding is not restricted to money. Foresters try to forecast the compound growth rate of trees, demographers the compound growth rate of popula- tion. A social commentator once observed that the number of lawyers in the United States is increasing at a higher compound rate than the population as a whole (3.6% versus .9% in the 1980s) and calculated that in about two centuries there will be more lawyers than people. In all these cases, the principle is the same: Compound growth means that value increases each period by the factor  (1  +   growth rate). The value after t periods will equal the initial value times  (1  +  growth rate) t . When money is invested at compound interest, the growth rate is the interest rate.

Though entertaining, this analysis is actually somewhat misleading. The 8% inter- est rate we’ve used to compute future values is high by historical standards. At a 3.5% interest rate, more consistent with historical experience, the future value of the $24 would be dramatically lower, only $24  ×  (1.035) 388   =  $15,033,737! On the other hand, we have understated the returns to Mr. Minuit and his successors: We have ignored all the rental income that the island’s land has generated over the last three or four centuries.

All things considered, if we had been around in 1626, we would have gladly paid $24 for the island.

5.2 Present Values Money can be invested to earn interest. If you are offered the choice between $100,000 now and $100,000 at the end of the year, you naturally take the money now to get a year’s interest. Financial managers make the same point when they say that money in hand today has a time value or when they quote perhaps the most basic financial prin- ciple: A dollar today is worth more than a dollar tomorrow.

We have seen that $100 invested for 1 year at 6% will grow to a future value of 100  ×  1.06  =  $106. Let’s turn this around: How much do we need to invest now in

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122 Part Two Value

order to produce $106 at the end of the year? In other words, what is the present value (PV) of the $106 payoff?

To calculate future value, we multiply today’s investment by 1 plus the interest rate, .06, or 1.06. To calculate present value, we simply reverse the process and divide the future value by 1.06:

Present value = PV = future value

1.06 =

$106

1.06 = $100

What is the present value of, say, $112.36 to be received 2 years from now? Again we ask, How much would we need to invest now to produce $112.36 after 2 years? The answer is obviously $100; we’ve already calculated that at 6% $100 grows to $112.36:

$100 × (1.06)2 = $112.36

However, if we don’t know, or forgot the answer, we just divide future value by (1.06) 2 :

Present value = PV = $112.36 (1.06)2

= $100

In general, for a future value or payment t periods away, present value is

Present value = future value after t periods

(1 + r)t (5.2)

To calculate present value, we discounted the future value at the interest rate r. The calculation is therefore termed a discounted cash-flow (DCF) calculation, and the interest rate r is known as the discount rate .

In this chapter we will be working through a number of more or less complicated DCF calculations. All of them involve a present value, a discount rate, and one or more future cash flows. If ever a DCF problem leaves you confused and flustered, just pause and write down which of these measures you know and which one you need to calculate.

present value (PV) Value today of a future cash flow.

discounted cash flow (DCF) Method of calculating present value by discounting future cash flows.

discount rate Interest rate used to compute present values of future cash flows.

Example 5.2 Saving for a Future Purchase Suppose you need $3,000 next year to buy a new computer. The interest rate is 8% per year. How much money should you set aside now in order to pay for the pur- chase? Just calculate the present value at an 8% interest rate of a $3,000 payment at the end of 1 year. To the nearest dollar, this value is

PV = $3,000

1.08 = $2,778

Notice that $2,778 invested for 1 year at 8% will prove just enough to buy your computer:

Future value = $2,778 × 1.08 = $3,000

The longer the time before you must make a payment, the less you need to invest today. For example, suppose that you can postpone buying that computer until the end of 2 years. In this case we calculate the present value of the future payment by dividing $3,000 by (1.08) 2 :

PV = $3,000 (1.08)2

= $2,572

Thus you need to invest $2,778 today to provide $3,000 in 1 year but only $2,572 to provide the same $3,000 in 2 years.

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Chapter 5 The Time Value of Money 123

You now know how to calculate future and present values: To work out how much you will have in the future if you invest for t years at an interest rate r, multiply the initial investment by  (1  +    r ) t  . To find the present value of a future payment, run the process in reverse and divide by  (1  +    r ) t .

Present values are always calculated using compound interest. The ascending lines in Figure 5.2 showed the future value of $1 invested with compound interest. In contrast, present values decline, other things equal, when future cash payments are delayed. The longer you have to wait for money, the less it’s worth today.

The descending line in Figure  5.3 shows the present value today of $100 to be received at some future date. Notice how even small variations in the interest rate can have a powerful effect on the value of distant cash flows. At an interest rate of 5%, a payment of $100 in year 20 is worth $37.69 today. If the interest rate increases to 10%, the value of the future payment falls by about 60% to $14.86.

The present value formula is sometimes written differently. Instead of dividing the future payment by (1  +   r ) t , we could equally well multiply it by 1/(1  +   r ) t :

PV = future payment

(1 + r)t = future payment ×

1 (1 + r)t

The expression 1/(1  +   r ) t is called the discount factor . It measures the present value of $1 received in year t.

The simplest way to find the discount factor is to use a calculator, but financial managers sometimes find it convenient to use tables of discount factors. For example, Table 5.3 shows discount factors for a small range of years and interest rates. Table A.2 at the end of the book provides a set of discount factors for a wide range of years and interest rates.

Try using Table 5.3 to check our calculations of how much to put aside for that $3,000 computer purchase. If the interest rate is 8%, the present value of $1 paid at the end of 1 year is $.9259. So the present value of $3,000 is (to the nearest dollar)

PV = $3,000 × 1

1.08 = $3,000 × .9259 = $2,778

which matches the value we obtained in Example 5.2.

discount factor Present value of a $1 future payment.

FIGURE 5.3 Present value of a future cash flow of $100. Notice that the longer you have to wait for your money, the less it is worth today

2 4 6 8 10 12 14 16 18 20

Number of years

P re

se n

t va

lu e

o f

$1 0

0 ($

)

100

80

90

70

60

50

40

30

20

10

0

r = 0%

r = 5%

r = 10%

r = 15%

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124 Part Two Value

What if the computer purchase is postponed until the end of 2 years? Table 5.3 shows that the present value of $1 paid at the end of 2 years is .8573. So the present value of $3,000 is

PV = $3,000 × 1

(1.08)2 = $3,000 × .8573 = $2,572

as we found in Example 5.2. Notice that as you move along the rows in Table  5.3 , moving to higher interest

rates, present values decline. As you move down the columns, moving to longer dis- counting periods, present values again decline. (Why does this make sense?)

Example 5.3 Italy Borrows Some Cash In September 2012 the Italian government needed to borrow several billion euros. It did so by selling IOUs. 2 Each IOU was a promise to pay the holder € 1,000 at the end of 2 years. If investors demanded an interest rate of 1.9% to lend to the Italian government, how much would they have been prepared to pay for that IOU? Easy! Because the IOU matured in 2 years, we calculate its present value by multiplying the €1,000 future payment by the 2-year discount factor:

PV = :1,000 × 1

(1.019)2

= :1,000 × .96306 = :963.06

2 “IOU” means “I owe you.” Italy’s IOUs are called bonds. Usually, bond investors receive a regular interest or coupon payment. This Italian bond will make only a single payment when it matures. It is therefore known as a zero-coupon bond . More on this in the next chapter.

Suppose that the Italian government had promised to pay € 1,000 at the end of 3 years. If the market interest rate was 2.5%, how much would you have been prepared to pay for a 3-year IOU of € 1,000?

Self-Test 5.3

Example 5.4 Finding the Value of Free Credit Kangaroo Autos is offering free credit on a $20,000 car. You pay $8,000 down and then the balance at the end of 2 years. Turtle Motors next door does not offer free credit but will give you $1,000 off the list price. If the interest rate is 10%, which com- pany is offering the better deal?

TABLE 5.3 An example of a present value table, showing the value today of $1 received in the future

Number of Years

Interest Rate per Year

5% 6% 7% 8% 9% 10%

1 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 2 0.9070 0.8900 0.8734 0.8573 0.8417 0.8264 3 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 4 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830 5 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209

10 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 20 0.3769 0.3118 0.2584 0.2145 0.1784 0.1486 30 0.2314 0.1741 0.1314 0.0994 0.0754 0.0573

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Chapter 5 The Time Value of Money 125

FIGURE 5.4 Drawing a time line can help us to calculate the present value of the payments to Kangaroo Autos

0 1 2

$12,000

$12,000 × $9,917.36

Present value today (time 0)

$17,917.36

$8,000.00

Year

Total

(1.10)2 1

$8,000

=

Notice that you pay more in total by buying through Kangaroo, but since part of the payment is postponed, you can keep this money in the bank where it will continue to earn interest. To compare the two offers, you need to calculate the present value of your payments to Kangaroo. The time line in Figure 5.4 shows the cash payments. The first payment, $8,000, takes place today. The second pay- ment, $12,000, takes place at the end of 2 years. To find its present value, we need to multiply by the 2-year discount factor. The total present value of the payments to Kangaroo is therefore

PV = $8,000 + $12,000 × 1

(1.10)2

= $8,000 + $9,917.36 = $17,917.36

Suppose you start with $17,917.36. You make a down payment of $8,000 to Kangaroo Autos and invest the balance of $9,917.36. At an interest rate of 10%, this will grow over 2 years to $9,917.36  ×  1.10 2   =  $12,000, just enough to make the final payment on your automobile. The total cost of $17,917.36 is a better deal than the $19,000 charged by Turtle Motors.

These calculations illustrate how important it is to use present values when com- paring alternative patterns of cash payment. You should never compare cash flows occurring at different times without first discounting them to a common date. By calculating present values, we see how much cash must be set aside today to pay future bills.

Calculating present and future values can entail a considerable amount of tedious arithmetic. Fortunately, financial calculators and spreadsheets are designed with present value and future value formulas already programmed. They can make your work much easier. In Section 5.4 we will show how they do so.

Finding the Interest Rate When we looked at the Italian government’s IOUs in Example 5.3, we used the inter- est rate to compute a fair market price for each IOU. Sometimes, however, you are given the price and have to calculate the interest rate that is being offered.

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126 Part Two Value

For example, when Italy borrowed money, it did not announce an interest rate. It simply offered to sell each IOU for €963.06 (see Example 5.3). Thus we know that

PV = €1,000 × 1

(1 + r)2 = €963.06

What is the interest rate? There are several ways to approach this. You might use a table of discount factors.

You need to find the interest rate for which the 2-year discount factor  =  .96306. A better approach is to rearrange the equation and use your calculator:

€963.06 × (1 + r)2 = €1,000

(1 + r)2 = €1,000

€963.06 = 1.0384

(1 + r) = (1.0384)1/2 = 1.019 r = .019, or 1.9%

Example 5.5 Double Your Money How many times have you heard of an investment adviser who promises to double your money? Is this really an amazing feat? That depends on how long it will take for your money to double. With enough patience, your funds eventually will double even if they earn only a very modest interest rate. Suppose your investment adviser promises to double your money in 8 years. What interest rate is implicitly being promised?

The adviser is promising a future value of $2 for every $1 invested today. There- fore, we find the interest rate by solving for r as follows:

Future value (FV) = PV × (1 + r)t

$2 = $1 × (1 + r)8

1 + r = 21/8 = 1.0905

r = .0905, or 9.05% ▲

5.3 Multiple Cash Flows So far, we have considered problems involving only a single cash flow. This is obvi- ously limiting. Most real-world investments, after all, will involve many cash flows over time. When there are many payments, you’ll hear managers refer to a stream of cash flows.

Future Value of Multiple Cash Flows Recall the computer you hope to purchase in 2 years (see Example 5.2). Now suppose that instead of putting aside one sum in the bank to finance the purchase, you plan to save some amount of money each year. You might be able to put $1,200 in the bank now, and another $1,400 in 1 year. If you earn an 8% rate of interest, how much will you be able to spend on a computer in 2 years?

The time line in Figure  5.5 shows how your savings grow. There are two cash inflows into the savings plan. The first cash flow will have 2 years to earn inter- est and therefore will grow to $1,200  ×   (1.08) 2   =   $1,399.68, while the second deposit, which comes a year later, will be invested for only 1 year and will grow to $1,400  ×  (1.08)  =  $1,512. After 2 years, then, your total savings will be the sum of these two amounts, or $2,911.68.

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Chapter 5 The Time Value of Money 127

Our examples show that problems involving multiple cash flows are simple exten- sions of single cash-flow analysis. To find the value at some future date of a stream of cash flows, calculate the future value of each cash flow and then add up these future values.

As we will now see, a similar adding-up principle works for present value calculations.

FIGURE 5.5 Drawing a time line can help to calculate the future value of your savings.

0 1 2

$1,400

$1,399.68

$2,911.68

$1,512.00

$1,200 × (1.08)2 $1,400 × 1.08

Year

Future value in year 2

$1,200

=

=

Example 5.6 Even More Savings Suppose that the computer purchase can be put off for an additional year and that you can make a third deposit of $1,000 at the end of the second year. How much will be available to spend 3 years from now?

Again we organize our inputs using a time line as in Figure 5.6 . The total cash available will be the sum of the future values of all three deposits. Notice that when we save for 3 years, the first two deposits each have an extra year for interest to compound:

$1,200 × (1.08)3 = $1,511.65

$1,400 × (1.08)2 = 1,632.96

$1,000 × (1.08) = 1,080.00

Total future value = $4,224.61 ▲

FIGURE 5.6 To find the future value of a stream of cash flows, you just calculate the future value of each flow and then add them.

0 1 3

$1,400

$1,511.65

$4,224.61

$1,632.96

$1,200 × (1.08)3 $1,400 × (1.08)2

Year Future value in year 3 2

$1,200 $1,000

=

$1,080.00 $1,000 × 1.08=

=

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128 Part Two Value

Present Value of Multiple Cash Flows When we calculate the present value of a future cash flow, we are asking how much that cash flow would be worth today. If there is more than one future cash flow, we simply need to work out what each flow would be worth today and then add these present values.

In order to avoid estate taxes, your rich aunt Frederica will pay you $10,000 per year for 4 years, starting 1 year from now. What is the present value of your benefactor’s planned gifts? The interest rate is 7%. How much will you have 4 years from now if you invest each gift at 7%?

Self-Test 5.4

Example 5.7 Cash Up Front versus an Installment Plan Suppose that your auto dealer gives you a choice between paying $15,500 for a used car or entering into an installment plan where you pay $8,000 down today and make payments of $4,000 in each of the next 2 years. Which is the better deal? Before reading this chapter, you might have compared the total payments under the two plans: $15,500 versus $16,000 in the installment plan. Now, how- ever, you know that this comparison is wrong, because it ignores the time value of money. For example, the last installment of $4,000 is less costly to you than paying out $4,000 now. The true cost of that last payment is the present value of $4,000.

Assume that the interest rate you can earn on safe investments is 8%. Suppose you choose the installment plan. As the time line in Figure 5.7 illustrates, the pres- ent value of the plan’s three cash flows is:

Year Initial

Balance - Payment = Remaining

Balance + Interest Earned =

Balance at Year-End

0 $15,133.06 $8,000 $7,133.06 $570.64 $7,703.70 1 7,703.70 4,000 3,703.70 296.30 4,000.00 2 4,000.00 4,000 0 0 0

Present Value

Immediate payment $8,000 = $ 8,000.00 Second payment $4,000/1.08 = 3,703.70 Third payment $4,000/(1.08)2 = 3,429.36 Total present value = $15,133.06

Because the present value of the three payments is less than $15,500, the install- ment plan is in fact the cheaper alternative.

The installment plan’s present value is the amount that you would need to invest now to cover the three payments. Let’s check.

Here is how your bank balance would change as you make each payment:

If you start with the present value of $15,133.06 in the bank, you could make the first $8,000 payment and be left with $7,133.06. After 1 year, your savings account would receive an interest payment of $7,133.06  ×   .08  =   $570.64, bringing your account to $7,703.70. Similarly, you would make the second $4,000 payment and be left with $3,703.70. This sum left in the bank would grow with interest to $4,000, just enough to make the last payment.

The present value of a stream of future cash flows is the amount you need to invest today to generate that stream.

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Chapter 5 The Time Value of Money 129

5.4 Reducing the Chore of the Calculations: Part 1 We have worked through a number of present value problems by hand because it is important that you understand how present values are calculated. But calculating val- ues in this way can be laborious. Therefore, financial managers generally turn to finan- cial calculators or computer spreadsheets to remove much of the tedium. In this section we show how these calculators and spreadsheets are used to solve the future and pres- ent value problems that we have encountered so far. Later in the chapter we will look at how they can also help to solve problems where there are recurring payments.

We start with an introduction to financial calculators and then look at spreadsheets.

Using Financial Calculators to Solve Simple Time-Value- of-Money Problems The basic financial calculator uses five keys that correspond to the inputs for common problems involving the time value of money:

FVPMTPVin

FIGURE 5.7 To find the present value of a stream of cash flows, you just calculate the present value of each flow and then add them.

0 1 2

$8,000

Present value today (time 0)

Year

1.08 4,000

$4,000$4,000

(1.08)2 4,000

$3,703.70

$15,133.06Total

$8,000.00

$3,429.36

=

=

Each key represents the following input:

• n is the number of periods. (We have been using t to denote the length of time or the number of periods.)

• i is the interest rate, expressed as a percentage (not a decimal). For example, if the interest rate is 8%, you would enter 8, not .08. On some calculators, this key appears as I/YR, I/Y, or just i. (We have been using r to denote the interest rate.)

• PV is the present value. • FV is the future value. • PMT is the amount of any recurring payment, that is, any intermediate payments that

come before the date when future value, FV, is calculated. We will start with exam- ples where there are no recurring payments, so for now we just set this key to zero.

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130 Part Two Value

Given any four of these inputs, the calculator will solve for the fifth. We can illus- trate using Examples 5.1 and 5.2. In Example 5.1, we calculated the future value of Peter Minuit’s $24 investment if invested at 8% for 388 years. Our inputs would be as follows:

For example, to enter the number of periods, type 388 and then press the n key. Similarly, enter an interest rate of 8 and a present value of 24. There are no recurring cash flows, so you need to enter a value of 0 for PMT. You now wish to solve for the future value given the other four inputs. On some calculators, you do this by pressing FV. On others, you need to first press the compute key, which may be labeled CPT or COMP, and then press FV. Your calculator should show a value of − $223.17 trillion, which, except for the minus sign, is the future value of $24. Try it.

Why does the minus sign appear? Most calculators treat cash flows as either inflows (shown as positive numbers) or outflows (negative numbers). For example, if you bor- row $100 today at an interest rate of 12%, you receive money now (a positive cash flow), but you will have to pay back $112 in a year, a negative cash flow at that time. Therefore, the calculator displays FV as a negative number. The following time line of cash flows shows the reasoning employed. The final negative cash flow of $112 has the same present value as the $100 borrowed today.

PV 5 $100

Year: 0 1

FV = $112

n i PV PMT FV

Inputs 388 8 24 0

n i PV PMT FV

Inputs 2 8 0 3000

If, instead of borrowing, you were to invest $100 today to reap a future benefit, you would enter PV as a negative number (first press 100, then press the + / −   key to change the value to negative, and finally press PV to enter the value into the PV regis- ter). In this case, FV would appear as a positive number, showing that you will reap a cash inflow when your investment comes to fruition.

In Example 5.2, we consider a simple savings problem. We need to solve for the amount that you must put aside today to produce $3,000 in 2 years. So our inputs look like this:

Now compute PV; you should get an answer of − 2572.02. Again the answer is displayed as a negative number because you need to make a cash outflow today (an investment) of $2,572.02 in order to reap a cash flow of $3,000 in 2 years.

Using Spreadsheets to Solve Simple Time-Value-of- Money Problems Just as financial calculators largely replaced interest rate tables in the 1980s, these cal- culators are today giving way to spreadsheets. Spreadsheets have a particular advantage when a problem involves a number of uneven cash flows. Such problems can rapidly become tedious and prone to errors from “typos,” even if you use a financial calculator.

Using financial calculators

BEYOND THE PAGE

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Chapter 5 The Time Value of Money 131

Like financial calculators, spreadsheets provide built-in functions that solve the equations linking the five variables in a time-value-of-money problem: the number of periods, the interest rate per period, the present value, the future value, and any recur- ring payment. For now we ignore recurring payments; later we will show you how to solve problems involving recurring payments.

Single Cash Flows We show first how spreadsheets, such as Microsoft Excel, can be used to solve the single cash-flow problems in Examples 5.1 and 5.2.

The two Excel functions for these single cash-flow problems are:

Future value = FV(rate, nper, pmt, PV)

Present value = PV(rate, nper, pmt, FV)

As you can see, each spreadsheet formula requires four inputs—just as financial calculators require four inputs. The spreadsheet then provides the solution for the fifth variable. Also, as with most calculators, the spreadsheet functions interpret cash inflows as positive values and cash outflows as negative values. Unlike financial cal- culators, however, most spreadsheets require that interest rates be input as decimals rather than whole numbers (e.g., .06 rather than 6%). Note also the use of = in front of the formulas to alert Excel to the fact that these are predefined formulas.

Spreadsheet 5.1 solves for the future value of the $24 spent to acquire Manhattan Island (Example 5.1). The interest rate is entered as a decimal in cell B3. The number of periods is 388 (cell B4). We enter the recurring payment as zero in cell B5. The present value is entered as -24 (cell B6), representing the purchase price, and there- fore the future value is a positive cash flow.

Of course, memorizing Excel functions such as the one in cell B8 may not come easily to everyone. (We admit that we’re still working on it.) But there is an easy cure for those of us with bad memories. You can pull down the appropriate function from Excel’s built-in functions (marked f x ), and you will be prompted for the neces- sary inputs. Spreadsheet 5.2 illustrates. Go to the Formula tab, click Financial formu- las, and then select FV. The “Function Arguments” screen shown in Spreadsheet 5.2 should now appear. At the bottom left of the function box there is a Help facility with an example of how the function is used.

Now let’s solve Example 5.2 in a spreadsheet. We can type the Excel function = PV(rate, nper, pmt, FV)  =  PV(.08, 2, 0, 3000), or we can select the PV function from the pull-down menu of financial functions and fill in our inputs as shown in the dialog box below. Either way, you should get an answer of − $2,572. (Notice that you

SPREADSHEET 5.1 Using a spreadsheet to find the future value of $24

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0.08

388

0

-24

$223,166,175,426,958

BA C D F

Finding the future value of $24 using a spreadsheet

Formula in cell B8

=FV(B3,B4,B5,B6)

INPUTS

Interest rate

Periods

Payment

Present value (PV)

Future value

Notice that we enter the present value in cell B6 as a negative number,

since the "purchase price" is a cash outflow. The interest rate in cell B3

is entered as a decimal, not a percentage.

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132 Part Two Value

don’t type the comma in 3,000 when entering the number in the spreadsheet. If you did, Excel would interpret the entry as two different numbers, 3 followed by zero.)

Multiple Cash Flows Valuing multiple cash flows with a spreadsheet is no dif- ferent from valuing single cash flows. You simply find the present value of each flow and then add them up. Spreadsheet 5.3 shows how to find the solution to Example 5.7.

The time until each payment is listed in column A. This value is then used to set the number of periods (nper) in the formula in column C. The values for the cash flow in each future period are entered as negative numbers in the PV formula. The present val- ues (column C) therefore appear as positive numbers. Column E shows an alternative to the use of the PV function, where we calculate present values directly. This allows us to see exactly what we are doing.

Using Excel to solve time- value-of-money problems

BEYOND THE PAGE

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SPREADSHEET 5.2 Using the financial function pull-down menu

A B C D E F G

1 Finding the future value of $24 using a spreadsheet 2

3 INPUTS 4 Interest rate 0.08

5 Periods 388

6 Payment 0

7 Present value (PV) –24

8 Formula in cell B8

9 Future value $223,166,175,426,958 = FV(B3,B4,B5,B6)

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

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Chapter 5 The Time Value of Money 133

The Beyond the Page icon in the margin will take you to an application that shows how each of the examples in this chapter can be solved using a spreadsheet.

5.5 Level Cash Flows: Perpetuities and Annuities Frequently, you may need to value a stream of equal cash flows. For example, a home mortgage might require the homeowner to make equal monthly payments for the life of the loan. For a 30-year loan, this would result in 360 equal payments. A 4-year car loan might require 48 equal monthly payments. Any such sequence of equally spaced, level cash flows is called an annuity . If the payment stream lasts forever, it is called a perpetuity .

How to Value Perpetuities Some time ago the British government borrowed by issuing loans known as consols. Consols are perpetuities. In other words, instead of repaying these loans, the British government pays the investors a fixed annual payment in perpetuity (forever).

How might we value such a security? Suppose that you could invest $100 at an interest rate of 10%. You would earn annual interest of .10  ×  $100  =  $10 per year and could withdraw this amount from your investment account each year without ever run- ning down your balance. In other words, a $100 investment could provide a perpetuity of $10 per year. In general,

Cash payment from perpetuity = interest rate × present value C = r × PV

We can rearrange this relationship to derive the present value of a perpetuity, given the interest rate r and the cash payment C:

PV of perpetuity = C r

=

cash payment

interest rate (5.3)

Suppose some worthy person wishes to endow a chair in finance at your university. If the rate of interest is 10% and the aim is to provide $100,000 a year forever, the amount that must be set aside today is

Present value of perpetuity = C r

=

$100,000

.10 = $1,000,000

Two warnings about the perpetuity formula. First, at a quick glance you can easily confuse the formula with the present value of a single cash payment. A payment of $1

annuity Level stream of cash flows at regular intervals with a finite maturity.

perpetuity Stream of level cash payments that never ends.

A B C D E 1 Finding the present value of multiple cash fl ows using a spreadsheet 2 3 Time until CF Cash fl ow Present value Formula in Col C Alternative formula for Col C 4 0 8000 $8,000.00 =PV($B$10, A4,0, -B4) =B4/(1 + $B$10)^A4 5 1 4000 $3,703.70 =PV($B$10, A5,0, -B5) =B5/(1 + $B$10)^A5

6 2 4000 $3,429.36 =PV($B$10, A6,0, -B6) =B6/(1 + $B$10)^A6 7 8 SUM $15,133.06 =SUM(C4:C6) =SUM(C4:C6) 9 10 Discount rate: 0.08 11 12 Notice that the time until each payment is found in column A. 13 Once we enter the formula for present value in cell C4, we can copy it to cells C5 and C6. 14 The present value for other interest rates can be found by changing the entry in cell B10.

SPREADSHEET 5.3 Using a spreadsheet to find the present value of multiple cash flows

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134 Part Two Value

at the end of 1 year has a present value 1/(1  +   r ). The perpetuity has a value of 1/ r. At a 10% interest rate, a perpetuity is 11 times more valuable than a single cash flow.

Second, the perpetuity formula tells us the value of a regular stream of payments starting one period from now. Thus our endowment of $1 million would provide the university with its first payment of $100,000 one year hence. If the worthy donor wants to provide the university with an additional payment of $100,000 up front, he or she would need to put aside $1,100,000.

Sometimes you may need to calculate the value of a perpetuity that does not start to make payments for several years. For example, suppose that our philanthropist decides to provide $100,000 a year with the first payment 4 years from now. We know that in year 3, this endowment will be an ordinary perpetuity with payments starting at the end of 1 year. So our perpetuity formula tells us that in year 3 the endowment will be worth $100,000/ r. But it is not worth that much now. To find today’s value we need to multiply by the 3-year discount factor. Thus, at an interest rate of 10%, the “delayed” perpetuity is worth

$100,000 × 1 r

×

1 (1 + r)3

= $1,000,000 × 1

(1.10)3 = $751,315

How to Value Annuities Let us return to Kangaroo Autos for (almost) the last time. Most installment plans call for level streams of payments. So let us suppose that Kangaroo now offers an “easy payment” scheme of $8,000 a year at the end of each of the next 3 years.

The payments on the Kangaroo plan constitute a 3-year annuity. Figure 5.8 shows a time line of these cash flows and calculates the present value of each year’s flow assuming an interest rate of 10%. You can see that the total present value of the pay- ments is $19,894.82.

You can always value an annuity by calculating the present value of each cash flow and finding the total. However, it is usually quicker to use a simple formula which

FIGURE 5.8 To find the value of an annuity, you can calculate the value of each cash flow. It is usually quicker to use the annuity formula.

$6,611.57

$19,894.82

$7,272.73

$6,010.52

Total

(1.10)2 8,000

1.10 8,000

(1.10)3 8,000

0 21 3 Present value

Year

$8,000$8,000 $8,000

=

=

=

A British government perpetuity pays £4 a year forever and is selling for £48. What is the interest rate?

Self-Test 5.5

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Chapter 5 The Time Value of Money 135

states that if the interest rate is r, then the present value of an annuity that pays C dol- lars a year for each of t periods is

Present value of t-year annuity = C c1 r

-

1

r (1 + r)t d (5.4)

The expression in brackets shows the present value of a t -year annuity of $1 starting in period 1. It is generally known as the t -year annuity factor . Therefore, another way to write the value of an annuity is

Present value of t-year annuity = payment × annuity factor

You can use this formula to calculate the present value of the payments to Kangaroo. The annual payment ( C ) is $8,000, the interest rate ( r ) is 10%, and the number of years ( t ) is 3. Therefore,

Present value = C c1 r

-

1

r (1 + r)t d = 8,000 c 1

.10 -

1

.10(1.10)3 d = $19,894.82

This is exactly the same answer that we got by separately valuing each cash flow. If the number of periods is small, there is little to choose between the two methods, but when you are valuing long-term annuities, it is far easier to use the formula.

If you are wondering where the annuity formula comes from, look at Figure 5.9 . It shows the payments and values of three investments.

Row 1 The investment in the first row provides a perpetual stream of $1 starting at the end of the first year. We have already seen that this perpetuity has a present value of 1/ r.

Row 2 Now look at the investment shown in the second row of Figure 5.9 . It also provides a perpetual stream of $1 payments, but these payments don’t start until year 4. This stream of payments is identical to the payments in row 1, except that they are delayed for an additional 3 years. In year 3, the investment will be an ordinary per- petuity with payments starting in 1 year and will therefore be worth 1/ r in year 3. To find the value today, we simply multiply this figure by the 3-year discount factor. Thus

PV = 1 r

×

1 (1 + r)3

=

1

r (1 + r)3

Row 3 Finally, look at the investment shown in the third row of Figure 5.9 . This provides a level payment of $1 a year for each of 3 years. In other words, it is a 3-year annuity. You can also see that, taken together, the investments in rows 2 and 3 provide exactly the same cash payments as the investment in row 1. Thus the value of our annuity (row 3) must be equal to the value of the row 1 perpetuity less the value of the delayed row 2 perpetuity:

Present value of a 3-year $1 annuity = 1 r

-

1

r (1 + r)3

annuity factor Present value of a $1 annuity.

FIGURE 5.9 The value of an annuity is equal to the difference between the value of two perpetuities.

Cash Flow

Year: 1 2 3 4 5 6 . . . Present Value

1. Perpetuity A $1 $1 $1 $1 $1 $1 . . .

2. Perpetuity B $1 $1 $1 . . .

3. Three-year annuity $1 $1 $1

1 r

1 r(1 + r)3

1 -

1 r r(1 + r)3

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136 Part Two Value

Remembering formulas is about as difficult as remembering other people’s birth- days. But as long as you bear in mind that an annuity is equivalent to the difference between an immediate and a delayed perpetuity, you shouldn’t have any difficulty.

You can use a calculator or spreadsheet to work out annuity factors (we show you how momentarily), or you can use a set of annuity tables. Table 5.4 is an abridged annuity table (an extended version is shown in Table A.3 at the end of the book). Check that you can find the 3-year annuity factor for an interest rate of 10%.

Compare Table 5.4 with Table 5.3 , which presented the present value of a single cash flow. In both tables, present values fall as we move across the rows to higher dis- count rates. But in contrast to those in Table 5.3 , present values in Table 5.4 increase as we move down the columns, reflecting the greater number of payments made by longer annuities.

TABLE 5.4 An example of an annuity table, showing the present value today of $1 a year received for each of t years

Number of Years

Interest Rate per Year

5% 6% 7% 8% 9% 10%

1 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 2 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355 3 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 4 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 5 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908

10 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 20 12.4622 11.4699 10.5940 9.8181 9.1285 8.5136 30 15.3725 13.7648 12.4090 11.2578 10.2737 9.4269

Example 5.8 Winning Big at the Lottery In May 2013 an 84-year-old Florida woman invested $10 in five Powerball lottery tickets and won a record $590.5 million. We suspect that she received unsolicited congratulations, good wishes, and requests for money from dozens of more or less worthy charities, relations, and newly devoted friends. In response, she could fairly point out that the prize wasn’t really worth $590.5 million. That sum was to be paid in 30 equal annual installments of $19.683 million each. Assuming that the first pay- ment occurred at the end of 1 year, what was the present value of the prize? The interest rate at the time was about 3.6%.

The present value of these payments is simply the sum of the present values of each annual payment. But rather than valuing the payments separately, it is much easier to treat them as a 30-year annuity. To value this annuity, we simply multiply $19.683 million by the 30-year annuity factor:

PV = 19.683 × 30-year annuity factor

= 19.683 × c1 r

-

1 r (1 + r)30

d At an interest rate of 3.6%, the annuity factor is

c 1 .036

-

1 .036(1.036)30

d = 18.1638

If the interest rate is 8%, what is the 4-year discount factor? What is the 4-year annuity factor? What is the relationship between these two numbers? Explain.

Self-Test 5.6

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Chapter 5 The Time Value of Money 137

Suppose you retire at age 70. You expect to live 20 more years and to spend $55,000 a year during your retirement. How much money do you need to save by age 70 to support this consumption plan? Assume an interest rate of 7%.

Self-Test 5.7

Example 5.10 Home Mortgages Sometimes you may need to find the series of cash payments that would provide a given value today. For example, home purchasers typically borrow the bulk of the house price from a lender. The most common loan arrangement is a 30-year loan that is repaid in equal monthly installments. Suppose that a house costs $125,000 and that the buyer puts down 20% of the purchase price, or $25,000, in cash, bor- rowing the remaining $100,000 from a mortgage lender such as the local savings bank. What is the appropriate monthly mortgage payment?

The borrower repays the loan by making monthly payments over the next 30 years (360 months). The savings bank needs to set these monthly payments so that they have a present value of $100,000. Thus

Present value = mortgage payment × 360-month annuity factor

= $100,000

Mortgage payment = $100,000

360-month annuity factor

The present value of the cash payments is $19.683  ×  18.163  =  $357.5 million, much less than the much-advertised prize, but still not a bad day’s haul.

Lottery operators generally make arrangements for winners with big spending plans to take an equivalent lump sum. In our example the winner could either take the $590.5 million spread over 30 years or receive $357.5 million up front. Both arrangements have the same present value.

Example 5.9 How Much Luxury and Excitement Can $67 Billion Buy? Bill Gates is one of the world’s richest persons, with wealth in 2013 reputed to be about $67 billion. Mr. Gates has devoted a large part of his fortune to the Bill and Melinda Gates Foundation; but suppose that he decides to allocate his entire remaining wealth to a life of luxury and entertainment (L&E). What annual expen- ditures on L&E could $67 billion support over a 30-year period? Assume that Mr. Gates can invest his funds at 6%.

The 30-year, 6% annuity factor is 13.7648. We set the present value of Mr. Gates’s spending stream equal to his total wealth:

Present value = annual spending × annuity factor

67,000,000,000 = annual spending × 13.7648

Annual spending = 4,867,400,000, or about $4.9 billion

Warning to Mr. Gates: We haven’t considered inflation. The cost of buying L&E will increase, so $4.9 billion won’t buy as much L&E in 30 years as it will today. More on that later.

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138 Part Two Value

The mortgage loan in Example 5.10 is an example of an amortizing loan. “Amortiz- ing” means that part of the monthly payment is used to pay interest on the loan and part is used to reduce the amount of the loan. Table 5.5 illustrates a 4-year amortizing loan of $1,000 with an interest rate of 10% and annual payments starting in 1 year. The annual payment (annuity) that would repay the loan is $315.47. (Confirm this for yourself.) At the end of the first year, the interest payment is 10% of $1,000, or $100. So $100 of your first payment is used to pay interest, and the remaining $215.47 is used to reduce (or “amortize”) the loan balance to $784.53.

Next year, the outstanding balance is lower, so the interest charge is only $78.45. Therefore, $315.47  −  $78.45  =  $237.02 can be applied to amortization. Amortiza- tion in the second year is higher than in the first, because the amount of the loan has declined and therefore less of the payment is taken up in interest. This procedure con- tinues until the last year, when the amortization is just enough to reduce the outstand- ing balance on the loan to zero.

Because the loan is progressively paid off, the fraction of each payment devoted to interest steadily falls over time, while the fraction used to reduce the loan (the amorti- zation) steadily increases. Figure 5.10 illustrates the amortization of the mortgage loan in Example 5.10. In the early years, almost all of the mortgage payment is for interest. Even after 15 years, the bulk of the monthly payment is interest.

Suppose that the interest rate is 1% a month. Then

Mortgage payment = $100,000

B 1 .01

-

1 .01(1.01)360

R =

$100,000 97.218

= $1,028.61

What will be the monthly payment if you take out a $100,000 fifteen-year mortgage at an interest rate of 1% per month? How much of the first payment is interest, and how much is amortization?

Self-Test 5.8

TABLE 5.5 An example of an amortizing loan. If you borrow $1,000 at an interest rate of 10%, you would need to make an annual payment of $315.47 over 4 years to repay the loan with interest.

Year

Beginning- of-Year Balance

Year-End Interest Due on Balance

Year-End Payment

Amortization of Loan

End-of-Year Balance

1 $1,000.00 $100.00 $315.47 $215.47 $784.53 2 784.53 78.45 315.47 237.02 547.51 3 547.51 54.75 315.47 260.72 286.79 4 286.79 28.68 315.47 286.79 0

Future Value of an Annuity You are back in savings mode again. This time you are setting aside $3,000 at the end of every year. If your savings earn interest of 8% a year, how much will they be worth at the end of 4 years? We can answer this question with the help of the time line in Figure 5.11 . Your first year’s savings will earn interest for 3 years, the second will earn interest for 2 years, the third will earn interest for 1 year, and the final savings in year 4 will earn no interest. The sum of the future values of the four payments is

($3,000 × 1.083) + ($3,000 × 1.082) + ($3,000 × 1.08) + $3,000 = $13,518

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Chapter 5 The Time Value of Money 139

But wait a minute! We are looking here at a level stream of cash flows—an annuity. We have seen that there is a shortcut formula to calculate the present value of an annu- ity. So there ought to be a similar formula for calculating the future value of a level stream of cash flows.

Think first how much your stream of savings is worth today. You are setting aside $3,000 in each of the next 4 years. The present value of this 4-year annuity is therefore equal to

PV = $3,000 × 4-year annuity factor

= $3,000 × c 1 .08

-

1

.08(1.08)4 d = $9,936

Now think how much you would have after 4 years if you invested $9,936 today. Simple! Just multiply by (1.08) 4 :

Value at end of year 4 = $9,936 × 1.084 = $13,518

We calculated the future value of the annuity by first calculating the present value and then multiplying by (1  +   r ) t . The general formula for the future value of a stream of cash flows of $1 a year for each of t years is therefore

FIGURE 5.10 Mortgage amortization. This figure shows the breakdown of mortgage payments between interest and amortization. Monthly payments within each year are summed, so the figure shows the annual payment on the mortgage.

1 4 7 10 13 16 19 22 25 28

Year

D o

lla rs

14,000

10,000

12,000

8,000

6,000

4,000

2,000

0

Amortization Interest paid

FIGURE 5.11 Calculating the future value of an ordinary annuity of $3,000 a year for 4 years (interest rate  =  8%)

$3,000

$3,499

$13,518

$3,240

3,000 × (1.08)2 3,000 × 1.08

Year

Future value in year 4

$3,000 $3,000$3,000

=

$3,779 3,000 × (1.08)3=

$3,000 3,000=

=

0 1 432

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140 Part Two Value

Future value (FV) of annuity of $1 a year = present value of annuity of $1 a year × (1 + r)t

= c1 r

-

1

r (1 + r)t d × (1 + r)t

= (1 + r)t - 1

r (5.5)

If you need to find the future value of just four cash flows as in our example, it is a toss-up whether it is quicker to calculate the future value of each cash flow separately (as we did in Figure 5.11 ) or to use the annuity formula. If you are faced with a stream of 10 or 20 cash flows, there is no contest.

You can find the future value of an annuity in Table 5.6 or the more extensive Table A.4 at the end of the book. You can see that in the row corresponding to t   =  4 and the column corresponding to r   =  8%, the future value of an annuity of $1 a year is $4.5061. Therefore, the future value of the $3,000 annuity is $3,000  ×  4.5061  =  $13,518. In practice, you will tend to use a calculator or spreadsheet to find these values.

TABLE 5.6 An example of a table showing the future value of an investment of $1 a year for each of t years

Number of Years

Interest Rate per Year

5% 6% 7% 8% 9% 10%

1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 2 2.0500 2.0600 2.0700 2.0800 2.0900 2.1000 3 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100 4 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 5 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051

10 12.5779 13.1808 13.8164 14.4866 15.1929 15.9374 20 33.0660 36.7856 40.9955 45.7620 51.1601 57.2750 30 66.4388 79.0582 94.4608 113.2832 136.3075 164.4940

0 4948••••4321 •

$500,000

Level savings (cash outflows) in years 1–50 result in a future accumulated

value of $500,000

Example 5.11 Saving for Retirement In only 50 more years, you will retire. (That’s right—by the time you retire, the retire- ment age will be around 70 years. Longevity is not an unmixed blessing.) Have you started saving yet? Suppose you believe you will need to accumulate $500,000 by your retirement date in order to support your desired standard of living. How much savings each year would be necessary to produce $500,000 at the end of 50 years? Let’s say that the interest rate is 10% per year. You need to find how large the annuity in the following figure must be to provide a future value of $500,000:

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Chapter 5 The Time Value of Money 141

In Example 5.11 we showed that an annual savings stream of $420.59 invested for 50 years at 10% a year would satisfy a savings goal of $500,000. Suppose instead that you made 50 annual investments, but you made these investments at the beginning of each year rather than at the end. How much would these savings amount to by the end of year 50?

Self-Test 5.9

We know that if you were to save $1 each year your funds would accumulate to

Future value (FV) of annuity of $1 a year = (1 + r)t - 1

r =

(1.10)50 - 1 .10

= $1,163.91

We need to choose C to ensure that C   ×   1,163.91  =   $500,000. Thus C   =   $500,000/1,163.91  =  $429.59. This appears to be surprisingly good news. Saving $429.59 a year does not seem to be an extremely demanding savings program. Don’t celebrate yet, however. The news will get worse when we consider the impact of inflation.

You may also want to calculate the future value of an annuity due. If the first cash flow comes immediately, the future value of the cash-flow stream is greater, since each flow has an extra year to earn interest. For example, at an interest rate of 10%, the future value of an annuity due would be exactly 10% greater than the future value of an ordinary annuity. More generally,

Future value of annuity due = future value of ordinary annuity × (1 + r) (5.7)

Annuities Due Remember that our annuity formulas assume that the first cash flow does not occur until the end of the first period. The present value of an annuity is the value today of a stream of payments that starts in one period. Similarly, the future value of an annuity assumes that the first cash flow comes at the end of one period.

But in many cases cash payments start immediately. For example, when Kangaroo Autos (see Figure 5.8 ) sells you a car on credit, it may insist that the first payment be made at the time of the sale. A level stream of payments starting immediately is known as an annuity due .

Figure 5.12 depicts the cash-flow streams of an ordinary annuity and an annuity due. Comparing panels a and b, you can see that each of the three cash flows in the annuity due comes one period earlier than the corresponding cash flow of the ordi- nary annuity. Therefore, each is discounted for one less period, and its present value increases by a factor of (1  +   r ). Therefore,

Present value of annuity due = present value of ordinary annuity × (1 + r) (5.6)

Figure 5.12 shows that bringing the Kangaroo loan payments forward by 1 year increases their present value from $19,894.82 (as an ordinary annuity) to $21,884.30 (as an annuity due). Notice that $21,884.30  =  $19,894.82  ×  1.10.

annuity due Level stream of cash flows starting immediately.

Valuing annuities

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142 Part Two Value

FIGURE 5.12 The cash payments on the ordinary annuity in panel a start in year 1. The first payment on the annuity due in panel b occurs immediately. The annuity due is therefore more valuable.

3-year ordinary annuity

$6,611.57

$19,894.82

$7,272.73

$6,010.52

Total

(1.10)2 8,000

1.10 8,000

(1.10)3 8,000

0 21 3 Present value

Year

$8,000$8,000 $8,000

=

=

=

(a)

3-year annuity due

0 21 3

$7,272.73

Present value

$21,884.30

Year

Total

1.10 8,000

$8,000.00

$8,000 $8,000 $8,000

$6,611.57 (1.10)2 8,000

=

=

(b)

Example 5.12 Good News for the Powerball Lottery Winner When calculating the value of the Powerball lottery prize in Example 5.8, we assumed that the first of the payments occurred at the end of 1 year. However, if the winner of the lottery had chosen to receive the prize in installments, she would not, in fact, have needed to wait before receiving any cash. She would have got- ten her first installment of $19.683 million up front, and the remaining payments would have been spread over the following 29 years. How would this affect the value of the prize?

We saw in Example 5.8 that the 30-year annuity factor for an ordinary annu- ity is 18.1638. Therefore, the 30-year annuity-due factor would be 18.1638  ×  1.036  =  18.8177. The present value of the winnings would be $19.683  ×  18.8177  =  $370.4 million, an increase of about $13 million.

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Chapter 5 The Time Value of Money 143

5.6 Reducing the Chore of the Calculations: Part 2 In Section 5.4 we showed how managers use financial calculators or spreadsheets to solve present value problems. At that point we had not encountered annuities, and we assumed that there were no recurring cash flows. We were simply concerned with the present value (PV) and the future value (FV). However, when we need to value an annuity, we are concerned with the present value, the future value, and the regular annuity payment (PMT). Here are some examples of how you can use a financial cal- culator and a spreadsheet to value annuities.

Using Financial Calculators to Solve Annuity Problems We looked earlier at the “easy payment” scheme offered by Kangaroo Autos. It called for a payment of $8,000 at the end of each of the next 3 years. What is the present value of these payments if the interest rate is 10%?

To find the answer on your financial calculator, you must enter the following numbers:

n i PV PMT FV

Inputs 360 1 100000 0

n i PV PMT FV

Inputs 3 10 -8000 0

Notice that PMT is no longer set at zero; instead, you need to enter the regular annu- ity payment (-8000). Note also that PMT is entered as a negative number; you are paying out $8,000 a year to Kangaroo Autos. There are no other payments involved, so FV is set at zero. (If, say, you were also required to pay an additional $5,000 in year 3, you would need to enter a future value, FV, of -5000.) Now compute PV; you should get an answer of 19,894.82.

Now let us use a financial calculator to solve Example 5.10. A savings bank needed to set the monthly payments on a mortgage so that they would have a present value, PV, of $100,000. There were 360 monthly payments, and the interest rate was 1% per month. To find the regular monthly payment (PMT), you need to enter the following data:

Notice that we enter PV as a positive number: You get a cash inflow when the bank lends you the money. When you press the PMT key, you should get the answer − 1,028.61 because the payment is a cash outflow.

Suppose that the mortgage is an annuity due with the first monthly payment made immediately. You can solve for annuities due by pressing the begin key on your calcu- lator. The calculator will automatically interpret the cash-flow series as an annuity due with the cash flows coming at the beginning of each period. To return to the ordinary annuity mode, just press the begin key again.

Using Spreadsheets to Solve Annuity Problems Solving annuity problems with a spreadsheet involves exactly the same functions that we used to solve single cash-flow problems. However, with an annuity, the recurring payment (PMT) is no longer zero.

Annuities and financial calculators

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144 Part Two Value

Think again of the “easy payment” scheme offered by Kangaroo Autos. This called for a payment of $8,000 at the end of each of the next 3 years. We need to calculate the present value of these payments at an interest rate of 10%. The following spreadsheet shows the solution to this problem.

1

2

3

4

5

6

7

8

9

10

A B C

Interest rate (i) 0.1

Number of periods (nper) 3

Payment per period (pmt) 8000

Formula in cell B8

Present value (PV) $19,894.82 =PV(B3,B4,−B5)

Notice that the interest rate is entered as a decimal, not a percentage.

Finding the present value of an annuity using a spreadsheet

5.7 Effective Annual Interest Rates We realize that by this point in the chapter you probably feel overwhelmed by formu- las. We have, however, two more tasks; so, if your head is spinning, now might be a good time to take a break and drink a strong cup of coffee.

So far in this chapter we have mainly used annual interest rates to value a series of annual cash flows. But interest rates may be quoted for days, months, years, or any convenient interval. How should we compare rates when they are quoted for different periods, such as monthly versus annually?

Consider your credit card. Suppose you have to pay interest on any unpaid balances at the rate of 1% per month. What is it going to cost you if you neglect to pay off your unpaid balance for a year?

Don’t be put off because the interest rate is quoted per month rather than per year. The important thing is to maintain consistency between the interest rate and the num- ber of periods. If the interest rate is quoted as a percent per month, then we must define the number of periods in our future value calculation as the number of months. So if you borrow $100 from the credit card company at 1% per month for 12 months, you will need to repay $100  ×  (1.01) 12   =  $112.68. Thus your debt grows after 1 year to $112.68. Therefore, we can say that the interest rate of 1% a month is equivalent to an effective annual interest rate , or annually compounded rate, of 12.68%.

In general, the effective annual interest rate is defined as the rate at which your money grows, allowing for the effect of compounding. Therefore, for the credit card,

1 + effective annual rate = (1 + monthly rate)12

When comparing interest rates, it is best to use effective annual rates. This com- pares interest paid or received over a common period (1 year) and allows for possible compounding during the period. Unfortunately, short-term rates are sometimes annu- alized by multiplying the rate per period by the number of periods in a year. In fact, truth-in-lending laws in the United States require that rates be annualized in this man- ner. Such rates are called annual percentage rates (APRs) . 3 The interest rate on your credit card loan was 1% per month. Since there are 12 months in a year, the APR on the loan is 12  ×  1%  =  12%. 4

effective annual interest rate Interest rate that is annualized using compound interest.

3 The truth-in-lending laws apply to credit card loans, auto loans, home improvement loans, and some loans to small businesses. The term “APR” is not commonly used or quoted in the big leagues of finance. 4 The rules for calculating the APR differ from one country to another. For example, in the EU, companies are obliged to quote the effective annual interest rate on most loans.

annual percentage rate (APR) Interest rate that is annualized using simple interest.

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Chapter 5 The Time Value of Money 145

If the credit card company quotes an APR of 12%, how can you find the effective annual interest rate? The solution is simple:

Step 1. Take the quoted APR and divide by the number of compounding periods in a year to recover the rate per period actually charged. In our example, the interest was calculated monthly. So we divide the APR by 12 to obtain the interest rate per month:

Monthly interest rate = APR

12 =

12%

12 = 1%

Step 2. Now convert to an annually compounded interest rate:

1 + effective annual rate = (1 + monthly rate)12 = (1 + .01)12 = 1.1268

The effective annual interest rate is .1268, or 12.68%. In general, if an investment is quoted with a given APR and there are m compound-

ing periods in a year, then $1 will grow to $1  ×  (1  +  APR/ m ) m after 1 year. The effec- tive annual interest rate is (1  +  APR/ m ) m   −  1. For example, a credit card loan that charges a monthly interest rate of 1% has an APR of 12% but an effective annual inter- est rate of (1.01) 12   −  1  =  .1268, or 12.68%. To summarize: The effective annual rate is the rate at which invested funds will grow over the course of a year. It equals the rate of interest per period compounded for the number of periods in a year.

Example 5.13 The Effective Interest Rates on Bank Accounts Back in the 1960s and 1970s federal regulation limited the (APR) interest rates banks could pay on savings accounts. Banks were hungry for depositors, and they searched for ways to increase the effective rate of interest that could be paid within the rules. Their solution was to keep the same APR but to calculate the inter- est on deposits more frequently. As interest is compounded at shorter and shorter intervals, less time passes before interest can be earned on interest. Therefore, the effective annually compounded rate of interest increases. Table 5.7 shows the cal- culations assuming that the maximum APR that banks could pay was 6%. (Actu- ally, it was a bit less than this, but 6% is a nice round number to use for illustration.)

You can see from Table 5.7 how banks were able to increase the effective inter- est rate simply by calculating interest at more frequent intervals.

The ultimate step was to assume that interest was paid in a continuous stream rather than at fixed intervals. With 1 year’s continuous compounding, $1 grows to e APR , where e   =  2.718 (a figure that may be familiar to you as the base for natu- ral logarithms). Thus if you deposited $1 with a bank that offered a continuously compounded rate of 6%, your investment would grow by the end of the year to (2.718) .06   =   $1.061837, just a hair’s breadth more than if interest were com- pounded daily.

TABLE 5.7 These investments all have an APR of 6%, but the more frequently interest is compounded, the higher is the effective annual rate of interest.

Compounding Period

Periods per Year (m)

Per-Period Interest Rate

Growth Factor of Invested Funds

Effective Annual Rate

1 year 1 6% 1.06 6.0000% Semiannually 2 3 1.032 = 1.0609 6.0900 Quarterly 4 1.5 1.0154 = 1.061364 6.1364 Monthly 12 0.5 1.00512 = 1.061678 6.1678 Weekly 52 0.11538 1.001153852 = 1.061800 6.1800 Daily 365 0.01644 1.0001644365 = 1.061831 6.1831 Continuous e.06 = 1.061837 6.1837

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146 Part Two Value

5.8 Inflation and the Time Value of Money When a bank offers to pay 6% on a savings account, it promises to pay interest of $60 for every $1,000 you deposit. The bank fixes the number of dollars that it pays, but it doesn’t provide any assurance of how much those dollars will buy. If the value of your investment increases by 6% while the prices of goods and services increase by 10%, you actually lose ground in terms of the goods you can buy.

Real versus Nominal Cash Flows Prices of goods and services continually change. Textbooks may become more expen- sive (sorry) while computers become cheaper. An overall general rise in prices is known as inflation . If the inflation rate is 5% per year, then goods that cost $1.00 a year ago typically cost $1.05 this year. The increase in the general level of prices means that the purchasing power of money has eroded. If a dollar bill bought one loaf of bread last year, the same dollar this year buys only part of a loaf.

Economists track the general level of prices using several different price indexes. The best known of these is the consumer price index, or CPI. This measures the num- ber of dollars that it takes to buy a specified basket of goods and services that is sup- posed to represent the typical family’s purchases. 5 Thus the percentage increase in the CPI from one year to the next measures the rate of inflation.

Table 5.8 shows the CPI for selected years. The base period for the index is 1982– 1984, so the index shows the price level in each year as a percentage of the average price level during these 3 years. For example, the index in 1950 was 25.0. This means that on average $25 in 1950 would have bought the same quantity of goods and ser- vices as $100 in 1982–1984. By the end of 2013 the index had risen to 233.0. In other words, prices in 2013 were 9.32 times their level in 1950 (233.0/25.0  =  9.32). 6

It is interesting to look at annual inflation rates over a somewhat longer period. These are shown in Figure 5.13 . The peak year for inflation was 1918, when prices rose by 20%, but you can see that there have also been a few years when prices have fallen quite sharply.

inflation Rate at which prices as a whole are increasing.

5 Don’t ask how you buy a “basket” of services. 6 The choice by the Bureau of Labor Statistics of 1982–1984 as a base period is arbitrary. For example, it could have set December 1950 as the base period. In this case the index would have been 100 in 1950 and 932.0 in 2013.

A car loan requiring quarterly payments carries an APR of 8%. What is the effective annual rate of interest?

Self-Test 5.10

CPI Percent Change since 1950

1950 25.0 1960 29.8 + 19.2% 1970 39.8 + 59.2 1980 86.3 + 245.2 1990 133.8 + 435.2 2000 174.0 + 596.0 2013 233.0 + 832.0

TABLE 5.8 The consumer price index (CPI) shows how inflation has increased the cost of a typical family’s purchases.

World inflation rates

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Chapter 5 The Time Value of Money 147

Example 5.14 The Outrageous Price of Gasoline Motorists in 2013, who were paying about $3.60 for a gallon of gasoline, may have looked back longingly to 1981, when they were paying just $1.40 a gallon. But how much had the real price of gasoline changed over this period? Let’s check.

In 2013 the consumer price index was about 2.5 times its level in 1981. If the price of gasoline had risen in line with inflation, it would have cost 2.5  ×  $1.40  =  $3.50 a gallon in 2013. That was the cost of gasoline in 1981 but measured in terms of 2013 dollars rather than 1981 dollars. Thus the real price of gasoline had barely changed over the 32-year period.

Consider a telephone call to London that currently would cost $5. If the real price of telephone calls does not change in the future, how much will it cost you to make a call to London in 50 years if the inflation rate is 5% (roughly its average over the past 30 years)? What if inflation is 10%?

Self-Test 5.11

FIGURE 5.13 Annual rates of inflation in the United States from 1900 to 2013

A n

n u

al in

fla ti

o n

( %

)

25

20

15

5

0

10

-15

-10

-5

20 13

19 10

19 20

19 30

19 40

19 50

19 70

19 60

19 80

20 00

19 90

19 00

Economists sometimes talk about current or nominal dollars versus constant or real dollars. Current or nominal dollars refer to the actual number of dollars of the day; constant or real dollars refer to the amount of purchasing power.

Some expenditures are fixed in nominal terms and therefore decline in real terms when the CPI increases. Suppose you took out a 30-year house mortgage in 1990. The monthly payment was $800. It was still $800 in 2013, even though the CPI increased by a factor of 233.0/133.8 = 1.74 over those years.

What’s the monthly payment for 2013 expressed in real 1990 dollars? The answer is $800/1.74, or $460 per month. The real burden of paying the mortgage was much less in 2013 than in 1990.

Source: Bureau of Labor Statistics.

As we write this in early 2014, all appears quiet on the inflation front. In the United States inflation is running at about 1.5% a year and a few countries are even experienc- ing falling prices, or deflation. This has led some economists to argue that inflation is dead; others are less sure.

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148 Part Two Value

Inflation and Interest Rates Whenever anyone quotes an interest rate, you can be fairly sure that it is a nominal, not a real, rate. It sets the actual number of dollars you will be paid with no offset for future inflation.

If you deposit $1,000 in the bank at a nominal interest rate of 6%, you will have $1,060 at the end of the year. But this does not mean you are 6% better off. Suppose that the inflation rate during the year is also 6%. Then the goods that cost $1,000 last year will now cost $1,000  ×  1.06  =  $1,060, so you’ve gained nothing:

Real future value of investment = $1,000 × (1 + nominal interest rate)

(1 + inflation rate)

= $1,000 × 1.06

1.06 = $1,000

In this example, the nominal rate of interest is 6%, but the real interest rate is zero. The real rate of interest is calculated by

1 + real interest rate = 1 + nominal interest rate

1 + inflation rate (5.8)

In our example both the nominal interest rate and the inflation rate were 6%. So

1 + real interest rate = 1.06

1.06 = 1

Real interest rate = 0

What if the nominal interest rate is 6% but the inflation rate is only 2%? In that case the real interest rate is 1.06/1.02  −  1  =  .039, or 3.9%. Imagine that the price of a loaf of bread is $1, so that $1,000 would buy 1,000 loaves today. If you invest that $1,000 at a nominal interest rate of 6%, you will have $1,060 at the end of the year. However, if the price of loaves has risen in the meantime to $1.02, then your money will buy you 1,060/1.02  =  1,039 loaves. The real rate of interest is 3.9%.

nominal interest rate Rate at which money invested grows.

real interest rate Rate at which the purchasing power of an investment increases.

If a family spent $250 a week on their typical purchases in 1950, how much would those purchases have cost in 1980? If your salary in 1980 was $30,000 a year, what would be the real value of that salary in terms of 1950 dollars? Use the data in Table 5.8 .

Self-Test 5.12

a. Suppose that you invest your funds at an interest rate of 8%. What will be your real rate of interest if the inflation rate is zero? What if it is 5%?

b. Suppose that you demand a real rate of interest of 3% on your invest- ments. What nominal interest rate do you need to earn if the inflation rate is zero? If it is 5%?

Self-Test 5.13

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Chapter 5 The Time Value of Money 149

Here is a useful approximation. The real rate approximately equals the difference between the nominal rate and the inflation rate: 7

Real interest rate < nominal interest rate - inflation rate (5.9)

Our example used a nominal interest rate of 6%, an inflation rate of 2%, and a real rate of 3.9%. If we round to 4%, the approximation gives the same answer:

Real interest rate < nominal interest rate - inflation rate < 6 - 2 = 4%

The approximation works best when both the inflation rate and the real rate are small. When they are not small, throw the approximation away and do it right.

7 The squiggle (≈) means “approximately equal to.”

Example 5.15 Real and Nominal Rates In the United States in mid-2013, long-term high-grade Aaa corporate bonds offered a yield of 3.35%. If inflation is expected to be about 1%, the real yield is

1 + real interest rate = 1 + nominal interest rate

1 + inflation rate =

1.0335 1.01

= 1.0233

Real interest rate = .0233, or 2.33%

The approximation rule gives a similar value of 3.35  −  1.0  =  2.35%. But the approxi- mation would not have worked in the German hyperinflation of 1922–1923, when the inflation rate was well over 100% per month (at one point you needed 1 million marks to mail a letter).

German hyperinflation

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Valuing Real Cash Payments Think again about how to value future cash payments. Earlier in the chapter you learned how to value payments in current dollars by discounting at the nominal inter- est rate. For example, suppose that the nominal interest rate is 10%. How much do you need to invest now to produce $100 in a year’s time? Easy! Calculate the present value of $100 by discounting by 10%:

PV = $100

1.10 = $90.91

You get exactly the same result if you discount the real payment by the real interest rate. For example, assume that you expect inflation of 7% over the next year. The real value of that $100 is therefore only $100/1.07  =  $93.46. In one year’s time your $100 will buy only as much as $93.46 today. Also, with a 7% inflation rate the real rate of interest is only about 3%. We can calculate it exactly from the formula

1 + real interest rate = 1 + nominal interest rate

1 + inflation rate =

1.10

1.07 = 1.028

Real interest rate = .028, or 2.8%

If we now discount the $93.46 real payment by the 2.8% real interest rate, we have a present value of $90.91, just as before:

PV = $93.46

1.028 = $90.91

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150 Part Two Value

The two methods should always give the same answer. Remember: Current dollar cash flows must be discounted by the nominal

interest rate; real cash flows must be discounted by the real interest rate. Mixing up nominal cash flows and real discount rates (or real rates and nominal

flows) is an unforgivable sin. It is surprising how many sinners one finds.

You are owed $5,000 by a relative who will pay it back in 1 year. The nominal interest rate is 8%, and the inflation rate is 5%. What is the present value of your relative’s IOU? Show that you get the same answer (a) discounting the nominal payment at the nominal rate and (b) discounting the real payment at the real rate.

Self-Test 5.14

Example 5.16 How Inflation Might Affect Bill Gates We showed earlier (Example 5.9) that at an interest rate of 6% Bill Gates could, if he wished, turn his $67 billion wealth into a 30-year annuity of $4.9 billion per year of luxury and excitement (L&E). Unfortunately, L&E expenses inflate just like gasoline and groceries. Thus Mr. Gates would find the purchasing power of that $4.9 billion steadily declining. If he wants the same luxuries in 2043 as in 2013, he’ll have to spend less in 2013 and then increase expenditures in line with inflation. How much should he spend in 2013? Assume the long-run inflation rate is 3%.

Mr. Gates needs to calculate a 30-year real annuity. The real interest rate is a little less than 3%:

1 + real interest rate = 1 + nominal interest rate

1 + inflation rate

= 1.06 1.03

= 1.029

so the real rate is 2.9%. The 30-year annuity factor at 2.9% is 19.8562. Therefore, annual spending (in 2013 dollars) should be chosen so that

$67,000,000,000 = annual spending × 19.8562

Annual spending = $3,374,000,000

Mr. Gates could spend that amount on L&E in 1 year’s time and 3% more (in line with inflation) in each subsequent year. This is only about 70% of the value we calcu- lated when we ignored inflation. Life has many disappointments, even for tycoons.

You have reached age 60 with a modest fortune of $3 million and are con- sidering early retirement. How much can you spend each year for the next 30 years? Assume that spending is stable in real terms. The nominal interest rate is 10%, and the inflation rate is 5%.

Self-Test 5.15

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Chapter 5 The Time Value of Money 151

Real or Nominal? Any present value calculation done in nominal terms can also be done in real terms, and vice versa. Most financial analysts forecast in nominal terms and discount at nominal rates. However, in some cases real cash flows are easier to deal with. In our example of Bill Gates, the real expenditures were fixed. In this case, it was easiest to use real quantities. On the other hand, if the cash-flow stream is fixed in nominal terms (for example, the payments on a loan), it is easiest to use all nominal quantities.

SUMMARY An investment of $1 earning an interest rate of r will increase in value each period by the factor (1  +   r ). After t periods its value will grow to $(1  +   r ) t . This is the future value of the $1 investment with compound interest.

The present value of a future cash payment is the amount that you would need to invest today to match that future payment. To calculate present value, we divide the cash payment by (1  +   r ) t or, equivalently, multiply by the discount factor 1/(1  +   r ) t . The discount factor measures the value today of $1 received in period t.

A level stream of cash payments that continues indefinitely is known as a perpetuity; one that continues for a limited number of years is called an annuity. The present value of a stream of cash flows is simply the sum of the present value of each individual cash flow. Similarly, the future value of an annuity is the sum of the future value of each individual cash flow. Shortcut formulas make the calculations for perpetuities and annui- ties easy.

Interest rates for short time periods are often quoted as annual rates by multiplying the per-period rate by the number of periods in a year. These annual percentage rates (APRs) do not recognize the effect of compound interest; that is, they annualize assuming simple interest. The effective annual rate annualizes using compound interest. It equals the rate of interest per period compounded for the number of periods in a year.

A dollar is a dollar, but the amount of goods that a dollar can buy is eroded by inflation. If prices double, the real value of a dollar halves. Financial managers and economists often find it helpful to reexpress future cash flows in terms of real dollars—that is, dollars of constant purchasing power.

Be careful to distinguish the nominal interest rate and the real interest rate —that is, the rate at which the real value of the investment grows. Discount nominal cash flows (that is, cash flows measured in current dollars) at nominal interest rates. Discount real cash flows (cash flows measured in constant dollars) at real interest rates. Never mix and match nominal and real.

If you invest money at a given interest rate, what will be the future value of your investment? (LO5-1)

What is the present value of a cash flow to be received in the future? (LO5-2)

How can we calculate present and future values of streams of cash payments? (LO5-3)

How should we compare interest rates quoted over different time intervals, for example, monthly versus annual rates? (LO5-4)

What is the difference between real and nominal cash flows and between real and nominal interest rates? (LO5-5)

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152 Part Two Value

L I S T I N G O F E Q UAT I O N S

5.1 Future value  =  present value  ×  (1  +   r ) t

5.2 Present value = future value after t periods

(1 + r)t

5.3 PV of perpetuity = C r

=

cash payment

interest rate

5.4 Present value of t-year annuity = C c1 r

-

1

r(1 + r)t d

5.5 Future value (FV) of annuity of $1 a year = present value of annuity of $1 a year × (1 + r)t

= c1 r

-

1

r(1 + r)t d × (1 + r)t

= (1 + r)t - 1

r

5.6 Present value of annuity due  =  (1  +   r )  ×  present value of annuity

5.7 Future value of annuity due  =  future value of ordinary annuity  ×  (1  +   r )

5.8 1 + real interest rate = 1 + nominal interest rate

1 + inflation rate

5.9 Real interest rate ≈ nominal interest rate  −  inflation rate

QUESTIONS AND PROBLEMS 1. Compound Interest. Old Time Savings Bank pays 4% interest on its savings accounts. If you

deposit $1,000 in the bank and leave it there: (LO5-1)

a. How much interest will you earn in the first year? b. How much interest will you earn in the second year? c. How much interest will you earn in the tenth year?

2. Compound Interest. New Savings Bank pays 4% interest on its deposits. If you deposit $1,000 in the bank and leave it there, will it take more or less than 25 years for your money to double? You should be able to answer this without a calculator or interest rate tables. (LO5-1)

3. Compound Interest. Investments in the stock market have increased at an average compound rate of about 5% since 1900. It is now 2013. (LO5-1)

a. If you invested $1,000 in the stock market in 1900, how much would that investment be worth today?

b. If your investment in 1900 has grown to $1 million, how much did you invest in 1900?

4. Future Values. Compute the future value of a $100 cash flow for the following combinations of rates and times. (LO5-1)

a. r   =  8%,  t   =  10 years b. r   =  8%,  t   =  20 years c. r   =  4%,  t   =  10 years d. r   =  4%,  t   =  20 years

finance

®

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Chapter 5 The Time Value of Money 153

5. Future Values. You deposit $1,000 in your bank account. (LO5-1)

a. If the bank pays 4% simple interest, how much will you accumulate in your account after 10 years?

b. How much will you accumulate if the bank pays compound interest?

6. Future Values. If you earn 6% per year on your bank account, how long will it take an account with $100 to double to $200? (LO5-1)

7. Future Values. In 1880 five aboriginal trackers were each promised the equivalent of 100 Aus- tralian dollars for helping to capture the notorious outlaw Ned Kelley. In 1993 the granddaugh- ters of two of the trackers claimed that this reward had not been paid. The Victorian prime minister stated that if this was true, the government would be happy to pay the $100. However, the granddaughters also claimed that they were entitled to compound interest. (LO5-1)

a. How much was each granddaughter entitled to if the interest rate was 4%? b. How much was each entitled to if the interest rate was 8%?

8. Future Values. How long will it take for $400 to grow to $1,000 at the following interest rates? (LO5-1)

a. 4% b. 8% c. 16%

9. Future Values. You invest $1,000 today and expect to sell your investment for $2,000 in 10 years. (LO5-1)

a. Is this a good deal if the interest rate is 6%? b. What if the interest rate is 10%?

10. Present Values. You can buy property today for $3 million and sell it in 5 years for $4 million. (You earn no rental income on the property.) (LO5-2)

a. If the interest rate is 8%, what is the present value of the sales price? b. Is the property investment attractive to you? c. Would your answer to (b) change if you also could earn $200,000 per-year rent on the prop-

erty? The rent is paid at the end of each year.

11. Present Values. Compute the present value of a $100 cash flow for the following combinations of discount rates and times. (LO5-2)

a. r   =  8%,  t   =  10 years b. r   =  8%,  t   =  20 years c. r   =  4%,  t   =  10 years d. r   =  4%,  t   =  20 years

12. Present Values. You will require $700 in 5 years. If you earn 5% interest on your funds, how much will you need to invest today in order to reach your savings goal? (LO5-2)

13. Present Values. What is the present value of the following cash-flow stream if the interest rate is 6%? (LO5-2)

Present Value Years Future Value

$400 11 $684 183 4 249 300 7 300

Year Cash Flow

1 $200 2 400 3 300

14. Calculating the Interest Rate. Find the interest rate implied by the following combinations of present and future values. (LO5-2)

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154 Part Two Value

16. Calculating the Interest Rate. A zero-coupon bond that will pay $1,000 in 10 years is selling today for $422.41. What interest rate does the bond offer? (LO5-2)

17. Present Values. A factory costs $400,000. You forecast that it will produce cash inflows of $120,000 in year 1, $180,000 in year 2, and $300,000 in year 3. The discount rate is 12%. (LO5-2)

a. What is the value of the factory? b. Is the factory a good investment?

18. Annuities. A famous quarterback just signed a $15 million contract providing $3 million a year for 5 years. A less famous receiver signed a $14 million 5-year contract providing $4 million now and $2 million a year for 5 years. The interest rate is 10%. Who is better paid? (LO5-3)

19. Annuities. Would you rather receive $1,000 a year for 10 years or $800 a year for 15 years if the interest rate is 5%? What if the interest rate is 20%? (LO5-3)

20. Perpetuities. A local bank advertises the following deal: “Pay us $100 a year for 10 years and then we will pay you (or your beneficiaries) $100 a year forever.” Is this a good deal if the inter- est rate available on other deposits is 6%? (LO5-3)

21. Perpetuities. A local bank will pay you $100 a year for your lifetime if you deposit $2,500 in the bank today. If you plan to live forever, what interest rate is the bank paying? (LO5-3)

22. Perpetuities. A property will provide $10,000 a year forever. If its value is $125,000, what must be the discount rate? (LO5-3)

23. Perpetuities. British government 4% perpetuities pay £4 interest each year forever. Another bond, 2.5% perpetuities, pays £2.50 a year forever. (LO5-3)

a. What is the value of 4% perpetuities if the long-term interest rate is 6%? b. What is the value of 2.5% perpetuities?

24. Annuities. (LO5-3)

a. What is the present value of a 3-year annuity of $100 if the discount rate is 6%? b. What is the present value of the annuity in (a) if you have to wait 2 years instead of 1 year

for the first payment?

25. Annuities. Professor’s Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $80,000 at age 65, the firm will pay the retiring professor $600 a month until death. (LO5-3)

a. If the professor’s remaining life expectancy is 20 years, what is the monthly interest rate on this annuity?

b. What is the effective annual interest rate? c. If the monthly interest rate is .5%, what monthly annuity payment can the firm offer to the

retiring professor?

26. Annuities. You want to buy a new car, but you can make an initial payment of only $2,000 and can afford monthly payments of at most $400. (LO5-3)

a. If the APR on auto loans is 12% and you finance the purchase over 48 months, what is the maximum price you can pay for the car?

b. How much can you afford if you finance the purchase over 60 months?

27. Annuities. You can buy a car that is advertised for $24,000 on the following terms: (a) pay $24,000 and receive a $2,000 rebate from the manufacturer; (b) pay $500 a month for 4 years for total payments of $24,000, implying zero percent financing. Which is the better deal if the interest rate is 1% per month? (LO5-3)

28. Annuities. You have just borrowed $100,000 to buy a condo. You will repay the loan in equal monthly payments of $804.62 over the next 30 years. (LO5-4)

a. What monthly interest rate are you paying on the loan? What is the APR? b. What is the effective annual rate on that loan? c. What rate is the lender more likely to quote on the loan?

15. Calculating the Interest Rate. Find the annual interest rate. (LO5-2)

Present Value Future Value Time Period

$100 $115.76 3 years 200 262.16 4 100 110.41 5

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Chapter 5 The Time Value of Money 155

29. Future Value of Annuities. I now have $20,000 in the bank earning interest of .5% per month. I need $30,000 to make a down payment on a house. I can save an additional $100 per month. How long will it take me to accumulate the $30,000? (LO5-3)

30. Real Annuities. A retiree wants level consumption in real terms over a 30-year retirement. If the inflation rate equals the interest rate she earns on her $450,000 of savings, how much can she spend in real terms each year over the rest of her life? (LO5-3)

31. Delayed Annuities. Suppose that you will receive annual payments of $10,000 for a period of 10 years. The first payment will be made 4 years from now. If the interest rate is 5%, what is the present value of this stream of payments? (LO5-3)

32. Annuity Due. Your landscaping company can lease a truck for $8,000 a year (paid at year-end) for 6 years. It can instead buy the truck for $40,000. The truck will be valueless after 6 years. The interest rate your company can earn on its funds is 7%. (LO5-3)

a. What is the cost of leasing? b. Is it cheaper to buy or lease? c. What if the lease payments are an annuity due, so the first payment comes immediately? Is

it cheaper to buy or lease?

33. Annuity Due. Recall that an annuity due is like an ordinary annuity except that the first pay- ment is made immediately instead of at the end of the first period. (LO5-3)

a. Why is the present value of an annuity due equal to (1  +   r ) times the present value of an ordinary annuity?

b. Why is the future value of an annuity due equal to (1  +   r ) times the future value of an ordi- nary annuity?

34. Annuity Due. A store offers two payment plans. Under the installment plan, you pay 25% down and 25% of the purchase price in each of the next 3 years. If you pay the entire bill immediately, you can take a 10% discount from the purchase price. (LO5-3)

a. Which is a better deal if you can borrow or lend funds at a 5% interest rate? b. How will your answer change if the payments on the 4-year installment plan do not start for

a full year?

35. Annuity Due. (LO5-3)

a. If you borrow $1,000 and agree to repay the loan in five equal annual payments at an interest rate of 12%, what will your payment be?

b. What will your payment be if you make the first payment on the loan immediately instead of at the end of the first year?

36. Annuity Due. The $40 million lottery payment that you have just won actually pays $2 million per year for 20 years. The interest rate is 8%. (LO5-3)

a. If the first payment comes in 1 year, what is the present value of the winnings? b. What is the present value if the first payment comes immediately?

37. Amortizing Loan. You take out a 30-year $100,000 mortgage loan with an APR of 6% and monthly payments. In 12 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan? (LO5-3)

38. Amortizing Loan. Consider a 4-year amortizing loan. You borrow $1,000 initially and repay it in four equal annual year-end payments. (LO5-3)

a. If the interest rate is 8%, what is the annual payment? b. Fill in the following table, which shows how much of each payment is interest versus princi-

pal repayment (that is, amortization) and the outstanding balance on the loan at each date.

Time Loan

Balance, $ Year-End Interest Due on

Loan Balance, $ Total Year-End

Payment, $ Amortization of

Loan, $

0 1,000 80 301.92 221.92 1 ——— ——— 301.92 ——— 2 ——— ——— 301.92 ——— 3 ——— ——— 301.92 ——— 4 0 0

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156 Part Two Value

39. Mortgage with Points. Home loans typically involve “points,” which are fees charged by the lender. Each point charged means that the borrower must pay 1% of the loan amount as a fee. For example, if the loan is for $100,000 and 2 points are charged, the loan repayment schedule is calculated on a $100,000 loan but the net amount the borrower receives is only $98,000. Assume the interest rate is 1% per month. What is the effective annual interest rate charged on such a loan, assuming loan repayment occurs over 360 months? (LO5-4)

40. Retirement Savings. A couple will retire in 50 years; they plan to spend about $30,000 a year in retirement, which should last about 25 years. They believe that they can earn 8% interest on retirement savings. (LO5-3)

a. If they make annual payments into a savings plan, how much will they need to save each year? Assume the first payment comes in 1 year.

b. How would the answer to part (a) change if the couple also realize that in 20 years they will need to spend $60,000 on their child’s college education?

41. Retirement Savings. You believe you will need to have saved $500,000 by the time you retire in 40 years in order to live comfortably. If the interest rate is 6% per year, how much must you save each year to meet your retirement goal? (LO5-3)

42. Retirement Savings. You believe you will need to have saved $500,000 by the time you retire in 40 years in order to live comfortably. You also believe that you will inherit $100,000 in 10 years. If the interest rate is 6% per year, how much must you save each year to meet your retire- ment goal? (LO5-3)

43. Retirement Savings. You believe you will spend $40,000 a year for 20 years once you retire in 40 years. If the interest rate is 6% per year, how much must you save each year until retirement to meet your retirement goal? (LO5-3)

44. Retirement Savings. A couple thinking about retirement decide to put aside $3,000 each year in a savings plan that earns 8% interest. In 5 years they will receive a gift of $10,000 that also can be invested. (LO5-3)

a. How much money will they have accumulated 30 years from now? b. If their goal is to retire with $800,000 of savings, how much extra do they need to save

every year?

45. Effective Interest Rate. A store will give you a 3% discount on the cost of your purchase if you pay cash today. Otherwise, you will be billed the full price with payment due in 1 month. What is the implicit borrowing rate being paid by customers who choose to defer payment for the month? (LO5-4)

46. Effective Interest Rate. You’ve borrowed $4,248.68 and agreed to pay back the loan with monthly payments of $200. If the interest rate is 12% stated as an APR, how long will it take you to pay back the loan? What is the effective annual rate on the loan? (LO5-4)

47. Effective Interest Rate. You invest $1,000 at a 6% annual interest rate, stated as an APR. Inter- est is compounded monthly. How much will you have in 1 year? In 1.5 years? (LO5-4)

48. Effective Interest Rate. If a bank pays 6% interest with continuous compounding, what is the effective annual rate? (LO5-4)

49. Effective Interest Rate. In a discount interest loan, you pay the interest payment up front. For example, if a 1-year loan is stated as $10,000 and the interest rate is 10%, the borrower “pays” .10  ×  $10,000  =  $1,000 immediately, thereby receiving net funds of $9,000 and repay- ing $10,000 in a year. (LO5-4)

a. What is the effective interest rate on this loan? b. What is the effective annual rate on a 1-year loan with an interest rate quoted on a discount

basis of 20%?

50. Effective Interest Rate. Banks sometimes quote interest rates in the form of “add-on interest.” In this case, if a 1-year loan is quoted with a 20% interest rate and you borrow $1,000, then you pay back $1,200. But you make these payments in monthly installments of $100 each. (LO5-4)

a. What is the true APR on this loan? b. What is the effective annual rate on the loan?

51. Effective Interest Rate. You borrow $1,000 from the bank and agree to repay the loan over the next year in 12 equal monthly payments of $90. However, the bank also charges you a loan initiation fee of $20, which is taken out of the initial proceeds of the loan. What is the effective annual interest rate on the loan, taking account of the impact of the initiation fee? (LO5-4)

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Chapter 5 The Time Value of Money 157

56. Effective Interest Rate. Find the APR (the stated interest rate) for each case. (LO5-4)

52. Effective Interest Rate. First National Bank pays 6.2% interest compounded semiannually. Second National Bank pays 6% interest compounded monthly. Which bank offers the higher effective annual interest rate? (LO5-4)

53. Loan Payments. You take out an $8,000 car loan that calls for 48 monthly payments starting after 1 month at an APR of 10%. (LO5-4)

a. What is your monthly payment? b. What is the effective annual interest rate on the loan? c. What if the payments are made in four annual year-end installments? What annual payment

would have the same present value as the monthly payment you calculated?

54. Continuous Compounding. How much will $100 grow to if invested at a continuously com- pounded interest rate of 10% for 8 years? What if it is invested for 10 years at 8%? (LO5-4)

55. Effective Interest Rate. Find the effective annual interest rate for each case. (LO5-4)

APR Compounding Period

12% 1 month 8 3

10 6

Effective Annual Interest Rate

Compounding Period

10.00% 1 month 6.09 6 8.24 3

57. Effective Interest Rate. Lenny Loanshark charges “1 point” per week (that is, 1% per week) on his loans. What APR must he report to consumers? Assume exactly 52 weeks in a year. What is the effective annual rate? (LO5-4)

58. Effective Interest Rate. Suppose you can borrow money at 8.6% per year (APR) compounded semiannually or 8.4% per year (APR) compounded monthly. Which is the better deal? (LO5-4)

59. Effective Interest Rate. If you take out an $8,000 car loan that calls for 48 monthly payments of $240 each, what is the APR of the loan? What is the effective annual interest rate on the loan? (LO5-4)

60. Inflation. In April 2013 a pound of apples cost $1.41, while oranges cost $1.05. Four years ear- lier the price of apples was only $1.20 a pound and that of oranges was $.91 a pound. (LO5-5)

a. What was the annual compound rate of growth in the price of apples? b. What was the annual compound rate of growth in the price of oranges? c. If the same rates of growth persist in the future, what will be the price of apples in 2030? d. What about the price of oranges?

61. Real versus Nominal Dollars. An engineer in 1950 was earning $6,000 a year. Today she earns $60,000 a year. However, on average, goods today cost 8.8 times what they did in 1950. What is her real income today in terms of constant 1950 dollars? (LO5-5)

62. Real versus Nominal Dollars. Your consulting firm will produce cash flows of $100,000 this year, and you expect cash flow to keep pace with any increase in the general level of prices. The interest rate currently is 6%, and you anticipate inflation of about 2%. (LO5-5)

a. What is the present value of your firm’s cash flows for years 1 through 5? b. How would your answer to (a) change if you anticipated no growth in cash flow?

63. Real versus Nominal Rates. If investors are to earn a 3% real interest rate, what nominal inter- est rate must they earn if the inflation rate is zero? 4%? 6%? (LO5-5)

64. Real versus Nominal Rates. If investors receive a 6% interest rate on their bank deposits, what real interest rate will they earn if the inflation rate over the year is zero? 3%? 6%? (LO5-5)

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158 Part Two Value

65. Real versus Nominal Rates. You will receive $100 from a savings bond in 3 years. The nomi- nal interest rate is 8%. (LO5-5)

a. What is the present value of the proceeds from the bond? b. If the inflation rate over the next few years is expected to be 3%, what will the real value of

the $100 payoff be in terms of today’s dollars? c. What is the real interest rate? d. Show that the real payoff from the bond [from part (b)] discounted at the real interest rate

[from part (c)] gives the same present value for the bond as you found in part (a).

CHALLENGE PROBLEMS 66. Future Values. Your wealthy uncle established a $1,000 bank account for you when you were

born. For the first 8 years of your life, the interest rate earned on the account was 6%. Since then, rates have been only 4%. Now you are 21 years old and ready to cash in. How much is in your account? (LO5-1)

67. Present Values. If the interest rate this year is 8% and the interest rate next year will be 10%, what is the future value of $1 after 2 years? What is the present value of a payment of $1 to be received in 2 years? (LO5-2)

68. Perpetuities and Effective Interest Rate. What is the value of a perpetuity that pays $100 every 3 months forever? The interest rate quoted on an APR basis is 6%. (LO5-3)

69. Amortizing Loans and Inflation. Suppose you take out a $100,000, 20-year mortgage loan to buy a condo. The interest rate on the loan is 6%, and to keep things simple, we will assume you make payments on the loan annually at the end of each year. (LO5-3)

a. What is your annual payment on the loan? b. Construct a mortgage amortization table in Excel similar to Table 5.5 in which you compute

the interest payment each year, the amortization of the loan, and the loan balance each year. (Allow the interest rate to be an input that the user of the spreadsheet can enter and change.)

c. What fraction of your initial loan payment is interest? d. What fraction of your initial loan payment is amortization? e. What fraction of the loan has been paid off after 10 years (halfway through the life of

the loan)? f. If the inflation rate is 2%, what is the real value of the first (year-end) payment? g. If the inflation rate is 2%, what is the real value of the last (year-end) payment? h. Now assume the inflation rate is 8% and the real interest rate on the loan is unchanged. What

must be the new nominal interest rate? i. Recompute the amortization table. What is the real value of the first (year-end) payment in

this high-inflation scenario? j. What is the real value of the last payment in this high-inflation scenario?

70. Real versus Nominal Perpetuities. If the interest rate is 6% per year, how long will it take for your money to quadruple in value? If the inflation rate is 4% per year, what will be the change in the purchasing power of your money over this period? (LO5-5)

71. Real versus Nominal Annuities. Good news: You will almost certainly be a millionaire by the time you retire in 50 years. Bad news: The inflation rate over your lifetime will average about 3%. (LO5-5)

a. What will be the real value of $1 million by the time you retire in terms of today’s dollars? b. What real annuity (in today’s dollars) will $1 million support if the real interest rate at retire-

ment is 2% and the annuity must last for 20 years?

72. Inflation. In the summer of 2007, Zimbabwe’s official inflation rate was about 110% per month. What was the annual inflation rate? (LO5-5)

73. Real versus Nominal Annuities. You plan to retire in 30 years and want to accumulate enough by then to provide yourself with $30,000 a year for 15 years. (LO5-5)

a. If the interest rate is 10%, how much must you accumulate by the time you retire? b. How much must you save each year until retirement in order to finance your retirement

consumption?

Templates can be found in Connect.

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Chapter 5 The Time Value of Money 159

c. Now you remember that the annual inflation rate is 4%. If a loaf of bread costs $1 today, what will it cost by the time you retire?

d. You really want to consume $30,000 a year in real dollars during retirement and wish to save an equal real amount each year until then. What is the real amount of savings that you need to accumulate by the time you retire?

e. Calculate the required preretirement real annual savings necessary to meet your consump- tion goals.

f. What is the nominal value of the amount you need to save during the first year? (Assume the savings are put aside at the end of each year.)

g. What is the nominal value of the amount you need to save during the thirtieth year?

74. Retirement and Inflation. A couple will retire in 50 years; they plan to spend about $30,000 a year in retirement, which should last about 25 years. They believe that they can earn 8% interest on retirement savings. The inflation rate over the next 75 years is expected to average 5%. (LO5-5)

a. What is the real annual savings the couple must set aside? b. How much do they need to save in nominal terms in the first year? c. How much do they need to save in nominal terms in the last year? d. What will be their nominal expenditures in the first year of retirement? e. What will be their nominal expenditures in the last year of retirement?

75. Real versus Nominal Cash Flows. (LO5-5)

a. It is 2015, you’ve just graduated college, and you are contemplating your lifetime budget. You think your general living expenses will average around $50,000 a year. For the next 8 years, you will rent an apartment for $16,000 a year. After that, you will want to buy a house that should cost around $250,000. In addition, you will need to buy a new car roughly once every 10 years, costing around $30,000 each. In 25 years, you will have to put aside around $150,000 to put a child through college, and in 30 years you’ll need to do the same for another child. In 50 years, you will retire and will need to have accumulated enough sav- ings to support roughly 20 years of retirement spending of around $35,000 a year on top of your Social Security benefits. The interest rate is 5% per year. What average salary will you need to earn to support this lifetime consumption plan?

b. Whoops! You just realized that the inflation rate over your lifetime is likely to average about 3% per year, and you need to redo your calculations. As a rough cut, it seems reasonable to assume that all relevant prices and wages will increase at around the rate of inflation. What is your new estimate of the required salary (in today’s dollars)?

76. Time Value of Money. Solve the following crossword. (Round your final answers to the nearest dollar, but do not round intermediate calculations.)

1

11

15 16

20 21

22

18 19

12

10

8

13

17

14

23 24

2

9

3 4 5 6 7

Templates can be found in Connect.

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160 Part Two Value

ACROSS 1. A rich uncle has promised to pay you $3,160 a year for the next 25 years. If you invest this

money at 4.9%, how much will you have at the end of the 25 years?

5. Alexander put $10,000 under his mattress 20 years ago. Since then inflation has averaged 1%. What is the real value of his savings?

9. A 20-year annuity has a present value of $42,419,233. If the interest rate is 15%, what is the annual cash flow?

10. A Treasury bond pays $1 million at the end of 20 years. What is its present value if the interest rate is 4%?

11. A project is forecast to produce a safe cash flow of $800,000 a year for 20 years. If the cost of capital is 4%, what is the present value of the project?

12. If you invest $100,000 today, how much will your savings be worth at the end of 9 years if the interest rate is 10%?

15. An annuity due with 10 annual payments has a present value of 1,244,353. If the interest rate is 15%, what is the annual payment?

18. Investment in a Dustinbourne grinder is expected to produce cash flows over the following 7 years of $7 million, $8 million, $9 million, $10 million, $9 million, $8 million, and $7 million. What is the present value of the project if the cost of capital is 5%?

20. You invest $95,525 for 20 years at 11.7%. Inflation over the same period is 4% a year. What is the real value of your savings at the end of that period?

22. You invest $1 million for 7 years at 5% and then for a further 7 years at 8%. How much will you have at the end of this time?

23. The discount factor is .8, and the present value of a cash flow is $2,703. What is the cash flow?

24. A deferred annuity makes four equal payments of $129,987 a year starting at the end of year 8. If the interest rate is 12%, what is its present value?

DOWN 2. The winning lottery ticket promises to make 30 payments of $30,000 a year starting immedi-

ately. If the interest rate is 5.8%, what is the present value of these payments?

3. An investment in consol bonds promises to provide an interest payment of $2.5 million a year in perpetuity. If the interest rate is 3.3%, what is the value of this investment?

4. The discount factor is .9. What is the present value of $63,269?

6. If you pay the bank $50 a year for 10 years, it promises to pay you $100 a year forever starting in year 11. If the interest rate is 4.2%, what is the value of this proposal to you?

7. The nominal interest rate is 13% and inflation is 4%. If you invest $100,000 today, what will be the real value of your investment at the end of 20 years?

8. What is the value of a payment of $2,125,000 in year 30 if the interest rate is 3.8%?

13. What is the future value of an investment of $20 million at the end of 11 years if the interest rate is 9%?

14. Henry Hub has 25 years to retirement and expects to spend a further 20 years in retirement (i.e., years 21–45). He lives an extravagant lifestyle and has drawn up a detailed spreadsheet which suggests that he will spend $256,880 a year in real terms in retirement. If the real interest rate is 3%, how much does Henry need to save each year in real terms until retirement to attain his spending goal?

16. A factory is forecast to produce the following cash flows: year 1, $6,516; year 2, $7,000; year 3 $11,400; year 4 onward in perpetuity, $12,000. If the cost of capital is 6%, what is the factory’s present value?

17. What is the future value of $189,956 at the end of 7 years if the interest rate is 11%?

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Chapter 5 The Time Value of Money 161

19. Natasha has savings of $78,780. If she invests the full amount in a bank at an interest rate of 4%, how much will she have after 4 years?

21. You plan to save $1,000 a year. If the interest rate is 8%, how much will you have saved by the end of year 5?

SOLUTIONS TO SELF-TEST QUESTIONS 5.1 Value after 5 years would have been 24  ×   (1.05) 5   =   $30.63; after 50 years,

24  ×  (1.05) 50   =  $275.22.

5.2 Call g the annual growth rate of transistors over the 39-year period between 1971 and 2010. Then

2,250 × (1 + g)39 = 2,300,000,000

(1 + g)39 = 1,022,222

1 + g = 1,022,2221/39 = 1.43

So the actual growth rate was g   =  .43, or 43%, not quite as high as Moore’s prediction, but not so shabby either.

5.3 Multiply the €1,000 payment by the 3-year discount factor:

PV = €1,000 × 1

(1.025)3 = €928.60

5.4

WEB EXERCISES 1. You can buy a car for $20,000, or you can lease it for 36 monthly payments of $350 each, with

the first payment due immediately. At the end of the 36 months the car will be worth $10,000. Which alternative should you prefer if the interest rate (APR) is 12%? You can check your answer by logging on to the personal finance page of www.smartmoney.com and using the buy or lease calculator.

2. In Example 5.10 we showed you how to work out mortgage payments. Log on to the personal finance page of www.smartmoney.com and find the mortgage payment calculator. Assume a 20-year mortgage loan of $100,000 and an interest rate (APR) of 12%. What is the amount of the monthly payment? Check that you get the same answer when using the annuity formula. Now look at how much of the first month’s payment goes to reduce the size of the mortgage. How much of the payment by the tenth year? Can you explain why the figure changes? If the interest rate doubles, would you expect the mortgage payment to double? Check whether you are right.

3. You can find data on the consumer price index (CPI) on the Bureau of Labor Statistics Website, www.bls.gov/cpi/home.htm . Tables of historical data can be formatted to provide either levels of the index or changes in the index (i.e., the rate of inflation). Construct a table of annual infla- tion rates since 1913. When did the USA last experience a year of deflation (i.e., falling prices)? Find the inflation rate in the latest year. Now log on to www.bloomberg.com , and on the first page find a measure of the short-term interest rate (e.g., the 2-year rate). Use the recent level of inflation to calculate the real interest rate. Consider the case of Herbert Protheroe, who in 1920 was an eligible bachelor with an income of $2,000 a year. What is that equivalent to today?

Gift at Year Present Value

1 10,000/(1.07)    =  $9,345.79 2 10,000/(1.07) 2    =     8,734.39 3 10,000/(1.07) 3    =     8,162.98 4 10,000/(1.07) 4    =     7,628.95

  $33,872.11

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162 Part Two Value

5.5 The rate is 4/48  =  .0833, about 8.3%.

5.6 The 4-year discount factor is 1/(1.08) 4   =   .7350. The 4-year annuity factor is [1/.08  − 1/(.08  ×  1.08 4 )]  =  3.3121. This is the difference between the present value of a $1 perpetuity starting next year and the present value of a $1 perpetuity starting in year 5:

PV (perpetuity starting next year) = 1

.08 = 12.50

-PV (perpetuity starting in year 5) = 1

.08 ×

1 (1.08)4

= 9.1879

= PV (4-year annuity) = 12.50 - 9.1879 = 3.3121

which matches the annuity factor.

5.7 You will need the present value at 7% of a 20-year annuity of $55,000:

Present value = annual spending × annuity factor

The annuity factor is [1/.07  −  1/(.07  ×  1.07 20 )]  =  10.5940. Thus you need $55,000  ×  10.594  =   $582,670.

5.8 Fifteen years means 180 months. Then

Mortgage payment = 100,000

180-month annuity factor

= 100,000

83.32

= $1,200.17 per month

$1,000 of the payment is interest. The remainder, $200.17, is amortization.

5.9 We know that the future value of an annuity due is equal to the future value of an ordinary annuity ×  (1  +   r ). Therefore, if you make the first of your 50 annual investments immediately, then by the end of the 50 years your retirement savings will be 10% higher, $550,000.

5.10 The quarterly rate is 8/4  =  2%. The effective annual rate is (1.02) 4   −  1  =  .0824, or 8.24%.

5.11 The cost in dollars will increase by 5% each year, to a value of $5  ×  (1.05) 50   =  $57.34. If the inflation rate is 10%, the cost will be $5  ×  (1.10) 50   =  $586.95.

5.12 The CPI in 1980 was 3.452 times its value in 1950 (see Table 5.8 ). Therefore, purchases that cost $250 in 1950 would have cost $250  ×  3.452  =  $863 in 1980. The value of a 1980 salary of $30,000, expressed in real 1950 dollars, is $30,000  ×  (1/3.452)  =  $8,691.

5.13 a. If there’s no inflation, real and nominal rates are equal at 8%. With 5% inflation, the real rate is (1.08/1.05)  −  1  =  .02857, a bit less than 3%.

b. If you want a 3% real interest rate, you need a 3% nominal rate if inflation is zero and an 8.15% rate if inflation is 5%. Note that 1.03  ×  1.05  =  1.0815.

5.14 The present value is

PV = $5,000

1.08 = $4,629.63

The real interest rate is 2.857% (see Self-Test 5.13a). The real cash payment is $5,000/1.05  =  $4,761.90. Thus,

PV = $4,761.90

1.02857 = $4,629.63

Gift at Year Future Value

1 10,000 × (1.07) 3    =  $12,250.43 2 10,000 × (1.07) 2    =    11,449 3 10,000 × (1.07)     =     10,700 4 10,000   =   10,000 $44,399.43

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Chapter 5 The Time Value of Money 163

5.15 Calculate the real annuity. The real interest rate is 1.10/1.05  −   1  =   .0476. We’ll round to 4.8%. The real annuity is

Annual payment = $3,000,000

30-year annuity factor =

$3,000,000

1

.048 -

1

.048(1.048)30

=

$3,000,000

15.7292 = $190,728

You can spend this much each year in dollars of constant purchasing power. The purchasing power of each dollar will decline at 5% per year, so you’ll need to spend more in nominal dol- lars: $190,728  ×  1.05  =  $200,264 in the second year, $190,728  ×  1.05 2   =  $210,278 in the third year, and so on.

MINICASE Old Alfred Road, who is well-known to drivers on the Maine Turn- pike, has reached his seventieth birthday and is ready to retire. Mr. Road has no formal training in finance but has saved his money and invested carefully.

Mr. Road owns his home—the mortgage is paid off—and does not want to move. He is a widower, and he wants to bequeath the house and any remaining assets to his daughter.

He has accumulated savings of $180,000, conservatively invested. The investments are yielding 9% interest. Mr. Road also has $12,000 in a savings account at 5% interest. He wants to keep the savings account intact for unexpected expenses or emergencies.

Mr. Road’s basic living expenses now average about $1,500 per month, and he plans to spend $500 per month on travel and hob- bies. To maintain this planned standard of living, he will have to rely on his investment portfolio. The interest from the portfolio is $16,200 per year (9% of $180,000), or $1,350 per month.

Mr. Road will also receive $750 per month in Social Security payments for the rest of his life. These payments are indexed for

inflation. That is, they will be automatically increased in propor- tion to changes in the consumer price index.

Mr. Road’s main concern is with inflation. The inflation rate has been below 3% recently, but a 3% rate is unusually low by his- torical standards. His Social Security payments will increase with inflation, but the interest on his investment portfolio will not.

What advice do you have for Mr. Road? Can he safely spend all the interest from his investment portfolio? How much could he withdraw at year-end from that portfolio if he wants to keep its real value intact?

Suppose Mr. Road will live for 20 more years and is will- ing to use up all of his investment portfolio over that period. He also wants his monthly spending to increase along with inflation over that period. In other words, he wants his monthly spending to stay the same in real terms. How much can he afford to spend per month?

Assume that the investment portfolio continues to yield a 9% rate of return and that the inflation rate will be 4%.

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164

Valuing Bonds

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

6-1 Distinguish among a bond’s coupon rate, current yield, and yield to maturity.

6-2 Find the market price of a bond given its yield to maturity, find a bond’s yield given its price, and demonstrate why prices and yields move in opposite directions.

6-3 Show why bonds exhibit interest rate risk.

6-4 Understand why investors draw a plot of bond yields against maturity.

6-5 Understand why investors pay attention to bond ratings and demand a higher interest rate for bonds with low ratings.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

6 CHAPTE R

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165

P A

R T

TW O

W hen a corporation needs external financ-ing, it can borrow money. If it needs the money for a month, quarter, or year, it will probably borrow from a bank. If it needs to make a

long-term investment, it may instead issue a bond,

which is a debt security held by individual and insti-

tutional investors.

You can’t be financially literate without under-

standing how bonds are priced. For example, bond

prices determine interest rates and therefore the time

value of money.

Companies are not the only bond issuers. State

and local governments also raise money by selling

bonds. So does the U.S. Treasury. Most investors would

regard the risk of default on Treasury bonds as neg-

ligible, and therefore these issues offer a lower rate

of interest than corporate bonds. Nevertheless, the

interest rates on government bonds provide a bench-

mark for all interest rates. When government interest

rates go up or down, corporate rates follow more or

less proportionally. Therefore, in the first part of this

chapter we focus on Treasury bonds and sidestep

the issue of default.

We begin by showing you how to understand the

bond pages in the financial press, and we explain

what bond dealers mean when they quote yields to

maturity. We look at why short-term rates are usually

lower (but sometimes higher) than long-term rates

and why the longest-term bond prices are most sen-

sitive to fluctuations in interest rates. We distinguish

real (inflation-adjusted) interest rates and nominal

(money) rates and explain how future inflation can

affect interest rates.

Toward the end of the chapter we return to cor-

porate bonds, which carry a possibility of default.

We look at how bond ratings provide a guide to that

default risk and how low-rated bonds offer higher

promised yields. There is enormous variation in the

design of corporate bonds, but we postpone that

topic until Chapter 14.

Va lu

e

Bondholders once received a beautifully engraved certificate like this one issued by a railroad. Nowadays their ownership is simply recorded on an electronic database.

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166 Part Two Value

6.1 The Bond Market Governments and corporations borrow money by selling bonds to investors. The mar- ket for these bonds is huge. In 2013 public holdings of U.S. government bonds totaled $12 trillion ($12,000,000,000,000). Companies also raise very large sums of money by selling bonds. For example, in 2013 Apple borrowed $17 billion by an issue of bonds. The market for bonds is sophisticated and active. Bond traders frequently make massive trades motivated by tiny price discrepancies.

Bonds sometimes acquire different names. For example, Treasury bonds with when-issued maturities of 2 to 10 years are called “notes.” Some corporate bonds are called notes or “debentures.” In this chapter we will simplify and just say “bonds.”

When governments or companies issue bonds, they promise to make a series of inter- est payments and then to repay the debt. But don’t get the idea that all bonds are alike. For example, most bonds make a fixed interest payment, but in other cases the payment may go up or down as short-term interest rates change. Bonds may also have different maturities. Sometimes a company may borrow for only a few years, but there have been a few occasions when bonds have been issued with maturities of 100 years or more.

Bond Characteristics In May 1986 the U.S. government made a typical issue of a Treasury bond. It auc- tioned off to investors $9 billion of 7.25% bonds maturing in 2016. The bonds have a face value (also called the principal or par value ) of $1,000. Each year until the bond matures, the bondholder receives an interest payment of 7.25% of the face value, or $72.50. This 7.25% interest payment is called the bond’s coupon. (In the old days, most bonds used to have coupons that the investor clipped off and mailed to the bond issuer to claim the interest payment.) When the 7.25% coupon bond matures in 2016, the government must pay the $1,000 face value of the bond in addition to the final coupon payment.

At last count there were 269 different Treasury bonds. The prices at which you can buy and sell each of these bonds are shown each day in the financial press and on the web. Table 6.1 , which is compiled from The Wall Street Journal ’s web page, shows the prices for just a small sample of issues. The entry for the 7.25% bond maturing in May 2016 is highlighted.

Anyone buying the 7.25% bond would need to pay the asked price, which is 120.664. This means that the price is 120.664% of face value. Therefore, each bond costs $1,206.64. An investor who already owns the bond and wishes to sell it would receive the bid price, which is shown as 120.641. Just as the used-car dealer earns a living by reselling cars at higher prices than he paid for them, so the bond dealer needs to charge a spread between the bid and the asked price. Notice that the spread for these 7.25% bonds is about .02% of the bond’s value. Don’t you wish that used-car dealers charged similar spreads?

The final column in the table shows the asked yield to maturity. This measures the return to investors if they buy the bond at the asked price and hold it to maturity in 2016. You can see that the 7.25% coupon Treasury bond offers a yield to maturity of .35%. We will explain shortly how this figure was calculated.

bond Security that obligates the issuer to make specified payments to the bondholder.

face value Payment at the maturity of the bond. Also called principal or par value.

coupon The interest payments paid to the bondholder.

How much would an investor pay to buy one 4.5% Treasury bond of 2017 (see Table 6.1 )? If a Treasury bond costs $1,106.25, how would this price be quoted? How much would he receive if he sold a 3% Treasury bond of 2042?

Self-Test 6.1

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Chapter 6 Valuing Bonds 167

You can’t buy Treasury bonds on the stock exchange. Instead, they are traded by a network of bond dealers, who quote bid and ask prices at which they are prepared to buy and sell. For example, suppose that in 2013 you decide to buy the “7.25s of 2016,” that is, the 7.25% coupon bonds maturing in 2016. You approach a broker who checks the current price on her screen. If you are happy to go ahead with the purchase, your broker will contact a bond dealer and the trade is done.

If you plan to hold your bond until maturity, you can look forward to the cash flows shown in Figure 6.1 . For the first 2 years, the cash flows equal the 7.25% coupon pay- ment. Then, when the bond matures in 2016, you receive the $1,000 face value of the bond plus the final coupon payment.

TABLE 6.1 Sample Treasury bond quotes in May 2013

FIGURE 6.1 Cash flows to an investor in the 7.25% coupon bond maturing in the year 2016

$1,072.5

Year: 2013 2014 2015 2016

$72.5

$1,000

$72.5$72.5

-Price

Find the 1.75% coupon 2022 Treasury bond in Table 6.1 .

a. How much does it cost to buy the bond? b. If you already owned the bond, how much would a bond dealer pay you for it? c. What annual interest payment does the bond make? d. What is the bond’s yield to maturity?

Self-Test 6.2

Maturity Coupon Bid Price Asked Price Asked Yield, %

2015, May 15 4.125 107.7969 107.8203 0.23 2016, May 15 7.25 120.641 120.664 0.35 2017, May 15 4.5 115.6719 115.7031 0.54 2022, May 15 1.75 100.9922 101.0078 1.63 2030, May 15 6.25 152.7422 152.8203 2.44 2037, May 15 5 138.7031 138.7813 2.78 2042, May 15 3 100.2422 100.2578 2.99

Source: The Wall Street Journal, www.wsj.com.

6.2 Interest Rates and Bond Prices In Figure 6.1 we set out the cash flows from your 7.25% Treasury bond. The value of the bond is the present value of these cash flows. To find this value, you need to dis- count each future payment by the current interest rate.

The 7.25s were not the only Treasury bonds that matured in 2016. Almost identical bonds maturing at the same time offered an unusually low interest rate of about .35%.

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168 Part Two Value

If the 7.25s had offered a lower return than .35%, no one would have been willing to hold them. Equally, if they had offered a higher return, everyone would have rushed to sell their other bonds and buy the 7.25s. In other words, if investors were on their toes, the 7.25s had to offer the same .35% rate of interest as similar Treasury bonds. You might recognize .35% as the opportunity cost of the funds invested in the bond, as we discussed in Chapter 1. This is the rate that investors could earn by placing their funds in similar securities rather than in this bond.

We can now calculate the present value of the 7.25s of 2016 by discounting the cash flows at .35%:

PV = $72.50 (1 + r)

+ $72.50

(1 + r)2 +

$1,072.50 (1 + r)3

= $72.50

(1.0035) +

$72.50 (1.0035)2

+ $1,072.50 (1.0035)3

= $1,205.56

Bond prices are usually expressed as a percentage of their face value. Thus we can say that your 7.25% Treasury bond is worth 120.556% of face value. 1

Did you notice that your bond is like a package of two investments? The first pro- vides a level stream of coupon payments of $72.50 a year for each of 3 years. The second consists of the final repayment of the $1,000 face value. Therefore, you can use the annuity formula to value the coupon payments and then add on the present value of the final payment of face value:

PV = PV(coupons) + PV(face value) (6.1)

= (coupon × annuity factor) + (face value × discount factor)

= $72.50 × B 1 .0035

- 1

.0035(1.0035)3 R + $1,000 × 1

1.00353

= $215.99 + $989.57 = $1,205.56

If you need to value a bond with many years to run before maturity, it is usually easiest to value the coupon payments as an annuity and then add on the present value of the final payment.

1 Our calculated value of $1,205.56 (120.556%) is a little lower than the asked price of 120.664% quoted in Table 6.1 . One reason is minor rounding error in the interest rate. Another is that the bond’s actual coupon is not $72.50 per year, but $36.25 every 6 months. In the next example, we’ll show how to handle semiannual coupons.

Calculate the present value of a 6-year bond with a 9% coupon. The interest rate is 12%.

Self-Test 6.3

You can calculate bond prices easily using a financial calculator or spreadsheet. The trick is to recognize that the bond provides its owner both a recurring payment (the coupons) and an additional one-time cash flow (the face value). For this bond, the time to maturity is 3 years, annual coupon payment is $72.50, and face value is $1,000. The interest rate is .35%. Therefore, the inputs for a financial calculator would be:

n i PV PMT FV

Inputs 3 .35 72.50 1000 Compute 21205.56

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Chapter 6 Valuing Bonds 169

Now compute PV, and you should get an answer of − 1205.56, which is the initial cash outflow required to purchase the bond.

For an introduction to bond pricing using Excel, turn to the box on page 175.

Example 6.1 Bond Prices and Semiannual Coupon Payments When we valued our Treasury bond, we assumed that interest payments occur annually. This is the case for bonds in many European countries, but in the United States most bonds make coupon payments semiannually. So when you hear that a bond in the United States has a coupon rate of 7.25%, you can generally assume that the bond makes a payment of $72.5/2  =   $36.25 every 6 months. Similarly, when investors in the United States refer to the bond’s interest rate, they usually mean the semiannually compounded interest rate. Thus an interest rate quoted at .35% really means that the 6-month rate is .35/2  =  .175%. 2 The actual cash flows on the Treasury bond are illustrated in Figure 6.2 . To value the bond a bit more pre- cisely, we should have discounted the series of semiannual payments by the semi- annual rate of interest as follows:

PV = $36.25

(1.00175) +

$36.25 (1.00175)2

+ $36.25

(1.00175)3 +

$36.25 (1.00175)4

+ $36.25

(1.00175)5 +

$1,036.25 (1.00175)6

= $1,205.74

2 You may have noticed that the semiannually compounded interest rate on the bond is also the bond’s APR, although this term is not generally used by bond investors. To find the effective rate, we can use a formula that we presented in Section 5.7:

Effective annual rate = a1 + APR m

bm - 1 where m is the number of payments each year. In the case of our Treasury bond,

Effective annual rate = a1 + .0035 2

b2 - 1 = 1.001752 - 1 = .003503, or .3503% When interest rates are low, there is negligible difference between the annually compounded interest rate and the semiannually compounded rate. The difference is greater when rates are high.

FIGURE 6.2 Cash flows to an investor in the 7.25% coupon bond maturing in 2016. The bond pays semiannual coupons, so there are two payments of $36.25 each year.

$1,036.25

May 2015

Nov 2015

May 2016

May 2013

$36.25

$1,000

$36.25

Nov 2014

$36.25 $36.25

May 2014

Nov 2013

$36.25

-Price

$36.25

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170 Part Two Value

How Bond Prices Vary with Interest Rates Figure 6.3 plots the interest rate on 10-year Treasury bonds from 1900 to 2012. Notice how much the interest rate fluctuates. For example, interest rates climbed steeply after 1979 when the Federal Reserve instituted a policy of tight money to rein in inflation. Within 2 years the rate on 10-year government bonds rose from 10% to 14%. Contrast this with 2013, when long-term Treasuries offered a measly 1.7% rate of interest.

As interest rates change, so do bond prices. For example, suppose that investors demanded an interest rate of 7.25% on 3-year Treasury bonds. What would be the price of the Treasury 7.25s of 2016? Just repeat our PV calculation with a discount rate of r   =  .0725:

PV at 7.25% = $72.5

(1.0725) +

$72.5 (1.0725)2

+ $1,072.5 (1.0725)3

= $1,000.00

Thus when the interest rate is the same as the coupon rate (7.25% in our example), the bond sells for its face value.

We first valued the Treasury bond using an interest rate of .35%, which is lower than the coupon rate. In that case the price of the bond was higher than its face value. We then valued it using an interest rate that is equal to the coupon and found that bond price equaled face value. You have probably already guessed that when the cash flows are discounted at a rate that is higher than the bond’s coupon rate, the bond is worth less than its face value. The following example confirms that this is the case.

Thus, once we allow for the fact that coupon payments are semiannual, the value of the 7.25s is 120.574% of face value, which is slightly higher than the value that we obtained when we assumed annual coupon payments. 3 Since semian- nual coupon payments just add to the arithmetic, we will stick for the most part to our simplification and assume annual interest payments.

3 Why is the present value a bit higher in this case? Because now we recognize that half the annual coupon payment is received only 6 months into the year, rather than at year-end. Since part of the coupon income is received earlier, its present value is higher.

FIGURE 6.3 The interest rate on 10-year U.S. Treasury bonds, 1900–2012

0

2

4

6

8

10

12

14

16

19 00

19 04

19 08

19 12

19 16

19 20

19 24

19 28

19 32

19 36

19 40

19 44

19 48

19 52

19 56

19 60

19 64

19 68

19 72

19 76

19 80

19 84

19 88

19 92

19 96

20 00

20 04

20 08

20 12

Y ie

ld (

% )

Year

Source: www.econ.yale.edu/∼ shiller/data.htm .

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Chapter 6 Valuing Bonds 171

This is a general result. When the market interest rate exceeds the coupon rate, bonds sell for less than face value. When the market interest rate is below the coupon rate, bonds sell for more than face value.

Suppose that interest rates rise. On hearing the news, bond investors appear discon- solate. Why? Don’t they like higher interest rates? If you are not sure of the answer, look at Figure 6.4 , which shows the present value of the 7.25% Treasury bond for dif- ferent interest rates. For example, imagine yields soar from .35% to 10%. Our bond would then be worth only $931.61, creating a loss to bondholders of some 23%. Con- versely, bondholders have reason to celebrate when market interest rates fall. You can see this also from Figure 6.4 . For instance, if interest rates fall to zero, the value of our 7.25% bond would increase to $1,217.50. That was just about the biggest profit that investors in the 7.25s could hope for in 2013.

Figure 6.4 illustrates a fundamental relationship between interest rates and bond prices: When the interest rate rises, the present value of the payments to be received by the bondholder falls and bond prices fall. Conversely, a decline in the interest rate increases the present value of those payments and results in a higher price.

A warning! People sometimes confuse the interest, or coupon, payment on the bond with the interest rate —that is, the return that investors require. The $72.50 coupon payments on our Treasury bond are fixed when the bond is issued. The coupon rate, 7.25%, measures the coupon payment ($72.50) as a percentage of the bond’s face value ($1,000) and is therefore also fixed. However, the interest rate changes from day to day. These changes affect the present value of the coupon payments but not the payments themselves.

coupon rate Annual interest payment as a percentage of face value.

Example 6.2 Interest Rates and Bond Prices Investors will pay $1,000 for a 7.25%, 3-year Treasury bond when the interest rate is 7.25%. Suppose that the interest rate is higher than the coupon rate at (say) 10%. Now what is the value of the bond? Simple! We just repeat our calculation but with r   =  .10:

PV at 10% = $72.5 (1.10)

+ $72.5

(1.10)2 +

$1,072.5 (1.10)3

= $931.61

The bond sells for 93.16% of face value.

FIGURE 6.4 The value of the 7.25% bond falls as interest rates rise.

700

800

900

1,000

1,100

1,200

1,300

0 2 4 6 8 10 12 14

Interest rate (%)

B o

n d

p ri

ce (

$)

Price = $931.61

Interest rate = 10%

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172 Part Two Value

Interest Rate Risk We have just seen that bond prices fluctuate as interest rates change. In other words, bonds exhibit interest rate risk. Bond investors cross their fingers that market inter- est rates will fall, so that the price of their bond will rise. If they are unlucky and the market interest rate rises, the value of their investment falls.

A change in interest rates has only a modest impact on the present value of near- term cash flows but a much greater impact on the value of distant cash flows. Therefore any change has a greater impact on the price of long-term bonds than the price of short- term bonds. For example, compare the two curves in Figure 6.5 . The green line shows how the value of the 3-year, 7.25% coupon bond varies with the interest rate. The blue line shows how the price of a 30-year, 7.25% bond varies. You can see that the 30-year bond is more sensitive to interest rate fluctuations than the 3-year bond. This should not surprise you. If you buy a 3-year bond and rates then rise, you will be stuck with a bad deal—you could have got a better interest rate if you had waited. However, think how much worse it would be if the loan had been for 30 years rather than 3 years. The longer the loan, the more income you have lost by accepting what turns out to be a low interest rate. This shows up in a bigger decline in the price of the longer-term bond. Of course, there is a flip side to this effect, which you can also see from Figure 6.5 . When interest rates fall, the longer-term bond responds with a greater increase in price.

interest rate risk The risk in bond prices due to fluctuations in interest rates.

Suppose that the market interest rate is 8% and then drops overnight to 4%. Calculate the present values of the 7.25%, 3-year bond and of the 7.25%, 30-year bond both before and after this change in interest rates. Assume annual coupon payments. Confirm that your answers correspond with Figure 6.5 . Use your financial calculator or a spreadsheet. You can find a box on bond pricing using Excel on page 176.

Self-Test 6.4

How changes in interest rates affect long- and

short-term bonds

BEYOND THE PAGE

brealey.mhhe.com/ch06-01

Which is the longer term bond?

BEYOND THE PAGE

brealey.mhhe.com/ch06-02

FIGURE 6.5 Plot of bond prices as a function of the interest rate. The price of long- term bonds is more sensitive to changes in the interest rate than is the price of short-term bonds.

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 2 4 6 8 10 12 14

Interest rate (%)

B o

n d

p ri

ce (

$)

30-year bond

3-year bond

When the interest rate equals the 7.25% coupon, both bonds sell for face value.

6.3 Yield to Maturity Suppose you are considering the purchase of a 3-year bond with a coupon rate of 10%. Your investment adviser quotes a price for the bond. How do you calculate the rate of return the bond offers?

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Chapter 6 Valuing Bonds 173

For bonds priced at face value the answer is easy. The rate of return is the coupon rate. We can check this by setting out the cash flows on your investment:

Cash Paid to You in Year:

You Pay 1 2 3 Rate of Return

$1,000 $100 $100 $1,100 10%

Cash Paid to You in Year:

You Pay 1 2 3 Rate of Return

$1,136.16 $100 $100 $1,100 ?

Notice that in each year you earn 10% on your money ($100/$1,000). In the final year you also get back your original investment of $1,000. Therefore, your total return is 10%, the same as the coupon rate.

Now suppose that the market price of the 3-year bond is $1,136.16. Your cash flows are as follows:

Notice that you are paying out $1,136.16 and receiving an annual income of $100. So your income as a proportion of the initial outlay is $100/$1,136.16  =  .088, or 8.8%. This is sometimes called the bond’s current yield.

However, your total return depends on both interest income and any capital gains or losses. A current yield of 8.8% may sound attractive only until you realize that the bond’s price must fall. The price today is $1,136.16, but when the bond matures 3 years from now, the bond will sell for its face value, or $1,000. A price decline (i.e., a capital loss ) of $136.16 is guaranteed, so the overall return over the next 3 years must be less than the 8.8% current yield.

Let us generalize. A bond that is priced above its face value is said to sell at a pre- mium. Investors who buy a bond at a premium must absorb a capital loss over the life of the bond, so the return on these bonds is always less than the bond’s current yield. A bond priced below face value sells at a discount. Investors in discount bonds receive a capital gain over the life of the bond; the return on these bonds is greater than the current yield: Because it focuses only on current income and ignores prospec- tive price increases or decreases, the current yield does not measure the bond’s total rate of return. It overstates the return of premium bonds and understates that of discount bonds.

We need a measure of return that takes account of both coupon payments and the change in a bond’s value over its life. The standard measure is called yield to maturity. The yield to maturity is the answer to the following question: At what interest rate would the bond be correctly priced? The yield to maturity is defined as the discount rate that makes the present value of the bond’s payments equal to its price.

If you can buy the 3-year bond at face value, the yield to maturity is the coupon rate, 10%. We can check this by noting that when we discount the cash flows at 10%, the present value of the bond is equal to its $1,000 face value:

PV at 10% = $100 (1.10)

+ $100

(1.10)2 +

$1,100 (1.10)3

= $1,000.00

But suppose the price of the 3-year bond is $1,136.16. In this case the yield to maturity is only 5%. At that discount rate, the bond’s present value equals its actual market price, $1,136.16:

PV at 5% = $100 (1.05)

+ $100

(1.05)2 +

$1,100 (1.05)3

= $1,136.16

The yield to maturity is a measure of a bond’s total return, including both coupon income and capital gain. If you buy the bond today and hold it to maturity, your return

current yield Annual coupon payment divided by bond price.

yield to maturity Interest rate for which the present value of the bond’s payments equals the price.

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174 Part Two Value

will be the yield to maturity. Bond investors often refer loosely to a bond’s “yield.” It’s a safe bet that they are talking about its yield to maturity rather than its current yield.

Calculating the Yield to Maturity To find the price of the 7.25% Treasury bond, we discounted the cash payments at the interest rate r. If r   =  .35%, then bond price =  $1,205.56:

Price = $72.5

(1 + r) +

$72.5 (1 + r)2

+ $1,072.5 (1 + r)3

= $72.5

(1.0035) +

$72.5 (1.0035)2

+ $1,072.5 (1.0035)3

= $1,205.56

We could have phrased the question the other way round and asked, “If the price of the bond is $1,205.56, what is the bond’s yield to maturity?”

To calculate yield, we need to find the discount rate, r, that gives the correct bond price. The only general procedure for doing this is trial and error. You guess at an inter- est rate and calculate the present value of the bond’s payments. If the present value is greater than the actual price, your discount rate must have been too low, so you try a higher interest rate (since a higher rate results in a lower PV). Conversely, if PV is less than price, you must reduce the interest rate. Of course, this would be a mind-numbing procedure to do by hand. Fortunately, financial calculators or spreadsheet programs can rapidly find a bond’s yield to maturity, using a similar trial-and-error process. We give examples in the nearby boxes.

Example 6.3 Rate of Return versus Yield to Maturity On May 15, 2008, the U.S. Treasury sold $9 billion of 4.375% bonds maturing in February 2038. The bonds were issued at a price of 96.38% and offered a yield to maturity of 4.60%. This was the return to anyone buying at the issue price and holding the bonds to maturity. In the months following the issue the financial crisis reached its peak. Lehman Brothers filed for bankruptcy with assets of $691 bil- lion, and the government poured money into rescuing Fannie Mae, Freddie Mac,

A 4-year maturity bond with a 14% coupon rate can be bought for $1,200. What is the yield to maturity if the coupon is paid annually? What if it is paid semiannually? You will need a spreadsheet or a financial calculator to answer this question.

Self-Test 6.5

6.4 Bond Rates of Return The yield to maturity is defined as the discount rate that equates the bond’s price to the present value of all its promised future cash flows. It measures the rate of return that you will earn if you buy the bond today and hold it to maturity. However, as interest rates fluctuate, the return that you earn in the interim may be very different from the yield to maturity. If interest rates rise in a particular week, month, or year, the price of your bond will fall and your return for that period will be lower than the yield to maturity. Conversely, if rates fall, the price of your bond will rise and your return will be higher. This is emphasized in the following example.

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175

Is there any connection between the yield to maturity and the rate of return during a particular period? Yes: If the bond’s yield to maturity remains unchanged during the period, the bond price changes with time so that the total return on the bond is equal to the yield to maturity. The rate of return will be less than the yield to maturity if interest rates rise, and it will be greater than the yield to maturity if interest rates fall.

Calculator Financial You can use a fi nancial calculator to calculate the yield to maturity on our 7.25% Treasury bond. The inputs are:

Using a Financial Calculator to Compute Bond Yield

n i PV PMT FV

Inputs 3 –1205.56 72.5 1000 Compute .35

n i PV PMT FV

Inputs 6 –1205.56 36.25 1000 Compute .1777

Now compute i and you should get an answer of .35%. Let’s now redo this calculation but recognize that the cou-

pons are paid semiannually. Instead of three annual coupon payments of $72.5, the bond makes six semiannual payments

This yield to maturity, of course, is a 6-month yield, not an annual one. Bond dealers would typically annualize the semiannual rate by doubling it, so the yield to maturity would be quoted as .1777  ×  2  =  .3554%.

of $36.25. Therefore, we can fi nd the semiannual yield as follows:

AIG, and a host of banks. As investors rushed to the safety of Treasury bonds, their prices soared. By mid-December the price of the 4.375s of 2038 had reached 138.05% of face value and the yield had fallen to 2.5%. Anyone fortunate enough to have bought the bond at the issue price would have made a capital gain of $1,380.50  −  $963.80  =  $416.70. In addition, on August 15 the bond made its first coupon payment of $21.875 (this is the semiannual payment on the 4.375% cou- pon bond with a face value of $1,000). Our lucky investor would therefore have earned a 7-month rate of return of 45.5%:

Rate of return = coupon income + price change

investment (6.2)

= $21.875 + $416.70

$963.80 = .455 = 45.5%

Suddenly, government bonds did not seem quite so boring as before.

rate of return Total income per period per dollar invested.

Suppose that you purchased 8% coupon, 10-year bonds for $1,324.4 when they were yielding 4% (we assume annual coupon payments). One year later you receive the annual coupon payment of $80, but the yield to maturity has risen to 6%. Confirm that the rate of return on your bond over the year is less than the original 4% yield to maturity.

Self-Test 6.6

Suppose that you buy 8%, 2-year bonds for $1,036.67 when they yield 6%. At the end of the year they still yield 6%. Show that if you continue to hold the bond until maturity, your return in each of the two years will also be 6%.

Self-Test 6.7

Bond prices and approaching maturity

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Bond pricing using financial calculators

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176

The solid curve in Figure 6.6 plots the price of a 30-year maturity, 6% coupon bond over time assuming that its yield to maturity is currently 4% and does not change. The price declines gradually until the maturity date, when it finally reaches face value. In each period, the price decline offsets the coupon income by just enough to reduce total

FIGURE 6.6 How bond prices change as they approach maturity, assuming an unchanged yield. Prices of both premium and discount bonds approach face value as their maturity date approaches.

The DATE function in Excel, which we use for both the settlement and maturity dates, uses the format DATE(year, month,day).

Notice that the coupon rate and yield to maturity are expressed as decimals, not percentages. In most cases, redemption value will be 100 (i.e., 100% of face value), and the resulting price will be expressed as a percent of face value. Occasionally, however, you may encounter bonds that pay off at a premium or discount to face value. One example would be callable bonds, which give the company the right to buy back the bonds at a premium before maturity.

The value of the bond assuming annual coupon payments is 120.556% of face value, or $1,205.56. If we wanted to assume semiannual coupon payments, as in Example 6.1, we would simply change the entry in cell B10 to 2 (see col- umn D), and the bond value would change to 120.574% of face value, as we found in that example.

Excel and most other spreadsheet programs provide built-in functions to compute bond values and yields. They typically ask you to input both the date you buy the bond (called the settlement date ) and the maturity date of the bond.

The Excel function for bond value is:

= PRICE(settlement date, maturity date, annual coupon rate, yield to maturity, redemption value as percent of face value, number of coupon payments per year)

(If you can’t remember the formula, just remember that you can go to the Formulas tab in Excel, and from the Financial tab pull down the PRICE function, which will prompt you for the necessary inputs.) For our 7.25% coupon bond, we would enter the values shown in the spreadsheet below. Alterna- tively, we could simply enter the following function in Excel:

= PRICE(DATE(2013,5,15),DATE(2016,5,15),.0725, .0035,100,1)

Solutions Spreadsheet Bond Valuation

1

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8

9

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13

5/15/2013

5/15/2016

0.0725

0.0035

100

1

120.556

=DATE(2013,5,15)

=DATE(2016,5,15)

=PRICE(B5,B6,B7,B8,B9,B10)

BA C E FD

Settlement date

Maturity date

Annual coupon rate

Yield to maturity

Redemption value (% of face value)

Coupon payments per year

Bond price (% of face value)

7.25% annual coupon bond,

maturing May 2016

5/15/2013

5/15/2016

0.0725

0.0035

100

2

120.574

7.25% semiannual coupon bond,

maturing May 2016

1/1/2000

1/1/2030

0.06

0.07

100

1

87.591

6% annual coupon bond,

30-year maturityFormula in column B

262830 24 20 16 12 8 4 022 18 14 10 6 2

Years to maturity

Maturity dateToday

B o

n d

p ri

ce (

$)

1,400

1,300

1,200

1,100

1,000

900

800

700

600

Price path for discount bond

Price path for premium bond selling for more than face value

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177

We have also assumed that the fi rst coupon payment comes in exactly one period (either a year or a half-year). In other words, the settlement date is precisely at the begin- ning of the period. However, the PRICE function will make the necessary adjustments for intraperiod purchase dates.

Suppose now that you wish to fi nd the price of a 30-year maturity bond with a coupon rate of 6% (paid annually) sell- ing at a yield to maturity of 7%. You are not given a specifi c settlement or maturity date. You can still use the PRICE func- tion to value the bond. Simply choose an arbitrary settlement date (January 1, 2000, is convenient) and let the maturity date be 30 years hence. The appropriate inputs appear in

column F of the spreadsheet above, with the resulting price, 87.591% of face value, appearing in cell F13.

Excel also provides a function for yield to maturity. It is:

= YIELD(settlement date, maturity date, annual coupon rate, bond price, redemption value as percent of face value, number of coupon payments per year)

For example, to fi nd the yield to maturity of our 7.25% bond we would use column B of the following spreadsheet if the coupons were paid annually. If the coupons were paid semi- annually, we would change the entry for payments per year to 2 (see cell D8), and the yield would increase to 3.55%.

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5/15/2013

5/15/2016

0.0725

120.556

100

1

0.0350

5/15/2013

5/15/2016

0.0725

120.556

100

2

0.0355

BA C ED

The formula entered here is =YIELD(B3,B4,B5,B6,B7,B8)

Settlement date

Maturity date

Annual coupon rate

Bond price (% of face value)

Redemption value (% of face value)

Coupon payments per year

Yield to maturity (decimal)

Annual coupons Semiannual coupons

You can find this spreadsheet in Connect.

return to 4%. The dashed curve in Figure 6.6 shows the corresponding price path for a bond with a 2% coupon that sells at a discount to face value. In this case, the coupon income would provide less than a competitive rate of return, so the bond sells below face value. Its price gradually approaches face value, however, and the price gain each year brings its total return up to the market interest rate.

6.5 The Yield Curve When you buy a bond, you buy a package of coupon payments plus the final repay- ment of face value. But sometimes it is inconvenient to buy things in packages. For example, perhaps you do not need a regular income and would prefer to buy just the final repayment. That’s not a problem. The Treasury is prepared to split its bonds into a series of mini-bonds, each of which makes a single payment. These single-payment bonds are called strips.

The prices of strips are shown regularly in the financial press or on the web. For example, in May 2013 it would have cost you $989.27 to buy a strip that just paid out $1,000 in May 2016. The yield on this 3-year mini-bond was 0.36%. In other words, $989.27  ×  1.0036 3   =  $1,000.

Bond investors often draw a plot of the relationship between bond yields and matu- rity. This is known as the yield curve. Treasury strips provide a convenient way to

yield curve Plot of relationship between bond yields to maturity and time to maturity.

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178 Part Two Value

measure this yield curve. For example, if you look at Figure 6.7 , you will see that in May 2013 one-year strips offered a yield to maturity of just .14%; those with 20 or more years to run provided a yield of about 3%. In this case, the yield curve sloped upward. 4 This is usually the case, though sometimes long-term bonds offer lower yields, so the curve slopes downward.

But that raises a question. If long-term bonds offered much higher yields, why didn’t everyone buy them? Who were the (foolish?) investors who put their money into short-term Treasuries at such low yields?

Even when the yield curve is upward-sloping, investors might rationally stay away from long-term bonds for two reasons. First, the prices of long-term bonds fluctu- ate much more than prices of short-term bonds. We saw in Figure 6.5 that long-term bond prices are more sensitive to shifting interest rates. A sharp increase in interest rates could easily knock 20% or 30% off long-term bond prices. If investors don’t like price fluctuations, they will invest their funds in short-term bonds unless they receive a higher yield to maturity on long-term bonds.

Second, short-term investors can profit if interest rates rise. Suppose you hold a 1-year bond. A year from now, when the bond matures, you can reinvest the proceeds and enjoy whatever rates the bond market offers then. These rates may be high enough to offset the first year’s relatively low yield on the 1-year bond. Thus you often see an upward-sloping yield curve when future interest rates are expected to rise.

4 Coupon bonds are like packages of strips. Investors often plot the yield curve using the yields on these pack- ages. For example, you could plot the yields on the small sample of bonds in Table 6.1 against their maturity.

One-year Treasury bonds yield 5%, while 2-year bonds yield 6%. You are quite confident that in 1 year’s time 1-year bonds will yield 8%. Would you buy the 2-year bond today? Show that there is a better strategy.

Self-Test 6.8

Nominal and Real Rates of Interest In Chapter 5 we drew a distinction between nominal and real rates of interest. The cash flows on the Treasury bonds that we have been discussing are fixed in nominal terms. Investors are sure to receive a fixed interest payment each year, but they do not know

FIGURE 6.7 Treasury strips are bonds that make a single payment. The yields on Treasury strips in May 2013 show that investors received a higher yield on longer-term bonds.

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1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Maturity (years)

Y ie

ld (

% )

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Chapter 6 Valuing Bonds 179

what that money will buy them. The real interest rate on the Treasury bonds depends on the rate of inflation. For example, if the nominal rate of interest is 8% and the infla- tion rate is 4%, then the real interest rate is calculated as follows:

1 + real interest rate = 1 + nominal interest rate

1 + inflation rate =

1.08

1.04 = 1.0385

Real interest rate = .0385 = 3.85%

Since the inflation rate is uncertain, so is the real rate of interest on the Treasury bonds. You can nail down a real rate of interest by buying an indexed bond, whose pay-

ments are linked to inflation. Indexed bonds have been available in some countries for many years, but they were almost unknown in the United States until 1997 when the U.S. Treasury began to issue inflation-indexed bonds known as Treasury Inflation- Protected Securities, or TIPS. 5 The real cash flows on TIPS are fixed, but the nominal cash flows (interest and principal) are increased as the consumer price index increases. For example, suppose the U.S. Treasury issues 3% coupon, 2-year TIPS. The real cash flows on the 2-year TIPS are therefore:

5 Indexed bonds were not completely unknown in the United States before 1997. For example, in 1780 American Revolution soldiers were compensated with indexed bonds that paid the value of “five bushels of corn, 68 pounds and four-sevenths part of a pound of beef, ten pounds of sheep’s wool, and sixteen pounds of sole leather.”

Year 1 Year 2

Real cash fl ows $30 $1,030

Year 1 Year 2

Nominal cash fl ows $30 × 1.05 = $31.50 $1,030 × 1.05 × 1.04 = $1,124.76

The nominal cash flows on TIPS depend on the inflation rate. For example, suppose inflation turns out to be 5% in year 1 and a further 4% in year 2. Then the nominal cash flows would be:

These cash payments are just sufficient to provide the holder with a 3% real rate of interest. As we write this in April 2014, 10-year TIPS offer a yield of about .5%. This yield

is a real interest rate. It measures the amount of extra goods your investment will allow you to buy. The .5% real yield on TIPS was 2.1% less than the 2.6% nominal yield on nominal 10-year Treasury bonds. If the annual inflation rate proves to be higher than 2.1%, you will earn a higher real return by holding TIPS; if the inflation rate is lower than 2.1%, the reverse will be true.

Real interest rates depend on the supply of savings and the demand for new invest- ment. As this supply-demand balance changes, real interest rates change. But they do so gradually. We can see this by looking at the United Kingdom, where the govern- ment has issued indexed bonds since 1982. The red line in Figure 6.8 shows that the (real) interest rate on these bonds has fluctuated within a relatively narrow range.

Suppose that investors revise upward their forecast of inflation by 1%. How will this affect interest rates? If investors are concerned about the purchasing power of their money, the changed forecast should not affect the real rate of interest. The nominal interest rate must therefore rise by 1% to compensate investors for the higher inflation prospects.

The blue line in Figure 6.8 shows the nominal rate of interest in the United King- dom since 1985. You can see that the nominal rate is much more variable than the real rate. For example, when investors were worried about inflation in the late 1980s, the nominal interest rate was about 7 percentage points above the real rate. Notice how low the real interest rate has been recently. Since the fall of 2010, the yield on U.K. inflation-indexed bonds has been negative. This means that your savings in these bonds would buy less and less each year.

The yield on TIPS

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Inflation and nominal interest rates

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Nominal interest rates can be negative

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180 Part Two Value

6.6 Corporate Bonds and the Risk of Default Our focus so far has been on U.S. Treasury bonds. But the federal government is not the only issuer of bonds. State and local governments borrow by selling bonds. 6 So do corporations. Many foreign governments and corporations also borrow in the United States. At the same time, U.S. corporations may borrow dollars or other currencies by issuing their bonds in other countries. For example, they may issue dollar bonds in London that are then sold to investors throughout the world.

Investors usually regard bonds issued by the U.S. Treasury as completely safe. They know that the government can always print the money needed to pay off the debt. But when a foreign government borrows dollars, investors do worry that in some future crisis the government may not be able to come up with enough dollars to repay the debt. This worry shows up in bond prices and yields to maturity. For example, in 2001 the Argentinian government defaulted on $95 billion of debt. As the prospect of default loomed, the price of Argentinian bonds slumped and the promised yield climbed to more than 40 percentage points above the yield on U.S. Treasuries.

Unlike governments, corporations cannot print their own money, and the specter of default is always lurking in the shadows. The payments promised to the bondholders therefore represent a best-case scenario: The firm will never pay more than the prom- ised cash flows, but in hard times it may pay less. 7

The risk that a bond issuer may default on its obligations is called default risk (or credit risk ). Companies need to compensate for this default risk by promising a higher rate of interest on their bonds. The difference between the promised yield on a corporate bond and the yield on a U.S. Treasury bond with the same coupon and matu- rity is called the default premium. The greater the chance that the company will get into trouble, the higher the default premium demanded by investors.

The safety of most corporate bonds can be judged from bond ratings provided by Moody’s, Standard & Poor’s, or other bond rating firms. Table 6.2 lists the possible bond ratings in declining order of quality. For example, the bonds that receive the

6 These municipal bonds enjoy a special tax advantage; investors are exempt from federal income tax on the coupon payments on state and local government bonds. As a result, investors are prepared to accept lower yields on this debt. 7 Municipalities also cannot print their own money, and they too are liable to default. This was brought home to investors in 2013 when the city of Detroit with $18.5 billion of debt outstanding stopped making payments on some of its bonds.

default ( or credit) risk The risk that a bond issuer may default on its bonds.

default premium The additional yield on a bond that investors require for bearing credit risk.

FIGURE 6.8 The bottom line shows the real yield on long- term indexed bonds issued by the U.K. government. The top line shows the yield on U.K. government long-term nominal bonds. Notice that the real yield has been more stable than the nominal yield.

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Real yield on U.K. index linked bonds

Sovereign defaults

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Chapter 6 Valuing Bonds 181

highest Moody’s rating are known as Aaa (or “triple A”) bonds. Then come Aa (“dou- ble A”), A, Baa bonds, and so on. Bonds rated Baa and above are called investment grade, while those with a rating of Ba or below are referred to as speculative grade, high yield, or junk bonds. 8

Table 6.2 shows how the chances of default vary by Standard & Poor’s bond rating. You can see that it is rare for highly rated bonds to default. Since 1981 only 9 in 1,000 triple-A U.S. corporate bonds have defaulted within 10 years of issue. However, when an investment-grade bond is downgraded or defaults, the shock waves can be consider- able. For example, in May 2001 WorldCom sold $11.8 billion of bonds with an invest- ment-grade rating. Within little more than a year WorldCom filed for bankruptcy, and its bondholders lost more than 80% of their investment. For low-grade issues, defaults are more common. For example, over 50% of the bonds that were rated CCC or below by Standard & Poor’s at issue have defaulted within 10 years. 9

Table 6.3 shows prices and yields to maturity in May 2013 for a sample of the most heavily traded corporate bonds. As you would expect, corporate bonds offer higher yields than U.S. Treasuries. You can see that the yield differential rises as safety falls off.

8 Rating agencies also distinguish between bonds in the same class. For example, the most secure A-rated bonds would be rated A1 by Moody’s and A + by Standard & Poor’s. The least secure bonds in this risk class would be rated A3 by Moody’s and A- by Standard & Poor’s.

investment grade Bonds rated Baa or above by Moody’s or BBB or above by Standard & Poor’s.

junk bond Bond with a rating below Baa or BBB.

9 Standard & Poor’s, “2013 Annual U.S. Corporate Default Study and Rating Transitions, 25 March 2014,” www.standardandpoors.com .

Bond rating definitions

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Source: fi nance.yahoo.com and www.fi nra.com .

TABLE 6.3 Prices and yields of a sample of heavily traded corporate bonds, May 2013

Issuer Name Coupon, % Maturity S&P Rating Price, $ Yield, %

Johnson & Johnson 6.73 2023 AAA 140.2 2.38 Walmart 6.75 2023 AA 137.83 2.58 Bristol Myers 7.15 2023 A 134.54 3.12 Corning 7 2024 BBB 126.36 4.01 Ford 8.875 2022 BB 118.62 6.35 HCA 7.5 2022 B 101.5 7.29 Borden Chemical 7.875 2023 CCC 81 10.84

TABLE 6.2 Key to Moody’s and Standard & Poor’s bond ratings. The highest-quality bonds are rated triple A, then come double-A bonds, and so on.

Moody’s Standard & Poor’s

Percent of Bonds Defaulting within 10 Years of Issue Safety

Investment-Grade Bonds Aaa AAA 0.9% The strongest rating; ability to repay interest

and principal is very strong. Aa AA 1.1 Very strong likelihood that interest and

principal will be repaid. A A 2.1 Strong ability to repay, but some vulnerability

to changes in circumstances. Baa BBB 5.1 Adequate capacity to repay; more

vulnerability to changes in economic circumstances.

High-Yield Bonds Ba BB 16.0 Considerable uncertainty about ability to

repay. B B 29.0 Likelihood of interest and principal payments

over sustained periods is questionable. Caa CCC

56.6 Bonds that may already be in default or in danger of imminent default.Ca CC

C C — Little prospect for interest or principal on the debt ever to be repaid.

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182

Finance in Practice Insuring against Default Look, for example, at the fi gure below, which shows the annual fee for insuring the bonds of four eurozone countries between 2007 and 2013. Notice that it typically cost very little to insure German government bonds, but the cost of insur- ing Irish and Italian bonds exceeded 5% a year. Insurance costs for Greek government bonds go off the top of our chart. When Greece eventually defaulted on its bonds in 2012, the owners that had insured their holdings received about $2.5 billion in insurance payouts.

Wouldn’t it be nice if you could insure yourself against a pos- sible default on your bonds? Well, you can; you do so by buying a credit default swap (CDS). You pay an annual insur- ance premium or spread, and in return the insurer will make good any loss that you incur if there is a default.

For example, in Chapter 2 we saw how individual coun- tries in the eurozone do not have the freedom to print euros to pay off their debts. So when countries such as Greece and Ireland began to get into difficulties after the banking crisis, the cost of insuring their government bonds soared.

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S s

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Italy Germany

Greece Ireland

Annual cost (CDS spread) of insuring eurozone government debt

Source: Bloomberg and Datastream.

Investors also prefer liquid bonds that they can easily buy and sell. So additionally we find that the heavily traded bonds are more highly prized and offer lower yields than their less liquid brethren. This became important during the banking crisis of 2007–2009 when the market for many corporate bonds effectively dried up and inves- tors found it almost impossible to sell their holdings.

Figure 6.9 shows the yield spread between corporate bonds and Treasuries since 1953. During periods of uncertainty the spread shoots up. For example, as worries about the economy intensified in 2008, the promised yield on Baa bonds climbed to 6% above the yield on Treasuries. You might have been tempted by the higher prom- ised yields on the lower-grade bonds. But remember, these bonds do not always keep their promises.

By the way, you can, if you wish, insure your bonds against default. The nearby box explains how.

Example 6.4 Promised versus Expected Yield to Maturity Bad Bet Inc. issued bonds several years ago with a coupon rate (paid annually) of 10% and face value of $1,000. The bonds are due to mature in 6 years. However, the firm is currently in bankruptcy proceedings, the firm has ceased to pay interest, and the bonds sell for only $200. Based on promised cash flow, the yield to maturity on the bond is 63.9%. (On your calculator, set PV  =   − 200, FV  =  1000, PMT  =  100,  n   =  6, and compute i. ) But this calculation is based on the very unlikely possibility that

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Chapter 6 Valuing Bonds 183

Protecting against Default Risk Corporate debt can be dependable or as risky as a dizzy tightrope walker—it depends on the value and the risk of the firm’s assets. Bondholders can never eliminate default risk, but they can take steps to minimize it. Here are some of the ways that they do so.

Seniority Some debts are subordinated. In the event of default, the subordinated lender gets in line behind the firm’s general creditors. The subordinated lender holds a junior claim and is paid only after all senior creditors are satisfied.

When you lend money to a firm, you can assume that you hold a senior claim unless the debt agreement says otherwise. However, this does not always put you at the front of the line, for the firm may have set aside some of its assets specifically for the protec- tion of other lenders. That brings us to our next classification .

Security When you borrow to buy your home, the savings and loan company will take out a mortgage on the house. The mortgage acts as security for the loan. If you default on the loan payments, the S&L can seize your home.

When companies borrow, they also may set aside some assets as security for the loan. These assets are termed collateral, and the debt is said to be secured. In the event of default, the secured lender has first claim on the collateral but has the same claim as other lenders on the rest of the firm’s assets.

Protective Covenants When investors lend to a company, they know that they might not get their money back. But they expect that the company will use the money well and not take unreasonable risks. To help ensure this, lenders usually impose a number of conditions, or protective covenants, on companies that borrow from them.

secured debt Debt that, in the event of a default, has first claim on specified assets.

protective covenants Conditions imposed on borrowers to protect lenders from unreasonable risks.

the firm will resume paying interest and come out of bankruptcy. Suppose that the most likely outcome is that after 3 years of litigation, during which no interest will be paid, debtholders will receive 27 cents on the dollar—that is, they will receive $270 for each bond with $1,000 face value. In this case the expected yield on the bond is 10.5%. (On your calculator, set PV  =   − 200, FV  =  270, PMT  =  0,  n   =  3, and compute i. ) When default is a real possibility, the promised yield can depart con- siderably from the expected return.

FIGURE 6.9 Yield spreads between corporate and 10-year Treasury bonds

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184 Part Two Value

An honest firm is willing to accept these conditions because it knows that they allow the firm to borrow at a reasonable rate of interest.

Companies that borrow in moderation are less likely to get into difficulties than those that are up to the gunwales in debt. So lenders usually restrict the amount of extra debt that the firm can issue. Lenders are also eager to prevent others from push- ing ahead of them in the queue if trouble occurs. So they may not allow the company to create new debt that is senior to them or to set aside assets for other lenders.

In 1987 RJR Nabisco, the food and tobacco giant, had $5 billion of A-rated debt outstanding. In that year the company was taken over, and $19 billion of debt was issued and used to buy back equity. The debt ratio skyrocketed, and the debt was downgraded to a BB rating. The holders of the previously issued debt were furious, and one filed a lawsuit claiming that RJR had violated an implicit obligation not to undertake major financing changes at the expense of existing bondholders. Why did these bondholders believe they had been harmed by the massive issue of new debt? What type of explicit restriction would you have wanted if you had been one of the original bondholders?

Self-Test 6.9

Not All Corporate Bonds Are Plain Vanilla In finance, “plain vanilla” means simple, standard, and common. In this chapter we have stuck with plain-vanilla bonds. In Chapter 14 we will introduce bonds and other ways of borrowing money that are not plain vanilla. We thought it might be fun to mention a few examples here:

• Zero-coupon bonds, which repay principal at maturity but do not have coupon pay- ments along the way. (Zero-coupon Treasuries are called “strips,” because coupons are stripped away from the bonds and sold separately.)

• Floating-rate bonds, which have coupon payments that are not fixed but fluctuate with short-term interest rates.

• Convertible bonds, which can be exchanged for a specified number of shares of the issuing corporation’s common stock.

SUMMARY A bond is a long-term debt of a government or corporation. When you own a bond, you receive a fixed interest payment each year until the bond matures. This payment is known as the coupon. The coupon rate is the annual coupon payment expressed as a fraction of the bond’s face value. At maturity the bond’s face value is repaid. In the United States most bonds have a face value of $1,000. The current yield is the annual coupon payment expressed as a percentage of the bond price. The yield to maturity measures the average rate of return to an investor who purchases the bond and holds it until maturity, accounting for coupon income as well as the difference between purchase price and face value.

Bonds are valued by discounting the coupon payments and the final repayment by the yield to maturity on comparable bonds. The bond payments discounted at the bond’s yield to maturity equal the bond price. You may also start with the bond price and ask what inter- est rate the bond offers. The interest rate that equates the present value of bond payments

What are the differences between the bond’s coupon rate, current yield, and yield to maturity? (LO6-1)

How can one find the market price of a bond given its yield to maturity or find a bond’s yield given its price? Why do prices and yields vary inversely? (LO6-2)

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Chapter 6 Valuing Bonds 185

to the bond price is the yield to maturity. Because present values are lower when discount rates are higher, price and yield to maturity vary inversely.

Bond prices are subject to interest rate risk, rising when market interest rates fall and fall- ing when market rates rise. Long-term bonds exhibit greater interest rate risk than short- term bonds.

The yield curve plots the relationship between bond yields and maturity. Yields on long-term bonds are usually higher than those on short-term bonds. These higher yields compensate holders for the fact that prices of long-term bonds are more sensitive to changes in interest rates. Investors may also be prepared to accept a lower interest rate on short-term bonds when they expect interest rates to rise.

Investors demand higher promised yields if there is a high probability that the borrower will run into trouble and default. Credit risk implies that the promised yield to maturity on the bond is higher than the expected yield. The additional yield investors require for bear- ing credit risk is called the default premium. Bond ratings measure the bond’s credit risk.

Why do bonds exhibit interest rate risk? (LO6-3)

What is the yield curve and why do investors pay attention to it? (LO6-4)

Why do investors pay attention to bond ratings and demand a higher interest rate for bonds with low ratings? (LO6-5)

L I S T I N G O F E Q UAT I O N S 6.1 Bond price = PV(coupons) + PV(face value)

= (coupon × annuity factor) + (face value × discount factor)

6.2 Bond rate of return = coupon income + price change

investment

QUESTIONS AND PROBLEMS 1. Financial Pages. Turn back to Table 6.1. What is the current yield of the 6.25% 2030 maturity

bond? Why is this more than its yield to maturity? (LO6-1)

2. Bond Yields. A 30-year Treasury bond is issued with face value of $1,000, paying interest of $60 per year. If market yields increase shortly after the T-bond is issued, what happens to the bond’s: (LO6-1)

a. coupon rate? b. price? c. yield to maturity? d. current yield?

3. Bond Yields. If a bond with face value of $1,000 and a coupon rate of 8% is selling at a price of $970, is the bond’s yield to maturity more or less than 8%? (LO6-1)

4. Bond Yields. A bond with face value $1,000 has a current yield of 6% and a coupon rate of 8%. (LO6-1)

a. If interest is paid annually, what is the bond’s price? b. Is the bond’s yield to maturity more or less than 8%?

5. Bond Pricing. A General Power bond carries a coupon rate of 8%, has 9 years until maturity, and sells at a yield to maturity of 7%. (Assume annual interest payments.) (LO6-1 and LO6-2)

a. What interest payments do bondholders receive each year? b. At what price does the bond sell? c. What will happen to the bond price if the yield to maturity falls to 6%?

6. Bond Yields. A bond has 8 years until maturity, carries a coupon rate of 8%, and sells for $1,100. (LO6-1 and LO6-2)

finance

®

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186 Part Two Value

a. What is the current yield on the bond? b. What is the yield to maturity if interest is paid once a year? c. What is the yield to maturity if interest is paid semiannually?

7. Bond Prices and Returns. One bond has a coupon rate of 8%, another a coupon rate of 12%. Both bonds pay interest annually, have 10-year maturities, and sell at a yield to maturity of 10%. (LO6-2)

a. If their yields to maturity next year are still 10%, what is the rate of return on each bond? b. Does the higher-coupon bond give a higher rate of return?

8. Bond Pricing. A 6-year Circular File bond pays interest once a year of $80 and sells for $950. (LO6-2)

a. What are its coupon rate and yield to maturity? b. If Circular wants to issue a new 6-year bond at face value, what coupon rate must the bond

offer?

9. Coupon Rate. General Matter’s outstanding bond issue has a coupon rate of 10%, and it sells at a yield to maturity of 9.25%. The firm wishes to issue additional bonds to the public at face value. What coupon rate must the new bonds offer in order to sell at face value? (LO6-2)

10. Bond Pricing. A 30-year maturity bond with face value of $1,000 makes annual coupon pay- ments and has a coupon rate of 8%. What is the bond’s yield to maturity if the bond is selling for: (LO6-2)

a. $900? b. $1,000? c. $1,100?

11. Bond Pricing. A 30-year maturity bond with face value of $1,000 makes semiannual coupon payments and has a coupon rate of 8%. What is the bond’s yield to maturity if the bond is selling for: (LO6-2)

a. $900? b. $1,000? c. $1,100?

12. Bond Pricing. The table below shows some data for three zero-coupon bonds. The face value of each bond is $1,000. (LO6-2)

Bond Price Maturity (years) Yield to Maturity

A $300 30 — B 300 — 8% C — 10 10

a. What is the yield to maturity of bond A? (Express your answer as a percentage rather than a decimal.)

b. What is the maturity of B? c. What is the price of C?

13. Pricing Consol Bonds. Perpetual Life Corp. has issued consol bonds with coupon payments of $60. (Consols pay interest forever and never mature. They are perpetuities.) (LO6-2)

a. If the required rate of return on these bonds at the time they were issued was 6%, at what price were they sold to the public?

b. If the required return today is 10%, at what price do the consols sell?

14. Bond Pricing. Sure Tea Co. has issued 9% annual coupon bonds that are now selling at a yield to maturity of 10% and current yield of 9.8375%. What is the remaining maturity of these bonds? (LO6-2)

15. Bond Pricing. Maxcorp’s bonds sell for $1,065.15. The bond life is 9 years, and the yield to maturity is 7%. What is the coupon rate on the bonds? (Assume annual coupon payments.) (LO6-2)

16. Bond Returns. You buy an 8% coupon, 10-year maturity bond for $980. A year later, the bond price is $1,200. (Assume annual coupon payments.) (LO6-2)

a. What is the new yield to maturity on the bond? b. What is your rate of return over the year?

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Chapter 6 Valuing Bonds 187

17. Bond Returns. A bond has 10 years until maturity, carries a coupon rate of 9%, and sells for $1,100. Interest is paid annually. (LO6-2 and LO6-3)

a. If the bond has a yield to maturity of 9% 1 year from now, what will its price be at that time? b. What will be the rate of return on the bond? c. Now assume that interest is paid semiannually. What will be the rate of return on the bond? d. If the inflation rate during the year is 3%, what is the real rate of return on the bond?

18. Bond Returns. You buy an 8% coupon, 20-year maturity bond when its yield to maturity is 9%. (Assume semiannual coupon payments.) Six months later, the yield to maturity is 10%. What is your return over the 6 months? (LO6-3)

19. Interest Rate Risk. Consider three bonds with 8% coupon rates, all making annual coupon payments and all selling at face value. The short-term bond has a maturity of 4 years, the inter- mediate-term bond has maturity 8 years, and the long-term bond has maturity 30 years. (LO6-3)

a. What will be the price of each bond if their yields increase to 9%? b. What will be the price of each bond if their yields decrease to 7%? c. Are long-term bonds more or less affected than short-term bonds by a rise in interest rates? d. Would you expect long-term bonds to be more or less affected by a fall in interest rates?

20. Rate of Return. A 2-year maturity bond with face value of $1,000 makes annual coupon pay- ments of $80 and is selling at face value. What will be the rate of return on the bond if its yield to maturity at the end of the year is 6%? 8%? 10%? (LO6-3)

21. Rate of Return. A bond is issued with a coupon of 4% paid annually, a maturity of 30 years, and a yield to maturity of 7%. What rate of return will be earned by an investor who purchases the bond for $627.73 and holds it for 1 year if the bond’s yield to maturity at the end of the year is 8%? (LO6-3)

22. Real Returns. Suppose that you buy a 1-year maturity bond with a coupon of 7% paid annually. If you buy the bond at its face value, what real rate of return will you earn if the inflation rate is 4%? 6%? 8%? (LO6-3)

23. Real Returns. Suppose that you buy a TIPS (inflation-indexed) bond with a 1-year maturity and a coupon of 4% paid annually. If you buy the bond at its face value, and the inflation rate is 8%: (LO6-3)

a. What will be your cash flow at the end of the year? b. What will be your real return? c. What will be your nominal return?

24. Real Returns. Suppose that you buy a TIPS (inflation-indexed) bond with a 2-year maturity and a coupon of 4% paid annually. If you buy the bond at its face value, and the inflation rate is 8% in each year: (LO6-3)

a. What will be your cash flow in year 1? b. What will be your cash flow in year 2? c. What will be your real rate of return over the two-year period?

25. Interest Rate Risk. Consider two bonds, a 3-year bond paying an annual coupon of 5% and a 10-year bond also with an annual coupon of 5%. Both currently sell at face value. Now suppose interest rates rise to 10%. (LO6-3)

a. What is the new price of the 3-year bonds? b. What is the new price of the 10-year bonds? c. Do you conclude that long-term or short-term bonds are more sensitive to a change in inter-

est rates?

26. The Yield Curve. Suppose that investors expect interest rates to fall sharply. Would you expect short-term bonds to offer higher or lower yields than long-term bonds? (LO6-4)

27. Yield Curve. The following table shows the prices of a sample of Treasury strips. Each strip makes a single payment at maturity. Calculate the interest rate offered by each of these strips. (LO6-4)

Years to Maturity Price, %

1 96.852% 2 93.351 3 89.544 4 85.480

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188 Part Two Value

a. What is the 1-year interest rate? b. What is the 4-year rate? c. Is the yield curve upward-sloping, downward-sloping, or flat? d. Is this the usual shape of the yield curve?

28. Credit Risk. (LO6-4)

a. Several years ago, Castles in the Sand Inc. issued bonds at face value at a yield to maturity of 7%. Now, with 8 years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to 15%. What is now the price of the bond? (Assume semiannual coupon payments.)

b. Suppose that investors believe that Castles can make good on the promised coupon pay- ments but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only 80% of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive?

29. Credit Risk. Suppose that Casino Royale has issued bonds that mature in 1 year. They currently offer a yield of 20%. However, there is a 50% chance that Casino will default and bondholders will receive nothing. What is the expected yield on the bonds? (LO6-5)

30. Credit Risk. Bond A is a 10-year U.S. Treasury bond. Bond B is a 10-year corporate bond. True or false? (LO6-3 and LO6-5)

a. If you hold bond A to maturity, your return will be equal to the yield to maturity. b. If you hold bond B to maturity, your return will be equal to or less than the yield to maturity. c. If you hold bond A for 5 years and then sell it, your return could be greater than the yield to

maturity.

31. Credit Risk. A bond’s credit rating provides a guide to its risk. Long-term bonds rated Aa currently offer yields to maturity of 7.5%. A-rated bonds sell at yields of 7.8%. Suppose that a 10-year bond with a coupon rate of 7% is downgraded by Moody’s from an Aa to A rating. (LO6-5)

a. What is the likely bond price before the downgrade? b. What is the likely bond price after the downgrade?

32. Credit Risk. Sludge Corporation has two bonds outstanding, each with a face value of $2 mil- lion. Bond A is a senior bond; bond B is subordinated. Sludge has suffered a severe downturn in demand, and its assets are now worth only $3 million. If the company defaults, what payoff can the holders of bond B expect? (LO6-5)

CHALLENGE PROBLEMS 33. Interest Rate Risk. Suppose interest rates increase from 8% to 9%. Which bond will suffer the

greater percentage decline in price: a 30-year bond paying annual coupons of 8% or a 30-year zero-coupon bond? (LO6-3)

34. Interest Rate Risk. Look again at the previous question. Can you explain intuitively why the zero exhibits greater interest rate risk even though it has the same maturity as the coupon bond? (LO6-3)

35. Interest Rate Risk. Consider two 30-year maturity bonds. Bond A has a coupon rate of 4%, while bond B has a coupon rate of 12%. Both bonds pay their coupons semiannually. (LO6-3)

a. Construct an Excel spreadsheet showing the prices of each of these bonds for yields to matu- rity ranging from 2% to 15% at intervals of 1%. Column A should show the yield to maturity (ranging from 2% to 15%), and columns B and C should compute the prices of the two bonds (using Excel’s bond price function) at each interest rate.

b. In columns D and E, compute the percentage difference between the bond price and its value when yield to maturity is 8%.

Templates can be found in Connect.

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Chapter 6 Valuing Bonds 189

c. Plot the values in columns D and E as a function of the interest rate. Which bond’s price is proportionally more sensitive to interest rate changes?

d. Can you explain the result you found in part (c)? Hint: Is there any sense in which a bond that pays a high coupon rate has lower “average” or “effective” maturity than a bond that pays a low coupon rate?

36. Yield Curve. In Figure 6.7, we saw a plot of the yield curve on stripped Treasury bonds and pointed out that bonds of different maturities may sell at different yields to maturity. In prin- ciple, when we are valuing a stream of cash flows, each cash flow should be discounted by the yield appropriate to its particular maturity. Suppose the yield curve on (zero-coupon) Treasury strips is as follows:

Years to Maturity Yield to Maturity

1 4.0% 2 5.0

3–5 5.5 6–10 6.0

You wish to value a 10-year bond with a coupon rate of 10%, paid annually. (LO6-4)

a. Set up an Excel spreadsheet to value each of the bond’s annual cash flows using this table of yields. Add up the present values of the bond’s 10 cash flows to obtain the bond price.

b. What is the bond’s yield to maturity? c. Compare the yield to maturity of the 10-year, 10% coupon bond with that of a 10-year

zero-coupon bond or Treasury strip. Which is higher? Why does this result make sense given this yield curve?

37. Credit Risk. Slush Corporation has two bonds outstanding, each with a face value of $2 mil- lion. Bond A is secured on the company’s head office building; bond B is unsecured. Slush has suffered a severe downturn in demand. Its head office building is worth $1 million, but its remaining assets are now worth only $2 million. If the company defaults, what payoff can the holders of bond B expect? (LO6-5)

WEB EXERCISES 1. Log on to www.investopedia.com to find a simple calculator for working out bond prices.

Check whether a change in yield has a greater effect on the price of a long-term or a short-term bond.

2. When we plotted the yield curve in Figure 6.7, we used the prices of Treasury strips. You can find current prices of strips by logging on to the Wall Street Journal website (www.wsj.com) and clicking on Markets Data Center and then Bonds, Rates and Credit Markets. Try plotting the yields on stripped coupons against maturity. Do they currently increase or decline with maturity? Can you explain why? You can also use the Wall Street Journal site to compare the yields on nominal Treasury bonds with those on TIPS. Suppose that you are confident that infla- tion will be 3% per year. Which bonds are the better buy?

3. You can find the most recent bond rating for many companies by logging on to finance.yahoo. com and going to the Bond Center. Find the bond rating for some major companies. Were they investment-grade or below?

4. In Figure 6.9 we showed how bonds with greater credit risk have promised higher yields to maturity. This yield spread goes up when the economic outlook is particularly uncer- tain. You can check how much extra yield lower-grade bonds offer today by logging on to www.federalreserve.gov and comparing the yields on Aaa and Baa bonds. How does the spread in yields compare with the spread in November 2008 at the height of the financial crisis?

Templates can be found in Connect.

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190 Part Two Value

SOLUTIONS TO SELF-TEST QUESTIONS 6.1 The asked price of the 4.5s is 115.7031. So one bond would cost $1,157.031. The bid price of

the 3s of 2042 is 100.2422. So you would receive $1,002,422.

6.2 a. The asked price is 101.0078% of face value, or $1,010.078. b. The bid price is 100.9922% of face value, or $1,009.922. c. The annual coupon is 1.75% of face value, or $17.50, a year. d. The yield to maturity, based on the asked price, is given as 1.63%.

6.3 The coupon is 9% of $1,000, or $90 a year. First value the 6-year annuity of coupons:

PV = $90 × (6-year annuity factor)

= $90 × B 1 .12

- 1

.12(1.12)6 R

= $90 × 4.1114 = $370.03

Then value the final payment and add:

PV = $1,000 (1.12)6

= $506.63

PV of bond = $370.03 + $506.63 = $876.66

Using a financial calculator, your inputs would be: n = 6; i = 12; PMT = 90; FV = 1000. Now compute PV.

6.4 At an interest rate of 4%, the 3-year bond sells for $1,090.19. If the interest rate jumps to 8%, the bond price falls to $980.67, a decline of 10%. The 30-year bond sells for $1,561.99 when the interest rate is 4%, but its price falls to $915.57 at an interest rate of 8%, a much larger percentage decline of 41.4%. Thank goodness, interest rates rarely change by this amount overnight.

6.5 The yield to maturity assuming annual coupons is about 8%, because the present value of the bond’s cash returns is $1,199, almost exactly $1,200, when discounted at 8%:

PV = PV(coupons) + PV(final payment)

= (coupon × annuity factor) + (face value × discount factor)

= $140 × B 1 .08

- 1

.08(1.08)4 R + $1,000 × 1

1.084

= $463.70 + $735.03 = $1,199

To obtain a more precise solution on your calculator, these would be your inputs:

Annual Payments Semiannual Payments

n 4 8 PV −1200 −1200 FV 1000 1000 PMT 140 70

Compute i to find yield to maturity (annual payments) = 7.97%. Yield to maturity (semian- nual payments) = 4.026% per 6 months, which would be reported in the financial press as 8.05% annual yield.

6.6 With a yield of 4%, the 8% coupon, 10-year bond sells for $1,324.44. At the end of the year, the bond has only 9 years to maturity and investors demand an interest rate of 6%. Therefore, the value of the bond becomes $1,136.03. (On your calculator, input n = 9; i = 6; PMT = 8;  FV = 1000; compute PV.)

You therefore have received a coupon payment of $80 but have a capital loss of 1,324.44 − 1,136.03 = $188.41. Your total return is therefore (80 − 188.41)/1,324.44 = −.082, or −8.2%. Because interest rates rose over the year, your return was less than the yield to maturity.

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Chapter 6 Valuing Bonds 191

6.7 By the end of the year, the bond will have only 1 year left until maturity. So its price will be $1,080/1.06  =  $1,018.87. You will therefore receive a coupon payment of $80 and make a capital loss of $1,036.67 − $1,018.87 = $17.80. Your total return over the year is (80 − 17.80)/1,036.67 = .060, or 6.0%. When the bond matures, you receive the face value of $1,000. So in the final year you receive a coupon payment of $80 and make a capital loss of $18.87. Your total return over this year is (80 − 18.87)/1,018.87 = .060, or 6.0%. When the yield to maturity does not change, your return is equal to the yield to maturity.

6.8 If you invest in a 2-year bond, you will have $1,000 × 1.062 = $1,123.60. If you are right in your forecast about 1-year rates, then an investment in 1-year bonds will produce $1,000 × 1.05 × 1.08 = $1,134.00 by the end of 2 years. You would do better to invest in the 1-year bond.

6.9 The extra debt makes it more likely that the firm will not be able to make good on its prom- ised payments to its creditors. If the new debt is not junior to the already-issued debt, then the original bondholders suffer a loss when their bonds become more susceptible to default risk. A protective covenant limiting the amount of new debt that the firm can issue would have prevented this problem. Investors, having witnessed the problems of the RJR bondholders, generally demanded the covenant on later debt issues.

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Rev. Confirming Pages

192

Valuing Stocks

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

7-1 Understand the stock trading reports on the Internet or in the financial pages of the newspaper.

7-2 Calculate the present value of a stock given forecasts of future dividends and future stock price.

7-3 Use stock valuation formulas to infer the expected rate of return on a common stock.

7-4 Interpret price-earnings ratios.

7-5 Understand what professionals mean when they say that there are no free lunches on Wall Street.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

7CHAPTE R

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193

P A

R T

TW O

A corporation can raise cash for investment by borrowing or by selling new shares of com-mon stock to investors. If it borrows, it has a fixed obligation to repay the lender. If it issues shares,

there is no fixed obligation, but the new stockholders

become partial owners of the firm. All old and new

stockholders share in its fortunes, in proportion to the

number of shares that they hold. In this chapter, we

take a first look at common stocks, the stock market,

and the principles of stock valuation.

We start by looking at how stocks are bought and

sold. Then we look at what determines stock prices

and how stock valuation formulas can be used to

infer the rate of return that investors are expecting. We

will see how the firm’s investment opportunities are

reflected in its stock price and why stock market ana-

lysts focus so much attention on the price-earnings,

or P/E, ratio of the company.

Why should you care how stocks are valued? After

all, if you want to know the value of a firm’s stock,

you can look up the stock price on the Internet or in

The Wall Street Journal. But you need to know what

determines prices for at least two reasons. First, you

may need to value the common stock of a business

that is not traded on a stock exchange. For example,

you may be the founder of a successful business

that wishes to sell stock to the public for the first time.

You and your advisers need to estimate the price at

which those shares can be sold.

Second, in order to make good capital budgeting

decisions, corporations need to have some under-

standing of how the market values firms. A project is

attractive if it increases shareholder wealth. But you

can’t judge that unless you know how shares are

valued.

There may be a third reason why you would like

to know how stocks are valued. You may be hoping

that the knowledge will allow you to make a killing

on Wall Street. It’s a pleasant thought, but we will see

that even professional investors find it difficult to out-

smart the competition and earn consistently superior

returns.

Va lu

e

Charts of stock prices. Looking at past fluctuations in stock prices can be mesmerizing, but what determines those prices?

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Rev. Confirming Pages

194 Part Two Value

7.1 Stocks and the Stock Market In Chapter 1 we saw how FedEx was founded and how it grew and prospered. To fund this growth, FedEx needed capital. Initially, that capital came largely from borrow- ing, but in 1978 FedEx sold shares of common stock to the public for the first time. Those investors who bought shares in the initial public offering, or IPO, became part-owners of the business, and as shareholders they shared in the company’s future successes and setbacks.1

A company’s initial public offering is rarely its last, and since 1978 FedEx has raised more capital by selling additional shares. These sales of shares by the company are called primary offerings and are said to be made in the primary market.

Owning shares is a risky occupation. For example, if at the start of 2013 you had the misfortune to buy shares in the mining company Prospect Global Resources, you would have lost 97% of your money by the year-end. You can understand, therefore, why investors would be reluctant to buy shares if they were forced to tie the knot with a particular company forever. So large companies usually arrange for their com- mon stock to be listed on a stock exchange so that investors can trade shares among themselves. Exchanges are really markets for secondhand stocks, but they prefer to describe themselves as secondary markets, which sounds more important.

The two principal stock markets in the United States are the New York Stock Exchange (NYSE) and NASDAQ.2 In addition, there are many computer networks called electronic communication networks (ECNs) that connect traders with each other. All of these markets compete vigorously for the business of traders and just as vigorously tout the advantages of their own trading venue. The volume of trades in these markets is immense. For example, every day the NYSE alone trades more than 3.4 billion shares with market value exceeding $80 billion.

Of course, there are stock exchanges in many other countries. Some are tiny, such as the stock exchange in the Maldives, which trades shares in just 6 companies. Oth- ers, such as the London, Tokyo, Frankfurt, and pan-European Euronext exchanges, trade the shares of thousands of firms.

Suppose that Ms. Jones, a longtime FedEx shareholder, no longer wishes to hold her shares in the company. She can sell them via a stock exchange to Mr. Brown, who wishes to increase his stake in the firm. The transaction merely transfers (partial) own- ership of the firm from one investor to another. No new shares are created, and FedEx usually will neither care nor even be aware that such a trade has taken place.3

Ms. Jones and Mr. Brown do not buy or sell FedEx shares themselves. Instead, each must hire a brokerage firm with trading privileges on an exchange to arrange the transaction for them. Not so long ago, such trades would have involved hands-on negotiation. The broker would have had to agree on an acceptable price with a dealer in the stock or would have brought the trade to the floor of an exchange where a spe- cialist in FedEx would have coordinated the transaction. But today the vast majority of trades are executed automatically and electronically, even on the more traditional exchanges.

When Ms. Jones and Mr. Brown decide to buy or sell FedEx stock, they need to give their brokers instructions about the price at which they are prepared to transact. Ms. Jones, who is anxious to sell quickly, might give her broker a market order to sell

common stock Ownership shares in a publicly held corporation.

initial public offering (IPO) First offering of stock to the general public.

primary offering The corporation sells shares in the firm.

primary market Market for the sale of new securities by corporations.

secondary market Market in which previously issued securities are traded among investors.

1 We use the terms “shares,” “stock,” and “common stock” interchangeably, as we do “shareholders” and “stockholders.” 2 This originally was an acronym for National Association of Security Dealers Automated Quotation system, but now is simply known as the NASDAQ market. 3 Eventually, FedEx must know to whom it should send dividend checks, but this information is needed only when such payments are being prepared. In some cases, FedEx might care about a stock transaction, for exam- ple, if a large investor is building a big stake in the firm. But this is the exception.

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The world’s stock exchanges

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FIGURE 7.1 A portion of the limit order book for Federal Express from the NYSE/ Archipelago Exchange, July 16, 2013

Chapter 7 Valuing Stocks 195

stock at the best available price. On the other hand, Mr. Brown might give his broker a price limit at which he is willing to buy FedEx stock. If his order cannot be executed immediately, it is recorded in the exchange’s limit order book until it can be executed.

Figure 7.1 shows a portion of the limit order book for FedEx from the Archipelago Exchange, an electronic market run by the NYSE. The bid prices on the left are the prices (and numbers of shares) at which investors are willing to buy. The Ask column presents offers to sell. The prices are arranged from best to worst, so the highest bids and lowest asks are at the top of the list. The broker might electronically enter Ms. Jones’s market order to sell 100 shares on the Archipelago Exchange, where it would be automatically matched or crossed with the best offer to buy, which at that moment was $103.24 a share. Similarly, a market order to buy would be crossed with the best ask price, $103.38. The bid-ask spread at that moment was therefore 14 cents per share.

Reading Stock Market Listings If you are thinking about buying shares in FedEx, you will wish to see its current price. Until recently, you probably would have looked for that information in The Wall Street Journal or the financial pages of your local newspaper. But those pages contain less and less information about individual stocks, and most investors today turn to the Internet for their information. For example, if you go to finance.yahoo.com, enter FedEx’s ticker symbol, FDX, and ask to “Get Quotes,” you will find recent trading data such as those presented in Figure 7.2.4

The most recent price at which the stock traded on July 16 was $103.29 per share, which was $.41 lower than its closing price the previous day, $103.70. The range of prices at which the stock traded that day, as well as over the previous 52 weeks, is provided. In the set of columns on the right, Yahoo tells us that the average daily trad- ing volume over the last 3 months was 2,796,770 shares. Trading as of 3:06 p.m. on this day totaled 1,480,334 shares. FedEx’s market cap (shorthand for market capital- ization) is the total value of its outstanding shares of stock, $32.95 billion. You will frequently hear traders referring to large-cap or small-cap firms, which is a convenient way to summarize the size of the company.

4 Other good sources of trading data are moneycentral.msn.com/investor/home.asp or the online edition of The Wall Street Journal at www.wsj.com (look for the Market and then Market Data tabs).

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FIGURE 7.3 Share price history for FedEx

Source: Yahoo! Finance, November 1, 2013.

80

90

100

110

120

130

140

May 13 Jun 13 Jul 13 Aug 13 Sep 13 Oct 13 Nov 13

S h

ar e

p ri

ce (

$)

196 Part Two Value

FedEx earned $4.91 per share in the past year. (The abbreviation “ttm” in the paren- theses stands for trailing 12 months.) Therefore, the ratio of price per share to earnings per share, known as the price-earnings multiple or, equivalently, P/E ratio, is (aside from a little rounding error) 103.29/4.91 = 21.08. The P/E ratio is a key tool of stock market analysts, and we will have much to say about it later in the chapter.

The dividend yield tells you how much dividend income you would receive for every $100 invested in the stock. FedEx paid annual dividends of $.60 per share, so its yield was .60/103.29 = .6%. For every $100 invested in the stock, you would have received $.60 in dividends. Of course, this would not be the total rate of return on your investment, as you would also hope for some increase in the stock price. The dividend yield is thus much like the current yield of a bond. Both measures ignore prospective capital gains or losses.

The price at which you can buy shares in FedEx changes day to day and minute to minute. Remember, each share represents partial ownership in the firm, and share values will wax or wane with investors’ perceptions of the prospects for the company. Figure 7.3 shows the share price of FedEx over a 6-month period in 2013. The price rose by 19% in just over 2 weeks during October. Why would the price that investors were willing to pay for each share change so suddenly? And for that matter, why were they willing that month to pay $131 a share for FedEx but only $35 a share for Micro- soft? To answer these questions, we need to look at what determines value.

P/E ratio Ratio of stock price to earnings per share.

FIGURE 7.2 Trading information for FedEx

Source: Yahoo! Finance, July 16, 2013.

Prev Close:

Open:

Bid:

Ask:

1y Target Est:

Beta:

Next Earnings Date:

103.70

103.38

103.49 × 500

103.50 × 800

114.62

1.18

18-Sep-13

FedEx Corporation (FDX) - NYSE

103.29 0.41(0.40%) 3:06PM EDT - Nasdaq Real Time Price

Day’s Range:

52wk Range:

Volume:

Avg Vol (3m)

Market Cap:

P/E (ttm):

EPS (ttm):

102.96 - 103.98

83.92 - 109.66

1,480,334

2,796,770

32.95B

21.08

4.91

0.60 (0.60%)Div & Yield:

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Chapter 7 Valuing Stocks 197

7.2 Market Values, Book Values, and Liquidation Values Finding the value of FedEx stock may sound like a simple problem. Each quarter, the company publishes a balance sheet, which lists the value of the firm’s assets and liabil- ities. The simplified balance sheet in Table 7.1 shows that in May 2013 the book value of all FedEx’s assets—plant and machinery, inventories of materials, cash in the bank, and so on—was $33,567 million. FedEx’s debt and other liabilities—money that it owes the banks, taxes that are due to be paid, and the like—amounted to $16,169 mil- lion. The difference between the value of the assets and the liabilities was $17,398 million. This was the book value of the firm’s equity.5 Book value records all the money that FedEx has raised from its shareholders plus all the earnings that have been plowed back on their behalf.

Book value is a reassuringly definite number. But does the stock price equal book value? FedEx shares in July 2013 were selling at around $103, but as Table 7.2 shows, its book value per share was only $54.95. So the shares were worth about 1.9 times book value. This and the other cases shown in Table 7.2 tell us that investors in the stock market do not just buy and sell at book value per share.

Investors know that accountants don’t even try to estimate market values. The value of the assets reported on the firm’s balance sheet is equal to their original (or “histori- cal”) cost less an allowance for depreciation. But that may not be a good guide to what the firm could sell its assets for today.

Well, maybe stock price equals liquidation value per share, that is, the amount of cash per share a company could raise if it sold off all its assets in secondhand markets and paid off all its debts. Wrong again. A successful company ought to be worth more

book value Net worth of the firm according to the balance sheet.

5 “Equity” is still another word for stock. Thus, stockholders are often referred to as equity investors.

liquidation value Net proceeds that could be realized by selling the firm’s assets and paying off its creditors.

TABLE 7.1 Simplified balance sheet for FedEx, May 30, 2013 (figures in $ millions)

Note: Shares of stock outstanding: 316.6 million. Book value of equity (per share): 17,398/316.6 = $54.95.

Assets Liabilities and Shareholders’ Equity

Current assets 11,274 Current liabilities 5,750 Plant, equipment and other long-term assets

22,293 Debt and other long-term liabilities

10,419

Shareholders’ equity 17,398 Total assets 33,567 Total liabilities and equity 33,567

Stock Price Book Value per Share

Market-to-Book- Value Ratio

FedEx $103.39 $54.95 1.9 Johnson & Johnson 90.40 23.85 3.8 Campbell Soup 46.11 4.22 10.9 PepsiCo 83.99 14.55 5.8 Walmart 77.33 21.37 3.6 Dow Chemical 33.94 14.05 2.4 Amazon 306.77 18.53 16.6 McDonald’s 100.84 15.19 6.6 American Electric Power 47.21 31.73 1.5 General Electric 23.41 11.96 2.0

TABLE 7.2 Market values versus book values, July 2013

Source: Yahoo! Finance, fi nance.yahoo.com.

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198 Part Two Value

than liquidation value. After all, that’s the goal of bringing all those assets together in the first place.

The difference between a company’s actual value and its book or liquidation value is often attributed to going-concern value, which refers to three factors:

1. Extra earning power. A company may have the ability to earn more than an adequate rate of return on assets. In this case the value of those assets will be higher than their book value or secondhand value.

2. Intangible assets. There are many assets that accountants don’t put on the balance sheet. Some of these assets are extremely valuable. Take Johnson & Johnson, a health care product and pharmaceutical company. As you can see from Table 7.2, it sells at 3.8 times book value per share. Where did all that extra value come from? Largely from the cash flow generated by the drugs it has developed, patented, and marketed. These drugs are the fruits of a research and development (R&D) program that has grown to over $7 billion per year. But U.S. accountants don’t recognize R&D as an investment and don’t put it on the company’s balance sheet. Nevertheless, expertise, experience, and knowledge are crucial assets, and their values do show up in stock prices.

3. Value of future investments. If investors believe a company will have the opportunity to make very profitable investments in the future, they will pay more for the company’s stock today. When eBay, the Internet auction house, first sold its stock to investors in 1998, the book value of shareholders’ equity was about $100 million. Yet 1 day after the issue investors valued the equity at over $6 billion. In part, this difference reflected an intangible asset, eBay’s unique platform for trading a wide range of goods over the Internet. But investors also judged that eBay was a growth company. In other words, they were betting that the company’s know-how and brand name would allow it to expand internationally and make it easier for customers to trade and pay online. By 2013, eBay earned annual profits of $2.9 billion and had a market capitalization of $70 billion.

Market price is not the same as book value or liquidation value. Market value, unlike book value and liquidation value, treats the firm as a going concern.

It is not surprising that stocks virtually never sell at book or liquidation values. Investors buy shares on the basis of present and future earning power. Two key features determine the profits the firm will be able to produce: first, the earnings that can be generated by the firm’s current tangible and intangible assets, and second, the oppor- tunities the firm has to invest in lucrative projects that will increase future earnings.

Example 7.1 Amazon.com and Consolidated Edison Amazon.com is a growth company. In 2012, its profit was actually negative, -$39  million.6 Yet investors in December 2012 were prepared to pay about $110 billion for Amazon’s common stock. The value of the stock came from the com- pany’s market position, its highly regarded distribution system, and the promise of new related products that will generate increased future earnings. Amazon was a growth firm, because its market value depended so heavily on intangible assets and the anticipated profitability of new investments.

Contrast this with Consolidated Edison (Con Ed), the electric utility servicing the New York City area. Con Ed is not a growth company. Its market is limited, and it is expanding capacity at a very deliberate pace. More important, it is a regulated

6 The $39 million loss that Amazon reported probably understated its true income. Amazon was growing rap- idly, and this required large investments. Accounting rules required that Amazon treat many of those invest- ments as expenses and deduct them from operating income. As Amazon’s growth and investments decline, its reported income should increase.

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Chapter 7 Valuing Stocks 199

Investors refer to Amazon as a growth stock and Con Ed as an income stock. A few stocks, like Google, offer both income and growth. Google earns plenty from its cur- rent products. These earnings are part of what makes the stock attractive to investors. In addition, investors are willing to pay for the company’s ability to invest profitably in new ventures that will increase future earnings.

Let’s summarize. Just remember:

• Book value records what a company has paid for its assets, less a deduction for depreciation. It does not capture the true value of a business.

• Liquidation value is what the company could net by selling its assets and repaying its debts. It does not capture the value of a successful going concern.

• Market value is the amount that investors are willing to pay for the shares of the firm. This depends on the earning power of today’s assets and the expected profit- ability of future investments.

The next question is, What determines market value?

utility, so its returns on present and future investments are constrained. Con Ed’s value derives mostly from the stream of income generated by its existing assets. Therefore, while Amazon shares in 2013 sold for 16.5 times book value, Con Ed shares sold at only about 1.5 times book value.

In the 1970s, the computer industry was growing rapidly. In the 1980s, many new competitors entered the market, and computer prices fell. Since then computer makers have struggled with thinning profit margins and intense competition. How has the industry’s market-value balance sheet changed over time? Have assets in place become proportionately more or less impor- tant? Do you think this progression is unique to the computer industry?

Self-Test7.1

7.3 Valuing Common Stocks

Valuation by Comparables When financial analysts need to value a business, they often start by identifying a sample of similar firms. They then examine how much investors in these companies are prepared to pay for each dollar of assets or earnings. This is often called valuation by comparables. Look, for example, at Table 7.3. The first column of numbers shows, for some well-known companies, the ratio of the market value of the equity to the book value. Notice that in each case market value is higher than book value.

The second column of numbers shows the market-to-book ratio for competing firms. For example, you can see from the second row of the table that the stock of the typical large pharmaceutical firm sells for 3.8 times its book value. If you did not have a market price for the stock of Johnson & Johnson (J&J), you might estimate that it would also sell at 3.8 times book value. In this case your estimate of J&J’s market price would have been almost spot on.

An alternative would be to look at how much investors in other pharmaceutical stocks are prepared to pay for each dollar of earnings. The second row of Table 7.3 shows that the typical price-earnings (P/E) ratio for pharmaceutical stocks in 2013 was 22.3. If you assumed that Johnson & Johnson should sell at a similar multiple of earnings, you would have gotten a value for the stock of $119, somewhat higher than its actual price of $91.60 in July 2013.

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200 Part Two Value

Market-to-book and price-earnings ratios are the most popular rules of thumb for valuing common stocks, but financial analysts sometimes look at other multiples. For example, infant firms often do not have any earnings. So, rather than calculate a price- earnings ratio, analysts may look at the price-to-sales ratio for these firms. In the late 1990s, when dot-com companies were growing rapidly and losing lots of money, mul- tiples were often based on the number of subscribers or website visits.

There is nothing wrong with such rules of thumb if intelligently applied. Valuation by comparables worked very well for PepsiCo in 2013. However, that is not the case for all the companies shown in Table 7.3. For example, if you had naively assumed that Amazon stock would sell at similar ratios to comparable Internet retail stocks, you would have been out by a wide margin. Both the market-to-book ratio and the price- earnings ratio can vary considerably from stock to stock even for firms that are in the same line of business. To understand why this is so, we need to dig deeper and look at what determines a stock’s market value.

Price and Intrinsic Value In the previous chapter, we saw that the value of a bond is the present value of its coupon payments plus the present value of its final payment of face value. You can think of stocks in a similar way. Instead of receiving coupon payments, investors may receive dividends; and instead of receiving face value, they will receive the stock price at the time they sell their shares.

Consider, for example, an investor who buys a share of Blue Skies Inc. today and plans to sell it in 1 year. Call the predicted stock price in 1 year P1, the expected divi- dend per share over the year DIV1, and the discount rate for the stock’s expected cash flows r. Remember, the discount rate reflects the risk of the stock. Riskier firms will have higher discount rates. Then the present value of the cash flows the investor will receive from Blue Skies is

V0 = DIV1 + P1

1 + r (7.1)

We call V0 the intrinsic value of the share. Intrinsic value is just the present value of the cash payoffs anticipated by the investor in the stock.

To illustrate, suppose investors expect a cash dividend of $3 over the next year (DIV1 = $3) and expect the stock to sell for $81 a year hence (P1 = $81). If the dis- count rate is 12%, then intrinsic value is $75:

V0 = 3 + 81

1.12 = $75

intrinsic value Present value of future cash payoffs from a stock or other security.

Market-to-Book Value Ratio Price-Earnings Ratio

Company Industry* Company Industry*

FedEx 1.9 2.2 17.5 19.7 Johnson & Johnson 3.8 3.8 17.1 22.3 Campbell Soup 11.0 2.4 17.6 22.1 PepsiCo 6.0 5.6 21.1 21.1 Walmart 3.6 2.6 15.3 19.2 Dow Chemical 2.5 2.2 19.2 17.7 Amazon 16.4 4.5 NA** 30.9 McDonald’s 6.6 4.8 18.6 19.8 American Electric Power 1.5 1.6 13.5 16.9 General Electric 2.0 2.4 15.3 16.8

TABLE 7.3 Market-to-book- value ratios and price- earnings ratios for selected companies and their principal competitors, July 2013

* Figures are median values for companies in the same industry. ** Amazon had negative earnings in 2012, so its P/E ratio is meaningless.

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Chapter 7 Valuing Stocks 201

You can think of intrinsic value as the “fair” price for the stock. If investors buy the stock for $75, their expected rate of return will precisely equal the discount rate—in other words, their investment will just compensate them for the opportunity cost of their money.

To confirm this, note that the expected rate of return over the next year is the expected dividend plus the expected increase in price, P1 - P0, all divided by price at the start of the year, P0. If the investor buys the shares for intrinsic value, then P0 = $75 and

Expected return = DIV1 + P1 - P0

P0 =

3 + 81 - 75

75 = .12, or 12%

Notice that this expected return comes in two parts, the dividend and the capital gain:

Expected rate of return = expected dividend yield + expected capital gain

= DIV1

P0 +

P1 - P0 P0

= 3

75 +

81 - 75

75

= .04 + .08 = .12, or 12%

Of course, the actual return for Blue Skies may turn out to be more or less than investors expect. For example, in 2013, one of the best-performing industries was semi-conductor firms, with a return of 32%. This was almost certainly better than investors expected at the start of the year. At the other extreme, the share prices of min- ing firms declined on average by 2%. No investor at the start of the year would have purchased these shares anticipating a loss. Never confuse the actual outcome with the expected outcome.

The dream of every investor is to buy shares at a bargain price, that is, a price less than intrinsic value. But in competitive markets, no price other than intrinsic value could survive for long. To see why, imagine that Blue Skies’ current price were above $75. Then the expected rate of return on Blue Skies stock would be lower than that on other securities of equivalent risk. (Check this!) Investors would bail out of Blue Skies stock and move into other securities. In the process they would force down the price of Blue Skies stock. If P0 were less than $75, Blue Skies stock would offer a higher expected rate of return than equivalent-risk securities. (Check this, too.) Every- one would rush to buy, forcing the price up to $75. When the stock is priced correctly (that is, price equals present value), the expected rate of return on Blue Skies stock is also the rate of return that investors require to hold the stock. At each point in time all securities of the same risk are priced to offer the same expected rate of return. This is a fundamental characteristic of prices in well-functioning markets. It is also common sense.

Equation 7.1 is just a definition of intrinsic value, which works for any discount rate  r. Now we can go beyond the definition and identify r as the expected rate of return on all securities with a particular level of risk. If a stock is priced correctly, it will offer an expected rate of return equal to that of other equally risky stocks and price will equal intrinsic value:

P0 = DIV1 + P1

1 + r

Thus today’s price will equal the present value of dividend payments plus the present value of future price. But now we need to take a further step: How do we estimate the future price P1?

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Androscoggin Copper is increasing next year’s dividend to $5 per share. The forecast stock price next year is $105. Equally risky stocks of other compa- nies offer expected rates of return of 10%. What should Androscoggin com- mon stock sell for?

Self-Test7.2

202 Part Two Value

Of course, many corporations do not pay cash dividends. Investors in a young, growing company may have to wait a decade or more before the firm matures and starts paying out cash to shareholders. Our formula for P0 still applies to such firms if we set the immediate dividend DIV1 equal to zero. In this case value depends on the subsequent dividends. But let’s begin with a mature firm that is paying dividends now. We will say more about growth firms later.

The Dividend Discount Model Our equation for stock price depends on DIV1 + P1, that is, next period’s dividend and next period’s price. Suppose you have forecast the dividend. How do you forecast the price P1? We can answer this question by moving our stock price equation forward one period and applying it in period 1. The equation then says that P1 depends on the sec- ond period’s dividend DIV2 and the second-period price P2. The second-period price P2 in turn depends on the third period’s dividend DIV3 and the third-period price P3, which depends on DIV4 . . . you can see where this logic is going.

As it turns out, we can express a stock’s intrinsic value (and, therefore, price) as the present value of all the forecasted future dividends paid by the company to its share- holders without referring to the future stock price. This is the dividend discount model:

P0 = present value of (DIV1, DIV2, DIV3, c , DIVt, c)

= DIV1 1 + r

+

DIV2 (1 + r)2

+

DIV3 (1 + r)3

+ c

+

DIVt (1 + r)t

+ c

How far out in the future could we look? In principle, 40, 60, or 100 years or more— corporations are potentially immortal. However, far-distant dividends will not have significant present values. For example, the present value of $1 received in 30 years using a 10% discount rate is only $.057. Most of the value of established companies comes from dividends to be paid within a person’s working lifetime.

How do we get from the one-period formula P0 = (DIV1 + P1)/(1 + r) to the divi- dend discount model? We look at increasingly long investment horizons.

Let’s consider investors with different investment horizons. Each investor will value the share of stock as the present value of the dividends that she or he expects to receive plus the present value of the price at which the stock is eventually sold. Unlike bonds, however, the final horizon date for stocks is not specified—stocks do not “mature.” Moreover, both dividends and final sales price can only be estimated. But the general valuation approach is the same. For a one-period investor, the valuation formula looks like this:

P0 = DIV1 + P1

1 + r

A 2-year investor would value the stock as

P0 = DIV1 1 + r

+

DIV2 + P2 (1 + r)2

and a 3-year investor would use the formula

P0 = DIV1 1 + r

+

DIV2 (1 + r)2

+

DIV3 + P3 (1 + r)3

dividend discount model Discounted cash-flow model which states that today’s stock price equals the present value of all expected future dividends.

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Chapter 7 Valuing Stocks 203

In fact we can look as far out into the future as we like. Suppose we call our horizon date H. Then the stock valuation formula would be

P0 = DIV1 1 + r

+

DIV2 (1 + r)2

+ c

+

DIVH + PH (1 + r)H

(7.2)

In words, the value of a stock is the present value of the dividends it will pay over the investor’s horizon plus the present value of the expected stock price at the end of that horizon.

Does this mean that investors with different horizons will come to different con- clusions about the value of the stock? No! Regardless of the investment horizon, the stock value will be the same. This is because the stock price at the horizon date is determined by expectations of dividends from that date forward. Therefore, as long as investors agree about a firm’s prospects, they will also agree on its present value. Let’s confirm this with an example.

Example 7.2 Valuing Blue Skies Stock Take Blue Skies. The firm is growing steadily, and investors expect both the stock price and the dividend to increase at 8% per year. Now consider three investors, Erste, Zweiter, and Dritter. Erste plans to hold Blue Skies for 1 year, Zweiter for 2, and Dritter for 3. Compare their payoffs:

Remember, we assumed that dividends and stock prices for Blue Skies are expected to grow at a steady 8%. Thus DIV2 = $3 × 1.08 = $3.24, DIV3 = $3.24 ×  1.08 = $3.50, and so on.

Each investor requires the same 12% expected return. So we can calculate pres- ent value over Erste’s 1-year horizon:

PV = DIV1 + P1

1 + r =

$3 + $81 1.12

= $75

or Zweiter’s 2-year horizon:

PV = DIV1 1 + r

+

DIV2 + P2 (1 + r)2

= $3

1.12 +

$3.24 + $87.48 (1.12)2

= $2.68 + $72.32 = $75

or Dritter’s 3-year horizon:

PV = DIV1 1 + r

+

DIV2 (1 + r)2

+

DIV3 + P3 (1 + r)3

= $3

1.12 +

$3.24 (1.12)2

+

$3.50 + $94.48 (1.12)3

= $2.68 + $2.58 + $69.74 = $75

Year 1 Year 2 Year 3

Erste DIV1 = 3 P1 = 81

Zweiter DIV1 = 3 DIV2 = 3.24 P2 = 87.48

Dritter DIV1 = 3 DIV2 = 3.24 DIV3 = 3.50 P3 = 94.48

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Refer to Self-Test 7.2. Assume that Androscoggin Copper’s dividend and share price are expected to grow at a constant 5% per year. Calculate the current value of Androscoggin stock with the dividend discount model using a 3-year horizon. You should get the same answer as in Self-Test 7.2.

Self-Test7.3

204 Part Two Value

Look at Table 7.4, which continues the Blue Skies example for various time hori- zons, still assuming that the dividends are expected to increase at a steady 8% com- pound rate. The expected price increases at the same 8% rate. Each row in the table represents a present value calculation for a different horizon year. Note that total pres- ent value does not depend on the investment horizon. Figure 7.4 presents the same data in a graph. Each column shows the present value of the dividends up to the horizon and the present value of the price at the horizon. As the horizon recedes, the dividend stream accounts for an increasing proportion of present value but the total present value of dividends plus terminal price always equals $75.

Horizon, Years PV (Dividends)  + PV (Terminal Price)  = Value per Share

1 $2.68 $72.32 $75 2 5.26 69.74 75 3 7.75 67.25 75

10 22.87 52.13 75 20 38.76 36.24 75 30 49.81 25.19 75 50 62.83 12.17 75

100 73.02 1.98 75

TABLE 7.4 Value of Blue Skies

All agree the stock is worth $75 per share. This illustrates our basic principle: The value of a common stock equals the present value of dividends received out to the investment horizon plus the present value of the forecast stock price at the hori- zon. Moreover, when you move the horizon date, the stock’s present value should not change. The principle holds for horizons of 1, 3, 10, 20, and 50 years or more.

BEYOND THE PAGE

brealey.mhhe.com/ch07-03

The dividend discount model

FIGURE 7.4 Value of Blue Skies for different horizons

V al

u e

p er

s h

ar e

($ )

1 2 3 10 20 30 50 100

Investment horizon (years)

70

80

50

60

40

30

20

10

0

PV (terminal price)

PV (dividends)

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Moonshine Industries has produced a barrel per week for the past 20 years but cannot grow because of certain legal hazards. It earns $25 per share per year and pays it all out to stockholders. The stockholders have alternative, equivalent-risk ventures yielding 20% per year on average. How much is one share of Moonshine worth? Assume the company can keep going indefinitely.

Self-Test7.4

Chapter 7 Valuing Stocks 205

If the horizon is infinitely far away, then we can forget about the final horizon price—it has almost no present value—and simply say,

Stock price = PV(all future dividends per share)

This is the dividend discount model.

7.4 Simplifying the Dividend Discount Model

The Dividend Discount Model with No Growth Consider a company that pays out all its earnings to its common shareholders. Such a company could not grow because it could not reinvest.7 Stockholders might enjoy a generous immediate dividend, but they could not look forward to higher future divi- dends. The company’s stock would offer a perpetual stream of equal cash payments, DIV1 = DIV2 = . . . = DIVt = . . ..

The dividend discount model says that these no-growth shares should sell for the present value of a constant, perpetual stream of dividends. We learned how to do that calculation when we valued perpetuities in Chapter 5. Just divide the annual cash pay- ment by the discount rate. The discount rate is the rate of return demanded by investors in other stocks with the same risk:

P0 = DIV1

r

Since our company pays out all its earnings as dividends, dividends and earnings are the same, and we could just as well calculate stock value by

Value of a no-growth stock = P0 = EPS1

r

where EPS1 represents next year’s earnings per share of stock. Thus some people loosely say, “Stock price is the present value of future earnings,” and calculate value by this formula. Be careful—this is a special case.

7 We assume it does not raise money by issuing new shares.

The Constant-Growth Dividend Discount Model The dividend discount model requires a forecast of dividends for every year into the future, which poses a bit of a problem for stocks with potentially infinite lives. Unless we want to spend a lifetime forecasting dividends, we must use simplifying assump- tions to reduce the number of estimates. As we have just seen, the simplest simplifica- tion assumes a no-growth perpetuity, which works only for no-growth shares.

Here’s another simplification that finds a good deal of practical use. Suppose fore- cast dividends grow at a constant rate into the indefinite future. If dividends grow at a steady rate, then instead of forecasting an infinite number of dividends, we need to forecast only the next dividend and the dividend growth rate.

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206 Part Two Value

Recall Blue Skies Inc. It will pay a $3 dividend in 1 year. If the dividend grows at a constant rate of g = .08 (8%) thereafter, then dividends in future years will be

DIV1 = $3 = $3.00 DIV2 = $3 × (1 + g) = $3 × 1.08 = $3.24 DIV3 = $3 × (1 + g)2 = $3 × 1.082 = $3.50

Plug these forecasts of future dividends into the dividend discount model:

P0 = DIV1 1 + r

+

DIV1(1 + g)

(1 + r)2 +

DIV1(1 + g)2

(1 + r)3 +

DIV1(1 + g)3

(1 + r)4 + c

= $3

1.12 +

$3.24 (1.12)2

+ $3.50 (1.12)3

+ $3.78 (1.12)4

+ c

= $2.68 + $2.58 + $2.49 + $2.40 + c

Although there is an infinite number of terms, each term is proportionately smaller than the preceding one as long as the dividend growth rate g is less than the discount rate r. Because the present value of far-distant dividends will be ever closer to zero, the sum of all of these terms is finite despite the fact that an infinite number of dividends will be paid. The sum can be shown to equal

P0 = DIV1 r - g

(7.3)

This equation is called the constant-growth dividend discount model, or the Gordon growth model after Myron Gordon, who did much to popularize it.8

constant-growth dividend discount model Version of the dividend discount model in which dividends grow at a constant rate.

8 Notice that the first dividend is assumed to come at the end of the first period and is discounted for a full period. If the stock has just paid a dividend DIV0, then next year’s dividend will be (1 + g) times the dividend just paid. So another way to write the valuation formula is

P0 = DIV1 r - g

=

DIV0 × (1 + g)

r - g

Example 7.3 Using the Constant-Growth Model to Value Aqua America Aqua America (ticker symbol WTR) is a water utility serving parts of 14 states from Maine to Texas. In July 2013 its stock was selling for $32 a share. Since there were 141 million shares outstanding, investors were placing a total value on the stock of 141  million × $32 = $4.5 billion. Can we explain this valuation?

In 2013 Aqua America could point to a remarkably consistent growth record. For each of the past two decades it had steadily increased its dividend payment (see Figure 7.5), and, with one minor hiccup, earnings had also grown steadily. The con- stant-growth model therefore seems tailor-made for valuing Aqua America’s stock.

In 2013 investors were forecasting that in the following year Aqua America would pay a dividend of $.84 (DIV1 = $.84). The forecast growth in dividend was about 4% a year over the foreseeable future (we explain in a moment where this figure comes from). If investors required a return of 6.6% from Aqua America’s stock, then the con- stant-growth model gives a share value in 2013 (P0) of just over $32:

P0 = DIV1 r - g

=

$.84 .066 - .04

= $32.31

The constant-growth formula is similar to the formula for the present value of a per- petuity. Suppose you forecast no growth in dividends (g = 0). Then the dividend stream is a simple perpetuity, and the valuation formula is P0 = DIV1/r. This is precisely the formula you used in Self-Test 7.4 to value Moonshine, a no-growth common stock.

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Chapter 7 Valuing Stocks 207

Sustainable Growth The constant-growth model generalizes the perpetuity formula to allow for constant growth in dividends. But how do we estimate that trend growth rate? Mature compa- nies grow mainly by reinvesting earnings. How rapidly they grow depends on both the proportion of earnings reinvested into the business and the profits generated by those new investments. The firm’s sustainable growth rate is the rate at which the firm can grow by reinvesting earnings, keeping its long-term debt ratio constant.

Suppose Aqua America (from Example 7.3) has book value per share of $11.20 and will generate a return on equity of 11.5%.9 Then earnings per share will be

EPS = book value per share × ROE = $11.20 × .115 = $1.288

Over the next several years, the firm is expected to maintain a payout ratio (the pro- portion of earnings to be paid out as dividends) of 65%, so dividends per share will be .65 × $1.288 = $.84. So the plowback ratio (the fraction of earnings reinvested in the firm) is 1 - .65 = .35, and .35 × $1.288 = $.45 a share will be plowed back into new plant, equipment, and other investments. Therefore, book value per share will increase by $.45 to $11.20 + $.45 = $11.65. The growth rate of equity generated by reinvesting earnings is

Growth rate in book equity = plowed-back earnings

initial equity =

$.45

$11.20 = .04, or 4.0%

To see how growth depends on plowback and ROE, we can rewrite this equation as follows:

Growth rate = plowed-back earnings

initial equity =

plowed-back earnings

total earnings ×

total earnings

initial equity = plowback ratio × ROE = .35 × .115 = .040, or 4.0%

This is the growth rate of the book value of equity. What about dividends and earn- ings? If ROE is constant, then earnings per share will grow in direct proportion to equity (remember that EPS = ROE × book equity), so earnings also will grow at 4%. And if the payout ratio is constant, dividends will be a fixed proportion of earnings, so they too will grow at that rate. Therefore, if ROE and plowback are stable, then book

sustainable growth rate The firm’s growth rate if it plows back a constant fraction of earnings, maintains a constant return on equity, and keeps its debt ratio constant.

payout ratio Fraction of earnings paid out as dividends.

plowback ratio Fraction of earnings retained by the firm.

9 We construct estimates of trend earnings and dividends using data from the Value Line Investment Survey, July 19, 2013.

FIGURE 7.5 Aqua America’s dividends have grown steadily

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014

D iv

id en

d s

p er

s h

ar e

($ )

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208 Part Two Value

equity, earnings, and dividends all increase at the sustainable growth rate. The sustain- able growth rate therefore is the natural choice for g in the constant-growth dividend discount model. This is the value we used for Aqua America in Example 7.3.

If a company earns a constant return on equity and plows back a constant proportion of earnings, then its growth rate, g, is

g = sustainable growth rate = ROE × plowback ratio (7.4)

The sustainable growth rate assumes that the firm’s long-term debt ratio is held constant. This means that debt and total capital also increase at the sustainable growth rate. Aqua America could grow its assets at a faster rate by borrowing more and more, but such a strategy, entailing ever-higher debt ratios, would not be sustainable.

A Caveat The sustainable growth rate that we found for Aqua America is moderate, and it is plau- sible that the firm can continue to grow at a trend rate of 4% for the indefinite future. But sometimes you will find that the formula for sustainable growth, ROE × plow- back, results in crazy values, for example, growth rates of 20% or even more. No company could expect to maintain growth rates like these forever. After all, the (real) growth rate of the economy as a whole is only around 2.5%. If a firm or industry grew indefinitely at 20%, it eventually would outgrow the entire economy and then move on to take over the galaxy!

Often when we observe rapid growth rates, the firms are in industries with new and promising investment opportunities and correspondingly high profit margins. For example, returns on investment in the computer software industry were commonly around 17% in 2012, and many firms in the industry responded to these attractive investment opportunities by reinvesting all their profits. The high values of both ROE and plowback imply growth rates commonly over 15%.10 But such a rate of growth is not sustainable. As the industry matures, price competition will increase and ROE therefore will decline. With fewer profitable opportunities for reinvestment, firms will reinvest a smaller share of their earnings. As ROE and plowback both decline, so will growth rates.

If you look back at Equation 7.3, you will see that it implies that given this year’s dividends, DIV1, the stock price will be higher when the dividend growth rate is assumed to be higher. But that equation is valid only if the growth rate is sustainable and is less than the discount rate. If you forecast perpetual dividend growth at a rate higher than investors’ required return, r, then two things happen:

1. The formula explodes and gives crazy values. (For example, what would be the “value” of Aqua America in Example 7.3 if you assumed a growth rate of 10%?)

2. You know your forecasts must be wrong, because the present value of far-distant dividends would be incredibly high. If projected dividends grow at a higher rate than the discount rate, the present value of each successive dividend will grow without limit. (Again, try a numerical example using Aqua America. Calculate the present value of a dividend paid after 100 years, assuming DIV1 = $.84, r = .066, and g = .10.)

Clearly, temporary nonsustainable growth requires more flexibility than the con- stant-growth model can offer. We will show you how to deal with this situation in a few pages.

Estimating Expected Rates of Return We argued earlier, in Section 7.3, that in competitive markets, common stocks with the same risk are priced to offer the same expected rate of return. But how do you figure out what that expected rate of return is?

10 These data are based on firms in the Value Line Investment Survey industry group.

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Chapter 7 Valuing Stocks 209

It’s not easy. Consensus estimates of future dividends, stock prices, or overall rates of return are not published in The Wall Street Journal or reported by TV newscasters. Economists argue about which statistical models give the best estimates. There are nevertheless some useful rules of thumb that can give sensible numbers.

One rule of thumb is based on the constant-growth dividend discount model, which forecasts a constant growth rate g in both future dividends and stock prices. That means expected capital gains equal g per year.

We can calculate the expected rate of return by rearranging the constant-growth formula as

r = DIV1

P0 + g (7.5)

= dividend yield + growth rate

For Aqua America from Example 7.3, the expected first-year dividend is $.84 and the growth rate is 4%. With an initial stock price of $32.31, the expected rate of return is

r = DIV1

P0 + g

= $.84

$32.31 + .04 = .026 + .040 = .066, or 6.6%

Suppose we found another stock with the same risk as Aqua America. It ought to offer the same expected total rate of return even if its immediate dividend or expected growth rate is very different. The required rate of return is not the unique property of Aqua America or any other company; it is set in the worldwide market for common stocks. Aqua America cannot change its value of r by paying higher or lower dividends or by growing faster or slower, unless these changes also affect the risk of the stock. When we use the rule-of-thumb formula, r = DIV1/P0 + g, we are not saying that r, the expected rate of return, is determined by DIV1 or g. It is determined by the rate of return offered by other equally risky stocks. That return determines how much inves- tors are willing to pay for Aqua America’s forecast future dividends:

DIV1 P0

+ g = r = expected rate of return offered by other, equally risky stocks

Example 7.4 Aqua America Gets a Windfall Suppose that a shift in water usage allows Aqua America to generate 5% per year future growth without sacrificing immediate dividends. Will that increase r, the expected rate of return?

This is good news for the firm’s stockholders. The stock price will jump to

P0 = DIV1 r - g

=

$.84 .066 - .05

= $52.50

But at the new price the stock will offer the same 6.6% expected return:

r = DIV1 P0

+ g

= $.84

$52.50 + .05 = .066, or 6.6%

Aqua America’s good news is reflected in a higher stock price today, not in a higher expected rate of return in the future. The unchanged expected rate of return corresponds to the firm’s unchanged risk.

('''''')''''''*('')''*

Given DIV1 and g, investors set the stock price

so that Aqua America offers an adequate expected rate of return r

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Androscoggin Copper can grow at 5% per year for the indefinite future. It’s selling at $100, and next year’s dividend is $5. What is the expected rate of return from investing in Carrabasset Mining common stock? Carrabasset and Androscoggin shares are equally risky.

Self-Test7.5

210 Part Two Value

Nonconstant Growth Water companies and other utilities tend to have steady rates of growth and are there- fore natural candidates for application of the constant-growth model. But many com- panies grow at rapid or irregular rates for several years before finally settling down. Obviously in such cases we can’t use the constant-growth model to estimate value. However, there is an alternative approach. Set the investment horizon (year H) at the future year by which you expect the company’s growth to settle down. Calculate the present value of dividends from now to the horizon year. Forecast the stock price in that year, and discount it also to present value. You can use the constant-growth for- mula to value later dividends because by then it is reasonable to forecast that dividends will be growing at a sustainable rate. Finally, add up to get the total present value of dividends plus the present value of the ending stock price. The formula is

P0 = DIV1 1 + r

+

DIV2 (1 + r)2

+ c

+

DIVH (1 + r)H

+

PH (1 + r)H

Example 7.5 Estimating the Value of McDonald’s Stock In mid-2013 the price of McDonald’s stock was nearly $100. The company earned about $5.50 a share and paid out about 55% of earnings as dividends. Let’s see how we might use the dividend discount model to estimate McDonald’s intrinsic value.

Investors in 2013 were optimistic about the prospects for McDonald’s and were forecasting that earnings would grow over the next 5 years by about 9% a year.11 This growth rate is almost certainly higher than the return, r, that investors required from McDonald’s stock, and it is implausible to suppose that such rapid growth could continue indefinitely. Therefore, we cannot use the simple constant-growth formula to value the shares. Instead, we will break the problem down into three steps:

Step 1: Value McDonald’s dividends over the period of rapid growth. Step 2: Estimate McDonald’s stock price at the horizon year, when growth

should have settled down. Step 3: Calculate the present value of McDonald’s stock by summing the pres-

ent value of dividends up to the horizon year and the present value of the stock price at the horizon.

11 Consensus analysts’ forecasts are collected by Zack’s, First Call, and IBES. They are available on the web at moneycentral.com and finance.yahoo.com.

(')'*

PV of dividends from year 1 to horizon

PV of stock price at horizon

(''''''')'''''''*

The stock price in the horizon year is often called terminal value.

BEYOND THE PAGE

brealey.mhhe.com/ch07-04

Estimating stock value with non-constant

growth

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Chapter 7 Valuing Stocks 211

Year 1 2 3 4 5

Earnings 5.50 6.00 6.53 7.12 7.76 Dividends (55% of earnings)

3.03 3.30 3.59 3.92 4.27

Step 1: Our first task is to value McDonald’s dividends over the next 5 years. If dividends keep pace with the growth in earnings, then forecast earnings and divi- dends are as follows:

In 2013 investors required a return of about 8.5% from McDonald’s stock.12 There- fore, the present value of the forecast dividends for years 1 to 5 was:

PV of dividends years 1–5 = $3.03 1.085

+

$3.30 (1.085)2

+

$3.59 (1.085)3

+

$3.92 (1.085)4

+

$4.27 (1.085)5

= $14.07

Step 2: The trickier task is to estimate the price of McDonald’s stock in the hori- zon year 5. The most likely scenario is that after year 5 growth will gradually settle down to a sustainable rate, but to keep life simple, we will assume that in year 6 the growth rate falls immediately to 5% a year.13 Thus the forecast dividend in year 6 is

DIV6 = 1.05 × DIV5 = 1.05 × $4.27 = $4.48

and the expected price at the end of year 5 is

P5 = DIV6 r - g

=

$4.48 .085 - .05

= $128

Step 3: Remember, the value of McDonald’s today is equal to the present value of forecast dividends up to the horizon date plus the present value of the price at the horizon. Thus,

P0 = PV(dividends years 1–5) + PV(price in year 5)

= $14.07 + $128

1.0855 = $99.20

12 For now, you can take this value purely as an assumption. In Chapter 12, we will show you how to estimate required returns. This value is about 4 percentage points higher than the 2013 yield to maturity on McDonald’s long-term bonds. The stock requires a higher discount rate because it is riskier than the bonds. 13 We showed earlier that if a company plows back a constant proportion of earnings and earns a constant return on these new investments, then earnings and dividends will grow by g = plowback ratio × return on new invest- ment. Thus, if from year 5 onward McDonald’s continues to reinvest 45% of its earnings and earns an ROE of 11.1% on this investment, earnings and dividends will grow by .45 × .111 = .05, or 5%.

A Reality Check Our estimate of McDonald’s value looks reasonable and almost matches McDonald’s actual market price. But does it make you nervous to note that your estimate of the terminal price accounts for such a large proportion of the stock’s value? It should. Only very minor changes in your assumptions about growth beyond year 5 could change your estimate of this terminal price by 10%, 20%, or 30%.

In the case of McDonald’s we know what the market price really was in the middle of 2013, but suppose that you are using the dividend discount model to value a com- pany going public for the first time or that you are wondering whether to buy Blue Skies’ concatenator division. In such cases you do not have the luxury of looking up the market price in The Wall Street Journal. A valuation error of 30% could amount to serious money. Wise managers, therefore, check that their estimate of value is in the right ballpark by looking at what the market is prepared to pay for similar businesses. For example, suppose you can find mature, public companies whose scale, risk, and

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Suppose that on further analysis you decide that after year 5 McDonald’s earnings and dividends will grow by a constant 4% a year. How does this affect your estimate of the value of McDonald’s stock at year 0?

Self-Test7.6

212 Part Two Value

growth prospects today roughly match those projected for McDonald’s at the invest- ment horizon. You look back at Table 7.3 and discover that the stocks in McDonald’s industry group typically sell at 19.8 times recent earnings. Then you can reasonably guess that McDonald’s value in year 5 will be about 19.8 times the earnings forecast for that year, that is, 19.8 × $7.76 = $153.6, somewhat higher than the $128 horizon value that we obtained from the dividend discount model.

Of course, these checks using price-earnings or price-to-book ratios are just an application of the valuation by comparables method introduced earlier in the chapter.

Repurchases and the Dividend Discount Model Dividends are not the only way that firms can return cash to their equity investors. They also can, and commonly do, engage in stock buybacks or repurchases. In a repur- chase, the firm buys a small fraction of the outstanding shares of its shareholders. In some years, repurchases of many firms exceed dividend payouts. Repurchases are attractive to firms that wish to distribute cash to equityholders but do not want to signal to them, even informally, that they should expect to receive such distributions on a regular basis in the future. In contrast, investors (rightly) interpret dividends as a repeated cash distribution that the firm will, in most circumstances, try to maintain or even increase. We discuss repurchases in some detail in Chapter 17.

When we use the dividend discount model, we should recognize that repurchases act much like dividends. For example, if the firm buys back 1% of all the shares of each of its shareholders, that action is nearly equivalent to paying a dividend equal to 1% of the share price. So can we simply adapt the dividend discount model by adding up distribu- tions of both dividends and repurchases and treating them equivalently? Yes . . . and no.

Repurchases certainly do not invalidate the dividend discount model. Value is still the present value of the cash distributions that each share will receive. But they do make the implementation of the model more complicated because as shares are bought back, it can be hard to forecast dividends on a “per share” basis. This can lead to difficult bookkeeping and complications working out the correct value for sustainable growth.

Here is our suggestion: When repurchases are important, it is often simpler to value the firm’s total free cash flow rather than just dividends. By free cash flow, we mean the cash the firm has available to distribute after paying for all investments necessary for its growth. In a sense, imagine that you own all the shares in the firm. Free cash flow is what you could receive as the single shareholder in the firm; importantly, it will not depend on the breakdown between dividends and repurchases. After all, as the sole shareholder, you won’t care whether you get free cash flow by receiving dividends or by selling some of your shares back to the firm. If you value the whole firm by apply- ing the dividend discount model to free cash flow, then you can find the share price by dividing the value of the firm by the current number of shares outstanding.

7.5 Growth and Growth Opportunities We often hear investors speak of growth stocks and income stocks. They buy growth stocks primarily in the expectation of capital gains, and they are interested in the future growth of earnings rather than in next year’s dividends. On the other hand, they buy

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Chapter 7 Valuing Stocks 213

income stocks principally for the cash dividends. Let us see whether these distinctions make sense.

Think back once more to Aqua America. It is expected to pay a dividend in 2014 of $.84 (DIV1 = .84), and this dividend is expected to grow at a steady rate of 4% a year (g = .04). If investors require a return of 6.6% (r = .066), then the price of Aqua America should be

P0 = DIV1/(r - g) = .84/(.066 - .04) = $32.31

What if Aqua America did not plow back any of its earnings into new plant and equipment? In that case it would pay out all of its earnings, $1.288 a share, but would forgo any further growth in earnings and dividends:

g = sustainable growth rate = return on equity × plowback ratio = .115 × 0 = 0

We could recalculate the value of Aqua America assuming it paid out all its forecast earnings and forwent any growth:

P0 = DIV1 r - g

=

EPS1 r

=

$1.288

.066 = $19.52

Thus, if Aqua America did not reinvest any of its earnings, its stock price would be not $32.31 but $19.52. The $19.52 represents the value of earnings from assets that are already in place. The rest of the stock price ($32.31 - $19.52 = $12.79) is the net present value of the future investments that Aqua America is expected to make.

What if the company kept to its policy of reinvesting 35% of its profits but the fore- cast return on new investments was only 6.6%? In that case the sustainable growth rate would also be lower:

g = sustainable growth rate = return on equity × plowback ratio = .066 × .35 = .0231, or 2.31%

If we plug this new figure into our valuation formula, we come up again with a value of $19.52 for Aqua America stock, no different from the value it would have if it chose not to grow at all:

P0 = DIV1 r - g

=

$.84

.066 - .0231 = $19.52

Plowing earnings back into new investments may result in growth in earnings and dividends, but it does not add to the current stock price if that money is expected to earn only the return that investors require. Plowing earnings back does add value if investors believe that the reinvested earnings will earn a higher rate of return.

To repeat, if Aqua America did not reinvest any of its earnings, the value of its stock would simply derive from the stream of earnings from the existing assets. The price of its stock would be $19.52. If the company did reinvest each year but earned only the return that investors require, then those new investments would not add any value. The price of the stock would still be $19.52. Fortunately, investors believe that Aqua America has the opportunity to earn 11.5% on its new investments, somewhat above the 6.6% return that investors require. This is reflected in the $32.31 that investors are prepared to pay for the stock. The total value of Aqua America stock is equal to the value of its assets in place plus the present value of its growth opportunities, or PVGO:

present value of growth opportunities (PVGO) Net present value of a firm’s future investments.

Value of assets in place $19.52 + Present value of growth opportunities (PVGO) 12.79 = Total value of Aqua America’s stock $32.31

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Suppose that instead of plowing money back into lucrative ventures, Aqua America’s management is investing at an expected return on equity of 5%, which is below the return of 6.6% that investors could expect to get from comparable securities.

a. Find the sustainable growth rate of dividends and earnings in these cir- cumstances. Continue to assume a 35% plowback ratio.

b. Find the new value of its investment opportunities. Explain why this value is negative despite the positive growth rate of earnings and dividends.

c. If you were a corporate raider, would Aqua America be a good candidate for an attempted takeover?

Self-Test7.7

214

The investment prospects of Aqua America are reflected in its price-earnings ratio. With a stock price of $32.31 and forecast earnings of $1.288, the P/E ratio is $32.31/$1.288 = 25.1. If the company had no growth opportunities, its stock price would be only $19.52 and its P/E would be $19.52/$1.288  =  15.2. The P/E ratio is, therefore, an indicator of Aqua’s prospects and the profitability of its growth opportunities.

Does this mean that the financial manager should celebrate if the firm’s stock sells at a high P/E? The answer is usually yes. The high P/E suggests that investors think that the firm has good growth opportunities. However, firms can have high P/E ratios not because the price is high but because earnings are temporarily depressed. A firm that earns nothing in a particular period will have an infinite P/E.

Of course, valuing stocks is always harder in practice than in principle. Forecast- ing cash flows and settling on an appropriate discount rate require skill and judgment. The difficulties are often greatest in the case of companies like Facebook, whose value comes largely from growth opportunities rather than assets that are already in place. As the nearby box shows, in these cases there is plenty of room for disagreement about value.

Finance in Practice Facebook’s IPO Facebook at around half of Google’s value at the time, even though Google’s profi ts that year were 10 times Facebook’s. But optimists argued that Facebook could generate much higher growth than Google in its advertising revenue, which would justify higher earnings multiples. Clearly, valuation by comparables was tricky given the difficulties in projecting and comparing growth opportunities.

In the end, investors were overly optimistic. Facebook’s closing stock price on the day of its IPO was $38 per share, implying total market capitalization of just over $100 billion. But the stock price almost immediately fell, bottoming out at $18 by September 2012; the price did not again reach $38 for just about another year.

Does this mean that Facebook’s IPO was a failure? While some fi rms seem to covet an “IPO pop,” that is, a stock price run-up on the day of the IPO, it is hard to see why a pop is in their interest. A pop signifi es that investors would have been willing to pay more for the shares or, in other words, that the IPO was underpriced and the issuing fi rm “left money on the table.” In contrast, Facebook seems to have received all it could from its IPO.

What is Facebook worth? This was the question that con- fronted investors as the company’s highly anticipated initial public offering approached in May 2012. Estimates of value in the months before the IPO ranged from as little as $50 billion to as much as $125 billion. The difference in these estimates turned on questions of growth.

Facebook’s revenue grew by 88% in 2011, and net income grew by 65%. Such growth was impressive but was sharply lower than in the previous few years. From 2009 to 2010, for example, revenue had increased by around 150%. What was a reasonable projection of growth in the years following the IPO?

It is notoriously difficult to guess what future opportuni- ties may be available to a high-tech company. Rather than attempting to make detailed growth forecasts, many investors used valuation by comparables, comparing Facebook to rival companies with similar business models.

Facebook’s reported profi ts in 2011 were around $1 bil- lion. Even at the low range for the IPO of $50 billion, this would imply a P/E ratio of 50, well above even successful Internet fi rms such as Google. At the higher end of the valu- ation estimates, say $100 billion, investors would be valuing

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Chapter 7 Valuing Stocks 215

Valuing Growth Stocks We used the dividend discount model to value Aqua America and to distinguish the value of its growth opportunities from its assets in place. Aqua America was an easy target, because its profitability was stable and its growth moderate. What about young, risky, and rapidly growing companies? These companies usually pay no cash divi- dends, and their current growth rates cannot be sustained for the longer run. Here the dividend discount model still works logically—we could project dividends as zero out to some distant date when the firm matures and payout commences. But forecasting far-off dividends is more easily said than done. In these cases, it’s more helpful to think about the value of a stock as the sum of the value of assets in place plus PVGO, the present value of growth opportunities.

The value per share of assets in place equals the firm’s average future earnings if it does not grow, that is, EPS/r. So we can express the value of a growth stock as

P0 = EPS/r + PVGO

If you can observe P0 and calculate EPS/r, you can subtract and see how much value investors are assigning to growth.

Market-Value Balance Sheets Financial managers are not bound by generally accepted accounting principles. Some- times they construct a market-value balance sheet to help identify sources of value. Table 7.5 shows the entries on such a balance sheet. Look at the assets in our market- value balance sheet. Some of the entries will be familiar, for example, current assets. The market and book values of current assets are usually similar. In contrast, recall that book values of plant, equipment, and other long-term assets are recorded at his- torical cost, which for older assets can be much less than current value, particularly in periods of high inflation. Other assets may be obsolete and worth much less than historical cost. Also there will be intangible assets, such as going-concern value, that do not appear at all on the company’s books.

The present value of growth opportunities (PVGO) never appears on a book balance sheet but belongs on a market-value balance sheet. For successful growth companies like Amazon, PVGO is far more valuable than assets in place. For mature companies like Con Ed, PVGO is relatively small and market value depends on assets in place. That is why Con Ed is an income stock.

The difference between the market and book values on the asset side of the balance sheet shows up in the market capitalization of the firm’s stock and in the market-to- book ratio. A market-to-book ratio greater than 1 means that (1) the assets shown on the firm’s books are undervalued, (2) there are intangible assets not shown on the books, and/or (3) there are valuable future investment opportunities.

7.6 There Are No Free Lunches on Wall Street We have explained how common stocks are valued. Does that mean that we have just given the game away and told you how to make an instant fortune on the stock market? We are sorry to disappoint you. It is not so easy to beat the market, and even highly paid pros find it very difficult to do so with any consistency.

market-value balance sheet Balance sheet showing market rather than book values of assets, liabilities, and stockholders’ equity.

Assets Liabilities and Shareholders’ Equity

Current assets Current liabilities

Assets in place Debt and other long-term liabilities Plant, equipment, and other tangible assets Intangible assets Shareholders’ equity Growth opportunities = PV of future investment opportunities (PVGO) Total value Total value

TABLE 7.5 A market-value balance sheet (all entries at current market, not book, values)

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216 Part Two Value

Why is it so difficult to beat the market consistently? Let’s look at two possible ways that you might attempt to do so.

Method 1: Technical Analysis Some investors try to achieve superior returns by spotting and exploiting patterns in stock prices. These investors are known as technical analysts.

Technical analysis sounds plausible. For example, you might hope to beat the mar- ket by buying stocks when they are on their way up and by selling them on their way down. Unfortunately, it turns out that such simple rules don’t work. A large price rise in one period may be followed by a further rise in the next period, but it is just as likely to be followed by a fall.

Look, for example, at Figure 7.6a. The horizontal axis shows the return on the New York Composite Index in one week (5 business days), while the vertical axis shows the return in the following week. Each point in the chart represents a different week over a 40-year period. If a market rise one week tended to be followed by a rise the next week, the points in the chart would plot along an upward-sloping line. But you can see that there was no such tendency; the points are scattered randomly across the chart. Statisticians sometimes measure the relationship between these changes by the correlation coefficient. In our example, the correlation between the market movements in successive weeks is -.022, in other words, effectively zero. Figure 7.6b shows a similar plot for monthly (20-business-day) moves. Again you can see that this month’s change in the index gives you almost no clue as to the likely change next month. The correlation between successive monthly changes is -.004.

Financial economists and statisticians who have studied stock price movements have concluded that you won’t get rich looking for consistent patterns in price changes. This seems to be so regardless of whether you look at the market as a whole (as we did in Fig- ure 7.6) or at individual stocks. Prices appear to wander randomly. They are equally likely to offer a high or low return on any particular day, regardless of what has occurred on previous days. In other words, prices seem to follow a random walk.

If you are not sure what we mean by “random walk,” consider the following exam- ple: You are given $100 to play a game. At the end of each week a coin is tossed. If it comes up heads, you win 3% of your investment; if it is tails, you lose 2.5%.

technical analysts Investors who attempt to identify undervalued stocks by searching for patterns in past stock prices.

random walk Security prices change randomly, with no predictable trends or patterns.

FIGURE 7.6a Each dot shows the returns on the New York Composite Index on two successive weeks between September 1970 and September 2010. The circled dot shows a weekly return of +3.1%, followed by +5.2% in the next week. The scatter diagram shows no significant relationship between returns on successive weeks.

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Chapter 7 Valuing Stocks 217

This process is a random walk because successive changes in the value of your stake are independent and determined by the flip of a fair coin. That is, the odds of making money each week are the same, regardless of the value at the start of the week or the pattern of heads or tails in the previous weeks.

If a stock’s price follows a random walk, the odds of an increase or decrease during any day, month, or year do not depend at all on the stock’s previous price moves. The historical path of prices gives no useful information about the future—just as a long series of recorded heads and tails gives no information about the next toss.

If you find it difficult to believe that stock prices could behave like our coin-tossing game, then look at the two charts in Figure 7.7. One of these charts shows the outcome from playing our game for 5 years; the other shows the actual performance of the S&P 500 Index for a 5-year period. Can you tell which one is which?14

Does it surprise you that stocks seem to follow a random walk? If so, imagine that it were not the case and that changes in stock prices were expected to persist for sev- eral months. Figure 7.8 provides a hypothetical example of such a predictable cycle. You can see that an upswing in the market started when the index was 1,600 and is expected to carry the price to 1,800 next month. What will happen when investors per- ceive this bonanza? Since stocks are a bargain at their current level, investors will rush to buy and, in so doing, will push up prices. They will stop buying only when stocks are fairly priced. Thus, as soon as a cycle becomes apparent to investors, they immediately eliminate it by their trading.

14 The top chart in Figure 7.7 shows the real Standard & Poor’s Index for the years 1980 through 1984. The bot- tom chart was generated by a series of random numbers. You may be among the 50% of our readers who guess right, but we bet it was just a guess.

Therefore, your payoff at the end of the first week is either $103 or $97.50. At the end of the second week the coin is tossed again. Now the possible outcomes are as follows:

Heads $106.09 Heads $103.00 Tails $100.43

$100 Tails $97.50 Heads $100.43

Tails $95.06

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Stock prices can appear to have patterns

FIGURE 7.6b This scatter diagram shows that there is also no relationship between market returns in successive months.

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True or false: If stock prices follow a random walk,

a. Successive stock prices are not related. b. Successive stock price changes are not related. c. Stock prices fluctuate above and below a normal long-run price. d. The history of stock prices cannot be used to predict future returns to investors.

Self-Test7.8

218 Part Two Value

Don’t confuse randomness in price changes with irrationality in the level of prices. If a stock is fairly priced, it will move only if new information changes the market perception of its fair price. But new information, by definition, is unrelated to earlier information.

FIGURE 7.8 Cycles self- destruct as soon as they are recognized by investors. The stock price instantaneously jumps to the present value of the expected future price.

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FIGURE 7.7 One of these charts shows the Standard & Poor’s Index for a 5-year period. The other shows the results of playing our coin- toss game for 5 years. Can you tell which is which? (The answer is given in footnote 14.)

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Method 2: Fundamental Analysis You may not be able to earn superior returns just by studying past stock prices, but what about other types of information? After all, most investors don’t just look at

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Chapter 7 Valuing Stocks 219

past stock prices. Instead, they try to gauge a firm’s business prospects by studying the financial and trade press, the company’s financial accounts, the president’s annual statements, and other items of news. These investors are called fundamental analysts, in contrast to technical analysts who focus on past stock price movements.

Fundamental analysts are paid to uncover stocks for which price does not equal intrinsic value. If intrinsic value exceeds price, for example, the stock is a bargain and will offer a superior expected return. But what happens if there are many talented and competitive fundamental analysts? If one of them uncovers a stock that appears to be a bargain, it stands to reason that others will as well, and there will be a wave of buying that pushes up the price. In the end, their actions will eliminate the original bargain opportunity. To profit, your insights must be different from those of your competitors, and you must act faster than they can. This is a tall order.

To illustrate the challenge facing stock market analysts, look at Figure 7.9, which shows how stock prices react to one particular item of news—the announcement of a takeover. In most takeovers the acquiring company is willing to pay a hefty premium to induce the shareholders of the target company to give up their shares. You can see from Figure 7.9 that the stock price of the target company typically jumps up on the day that the public becomes aware of a takeover attempt (day 0 in the graph). How- ever, this adjustment in the stock price is immediate; thereafter there is no further drift in the stock price, either upward or downward. By the time the acquisition has been made public, it is too late to buy.

Researchers have looked at the stock price reaction to many other types of news, such as earnings and dividend announcements and plans to issue additional stock or repurchase existing stock. All this information seems to be rapidly and accurately reflected in the price of the stock, so it is impossible to make superior returns by buy- ing or selling after the announcement.

A Theory to Fit the Facts Economists often refer to the stock market as an efficient market. By this they mean that the competition to find misvalued stocks is intense. So when new information comes out, investors rush to take advantage of it and thereby elimi- nate any profit opportunities. Professional investors express the same idea when they say that there are no free lunches on Wall Street.

It is useful to distinguish three types of information and three degrees of efficiency. The term weak-form efficiency describes a market in which prices already reflect all

fundamental analysts Investors who attempt to find mispriced securities by analyzing fundamental information, such as accounting performance and earnings prospects.

efficient market Market in which prices reflect all available information.

FIGURE 7.9 The performance of the stocks of target companies compared with that of the market. The prices of target stocks jump up on the announcement day, but from then on there are no unusual price movements. The announcement of the takeover attempt seems to be fully reflected in the stock price on the announcement day.

Source: Updated version of fi gure appearing in A. Keown and J. Pinkerton, “Merger Announcements and Insider Trading Activity,” Journal of Finance 36 (September 1981), pp. 855–869. We are grateful to Jinghua Yan for updating the calculations to the period 1979–2004.

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220 Part Two Value

the information contained in past prices. In such a market, share price changes are random, and technical analysis that searches for patterns in past returns is valueless. Figure 7.6, which looked at successive weekly and monthly changes in the market index, is evidence in favor of weak-form efficiency.

Semistrong-form efficiency describes a market in which prices reflect not just the information contained in past prices but all publicly available information. In such a market it is impossible (or exceptionally difficult) to earn consistently superior returns simply by reading the financial press, studying the company’s financial statements, and so on. Figure 7.9, which looked at the market reaction to merger announcements, was just one piece of evidence in favor of semistrong efficiency. As soon as informa- tion about the mergers became public, the stock prices jumped.

Finally, strong-form efficiency refers to a market where prices impound all available information. In such a market no investor, however hardworking, could expect to earn superior profits.

In fact, it appears that even professional investors, such as managers of mutual funds, do find it difficult to outperform the broad market consistently. Look, for exam- ple, at Figure 7.10, which shows the average performance of equity mutual funds over three decades. You can see that in some years these mutual funds did beat the market, but more often than not (in fact, in 26 of the 42 years since 1970) it was the other way around. Of course, it would be surprising if some of the managers were not smarter than others and were able to earn superior returns. But it seems hard to spot the smart ones, and the top-performing managers one year have about an average chance of fall- ing on their face the next year.

Example 7.6 Performance of Money Managers Forbes, a widely read investment magazine, publishes annually an “honor roll” of the most consistently successful mutual funds. Suppose that every year starting in 1975, you invested an equal sum in each of these successful funds when Forbes announced its honor roll. You would have outperformed the market in only 5 of the following 16 years, and your average annual return would have been more than 1% below the return on the market.15

15 See B. G. Malkiel, “Returns from Investing in Equity Mutual Funds 1971 to 1991,” Journal of Finance 50 (June 1995), pp. 549–572.

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Do mutual funds beat the market?

FIGURE 7.10 Annual returns on the Wilshire 5000 Market Index and equity mutual funds, 1971–2012. The market index provided a higher return than the average mutual fund in 26 of the 42 years.

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Technical analysts and fundamental analysts all try to earn superior returns in the stock market. Explain how their efforts help keep the market efficient.

Self-Test7.9

Chapter 7 Valuing Stocks 221

As this kind of discouraging evidence has accumulated, many investors have given up the search for superior investment returns. Instead, they simply buy and hold index funds or exchange-traded portfolios (ETFs) that track the entire stock market. We dis- cussed index funds and ETFs in Chapter 2. Recall that they provide maximum diver- sification, with very low management fees. Why pay higher fees to managers who attempt to “beat the market” but can’t do so consistently? Corporate pension funds now invest over one-quarter of their U.S. equity holdings in index funds.

7.7 Market Anomalies and Behavioral Finance

Market Anomalies Almost without exception, early researchers concluded that the efficient-market hypothesis was a remarkably good description of reality. But eventually, cracks in its armor began to appear, and soon the finance journals were packed with evidence of anomalies, or seeming profit opportunities, that investors have apparently failed to exploit. We will look at a couple of examples.

The Earnings Announcement Puzzle In an efficient stock market, a company’s stock price should react instantly at the announcement of unexpectedly good or bad earnings. But, in fact, stocks with the best earnings news typically outperform the stocks with the worst earnings news even after the news is made public. Figure 7.11 shows stock performance following the announcement of unexpectedly good or bad earnings during the years 1972 to 2001. The 10% of the stocks of firms with the best earnings news outperform those with the worst news by about 1% per month over the 6-month period following the announcement. It seems that investors underreact to the earnings announcement and become aware of the full significance only as further information arrives.

FIGURE 7.11 Average stock returns over the 6 months following announcements of quarterly earnings. The 10% of stocks with the best earnings news (portfolio 10) outperformed those with the worst news (portfolio 1) by about 1% per month.

Source: T. Chordia and L. Shivakumar, “Infl ation Illusion and the Post-earnings Announcement Drift,” Journal of Accounting Research 43 (2005), pp. 521–556.

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222 Part Two Value

The New-Issue Puzzle When firms issue stock to the public, investors typi- cally rush to buy. On average, those lucky enough to be awarded stock receive an immediate capital gain. However, researchers have found that these early gains often turn into losses. For example, suppose that you bought stock immediately following each initial public offering and then held that stock for 5 years. Over the period 1970 to 2008 your average annual return would have been 3.5% less than the return on a portfolio of similar-size stocks.16

The jury is still out on these studies of longer-term anomalies. We can’t be sure whether they are important exceptions to the efficient-market theory or a coincidence that stems from the efforts of many researchers to find interesting patterns in the data. There may also be other explanations. Take, for example, the new-issue puzzle. Most new issues during the past 30 years have involved growth stocks with high market values and limited book assets. Perhaps the stocks performed badly not because they had just been issued but because all growth stocks happened to perform badly during this period. Of course, if that is true, we need to address another question: Why have growth stocks performed poorly over such a long period of time? We will come back to this question in Chapter 12.

Bubbles and Market Efficiency Market anomalies, such as the earnings announcement puzzle, suggest that prices of individual stocks may occasionally get out of line. But are there also cases in which prices as a whole can no longer be justified? In the last few decades, we have wit- nessed several examples of apparent stock market bubbles when prices rose to levels hard to reconcile with reasonable outlooks for dividends and earnings.

Between 1985 and 1989, for example, the Japanese Nikkei index roughly quadru- pled. But in 1990, interest rates rose and stock prices started to fall. By October the Nikkei had sunk to about half its peak, and by March 2009 it was down 80% from its peak value 19 years earlier.

The boom in Japanese stock prices was matched by an even greater explosion in land prices. For example, Ziemba and Schwartz document that the few hundred acres of land under the Emperor’s Palace in Tokyo, evaluated at neighborhood land prices, was worth as much as all the land in Canada or California.17 But then the real estate bubble also burst. By 2005 land prices in the six major Japanese cities had slumped to just 13% of their peak.

The dot-com bubble in the United States was almost as dramatic. The technology- heavy NASDAQ stock index rose 580% from the start of 1995 to its eventual high in March 2000. But then, as rapidly as it began, the boom ended, and by October 2002 the index had fallen 78% from its peak.

Looking back at these episodes, it seems difficult to believe that expected future cash flows could ever have been sufficient to justify the initial price run-ups. If that is the case, we have two important exceptions to the theory of efficient markets.

But beware of jumping to the conclusion that prices are always arbitrary and capri- cious. First, most bubbles become obvious only after they have burst. At the time, there often seems to be a plausible explanation for the price run-up. In the dot-com boom, for example, many contemporary observers rationalized stock price gains as justified by the prospect of a new and more profitable economy, driven by technologi- cal advances.

16 An excellent resource for data and analysis of initial public offerings is Professor Jay Ritter’s web page, bear. cba.ufl.edu/ritter. 17 See W. T. Ziemba and S. L. Schwartz, Invest Japan (Chicago: Probus Publishing, 1992), p. 109.

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Chapter 7 Valuing Stocks 223

Here’s another conclusion not to jump to: Don’t assume that anyone can know intrinsic value with confidence. Security valuation is intrinsically difficult and impre- cise. Consider this example: Suppose that in mid-2013 you wanted to check whether the stocks forming the S&P 500 were fairly priced. As a first stab, you might have used the constant-growth dividend discount model. In 2013, the annual dividends of the 500 companies in the index came to roughly $290 billion. Suppose investors expected these dividends to grow at a steady rate of 4.0% and that they required a rate of return of 6.3%. Then the value of the stocks in the index would have been

PV = $290 billion

.063 - .04 = $12,608 billion

which was roughly their value in mid-2013. But what if the dividend growth rate was only 3.5%? Then the value of the stocks would decline to

PV = $290 billion

.063 - .035 = $10,357 billion

In other words, a reduction of just half a percentage point in the expected rate of divi- dend growth would reduce the value of common stocks by about 18%. Given this sen- sitivity of value to assumed growth rates, it is easy for investors to justify price run-ups when they are feeling optimistic about the future, and it is hard to identify bubbles— except of course in retrospect, at which point all bubbles seem to have been obvious.

Behavioral Finance Why might prices depart from fundamental values? Some scholars believe that the answer to this question lies in behavioral psychology. People are not 100% rational 100% of the time. This shows up in three broad areas—their attitudes to risk, the way that they assess probabilities, and their sentiment about the economy:

1. Attitudes toward risk. Psychologists have observed that, when making risky decisions, people are particularly loath to incur losses, even if those losses are small. Losers are liable to regret their actions and kick themselves for having been so foolish. To avoid this unpleasant possibility, individuals will tend to shun those actions that may result in loss.

The pain of a loss seems to depend on whether it comes on the heels of earlier losses. Once investors have suffered a loss, they may be even more cautious not to risk a further loss. Conversely, just as gamblers are known to be more willing to take large bets when they are ahead, so investors may be more prepared to run the risk of a stock market dip after they have experienced a period of substantial gains. If they do then suffer a small loss, they at least have the consolation of being up on the year.

You can see how this sort of behavior could lead to a stock price bubble. For example, early investors in the technology firms that boomed during the dot-com bubble were big winners. They may have stopped worrying about the risk of loss. They may have thrown caution to the winds and piled even more investment into these companies, driving stock prices far above fundamental values. The day of reckoning came when investors woke up and realized how far above fundamental value prices had soared.

2. Beliefs about probabilities. Most investors do not have a Ph.D. in probability theory and may make common errors in assessing the probability of uncertain outcomes. Psychologists have found that, when judging the possible future outcomes, individuals commonly look back to what has happened in recent periods and then

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224 Part Two Value

assume that this is representative of what may occur in the future. The temptation is to project recent experience into the future and to forget the lessons learned from the more distant past. For example, an investor who places too much weight on recent events may judge that glamorous growth companies are very likely to continue to grow rapidly, even though very high rates of growth cannot persist indefinitely.

A second common bias is overconfidence. Most of us believe that we are better- than-average drivers, and most investors think that they are better-than-average stockpickers.18 We know that two speculators who trade with one another cannot both make money from the deal; for every winner there must be a loser. But presumably investors are prepared to continue trading because each is confident that it is the other one who is the patsy.

You can see how such behavior may have reinforced the dot-com boom. As the bull market developed, it generated increased optimism about the future and stimulated demand for shares. The more that investors racked up profits on their stocks, the more confident they became in their views and the more willing they became to bear the risk that the next month might not be so good.

3. Sentiment. Efficient markets bring to mind absolutely rational investors on the lookout for every possible profit opportunity. But real investors are people, and they are subject to emotion. Sentiment may be interpreted as their general level of optimism or pessimism about the economy. If the sentiment of large groups of investors varies in tandem, it potentially could have a noticeable impact on security pricing. For example, one study concludes that patterns of discounts and premiums on closed-end funds seem to be driven by changes in investor sentiment.19 Discounts on various funds move together and are correlated with the return on small stocks, suggesting that all are affected by common variation in sentiment.

Sentiment is offered as another reason that stock market bubbles might develop. An improvement in sentiment can lead to an increase in stock prices. That increase can feed on itself, with investors extrapolating recent performance into the future and deciding that it is a good time to buy, thus pushing prices up even further.

Now it is not difficult to believe that your uncle Harry or aunt Hetty may become caught up in a scatty whirl of irrational exuberance,20 but why don’t hardheaded professional investors bail out of the overpriced stocks and force their prices down to fair value? Perhaps they feel that it is too difficult to predict when the boom will end and that their jobs will be at risk if they move aggressively into cash when others are raking up profits. In this case, sales of stock by the pros are simply not large enough to stem the tide of optimism sweeping the market.

It is too early to say how far behavioral finance scholars can help to sort out some of the puzzles and explain events like the dot-com boom. One thing, however, seems clear: It is relatively easy for statisticians to spot anomalies with the benefit of hindsight and for psychologists to provide an explanation for them. It is much more difficult for investment managers who are at the sharp end to spot and invest in mispriced securities. And that is the basic message of the efficient- market theory.

18 The term “irrational exuberance” was coined by Alan Greenspan, former chairman of the Federal Reserve Board, to describe the dot-com boom. It was also the title of a book by Robert Shiller that examined the boom. See R. Shiller, Irrational Exuberance (New York City: Broadway Books, 2001). 19 C. M. Lee, A. Shleifer, and R. H. Thaler, “Investor Sentiment and the Closed-End Fund Puzzle,” Journal of Finance 46 (March 1991), pp. 75–109. Closed-end funds are portfolios of stocks or other securities that can be bought or sold like individual shares. The difference between the price of the fund and the value of its underly- ing securities is taken as a proxy for investor sentiment about the economy. 20 One survey of British prison inmates even found that a majority believed that they were more honest and more law-abiding than average.

BEYOND THE PAGE

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Overconfident CFOs

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SUMMARY Large companies usually arrange for their stocks to be traded on a stock exchange. The stock listings report the stock’s price, price change, volume, dividend yield, and price- earnings (P/E) ratio.

Stockholders generally expect to receive (1) cash dividends and (2) capital gains or losses. The rate of return that they expect over the next year is defined as the expected dividend per share DIV1 plus the expected increase in price P1 - P0, all divided by the price at the start of the year P0.

Unlike the fixed interest payments that the firm promises to bondholders, the dividends that are paid to stockholders depend on the fortunes of the firm. That’s why a company’s common stock is riskier than its debt. The return that investors expect on any one stock is also the return that they demand on all stocks subject to the same degree of risk.

The present value of a share is equal to the stream of expected dividends per share up to some horizon date plus the expected price at this date, all discounted at the return that investors require. If the horizon date is far away, we simply say that stock price equals the present value of all future dividends per share. This is the dividend discount model.

If dividends are expected to grow forever at a constant rate g, then the expected return on the stock is equal to the dividend yield (DIV1/P0) plus the expected rate of dividend growth. The value of the stock according to this constant-growth dividend discount model is P0 = DIV1/(r - g).

You can think of a share’s value as the sum of two parts—the value of the assets in place and the present value of growth opportunities, that is, of future opportunities for the firm to invest in high-return projects. The price-earnings (P/E) ratio reflects the market’s assess- ment of the firm’s growth opportunities.

Competition between investors will tend to produce an efficient market—that is, a mar- ket in which prices rapidly reflect new information and investors have difficulty making consistently superior returns. Of course, we all hope to beat the market, but if the market is efficient, all we can rationally expect is a return that is sufficient on average to compensate for the time value of money and for the risks we bear.

The efficient-market theory comes in three flavors. The weak form states that prices reflect all the information contained in the past series of stock prices. In this case it is impossible to earn superior profits simply by looking for past patterns in stock prices. The semistrong form of the theory states that prices reflect all published information, so it is impossible to make consistently superior returns just by reading the newspaper, look- ing at the company’s annual accounts, and so on. The strong form states that stock prices effectively impound all available information. This form tells us that private information is hard to come by, because in pursuing it you are in competition with thousands—perhaps millions—of active and intelligent investors. The best you can do in this case is to assume that securities are fairly priced.

The evidence for market efficiency is voluminous, and there is little doubt that skilled professional investors find it difficult to win consistently. Nevertheless, there remain some puzzling instances where markets do not seem to be efficient. Some financial economists attribute these apparent anomalies to behavioral foibles.

What information is included in stock trading reports? (LO7-1)

How can one calculate the present value of a stock given forecasts of future dividends and future stock price? (LO7-2)

How can stock valuation formulas be used to infer the expected rate of return on a common stock? (LO7-3)

How should investors interpret price-earnings ratios? (LO7-4)

How does competition among investors lead to efficient markets? (LO7-5)

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226 Part Two Value

L I S T I N G O F E Q UAT I O N S

7.1 V0 = DIV1 + P1

1 + r

7.2 P0 = DIV1 1 + r

+

DIV2 (1 + r)2

+ c

+

DIVH + PH (1 + r)H

7.3 P0 = DIV1 r - g

7.4 g = sustainable growth rate = return on equity × plowback ratio

7.5 r = DIV1

P0 + g = dividend yield + growth rate

QUESTIONS AND PROBLEMS 1. Dividend Yield. Favored stock will pay a dividend this year of $2.40 per share. Its dividend

yield is 8%. At what price is the stock selling? (LO7-1)

2. Dividend Yield. BMM Industries pays a dividend of $2 per quarter. The dividend yield on its stock is reported at 4.8%. What price is the stock selling at? (LO7-1)

3. Market-Value Balance Sheets. Construct a market-value balance sheet for FedEx, using the information in Table 7.1 and stock prices reported in Sections 7.1 and 7.2. Assume that market and book values are equal for current assets, current liabilities, and debt and other long-term liabilities. How much extra value shows up on the asset side of the balance sheet? (LO7-1)

4. Preferred Stock. Preferred Products has issued preferred stock with an $8 annual dividend that will be paid in perpetuity. (LO7-2)

a. If the discount rate is 12%, at what price should the preferred sell? b. At what price should the stock sell 1 year from now? c. What are the dividend yield, the capital gains yield, and the expected rate of return of the

stock?

5. Dividend Discount Model. Amazon.com has never paid a dividend, but in July 2013 the market value of its stock was $139 billion. Does this invalidate the dividend discount model? (LO7-2)

6. Dividend Discount Model. How can we say that price equals the present value of all future dividends when many actual investors may be seeking capital gains and planning to hold their shares for only a year or two? Explain. (LO7-2)

7. Rate of Return. Steady As She Goes Inc. will pay a year-end dividend of $3 per share. Inves- tors expect the dividend to grow at a rate of 4% indefinitely. (LO7-2 and LO7-3)

a. If the stock currently sells for $30 per share, what is the expected rate of return on the stock? b. If the expected rate of return on the stock is 16.5%, what is the stock price?

8. Stock Values. Integrated Potato Chips paid a $1 per share dividend yesterday. You expect the dividend to grow steadily at a rate of 4% per year. (LO7-2)

a. What is the expected dividend in each of the next 3 years? b. If the discount rate for the stock is 12%, at what price will the stock sell? c. What is the expected stock price 3 years from now? d. If you buy the stock and plan to hold it for 3 years, what payments will you receive? What is

the present value of those payments? Compare your answer to (b).

9. Growth Opportunities. Stormy Weather has no attractive investment opportunities. Its return on equity equals the discount rate, which is 10%. Its expected earnings this year are $4 per share. Find the stock price, P/E ratio, and growth rate of dividends for the following plowback ratios: (LO7-2)

a. Zero b. .40 c. .80

finance

®

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10. Growth Opportunities. Trend-Line Inc. has been growing at a rate of 6% per year  and is expected to continue to do so indefinitely. The next dividend is expected to be $5 per share. (LO7-2)

a. If the market expects a 10% rate of return on Trend-Line, at what price must it be selling? b. If Trend-Line’s earnings per share will be $8, what part of Trend-Line’s value is due to assets

in place, and what part to growth opportunities?

11. Constant-Growth Model. Arts and Crafts Inc. will pay a dividend of $5 per share in 1 year. It sells at $50 a share, and firms in the same industry provide an expected rate of return of 14%. What must be the expected growth rate of the company’s dividends? (LO7-2)

12. Constant-Growth Model. Waterworks has a dividend yield of 8%. If its dividend is expected to grow at a constant rate of 5%, what must be the expected rate of return on the company’s stock? (LO7-3)

13. Constant-Growth Model. A stock sells for $40. The next dividend will be $4 per share. If the rate of return earned on reinvested funds is a constant 15% and the company reinvests 40% of earnings in the firm, what must be the discount rate? (LO7-3)

14. Constant-Growth Model. Gentleman Gym just paid its annual dividend of $3 per share, and it is widely expected that the dividend will increase by 5% per year indefinitely. (LO7-3)

a. What price should the stock sell at? The discount rate is 15%. b. How would your answer change if the discount rate were only 12%? Why does the answer

change?

15. Constant-Growth Model. Eastern Electric currently pays a dividend of about $1.64 per share and sells for $27 a share. (LO7-3)

a. If investors believe the growth rate of dividends is 3% per year, what rate of return do they expect to earn on the stock?

b. If investors’ required rate of return is 10%, what must be the growth rate they expect of the firm?

c. If the sustainable growth rate is 5% and the plowback ratio is .4, what must be the rate of return earned by the firm on its new investments?

16. Constant-Growth Model. You believe that the Non-stick Gum Factory will pay a dividend of $2 on its common stock next year. Thereafter, you expect dividends to grow at a rate of 6% a year in perpetuity. If you require a return of 12% on your investment, how much should you be prepared to pay for the stock? (LO7-2)

17. Negative Growth. Horse and Buggy Inc. is in a declining industry. Sales, earnings, and divi- dends are all shrinking at a rate of 10% per year. (LO7-2)

a. If r = 15% and DIV1 = $3, what is the value of a share? b. What price do you forecast for the stock next year? c. What is the expected rate of return on the stock? d. Can you distinguish between “bad stocks” and “bad companies”? Does the fact that the

industry is declining mean that the stock is a bad buy?

18. Constant-Growth Model. Metatrend’s stock will generate earnings of $6 per share this year. The discount rate for the stock is 15%, and the rate of return on reinvested earnings also is 15%. (LO7-2)

a. Find both the growth rate of dividends and the price of the stock if the company reinvests the following fraction of its earnings in the firm: (i) 0%; (ii) 40%; (iii) 60%.

b. Redo part (a) now assuming that the rate of return on reinvested earnings is 20%. What is the present value of growth opportunities for each reinvestment rate?

c. Considering your answers to parts (a) and (b), can you briefly state the difference between companies experiencing growth and companies with growth opportunities?

19. Nonconstant Growth. You expect a share of stock to pay dividends of $1.00, $1.25, and $1.50 in each of the next 3 years. You believe the stock will sell for $20 at the end of the third year. (LO7-2)

a. What is the stock price if the discount rate for the stock is 10%? b. What is the dividend yield?

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228 Part Two Value

20. Constant-Growth Model. Here are data on two stocks, both of which have discount rates of 15%: (LO7-2)

a. What are the dividend payout ratios for each firm? b. What are the expected dividend growth rates for each firm? c. What is the proper stock price for each firm?

21. Dividend Growth. Grandiose Growth has a dividend growth rate of 20%. The discount rate is 10%. The end-of-year dividend will be $2 per share. (LO7-2)

a. What is the present value of the dividend to be paid in year 1? Year 2? Year 3? b. Could anyone rationally expect this growth rate to continue indefinitely?

22. Stock Valuation. Start-Up Industries is a new firm that has raised $200 million by selling shares of stock. Management plans to earn a 24% rate of return on equity, which is more than the 15% rate of return available on comparable-risk investments. Half of all earnings will be reinvested in the firm. (LO7-2)

a. What will be Start-Up’s ratio of market value to book value? b. How would that ratio change if the firm can earn only a 10% rate of return on its investments?

23. Nonconstant Growth. Planned Obsolescence has a product that will be in vogue for 3 years, at which point the firm will close up shop and liquidate the assets. As a result, forecast dividends are DIV1 = $2, DIV2 = $2.50, and DIV3 = $18. What is the stock price if the discount rate is 12%? (LO7-2)

24. Nonconstant Growth. Tattletale News Corp. has been growing at a rate of 20% per year, and you expect this growth rate in earnings and dividends to continue for another 3 years. (LO7-2)

a. If the last dividend paid was $2, what will the next dividend be? b. If the discount rate is 15% and the steady growth rate after 3 years is 4%, what should the

stock price be today?

25. Nonconstant Growth. Reconsider Tattletale News from the previous problem. (LO7-2 and LO7-3)

a. What is your prediction for the stock price in 1 year? b. Show that the expected rate of return equals the discount rate.

26. Constant-Growth Model. Fincorp will pay a year-end dividend of $2.40 per share, which is expected to grow at a 4% rate for the indefinite future. The discount rate is 12%. (LO7-2)

a. What is the stock selling for? b. If earnings are $3.10 a share, what is the implied value of the firm’s growth opportunities?

27. P/E Ratios. No-Growth Industries pays out all of its earnings as dividends. It will pay its next $4 per share dividend in a year. The discount rate is 12%. (LO7-4)

a. What is the price-earnings ratio of the company? b. What would the P/E ratio be if the discount rate were 10%?

28. P/E Ratios. Castles in the Sand generates a rate of return of 20% on its investments and main- tains a plowback ratio of .30. Its earnings this year will be $4 per share. Investors expect a 12% rate of return on the stock. (LO7-2 and LO7-4)

a. Find the price and P/E ratio of the firm. b. What happens to the P/E ratio if the plowback ratio is reduced to .20? Why? c. Show that if plowback equals zero, the earnings-price ratio, E/P, falls to the expected rate of

return on the stock.

Stock A Stock B

Return on equity 15% 10% Earnings per share $2.00 $1.50 Dividends per share $1.00 $1.00

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29. P/E Ratios. Web Cites Research projects a rate of return of 20% on new projects. Management plans to plow back 30% of all earnings into the firm. Earnings this year will be $3 per share, and investors expect a 12% rate of return on stocks facing the same risks as Web Cites. (LO7-4)

a. What is the sustainable growth rate? b. What is the stock price? c. What is the present value of growth opportunities? d. What is the P/E ratio? e. What would the price and P/E ratio be if the firm paid out all earnings as dividends? f. What do you conclude about the relationship between growth opportunities and P/E ratios?

30. Forms of Efficient Markets. Fill in the missing words from the following list: fundamental, semistrong, strong, technical, weak. (LO7-5)

There are three forms of the efficient-market theory. Tests that have found there are no patterns in share price changes provide evidence for the _____ form of the theory. Evidence for the _____ form of the theory is provided by tests that look at how rapidly markets respond to new public information, and evidence for the _____ form of the theory is provided by tests that look at the performance of professionally managed portfolios. Market efficiency results from compe- tition between investors. Many investors search for information about the company’s business that would help them to value the stock more accurately. This is known as _____ analysis. Such research helps to ensure that prices reflect all available information. Other investors study past stock prices for recurrent patterns that would allow them to make superior profits. This is known as _____ analysis. Such research helps to eliminate any patterns.

31. Information and Efficient Markets. “It’s competition for information that makes securities markets efficient.” Is this statement correct? Explain. (LO7-5)

32. Behavioral Finance. Some finance scholars cite well-documented behavioral biases to explain apparent cases of market inefficiency. Describe two of these biases. (LO7-5)

33. Interpreting the Efficient-Market Theory. How would you respond to the following comments? (LO7-5)

a. “Efficient market, my eye! I know lots of investors who do crazy things.” b. “Efficient market? Balderdash! I know at least a dozen people who have made a bundle in

the stock market.” c. “The trouble with the efficient-market theory is that it ignores investors’ psychology.”

34. Real versus Financial Investments. Why do investments in financial markets almost always have zero NPVs, whereas firms can find many investments in their product markets with posi- tive NPVs? (LO7-5)

35. Investment Performance. It seems that every month we read an article in The Wall Street Jour- nal about a stockpicker with a marvelous track record. Do these examples mean that financial markets are not efficient? (LO7-5)

36. Implications of Efficient Markets. The president of Good Fortunes Inc. states at a press con- ference that the company has a 30-year history of ever-increasing dividend payments. Good Fortunes is widely regarded as one of the best-run firms in its industry. Does this make the firm’s stock a good buy? Explain. (LO7-5)

37. Implications of Efficient Markets. “Long-term interest rates are at record highs. Most com- panies, therefore, find it cheaper to finance with common stock or relatively inexpensive short- term bank loans.” Discuss. (LO7-5)

38. Expectations and Efficient Markets. Geothermal Corp. just announced good news: Its earn- ings have increased by 20%. Most investors had anticipated an increase of 25%. Will Geother- mal’s stock price increase or decrease when the announcement is made? (LO7-5)

39. Behavioral Finance. In Section 7.6 we gave two examples of market anomalies (the earnings announcement puzzle and the new-issue puzzle). Do you think that behavioral finance can help to explain these anomalies? (LO7-5)

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CHALLENGE PROBLEMS 40. Sustainable Growth. Computer Corp. reinvests 60% of its earnings in the firm. The stock sells

for $50, and the next dividend will be $2.50 per share. The discount rate is 15%. What is the rate of return on the company’s reinvested funds? (LO7-2)

41. Nonconstant Growth. A company will pay a $2 per share dividend in 1 year. The dividend in 2 years will be $4 per share, and it is expected that dividends will grow at 5% per year there- after. The expected rate of return on the stock is 12%. (LO7-2)

a. What is the current price of the stock? b. What is the expected price of the stock in a year? c. Show that the expected return, 12%, equals dividend yield plus capital appreciation.

42. Nonconstant Growth. Phoenix Industries has pulled off a miraculous recovery. Four years ago it was near bankruptcy. Today, it announced a $1 per share dividend to be paid a year from now, the first dividend since the crisis. Analysts expect dividends to increase by $1 a year for another 2 years. After the third year (in which dividends are $3 per share) dividend growth is expected to settle down to a more moderate long-term growth rate of 6%. If the firm’s investors expect to earn a return of 14% on this stock, what must be its price? (LO7-2)

43. Nonconstant Growth. Compost Science Inc. (CSI) is in the business of converting Boston’s sewage sludge into fertilizer. The business is not in itself very profitable. However, to induce CSI to remain in business, the Metropolitan District Commission (MDC) has agreed to pay whatever amount is necessary to yield CSI a 10% return on investment. At the end of the year, CSI is expected to pay a $4 dividend. It has been reinvesting 40% of earnings and growing at 4% a year. (LO7-2)

a. Suppose CSI continues on this growth trend. What is the expected rate of return for an inves- tor who purchases the stock at the market price of $100?

b. What part of the $100 price is attributable to the present value of growth opportunities? c. Now the MDC announces a plan for CSI to also treat Cambridge sewage. CSI’s plant will

therefore be expanded gradually over 5 years. This means that CSI will have to reinvest 80% of its earnings for 5 years. Starting in year 6, however, it will again be able to pay out 60% of earnings. What will be CSI’s stock price once this announcement is made and its conse- quences for CSI are known?

44. Nonconstant Growth. Better Mousetraps has come out with an improved product, and the world is beating a path to its door. As a result, the firm projects growth of 20% per year for 4 years. By then, other firms will have copycat technology, competition will drive down profit margins, and the sustainable growth rate will fall to 5%. The most recent annual dividend was DIV0 = $1 per share. (LO7-2)

a. What are the expected values of DIV1, DIV2, DIV3, and DIV4? b. What is the expected stock price 4 years from now? The discount rate is 10%. c. What is the stock price today? d. Find the dividend yield, DIV1/P0. e. What will next year’s stock price, P1, be? f. What is the expected rate of return to an investor who buys the stock now and sells it in

1 year?

45. Nonconstant Growth. (LO7-2)

a. Return to the previous problem, and compute the value of Better Mousetraps for assumed sustainable growth rates of 6% through 9%, in increments of .5%.

b. Compute the percentage change in the value of the firm for each 1-percentage-point increase in the assumed final growth rate, g.

c. What happens to the sensitivity of intrinsic value to changes in g? What do you conclude about the reliability of the dividend growth model when the assumed sustainable growth rate begins to approach the discount rate?

46. Yield Curve and Efficient Markets. If the yield curve is downward-sloping, meaning that long-term interest rates are lower than short-term interest rates, what might investors believe about future short-term interest rates? (LO7-5)

Templates can be found in Connect.

Templates can be found in Connect.

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WEB EXERCISES 1. Review Table 7.2, which lists the market values of several firms. Update the table. Which com-

pany’s value has changed by the greatest percentage since 2013, when the table was created? (Hint: Look for the price per share and the number of shares outstanding. The product of the two is total market capitalization.) Now calculate book value per share. Have the book values for any firm changed? Which seems to be more stable, book or market value? Why?

2. From finance.yahoo.com, obtain the price-earnings ratios of Adobe Systems (ADBE) and American Electric Power (AEP). Which of these two firms seems to be more of a “growth stock”? Now obtain a forecast of each firm’s expected earnings per share in the coming year. You can find earnings forecasts on yahoo.com under “Analysts Estimates.” What is the pres- ent value of growth opportunities for each firm as a fraction of the stock price? (Assume, for simplicity, that the required rate of return on the stocks is r = 8%.) Are the relative values you obtain for PVGO consistent with the P/E ratios?

SOLUTIONS TO SELF-TEST QUESTIONS 7.1 Expected industry profitability has fallen. Thus the value of future investment opportunities

has fallen relative to the value of assets in place. This happens in all growth industries sooner or later, as competition increases and profitable new investment opportunities shrink.

7.2 P0 = DIV1 + P1

1 + r =

$5 + $105

1.10 = $100

7.3 Since dividends and share price grow at 5%,

DIV2 = $5 × 1.05 = $5.25, DIV3 = $5 × 1.052 = $5.51

P3 = $100 × 1.053 = $115.76

P0 = DIV1 1 + r

+

DIV2 (1 + r)2

+

DIV3 + P3 (1 + r)3

= $5.00

1.10 +

$5.25 (1.10)2

+

$5.51 + $115.76 (1.10)3

= $100

7.4 P0 = DIV

r =

$25

.20 = $125

7.5 The two firms have equal risk, so we can use the data for Androscoggin to find the expected return on either stock:

r = DIV1

P0 + g =

$5

$100 + .05 = .10, or 10%

7.6 The present value of dividends in years 1 to 5 is still $14.07. However, with a lower terminal growth rate after year 5, the stock price in year 5 will be lower. If we assume a 4% growth rate, then the forecast dividend in year 6 is

DIV6 = 1.04 × DIV5 = 1.04 × 4.27 = $4.441

and the expected price at the end of year 5 is

P5 = DIV6 r - g

= $4.441

.085 - .04 = $98.69

Therefore, present value is

P0 = PV(dividends years 1–5) + PV(price in year 5)

= $14.07 + $98.69

1.0855 = $79.70

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232 Part Two Value

7.7 a. The sustainable growth rate is

g = return on equity × plowback ratio

= .05 × .35 = .0175, or 1.75% b. First value the company. At a 65% payout ratio, DIV1  =  $.84 as before. Using the

constant-growth model,

P0 = $.84

.066 - .0175 = $17.32

which is $2.20 per share less than the company’s no-growth value of $19.52. In this exam- ple Aqua America would be throwing away $2.20 of potential value by investing in proj- ects with unattractive rates of return.

c. Sure. A raider could take over the company and generate a profit of $2.20 per share just by halting all investments offering less than the 6.6% rate of return demanded by investors. This assumes the raider could buy the shares for $17.32.

7.8 a. False. The levels of successive stock prices are related. If a stock is selling for $100 per share today, the best guess of its price tomorrow is $100.

b. True. Changes in stock prices are unrelated. Whether a stock price increases or decreases today has no bearing on whether it will do so tomorrow.

c. False. There is no such thing as a “normal” price. If there were, you could make easy prof- its by buying shares selling below their normal prices (which would tend to be rising back toward those normal levels) and selling shares currently selling above their normal prices. Under a random walk, prices are equally likely to rise or fall.

d. True. Under a random walk, prices are equally likely to over- or underperform regardless of their past history.

7.9 Fundamental analysts ensure that stock prices reflect all publicly available information about the underlying value of the firm. If share prices deviate from their fundamental values, such analysts will generate buying or selling pressure that will return prices to their proper levels. Similarly, technical analysts ensure that if there is useful information in stock price history, it will be reflected in current share prices.

MINICASE Terence Breezeway, the CEO of Prairie Home Stores, wondered what retirement would be like. It was almost 20 years to the day since his uncle Jacob Breezeway, Prairie Home’s founder, had asked him to take responsibility for managing the company. Now it was time to spend more time riding and fishing on the old Lazy Beta Ranch.

Under Mr. Breezeway’s leadership Prairie Home had grown slowly but steadily and was solidly profitable. (Table  7.6 shows earnings, dividends, and book asset values for the last 5 years.) Most of the company’s supermarkets had been modernized, and its brand name was well known.

Mr. Breezeway was proud of this record, although he wished that Prairie Home could have grown more rapidly. He had passed up several opportunities to build new stores in adjacent counties. Prairie Home was still just a family company. Its common stock was distributed among 15 grandchildren and nephews of Jacob Breezeway, most of whom had come to depend on generous regu- lar dividends. The commitment to high dividend payout21 had reduced the earnings available for reinvestment and thereby con- strained growth.

Mr. Breezeway believed the time had come to take Prairie Home public. Once its shares were traded in the public market, the Breezeway descendants who needed (or just wanted) more cash to

spend could sell off part of their holdings. Others with more inter- est in the business could hold on to their shares and be rewarded by higher future earnings and stock prices.

But if Prairie Home did go public, what should its shares sell for? Mr. Breezeway worried that shares would be sold, either by Breezeway family members or by the company itself, at too low a price. One relative was about to accept a private offer for $200, the current book value per share, but Mr. Breezeway had intervened and convinced the would-be seller to wait.

Prairie Home’s value depended not just on its current book value or earnings but on its future prospects, which were good. One financial projection (shown in the top panel of Table  7.7) called for growth in earnings of over 100% by 2025. Unfortunately, this plan would require reinvestment of all of Prairie Home’s earnings from 2019 to 2022. After that the company could resume its normal dividend payout and growth rate. Mr. Breezeway believed this plan was feasible.

He was determined to step aside for the next generation of top management. But before retiring, he had to decide whether to rec- ommend that Prairie Home Stores “go public”—and before that decision he had to know what the company was worth.

The next morning he rode thoughtfully to work. He left his horse at the south corral and ambled down the dusty street to Mike

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Rev. Confirming Pages

Chapter 7 Valuing Stocks 233

2014 2015 2016 2017 2018

Book value, start of year $62.7 $66.1 $69.0 $73.9 $76.5 Earnings 9.7 9.5 11.8 11.0 11.2 Dividends 6.3 6.6 6.9 7.4 7.7 Retained earnings 3.4 2.9 4.9 2.6 3.5 Book value, end of year 66.1 69.0 73.9 76.5 80.0

TABLE 7.6 Financial data for Prairie Home Stores, 2014–2018 (figures in millions)

Notes: 1. Prairie Home Stores has 400,000 common shares. 2. The company’s policy is to pay cash dividends equal to 10% of start-of-year book value.

2019 2020 2021 2022 2023 2024

Rapid-Growth Scenario

Book value, start of year $80 $ 92 $105.8 $121.7 $139.9 $146.9 Earnings 12 13.8 15.9 18.3 21.0 22.0 Dividends 0 0 0 0 14 14.7 Retained earnings 12 13.8 15.9 18.3 7.0 7.4 Book value, end of year 92 105.8 121.7 139.9 146.9 154.3

Constant-Growth Scenario

Book value, start of year $80 $84 $88.2 $92.6 $ 97.2 $102.1 Earnings 12 12.6 13.2 13.9 14.6 15.3 Dividends 8 8.4 8.8 9.3 9.7 10.2 Retained earnings 4 4.2 4.4 4.6 4.9 5.1 Book value, end of year 84 88.2 92.6 97.2 102.1 107.2

TABLE 7.7 Financial projections for Prairie Home Stores, 2019–2024 (figures in millions)

Notes: 1. Both panels assume earnings equal to 15% of start-of-year book value. This profi tability rate is constant. 2. The top panel assumes all earnings are reinvested from 2019 to 2022. In 2023 and later years, two-thirds of earnings are paid

out as dividends and one-third reinvested. 3. The bottom panel assumes two-thirds of earnings are paid out as dividends in all years. 4. Columns may not add up because of rounding.

Gordon’s Saloon, where Francine Firewater, the company’s CFO, was having her usual steak-and-beans breakfast. He asked Ms. Firewater to prepare a formal report to Prairie Home stockhold- ers, valuing the company on the assumption that its shares were publicly traded.

Ms. Firewater asked two questions immediately. First, what should she assume about investment and growth? Mr. Breezeway suggested two valuations, one assuming more rapid expansion (as in the top panel of Table 7.7) and another just projecting past growth (as in the bottom panel of Table 7.7).

Second, what rate of return should she use? Mr. Breezeway said that 15%, Prairie Home’s usual return on book equity, sounded right to him, but he referred her to an article in the Journal of Finance indicating that investors in rural supermarket chains, with risks similar to Prairie Home Stores, expected to earn about 11% on average.

21 The company traditionally paid out cash dividends equal to 10% of start-of-period book value. See Table 7.6.

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234

Net Present Value and Other Investment Criteria

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

8-1 Calculate the net present value of a project.

8-2 Calculate the internal rate of return of a project and know what to look out for when using the internal rate of return rule.

8-3 Calculate the profitability index and use it to choose between projects when funds are limited.

8-4 Understand the payback rule and explain why it doesn’t always make shareholders bet- ter off.

8-5 Use the net present value rule to analyze three common problems that involve com- peting projects: (a) when to postpone an investment expenditure, (b) how to choose between projects with unequal lives, and (c) when to replace equipment.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

8 CHAPTE R

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235

P A

R T

TW O

T he investment decision, also known as capital budgeting, is central to the success of the com-pany. We have already seen that capital invest- ments can sometimes absorb substantial amounts of

cash; they also have very long-term consequences.

The assets you buy today may determine the busi-

ness you are in many years hence.

For some investment projects “substantial” is an

understatement. Consider the following examples:

● Verizon spent $23 billion rolling out its fiber-optic

network, FiOS.

● The cost of bringing one new prescription drug to

market is estimated to be $800 million.

● The eventual cost of the Gorgon natural gas proj-

ect in Western Australia is estimated at $46 billion.

● General Motors’ research and development costs

for the Chevrolet Volt have been about $1.2 billion.

● Estimated production costs for the latest Pirates

of the Caribbean movie have been estimated at

about $300 million.

● The development costs of the Boeing 787 Dream-

liner jet are estimated at over $30 billion.

Notice that many of these big capital projects

require heavy investment in intangible assets. For

example, almost all the cost of drug development

is for research and testing. So is much of the cost of

developing the electric auto. Any expenditure made

in the hope of generating more cash later can be

called a capital investment project, regardless of

whether the cash outlay goes to tangible or intan-

gible assets.

A company’s shareholders prefer to be rich rather

than poor. Therefore, they want the firm to invest in

every project that is worth more than it costs. The

difference between a project’s value and its cost is

termed the net present value. Companies can best

help their shareholders by investing in projects with a

positive net present value.

We start this chapter by showing how to calcu-

late the net present value of some simple investment

projects. We then examine three other criteria that

Va lu

e

High-tech businesses often require huge investments. How do companies decide which investments are worth undertaking?

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236

companies sometimes use to evaluate investments.

Often they compare the expected rate of return

offered by a project to the return that their sharehold-

ers could earn on equivalent-risk investments in the

capital market. They accept only projects that pro-

vide a higher return than shareholders could earn for

themselves. Generally, this rule will give the same guid-

ance as the net present value rule, but, as we will see,

it presents some pitfalls, especially when choosing

among alternative projects. We explore the key pitfalls

of the rate of return rule, and in the appendix we show

you some tricks for avoiding them.

Another measure of project worth is the profitability

index, which is net present value per dollar invested.

This can be a handy tool when the company does

not have enough money to take on every project with

a positive net present value.

The third measure, the payback rule, is a simple

rule of thumb that companies may use to separate

the no-brainers from more marginal cases. But we

shall see that this rule is an unreliable guide to proj-

ect viability and is even more unreliable when used

to choose among competing projects. We will spend

relatively little time on it.

We start the chapter by looking at some simple take-

it-or-leave-it decisions. However, in practice, projects

can rarely be considered in isolation because you will

have to sort through several alternatives, only one of

which can be chosen. For example, suppose you are

considering whether to build a new factory. Should you

build the factory to 100,000 square feet or 150,000?

Should you design it to last 20 years or 30? Should it

be built today, or should you wait a year? Later in the

chapter we explain how to make such choices.

8.1 Net Present Value In Chapters 6 and 7, you learned how to value bonds and stocks by adding up the pres- ent values of the cash flows that they are expected to provide to their investors. Now we will do the same for investment projects.

Suppose that you are in the real estate business. You are considering construction of an office block. The land would cost $50,000, and construction would cost a further $300,000. You foresee a shortage of office space and predict that a year from now you will be able to sell the building for $400,000. Thus you would be investing $350,000 now in the expectation of realizing $400,000 at the end of the year. Therefore, pro- jected cash flows may be summarized in a simple time line as follows:

$400,000 0 Year 1

–$350,000

You should go ahead if the present value of the $400,000 payoff is greater than the investment of $350,000.

Assume for the moment that the $400,000 payoff is a sure thing. The office build- ing is not the only way to obtain $400,000 a year from now. You could instead invest in 1-year U.S. Treasury bills. Suppose Treasury securities offer interest of 7%. How much would you have to invest in them in order to receive $400,000 at the end of the year? That’s easy: You would have to invest

$400,000 × 1

1.07 = $400,000 × .9346 = $373,832

Let’s assume that as soon as you have purchased the land and laid out the money for construction, you decide to cash in on your project. How much could you sell it for? Since the property will be worth $400,000 in a year, investors would be willing to pay at most $373,832 for it now. That’s all it would cost them to get precisely the same $400,000 payoff by investing in government securities. Of course, you could always sell your property for less, but why sell for less than the market will bear?

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Chapter 8 Net Present Value and Other Investment Criteria 237

Therefore, at an interest rate of 7%, the present value of the $400,000 payoff from the office building is $373,832. The $373,832 present value is the only price that satis- fies both buyer and seller. In general, the present value is the only feasible price, and the present value of the property is also its market price or market value.

To calculate present value, we discounted the expected future payoff by the rate of return offered by comparable investment alternatives. The discount rate—7% in our example—is often known as the opportunity cost of capital. It is called the oppor- tunity cost because if you decide to invest in this project, you will forgo other similar investment opportunities such as the purchase of Treasury securities.

The building is worth $373,832, but this does not mean that you are $373,832 better off. You committed $350,000, and therefore your net present value (NPV) is $23,832. Net present value is found by subtracting the required initial investment from the pres- ent value of the project cash flows:

NPV = PV - required investment (8.1)

= $373,832 - $350,000 = $23,832

In other words, your office development is worth more than it costs—it makes a net contribution to value. The net present value rule states that managers increase shareholders’ wealth by accepting projects that are worth more than they cost. Therefore, they should accept all projects with a positive net present value.

A Comment on Risk and Present Value In our discussion of the office development we assumed we knew the value of the completed project. Of course, you will never be certain about the future values of office buildings. The $400,000 represents the best forecast, but it is not a sure thing.

Therefore, our initial conclusion about how much investors would pay for the building is premature. Since they could achieve $400,000 risklessly by investing in $373,832 worth of U.S. Treasury bills, they would not buy your risky project for that amount. You would have to cut your asking price to attract investors’ interest.

Here we can invoke a basic financial principle: A risky dollar is worth less than a safe one.

Most investors avoid risk when they can do so without sacrificing return. However, the concepts of present value and the opportunity cost of capital still apply to risky investments. It is still proper to discount the payoff by the rate of return offered by a comparable investment. But we have to think of expected payoffs and the expected rates of return on other investments. And we need to make sure that those other invest- ments have comparable risk.

Not all investments are equally risky. The office development is riskier than a Treasury bill but is probably less risky than investing in a start-up biotech company. Suppose you believe the office development is as risky as an investment in the stock market and that you forecast a 12% rate of return for stock market investments. Then 12% would be the appropriate opportunity cost of capital. That is what you are giving up by not investing in securities with similar risk. You can now recompute NPV:

PV = $400,000 × 1

1.12 = $400,000 × .8929 = $357,143

NPV = PV - $350,000 = $7,143

If other investors agree with your forecast of a $400,000 payoff and with your assess- ment of a 12% opportunity cost of capital, then the property ought to be worth $357,143 once construction is under way. If you tried to sell for more than that, there would be no takers, because the property would then offer a lower expected rate of return than the 12% available in the stock market. Even at a discount rate of 12%, the office building still makes a net contribution to value, but it is much smaller than our earlier calculations indicated.

opportunity cost of capital Expected rate of return given up by investing in a project.

net present value (NPV) Present value of cash flows minus investment.

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238 Part Two Value

What is the office development’s NPV if construction costs increase to $355,000? Assume the opportunity cost of capital is 12%. Is the development still a worthwhile investment? How high can development costs be before the project is no longer attractive? Now suppose that the opportunity cost of capital is 20% with construction costs of $355,000. Why is the office develop- ment no longer an attractive investment?

Self-Test 8.1

Valuing Long-Lived Projects The net present value rule works for projects of any length. For example, suppose that you are approached by a possible tenant who is prepared to rent your office block for 3 years at a fixed annual rent of $25,000. You would need to expand the reception area and add some other tailor-made features. This would increase the initial investment to $375,000, but you forecast that after you have collected the third year’s rent the build- ing could be sold for $450,000. The projected cash flow (denoted C ) in each year is shown below (the final cash flow is the sum of rental income plus the proceeds from selling the building).

C3 = $475,000 C1 = $25,000 C2 = $25,000 0 Year 1 2 3

C0 = –$375,000

Notice that the initial investment shows up as a negative cash flow. That first cash flow, C 0 , is - $375,000. For simplicity, we will again assume that these cash flows are cer- tain and that the opportunity cost of capital is r   =  7%.

Figure 8.1 shows a time line of the cash inflows and their present values. To find the present value of the project, we discount these cash inflows at the 7% opportunity cost of capital:

PV = C1

1 + r +

C2 (1 + r)2

+

C3 (1 + r)3

= $25,000

1.07 +

$25,000

1.072 +

$475,000

1.073 = $432,942

The net present value of the revised project is NPV  =   $432,942  -   $375,000  = $57,942. Constructing the office block and renting it for 3 years makes a greater addi- tion to your wealth than selling it at the end of the first year.

Of course, rather than subtracting the initial investment from the project’s pres- ent value, you could calculate NPV directly, as in the following equation, where C 0 denotes the initial cash outflow required to build the office block.

NPV = C0 + C1

1 + r +

C2 (1 + r)2

+

C3 (1 + r)3

= -$375,000 + $25,000

1.07 +

$25,000

1.072 +

$475,000

1.073 = $57,942

Let’s check that the owners of this project really are better off. Suppose you put up $375,000 of your own money, commit to build the office building, and sign a lease that will bring in $25,000 a year for 3 years. Now you can cash in by selling the project to other investors.

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Chapter 8 Net Present Value and Other Investment Criteria 239

Suppose you sell 1,000 shares in the project. Each share represents a claim to 1/1,000 of the future cash flows. Since the cash flows are certain, and the interest rate offered by other certain investments is 7%, investors will value each share at

Price per share = $25

1.07 +

$25

1.072 +

$475

1.073 = $432.94

Thus you can sell the project to outside investors for 1,000  ×  $432.94  =  $432,940, which, save for rounding, is exactly the present value we calculated earlier. Your net gain is

Net gain = $432,942 - $375,000 = $57,942

which is the project’s NPV. This equivalence should be no surprise, since the present value calculation is designed to calculate the value of future cash flows to investors in the capital markets.

Notice that in principle there could be a different opportunity cost of capital for each period’s cash flow. In that case we would discount C 1 by r 1 , the discount rate for 1-year cash flows; C 2 would be discounted by r 2 ; and so on. Here we assume that the cost of capital is the same regardless of the date of the cash flow. We do this for one reason only—simplicity. But we are in good company: With only rare exceptions firms decide on an appropriate discount rate and then use it to discount all cash flows from the project.

FIGURE 8.1 Cash flows and their present values for the office-block project. Final cash flow of $475,000 is the sum of the rental income in year 3 plus the forecast sales price for the building.

0

= 21,836

Present value

432,942

1.072 25,000

= 23,364 1.07

25,000

=387,741 1.073

475,000

2 31

$450,000

$25,000

$25,000 $25,000

$475,000

Example 8.1 Valuing a New Computer System Obsolete Technologies is considering the purchase of a new computer system to help handle its warehouse inventories. The system costs $50,000, is expected to last 4 years, and should reduce the cost of managing inventories by $22,000 a year. The opportunity cost of capital is 10%. Should Obsolete go ahead?

Don’t be put off by the fact that the computer system does not generate any sales. If the expected cost savings are realized, the company’s cash flows will be $22,000 a year higher as a result of buying the computer. Thus we can say that the computer increases cash flows by $22,000 a year for each of 4 years. To calculate present value, you can discount each of these cash flows by 10%. However, it is

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240 Part Two Value

Example 8.2 Calculating NPV for the Cape Wind Project Cape Wind is a wind-power project to be built offshore, south of Cape Cod, Massachusetts, in Nantucket Sound. The project will cost over $5 billion and gener- ate 420 megawatts (MW) of electricity when the wind is sufficiently strong—enough to supply about 75% of the electricity demand for Cape Cod, Martha’s Vineyard, and Nantucket.

Who could object to Cape Wind’s renewable energy? Local residents, that’s who, including well-off owners of vacation homes who believe that Cape Wind, though located several miles out to sea, will spoil views of Nantucket Sound. The project finally received all federal and state permits in 2013, after more than a decade of argument.

You can explore whether the project was a good deal for Cape Wind’s inves- tors. Table 8.1 shows illustrative cash flows based on regulatory filings before the Massachusetts Department of Public Utilities and on the terms of power purchase agreements (PPAs) between Cape Wind and local electric utilities. 1

The cash flows are shown in column C of Table 8.1 . These projections assume that the project is built in 2014 and 2015 and goes online in 2016. The project then sells electricity at predetermined PPA prices for 15 years, through 2030. Cash flows are high in the first few years of operation because of federal tax subsidies, but decline by 2022, when the tax subsidies run out. Then the cash flows increase gradually because of inflation adjustments in the PPAs. Revenues and cash flows decline after 2030, when the PPAs expire. The project’s economic life is assumed to end in 2038.

The cash flows in Table 8.1 are not a sure thing. For example, construction cost overruns could sink the project’s economics beyond recovery. But the PPA prices are locked in by contract, so cash flows should be low-risk once the project is operating. Suppose that investors expected an 8% rate of return from investments in financial markets with the same risk as Cape Wind. That 8% return is what the investors give up if they put up the funds necessary to build Cape Wind. On this assumption, the opportunity cost of capital for Cape Wind is 8%. Therefore we dis- count the cash flows in Table 8.1 at 8% ( r   =  .08).

We will calculate NPV standing in 2014, which we call “year 0.” The first negative cash flow in column C occurs in year 0 and is not discounted. The negative cash flow in year 1 (2015) is discounted for 1 year. Then the positive cash flow in year 2 (i.e., 2016) is discounted for 2 years, the cash flow in year 3 (2017) for 3 years, and so on. The final cash flow in year 24 (2038) is discounted for 24 years. We can write the NPV calculation algebraically as

1 We thank Judy Chang and Jurgen Weiss of The Brattle Group Inc. for help in constructing this example.

smarter to recognize that the cash flows are level, and therefore you can use the annuity formula to calculate the present value:

PV = cash flow × annuity factor = $22,000 × c 1 .10

-

1 .10(1.10)4

d = $22,000 × 3.1699 = $69,738

The net present value is

NPV = -$50,000 + $69,738 = $19,738

The project has a positive NPV of $19,738. Undertaking it would increase the value of the firm by that amount.

The first two steps in calculating NPVs—forecasting the cash flows and estimating the opportunity cost of capital—are tricky, and we will have a lot more to say about them in later chapters. But once you have assembled the data, the calculation of pres- ent value and net present value should be routine. Here is another example.

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Chapter 8 Net Present Value and Other Investment Criteria 241

NPV = C0 + C1

1 + r +

C2 (1 + r)2

+ c

+

C23 (1 + r)23

+

C24 (1 + r)24

The C s in this equation are the cash flows, and r is the discount rate, 8% or .08. The PV of each cash flow is shown in column D of Table 8.1 . The sum of these

cash flows is NPV  =  $644 million, so the project appears to make economic sense, though perhaps not by a wide margin, considering the risk of cost overruns. Also, by 2014 Cape Wind had already spent 10 years and over $50 million on planning and engineering design and on the cost of obtaining all required permits.

The nearby box provides additional guidance on how to calculate NPVs using spreadsheets.

BEYOND THE PAGE

brealey.mhhe.com/ch08-01

Cape Wind

TABLE 8.1 Forecast cash flows and present values in 2014 for the Cape Wind project. The investment at the time appeared to have a positive NPV of $644.1 million.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

A B C D E

2014

2015

2016

2017

2018

2019

2020

2021

2022

2023

2024

2025

2026

2027

2028

2029

2030

2031

2032

2033

2034

2035

2036

2037

2038

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

–2,685

–2,486

1,428

1,640

637

519

531

446

361

374

387

400

414

429

444

459

475

114

116

118

118

120

121

122

124

–2,685

–2,302

1,224

1,302

468

353

335

260

195

187

179

172

164

158

151

145

139

31

29

27

25

24

22

21

20

644

644

=C3

=C4/1.08`B4

=C7/1.08`B7

=C8/1.08`B8

=C9/1.08`B9

=C10/1.08`B10

=C11/1.08`B11

=C12/1.08`B12

=C13/1.08`B13

=C14/1.08`B14

=C15/1.08`B15

=C16/1.08`B16

=C17/1.08`B17

=C18/1.08`B18

=C19/1.08`B19

=C20/1.08`B20

=C21/1.08`B21

=C22/1.08`B22

=C23/1.08`B23

=C24/1.08`B24

=C25/1.08`B25

=C26/1.08`B26

=C27/1.08`B27

=SUM(D3:D27)

=NPV(.08,C4:C27)+C3

Cash Flow

($ millions)Year

Sum:

Using Excel's NPV function

Time PV at 8% Formula in Column D

=C5/1.08`B5

=C6/1.08`B6

You can find this spreadsheet in Connect.

So far, the simple projects that we have considered all involved take-it-or-leave it decisions. But real-world decisions are rarely straightforward go-or-no-go choices; rather, you will almost always be forced to choose among several alternatives. In these cases, you need to rank your alternatives and select the most attractive one. In prin- ciple, the decision rule is easy:

When choosing among mutually exclusive projects, choose the one that offers the highest net present value.

In reality, however, it can be surprisingly tricky to compare projects properly. We treat some of the challenging cases later in the chapter, in Section 8.5. For now, we illustrate the general rule with a simple example.

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242

The formulas used in column D (specifi cally, in cells D4 through D27) and spelled out in column E all contain 1.08. What if you want to see how the PVs change at a different discount rate, say 9%? You would have to change 24 formulas manually. However, there is an easier way. Instead of repeat- edly replacing 1.08 with 1.09 in each of those cells, fi rst enter the appropriate discount rate in cell E1, and then replace every incidence of 1.08 with (1  +  $E$1) in column D. This tells Excel that the discount factor is 1 plus the number in cell E1, where the discount rate resides. (The dollar signs in $E$1 ensure that the Excel formula always refers to exactly that cell, regard- less of where the formula is located in the spreadsheet.) Now you can easily experiment with different discount rates by changing just one number, the rate entered in cell E1; Excel will recalculate the PVs and NPV automatically using that rate.

For example, the formula used in cell D9 and displayed in E9 becomes = C9/(1  +   $E$1)∧B9. The NPV formula becomes = NPV($E$1, C4:C27) + C3. The “live” version of the spreadsheet in Table 8.1 , which is available in Connect, is set up in this way.

Spreadsheet Questions 1. Go to the spreadsheet version of Table 8.1 . How does NPV

change if the discount rate increases? What discount rate would drive NPV down to zero?

2. Try calculating Cape Wind’s NPV using the formula = NPV($E$1, C3:C27), using a discount rate of 8%. You should fi nd that NPV decreases by a factor of exactly 1/1.08. Why?

Brief solutions appear at the end of the chapter.

Computer spreadsheets are tailor-made to calculate the present value of a series of cash fl ows. Table 8.1 is an Excel spreadsheet for Cape Wind. Cells D3 through D27 calculate the PV of each year’s cash fl ow by discounting at 8% for the length of time given in column B. Cell D29 calculates NPV as the sum of the PVs of all years’ cash fl ows. Column E shows the Excel formulas used to calculate the results in column D.

Excel also provides a built-in function to calculate NPVs. The formula is = NPV(discount rate, list of cash fl ows). So, instead of calculating the PV of each cash fl ow and summing up, we can use the NPV function in cell D31. (The formula used in that cell is shown in E31.) The fi rst entry in the function is the discount rate expressed as a decimal, in this case .08. That is followed by C4:C27, which tells Excel to discount all cash fl ows in column C from cells C4 to C27.

Why is the fi rst cash fl ow in the NPV formula from cell C4, which contains the cash fl ow for year 1, rather than C3, which contains the immediate investment in year 0? It turns out that Excel always assumes that the fi rst cash fl ow comes after one period, the next after two periods, and so on. If the fi rst cash fl ow actually comes at year 0, we do not want it discounted, nor do we want later cash fl ows dis- counted for an extra period. Therefore we don’t include the immediate cash fl ow in the NPV function. Instead, we add it undiscounted to the NPV of other cash fl ows. See cell E31 for the formula.

Be careful with the timing of cash fl ows when you use the NPV function. If in doubt, discount each cash fl ow and add them up, as in cell D29.

Solutions Spreadsheet Present Values

Example 8.3 Choosing between Two Projects It has been several years since your office last upgraded its office networking soft- ware. Two competing systems have been proposed. Both have an expected use- ful life of 3 years, at which point it will be time for another upgrade. One proposal is for an expensive, cutting-edge system, which will cost $800,000 and increase firm cash flows by $350,000 a year through increased productivity. The other proposal is for a cheaper, somewhat slower system. This system would cost only $700,000 but would increase cash flows by only $300,000 a year. If the cost of capital is 7%, which is the better option?

The following table summarizes the cash flows and the NPVs of the two proposals:

In both cases, the software systems are worth more than they cost, but the faster system would make the greater contribution to value and therefore should be your preferred choice.

Cash Flows (thousands of dollars)

System C0 C1 C2 C3 NPV at 7%

Faster -800 +350 +350 +350 118.5 Slower -700 +300 +300 +300 87.3

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Chapter 8 Net Present Value and Other Investment Criteria 243

8.2 The Internal Rate of Return Rule Instead of calculating a project’s net present value, companies often prefer to ask whether the project’s return is higher or lower than the opportunity cost of capital. For example, think back to the original proposal to build the office block. You planned to invest $350,000 to get back a cash flow of C 1   =  $400,000 in 1 year. Therefore, you forecast a profit on the venture of $400,000  -  $350,000  =  $50,000. In a one-period project like this one, it is easy to calculate the rate of return. Simply compute end-of- year profit per dollar invested in the project:

Rate of return = profit

investment =

C 1 - investment

investment =

$400,000 - $350,000

$350,000

= .1429, or about 14.3%

The alternative of investing in a U.S. Treasury bill would provide a return of only 7%. Thus the return on your office building is higher than the opportunity cost of capital. 2

This suggests two rules for deciding whether to go ahead with an investment project:

1. The NPV rule. Invest in any project that has a positive NPV when its cash flows are discounted at the opportunity cost of capital.

2. The rate of return rule. Invest in any project offering a rate of return that is higher than the opportunity cost of capital.

Both rules set the same cutoff point. An investment that is on the knife edge with an NPV of zero will also have a rate of return that is just equal to the cost of capital.

Suppose that the rate of interest on Treasury securities is not 7% but 14.3%. Since your office project also offers a return of 14.3%, the rate of return rule suggests that there is now nothing to choose between taking the project and leaving your money in Treasury securities.

The NPV rule also tells you that if the interest rate is 14.3%, the project is evenly balanced with an NPV of zero:

NPV = C 0 + C 1

1 + r = -$350,000 +

$400,000

1.143 = 0

The project would make you neither richer nor poorer; it is worth just what it costs. Thus the NPV rule and the rate of return rule both give the same decision on accepting the project.

A Closer Look at the Rate of Return Rule We know that if the office project’s cash flows are discounted at a rate of 7%, the project has a net present value of $23,832. If they are discounted at a rate of 14.3%, it has an NPV of zero. In Figure 8.2 the project’s NPV for a variety of discount rates is plotted. This is often called the NPV profile of the project. Notice two important things about Figure 8.2 :

1. The project rate of return (in our example, 14.3%) is also the discount rate that would give the project a zero NPV. This gives us a useful definition: The rate of return is the discount rate at which NPV equals zero.

2. If the opportunity cost of capital is less than the project rate of return, then the NPV of your project is positive. If the cost of capital is greater than the project rate of return, then NPV is negative. Thus, for this accept-or-reject decision, the rate of return rule and the NPV rule are equivalent.

Calculating the Rate of Return for Long-Lived Projects There is no ambiguity in calculating the rate of return for an investment that gener- ates a single payoff after one period. But how do we calculate return when the proj- ect produces cash flows in several periods? Just think back to the definition that we

2 Recall that we are assuming the profit on the office building is risk-free. Therefore, the opportunity cost of capital is the rate of return on other risk-free investments.

IRR is the discount rate at which NPV  =  0

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244 Part Two Value

Year: 0 1 2 3

Cash fl ows -$375,000 +$25,000 +$25,000 +$475,000

introduced above— the project rate of return is also the discount rate that gives the project a zero NPV. We can use this idea to find the return on a project that has many cash flows. The discount rate that gives the project a zero NPV is known as the project’s internal rate of return, or IRR. It is also called the discounted cash-flow (DCF) rate of return.

Let’s calculate the IRR for the revised office project. If you rent out the office block for 3 years, the cash flows are as follows:

internal rate of return (IRR) Discount rate at which project NPV  =  0.

FIGURE 8.2 The value of the office project is lower when the discount rate is higher. The project has a positive NPV if the discount rate is less than 14.3%.

N et

p re

se n

t va

lu e

($ t

h o

u sa

n d

s)

Discount rate (%)

-80

-60

-40

-20

0

20

40

60

120 4 8 2016

Rate of return = 14.3%

NPV profile

24 32 3628 40

The IRR is the discount rate at which these cash flows would have zero NPV. Thus,

NPV = -$375,000 + $25,000

1 + IRR +

$25,000 (1 + IRR)2

+

$475,000 (1 + IRR)3

= 0

There is no simple general method for solving this equation. You have to rely on a little trial and error. Let us arbitrarily try a zero discount rate. This gives an NPV of $150,000:

NPV = -$375,000 + $25,000

1.0 +

$25,000 (1.0)2

+

$475,000 (1.0)3

= $150,000

With a zero discount rate the NPV is positive. So the IRR must be greater than zero. The next step might be to try a discount rate of 50%. In this case NPV is - $206,481:

NPV = -$375,000 + $25,000

1.50 +

$25,000 (1.50)2

+

$475,000 (1.50)3

= -$206,481

At this higher discount rate, NPV turns negative. So the IRR must lie somewhere between zero and 50%. In Figure  8.3 we have plotted the net present values for a range of discount rates. You can see that a discount rate of 12.56% gives an NPV of zero. Therefore, the IRR is 12.56%. You can always find the IRR by plotting an NPV profile, as in Figure 8.3 , but it is quicker and more accurate to let a spreadsheet or spe- cially programmed financial calculator do the trial and error for you. The nearby boxes illustrate how to do so.

The rate of return rule tells you to accept a project if the rate of return exceeds the opportunity cost of capital. You can see from Figure 8.3 why this makes sense. Because the NPV profile is downward-sloping, the project has a positive NPV as long as the opportunity cost of capital is less than the project’s 12.56% IRR. If the opportunity

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Chapter 8 Net Present Value and Other Investment Criteria 245

cost of capital is higher than the 12.56% IRR, NPV is negative. Therefore, when we compare the project IRR with the opportunity cost of capital, we are effectively asking whether the project has a positive NPV. This was true for our one-period office project. It is also true for our three-period office project. We conclude that the rate of return rule will give the same answer as the NPV rule as long as the NPV of a project declines smoothly as the discount rate increases. 3

The usual agreement between the net present value and internal rate of return rules should not be a surprise. Both are discounted cash-flow methods of choosing between projects. Both are concerned with identifying those projects that make shareholders better off, and both recognize that companies always have a choice: They can invest in a project, or if the project is not sufficiently attractive, they can give the money back to shareholders and let them invest it for themselves in the capital market.

3 In Chapter 6 we showed how to calculate the yield to maturity on a bond. A bond’s yield to maturity is simply its IRR by another name.

FIGURE 8.3 The internal rate of return is the discount rate for which NPV equals zero.

N et

p re

se n

t va

lu e

($ t

h o

u sa

n d

s) Discount rate (%)

-100

-150

-50

0

50

100

150

12 140 4 62 8 10 20 2216 18 24 26 28 30

NPV profile

IRR = 12.56%

Suppose the cash flow in year 3 is only $420,000. Redraw Figure 8.3 . How would the IRR change?

Self-Test 8.2

A Word of Caution Some people confuse the internal rate of return on a project with the opportunity cost of capital. Remember that the project IRR measures the profitability of the project. It is an internal rate of return in the sense that it depends only on the project’s own cash flows. The opportunity cost of capital is the standard for deciding whether to accept the proj- ect. It is equal to the return offered by equivalent-risk investments in the capital market.

Some Pitfalls with the Internal Rate of Return Rule Many firms use the internal rate of return rule instead of net present value. We think that this is a pity. When used properly, the two rules lead to the same decision, but the rate of return rule has several pitfalls that can trap the unwary. In particular, it is poorly suited to choosing between two (or more) competing proposals. Here are three examples.

Pitfall 1: Mutually Exclusive Projects We have seen that firms are seldom faced with take-it-or-leave-it projects. Usually they need to choose from a number of mutually exclusive alternatives. Given a choice between competing projects, you should accept the one that adds most to shareholder wealth. This is the one with the higher NPV.

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246

But what about the rate of return rule? Would it make sense just to choose the project with the highest internal rate of return? Unfortunately, no. Mutually exclusive projects therefore entail a dangerous pitfall for users of the IRR rule.

Think once more about the two office-block proposals from Section 8.1. You initially intended to invest $350,000 in the building and then sell it at the end of the year for $400,000. Under the revised proposal, you planned to invest $375,000, rent out the offices for 3 years at a fixed annual rent of $25,000, and then sell the building for $450,000. The following table shows both projects’ cash flows, their IRRs, and their NPVs:

Calculating internal rate of return in Excel is as easy as listing the project cash fl ows. For exam- ple, to calculate the IRR of the office-block proj- ect, you could simply type in its cash fl ows as in the spreadsheet above, and then calculate IRR as we do in cell E4. As always, the interest rate is returned as a decimal.

Solutions Spreadsheet Internal Rate of Return

You can find this spreadsheet in Connect.

Year: 0 1 2 3 IRR NPV at 7%

Initial proposal -350,000 +400,000 14.29% +$23,832

Revised proposal -375,000 +25,000 +25,000 +475,000 12.56% +$57,942

Both projects are good investments; both offer a positive NPV. But the revised pro- posal has the higher net present value and therefore is the better choice. Unfortunately, the superiority of the revised proposal doesn’t show up as a higher rate of return. The IRR rule seems to say you should go for the initial proposal because it has the higher IRR. If you follow the IRR rule, you have the satisfaction of earning a 14.29% rate of return; if you use NPV, you are nearly $58,000 richer.

Figure 8.4 shows why the IRR rule gives the wrong signal. The figure plots the NPV of each project for different discount rates. These two NPV profiles cross at an interest rate of 11.72%. So if the opportunity cost of capital is higher than 11.72%, the initial proposal, with its rapid cash inflow, is the superior investment. If the cost of capital is lower than 11.72%, then the revised proposal dominates. Depending on the discount rate, either proposal may be superior. For the 7% cost of capital that we have assumed, the revised proposal is the better choice.

FIGURE 8.4 The initial proposal offers a higher IRR than the revised proposal, but its NPV is lower if the discount rate is less than 11.72%.

N P

V (

$ th

o u

sa n

d s)

Discount rate (%)

-75

-50

-25

0

25

50

75

150

125

100

10861 2 4 1814 1612 20

IRR = 12.56%

IRR = 14.29%

Revised proposal

Initial proposal

1

2

3

4

5

6

7

Cash Flow

–375,000

25,000

25,000

475,000

Formula

=IRR(B4:B7)

BA C D E

Year

0

1

2

3

IRR=

Calculating IRR by using a spreadsheet

F

0.1256

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Calculator Financial To calculate project NPV, the procedure is similar. You

need to enter the discount rate in addition to the project cash fl ows, and then simply press the NPV key. Here is the specifi c sequence of keystrokes, assuming that the opportunity cost of capital is 7%:

We saw in Chapter 5 that the formulas for the present and future values of level annuities and one-time cash fl ows are built into fi nancial calculators. However, as the example of the office block illustrates, most investment projects entail multiple cash fl ows that cannot be expected to remain level over time. Fortunately, many calculators are equipped to handle problems involving a sequence of uneven cash fl ows. In general, the pro- cedure is quite simple. You enter the cash fl ows one by one into the calculator, and then you press the IRR key to fi nd the project’s internal rate of return. The fi rst cash fl ow you enter is interpreted as coming immediately, the next cash fl ow is inter- preted as coming at the end of one period, and so on. We can illustrate using the office block as an example. To fi nd the proj- ect IRR, you would use the following sequence of keystrokes: *

*Various calculators entail minor variations on these key strokes. For example, on the HP12C, the fi rst cash fl ow is entered using the CF 0 key, to signify that the cash fl ow comes immediately and not after 1 year. The other cash fl ows are entered using the CF j key. On the Texas Instruments BAII Plus calculator, you would begin by hitting the CF key to signify that the following entries should be interpreted as cash fl ows. Each cash fl ow entry is then followed by the down arrow, rather than the CF j key. After hitting the IRR key, you would then hit CPT (the compute key). If you don’t have your own fi nancial calculator, you can download an emulator for the HP onto your personal computer and practice using that. See the nearby Beyond the Page icon.

Using Financial Calculators to Find NPV and IRR

-375,000 CFj

25,000 CFj

25,000 CFj

475,000 CFj

{IRR/YR}

-375,000 CFj

25,000 CFj

25,000 CFj

475,000 CFj

7 I/YR

{NPV}

The calculator should display the value 12.56%, the proj- ect’s internal rate of return.

The calculator should display the value 57,942, the project’s NPV when the discount rate is 7%.

By the way, you can check the accuracy of our earlier cal- culations using your calculator. Enter 50% for the discount rate (press 50, then press the interest rate key ) and then press the NPV key to fi nd that NPV  =   - 206,481. Enter 12.56 (the project’s IRR) as the interest rate, and you will fi nd that NPV is just about zero (it is not exactly zero, because we are rounding off the IRR to only two decimal places).

A rich, friendly, and probably slightly unbalanced benefactor offers you the opportunity to invest $1 million in two mutually exclusive ways. The payoffs are:

a. $2 million after 1 year, a 100% return b. $300,000 a year forever

Neither investment is risky, and safe securities are yielding 7.5%. Which investment will you take? You can’t take both, so the choices are mutually exclusive. Do you want to earn a high percentage return, or do you want to be rich? By the way, if you really had this investment opportunity, you’d have no trouble borrowing the money to undertake it.

Self-Test 8.3

247

Now consider the IRR of each proposal. The IRR is simply the discount rate at which NPV equals zero, that is, the discount rate at which the NPV profile crosses the horizontal axis in Figure 8.4 . As noted, these rates are 14.29% for the initial proposal and 12.56% for the revised proposal. However, as you can see from Figure 8.4 , the higher IRR for the initial proposal does not mean that it has a higher NPV.

In our example both projects involved the same outlay, but the revised proposal had the longer life. The IRR rule mistakenly favored the quick payback project with the high percentage return but the lower NPV. Remember, a high IRR is not an end in itself. You want projects that increase the value of the firm. Projects that earn a good rate of return for a long time often have higher NPVs than those that offer high percentage rates of return but die young.

Finding NPV and IRR on financial calculators

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248 Part Two Value

Pitfall 1a: Mutually Exclusive Projects Involving Different Outlays A similar misranking also may occur when comparing projects with the same lives but different outlays. In this case the IRR may mistakenly favor small projects with high rates of return but low NPVs. When you are faced with a straightforward either-or choice, the simple solution is to compare their NPVs. However, if you are determined to use the IRR rule, there is a way to do so. We explain how in the appendix.

Your wacky benefactor (see Self-Test 8.3) now offers you the choice of two opportunities:

a. Invest $1,000 today and quadruple your money—a 300% return—in 1 year with no risk.

b. Invest $1 million for 1 year at a guaranteed 50% return.

Which will you take? Do you want to earn a wonderful rate of return (300%), or do you want to be rich? Safe securities still yield 7.5%.

Self-Test 8.4

Pitfall 2: Lending or Borrowing? Remember our condition for the IRR rule to work: The project’s NPV must fall as the discount rate increases. Now consider the following projects:

Cash Flows (dollars)

Project C0 C1 IRR, % NPV at 10%

A -100 +150 +50 +$36.4 B +100 -150 +50 - 36.4

Each project has an IRR of 50%. In other words, if you discount the cash flows at 50%, both projects would have zero NPV.

Does this mean that the two projects are equally attractive? Clearly not. In the case of project A we are paying out $100 now and getting $150 back at the end of the year. That is better than any bank account. But what about project B? Here we are getting paid $100 now but we have to pay out $150 at the end of the year. That is equivalent to borrowing money at 50%.

If someone asked you whether 50% was a good rate of interest, you could not answer unless you also knew whether that person was proposing to lend or borrow at that rate. Lending money at 50% is great (as long as the borrower does not flee the country), but borrowing at 50% is not usually a good deal (unless, of course, you plan to flee the country). When you lend money, you want a high rate of return; when you borrow, you want a low rate of return.

If you plot a graph like Figure 8.2 for project B, you will find the NPV increases as the discount rate increases. (Try it!) Obviously, the rate of return rule will not work in this case.

Project B is a fairly obvious trap, but if you want to make sure you don’t fall into it, calculate the project’s NPV. For example, suppose that the cost of capital is 10%. Then the NPV of project A is + $36.4 and the NPV of project B is - $36.4. The NPV rule correctly warns us away from a project that is equivalent to borrowing money at 50%.

When NPV rises as the interest rate rises, the rate of return rule is reversed: A project is acceptable only if its internal rate of return is less than the opportu- nity cost of capital.

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Chapter 8 Net Present Value and Other Investment Criteria 249

Pitfall 3: Multiple Rates of Return Here is a tricky problem: King Coal Corporation is considering a project to strip-mine coal. The project requires an invest- ment of $210 million and is expected to produce a cash inflow of $125 million in the first 2 years, building up to $175 million in years 3 and 4. However, the company is obliged in year 5 to reclaim the land at a cost of $400 million. At a 20% opportunity cost of capital the project has an NPV of $5.9 million.

To find the IRR of King Coal’s project, we have calculated the NPV for various dis- count rates and plotted the results in Figure 8.5 . You can see that there are two discount rates at which NPV  =  0. That is, each of the following statements holds:

NPV = -210 + $125

1.03 +

125

1.032 +

175

1.033 +

175

1.034 -

400

1.035 = 0

and

NPV = -210 + $125

1.25 +

125

1.252 +

175

1.253 +

175

1.254 -

400

1.255 = 0

In other words, the investment has an IRR of both 3% and 25%. The reason for this is the double change in the sign of the cash flows. There can be as many different internal rates of return as there are changes in the sign of the cash-flow stream. 4

Is the coal mine worth developing? The simple IRR rule—accept if the IRR is greater than the cost of capital—won’t help. For example, you can see from Figure 8.5 that with a low cost of capital (less than 3%) the project has a negative NPV. It has a positive NPV only if the cost of capital is between 3% and 25%.

Decommissioning and clean-up costs, which make King Coal’s final cash flow negative, can sometimes be huge. For example, the ultimate cost of removing North Sea oil platforms in the United Kingdom is estimated to be more than $50 billion. It can cost over $300 million to decommission a nuclear power plant. These are obvious examples where cash flows go from positive to negative, but you can probably think of a number of other cases where the company needs to plan for later expenditures. Ships periodically need to go into dry dock for a refit, hotels may receive a major facelift, machine parts may need replacement, and so on.

Whenever the cash-flow stream is expected to change sign more than once, the project typically has more than one IRR and there is no simple IRR rule. It is possible to get around the problem of multiple rates of return by calculating a modified internal

4 There may be fewer IRRs than the number of sign changes. You may even encounter projects for which there is no IRR. For example, there is no IRR for a project that has cash flows of + $1,000 in year 0, - $3,000 in year 1, and + $2,500 in year 2. If you don’t believe us, try plotting NPV for different discount rates. Can such a project ever have a negative NPV?

FIGURE 8.5 King Coal’s project has two internal rates of return. NPV  =  0 when the discount rate is either 3% or 25%.

N et

p re

se n

t va

lu e

($ m

ill io

n s)

Discount rate (%)

-10

-15

-5

0

5

10

15

13 150 5 71 3 9 11 21 2317 19 25 27 29 3331 35

IRR = 25% IRR = 3%

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250 Part Two Value

rate of return (MIRR). We explain how to do so in the appendix to this chapter. How- ever, it would be much easier in such cases to abandon the IRR rule and just calculate project NPV.

8.3 The Profitability Index The profitability index measures the net present value of a project per dollar of investment:

Profitability index = net present value

initial investment (8.2)

For example, our initial proposal to construct an office building involved an invest- ment of $350,000 and had an NPV of $23,832. Its profitability index 5 was

23,832

350,000 = .068

The profitability index is also known as the benefit-cost ratio. The “benefit” of the project is its net present value. The “cost” is the required investment. The index mea- sures the benefit realized per dollar of cost.

Any project with a positive profitability index must also have a positive NPV, so it would seem that either criterion must result in identical decisions. Why go to the trouble of calculating the profitability index? The answer is that whenever there is a limit on the amount the company can spend, it makes sense to concentrate on getting the biggest bang for each investment buck. In other words, when there is a shortage of funds, the firm needs to pick those projects that have the highest profitability index.

Let us illustrate. Assume that you are faced with the following investment opportunities:

profitability index Ratio of net present value to initial investment.

5 Sometimes the profitability index is defined as the ratio of total present value (rather than net present value) to required investment. By this definition, all the profitability indexes calculated below are increased by 1. For example, the office building’s profitability index would be PV/investment  =  373,832/350,000  =  1.068. Note that project rankings under either definition are identical.

Cash Flows ($ millions)

Project C0 C1 C2 NPV at 10% Profi tability Index

C -10 +30 +5 21 21/10 = 2.1 D -5 +5 +20 16 16/5 = 3.2 E -5 +5 +15 12 12/5 = 2.4

All three projects are attractive, but suppose that the firm is limited to spending $10 million. In that case, you can invest either in project C or in projects D and E, but you can’t invest in all three. The solution is to start with the project that has the highest profitability index and continue until you run out of money. In our example, D pro- vides the highest NPV per dollar invested, followed by E. These two projects exactly use up the $10 million budget. Between them they add $28 million to shareholder wealth. The alternative of investing in C would have added only $21 million.

Capital Rationing Economists use the term capital rationing to refer to a shortage of funds available for investment. In simple cases of capital rationing the profitability index can provide a

capital rationing Limit set on the amount of funds available for investment.

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Chapter 8 Net Present Value and Other Investment Criteria 251

measure of which projects to accept. 6 But that raises a question. Most large corpora- tions can obtain very large sums of money on fair terms and at short notice. So why does top management sometimes tell subordinates that capital is limited and that they may not exceed a specified amount of capital spending? There are two reasons.

Soft Rationing For many firms the limits on capital funds are “soft.” By this we mean that the capital rationing is not imposed by investors. Instead, the limits are imposed by top management. For example, suppose that you are an ambitious, upwardly mobile junior manager. You are keen to expand your part of the business, and as a result you tend to overstate the investment opportunities. Rather than trying to determine which of your many bright ideas are truly worthwhile, senior management may find it simpler to impose a limit on the amount that you and other junior managers can spend. This limit forces you to set your own priorities.

Even if capital is not rationed, other resources may be. For example, very rapid growth can place considerable strains on management and the organization. A some- what rough-and-ready response to this problem is to ration the amount of capital that the firm spends.

Hard Rationing Soft rationing should never cost the firm anything. If the lim- its on investment become so tight that truly good projects are being passed up, then management should raise more money and relax the limits it has imposed on capital spending. But what if there is “hard rationing,” meaning that the firm actually cannot raise the money it needs? In that case, it may be forced to pass up positive-NPV proj- ects. With hard rationing you may still be interested in net present value, but you now need to select the package of projects that is within the company’s resources and yet gives the highest net present value. This is when the profitability index can be useful.

Pitfalls of the Profitability Index The profitability index is sometimes used to rank projects even when there is nei- ther soft nor hard capital rationing. In this case the unwary user may be led to favor small projects over larger projects that have higher NPVs. The profitability index was designed to select projects with the most bang per buck—the greatest NPV per dollar spent. That’s the right objective when bucks are limited. When they are not, a bigger bang is always better than a smaller one, even when more bucks are spent. This is another case where project comparisons can go awry once we abandon the NPV rule. Self-Test 8.5 is a numerical example.

6 Unfortunately, when capital is rationed in more than one period, or when personnel, production capacity, or other resources are rationed in addition to capital, it isn’t always possible to get the NPV-maximizing package just by ranking projects on their profitability index. Tedious trial and error may be called for, or linear program- ming methods may be used.

Calculate the profitability indexes of the two pairs of mutually exclusive investments in Self-Tests 8.3 and 8.4. Use a 7.5% discount rate. Does the profitability index give the right ranking in each case?

Self-Test 8.5

8.4 The Payback Rule A project with a positive net present value is worth more than it costs. So whenever a firm invests in such a project, it is making its shareholders better off.

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252 Part Two Value

These days almost every large corporation calculates the NPV of proposed invest- ments, but management may also consider other criteria when making investment decisions. When properly used, the internal rate of return and profitability index lead to the same decisions as net present value. However, payback is no better than a very rough guide to an investment’s worth.

We suspect that you have often heard conversations that go something like this: “A washing machine costs about $800. But we are currently spending $6 a week, or around $300 a year, at the laundromat. So the washing machine should pay for itself in less than 3 years.” You have just encountered the payback rule.

A project’s payback period is the length of time before you recover your initial investment. For the washing machine the payback period was just under 3 years. The payback rule states that a project should be accepted if its payback period is less than a specified cutoff period. For example, if the cutoff period is 4 years, the washing machine makes the grade; if the cutoff is 2 years, it doesn’t.

As a rough rule of thumb the payback rule may be adequate, but it is easy to see that it can lead to nonsensical decisions, especially when used to compare projects. For example, compare projects F and G. Project F has a 2-year payback and a large positive NPV. Project G also has a 2-year payback but a negative NPV. Project F is clearly superior, but the payback rule ranks both equally. This is because payback does not consider any cash flows that arrive after the payback period. A firm that uses the payback criterion with a cutoff of 2 or more years would accept both F and G despite the fact that only F would increase shareholder wealth.

payback period Time until cash flows recover the initial investment in the project.

Cash Flows (dollars) Payback Period, Years

NPV at 10%Project C0 C1 C2 C3

F -2,000 +1,000 +1,000 +10,000 2 $7,249 G -2,000 +1,000 +1,000 0 2 -264 H -2,000 0 +2,000 0 2 -347

A second problem with payback is that it gives equal weight to all cash flows arriv- ing before the cutoff period, despite the fact that the more distant flows are less valu- able. For example, look at project H. It also has a payback period of 2 years, but it has an even lower NPV than project G. Why? Because its cash flows arrive later within the payback period.

To use the payback rule, a firm has to decide on an appropriate cutoff period. If it uses the same cutoff regardless of project life, it will tend to accept too many short- lived projects and reject too many long-lived ones. The payback rule will bias the firm against accepting long-term projects because cash flows that arrive after the payback period are ignored.

Earlier in the chapter we evaluated the Cape Wind project. Large construction proj- ects of this kind inevitably have long payback periods. The cash flows that we pre- sented in Table 8.1 implied a payback period of nearly 7 years from the initial outlay. But most firms that employ the payback rule use a shorter cutoff period than this. If they used the payback rule mechanically, long-lived projects like Cape Wind wouldn’t have a chance.

The primary attraction of the payback criterion is its simplicity. But remember that the hard part of project evaluation is forecasting the cash flows, not doing the arithme- tic. Today’s spreadsheets make discounting a trivial exercise. Therefore, the payback rule saves you only the easy part of the analysis.

We have had little good to say about payback. So why do many companies continue to use it? Senior managers don’t truly believe that all cash flows after the payback period are irrelevant. It seems more likely (and more charitable to those managers) that payback survives because there are some offsetting benefits. Thus managers may point out that payback is the simplest way to communicate an idea of project desirability.

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Chapter 8 Net Present Value and Other Investment Criteria 253

Investment decisions require discussion and negotiation between people from all parts of the firm, and it is important to have a measure that everyone can understand. Per- haps, also, managers favor quick payback projects even when the projects have lower NPVs because they believe that quicker profits mean quicker promotion. That takes us back to Chapter 1, where we discussed the need to align the objectives of managers with those of the shareholders.

In practice payback is most commonly used when the capital investment is small or when the merits of the project are so obvious that more formal analysis is unnecessary. For example, if a project is expected to produce constant cash flows for 10 years and the payback period is only 2 years, the project in all likelihood has a positive NPV.

Discounted Payback Sometimes managers calculate the discounted-payback period. This is the number of periods before the present value of prospective cash flows equals or exceeds the initial investment. The discounted-payback measure asks, How long must the project last in order to offer a positive net present value? If the discounted payback meets the com- pany’s cutoff period, the project is accepted; if not, it is rejected. The discounted-pay- back rule has the advantage that it will never accept a negative-NPV project. On the other hand, it still takes no account of cash flows after the cutoff date, so a company that uses the discounted-payback rule risks rejecting good long-term projects and can easily misrank competing projects.

Rather than automatically rejecting any project with a long discounted-payback period, many managers simply use the measure as a warning signal. These managers don’t unthinkingly reject a project with a long discounted-payback period. Instead, they check that the proposer is not unduly optimistic about the project’s ability to generate cash flows into the distant future. They satisfy themselves that the equipment truly has a long life or that competitors will not enter the market and eat into the proj- ect’s cash flows.

A project costs $5,000 and will generate annual cash flows of $660 for 20 years. What is the payback period? If the interest rate is 6%, what is the discounted payback period? What is the project NPV? Should the project be accepted?

Self-Test 8.6

8.5 More Mutually Exclusive Projects We’ve seen that almost all real-world decisions entail either-or choices among com- peting alternatives. A real estate developer can build an apartment block or an office block on an available lot. Either can be heated with oil or with natural gas. Building can start today or a year from now. All of these choices are said to be mutually exclu- sive. When choosing among mutually exclusive projects, we must calculate the NPV of each alternative and choose the one with the highest positive NPV.

Sometimes it is enough simply to compare the NPV of two or more projects. But in other cases, choices you make today will affect your future investment opportuni- ties. In that event, choosing between competing projects can be trickier. Here are three important, but often challenging, problems:

• The investment timing problem. Should you buy a computer now or wait and think about it again next year? (Here, today’s investment is competing with possible future investments.)

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254 Part Two Value

• The choice between long- and short-lived equipment. Should the company save money today by installing cheaper machinery that will not last as long? (Here, today’s decision would accelerate a later investment in machine replacement.)

• The replacement problem. When should existing machinery be replaced? (Using it another year could delay investment in more modern equipment.)

We will look at each of these problems in turn.

Problem 1: The Investment Timing Decision In Example 8.1 Obsolete Technologies is contemplating the purchase of a new com- puter system. The proposed investment has a net present value of almost $20,000, so it appears that the cost savings would easily justify the expense of the system. How- ever, the financial manager is not persuaded. She reasons that the price of comput- ers is continually falling and therefore suggests postponing the purchase, arguing that the NPV of the system will be even higher if the firm waits until the following year. Unfortunately, she has been making the same argument for 10 years, and the company is steadily losing business to competitors with more efficient systems. Is there a flaw in her reasoning?

This is a problem in investment timing. When is it best to commit to a positive-NPV investment? Investment timing problems all involve choices among mutually exclusive investments. You can either proceed with the project now or do so later. You can’t do both.

Table 8.2 lays out the basic data for Obsolete. You can see that the cost of the com- puter is expected to decline from $50,000 today to $45,000 next year, and so on. The new computer system is expected to last for 4 years from the time it is installed. The present value of the savings at the time of installation is expected to be $70,000. Thus, if Obsolete invests today, it achieves an NPV of $70,000  -  $50,000  =  $20,000; if it invests next year, it will have an NPV of $70,000  -  $45,000  =  $25,000.

Isn’t a gain of $25,000 better than one of $20,000? Well, not necessarily—you may prefer to be $20,000 richer today than $25,000 richer next year. Your decision should depend on the cost of capital. The fourth column of Table 8.2 shows the value today (year 0) of those net present values at a 10% cost of capital. For example, you can see that the discounted value of that $25,000 gain is $25,000/1.10  =  $22,700. The finan- cial manager has a point. It is worth postponing investment in the computer: Today’s NPV is higher if she waits a year. But the investment should not be postponed indefi- nitely. You maximize net present value today by buying the computer in year 3.

Notice that you are involved in a trade-off. The sooner you can capture the $70,000 savings the better, but if it costs you less to realize those savings by postponing the investment, it may pay for you to wait. If you postpone purchase by 1 year, the gain from buying a computer rises from $20,000 to $25,000, an increase of 25%. Since the cost of capital is only 10%, it pays to postpone at least until year 1. If you postpone from year 3 to year 4, the gain rises from $34,000 to $37,000, a rise of just under 9%. Since this is less than the cost of capital, this postponement would not make sense. The decision rule for investment timing is to choose the investment date that produces the highest net present value today .

Investment timing decisions

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Unfortunately, Obsolete Technologies’ business is shrinking as the company dithers and dawdles. Its chief financial officer realizes that the savings from installing the new computer will likewise shrink by $4,000 per year, from a present value of $70,000 now, to $66,000 next year, then to $62,000, and so on. Redo Table 8.2 with this new information. When should Obsolete buy the new computer?

Self-Test 8.7

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Chapter 8 Net Present Value and Other Investment Criteria 255

Problem 2: The Choice between Long- and Short-Lived Equipment Suppose the firm is forced to choose between two machines, I and J. The machines are designed differently but have identical capacity and do exactly the same job. Machine I costs $15,000 and will last 3 years. It costs $4,000 per year to run. Machine J is an “economy” model, costing only $10,000, but it will last only 2 years and costs $6,000 per year to run.

Because the two machines produce exactly the same product, the only way to choose between them is on the basis of cost. Suppose we compute the present value of the costs:

Year of Purchase

Cost of Computer PV Savings

NPV at Year of Purchase  ( r     =  10%) NPV Today

0 $50 $70 $20 $20.0 1 45 70 25 22.7 2 40 70 30 24.8 3 36 70 34 25.5 ←⎯ optimal purchase date 4 33 70 37 25.3 5 31 70 39 24.2

TABLE 8.2 Obsolete Technologies: The gain from purchase of a computer is rising, but the NPV today is highest if the computer is purchased in year 3 (dollar values in thousands).

Costs (thousands of dollars)

Year: 0 1 2 3 PV at 6%

Machine I 15 4 4 4 $25.69 Machine J 10 6 6 — 21.00

Costs (thousands of dollars)

Year: 0 1 2 3 PV at 6%

Machine I 15 4 4 4 $25.69 Equivalent annual annuity 9.61 9.61 9.61 25.69

Should we take machine J, the one with the lower present value of costs? Not nec- essarily. All we have shown is that machine J offers 2 years of service for a lower total cost than 3 years of service from machine I. But is the annual cost of using J lower than that of I?

Suppose the financial manager in corporate headquarters agrees to buy machine I and pay for its operating costs out of her budget. She then charges the plant manager an annual amount for use of the machine. There will be three equal payments starting in year 1. Obviously, the financial manager has to make sure that the present value of these payments equals the present value of the costs of machine I, $25,690. When the discount rate is 6%, the payment stream with such a present value turns out to be $9,610 a year. In other words, the cost of buying and operating machine I over its 3-year life is equivalent to an annual charge of $9,610 a year for 3 years. This figure is therefore termed the equivalent annual annuity of operating machine I. equivalent annual annuity

The cash flow per period with the same present value as the cost of buying and operating a machine.

How did we know that an annual charge of $9,610 has a present value of $25,690? The annual charge is a 3-year annuity. So we calculate the value of this annuity and set it equal to $25,690:

Equivalent annual annuity × 3-year annuity factor = PV of costs = $25,690

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256 Part Two Value

If the cost of capital is 6%, the 3-year annuity factor is 2.6730. So

Equivalent annual annuity = PV of costs

3-year annuity factor (8.3)

= $25,690

3-year annuity factor =

$25,690

2.6730 = $9,610

If we make a similar calculation of costs for machine J, we get:

Costs (thousands of dollars)

Year: 0 1 2 PV at 6%

Machine J 10 6 6 $21.00 Equivalent annual annuity 11.45 11.45 21.00

We see now that machine I is better, because its equivalent annual annuity is less ($9,610 for I versus $11,450 for J). In other words, the financial manager could afford to set a lower annual charge for the use of I. We thus have a rule for comparing assets with different lives: Select the machine that has the lowest equivalent annual annuity .

Think of the equivalent annual annuity as the level annual charge that is necessary to recover the present value of investment outlays and operating costs. 7 The annual charge continues for the life of the equipment. Calculate the equivalent annual annuity by dividing the present value by the annuity factor.

7 We have implicitly assumed that inflation is zero. If that is not the case, it would be better to calculate the equiv- alent annuities for machines I and J in real terms, using the real rate of interest to calculate the annuity factor.

Equivalent annual annuities

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Example 8.4 Equivalent Annual Annuity You need a new car. You can either purchase one outright for $15,000 or lease one for 7 years for $3,000 a year. If you buy the car today, you can sell it in 7 years for $500. The discount rate is 10%. Should you buy or lease? What is the maximum lease payment you would be willing to pay?

The present value of the cost of purchasing is

PV = $15,000 - $500

(1.10)7 = $14,743

The equivalent annual cost of purchasing the car is therefore the annuity with this present value:

Equivalent annual annuity × 7-year annuity factor at 10% = PV costs of buying

= $14,743

Equivalent annual annuity = $14,743

7-year annuity factor =

$14,743 4.8684

= $3,028

Therefore, the annual lease payment of $3,000 is less than the equivalent annual annuity of buying the car. You should be willing to pay up to $3,028 annually to lease.

Example 8.5 Another Equivalent Annual Annuity Low-energy lightbulbs typically cost $3.50, have a life of 9 years, and use about $1.60 of electricity a year. Conventional lightbulbs are cheaper to buy, for they cost only $.50. On the other hand, they last only about a year and use about $6.60 of energy. If the discount rate is 5%, which product is cheaper to use?

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Chapter 8 Net Present Value and Other Investment Criteria 257

Problem 3: When to Replace an Old Machine Our earlier comparison of machines I and J took the life of each machine as fixed. In practice, the point at which equipment is replaced reflects economics, not physical collapse. We usually decide when to replace. For example, we usually replace a car not when it finally breaks down but when it becomes more expensive and troublesome to keep up than a replacement.

Here is an example of a replacement problem: You are operating an old machine that will last 2 more years before it gives up the ghost. It costs $12,000 per year to operate. You can replace it now with a new machine that costs $25,000 but is much more efficient (only $8,000 per year in operating costs) and will last for 5 years. Should you replace the machine now or stick with it for a while longer? The opportunity cost of capital is 6%.

We calculate the NPV of the new machine and its equivalent annual annuity in the following table:

To answer this question, you need first to convert the initial cost of each bulb to an annual figure and then to add in the annual energy cost. 8 The following table sets out the calculations:

8 Our calculations ignore any environmental costs.

Low-Energy Bulb Conventional Bulb

1. Initial cost, $ 3.50 0.50

2. Estimated life, years 9 1 3. Annuity factor at 5% 7.1078 .9524 4. Equivalent annual annuity, $, =(1)/(3) .49 .52 5. Annual energy cost, $ 1.60 6.60 6. Total annual cost, $, = (4) + (5) 2.09 7.12 Assumption: Energy costs are incurred at the end of each year.

It seems that a low-energy bulb provides an annual saving of about $7.12  -  $2.09 =  $5.03.

Costs (thousands of dollars)

Year: 0 1 2 3 4 5 PV at 6%

New machine 25 8 8 8 8 8 $58.70 Equivalent annual annuity 13.93 13.93 13.93 13.93 13.93 58.70

The cash flows of the new machine are equivalent to an annuity of $13,930 per year. So we can equally well ask whether you would want to replace your old machine, which costs $12,000 a year to run, with a new one costing $13,930 a year. When the question is posed this way, the answer is obvious. As long as your old machine costs only $12,000 a year, why replace it with a new machine that costs $1,930 a year more?

Year: 0 1 2 3

K $10,000 $1,100 $1,200 — L 12,000 1,100 1,200 $1,300

Machines K and L are mutually exclusive and have the following investment and operating costs. Note that machine K lasts for only 2 years.

Self-Test 8.8

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258 Part Two Value

8.6 A Last Look We’ve covered several investment criteria, each with its own nuances. If your head is spinning, you might want to take a look at Table 8.3 , which gives an overview and summary of these decision rules.

Clearly, NPV is the gold standard. It is designed to tell you whether an investment will increase the value of the firm and by how much it will do so. It is the only rule that can always be used to rank and choose among mutually exclusive investments. The only instance in which NPV fails as a decision rule occurs when the firm faces capital rationing. In this case, there may not be enough cash to take every project with positive NPV, and the firm must then rank projects by the profitability index, that is, net present value per dollar invested.

For managers in the field, discounted cash-flow analysis is in fact the dominant tool for project evaluation. Table 8.4 provides a sample of the results of a large survey of CFOs. Notice that 75% of firms either always or almost always use NPV or IRR to evaluate projects. The dominance of these criteria is even stronger among larger, pre- sumably more sophisticated, firms. Despite the clear advantages of discounted cash- flow methods, however, firms do use other investment criteria to evaluate projects. For example, just over half of corporations always or almost always compute a project’s payback period. Profitability index is routinely computed by about 12% of firms.

What explains such wide use of presumably inferior decision rules? To some extent, these rules present rough reality checks on the project. As we noted in Section 8.4, managers might want to consider some simple ways to describe project profitabil- ity, even if they present obvious pitfalls. For example, managers talk casually about

a. Calculate the equivalent annual annuity of each investment by using a dis- count rate of 10%. Which machine is the better buy?

b. Now suppose you have an existing machine. You can keep it going for 1 more year only, but it will cost $2,500 in repairs and $1,800 in operating costs. Is it worth replacing now with either K or L?

TABLE 8.3 A comparison of investment decision rules

Criterion Defi nition Investment Rule Comments

Net present value (NPV)

Present value of cash infl ows minus present value of cash outfl ows

Accept project if NPV is positive. For mutually exclusive projects, choose the one with the highest (positive) NPV.

The “gold standard” of investment criteria. Only criterion necessarily consistent with maximizing the value of the fi rm. Provides appropriate rule for choosing among mutually exclusive investments. Only pitfall involves capital rationing, when one cannot accept all positive-NPV projects.

Internal rate of return (IRR)

The discount rate at which project NPV equals zero

Accept project if IRR is greater than opportunity cost of capital.

If used properly, results in same accept-reject decision as NPV in the absence of project interactions. However, beware of the following pitfalls: IRR cannot rank mutually exclusive projects—the project with higher IRR may have lower NPV. The simple IRR rule cannot be used in cases of multiple IRRs or an upward-sloping NPV profi le.

Profi tability index Ratio of net present value to initial investment

Accept project if profi tability index is greater than 0. In case of capital rationing, accept projects with highest profi tability index.

Results in same accept-reject decision as NPV in the absence of project interactions. Useful for ranking projects in case of capital rationing, but misleading in the presence of interactions. Cannot rank mutually exclusive projects.

Payback period Time until the sum of project cash fl ows equals the initial investment

Accept project if payback period is less than some specifi ed number of years.

A quick and dirty rule of thumb, with several critical pitfalls. Ignores cash fl ows beyond the acceptable payback period. Ignores discounting. Tends to improperly reject long-lived projects.

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Chapter 8 Net Present Value and Other Investment Criteria 259

quick-payback projects in the same way that investors talk about high-P/E stocks. The fact that they talk about payback does not mean that the payback rule governs their decisions. Shortcuts like payback may work for very simple go-or-no-go decisions, but they are dangerous when used to compare projects.

SUMMARY The net present value of a project measures the difference between its value and cost. NPV is therefore the amount that the project will add to shareholder wealth. A company maximizes shareholder wealth by accepting all projects that have a positive NPV.

Instead of asking whether a project has a positive NPV, many businesses prefer to ask whether it offers a higher return than shareholders could expect to get by investing in the capital market. Return is usually defined as the discount rate that would result in a zero NPV. This is known as the internal rate of return, or IRR. The project is attractive if the IRR exceeds the opportunity cost of capital.

There are some pitfalls in using the internal rate of return rule. Be careful about using the IRR when (1) you need to choose between two mutually exclusive projects, (2) there is more than one change in the sign of the cash flows, or (3) the early cash flows are positive.

If there is a shortage of capital, companies need to choose projects that offer the highest net present value per dollar of investment. This measure is known as the profitability index.

The net present value rule and the rate of return rule both properly reflect the time value of money. But companies sometimes use rules of thumb to judge projects. One is the payback rule, which states that a project is acceptable if you get your money back within a specified period. The payback rule takes no account of any cash flows that arrive after the payback period and fails to discount cash flows within the payback period.

Sometimes a project may have a positive NPV if undertaken today but an even higher NPV if the investment is delayed. Choose between these alternatives by comparing their NPVs today.

When you have to choose between projects with different lives, you should put them on an equal footing by comparing the equivalent annual annuity of the two projects. When you are considering whether to replace an aging machine with a new one, you should compare the annual cost of operating the old one with the equivalent annual annuity of the new one.

What is the net present value of an investment, and how do you calculate it? ( LO8-1 )

How is the internal rate of return of a project calculated, and what must one look out for when using the internal rate of return rule? ( LO8-2 )

How is the profitability index calculated, and how can it be used to choose between projects when funds are limited? ( LO8-3 )

Why doesn’t the payback rule always make shareholders better off? ( LO8-4 )

How can the net present value rule be used to analyze three common problems that involve competing projects: when to postpone an investment expenditure; how to choose between projects with unequal lives; and when to replace equipment? ( LO8-5 )

TABLE 8.4 Capital budgeting techniques used in practice

Source: Reprinted from the Journal of Financial Economics, Vol. 60, Issue 2–3, J. R. Graham and C. R. Harvey, “The Theory and Practice of Corporate Finance: Evidence from the Field,” May 2001, pp. 187–243. © 2001 with permission from Elsevier Science.

Investment Criterion

Percentage of Firms That Always or Almost Always Use Criterion

Average Score on 0–4 Scale  (0   =    never use; 4   =  always use)

All Firms Small Firms Large Firms

Internal rate of return 76 3.1 2.9 3.4

Net present value 75 3.1 2.8 3.4

Payback period 57 2.5 2.7 2.3

Profi tability index 12 0.8 0.9 0.8

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260 Part Two Value

1. IRR/NPV. If the opportunity cost of capital is 11%, which of these projects is worth pursuing? (LO8-1)

2. Mutually Exclusive Investments. Suppose that you can choose only one of these projects. Which would you choose? The discount rate is still 11%. (LO8-1)

3. IRR/NPV. Which project would you choose if the opportunity cost of capital were 16%? (LO8-1)

4. IRR. What are the internal rates of return on projects A and B? (LO8-2)

5. Investment Criteria. In light of your answers to Problems 2–4, is there any reason to believe that the project with the higher IRR is the better project? (LO8-2)

6. Profitability Index. If the opportunity cost of capital is 11%, what is the profitability index for each project? Is the project with the highest profitability index also the one with the highest NPV? Which criterion should you use? (LO8-3)

7. Payback. What is the payback period of each project? (LO8-4)

8. Investment Criteria. Is the project with the shortest payback period also the one with the high- est NPV? Which criterion should you use? (LO8-4)

9. NPV and IRR. A project that costs $3,000 to install will provide annual cash flows of $800 for each of the next 6 years. What is NPV if the discount rate is 10%? Is this project worth pursu- ing? How high can the discount rate be before you would reject the project? (LO8-1)

10. NPV. A proposed nuclear power plant will cost $2.2 billion to build and then will produce cash flows of $300 million a year for 15 years. After that period (in year 15), it must be decommis- sioned at a cost of $900 million. What is project NPV if the discount rate is 5%? What if it is 18%? (LO8-1)

11. NPV/IRR. A new computer system will require an initial outlay of $20,000, but it will increase the firm’s cash flows by $4,000 a year for each of the next 8 years. Is the system worth installing if the required rate of return is 9%? What if it is 14%? How high can the discount rate be before you would reject the project? (LO8-1)

L I S T I N G O F E Q UAT I O N S

8.1 NPV  =  PV  -  required investment

8.2 Profitability index = net present value

initial investment

8.3 Equivalent annual annuity = present value of costs

annuity factor

QUESTIONS AND PROBLEMS Problems 1–8 refer to two projects with the following cash flows:

finance

®

Year Project A Project B

0 -$200 -$200 1 80 100 2 80 100 3 80 100 4 80

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Chapter 8 Net Present Value and Other Investment Criteria 261

13. NPV versus IRR. Here are the cash flows for two mutually exclusive projects: (LO8-1 and LO8-2)

Project C0 C1 C2 C3 A -$20,000 +$8,000 +$8,000 +$ 8,000 B - 20,000 0 0 + 25,000

12. NPV/IRR. Here are the cash flows for a project under consideration: (LO8-1 and LO8-2)

a. Calculate the project’s net present value for discount rates of 0, 50%, and 100%. b. What is the IRR of the project?

C0 C1 C2

-$6,750 +$4,500 +$18,000

a. At what interest rates would you prefer project A to B? ( Hint: Try drawing the NPV profile of each project.)

b. What is the IRR of each project?

14. IRR/NPV. Consider this project with an internal rate of return of 13.1%. Should you accept or reject the project if the discount rate is 12%? What is project NPV? (LO8-2)

Year Cash Flow

0 +$100 1 -60

2 -60

15. IRR. Marielle Machinery Works forecasts the following cash flows on a project under consid- eration. It uses the internal rate of return rule to accept or reject projects. Find IRR. Should this project be accepted if the required return is 12%? (LO8-3)

C0 C1 C2 C3 -$10,000 0 +$7,500 +$8,500

16. NPV/IRR. Consider projects A and B:

Calculate IRRs for A and B. Which project does the IRR rule suggest is best? Which project is really best? (LO8-3)

17. IRR. You are offered the chance to participate in a project that produces the following cash flows:

C0 C1 C2 +$5,000 +$4,000 -$11,000

The internal rate of return is 13.6%. If the opportunity cost of capital is 12%, would you accept the offer? (What is the net present value of the project?) (LO8-3)

Cash Flows (dollars)

Project C0 C1 C2 NPV at 10%

A -30,000 21,000 21,000 +$6,446 B -50,000 33,000 33,000 + 7,273

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262 Part Two Value

18. Multiple IRR. Consider the following cash flows: (LO8-3)

C0 C1 C2 C3 C4 -$22 +$20 +$20 +$20 -$40

a. Confirm that one internal rate of return on this project is (a shade above) 7% and that the other is (a shade below) 34%.

b. What is project NPV if the discount rate is 5%? c. What if it is 20%? 40%? d. Why is NPV positive at midrange discount rates but not at very high or very low rates?

19. Profitability Index. What is the profitability index of a project that costs $10,000 and provides cash flows of $3,000 in years 1 and 2 and $5,000 in years 3 and 4? The discount rate is 9%. (LO8-3)

20. Profitability Index. Consider the following projects: (LO8-3)

Project C0 C1 C2 A -$2,100 +$2,000 +$1,200

B - 2,100 + 1,440 + 1,728

a. Calculate the profitability index for A and B assuming a 22% opportunity cost of capital. b. According to the profitability index rule, which project(s) should you accept?

21. Capital Rationing. You are a manager with an investment budget of $8 million. You may invest in the following projects. Investment and cash-flow figures are in millions of dollars. (LO8-3)

Project Discount Rate, % Investment

Annual Cash Flow

Project Life, Years

A 10 3 1 5 B 12 4 1 8 C 8 5 2 4 D 8 3 1.5 3 E 12 3 1 6

a. Why might these projects have different discount rates? b. Which projects should the manager choose? c. Which projects will be chosen if there is no capital rationing?

22. Profitability Index versus NPV. Consider projects A and B with the following cash flows: (LO8-3)

C0 C1 C2 C3 A -$36 +$20 +$20 +$20

B - 50 + 25 + 25 + 25

a. Which project has the higher NPV if the discount rate is 10%? b. Which has the higher profitability index? c. Which project is most attractive to a firm that can raise an unlimited amount of funds to pay

for its investment projects? Which project is most attractive to a firm that is limited in the funds it can raise?

23. Investment Criteria. If you insulate your office for $10,000, you will save $1,000 a year in heating expenses. These savings will last forever. (LO8-1, LO8-2, and LO8-4)

a. What is the NPV of the investment when the cost of capital is 8%? 10%? b. What is the IRR of the investment? c. What is the payback period on this investment?

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Chapter 8 Net Present Value and Other Investment Criteria 263

24. Payback. A project that costs $2,500 to install will provide annual cash flows of $600 for the next 6 years. (LO8-4)

a. The firm accepts projects with payback periods of less than 5 years. What is this project’s payback period? Will it be accepted?

b. Should this project be pursued if the discount rate is 2%? (What is its NPV?) What if the discount rate is 12%? Will the firm’s decision change as the discount rate changes?

25. Payback and NPV. A project has a life of 10 years and a payback period of 10 years. What must be true of project NPV? (LO8-4)

26. Payback and NPV. Here are the expected cash flows for three projects: (LO8-4)

Cash Flows (dollars)

Project Year: 0 1 2 3 4

A -5,000 +1,000 +1,000 +3,000 0

B -1,000 0 +1,000 +2,000 +3,000

C -5,000 +1,000 +1,000 +3,000 +5,000

a. What is the payback period on each of the projects? b. Given that you wish to use the payback rule with a cutoff period of 2 years, which projects

would you accept? c. If you use a cutoff period of 3 years, which projects would you accept? d. If the opportunity cost of capital is 10%, which projects have positive NPVs? e. “Payback gives too much weight to cash flows that occur after the cutoff date.” True or

false?

27. Mutually Exclusive Investments. Here are the cash-flow forecasts for two mutually exclusive projects: (LO8-5)

Cash Flows (dollars)

Year Project A Project B

0 -100 -100 1 30 49 2 50 49 3 70 49

a. Which project would you choose if the opportunity cost of capital is 2%? b. Which would you choose if the opportunity cost of capital is 12%? c. Why does your answer change?

28. Equivalent Annual Annuity. A precision lathe costs $10,000 and will cost $20,000 a year to operate and maintain. If the discount rate is 10% and the lathe will last for 5 years, what is the equivalent annual cost of the tool? (LO8-5)

29. Equivalent Annual Annuity. A firm can lease a truck for 4 years at a cost of $30,000 annually. It can instead buy a truck at a cost of $80,000, with annual maintenance expenses of $10,000. The truck will be sold at the end of 4 years for $20,000. What is the equivalent annual cost of buying and maintaining the truck if the discount rate is 10%? Which is the better option: leasing or buying? (LO8-5)

30. Equivalent Annual Annuity. Econo-Cool air conditioners cost $300 to purchase, result in elec- tricity bills of $150 per year, and last for 5 years. Luxury Air models cost $500, result in elec- tricity bills of $100 per year, and last for 8 years. The discount rate is 21%. (LO8-5)

a. What are the equivalent annual costs of the Econo-Cool and Luxury Air models? b. Which model is more cost-effective? c. Now you remember that the inflation rate is expected to be 10% per year for the foreseeable

future. Redo parts (a) and (b).

31. Investment Timing. You can purchase an optical scanner today for $400. The scanner provides benefits worth $60 a year. The expected life of the scanner is 10 years. Scanners are expected to decrease in price by 20% per year. Suppose the discount rate is 10%. Should you purchase the scanner today or wait to purchase? When is the best purchase time? (LO8-5)

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264 Part Two Value

32. Replacement Decision. You are operating an old machine that is expected to produce a cash inflow of $5,000 in each of the next 3 years before it fails. You can replace it now with a new machine that costs $20,000 but is much more efficient and will provide a cash flow of $10,000 a year for 4 years. Should you replace your equipment now? The discount rate is 15%. (LO8-5)

33. Replacement Decision. A forklift will last for only 2 more years. It costs $5,000 a year to maintain. For $20,000 you can buy a new lift that can last for 10 years and should require main- tenance costs of only $2,000 a year. (LO8-5)

a. If the discount rate is 4% per year, should you replace the forklift? b. What if the discount rate is 12% per year? Why does your answer change?

CHALLENGE PROBLEMS 34. NPV/IRR. Growth Enterprises believes its latest project, which will cost $80,000 to install, will

generate a perpetual growing stream of cash flows. Cash flow at the end of the first year will be $5,000, and cash flows in future years are expected to grow indefinitely at an annual rate of 5%. (LO8-1 and LO8-2)

a. If the discount rate for this project is 10%, what is the project NPV? b What is the project IRR?

35. Multiple IRRs. Strip Mining Inc. can develop a new mine at an initial cost of $5 million. The mine will provide a cash flow of $30 million in 1 year. The land then must be reclaimed at a cost of $28 million in the second year. (LO8-2)

a. What are the IRRs of this project? b. Should the firm develop the mine if the discount rate is 10%? 20%? 350%? 400%?

36. Investment Criteria. A new furnace for your small factory will cost $27,000 a year to install and will require ongoing maintenance expenditures of $1,500 a year. But it is far more fuel- efficient than your old furnace and will reduce your consumption of heating oil by 2,400 gallons per year. Heating oil this year will cost $3 a gallon; the price per gallon is expected to increase by $.50 a year for the next 3 years and then to stabilize for the foreseeable future. The furnace will last for 20 years, at which point it will need to be replaced and will have no salvage value. The discount rate is 8%. (LO8-1, LO8-2, LO8-4, and LO8-5)

a. What is the net present value of the investment in the furnace? b. What is the IRR? c. What is the payback period? d. What is the equivalent annual cost of the furnace? e. What is the equivalent annual savings derived from the furnace? f. Compare the PV of the difference between the equivalent annual cost and savings to your

answer to part (a).

37. Investment Timing. A classic problem in management of forests is determining when it is most economically advantageous to cut a tree for lumber. When the tree is young, it grows very rap- idly. As it ages, its growth slows down. Why is the NPV-maximizing rule to cut the tree when its growth rate equals the discount rate? (LO8-5)

SOLUTIONS TO SELF-TEST QUESTIONS 8.1 Even if construction costs are $355,000, NPV is still positive:

NPV = PV - $355,000 = $357,143 - $355,000 = $2,143

Therefore, the project is still worth pursuing. The project is viable as long as construction costs are less than the PV of the future cash flow, that is, as long as construction costs are less than $357,143. However, if the opportunity cost of capital is 20%, the PV of the $400,000 sales price is lower and NPV is negative:

PV = $400,000 × 1

1.20 = $333,333

NPV = PV - $355,000 = -$21,667

Templates can be found in Connect.

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Chapter 8 Net Present Value and Other Investment Criteria 265

The present value of the future cash flow is not as high when the opportunity cost of capital is higher. The project would need to provide a higher payoff in order to be viable in the face of the higher opportunity cost of capital.

8.2 The IRR is now about 8.3% because

NPV = -$375,000 + $25,000

1.083 +

$25,000 (1.083)2

+

$420,000 (1.083)3

= 0

Note in Figure 8.6 that NPV falls to zero as the discount rate reaches 8.3%.

8.3 You want to be rich. The NPV of the long-lived investment is much larger.

Short: NPV = -$1 + $2

1.075 = +$.8605 million

Long: NPV = -$1 + $.3

.075 = +$3 million

8.4 You want to be richer. The second alternative generates greater value at any reasonable discount rate. Other risk-free investments offer 7.5%. Therefore,

NPV = -$1,000 + $4,000

1.075 = +$2,721

NPV = -$1,000,000 + $1,500,000

1.075 = +$395,349

8.5 The profitability index gives the correct ranking for the first pair, but the incorrect ranking for the second:

Project PV Investment NPV Profi tability Index (NPV/Investment)

Short $1,860,500 $1,000,000 $ 860,500 0.86 Long 4,000,000 1,000,000 3,000,000 3.0 Small 3,721 1,000 2,721 2.7 Large 1,395,349 1,000,000 395,349 0.395

8.6 The payback period is $5,000/$660  =  7.6 years. Discounted payback is just over 11 years. Calculate NPV as follows. The present value of a $660 annuity for 20 years at 6% is

PV annuity = $7,570

NPV = -$5,000 + $7,570 = +$2,570

The project should be accepted.

FIGURE 8.6 NPV falls to zero at an interest rate of 8.3%.

N et

p re

se n

t va

lu e

($ t

h o

u sa

n d

s)

Discount rate (%)

-250

-200

-150

-100

-50

0

50

100

120 4 8 2016 24 32 36 40 4428 48

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266 Part Two Value

8.7

Year of Purchase

Cost of Computer PV Savings

NPV at Year of Purchase NPV Today

0 $50 $70 $20 $20 1 45 66 21 19.1 2 40 62 22 18.2 3 36 58 22 16.5 4 33 54 21 14.3 5 31 50 19 11.8

Purchase the new computer now.

8.8

Year: 0 1 2 3 PV of Costs

K Cash fl ows $10,000 $1,100 $1,200 $11,992 Equivalent annual annuity 6,910 6,910 11,992 L Cash fl ows 12,000 1,100 1,200 $1,300 14,968 Equivalent annual annuity 6,019 6,019 6,019 14,968

Machine L is the better buy. However, it’s even better to keep the old machine going for 1 more year. That costs $4,300, which is less than L’s equivalent annual cost, $6,019.

MINICASE Flowton Products enjoys a steady demand for stainless steel infil- trators used in a number of chemical processes. Revenues from the infiltrator division are $50 million a year and production costs are $47.5 million. However, the 10 high-precision Munster stamp- ing machines that are used in the production process are coming to the end of their useful life. One possibility is simply to replace each existing machine with a new Munster. These machines would cost $800,000 each and would not involve any additional operat- ing costs. The alternative is to buy 10 centrally controlled Skilboro stampers. Skilboros cost $1.25 million each, but compared to the Munster, they would produce a total saving in operator and mate- rial costs of $500,000 a year. Moreover, the Skilboro is sturdily built and would last 10 years, compared with an estimated 7-year life for the Munster.

Analysts in the infiltrator division have produced the accom- panying summary table, which shows the forecast total cash flows from the infiltrator business over the life of each machine. Flowton’s standard procedures for appraising capital investments

involve calculating net present value, internal rate of return, and payback, and these measures are also shown in the table.

As usual, Emily Balsam arrived early at Flowton’s head office. She had never regretted joining Flowton. Everything about the place, from the mirror windows to the bell fountain in the atrium, suggested a classy outfit. Ms. Balsam sighed happily and reached for the envelope at the top of her in-tray. It was an analysis from the infiltrator division of the replacement options for the stamper machines. Pinned to the paper was the summary table of cash flows and a note from the CFO, which read, “Emily, I have read through 20 pages of excruciating detail and I still don’t know which of these machines we should buy. The NPV calculation seems to indi- cate that the Skilboro is best, while IRR and payback suggest the opposite. Would you take a look and tell me what we should do and why. You also might check that the calculations are OK.”

Can you help Ms. Balsam by writing a memo to the CFO? You need to justify your solution and also to explain why some or all of the measures in the summary table are inappropriate.

SOLUTIONS TO SPREADSHEET QUESTIONS 1. NPV is zero at .10385, or 10.385%. This is Cape Wind’s IRR.

2. The answer is 8% lower at 596.4. The Excel function treats the initial cash flow as if it occurs at the end of 1 year, and discounts each successive cash flow by an extra year.

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Appendix 267

Cash Flows (millions of dollars)

Year: 0 1–7 8 9 10

Munster Investment -8.0 Revenues 50.0 0 0 0 Costs 47.5 0 0 0 Net cash fl ow -8.0 2.5 0 0 0 NPV at 15% $2.40 million IRR 24.5% Payback period 3.2 years Skilboro Investment -12.5 Revenues 50.0 50.0 50.0 50.0 Costs 47.0 47.0 47.0 47.0 Net cash fl ow -12.5 3.0 3.0 3.0 3.0 NPV at 15% $2.56 million IRR 20.2% Payback period 4.2 years

More on the IRR Rule

In Section 8.2 we described several pitfalls that lie in wait for users of the IRR rule. However, there are some tricks that users of the rule may use to circumvent these hazards. In this appendix we show how you can adapt the IRR rule when you need to choose between competing projects or when there are multiple IRRs.

Using the IRR to Choose between Mutually Exclusive Projects

When you need to choose between mutually exclusive projects, a simple comparison of internal rates of return is liable to lead to poor decisions. We illustrated this by looking at two office building projects. Your initial proposal involved constructing the office building and then selling it. Under the revised proposal you would construct a more expensive building and rent it out before selling it at the end of 3 years. The cash flows from the two projects were as follows:

APPENDIX

Cash Flows

C0 C1 C2 C3 IRR NPV at 7%

Initial proposal -350,000 +400,000 14.29% +$23,832

Revised proposal -375,000 +25,000 +25,000 +475,000 12.56% +$57,942

Although the initial proposal has the higher IRR, it has the lower net present value. If you were misled into choosing the initial rather than the revised proposal, you would have been more than $30,000 poorer.

You can salvage the IRR rule in these cases; you do so by calculating the IRR on the incremen- tal cash flows, that is, the difference in cash flows between the two projects. Start with the smaller project, where you plan to invest $350,000 and sell the office building after 1 year. It has an IRR of 14.29%, which is well in excess of the 7% cost of capital. So you know that it is worthwhile. You

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268 Part Two Value

now ask yourself whether it is worth investing the additional $25,000 and renting out the building for 3 years. Here are the incremental cash flows from doing so, together with their IRR and NPV:

Cash Flows: C0 C1 C2 C3 IRR NPV at 7%

Incremental cash fl ows

-25,000 -375,000 +25,000 +475,000 11.72% +$34,110

The IRR on the incremental cash flows is 11.72%. Since this is greater than the opportunity cost of capital, you should prefer the revised proposal.

Using the Modified Internal Rate of Return When There Are Multiple IRRs

Whenever there is more than one change in the sign of the cash flows, there is generally more than one internal rate of return and therefore no simple IRR rule. Companies sometimes get around this problem by calculating a modified IRR (MIRR), which can then be compared with the cost of capital.

Think back to King Coal’s strip-mining project. Its cash flows are as follows:

Cash Flows: C0 C1 C2 C3 C4 C5 Cash fl ows, $ millions

-210 +125 +125 +175 +175 -400

The problem with the IRR rule arises because the cash flow in year 5 is negative. So let us try replac- ing the last two cash flows with a single year-4 cash flow that has the same present value. If the cost of capital is 20%, then we can replace the cash flows in years 4 and 5 with a single cash flow in year 4 of

+175 - 400

1.20 = -158

This figure is also negative. So we still have a problem. Therefore, we need to step back a further year and combine the last three cash flows into a single year-3 cash flow with the same present value:

+175 + 175

1.20 -

400

1.202 = +43

This value is positive, so if we use it in place of the last three cash flows, we will have only one change of sign. Now we can compute IRR using the modified cash-flow sequence:

Year: 0 1 2 3 4 5

Cash fl ows, $ millions

-210 +125 +125 +43 — —

The modified IRR (MIRR) is the discount rate at which the net present value of these cash flows is zero:

-210 + 125

1 + MIRR +

125 (1 + MIRR)2

+

43 (1 + MIRR)3

= 0

We solve to find that MIRR  =  .22, or 22%, which is greater than the cost of capital of 20%. If the modified IRR is greater than the cost of capital, then the project must have a positive NPV.

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270

Using Discounted Cash-Flow Analysis to Make Investment Decisions

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

9-1 Identify the cash flows from a proposed new project.

9-2 Calculate the cash flows of a project from standard financial statements.

9-3 Understand how the company’s tax bill is affected by depreciation and how this affects project value.

9-4 Understand how changes in working capital affect project cash flows.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

9 CHAPTE R

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271

P A

R T

TW O

T hink of the problems that Toyota’s managers face when considering whether to introduce a new model. What investment must be made in new plant and equipment? What will it cost to

market and promote the new car? How soon can

the car be put into production? What is the likely

production cost? How much must be invested in

inventories of raw materials and finished cars? How

many cars can be sold each year and at what

price? What credit arrangements should be given

to dealers? How long will the model stay in produc-

tion? When production comes to an end, can the

plant and equipment be used elsewhere in the

company? All of these issues affect the level and

timing of project cash flows. In this chapter we con-

tinue our analysis of the capital budgeting decision

by turning our focus to how the financial manager

should prepare cash-flow estimates for use in net

present value analysis.

In Chapter 8 you used the net present value rule to

make a simple capital budgeting decision. You tack-

led the problem in four steps:

Step 1. Forecast the project cash flows.

Step 2. Estimate the opportunity cost of capital—

that is, the rate of return that your share-

holders could expect to earn if they

invested their money in the capital market.

Step 3. Use the opportunity cost of capital to dis-

count the future cash flows. The project’s

present value (PV) is equal to the sum of

the discounted future cash flows.

Step 4. Net present value (NPV) measures

whether the project is worth more than it

costs. To calculate NPV, you need to sub-

tract the required investment from the

present value of the future payoffs:

NPV = PV - required investment

You should go ahead with the project if it has a posi-

tive NPV.

We now need to consider how to apply the net pres-

ent value rule to practical investment problems. The

first step is to decide what to discount. We know the

answer in principle: Discount cash flows. This is why

Va lu

e

A working magnoosium mine. But how do you find its net present value?

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272

We look first at what cash flows should be dis-

counted. We then present an example designed to

show how cash flows can be derived from standard

accounting information and why cash flows and

accounting income usually differ. The example will

lead us to various further points, including the links

between depreciation and taxes and the importance

of tracking investments in working capital.

capital budgeting is often referred to as discounted

cash-flow, or DCF, analysis. But useful forecasts of cash

flows do not arrive on a silver platter. Often the finan-

cial manager has to make do with raw data supplied

by specialists in design, production, marketing, and so

on. In addition, most financial forecasts are prepared

in accordance with accounting principles that do not

necessarily recognize cash flows when they occur.

These forecasts must also be adjusted.

9.1 Identifying Cash Flows

Discount Cash Flows, Not Profits Up to this point we have been concerned mainly with the mechanics of discounting and with the various methods of project appraisal. We have had almost nothing to say about the problem of what you should discount. The first and most important point is this: To calculate net present value, you need to discount cash flows, not accounting profits.

We stressed the difference between cash flows and profits in Chapter 3. Here we stress it again. Income statements are intended to show how well the firm has per- formed. They do not track cash flows.

If the firm lays out a large amount of money on a big capital project, you do not conclude that the firm performed poorly that year, even though a lot of cash is going out the door. Therefore, the accountant does not deduct capital expenditure when cal- culating the year’s income but, instead, depreciates it over several years.

That is fine for computing year-by-year profits, but it could get you into trouble when working out net present value. For example, suppose that you are analyzing an investment proposal. It costs $2,000 and is expected to bring in a cash flow of $1,500 in the first year and $500 in the second. You think that the opportunity cost of capital is 10% and so calculate the present value of the cash flows as follows:

PV = $1,500

1.10 +

$500 (1.10)2

= $1,776.86

The project is worth less than it costs; it has a negative NPV:

NPV = $1,776.86 - $2,000 = -$223.14

The project costs $2,000 today, but accountants would not treat that outlay as an immediate expense. They would depreciate that $2,000 over 2 years and deduct the depreciation from the cash flow to obtain accounting income:

Year 1 Year 2

Cash infl ow + $1,500 + $ 500 Less depreciation - 1,000 - 1,000 Accounting income + 500 - 500

Thus an accountant would forecast income of $500 in year 1 and an accounting loss of $500 in year 2.

Suppose you were given this forecast income and loss and naively discounted them. Now NPV looks positive:

Apparent NPV = $500

1.10 +

-$500 (1.10)2

= $41.32

Of course we know that this is nonsense. The project is obviously a loser; we are spending money today ($2,000 cash outflow), and we are simply getting our money back later ($1,500 in year 1 and $500 in year 2). We are earning a zero return when we could get a 10% return by investing our money in the capital market.

The message of the example is this: When calculating NPV, recognize investment expenditures when they occur, not later when they show up as depreciation.

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Example 9.1 Sales before Cash Your firm’s ace computer salesman closed a $500,000 sale on December 15, just in time to count it toward his annual bonus. How did he do it? Well, for one thing he gave the customer 180 days to pay. The income statement will recognize the sale in December, even though cash will not arrive until June.

The accountant takes care of this timing difference by adding $500,000 to accounts receivable in December and then reducing accounts receivable when the money arrives in June. (The total of accounts receivable is just the sum of all cash due from customers.)

You can think of the increase in accounts receivable as an investment—it’s effectively a 180-day loan to the customer—and therefore a cash outflow. That investment is recovered when the customer pays. Thus financial analysts often find it convenient to calculate cash flow as follows:

December June

Sales $500,000 Sales 0 Less investment in accounts receivable -500,000

Plus recovery of accounts receivable +$500,000

Cash fl ow 0 Cash fl ow $500,000

Note that this procedure gives the correct cash flow of $500,000 in June.

Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 273

Projects are financially attractive because of the cash they generate, either for distribution to shareholders or for reinvestment in the firm. Therefore, the focus of capital budgeting must be on cash flow, not profits.

We saw another example of the distinction between cash flow and accounting prof- its in Chapter 3. Accountants try to show profit as it is earned, rather than when the company and the customer get around to paying their bills. For example, an income statement will recognize revenue when the sale is made, even if the bill is not paid for months. This practice also results in a difference between accounting profits and cash flow. The sale generates immediate profits, but the cash flow comes later.

It is not always easy to translate accounting data back into actual dollars. If you are in doubt about what is a cash flow, simply count the dollars coming in and take away the dollars going out.

A regional supermarket chain is deciding whether to install a tewgit machine in each of its stores. Each machine costs $250,000. Projected income per machine is as follows:

Year: 1 2 3 4 5

Sales $250,000 $300,000 $300,000 $250,000 $250,000 Operating expenses 200,000 200,000 200,000 200,000 200,000 Depreciation 50,000 50,000 50,000 50,000 50,000 Accounting income 0 50,000 50,000 0 0

Why would a store continue to operate a machine in years 4 and 5 if it pro- duces no profits? What are the cash flows from investing in a machine? Assume each tewgit machine has no salvage value at the end of its 5-year life.

Self-Test9.1

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Example 9.2

▲ Launching a New Product

Consider the decision by Apple to develop the iPhone 5S. If successful, the 5S could lead to several billion dollars in profits.

But are these profits all incremental cash flows? Certainly not. Our with-versus- without principle reminds us that we need also to think about what the cash flows would be without the new phone. By launching the 5S, Apple will reduce demand for the iPhone 5. The incremental cash flows therefore are

Cash flow with 5S (including lower cash flow

from iPhone 5) -

cash flow without 5S (with higher cash flow

from iPhone 5)

274 Part Two Value

Discount Incremental Cash Flows A project’s present value depends on the extra cash flows that it produces. So you need to forecast first the firm’s cash flows if you go ahead with the project. Then forecast the cash flows if you don’t accept the project. Take the difference and you have the extra (or incremental ) cash flows produced by the project:

Incremental cash flow

=

cash flow with project

-

cash flow without project

The trick in capital budgeting is to trace all the incremental flows from a proposed project. Here are some things to look out for.

Include All Indirect Effects The decision to launch a new smartphone illustrates a common indirect effect. New products often damage sales of an existing product. Of course, companies frequently introduce new products anyway, usually because they believe that their existing product line is under threat from competition. Even if Apple doesn’t go ahead with a new product, Samsung and other competitors will surely con- tinue to improve their Android phones, so there is no guarantee that sales of the exist- ing product line will continue at their present level. Sooner or later they will decline.

Sometimes a new project will help the firm’s existing business. Suppose that you are the financial manager of an airline that is considering opening a new short-haul route from Peoria, Illinois, to Chicago’s O’Hare Airport. When considered in isola- tion, the new route may have a negative NPV. But once you allow for the additional business that the new route brings to your other traffic out of O’Hare, it may be a very worthwhile investment. To forecast incremental cash flow, you must trace out all indirect effects of accepting the project.

Some capital investments have very long lives once all indirect effects are recog- nized. Consider the introduction of a new jet engine. Engine manufacturers often offer attractive pricing to achieve early sales, because once an engine is installed, 15 years’ sales of replacement parts are almost ensured. Also, since airlines prefer to limit the number of different engines in their fleet, selling jet engines today improves sales tomorrow as well. Later sales will generate further demands for replacement parts. Thus the string of incremental effects from the first sales of a new-model engine can run for 20 years or more.

Forget Sunk Costs Sunk costs are like spilled milk: They are past and irrevers- ible outflows. Sunk costs remain the same whether or not you accept the project. Therefore, they do not affect project NPV.

Unfortunately, managers often are influenced by sunk costs. A classic case occurred in 1971, when Lockheed sought a federal guarantee for a bank loan to continue

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Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 275

development of the Tristar airplane. Lockheed and its supporters argued that it would be foolish to abandon a project on which nearly $1 billion had already been spent. This was a poor argument, however, because the $1 billion was sunk. The relevant ques- tions were how much more needed to be invested and whether the finished product warranted the incremental investment.

Lockheed’s supporters were not the only ones to appeal to sunk costs. Some of its critics claimed that it would be foolish to continue with a project that offered no prospect of a satisfactory return on that $1 billion. This argument too was faulty. The $1 billion was gone, and the decision to continue with the project should have depended only on the return on the incremental investment.

Include Opportunity Costs Resources are almost never free, even when no cash changes hands. For example, suppose a new manufacturing operation uses land that could otherwise be sold for $100,000. This resource is costly; by using the land, you pass up the opportunity to sell it. There is no out-of-pocket cost, but there is an opportunity cost, that is, the value of the forgone alternative use of the land.

This example prompts us to warn you against judging projects “before versus after” rather than “with versus without.” A manager comparing before versus after might not assign any value to the land because the firm owns it both before and after:

opportunity cost Benefit or cash flow forgone as a result of an action.

Before Take Project After Cash Flow,

Before versus After

Firm owns land Firm still owns land 0

Before Take Project After Cash Flow, with Project

Firm owns land Firm still owns land 0

Before Do Not Take

Project After Cash Flow,

without Project

Firm owns land Firm sells land for $100,000 $100,000

The proper comparison, with versus without, is as follows:

If you compare the cash flows with and without the project, you see that $100,000 is given up by undertaking the project. The original cost of purchasing the land is irrelevant— that cost is sunk. The opportunity cost equals the cash that could be realized from selling the land now and therefore is a relevant cash flow for project evaluation.

When the resource can be freely traded, its opportunity cost is simply the market price. 1 However, sometimes opportunity costs are difficult to estimate. Suppose that you go ahead with a project to develop Computer Nouveau, pulling your software team off their work on a new operating system that some existing customers are not-so-patiently awaiting. The exact cost of infuriating those customers may be impossible to calculate, but you’ll think twice about the opportunity cost of moving the software team to Computer Nouveau.

Recognize the Investment in Working Capital Net working capital (often referred to simply as working capital ) is the difference between a company’s short-term assets and its liabilities. The principal short-term assets that you need to consider are accounts receivable (customers’ unpaid bills) and inventories of raw materials and finished goods, and the principal short-term liabilities are accounts pay- able (bills that you have not paid) and accruals (liabilities for items such as wages or taxes that have recently been incurred but have not yet been paid).

1 If the value of the land to the firm were less than the market price, the firm would sell it. On the other hand, the opportunity cost of using land in a particular project cannot exceed the cost of buying an equivalent parcel to replace it.

net working capital Current assets minus current liabilities.

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276 Part Two Value

Most projects entail an additional investment in working capital. For example, before you can start production, you need to invest in inventories of raw materials. Then, when you deliver the finished product, customers may be slow to pay and accounts receivable will increase. (Remember the computer sale described in Example 9.1. It required a $500,000, 6-month investment in accounts receivable.) Next year, as business builds up, you may need a larger stock of raw materials and you may have even more unpaid bills. Investments in working capital, just like investments in plant and equipment, result in cash outflows.

We find that working capital is one of the most common sources of confusion in forecasting project cash flows. 2 Here are the most common mistakes:

1. Forgetting about working capital entirely. We hope that you never fall into that trap. 2. Forgetting that working capital may change during the life of the project. Imagine

that you sell $100,000 of goods per year and customers pay on average 6 months late. You will therefore have $50,000 of unpaid bills. Now you increase prices by 10%, so revenues increase to $110,000. If customers continue to pay 6 months late, unpaid bills increase to $55,000, and therefore you need to make an additional investment in working capital of $5,000.

3. Forgetting that working capital is recovered at the end of the project. When the project comes to an end, inventories are run down, any unpaid bills are (you hope) paid off, and you can recover your investment in working capital. This generates a cash inflow.

Remember Terminal Cash Flows The end of a project almost always brings additional cash flows. For example, you might be able to sell some of the plant, equipment, or real estate that was dedicated to it. Also, as we just mentioned, you may recover some of your investment in working capital as you sell off inventories of fin- ished goods and collect on outstanding accounts receivable.

Often, there are expenses to shutting down a project. For example, the decommis- sioning costs of nuclear power plants can soak up several hundred million dollars. Similarly, when a mine is exhausted, the surrounding environment may need rehabili- tation. The mining company FCX has earmarked over $400 million to cover the future closure and reclamation costs of its New Mexico mines. Don’t forget to include these terminal cash flows.

Beware of Allocated Overhead Costs We have already mentioned that the accountant’s objective in gathering data is not always the same as the project ana- lyst’s. A case in point is the allocation of overhead costs such as rent, heat, or electricity. These overhead costs may not be related to a particular project, but they must be paid for nevertheless. Therefore, when the accountant assigns costs to the firm’s projects, a charge for overhead is usually made. But our principle of incremental cash flows says that in investment appraisal we should include only the extra expenses of the project.

A project may generate extra overhead costs, but then again it may not. We should be cautious about assuming that the accountant’s allocation of over- head costs represents the incremental cash flow that would be incurred by accepting the project.

2 If you are not clear why working capital affects cash flow, look back to Chapter 3, where we gave a primer on working capital and a couple of simple examples.

A firm is considering an investment in a new manufacturing plant. The site already is owned by the company, but existing buildings would need to be demolished. Which of the following should be treated as incremental cash flows?

Self-Test9.2

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Example 9.3 Cash Flows and Inflation City Consulting Services is considering moving into a new office building. The cost of a 1-year lease is $8,000, paid immediately. This cost will increase in future years at the annual inflation rate of 3%. The firm believes that it will remain in the building for 4 years. What is the present value of its rental costs if the discount rate is 10%?

The present value can be obtained by discounting the nominal cash flows at the 10% discount rate as follows:

Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 277

Discount Nominal Cash Flows by the Nominal Cost of Capital Interest rates are usually quoted in nominal terms. If you invest $100 in a bank deposit offering 6% interest, then the bank promises to pay you $106 at the end of the year. It makes no promises about what that $106 will buy. The real rate of interest on the bank deposit depends on inflation. If inflation is 2%, that $106 will buy you only 4% more goods at the end of the year than your $100 could buy today. The nominal rate of inter- est is 6%, but the real rate is about 4%. 3

If the discount rate is nominal, consistency requires that cash flows be estimated in nominal terms as well, taking account of trends in selling price, labor and materials costs, and so on. This calls for more than simply applying a single assumed inflation rate to all components of cash flow. Some costs or prices increase faster than inflation, some slower. For example, perhaps you have entered into a 5-year fixed-price contract with a supplier. No matter what happens to inflation over this period, this part of your costs is fixed in nominal terms.

Of course, there is nothing wrong with discounting real cash flows at the real inter- est rate, although this is not commonly done. We saw in Chapter 5 that real cash flows discounted at the real discount rate give exactly the same present values as nominal cash flows discounted at the nominal rate.

While the need to maintain consistency may seem like an obvious point, analysts sometimes forget to account for the effects of inflation when forecasting future cash flows. As a result, they end up discounting real cash flows at a nominal discount rate. This can grossly understate project values.

It should go without saying that you cannot mix and match real and nominal quantities. Real cash flows must be discounted at a real discount rate, nominal cash flows at a nominal rate. Discounting real cash flows at a nominal rate is a big mistake.

3 Remember from Chapter 5, Real rate of interest < nominal rate of interest - inflation rate

The exact formula is

1 + real rate of interest = 1 + nominal rate of interest

1 + inflation rate =

1.06

1.02 = 1.0392

Therefore, the real interest rate is .0392, or 3.92%.

a. The market value of the site. b. The market value of the existing buildings. c. Demolition costs and site clearance. d. The cost of a new access road put in last year. e. Lost cash flows on other projects due to executive time spent on the new

facility. f. Future depreciation of the new plant.

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278 Part Two Value

Separate Investment and Financing Decisions Suppose you finance a project partly with debt. How should you treat the proceeds from the debt issue and the interest and principal payments on the debt? The probably surprising answer: You should neither subtract the debt proceeds from the required investment nor recognize the interest and principal payments on the debt as cash out- flows. Regardless of the actual financing, you should view the project as if it were all-equity-financed, treating all cash outflows required for the project as coming from stockholders and all cash inflows as going to them. 5

This procedure focuses exclusively on the project cash flows, not the cash flows associated with alternative financing schemes. It, therefore, allows you to separate the analysis of the investment decision from that of the financing decision. First, you ask

5 Notice that this means that when you calculate the working capital associated with the project, you should assume zero short-term debt or holdings of cash.

Year Cash Flow Present Value at

10% Discount Rate

0 8,000 8,000 1 8,000 × 1.03  = 8,240 8,240/1.10 = 7,491 2 8,000 × 1.032 = 8,487 8,487/(1.10)2 = 7,014 3 8,000 × 1.033 = 8,742 8,742/(1.10)3  = 6,568

$29,073

Alternatively, the real discount rate can be calculated as 1.10/1.03 - 1 = .06796 =  6.796%.4 The present value can then be computed by discounting the real cash flows at the real discount rate as follows:

Year Real Cash Flow Present Value at

6.796% Discount Rate

0 8,000 8,000 1 8,000 8,000/1.06796 =  7,491 2 8,000 8,000/(1.06796)2 =  7,014 3 8,000 8,000/(1.06796)3 =  6,568

$29,073

Notice the real cash flow is a constant, since the lease payment increases at the rate of inflation. The present value of each cash flow is the same regardless of the method used to discount it. The sum of the present values is, of course, also identical.

4 We calculate the real discount rate to three decimal places to avoid confusion from rounding. Such precision is rarely necessary in practice.

Nasty Industries is closing down an outmoded factory and throwing all of its workers out on the street. Nasty’s CEO is enraged to learn that the firm must continue to pay for workers’ health insurance for 4 years. The cost per worker next year will be $2,400 per year, but the inflation rate is 4%, and health costs have been increasing at 3 percentage points faster than inflation. What is the present value of this obligation? The (nominal) discount rate is 10%.

Self-Test9.3

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Example 9.4 Cash Flow from Capital Investment Slick Corporation plans to invest $800 million to develop the Mock4 razor blade. The specialized blade factory will run for 7 years until it is replaced by more advanced technology. At that point the machinery will be sold for $50 million. Taxes of $10 mil- lion will be assessed on the sale.

The initial cash flow from Slick’s investment is -$800 million. In year 7, when the firm sells the land and equipment, there will be a net inflow of $50  million - $10  mil- lion = $40 million. Thus, the initial investment involves a negative cash flow, and the salvage value results in a positive flow.

Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 279

whether the project has a positive net present value, assuming all-equity financing. Then you can undertake a separate analysis of any potential impact of your financing strategy. Financing decisions are considered later in the text.

9.2 Calculating Cash Flow It is helpful to think of a project’s cash flow as composed of three elements:

Total cash flow = cash flows from capital investments (9.1) + operating cash flows

+ cash flows from changes in working capital

We will look at each of these components in turn.

Capital Investment To get a project off the ground, a company typically needs to make considerable up-front investments in plant, equipment, research, marketing, and so on. For example, develop- ment of a new car model typically involves expenditure of $500 million or more. This expenditure is a negative cash flow—negative because cash goes out the door.

When the model finally goes out of production, the company can either sell the plant and equipment or redeploy the assets elsewhere in the business. This salvage value (net of any taxes if the equipment is sold) represents a positive cash flow to the firm. However, remember our earlier comment that final cash flows can be negative if there are significant shutdown costs.

Operating Cash Flow Think back to the decision to launch a new car model. In such cases, operating cash flow consists of revenues from the sale of the new product less the costs of production and any taxes:

Operating cash flow = revenues - costs - taxes

Undoubtedly, the revenues are expected to outweigh the costs, and therefore operating cash flows are positive.

Many investments do not result in additional revenues; they are simply designed to reduce the costs of the company’s existing operations. For example, a new computer system may provide labor savings, or a new heating system may be more energy- efficient than the one it replaces. Such projects also contribute to the operating cash flow of the firm—not by increasing revenues but by reducing costs. These cost savings therefore represent a positive contribution to net cash flow.

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Example 9.5 Operating Cash Flow of Cost-Cutting Projects Suppose a new heating system costs $100,000 but reduces heating costs by $30,000 a year. The firm’s tax rate is 35%. The new system does not change revenues, but, thanks to the cost savings, income increases by $30,000. Therefore, incremental operating cash flow is:

Increase in (revenues less expenses) $30,000 - Incremental tax at 35% - 10,500 = Increase in operating cash fl ow +$19,500

Notice that because the cost savings increase profits, the company must pay more tax. The net increase in cash flow equals the after-tax cost savings:

(1 - .35) × $30,000 = $19,500

280 Part Two Value

Here is another matter that you need to look out for when calculating cash flow. When the firm calculates its taxable income, it makes a deduction for depreciation. This depre- ciation charge is an accounting entry. It affects the tax that the company pays, but it is not a cash expense and should not be deducted when calculating operating cash flow. (Remember from our earlier discussion that you want to discount cash flows, not profits.)

When you work out a project’s cash flows, there are three possible ways to deal with depreciation.

Method 1: Dollars In Minus Dollars Out Take only the items from the income statement that represent actual cash flows. This means that you start with cash revenues and subtract cash expenses and taxes paid. You do not, however, subtract a charge for depreciation because this does not involve cash going out the door. Thus,

Operating cash flow = revenues - cash expenses - taxes (9.2)

Method 2: Adjusted Accounting Profits Alternatively, you can start with after-tax accounting profits and add back any noncash “accounting expenses,” specifically, the depreciation deduction. This gives

Operating cash flow = after-tax profit + depreciation (9.3)

Method 3: Add Back Depreciation Tax Shield Although the depre- ciation deduction is not a cash expense, it does affect the firm’s tax payment, which certainly is a cash item. Each additional dollar of depreciation reduces taxable income by $1. So, if the firm’s tax bracket is 35%, tax payments fall by $.35, and cash flow increases by the same amount. Financial managers often refer to this tax saving as the depreciation tax shield. It equals the product of the tax rate and the depreciation charge:

Depreciation tax shield = tax rate × depreciation

This suggests a third way to calculate operating cash flow. First, calculate net profit, initially assuming zero depreciation. This is equal to (revenues  -   cash expenses) ×  (1  -  tax rate). Now add back the tax shield based on the amount of depreciation actu- ally claimed to find operating cash flow:

Operating cash flow = (revenues - cash expenses) × (1 - tax rate) (9.4) + (tax rate × depreciation)

The following example confirms that the three methods all give the same figure for operating cash flow.

depreciation tax shield Reduction in taxes attributable to depreciation.

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Example 9.6 Operating Cash Flow A project generates revenues of $1,000, cash expenses of $600, and depreciation charges of $200 in a particular year. The firm’s tax bracket is 35%. Net income is cal- culated as follows:

Revenues 1,000 - Cash expenses 600 - Depreciation expense 200 = Profi t before tax 200 - Tax at 35% 70 = Net profi t 130

Methods 1, 2, and 3 all show that operating cash flow is $330:

Method 1: Operating cash flow = revenues - cash expenses - taxes = 1,000 + 600 - 70 = 330 Method 2: Operating cash flow = net profit + depreciation = 130 + 200 = 330 Method 3: Operating cash flow = (revenues - cash expenses) × (1 - tax rate) + (depreciation × tax rate) = (1,000 - 600) × (1 - .35) + (200 × .35) = 330

Example 9.7 Cash Flow from Changes in Working Capital Slick makes an initial (year 0) investment of $10 million in inventories of plastic and steel for its blade plant. Then in year 1 it accumulates an additional $20 million of raw materials. The total level of inventories is now $10  million + $20  million = $30  million, but the cash outlay in year 1 is simply the $20 million addition to inventory. The $20 million investment in additional inventory results in a cash flow of -$20 million. Notice that the increase in working capital is an investment in the project. Like other investments, a buildup of working capital requires cash. Increases in the level of working capital therefore show up as negative cash flows.

Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 281

Changes in Working Capital We pointed out earlier in the chapter that when a company builds up inventories of raw materials or finished product, the company’s cash is reduced; the reduction in cash reflects the firm’s investment in inventories. Similarly, cash is reduced when custom- ers are slow to pay their bills—in this case, the firm makes an investment in accounts receivable. Investment in working capital, just like investment in plant and equipment, represents a negative cash flow. On the other hand, later in the life of a project, when inventories are sold off and accounts receivable are collected, the firm’s investment in working capital is reduced as it converts these assets into cash.

A project generates revenues of $600, expenses of $300, and depreciation charges of $200 in a particular year. The firm’s tax bracket is 35%. Find the operating cash flow of the project by using all three approaches.

Self-Test9.4

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Later on, say, in year 5, the company begins planning for the next-generation blade. At this point, it decides to reduce its inventory of raw material from $30 mil- lion to $25 million. This reduction in inventory investment frees up $5 million of cash, which is a positive cash flow. Therefore, the cash flows from inventory investment are -$10 million in year 0, -$20 million in year 1, and +$5 million in year 5.

These calculations can be summarized in a simple table, as follows:

Year: 0 1 2 3 4 5

1. Total working capital, year-end ($ million) 10 30 30 30 30 25 2. Change in working capital ($ million) 10 20 0 0 0 -5 3. Cash fl ow from changes in working capital -10 -20 0 0 0 +5

In years 0 and 1, there is a net investment in working capital (line 2), corresponding to a negative cash flow (line 3), and an increase in the level of total working capital (line 1). In years 2 to 4, the level of working capital is unchanged at $30 million, so the net investment in working capital in those years is zero. But in year 5, the firm begins to disinvest in working capital, which frees up cash and thereby provides a positive cash flow.

282 Part Two Value

In general: An increase in working capital is an investment and therefore implies a negative cash flow; a decrease in working capital implies a positive cash flow. The cash flow is measured by the change in working capital, not the level of working capital.

9.3 An Example: Blooper Industries Now that we have examined the basic pieces of a cash-flow analysis, let’s try to put them together into a coherent whole. As the newly appointed financial manager of Blooper Industries, you are about to analyze a proposal for mining and selling a small deposit of high-grade magnoosium ore. 6 You are given the forecasts shown in the spreadsheet in Table 9.1 . We will walk through the lines in the table.

Cash-Flow Analysis Investment in Fixed Assets Panel A of the spreadsheet summarizes our assumptions. Panel B details investments and disinvestments in fixed assets. The proj- ect requires an initial investment of $10 million, as shown in cell B14. After 5 years, the ore deposit is exhausted, so the mining equipment may be sold for $2 million (cell B3), a forecast that already reflects the likely impact of inflation.

When you sell the equipment, the IRS will check to see whether any taxes are due on the sale. Any difference between the sale price ($2 million) and the book value of the equipment will be treated as a taxable gain.

We assume that Blooper depreciates the equipment to a final value of zero. There- fore, the book value of the equipment when it is sold in year 6 will be zero, and you will be subject to taxes on the full $2 million proceeds. Your sale of the equipment will

6 Readers have inquired whether magnoosium is a real substance. Here, now, are the facts: Magnoosium was created in the early days of television, when a splendid-sounding announcer closed a variety show by saying, “This program has been brought to you by Blooper Industries, proud producer of aleemiums, magnoosium, and stool.” We forget the company, but the blooper really happened.

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Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 283

land you with an additional tax bill in year 6 of .35  ×  $2  million  =  $.70 million. The net cash flow from the sale in year 6 is therefore

Salvage value - tax on gain = $2 million - $.70 million = $1.30 million

This amount is recorded in cell H15. Row 16 summarizes the cash flows from investments in and sales of fixed assets.

The entry in each cell equals the after-tax proceeds from asset sales (row 15) minus the investments in fixed assets (row 14).

Operating Cash Flow The company expects to be able to sell 750,000 pounds of magnoosium a year at a price of $20 a pound in year 1. That points to initial rev- enues of 750,000  ×  $20  =  $15,000,000. But be careful; inflation is running at about 5% a year. If magnoosium prices keep pace with inflation, you should increase your forecast of the second-year revenues by 5%. Third-year revenues should increase by a further 5%, and so on. Row 19 in Table 9.1 shows revenues rising in line with inflation.

The sales forecasts in Table 9.1 are cut off after 5 years. That makes sense if the ore deposit will run out at that time. But if Blooper could make sales for year 6, you should include them in your forecasts. We have sometimes encountered financial man- agers who assume a project life of (say) 5 years, even when they confidently expect

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

A. Inputs Initial investment 10,000 Salvage value 2,000 Initial revenue 15,000

B. Fixed assets Investment in fixed assets 10,000 Sales of fixed assets CF, invest. in fixed assets –10,000 0 0 0 0 0 1,300

1,300

Initial expenses 10,000 Inflation rate 0.05 Discount rate 0.12 Acct receiv. as % of sales 1/6 Inven. as % of expenses 0.15 Tax rate

Year:

Investment Salvage

Initial_rev Initial_exp Inflation

Disc_rate A_R

Inv_pct Tax_rate0.35

C. Operating cash flow Revenues 15,000 Expenses 10,000 Depreciation 2,000 Pretax profit 3,000 Tax 1,050 Profit after tax 1,950 Operating cash flow 3,950

15,750 10,500 2,000 3,250 1,138 2,113 4,113

16,538 11,025 2,000 3,513 1,229 2,283 4,283

17,364 11,576 2,000 3,788 1,326 2,462 4,462

18,233 12,155 2,000

D. Working capital Working capital 1,500 Change in working cap 1,500 CF, invest. in wk capital –1,500

4,075 2,575

–2,575

4,279 204

–204

4,493 214

–214

4,717 225

–225

3,039 –1,679 1,679

0 –3,039 3,039

E. Project valuation Total project cash flow –11,500 Discount factor 1.0 PV of cash flow –11,500

1,375 0.8929

1,228

3,909 0.7972

3,116

4,069 0.7118

2,896

4,238 0.6355

2,693

6,329 0.5674 3,591

4,339 0.5066

2,198 Net present value 4,223

4,078 1,427 2,650 4,650

A B C D E F G H

0 1 2 3 4 5 6

Spreadsheet Name TABLE 9.1 Financial projections for Blooper’s magnoosium mine (dollar values in thousands)

You can find this spreadsheet in Connect.

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Blooper Industries

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284 Part Two Value

revenues for 10 years or more. When asked the reason, they explain that forecasting beyond 5 years is too hazardous. We sympathize, but you just have to do your best. Do not arbitrarily truncate a project’s life.

Expenses in year 1 are $10,000 (cell C20). We assume that the expenses of mining and refining (row 20) also increase in line with inflation at 5% a year.

We also assume for now that the company applies straight-line depreciation to the mining equipment over 5 years. This means that it deducts one-fifth of the initial $10 million investment from profits. Thus row 21 shows that the annual depreciation deduction is $2 million.

Pretax profit, shown in row 22, equals (revenues  -  expenses  -  depreciation). Taxes (row 23) are 35% of pretax profit. For example, in year 1,

Tax = .35 × 3,000 = 1,050, or $1,050,000

Profit after tax (row 24) equals pretax profit less taxes. The last row of panel C presents operating cash flow. We calculate cash flow as the

sum of after-tax profits plus depreciation (method 2, above). Therefore, row 25 is the sum of rows 24 and 21.

Changes in Working Capital Row 28 shows the level of working capital. As the project gears up in the early years, working capital increases, but later in the project’s life, the investment in working capital is recovered and the level declines.

Row 29 shows the change in working capital from year to year. Notice that in years 1 to 4 the change is positive; in these years the project requires additional investments in working capital. Starting in year 5 the change is negative; there is a disinvestment as working capital is recovered. Cash flow associated with investments in working capital (row 30) is the negative of the change in working capital. Just like investment in plant and equipment, investment in working capital produces a negative cash flow, and disinvestment produces a positive cash flow.

Total Project Cash Flow Total cash flow is the sum of cash flows from each of the three sources: cash flow from investments in fixed assets and working capital and operating cash flow. Therefore, total cash flow in row 33 is just the sum of rows 16, 25, and 30.

Calculating the NPV of Blooper’s Project You have now derived (in row 33) the forecast cash flows from Blooper’s magnoosium mine. Suppose that investors expect a return of 12% from investments in the capital market with the same risk as the magnoosium project. This is the opportunity cost of the shareholders’ money that Blooper is proposing to invest in the project. Therefore, to calculate NPV, you need to discount the cash flows at 12%.

Rows 34 and 35 set out the calculations. Remember that to calculate the present value of a cash flow in year t you can divide the cash flow by (1  +   r ) t or you can multi- ply by a discount factor that is equal to 1/(1  +   r ) t . Row 34 presents the discount factors for each year, and row 35 calculates the present value of each cash flow by multiplying the cash flow (row 33) times the discount factor. When all cash flows are discounted and added up, the magnoosium project is seen to offer a positive net present value of $4,223 thousand (cell B36), or about $4.2 million.

Now here is a small point that often causes confusion: To calculate the present value of the first year’s cash flow, we divide by (1  +   r )  =  1.12. Strictly speaking, this makes sense only if all the sales and all the costs occur exactly 365 days, zero hours, and zero minutes from now. Of course the year’s sales don’t all take place on the stroke of midnight on December 31. However, when making capital budgeting deci- sions, companies are usually happy to pretend that all cash flows occur at 1-year inter- vals. They pretend this for one reason only—simplicity. When sales forecasts are

straight-line depreciation Constant depreciation for each year of the asset’s accounting life.

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Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 285

sometimes little more than intelligent guesses, it may be pointless to inquire how the sales are likely to be spread out during the year. 7

Further Notes and Wrinkles Arising from Blooper’s Project Before we leave Blooper and its magnoosium project, we should cover a few extra wrinkles.

Forecasting Working Capital Table  9.1 shows that Blooper expects its magnoosium mine to produce revenues of $15,000 in year 1 and $15,750 in year 2. But Blooper will not actually receive these amounts in years 1 and 2, because some of its customers will not pay up immediately. We have assumed that, on average, custom- ers pay with a 2-month lag, so that 2/12 of each year’s sales are not paid for until the following year. These unpaid bills show up as accounts receivable. For example, in year 1 Blooper will have accounts receivable of (2/12)  ×  15,000  =  $2,500. 8

Consider now the mine’s expenses. These are forecast at $10,000 in year 1 and $10,500 in year 2. But not all of this cash will go out of the door in these 2 years, for Blooper must produce the magnoosium before selling it. Each year, Blooper mines magnoosium ore, but some of this ore is not sold until the following year. The ore is put into inventory, but the accountant does not deduct the cost of its produc- tion until it is taken out of inventory and sold. We assume that 15% of each year’s expenses represent an investment in inventory that took place in the previous year. Thus the investment in inventory is forecast at .15  ×  10,000  =  $1,500 in year 0 and at .15  ×  $10,500  =  $1,575 in year 1.

We can now see how Blooper arrives at its forecast of working capital:

7 Financial managers sometimes assume cash flows arrive in the middle of the calendar year, that is, at the end of June. This midyear convention is roughly equivalent to assuming cash flows are distributed evenly throughout the year. This is a bad assumption for some industries. In retailing, for example, most of the cash flow comes late in the year, as the holiday season approaches. 8 For convenience, we assume that, although Blooper’s customers pay with a lag, Blooper pays all its bills on the nail. If it didn’t, these unpaid bills would be recorded as accounts payable. Working capital would be reduced by the amount of the accounts payable.

0 1 2 3 4 5 6

1. Receivables (2/12  ×  revenues) $ 0 $2,500 $2,625 $2,756 $2,894 $3,039 0 2. Inventories (.15  ×  following

year’s expenses) 1,500 1,575 1,654 1,736 1,823 0 0 3. Working capital (1  +  2) 1,500 4,075 4,279 4,493 4,717 3,039 0

Note: Columns may not sum due to rounding.

Notice that working capital builds up in years 1 to 4, as sales of magnoosium increase. Year 5 is the last year of sales, so Blooper can reduce its inventories to zero in that year. In year 6 the company expects to collect any unpaid bills from year 5, and so in that year receivables also fall to zero. This decline in working capital increases cash flow. For example, in year 6 cash flow is increased as the $3,039 of outstanding bills are paid.

The construction of the Blooper spreadsheet is discussed further in the box on page 288. Once the spreadsheet is set up, it is easy to try out different assumptions for work- ing capital. For example, you can adjust the level of receivables and inventories by changing the values in cells B8 and B9.

A Further Note on Depreciation We warned you earlier not to assume that all cash flows are likely to increase with inflation. The depreciation tax shield is a

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286 Part Two Value

case in point, because the Internal Revenue Service lets companies depreciate only the amount of the original investment. For example, if you go back to the IRS to explain that inflation mushroomed since you made the investment and you should be allowed to depreciate more, the IRS won’t listen. The nominal amount of depreciation is fixed, and therefore the higher the rate of inflation, the lower the real value of the deprecia- tion that you can claim.

We assumed in our calculations that Blooper could depreciate its investment in mining equipment by $2 million a year. That produced an annual tax shield of $2  mil- lion  ×  .35  =  $.70 million per year for 5 years. These tax shields increase cash flows from operations and therefore increase present value. So if Blooper could get those tax shields sooner, they would be worth more, right? Fortunately for corporations, tax law allows them to do just that. It allows accelerated depreciation.

The rate at which firms are permitted to depreciate equipment is known as the modified accelerated cost recovery system, or MACRS. MACRS places assets into one of six classes, each of which has an assumed life. Table 9.2 shows the rate of depreciation that the company can use for each of these classes. Most industrial equip- ment falls into the 5- and 7-year classes. To keep life simple, we will assume that all of Blooper’s mining equipment goes into 5-year assets. Thus Blooper can depreciate 20% of its $10 million investment in year 1. In the second year it can deduct deprecia- tion of .32  ×  10  =  $3.2 million, and so on. 9

modified accelerated cost recovery system (MACRS) Depreciation method that allows higher tax deductions in early years and lower deductions later.

9 You might wonder why the 5-year asset class provides a depreciation deduction in years 1 through 6. This is because the tax authorities assume that the assets are in service for only 6 months of the first year and 6 months of the last year. The total project life is 5 years, but that 5-year life spans parts of 6 calendar years. This assump- tion also explains why the depreciation allowance is lower in the first year than it is in the second.

Recovery Period Class

Year(s) 3 Year 5 Year 7 Year 10 Year 15 Year 20 Year

1 33.33 20.00 14.29 10.00 5.00 3.75 2 44.45 32.00 24.49 18.00 9.50 7.22 3 14.81 19.20 17.49 14.40 8.55 6.68 4 7.41 11.52 12.49 11.52 7.70 6.18 5 11.52 8.93 9.22 6.93 5.71 6 5.76 8.92 7.37 6.23 5.28 7 8.93 6.55 5.90 4.89 8 4.46 6.55 5.90 4.52 9 6.56 5.91 4.46 10 6.55 5.90 4.46 11 3.28 5.91 4.46 12 5.90 4.46 13 5.91 4.46 14 5.90 4.46 15 5.91 4.46 16 2.95 4.46

17–20 4.46 21 2.23

TABLE 9.2 Tax depreciation allowed under the modified accelerated cost recovery system (figures in percent of depreciable investment)

Notes: 1. Tax depreciation is lower in the fi rst year because assets are assumed to be in service for 6 months. 2. Real property is depreciated straight-line over 27.5 years for residential property and 39 years for nonresidential property.

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MACRS classes

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Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 287

How does MACRS depreciation affect the value of the depreciation tax shield for the magnoosium project? Table 9.3 gives the answer. Notice that MACRS does not affect the total amount of depreciation that is claimed. This remains at $10 million just as before. But MACRS allows companies to get the depreciation deduction ear- lier, which increases the present value of the depreciation tax shield from $2,523,000 to $2,583,000, an increase of $60,000. Before we recognized MACRS depreciation, we calculated project NPV as $4,223,000. When we recognize MACRS, we should increase that figure by $60,000.

All large corporations in the United States keep two sets of books, one for stock- holders and one for the Internal Revenue Service. It is common to use straight-line depreciation on the stockholder books and MACRS depreciation on the tax books. Only the tax books are relevant in capital budgeting.

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The value of MACRS tax savings

Straight-Line Depreciation MACRS Depreciation

Year Depreciation Tax Shield PV Tax Shield

at 12% Depreciation Tax Shield PV Tax Shield

at 12%

1 2,000 700 625 2,000 700 625 2 2,000 700 558 3,200 1,120 893 3 2,000 700 498 1,920 672 478 4 2,000 700 445 1,152 403 256 5 2,000 700 397 1,152 403 229 6 0 0 0 576 202 102

Totals 10,000 3,500 2,523 10,000 3,500 2,583

Note: Column sums subject to rounding error.

TABLE 9.3 The switch from straight-line to 5-year MACRS depreciation increases the value of Blooper’s depreciation tax shield from $2,523,000 to $2,583,000 (figures in $ thousands).

Suppose that Blooper’s mining equipment could be put in the 3-year recov- ery period class. What is the present value of the depreciation tax shield? Confirm that the change in the value of the depreciation tax shield equals the increase in project NPV from Question 1 of the Spreadsheet Solutions box.

Self-Test9.5

More on Salvage Value When you sell equipment, you must pay taxes on the difference between the sales price and the book value of the asset. The book value in turn equals the initial cost minus cumulative charges for depreciation. It is common when figuring tax depreciation to assume a salvage value of zero at the end of the asset’s depreciable life.

For reports to shareholders, however, positive expected salvage values are often recognized. For example, Blooper’s financial statements might assume that its $10 million investment in mining equipment would be worth $2 million in year 6. In this case, the depreciation reported to shareholders would be based on the difference between the investment and the salvage value, that is, $8 million. Straight-line depre- ciation then would be $1.6 million annually.

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1

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13

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25

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27

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34

35

36

BA C D G H

A. Inputs Initial investment 10,000

Salvage value 2,000

Initial revenue 15,000

Initial expenses 10,000

Inflation rate 0.05

Discount rate 0.12

Acct receiv. as % of sales =2/12

Inven. as % of expenses 0.15

Tax rate

Investment Spreadsheet Name

Salvage

Initial_rev

Initial_exp

Inflation

Disc_rate

A_R

Inv_pct

Tax_rate0.35

Year: 0 1 2 5 6

B. Fixed assets Investment in fixed assets =Investment

=–B14+B15 =–C14+C15 =–D14+D15 =–G14+G15 =–H14+H15

=Salvage*(1–Tax_rate)

=Inv_pct*C20+A_R*B19

=B28

=–B29

=B16+B30+B25

=1/(1+Disc_rate)^B12

=B33*B34 =SUM(B35:H35)

=Inv_pct*D20+A_R*C19

=C28–B28

=–C29

=C16+C30+C25

=1/(1+Disc_rate)^C12

=C33*C34

=Inv_pct*E20+A_R*D19

=D28–C28

=–D29

=D16+D30+D25

=1/(1+Disc_rate)^D12

=D33*D34

=Inv_pct*H20+A_R*G19

=G28–F28

=–G29

=G16+G30+G25

=1/(1+Disc_rate)^G12

=G33*G34

=Inv_pct*I20+A_R*H19

=H28–G28

=–H29

=H16+H30+H25

=1/(1+Disc_rate)^H12

=H33*H34

Sales of fixed assets

CF, invest. in fixed assets

C. Operations Revenues

Expenses

Depreciation

Pretax profit

Tax

Profit after tax

Operating cash flow

=Initial_rev

=Initial_exp

=Investment/5

=C19–C20–C21

=C22*Tax rate

=C22–C23

=C21 + C24

=C19*(1+Inflation)

=C20*(1+Inflation)

=Investment/5

=D19–D20–D21

=D22*Tax rate

=D22–D23

=D21 + D24

=F19*(1+Inflation)

=F20*(1+Inflation)

=Investment/5

=G19–G20–G21

=G22*Tax rate

=G22–G23

=G21 + G24

D. Working capital Working capital

Change in working cap

CF, invest. in wk capital

E. Project valuation Total project cash flow

Discount factor

PV of cash flow Net present value

288

SolutionsSpreadsheet Row 28 sets out the level of working capital, which is the

sum of accounts receivable and inventories. Because inven- tories tend to rise with production, we set them equal to .15 times expenses recognized in the following year when the product is sold. Similarly, accounts receivable rise with sales, so we assume that they will be 2/12 times current year’s rev- enues (in other words, that Blooper’s customers pay, on aver- age, 2 months after purchasing the product). Each entry in row 28 is the sum of these two quantities.

We calculate the discount factor in row 34, compute pres- ent values of each cash fl ow in row 35, and fi nd NPV in cell B36.

Once the spreadsheet is up and running, “what-if” analy- ses are easy. Here are a few questions to try your hand.

Discounted cash-fl ow analysis of proposed capital invest- ments is tailor-made for spreadsheet analysis. The formula view of the Excel spreadsheet used in the Blooper example appears below.

Notice that most of the entries in the spreadsheet are for- mulas rather than specifi c numbers. Once the relatively few input values in panel A are entered, the spreadsheet does most of the work.

Revenues and expenses in each year equal the value in the previous year times (1 +  infl ation rate). To make the spreadsheet easier to read, we have defi ned names for a few cells, such as B6 (Infl ation) and B7 (Disc_rate). These names can be assigned using the Insert command and thereafter can be used to refer to specifi c cells.

The Blooper Spreadsheet Model

Formula view, columns E and F hidden

You can find this spreadsheet in Connect.

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289

Spreadsheet Questions

1. What happens to cash fl ow in each year and the NPV of the project if the fi rm uses MACRS depreciation assuming a 3-year recovery period? Assume year 1 is the fi rst year that depreciation is taken.

2. Suppose the fi rm can economize on working capital by managing inventories more efficiently. If it reduces inven- tories from 15% to 10% of next year’s cost of goods sold, what will be the effect on project NPV?

3. What happens to NPV if the infl ation rate falls from 5% to zero and the discount rate falls from 12% to 7%? Given that the real discount rate is almost unchanged, why does project NPV increase? [To be consistent, you should assume that nominal salvage value will be lower in a zero-infl ation environment. If you set (before-tax) salvage value to $1.492 million, you will maintain its real value unchanged.]

Brief solutions appear at the end of the chapter.

SUMMARY Here is a checklist to bear in mind when forecasting a project’s cash flows:

• Discount cash flows, not profits. • Estimate the project’s incremental cash flows—that is, the difference between the

cash flows with the project and those without the project. • Include all indirect effects of the project, such as its impact on the sales of the firm’s

other products. • Forget sunk costs. • Include opportunity costs, such as the value of land that you could otherwise sell. • Beware of allocated overhead charges for heat, light, and so on. These may not

reflect the incremental effects of the project on these costs. • Remember the investment in working capital. As sales increase, the firm may need to

make additional investments in working capital, and as the project finally comes to an end, it will recover these investments.

• Treat inflation consistently. If cash flows are forecast in nominal terms (including the effects of future inflation), use a nominal discount rate. Discount real cash flows at a real rate.

• Do not include debt interest or the cost of repaying a loan. When calculating NPV, assume that the project is financed entirely by the shareholders and that they receive all the cash flows. This separates the investment decision from the financing decision.

Project cash flow does not equal profit. You must allow for noncash expenses such as depreciation as well as changes in working capital.

Depreciation is not a cash flow. However, because depreciation reduces taxable income, it reduces taxes. This tax reduction is called the depreciation tax shield. Modified acceler- ated cost recovery system (MACRS) depreciation schedules allow more of the deprecia- tion allowance to be taken in early years than is possible under straight-line depreciation. This increases the present value of the tax shield.

Increases in net working capital such as accounts receivable or inventory are investments and therefore use cash—that is, they reduce the net cash flow provided by the project in that period. When working capital is run down, cash is freed up, so cash flow increases.

How should the cash flows of a proposed new project be calculated? (LO9-1)

How can the cash flows of a project be computed from standard financial statements? (LO9-2)

How is the company’s tax bill affected by depreciation, and how does this affect project value? (LO9-3)

How do changes in working capital affect project cash flows? (LO9-4)

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290 Part Two Value

L I S T I N G O F E Q UAT I O N S 9.1 Total cash flow = cash flows from capital investments

+ cash flows from changes in working capital + operating cash flows

9.2 Operating cash flow =  revenues  -  cash expenses  -  taxes

9.3 Operating cash flow =  after-tax profit  +  depreciation

9.4 Operating cash flow = (revenues - cash expenses) × (1 - tax rate) + (tax rate × depreciation)

QUESTIONS AND PROBLEMS 1. Cash Flows. Quick Computing currently sells 10 million computer chips each year at a price

of $20 per chip. It is about to introduce a new chip, and it forecasts annual sales of 12 million of these improved chips at a price of $25 each. However, demand for the old chip will decrease, and sales of the old chip are expected to fall to 3 million per year. The old chip costs $6 each to manufacture, and the new ones will cost $8 each. What is the proper cash flow to use to evaluate the present value of the introduction of the new chip? (LO9-1)

2. Incremental Cash Flows. A corporation donates a valuable painting from its private collection to an art museum. Which of the following are incremental cash flows associated with the dona- tion? (LO9-1)

a. The price the firm paid for the painting b. The current market value of the painting c. The deduction from income that it declares for its charitable gift d. The reduction in taxes due to its declared tax deduction

3. Cash Flows. Conference Services Inc. has leased a large office building for $4 million per year. The building is larger than the company needs; two of the building’s eight stories are almost empty. A manager wants to expand one of her projects, but this will require using one of the empty floors. In calculating the net present value of the proposed expansion, senior manage- ment allocates one-eighth of $4 million of building rental costs (i.e., $.5 million) to the project expansion, reasoning that the project will use one-eighth of the building’s capacity. (LO9-1)

a. Is this a reasonable procedure for purposes of calculating NPV? b. Can you suggest a better way to assess a cost of the office space used by the project?

4. Cash Flows. A new project will generate sales of $74 million, costs of $42 million, and depre- ciation expense of $10 million in the coming year. The firm’s tax rate is 35%. Calculate cash flow for the year by using all three methods discussed in the chapter, and confirm that they are equal. (LO9-2)

5. Cash Flows. Tubby Toys estimates that its new line of rubber ducks will generate sales of $7 million, operating costs of $4 million, and a depreciation expense of $1 million. If the tax rate is 35%, what is the firm’s operating cash flow? Show that you get the same answer using all three methods to calculate operating cash flow. (LO9-2)

6. Calculating Net Income. The owner of a bicycle repair shop forecasts revenues of $160,000 a year. Variable costs will be $50,000, and rental costs for the shop are $30,000 a year. Depre- ciation on the repair tools will be $10,000. Prepare an income statement for the shop based on these estimates. The tax rate is 35%. (LO9-2)

7. Cash Flows. Calculate the operating cash flow for the repair shop in the previous problem using all three methods suggested in the chapter: (a) adjusted accounting profits; (b) cash inflow/cash outflow analysis; and (c) the depreciation tax shield approach. Confirm that all three approaches result in the same value for cash flow. (LO9-2)

8. Operating Cash Flows. Laurel’s Lawn Care Ltd. has a new mower line that can generate revenues of $120,000 per year. Direct production costs are $40,000, and the fixed costs of

finance

®

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Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 291

maintaining the lawn mower factory are $15,000 a year. The factory originally cost $1 million and is being depreciated for tax purposes over 25 years using straight-line depreciation. Calcu- late the operating cash flows of the project if the firm’s tax bracket is 35%. (LO9-2)

9. Equivalent Annual Cost. Gluon Inc. is considering the purchase of a new high pressure glue- ball. It can purchase the glueball for $120,000 and sell its old low-pressure glueball, which is fully depreciated, for $20,000. The new equipment has a 10-year useful life and will save $28,000 a year in expenses. The opportunity cost of capital is 12%, and the firm’s tax rate is 40%. What is the equivalent annual saving from the purchase if Gluon uses straight-line depreciation? (LO9-2)

10. Cash Flows and NPV. Johnny’s Lunches is considering purchasing a new, energy-efficient grill. The grill will cost $40,000 and will be depreciated according to the 3-year MACRS sched- ule. It will be sold for scrap metal after 3 years for $10,000. The grill will have no effect on revenues but will save Johnny’s $20,000 in energy expenses. The tax rate is 35%. (LO9-2)

a. What are the operating cash flows in each year? b. What are the total cash flows in each year? c. If the discount rate is 12%, should the grill be purchased?

11. Project Evaluation. Revenues generated by a new fad product are forecast as follows:

Year Revenues

1 $40,000 2 30,000 3 20,000 4 10,000

Thereafter 0

Expenses are expected to be 40% of revenues, and working capital required in each year is expected to be 20% of revenues in the following year. The product requires an immediate investment of $45,000 in plant and equipment. (LO9-2)

a. What is the initial investment in the product? Remember working capital. b. If the plant and equipment are depreciated over 4 years to a salvage value of zero using

straight-line depreciation, and the firm’s tax rate is 40%, what are the project cash flows in each year?

c. If the opportunity cost of capital is 12%, what is project NPV? d. What is project IRR?

12. Project Evaluation. Kinky Copies may buy a high-volume copier. The machine costs $100,000 and will be depreciated straight-line over 5 years to a salvage value of $20,000. Kinky antic- ipates that the machine actually can be sold in 5 years for $30,000. The machine will save $20,000 a year in labor costs but will require an increase in working capital, mainly paper supplies, of $10,000. The firm’s marginal tax rate is 35%, and the discount rate is 8%. Should Kinky buy the machine? (LO9-2)

13. Project Evaluation. Blooper Industries must replace its magnoosium purification system. Quick & Dirty Systems sells a relatively cheap purification system for $10 million. The system will last 5 years. Do-It-Right sells a sturdier but more expensive system for $12 million; it will last for 8 years. Both systems entail $1 million in operating costs; both will be depreciated straight-line to a final value of zero over their useful lives; neither will have any salvage value at the end of its life. The firm’s tax rate is 35%, and the discount rate is 12%. Which system should Blooper install? (Hint: Check the discussion of equivalent annual annuities in the previ- ous chapter.) (LO9-2)

14. Project Evaluation. Ilana Industries Inc. needs a new lathe. It can buy a new high-speed lathe for $1 million. The lathe will cost $35,000 per year to run, but it will save the firm $125,000 in labor costs and will be useful for 10 years. Suppose that for tax purposes, the lathe will be depreciated on a straight-line basis over its 10-year life to a salvage value of $100,000. The actual market value of the lathe at that time also will be $100,000. The discount rate is 8%, and the corporate tax rate is 35%. What is the NPV of buying the new lathe? (LO9-2)

15. Cash Flows. We’ve emphasized that the firm should pay attention only to cash flows when assessing the net present value of proposed projects. Depreciation is a noncash expense. Why

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292 Part Two Value

a. What was the change in net working capital during the year? b. If sales were $36,000 and costs were $24,000, what was cash flow for the year? Ignore taxes.

21. Cash Flows and Working Capital. A house painting business had revenues of $16,000 and expenses of $9,000 last summer. There were no depreciation expenses. However, the business reported the following changes in working capital:

then does it matter whether we assume straight-line or MACRS depreciation when we assess project NPV? (LO9-3)

16. Salvage Value. Quick Computing (from Problem 1) installed its previous generation of com- puter chip manufacturing equipment 3 years ago. Some of that older equipment will become unnecessary when the company goes into production of its new product. The obsolete equip- ment, which originally cost $40 million, has been depreciated straight-line over an assumed tax life of 5 years, but it can be sold now for $18 million. The firm’s tax rate is 35%. What is the after-tax cash flow from the sale of the equipment? (LO9-3)

17. Salvage Value. Your firm purchased machinery with a 7-year MACRS life for $10 million. The project, however, will end after 5 years. If the equipment can be sold for $4.5 million at the completion of the project, and your firm’s tax rate is 35%, what is the after-tax cash flow from the sale of the machinery? (LO9-3)

18. Depreciation and Project Value. Bottoms Up Diaper Service is considering the purchase of a new industrial washer. It can purchase the washer for $6,000 and sell its old washer for $2,000. The new washer will last for 6 years and save $1,500 a year in expenses. The opportunity cost of capital is 16%, and the firm’s tax rate is 40%. (LO9-3)

a. If the firm uses straight-line depreciation to an assumed salvage value of zero over a 6-year life, what are the cash flows of the project in years 0 to 6? The new washer will in fact have zero salvage value after 6 years, and the old washer is fully depreciated.

b. What is project NPV? c. What is NPV if the firm uses MACRS depreciation with a 5-year tax life?

19. Operating Cash Flows. Talia’s Tutus bought a new sewing machine for $40,000 that will be depreciated using the MACRS depreciation schedule for a 5-year recovery period. (LO9-3)

a. Find the depreciation charge each year. b. If the sewing machine is sold after 3 years for $22,000, what will be the after-tax proceeds

on the sale if the firm’s tax bracket is 35%?

20. Cash Flows. Canyon Tours showed the following components of working capital last year: (LO9-4)

Beginning End of Year

Accounts receivable $24,000 $23,000 Inventory 12,000 12,500 Accounts payable 14,500 16,500

Beginning End

Accounts receivable $1,200 $4,500 Accounts payable 700 300

Calculate net cash flow for the business for this period. (LO9-4)

22. Cash Flows and Working Capital. A firm had after-tax income last year of $1.2 million. Its depreciation expenses were $.4 million, and its total cash flow was $1.2 million. What hap- pened to net working capital during the year? (LO9-4)

23. Cash Flows and Working Capital. The only capital investment required for a small project is investment in inventory. Profits this year were $10,000, and inventory increased from $4,000 to $5,000. What was the cash flow from the project? (LO9-4)

24. Cash Flows and Working Capital. A firm’s balance sheets for year-end 2014 and 2015 contain the following data. What happened to investment in net working capital during 2015? All items are in millions of dollars. (LO9-4)

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Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 293

25. Project Evaluation. Suppose that Blooper’s customers paid their bills with an average 3-month delay (instead of 2 months) and that Blooper’s inventories were 20% rather than 15% of next year’s expenses. (LO9-4)

a. Would project NPV be higher or lower than that in the worked example in the chapter? b. Calculate Blooper’s working capital in each year of its project. c. What is the change in project NPV (use the Blooper spreadsheet)?

26. Project Evaluation. The following table presents sales forecasts for Golden Gelt Giftware. The unit price is $40. The unit cost of the giftware is $25.

Dec. 31, 2014 Dec. 31, 2015

Accounts receivable 32 36 Inventories 25 30 Accounts payable 12 26

Year Unit Sales

1 22,000 2 30,000 3 14,000 4 5,000

Thereafter 0

It is expected that net working capital will amount to 20% of sales in the following year. For example, the store will need an initial (year-0) investment in working capital of .20 × 22,000 × $40 = $176,000. Plant and equipment necessary to establish the giftware busi- ness will require an additional investment of $200,000. This investment will be depreciated using MACRS and a 3-year life. After 4 years, the equipment will have an economic and book value of zero. The firm’s tax rate is 35%. What is the net present value of the project? The dis- count rate is 20%. (LO9-4)

CHALLENGE PROBLEMS 27. Project Evaluation. Better Mousetraps has developed a new trap. It can go into production for

an initial investment in equipment of $6 million. The equipment will be depreciated straight line over 6 years to a value of zero, but in fact it can be sold after 6 years for $500,000. The firm believes that working capital at each date must be maintained at a level of 10% of next year’s forecast sales. The firm estimates production costs equal to $1.50 per trap and believes that the traps can be sold for $4 each. Sales forecasts are given in the following table. The project will come to an end in 5 years, when the trap becomes technologically obsolete. The firm’s tax bracket is 35%, and the required rate of return on the project is 12%. (LO9-2 and LO9-3)

Year: 0 1 2 3 4 5 6 Thereafter

Sales (millions of traps) 0 .5 .6 1.0 1.0 .6 .2 0

a. What is project NPV? b. By how much would NPV increase if the firm depreciated its investment using the 5-year

MACRS schedule?

28. Project Evaluation. PC Shopping Network may upgrade its modem pool. It last upgraded 2 years ago, when it spent $115 million on equipment with an assumed life of 5 years and an assumed salvage value of $15 million for tax purposes. The firm uses straight-line depreciation. The old equipment can be sold today for $80 million. A new modem pool can be installed today for $150 million. This will have a 3-year life and will be depreciated to zero using straight-line

Templates can be found in Connect.

Templates can be found in Connect.

Templates can be found in Connect.

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294 Part Two Value

depreciation. The new equipment will enable the firm to increase sales by $25 million per year and decrease operating costs by $10 million per year. At the end of 3 years, the new equipment will be worthless. Assume the firm’s tax rate is 35% and the discount rate for projects of this sort is 10%. (LO9-2)

a. What is the net cash flow at time 0 if the old equipment is replaced? b. What are the incremental cash flows in years 1, 2, and 3? c. What are the NPV and IRR of the replacement project?

29. Project Evaluation. In Example 8.2 in the previous chapter, we described a major investment in wind power by Cape Wind. Suppose that the company is now contemplating construction of a gas-fired power plant. The plant is likely to last 25 years and to have no salvage value. Deprecia- tion allowances for tax purposes on the investment of $386 million will be calculated using the 20-year MACRS schedule.

If the plant could be operated 24 hours a day every day, it would produce each year 6.04  million megawatt-hours (MWh) of electricity. However, a more realistic estimate is that the plant will operate at an average of 60% of this notional capacity. In the first year of opera- tion, the price of electricity is expected to average $66 per MWh, fuel costs are expected to be $38 per MWh, and labor and other costs are forecast to total $45 million. All prices and costs are expected to rise with inflation at 3% a year. The corporate tax rate is 35%. If the cost of capital is 12%, would you recommend that the company go ahead with the project? (LO9-2)

30. Project Evaluation. The efficiency gains resulting from a just-in-time inventory management system will allow a firm to reduce its level of inventories permanently by $250,000. What is the most the firm should be willing to pay for installing the system? (LO9-4)

31. Working Capital Management. Return to Problem 27. Suppose the firm can cut its require- ments for working capital in half by using better inventory control systems. By how much will this increase project NPV? (LO9-4)

WEB EXERCISE 1. Go to finance.yahoo.com and obtain the financial statements for Ford (F) and Microsoft

(MSFT). What were capital expenditures and sales for each firm? What were the ratios of capi- tal expenditure to sales for the last 3 years for both companies? What were the sales and net capital expenditures relative to total assets? What might explain the variation in these ratios for these two large corporations? Did the company make an investment or disinvestment in working capital in each of the 3 years?

SOLUTIONS TO SELF-TEST QUESTIONS 9.1 Remember, discount cash flows, not profits. Each tewgit machine costs $250,000 right away.

Recognize that outlay, but forget accounting depreciation. Cash flows per machine are:

Year: 0 1 2 3 4 5

Investment (outfl ow)

-250,000

Sales 250,000 300,000 300,000 250,000 250,000 Operating expenses -200,000 -200,000 -200,000 -200,000 -200,000 Cash fl ow -250,000 + 50,000 +100,000 +100,000 + 50,000 + 50,000

Each machine is forecast to generate $50,000 of cash flow in years 4 and 5. Thus it makes sense to keep operating for 5 years.

Templates can be found in Connect.

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Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 295

9.2 a,b. The site and buildings could have been sold or put to another use. Their values are oppor- tunity costs, which should be treated as incremental cash outflows.

c. Demolition costs are incremental cash outflows. d. The cost of the access road is sunk and not incremental. e. Lost cash flows from other projects are incremental cash outflows. f. Depreciation is not a cash expense and should not be included, except as it affects taxes.

(Taxes are discussed later in this chapter.)

9.3 Actual health costs will be increasing at about 7% a year.

Year: 1 2 3 4

Cost per worker $2,400 $2,568 $2,748 $2,940

The present value at 10% of these four cash flows is $8,377.

9.4 The tax rate is T = 35%. Taxes paid will be

T × (revenue - expenses - depreciation) = .35 × (600 - 300 - 200) = $35

Operating cash flow can be calculated as follows.

a. Revenue - expenses - taxes = 600 - 300 - 35 = $265 b. Net profit + depreciation = (600 - 300 - 200 - 35) + 200 = 65 + 200 = 265 c. (Revenues - cash expenses) × (1 - tax rate) + (depreciation × tax rate) 

= (600 - 300) × (1 - .35) + (200 × .35) = 265

9.5

Year MACRS 3-Year Depreciation Tax Shield

PV Tax Shield at 12%

1 3,333 1,167 1,042 2 4,445 1,556 1,240 3 1,481 518 369 4 741 259 165

Totals 10,000 3,500 2,816

The present value increases to 2,816, or $2,816,000.

SOLUTIONS TO SPREADSHEET QUESTIONS 1. NPV = $4,515

2. NPV = $4,459

3. NPV = $5,741. NPV rises because the real value of depreciation allowances and the deprecia- tion tax shield is higher when the inflation rate is lower.

MINICASE Jack Tar, CFO of Sheetbend & Halyard Inc. opened the company confidential envelope. It contained a draft of a competitive bid for a contract to supply duffel canvas to the U.S. Navy. The cover memo from Sheetbend’s CEO asked Mr. Tar to review the bid before it was submitted.

The bid and its supporting documents had been prepared by Sheetbend’s sales staff. It called for Sheetbend to supply 100,000 yards of duffel canvas per year for 5 years. The proposed selling price was fixed at $30 per yard.

Mr. Tar was not usually involved in sales, but this bid was unusual in at least two respects. First, if accepted by the navy, it

would commit Sheetbend to a fixed-price, long-term contract. Sec- ond, producing the duffel canvas would require an investment of $1.5 million to purchase machinery and to refurbish Sheetbend’s plant in Pleasantboro, Maine.

Mr. Tar set to work and by the end of the week had collected the following facts and assumptions:

• The plant in Pleasantboro had been built in the early 1900s and is now idle. The plant was fully depreciated on Sheetbend’s books, except for the purchase cost of the land (in 1947) of $10,000.

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296 Part Two Value

• Now that the land was valuable shorefront property, Mr. Tar thought the land and the idle plant could be sold, immediately or in the near future, for $600,000.

• Refurbishing the plant would cost $500,000. This investment would be depreciated for tax purposes on the 10-year MACRS schedule.

• The new machinery would cost $1 million. This investment could be depreciated on the 5-year MACRS schedule.

• The refurbished plant and new machinery would last for many years. However, the remaining market for duffel canvas was small, and it was not clear that additional orders could be obtained once the navy contract was finished. The machinery was custom-built and could be used only for duffel canvas. Its secondhand value at the end of 5 years was probably zero.

• Table 9.4 shows the sales staff’s forecasts of income from the navy contract. Mr. Tar reviewed this forecast and decided that

its assumptions were reasonable, except that the forecast used book, not tax, depreciation.

• But the forecast income statement contained no mention of working capital. Mr. Tar thought that working capital would average about 10% of sales.

Armed with this information, Mr. Tar constructed a spreadsheet to calculate the NPV of the duffel canvas project, assuming that Sheetbend’s bid would be accepted by the navy.

He had just finished debugging the spreadsheet when another confidential envelope arrived from Sheetbend’s CEO. It contained a firm offer from a Maine real estate developer to purchase Sheet- bend’s Pleasantboro land and plant for $1.5 million in cash.

Should Mr. Tar recommend submitting the bid to the navy at the proposed price of $30 per yard? The discount rate for this project is 12%.

Year: 1 2 3 4 5

1. Yards sold 100.00 100.00 100.00 100.00 100.00 2. Price per yard 30.00 30.00 30.00 30.00 30.00 3. Revenue (1 × 2) 3,000.00 3,000.00 3,000.00 3,000.00 3,000.00 4. Cost of goods sold 2,100.00 2,184.00 2,271.36 2,362.21 2,456.70 5. Operating cash fl ow (3 - 4) 900.00 816.00 728.64 637.79 543.30 6. Depreciation 250.00 250.00 250.00 250.00 250.00 7. Income (5 - 6) 650.00 566.00 478.64 387.79 293.30 8. Tax at 35% 227.50 198.10 167.52 135.72 102.65 9. Net income (7 - 8) $422.50 $367.90 $311.12 $252.07 $190.65

Notes: 1. Yards sold and price per yard would be fi xed by contract. 2. Cost of goods includes fi xed cost of $300,000 per year plus variable costs of $18 per yard. Costs are expected to

increase at the infl ation rate of 4% per year. 3. Depreciation: A $1 million investment in machinery is depreciated straight-line over 5 years ($200,000 per year).

The $500,000 cost of refurbishing the Pleasantboro plant is depreciated straight-line over 10 years ($50,000 per year).

TABLE 9.4 Forecast income statement for the U.S. Navy duffel canvas project (dollar values in thousands, except price per yard)

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298

Project Analysis

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

10-1 Appreciate the practical problems of capital budgeting in large corporations.

10-2 Use sensitivity, scenario, and break-even analyses to see how project profitability would be affected by an error in your forecasts.

10-3 Understand why an overestimate of sales is more serious for projects with high operating leverage.

10-4 Recognize the importance of managerial flexibility in capital budgeting.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

10 CHAPTE R

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299

P A

R T

TW O

I t helps to use discounted cash-flow techniques to value new projects, but good investment deci-sions also require good data. Therefore, we start this chapter by thinking about how firms organize the

capital budgeting operation to get the kind of infor-

mation they need. In addition, we look at how they

try to ensure that everyone involved works together

toward a common goal.

Project evaluation should never be a mechanical

exercise in which the financial manager takes a set

of cash-flow forecasts and cranks out a net present

value. Cash-flow estimates are just that—estimates.

Financial managers need to look behind the fore-

casts to try to understand what makes the project

tick and what could go wrong with it. A number of

techniques have been developed to help manag-

ers identify the key assumptions in their analysis.

These techniques involve asking a number of “what-

if” questions. What if your market share turns out to

be higher or lower than you forecast? What if energy

prices rise faster than you expect? In the second

part of this chapter we show how managers use the

techniques of sensitivity analysis, scenario analysis,

and break-even analysis to help answer these what-if

questions.

Books about capital budgeting sometimes create

the impression that once the manager has made

an investment decision, there is nothing to do but sit

back and watch the cash flows develop. But since

cash flows rarely proceed as anticipated, companies

constantly need to modify their operations. If cash

flows are better than anticipated, the project may

be expanded; if they are worse, it may be scaled

back or abandoned altogether. In the third section of

this chapter we describe how good managers take

account of these options when they analyze a proj-

ect and why they are willing to pay money today to

build in future flexibility.

Va lu

e

When undertaking capital investments, good managers maintain maximum flexibility.

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300 Part Two Value

10.1 How Firms Organize the Investment Process In the previous chapter you learned how to evaluate a proposed investment such as the Blooper project. But potential projects and accurate cash-flow forecasts don’t fall from the sky. Promising investment opportunities have to be identified, and they must fit in with the firm’s strategic goals. To evaluate these opportunities, financial manag- ers need unbiased cash-flow forecasts that have not been skewed to “sell” a project to upper management. Large firms in particular need to establish systems that facilitate effective communication across different parts of the organization.

For most sizable firms, investments are evaluated in two separate stages.

Stage 1: The Capital Budget Once a year, the head office generally asks each of its divisions and plants to provide a list of the investments that they would like to make. 1 These are gathered together into a proposed capital budget.

This budget is then reviewed and pruned by senior management and staff special- izing in planning and financial analysis. Usually there are negotiations between the firm’s senior management and its divisional management, and there may also be spe- cial analyses of major outlays or ventures into new areas. Once the budget has been approved, it generally remains the basis for planning over the ensuing year.

Many investment proposals bubble up from the bottom of the organization. But sometimes the ideas are likely to come from higher up. For example, the managers of plants A and B cannot be expected to see the potential benefits of closing their plants and consolidating production at a new plant C. We expect divisional management to propose plant C. Similarly, divisions 1 and 2 may not be eager to give up their own data processing operations to a large central computer. That proposal would come from senior management.

Senior management’s concern is to see that the capital budget matches the firm’s strategic plans. It needs to ensure that the firm is concentrating its efforts in areas where it has a real competitive advantage. As part of this effort, management must also identify declining businesses that should be sold or allowed to run down.

The firm’s capital investment choices should reflect both “bottom-up” and “top- down” processes—capital budgeting and strategic planning, respectively. The two pro- cesses should complement each other. Plant and division managers, who do most of the work in bottom-up capital budgeting, may not see the forest for the trees. Strategic planners may have a mistaken view of the forest because they do not look at the trees.

Stage 2: Project Authorizations The annual budget is important because it allows everybody to exchange ideas before attitudes have hardened and personal commitments have been made. However, the fact that your pet project has been included in the annual budget doesn’t mean you have permission to go ahead with it. At a later stage you will need to draw up a detailed pro- posal setting out particulars of the project, cash-flow forecasts, and present value cal- culations. If your project is large, this proposal may have to pass a number of hurdles before it is finally approved.

Your proposal will need to be backed up with supporting information, such as engi- neering analyses, cost estimates from a quantity surveyor, and market research reports. The type of backup information that you need to provide depends on the project cat- egory. For example, some firms use a fourfold breakdown:

1. Outlays required by law or company policy, for example, for pollution control equipment. These outlays do not need to be justified on financial grounds. The main

1 Large firms may be divided into several divisions. For example, International Paper has divisions that specialize in printing paper, packaging, and forest products. Each of these divisions may be responsible for a number of plants.

capital budget List of planned investment projects.

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Chapter 10 Project Analysis 301

issue is whether requirements are satisfied at the lowest possible cost. The decision is therefore likely to hinge on engineering analyses of alternative technologies.

2. Maintenance or cost reduction, such as machine replacement. Engineering analysis is also important in machine replacement, but new machines have to pay their own way. Here the firm faces the classical capital budgeting problems described in Chapters 8 and 9.

3. Capacity expansion in existing businesses. Projects in this category are less straightforward; these decisions may hinge on forecasts of demand, possible shifts in technology, and the reactions of competitors.

4. Investment for new products. Projects in this category are most likely to depend on strategic decisions. The first projects in a new area may not have positive NPVs if considered in isolation, but they may give the firm a valuable option to undertake follow-up projects. More about this later in the chapter.

Problems and Some Solutions Valuing capital investment opportunities is hard enough when you can do the entire job yourself. In most firms, however, capital budgeting is a cooperative effort, and this brings with it some challenges.

Ensuring That Forecasts Are Consistent Inconsistent assumptions often creep into investment proposals. For example, suppose that the manager of the furni- ture division is bullish (optimistic) on housing starts but the manager of the appliance division is bearish (pessimistic). This inconsistency makes the projects proposed by the furniture division look more attractive than those of the appliance division.

To ensure consistency, many firms begin the capital budgeting process by estab- lishing forecasts of economic indicators, such as inflation and the growth in national income, as well as forecasts of particular items that are important to the firm’s busi- ness, such as housing starts or the price of raw materials. These forecasts can then be used as the basis for all project analyses.

Eliminating Conflicts of Interest In Chapter 1 we pointed out that while managers want to do a good job, they are also concerned about their own futures. If the interests of managers conflict with those of stockholders, the result is likely to be poor investment decisions. For example, new plant managers naturally want to demonstrate good performance right away. So they might propose quick-payback projects even if NPV is sacrificed. Unfortunately, many firms measure performance and reward man- agers in ways that encourage such behavior. If the firm always demands quick results, it is unlikely that plant managers will concentrate only on NPV.

Reducing Forecast Bias Someone who is keen to get a project proposal accepted is also likely to look on the bright side when forecasting the project’s cash flows. Such overoptimism is a common feature in financial forecasts. For example, think of large public expenditure proposals. How often have you heard of a new mis- sile, dam, or highway that actually cost less than was originally forecast? Overop- timism is not altogether bad. Psychologists stress that optimism and confidence are likely to increase effort, commitment, and persistence. The problem is that it is dif- ficult for senior managers to judge the true prospects for each project.

Sometimes a head office seems actually to encourage project sponsors to overstate their case. For example, if middle managers believe that success depends on having the largest division rather than the most profitable one, they will propose large expan- sion projects that they do not believe have the highest possible net present value. Or if divisions must compete for limited resources, they will try to outbid each other for those resources. The fault in such cases is top management’s—if lower-level manag- ers are not rewarded on the basis of net present value and contribution to firm value, it should not be surprising that they focus their efforts elsewhere.

Overoptimism and cost overruns

BEYOND THE PAGE

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302 Part Two Value

Other problems stem from sponsors’ eagerness to obtain approval for their favorite projects. As the proposal travels up the organization, alliances are formed. Thus once a division has screened its own plants’ proposals, the plants in that division unite in competing against outsiders. The result is that the head office may receive several thousand investment proposals each year, all essentially sales documents presented by united fronts and designed to persuade. The forecasts have been doctored to ensure that NPV appears positive.

Since it is difficult for senior management to evaluate each specific assumption in an investment proposal, capital investment decisions are effectively decentralized whatever the rules say. Some firms accept this; others rely on head office staff to check capital investment proposals.

Sometimes senior managers try to offset bias by increasing the hurdle rate for capi- tal expenditure. Suppose the true cost of capital is 10% but the CEO is frustrated by the large fraction of projects that don’t subsequently earn 10%. Therefore, she directs project sponsors to use a 15% discount rate. In other words, she adds a 5% fudge fac- tor in an attempt to offset forecast bias. But it doesn’t work; it never works. Brealey, Myers, and Marcus’s Second Law explains why. The law states: The proportion of projects that promise positive NPVs at the corporate hurdle rate is independent of the hurdle rate.2

Sorting the Wheat from the Chaff Senior managers are continually bom- barded with requests for funds for capital expenditures. All these requests are sup- ported with detailed analyses showing that the projects have positive NPVs. How then can managers ensure that only worthwhile projects make the grade? One response of senior managers to this problem of poor information is to impose rigid expenditure limits on individual plants or divisions. These limits force the subunits to choose among projects. The firm ends up using capital rationing not because capital is unob- tainable but as a way of decentralizing decisions. 3

Senior managers might also ask some searching questions about why the project has a positive NPV. After all, if the project is so attractive, why hasn’t someone already undertaken it? Will others copy your idea if it is so profitable? Positive NPVs are plau- sible only if your company has some competitive advantage.

Such an advantage can arise in several ways. You may be smart or lucky enough to be the first to the market with a new or improved product for which customers will pay premium prices. Your competitors eventually will enter the market and squeeze out excess profits, but it may take them several years to do so. Or you may have a proprietary technology or production cost advantage that competitors cannot easily match. You may have a contractual advantage such as the distributorship for a particu- lar region. Or your advantage may be as simple as a good reputation and an established customer list.

Analyzing competitive advantage can also help ferret out projects that incorrectly appear to have a negative NPV. If you are the lowest-cost producer of a profitable product in a growing market, then you should invest to expand along with the market. If your calculations show a negative NPV for such an expansion, then you probably have made a mistake.

10.2 Some “What-If” Questions “What-if” questions ask what will happen to a project in various circumstances. For example, what will happen if the economy enters a recession? What if a competitor enters the market? What if costs turn out to be higher than anticipated?

2 There is no First Law. We think “Second Law” sounds better. 3 We discussed capital rationing in Chapter 8.

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Chapter 10 Project Analysis 303

You might wonder why one would bother with these sorts of questions. For instance, suppose your project seems to have a positive NPV based on the best available fore- casts, in which you have already factored in the chances of both positive and negative surprises. Won’t you commit to this project regardless of possible future surprises? If things later don’t work out as you had hoped, that is too bad, but you don’t have a crystal ball.

In fact, what-if analysis is crucial to capital budgeting. First recall that cash-flow forecasts are just estimates. You often have the opportunity to improve on those esti- mates if you are willing to commit additional resources to the effort. For example, if you wish to improve the precision of an estimate of the demand for a product, you might conduct additional market research. Or if cost uncertainty is a concern, you might commission additional engineering studies to evaluate the feasibility of a novel production process. But how do you know when to keep sharpening your forecasts or where it is best to devote your efforts? What-if analysis can help identify the inputs that are most worth refining before you commit to a project. These will be the ones that have the greatest potential to alter project NPV.

Moreover, managers don’t simply turn a key to start a project and then walk away and let the cash flows roll in. There are always surprises, adjustments, and refinements. What-if analysis indicates where the most likely need for adjustments will arise and where to undertake contingency planning. In this section, therefore, we examine some of the standard tools managers use when considering important types of what-if questions.

Sensitivity Analysis Uncertainty means that more things can happen than will happen. Therefore, whenever managers are given a cash-flow forecast, they try to determine what else might happen and the implications of those possible events. This is called sensitivity analysis.

Put yourself in the well-heeled shoes of the financial manager of the Finefodder supermarket chain. Finefodder is considering opening a new superstore in Grave- nstein, and your staff members have prepared the figures shown in Table 10.1 . To keep the example simple we have assumed no inflation. We have also assumed that the entire investment can be depreciated straight-line for tax purposes, we have neglected the working capital requirement, and we have ignored the fact that at the end of the 12 years you could sell off the land and buildings.

Some of the costs of running a supermarket are fixed. For example, regardless of the level of output, you still have to heat and light the store and pay the store manager. These fixed costs are forecast to be $2 million per year.

Other costs vary with the level of sales. In particular, the lower the sales, the less food you need to buy. Also, if sales are lower than forecast, you can operate a

sensitivity analysis Analysis of the effects on project profitability of changes in sales, costs, and so on.

fixed costs Costs that do not depend on the level of output.

TABLE 10.1 Cash-flow forecasts for Finefodder’s superstore

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Initial investment

1. Sales

2. Variable costs

3. Fixed costs

4. Depreciation

5. Pretax profit

6. Taxes (at 40%)

7. Profit after tax

8. Cash flow from operations

Variable costs as proportion of sales

Discount rate

12-year annuity factor

Net present value

16,000,000

13,000,000

2,000,000

450,000

550,000

220,000

330,000

780,000

0.8125

0.08

7.5361

478,141

-5,400,000

Year 0

BA C

Years 1-12

You can find this spreadsheet in Connect.

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304 Part Two Value

smaller number of checkouts and reduce the staff needed to restock the shelves. The new superstore’s variable costs are estimated at 81.25% of sales. Thus variable costs =  .8125  ×  $16  million  =  $13 million.

The initial investment of $5.4 million will be depreciated on a straight-line basis over the 12-year period, resulting in annual depreciation of $450,000. Profits are taxed at a rate of 40%.

Given these inputs, we add after-tax profit plus depreciation to obtain cash flow in periods 1 to 12 of $780,000. As an experienced financial manager, you recognize immediately that these cash flows constitute an annuity, and therefore you calculate the 12-year annuity factor at a discount rate of 8%. The net present value of the project is calculated as

NPV = -$5,400,000 + $780,000 × 12-year annuity factor = $478,141

It appears that the project is in fact viable, with a positive net present value. Before you agree to go ahead, however, you want to delve behind these forecasts and identify the key variables that will determine whether the project succeeds or fails.

You seem to have taken account of the important factors that will determine success or failure, but look out for things you may have forgotten. Perhaps there will be delays in obtaining planning permission, or perhaps you will need to undertake costly land- scaping. The greatest dangers often lie in these unknown unknowns, or “unk-unks,” as scientists call them.

Having found no unk-unks (no doubt you’ll find them later), you look at how NPV may be affected if you have made a wrong forecast of sales, costs, and so on. To do this, you first obtain optimistic and pessimistic estimates for the underlying variables. These are set out in the left-hand columns of Table 10.2 .

Next you see what happens to NPV under the optimistic or pessimistic forecasts for each of these variables. The right-hand side of Table 10.2 shows the project’s net present value if the variables are set one at a time to their optimistic and pessimis- tic values. For example, suppose fixed costs are $1.9 million rather than the forecast $2 million. When you redo the calculations with the lower figure for fixed costs, you find that NPV rises to $930,306, a gain of approximately $452,000. The other entries in the three columns on the right in Table 10.2 similarly show how the NPV of the project changes when an input is changed.

Your project is by no means a sure thing. The principal uncertainties appear to be sales and variable costs. For example, if sales are only $14 million rather than the forecast $16 million (and all other forecasts are unchanged), then the project has an NPV of -$1.217 million. If variable costs are 83% of sales (and all other forecasts are unchanged), then the project has an NPV of -$787,920.

variable costs Costs that change as the level of output changes.

Range NPV

Variable Pessimistic Expected Optimistic Pessimistic Expected Optimistic

Investment $ 6,200,000 $5,400,000 $5,000,000 -$ 120,897 + $478,141 + $777,660 Sales 14,000,000 16,000,000 18,000,000 - 1,217,477 + 478,141 + 2,173,758 Variable cost as percent of sales 83 81.25 80 - 787,920 + 478,141 + 1,382,470 Fixed cost 2,100,000 2,000,000 1,900,000 + 25,976 + 478,141 + 930,306

TABLE 10.2 Sensitivity analysis for superstore project

Sensitivity analysis

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Recalculate cash flow as in Table 10.1 , now assuming that variable costs are 83% of sales. Confirm that NPV will be -$787,920.

Self-Test 10.1

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Chapter 10 Project Analysis 305

Value of Information Now that you know the project could be thrown badly off course by a poor estimate of sales, you might like to see whether it is possible to resolve some of this uncertainty. Perhaps your worry is that the store will fail to attract sufficient shoppers from neighboring towns. In that case, additional survey data and more careful analysis of travel times may be worthwhile.

On the other hand, there is less value to gathering additional information about fixed costs. Because the project is marginally profitable even under pessimistic assump- tions about fixed costs, you are unlikely to be in trouble if you have misestimated that variable.

Limits to Sensitivity Analysis Your analysis of the forecasts for Finefodder’s new superstore is an example of sensitivity analysis. Sensitivity analysis expresses cash flows in terms of unknown variables and then calculates the consequences of misestimating those variables. It forces the manager to identify the underlying factors, indicates where additional information would be most useful, and helps to expose con- fused or inappropriate forecasts.

Of course, there is no law stating which variables you should consider in your sen- sitivity analysis. For example, you may wish to look separately at labor costs and the costs of the goods sold. Or if you are concerned about a possible change in the corpo- rate tax rate, you may wish to look at the effect of such a change on the project’s NPV.

One drawback to sensitivity analysis is that it gives somewhat ambiguous results. For example, what exactly does optimistic or pessimistic mean? One department may be interpreting the terms in a different way from another. Ten years from now, after hundreds of projects, hindsight may show that one department’s pessimistic limit was exceeded twice as often as the other’s; but hindsight won’t help you now while you’re making the investment decision.

Another problem with sensitivity analysis is that the underlying variables are likely to be interrelated. For example, if sales exceed expectations, demand will likely be stronger than you anticipated and your profit margins will be wider. Or, if wages are higher than your forecast, both variable costs and fixed costs are likely to be at the upper end of your range.

Because of these connections, you cannot push one-at-a-time sensitivity analysis too far. It is impossible to obtain optimistic and pessimistic values for total project cash flows from the information in Table 10.2 . Still, it does give a sense of which vari- ables should be most closely monitored.

Scenario Analysis When variables are interrelated, managers often find it helpful to look at how their project would fare under different scenarios. Scenario analysis allows them to look at different but consistent combinations of variables. Forecasters generally prefer to give an estimate of revenues or costs under a particular scenario rather than to give some absolute optimistic or pessimistic value.

Suppose that you are worried that Stop and Scoff (S&S) may decide to build a new store in nearby Salome. That would reduce sales in your Gravenstein store by 15%, and you might be forced into a price war to keep the remaining business. Prices might be reduced to the point that variable costs equal 82% of revenue. Table 10.3 shows that under this scenario of both lower sales and smaller margins your new venture would no longer be worthwhile. A bit more research into S&S’s intentions appears to be called for.

An extension of scenario analysis is called simulation analysis. Here, instead of specifying a relatively small number of scenarios, a computer generates several hun- dred or thousand possible combinations of variables according to probability distri- butions specified by the analyst. Each combination of variables corresponds to one scenario. Project NPV and other outcomes of interest can be calculated for each

scenario analysis Project analysis given a particular combination of assumptions.

simulation analysis Estimation of the probabilities of different possible outcomes, e.g., from an investment project.

Scenario analysis

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Monte Carlo simulation

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306 Part Two Value

combination of variables, and the entire probability distribution of outcomes can be constructed from the simulation results.

TABLE 10.3 Scenario analysis comparing NPV of superstore with and without competing store

What is the basic difference between sensitivity analysis and scenario analysis?

Self-Test 10.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Initial investment 1. Sales 2. Variable costs 3. Fixed costs 4. Depreciation 5. Pretax profit 6. Taxes (at 40%) 7. Profit after tax 8. Cash flow from operations

Variable costs as proportion of sales Discount rate 12-year annuity factor Net present value

Assumptions: Competing store causes (1) a 15% decline in sales and (2) variable costs to increase to 82% of sales.

16,000,000 13,000,000 2,000,000

450,000 550,000 220,000 330,000 780,000

0.8125 8%

7.5361 478,141

13,600,000 11,152,000 2,000,000

450,000 -2,000

-800 -1,200

448,800

0.8200 8%

7.5361 -2,017,808

-5,400,000 Year 0 Base Case Competing Store Scenario

BA C D Cash flows in years 1-12

10.3 Break-Even Analysis When you undertake a sensitivity analysis of a project or when you look at alternative scenarios, you are asking how serious it would be if you have misestimated sales or costs. Managers sometimes prefer to rephrase this question and ask how far off the estimates could be before the project begins to lose money. This exercise is known as break-even analysis.

For many projects, the make-or-break variable is sales volume. Therefore, managers most often focus on the break-even level of sales. However, you might also look at other variables, for example, at how high costs could be before the project goes into the red.

As it turns out, “losing money” can be defined in more than one way. Most often, the break-even condition is defined in terms of accounting profits. More properly, however, it should be defined in terms of net present value. We will start with account- ing break-even, show that it can lead you astray, and then show how NPV break-even can be used as an alternative.

Accounting Break-Even Analysis The accounting break-even point is the level of sales at which profits are zero or, equivalently, at which total revenues equal total costs. As we have seen, some costs are fixed regardless of the level of output. Other costs vary with the level of output.

When you first analyzed the superstore project, you came up with the following estimates:

break-even analysis Analysis of the level of sales at which the project breaks even.

Break-even analysis

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You can find this spreadsheet in Connect.

Sales $16 million Variable costs 13 million Fixed costs 2 million Depreciation 0.45 million

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Chapter 10 Project Analysis 307

Notice that variable costs are 81.25% of sales. So for each additional dollar of sales, costs increase by only $.8125. We can easily determine how much business the super- store needs to attract to avoid losses. If the store sells nothing, the income statement will show fixed costs of $2 million and depreciation of $450,000. Thus there will be an accounting loss before tax of $2.45 million. Each dollar of sales reduces this loss by $1.00  -  $.8125  =  $.1875. Therefore, to cover fixed costs plus depreciation, you need sales of 2.45  million/.1875  =  $13.067 million. At this sales level, the firm will break even. More generally,

Break-even level of revenues =

fixed costs including depreciation

additional profit from each additional dollar of sales

(10.1)

Table 10.4 shows the income statement with only $13.067 million of sales. Figure  10.1 shows how the break-even point is determined. The blue 45-degree

line shows the store’s accounting revenues. The dashed cost line shows how costs vary with sales. If the store doesn’t sell a cent, it still incurs fixed costs and depre- ciation amounting to $2.45 million. Each extra dollar of sales adds $.8125 to these costs. When sales are $13.067 million, the two lines cross, indicating that costs equal revenues. For lower sales, revenues are less than costs and the project is in the red; for higher sales, revenues exceed costs and the project moves into the black.

Is a project that breaks even in accounting terms an acceptable investment? If you are not sure about the answer, here’s a possibly easier question: Would you be happy about an investment in a stock that after 5 years gave you a total rate of return of zero? We hope not. You might break even on such a stock, but a zero return does not com- pensate you for the time value of money or the risk that you have taken.

Item $ Thousands

Revenues 13,067 Variable costs 10,617 (81.25% of sales) Fixed costs 2,000 Depreciation 450 Pretax profi t 0 Taxes 0 Profi t after tax 0

TABLE 10.4 Income statement, break-even sales volume

FIGURE 10.1 Accounting break-even analysis

Costs exceed revenue

Sales revenue ($ millions)

Revenue exceeds costs

13.067

Fixed costs

Variable costs

Revenue

Total costs

C o

st s

an d

r ev

en u

e ($

m ill

io n

s)

13.067

2.45

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308 Part Two Value

A project that simply breaks even on an accounting basis gives you your money back but does not cover the opportunity cost of the capital tied up in the project. A project that breaks even in accounting terms will surely have a negative NPV.

Let’s check this with the superstore project. Suppose that in each year the store has sales of $13.067 million—just enough to break even on an accounting basis. What would be its operating cash flow?

Operating cash flow = profit after tax + depreciation

= 0 + $450,000 = $450,000

The initial investment is $5.4 million. In each of the next 12 years, the firm receives a cash flow of $450,000. So the firm gets its money back:

Total operating cash flow = initial investment 12 × $450,000 = $5.4 million

But revenues are not sufficient to repay the opportunity cost of that $5.4 million invest- ment. NPV is negative.

NPV Break-Even Analysis A manager who calculates an accounting-based measure of break-even may be tempted to think that any project that earns more than this figure will help shareholders. But projects that break even on an accounting basis are really making a loss—they are fail- ing to cover the costs of capital employed. Managers who accept such projects are not helping their shareholders. Therefore, instead of asking what sales must be to produce an accounting profit, it is more useful to focus on the point at which NPV switches from negative to positive. This is called the NPV break-even point.

The cash flows of the superstore project in each year will depend on sales as follows: NPV break-even point Level of sales at which project net present value becomes positive.

1. Variable costs 81.25% of sales 2. Fixed costs $2 million 3. Depreciation $450,000 4. Pretax profi t (.1875 × sales) - $2.45 million 5. Tax (at 40%) .40 × (.1875 × sales - $2.45 million) 6. Profi t after tax .60 × (.1875 × sales - $2.45 million) 7. Cash fl ow (3 + 6) $450,000 + .6 × (.1875 × sales - $2.45 million)

= .1125 × sales - $1.02 million

This cash flow will last for 12 years. So to find its present value we multiply by the 12-year annuity factor. With a discount rate of 8%, the present value of $1 a year for each of 12 years is $7.536. Thus the present value of the cash flows is

PV(cash flows) = 7.536 × (.1125 × sales - $1.02 million)

The project breaks even in present value terms (that is, has a zero NPV) if the pres- ent value of these cash flows is equal to the initial $5.4 million investment. Therefore, break-even occurs when

PV(cash flows) = investment 7.536 × (.1125 × sales - $1.02 million) = $5.4 million .8478 × sales - $7.69 million = $5.4 million Sales = (5.4 + 7.69)/.8478 = $15.4 million

Therefore, the store needs sales of $15.4 million a year for the investment to have a zero NPV. This is more than 18% higher than the point at which the project has zero profit.

Figure 10.2 is a plot of the present value of the inflows and outflows from the super- store as a function of annual sales. The two lines cross when sales are $15.4 million.

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Chapter 10 Project Analysis 309

This is the point at which the project has zero NPV. As long as sales are greater than this, the present value of the inflows exceeds the present value of the outflows and the project has a positive NPV. 4

4 Think back to our discussion of economic value added (EVA) in Chapter 4. A project that breaks even on a present value basis will have a positive accounting profit but zero economic value added. In other words, it will just cover all its costs, including the cost of capital.

FIGURE 10.2 NPV break- even analysis

NPV is negative NPV is positive

15.4

PV of project cash flow

Investment

P ro

je ct

v al

u es

( $

m ill

io n

s)

5.4

0

-7.69

Sales revenue ($ millions)

What would be the NPV break-even level of sales if the capital investment was only $5 million?

Self-Test 10.3

Example 10.1 Break-Even Analysis We have said that projects that break even on an accounting basis are really making a loss—they are losing the opportunity cost of their investment. Here is a dramatic example. Lophead Aviation is contemplating investment in a new pas- senger aircraft, code-named the Trinova. Lophead’s financial staff has gathered together the following estimates:

1. The cost of developing the Trinova is forecast at $900 million, and this investment can be depreciated in six equal annual amounts.

2. Production of the plane is expected to take place at a steady annual rate over the following 6 years.

3. The average price of the Trinova is expected to be $15.5 million. 4. Fixed costs are forecast at $175 million a year. 5. Variable costs are forecast at $8.5 million a plane. 6. The tax rate is 50%. 7. The cost of capital is 10%.

Lophead’s financial manager has used this information to construct a forecast of the profitability of the Trinova program. This is shown in rows 1 to 7 of Table 10.5 (ignore row 8 for a moment).

How many aircraft does Lophead need to sell to break even? The answer depends on what is meant by “break even.” In accounting terms the venture will break even when net profit (row 7 in the table) is zero. In this case,

(3.5 × planes sold) - 162.5 = 0

Planes sold = 162.5/3.5 = 46.4

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TABLE 10.5 Forecast profitability for production of the Trinova airliner (figures in $ millions)

Year 0 Years 1–6

Investment $900 1. Sales 15.5 × planes sold 2. Variable costs 8.5 × planes sold 3. Fixed costs 175 4. Depreciation 900/6 = 150 5. Pretax profi t (1 - 2 - 3 - 4) (7 × planes sold) - 325 6. Taxes (at 50%) (3.5 × planes sold) - 162.5 7. Net profi t (5 - 6) (3.5 × planes sold) - 162.5 8. Net cash fl ow (4 + 7) -$900 (3.5 × planes sold) - 12.5

Thus Lophead needs to sell about 46 planes a year, or a total of 280 planes over the 6 years to show a profit. With a price of $15.5 million a plane, Lophead will break even in accounting terms with annual revenues of 46.4  ×  $15.5  million  =  $719 million.

We would have arrived at the same answer if we had used our formula to calcu- late the break-even level of revenues. Notice that the variable cost of each plane is $8.5 million, which is 54.8% of the $15.5 million sale price. Therefore, each dollar of sales increases pretax profits by $1  -  $.548  =  $.452. Now we use the formula for the accounting break-even point:

Break-even revenues = fixed costs including depreciation

additional profit from each additional dollar of sales

= $325 million

.452 = $719 million

If Lophead sells about 46 planes a year, it will recover its original investment, but it will not earn any return on the capital tied up in the project. Companies that earn a zero return on their capital can expect some unhappy shareholders. Sharehold- ers will be content only if the company’s investments earn at least the cost of the capital invested. True break-even occurs when the projects have zero NPV.

How many planes must Lophead sell to break even in terms of net present value? Development of the Trinova costs $900 million. If the cost of capital is 10%, the 6-year annuity factor is 4.3553. The last row of Table 10.5 shows that net cash flow (in millions of dollars) in years 1–6 equals (3.5  ×  planes sold  -  12.5). We can now find the annual plane sales necessary to break even in terms of NPV:

4.3553(3.5 × planes sold - 12.5) = 900

15.2436 × planes sold - 54.44 = 900

Planes sold = 954.44/15.2436 = 62.6

Thus, while Lophead will break even in terms of accounting profits with sales of 46.4 planes a year (about 280 in total), it needs to sell 62.6 a year (or about 375 in total) to recover the opportunity cost of the capital invested in the project and break even in terms of NPV.

Our example may seem fanciful, but it is based loosely on reality. In 1971 Lock- heed was in the middle of a major program to bring out the L-1011 TriStar airliner. This program was to bring Lockheed to the brink of failure, and it tipped Rolls-Royce (supplier of the TriStar engine) over the brink. In giving evidence to Congress, Lock- heed argued that the TriStar program was commercially attractive and that sales would eventually exceed the break-even point of about 200 aircraft. But in calculating this break-even point, Lockheed appears to have ignored the opportunity cost of the huge

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Chapter 10 Project Analysis 311

capital investment in the project. Lockheed probably needed to sell about 500 aircraft to reach a zero net present value. 5

5 The true break-even point for the TriStar program is estimated in U. E. Reinhardt, “Break-Even Analy- sis for Lockheed’s TriStar: An Application of Financial Theory,” Journal of Finance 28 (September 1973), pp. 821–838.

What is the basic difference between sensitivity analysis and break-even analysis?

Self-Test 10.4

Operating Leverage A project’s break-even point depends on both its fixed costs, which do not vary with sales, and the profit on each extra sale. Managers often face a trade-off between these variables. For example, we typically think of rental expenses as fixed costs. But super- market companies sometimes rent stores with contingent rent agreements. This means that the amount of rent the company pays is tied to the level of sales from the store. Rent rises and falls along with sales. In this case, the store replaces a fixed cost with a variable cost that is linked to sales. Because a greater proportion of the company’s expenses will fall when its sales fall, its break-even point is reduced.

Of course, a high proportion of fixed costs is not all bad. The firm whose costs are largely fixed fares poorly when demand is low, but it may make a killing during a boom. Let us illustrate.

Suppose that Finefodder is considering a contingent rental arrangement for its new store. The effect would be to reduce fixed costs from $2 million to $1.56 million, but variable costs would rise from 81.25% to 84% of sales. Table 10.6 shows that with the normal level of sales, the two policies fare equally. In a slump a store with a contingent rental agreement does better since its costs fall along with revenue. In a boom the reverse is true, and the store with the higher proportion of fixed costs has the advantage.

If Finefodder enters into a fixed rental agreement, each extra dollar of sales increases pretax profits by $1.00  -  $.8125  =  $.1875. With contingent rents, an extra dollar of sales increases profits by only $1.00  -  $.84  =  $.16. As a result, a store with high fixed costs is said to have high operating leverage. High operating leverage magnifies the effect on profits of a fluctuation in sales.

We can measure a business’s operating leverage by asking how much profits change for each 1% change in sales. The degree of operating leverage, often abbreviated as DOL, is this measure:

DOL = percentage change in profits

percentage change in sales (10.2)

operating leverage Degree to which costs are fixed.

degree of operating leverage (DOL) Percentage change in profits given a 1% change in sales.

TABLE 10.6 A store with high operating leverage performs relatively badly in a slump but flourishes in a boom (figures in $ thousands).

High Fixed Costs High Variable Costs

Slump Normal Boom Slump Normal Boom

Sales 13,000 16,000 19,000 13,000 16,000 19,000 - Variable costs 10,563 13,000 15,438 10,920 13,440 15,960 - Fixed costs 2,000 2,000 2,000 1,560 1,560 1,560 - Depreciation 450 450 450 450 450 450 = Pretax profi t -13 550 1,112 70 550 1,030

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312 Part Two Value

For example, Table 10.6 shows that as the store moves from normal conditions to boom, sales increase from $16 million to $19 million, a rise of 18.75%. For the policy with high fixed costs, profits increase from $550,000 to $1,112,000, a rise of 102.2%. Therefore,

DOL = 102.2

18.75 = 5.45

The percentage change in sales is magnified more than fivefold in terms of the per- centage impact on profits.

Now look at the operating leverage of the store if it uses the policy with low fixed costs but high variable costs. As the store moves from normal times to boom, profits increase from $550,000 to $1,030,000, a rise of 87.3%. Therefore,

DOL = 87.3

18.75 = 4.65

Because some costs remain fixed, a change in sales still generates a large percentage change in profits, but the degree of operating leverage is lower.

In fact, one can show that degree of operating leverage depends on fixed charges (including depreciation) in the following manner: 6

DOL = 1 + fixed costs

profits (10.3)

6 This formula for DOL can be derived as follows: If sales increase by 1%, then variable costs also should increase by 1%, and profits will increase by .01  ×  (sales  -  variable costs)  =  .01  ×  (profits  +  fixed costs). Now recall the definition of DOL:

DOL = percentage change in profits

percentage change in sales =

change in profits/level of profits

.01

= 100 × change in profits

level of profits = 100 ×

.01 × (profits + fixed costs)

level of profits

= 1 + fixed costs

profits

Example 10.2 Operating Leverage Suppose the firm adopts the high-fixed-cost policy. Then fixed costs including depreciation will be 2.00  +  .45  =  $2.45 million. Since the store produces profits of $.55 million at a normal level of sales, DOL should be

DOL = 1 + fixed costs

profits = 1 +

2.45 .55

= 5.45

This value matches the one we obtained by comparing the actual percentage changes in sales and profits.

Some companies have much higher fixed costs than others. Look, for example, at Table 10.7 , which shows the average impact of a change in sales on profits for a sample of large U.S. companies. Steel producers appear to have relatively high fixed costs. A 1% change in sales has on average resulted in a 6.31% change in profits. By contrast, food companies appear to have low fixed costs. A 1% change in their sales has led to only a 1.11% change in profits.

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Chapter 10 Project Analysis 313

Notice that operating leverage will affect the risk of a project. The greater the degree of operating leverage, the greater the sensitivity of profits to variation in sales. Risk depends on operating leverage. If a large proportion of costs is fixed, a shortfall in sales has a magnified effect on profits.

We will have more to say about risk in the next three chapters.

DOL DOL

Steel 6.31 Supermarkets 1.70 Paper 3.42 Clothing 1.17 Machinery 2.31 Food 1.11

Note: DOL is estimated from a regression of the change in EBIT on the corresponding change in sales, 1990–2012.

TABLE 10.7 Estimated degree of operating leverage (DOL) for large U.S. companies by industry

Suppose that store sales increase by 10% from the values in the normal sce- nario. Compute the percentage change in pretax profits from the normal level for both policies in Table 10.6 . Compare your answers to the values predicted by the DOL formula.

Self-Test 10.5

10.4 Real Options and the Value of Flexibility When you use discounted cash flow (DCF) to value a project, you implicitly assume that the firm will hold the assets passively. But managers are not paid to be dum- mies. After they have invested in a new project, they do not simply sit back and watch the future unfold. If things go well, the project may be expanded; if they go badly, the project may be cut back or abandoned altogether. Most tools for project analysis ignore these opportunities. For example, suppose the superstore’s sales are at the low end of your forecasts. It would pay the company to close down the store rather than amass continuing losses.

Projects that can easily be modified in these ways are more valuable than those that don’t provide such flexibility. The more uncertain the outlook, the more valuable this flexibility becomes.

The Option to Expand The scientists at MacCaugh have developed a diet whiskey, and the firm is ready to go ahead with pilot production and test marketing. The preliminary phase will take a year and cost $200,000. Management feels that there is only a 50–50 chance that the pilot production and market tests will be successful. If they are, then MacCaugh will build a $2 million production plant that will generate an expected annual cash flow in per- petuity of $480,000 after taxes. Given an opportunity cost of capital of 12%, project NPV in this case will be -$2  million  +  $480,000/.12  =  $2 million. If the tests are not successful, MacCaugh will discontinue the project and the cost of the pilot production will be wasted.

Notice that MacCaugh’s expenditure on the pilot program buys a valuable mana- gerial option. The firm is not obliged to enter full production, but it has the option to do so depending on the outcome of the tests. If there is some doubt as to whether the project will take off, expenditure on the pilot operation could help the firm to avoid a costly mistake. Therefore, when it proposed the expenditure, MacCaugh’s manage- ment was simply following the fundamental rule of swimmers: If you know the water temperature (and depth) dive in; if you don’t, try putting a toe in first.

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314

When faced with projects like this that involve future decisions, it is often helpful to draw a decision tree as in Figure 10.3 . You can think of the problem as a game between MacCaugh and fate. Each square represents an action or decision by the com- pany. Each circle represents an outcome revealed by fate. MacCaugh starts the play at the left-hand square. If it decides to test, then fate will cast the enchanted dice and decide the results of the tests. Once the results are known, MacCaugh faces a second decision: Should it wind up the project, or should it invest $2 million and start full- scale production?

The second-stage decision is obvious: Invest if the tests indicate that NPV is posi- tive, and stop if they indicate that NPV is negative. So now MacCaugh can move back to consider whether it should invest in the test program. This first-stage decision boils down to a simple problem: Should MacCaugh invest $200,000 now to obtain a 50% chance of a project with an NPV of $2 million a year later? At any reasonable discount rate the test program has a positive NPV.

You can probably now think of many other investments that take on added value because of the options they provide to expand in the future. For example:

• When designing a factory, it can make sense to provide extra land or floor space to reduce the future cost of a second production line.

• When building a four-lane highway, it may pay to build six-lane bridges so that the road can be converted later to six lanes if traffic proves higher than expected.

• An airline may acquire an option to buy a new aircraft (the nearby box explains how Singapore Airlines bought options on the Airbus A350 airliner).

In each of these cases you are paying out money today to give you the option to invest in real assets at some time in the future. Managers therefore often refer to such

decision tree Diagram of sequential decisions and possible outcomes.

Finance in Practice Singapore Airlines Buys an Option want more of them. But it could not be sure that they would be needed. Therefore, rather than placing additional fi rm orders in 2013, Singapore Airlines secured a place on the Air- bus production line by acquiring options to buy an additional 20 A350 aircraft. These options did not commit the company to expand but gave it the fl exibility to do so.

In 2013 Singapore Airlines placed a fi rm order for 70 Airbus A350 airliners, which it planned to operate on long- and medium-haul routes. The purchase would allow the airline to reduce its fuel costs by some 25% compared with its existing aircraft.

If Singapore Airlines’ business continues to expand and the new aircraft are efficient and reliable, the company will

Decision tree examples

BEYOND THE PAGE

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FIGURE 10.3 Decision tree for the diet-whiskey project

Pursue project NPV = $2 million

Stop project NPV = 0

Test (invest $200,000)

Don’t test

NPV = 0

Success

Failure

Today’s decision

Next year’s decision

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Chapter 10 Project Analysis 315

options as real options. These options do not show up in the assets that the company lists in its balance sheet, but investors are very aware of their existence. If a company has valuable real options that allow it to invest in profitable future projects, its market value will be higher than the value of its physical assets now in place. We consider the valuation of options in Chapter 23.

A Second Real Option: The Option to Abandon If the option to expand has value, what about the decision to bail out? Projects don’t just go on until the assets expire of old age. The decision to terminate a project is usu- ally taken by management, not by nature. Once the project is no longer profitable, the company will cut its losses and exercise its option to abandon the project.

Some assets are simpler to bail out of than others. Tangible assets are usually easier to sell than intangible ones. It helps to have active secondhand markets, which really exist only for standardized items. Real estate, airplanes, trucks, and certain machine tools are likely to be relatively easy to sell. On the other hand, the knowledge accu- mulated by a software company’s research and development program is a specialized intangible asset and probably would not have significant abandonment value. (Some assets, such as old mattresses, even have negative abandonment value; you have to pay to get rid of them. It is costly to decommission nuclear power plants or to reclaim land that has been strip-mined.)

real options Options to invest in, modify, or dispose of a capital investment project.

Example 10.3 Abandonment Option Suppose that the Widgeon Company must choose between two technologies for the manufacture of a new product, a Wankel-engined outboard motor:

1. Technology A uses custom-designed machinery to produce the complex shapes required for Wankel engines at low cost. But if the Wankel engine doesn’t sell, this equipment will be worthless.

2. Technology B uses standard machine tools. Labor costs are much higher, but the tools can easily be sold if the motor doesn’t sell.

Technology A looks better in an NPV analysis of the new product, because it is designed to have the lowest possible cost at the planned production volume. Yet you can sense the advantage of technology B’s flexibility if you are unsure whether the new outboard will sink or swim in the marketplace .

Draw a decision tree showing how the choices open to the Widgeon Company depend on demand for the new product. Pick some plausible numbers to illus- trate why it might make sense to adopt the more expensive technology B.

Self-Test 10.6

A Third Real Option: The Timing Option Suppose that you have a project that could be a big winner or a big loser. The project’s upside potential outweighs its downside potential, and it has a positive NPV if under- taken today. However, the project is not “now or never.” So should you invest right away or wait? It’s hard to say. If the project turns out to be a winner, waiting means the loss or deferral of its early cash flows. But if it turns out to be a loser, it would have been better to wait and get a better fix on the likely demand.

You can think of any project proposal as giving you the option to invest today. You don’t have to exercise that option immediately. Instead, you need to weigh the value of the cash flows lost by delaying against the possibility that you will pick up some

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316 Part Two Value

valuable information. Suppose, for example, you are considering development of a new oil field. At current oil prices the investment has a small positive NPV. But oil prices are highly volatile, occasionally halving or doubling in the space of a few years. If a small decline in crude prices could push your project into the red, it might be bet- ter to wait a little before investing.

Our example illustrates why companies sometimes turn down apparently profit- able projects. For example, suppose you approach your boss with a proposed project. It involves spending $1 million and has an NPV of $1,000. You explain to him how carefully you have analyzed the project, but nothing seems to convince him that the company should invest. Is he being irrational to turn down a positive-NPV project?

Faced by such marginal projects, it often makes sense to wait. One year later you may have much better information about the prospects for the project, and it may become clear whether it is really a winner or a loser. In the former case you can go ahead with confidence, but if it looks like a loser, the delay will have helped you to avoid a bad mistake. 7

A Fourth Real Option: Flexible Production Facilities A sheep is not a flexible production facility. It produces mutton and wool in roughly fixed proportions. If the price of mutton suddenly rises and that of wool falls, there is little that the farmer with a flock of sheep can do about it. Many manufacturing opera- tions are different, for they have built-in flexibility to vary their output mix as demand changes. Since we have mentioned sheep, we might point to the knitwear industry as a case in which manufacturing flexibility has become particularly important in recent years. Fashion changes have made the pattern of demand in the knitwear industry noto- riously difficult to predict, and firms have increasingly invested in computer-controlled knitting machines, which provide an option to vary the product mix as demand changes.

Companies also try to avoid becoming dependent on a single source of raw materi- als. For example, when high-tech firms realized that they were almost wholly depen- dent on China for supplies of rare-earth metals (a key ingredient in applications such as lasers, solar panels, and smartphones), they began to develop new recycling meth- ods and search for new suppliers. These strategies gave them options to shift toward cheaper sources of supply in response to changing market conditions.

7 Does this conclusion contradict our earlier dictum (see Chapter 8) that the firm should accept all positive-NPV projects? No. Notice that the investment timing problem involves a choice among mutually exclusive alterna- tives. You can build the project today or next year, but not both. In such cases, we have seen that the right choice is the one with the highest NPV. The NPV of the project today, even if positive, may well be less than the NPV of deferring investment and keeping alive the option to invest later.

Investments in new products or production capacity often include an option to expand. What are other major types of options encountered in capital investment decisions?

Self-Test 10.7

SUMMARY For most large corporations there are two stages in the investment process: the preparation of the capital budget, which is a list of planned investments, and the authorization process for individual projects. This process is usually a cooperative effort.

How do large corporations go about selecting positive- NPV projects? (LO10-1)

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Chapter 10 Project Analysis 317

Investment projects should never be selected through a purely mechanical process. Managers need to ask why a project should have a positive NPV. A positive NPV is plau- sible only if the company has some competitive advantage that prevents its rivals from stealing most of the gains.

Good managers realize that the forecasts behind NPV calculations are imperfect. There- fore, they explore the consequences of a poor forecast and check whether it is worth doing some more homework. They use the following principal tools to answer these what-if questions:

• Sensitivity analysis, where one variable at a time is changed. • Scenario analysis, where the manager looks at the project under alternative

scenarios. • Simulation analysis, an extension of scenario analysis in which a computer gener-

ates hundreds or thousands of possible combinations of variables. • Break-even analysis, where the focus is on how far sales could fall before the

project begins to lose money. Often the phrase “lose money” is defined in terms of accounting losses, but it makes more sense to define it as “failing to cover the oppor- tunity cost of capital”—in other words, as a negative NPV.

Operating leverage is the degree to which costs are fixed. A project’s break-even point will be affected by the extent to which costs can be reduced as sales decline. If the project has mostly fixed costs, it is said to have high operating leverage. High operating leverage implies that profits are more sensitive to changes in sales.

Some projects may take on added value because they give the firm the option to bail out if things go wrong or to capitalize on success by expanding. These options are known as real options. Other real options include the possibility to delay a project or to choose flexible production facilities. We showed how decision trees may be used to set out the possible choices.

How are sensitivity, scenario, and break- even analyses used to see the effect of an error in forecasts on project profitability? (LO10-2)

Why is an overestimate of sales more serious for projects with high operating leverage? (LO10-3)

Why is managerial flexibility important in capital budgeting? (LO10-4)

L I S T I N G O F E Q UAT I O N S

10.1 Break-even level of revenues =

fixed costs including depreciation

additional profit from each additional dollar of sales

10.2 DOL = percentage change in profits

percentage change in sales

10.3 DOL = 1 + fixed costs

profits

QUESTIONS AND PROBLEMS 1. Terminology. Match each of the following terms to one of the definitions or descriptions listed

below: sensitivity analysis, scenario analysis, break-even analysis, operating leverage, decision tree, real option. (LO10-1–LO10-4)

a. Recalculation of project NPV by changing several inputs to new but consistent values b. Opportunity to modify a project at a future date c. Analysis of how project NPV changes if different assumptions are made about sales, costs,

and other key variables

finance

®

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318 Part Two Value

d. The degree to which fixed costs magnify the effect on profits of a shortfall in sales e. A graphical technique for displaying possible future events and decisions taken in response

to those events f. Determination of the level of future sales at which project profitability or NPV equals zero

2. The Capital Budget. True or false? (LO10-1)

a. Approval of the capital budget allows manager to go ahead with any project included in the budget.

b. Project authorizations are mostly developed “bottom-up.” Strategic planning is a “top-down” process.

c. Project sponsors are likely to be overoptimistic. d. The problem of overoptimism in cash-flow forecasts can always be solved by setting a

higher discount rate.

3. Project Analysis. True or false? (LO10-2)

a. Sensitivity analysis can be used to identify the variables most crucial to a project’s success. b. Sensitivity analysis is used to obtain expected, optimistic, and pessimistic values for total

project cash flows. c. Rather than basing one’s estimate of NPV just on expected cash flows, it makes more sense

to average the NPVs calculated from the pessimistic and optimistic estimates of cash flow. d. Risk is reduced when a high proportion of costs are fixed. e. The break-even level of sales for a project is higher when break-even is defined in terms of

NPV rather than accounting income.

4. Fixed and Variable Costs. In a slow year, Deutsche Burgers will produce 2 million hamburgers at a total cost of $3.5 million. In a good year, it can produce 4 million hamburgers at a total cost of $4.5 million. (LO10-2)

a. What are the fixed costs of hamburger production? b. What are the variable costs? c. What is the average cost per burger when the firm produces 1 million hamburgers? d. What is the average cost when the firm produces 2 million hamburgers? e. Why is the average cost lower when more burgers are produced?

5. Sensitivity Analysis. A project currently generates sales of $10 million, variable costs equal 50% of sales, and fixed costs are $2 million. The firm’s tax rate is 35%. What are the effects of the following changes on cash flow? (LO10-2)

a. Sales increase from $10 million to $11 million. b. Variable costs increase to 65% of sales.

6. Sensitivity Analysis. Finefodder’s analysts have come up with the following revised estimates for the Gravenstein store (see Section 10.2):

Range

Pessimistic Expected Optimistic

Investment $ 5,400,000 $5,200,000 $5,000,000 Sales 16,000,000 18,000,000 21,000,000 Variable costs as % of sales 81 80 79.5 Fixed cost $3,000,000 $2,600,000 $2,300,000

Conduct a sensitivity analysis using the revised data. Label your answers as follows: (LO10-2)

NPV of Gravenstein Store

Pessimistic Expected Optimistic

Investment A B C Sales D E F Variable costs as % of sales G H I Fixed cost J K L

Templates can be found in Connect.

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Chapter 10 Project Analysis 319

7. Sensitivity Analysis. The Rustic Welt Company is proposing to replace its old welt-making machinery with more modern equipment. The new equipment costs $9 million (the existing equipment has zero salvage value). The attraction of the new machinery is that it is expected to cut manufacturing costs from their current level of $8 a welt to $4. However, as the following table shows, there is some uncertainty about both the future sales and the performance of the new machinery:

NPV of Replacement Decision

Pessimistic Expected Optimistic

Sales, million welts A B C Manufacturing cost, $ per welt D E F Life of new machinery, years G H I

Pessimistic Expected Optimistic

Sales, million welts .4 .5 .7 Manufacturing cost, $ per welt 6 4 3 Life of new machinery, years 7 10 13

Conduct a sensitivity analysis of the replacement decision assuming a discount rate of 12%. Rustic does not pay taxes. Label your answers as follows: (LO10-2)

8. Sensitivity Analysis. Emperor’s Clothes Fashions can invest $5 million in a new plant for pro- ducing invisible makeup. The plant has an expected life of 5 years, and expected sales are 6 mil- lion jars of makeup a year. Fixed costs are $2 million a year, and variable costs are $1 per jar. The product will be priced at $2 per jar. The plant will be depreciated straight-line over 5 years to a salvage value of zero. The opportunity cost of capital is 10%, and the tax rate is 40%. (LO10-2)

a. What is project NPV under these base-case assumptions? b. What is NPV if variable costs turn out to be $1.20 per jar? c. What is NPV if fixed costs turn out to be $1.5 million per year? d. At what price per jar would project NPV equal zero?

9. Scenario Analysis. The most likely outcomes for a particular project are estimated as follows:

Unit price: $50 Variable cost: $30 Fixed cost: $300,000 Expected sales: 30,000 units per year However, you recognize that some of these estimates are subject to error. Suppose that each variable may turn out to be either 10% higher or 10% lower than the initial estimate. The project will last for 10 years and requires an initial investment of $1 million, which will be depreciated straight-line over the project life to a final value of zero. The firm’s tax rate is 35%, and the required rate of return is 12%. (LO10-2)

a. What is project NPV in the best-case scenario, that is, assuming all variables take on the best possible value?

b. What about the worst-case scenario?

10. Break-Even Analysis. The following estimates have been prepared for a project: Fixed costs: $20,000 Depreciation: $10,000 Sales price: $2 Accounting break-even: 60,000 units What must be the variable cost per unit? (LO10-2)

11. Break-Even Analysis. Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $100. The materials cost for a standard diamond is $40. The fixed

Templates can be found in Connect.

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320 Part Two Value

costs incurred each year for factory upkeep and administrative expenses are $200,000. The machinery costs $1 million and is depreciated straight-line over 10 years to a salvage value of zero. (LO10-2)

a. What is the accounting break-even level of sales in terms of number of diamonds sold? b. What is the NPV break-even level of sales assuming a tax rate of 35%, a 10-year project life,

and a discount rate of 12%?

12. Break-Even Analysis. You are evaluating a project that will require an investment of $10 mil- lion that will be depreciated over a period of 7 years. You are concerned that the corporate tax rate will increase during the life of the project. (LO10-2)

a. Would this increase the accounting break-even point? b. Would it increase the NPV break-even point?

13. Break-Even Analysis. Define the cash-flow break-even point as the sales volume (in dollars) at which cash flow equals zero. (LO10-2)

a. Is the cash-flow break-even level of sales higher or lower than the zero-profit (accounting) break-even point?

b. If a project operates at cash-flow break-even [see part (a)] for its entire life, is its NPV posi- tive or negative?

14. NPV Break-Even Analysis. Modern Artifacts can produce keepsakes that will be sold for $80 each. Nondepreciation fixed costs are $1,000 per year, and variable costs are $60 per unit. The initial investment of $3,000 will be depreciated straight-line over its useful life of 5 years to a final value of zero, and the discount rate is 10%. (LO10-2)

a. What is the accounting break-even level of sales if the firm pays no taxes? b. What is the NPV break-even level of sales if the firm pays no taxes? c. What is the accounting break-even level of sales if the firm’s tax rate is 35%? d. What is the NPV break-even level of sales if the firm’s tax rate is 35%?

15. NPV Break-Even Analysis. A financial analyst has computed both accounting and NPV break- even sales levels for a project using straight-line depreciation over a 6-year period. The project manager wants to know what will happen to these estimates if the firm uses MACRS deprecia- tion instead. The capital investment will be in a 5-year recovery-period class under MACRS rules (see Table 9.2). The firm is in a 35% tax bracket. (LO10-2)

a. Would the accounting break-even level of sales in the first years of the project increase or decrease?

b. Would the NPV break-even level of sales in the first years of the project increase or decrease? c. If you were advising the analyst, would the answer to (a) or (b) be important to you? Specifi-

cally, would you say that the switch to MACRS makes the project more or less attractive?

16. NPV Break-Even Analysis. Reconsider Finefodder’s new superstore. Suppose that by invest- ing an additional $600,000 initially in more efficient checkout equipment, Finefodder could reduce variable costs to 80% of sales. (LO10-2)

a. Using the base-case assumptions ( Table 10.1 ), find the NPV of this alternative scheme. ( Hint: Remember to focus on the incremental cash flows from the project.)

b. At what level of sales will accounting profits be unchanged if the firm invests in the new equipment? Assume the equipment receives the same 12-year straight-line depreciation treatment as in the original example. ( Hint: Focus on the project’s incremental effects on fixed and variable costs.)

c. What is the NPV break-even point?

17. Break-Even Analysis and NPV. If the Finefodder superstore project (see Problem 16) operates at accounting break-even, will net present value be positive or negative? (LO10-2)

18. Operating Leverage. You estimate that your cattle farm will generate $1 million of profits on sales of $4 million under normal economic conditions and that the degree of operating leverage is 8. (LO10-3)

a. What will profits be if sales turn out to be $3.5 million? b. What if they are $4.5 million?

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Chapter 10 Project Analysis 321

19. Operating Leverage. (LO10-3)

a. What is the degree of operating leverage of Modern Artifacts (in Problem 14) when sales are $7,000?

b. What is the degree of operating leverage when sales are $12,000? c. Why is operating leverage different at these two levels of sales?

20. Operating Leverage. What is the lowest possible value for the degree of operating leverage for a profitable firm? Show with a numerical example that if Modern Artifacts (see Problem 14) has zero fixed costs, then DOL  =  1 and in fact sales and profits are directly proportional, so a 1% change in sales results in a 1% change in profits. (LO10-3)

21. Operating Leverage. A project has fixed costs of $1,000 per year, depreciation charges of $500 a year, annual revenue of $6,000, and variable costs equal to two-thirds of revenues. (LO10-3)

a. If sales increase by 10%, what will be the increase in pretax profits? b. What is the degree of operating leverage of this project?

22. Project Options. Section 10.4 describes four types of real option. For each of the following cases state which type of option is involved: (LO10-4)

a. Deutsche Metall postpones a major plant expansion. The expansion has a positive NPV on a discounted cash-flow basis, but before proceeding, management wants to see how product demand grows.

b. Western Telecom commits to production of digital switching equipment specially designed for the European market. The project has a negative NPV, but it is justified on strategic grounds by the need for a strong market position in a rapidly growing and potentially very profitable market.

c. Western Telecom vetoes a fully integrated, automated production line for the new switches. It relies on standard, less expensive equipment. The automated production line is more effi- cient overall, according to a discounted cash-flow calculation.

d. Mount Fuji Airways buys a jumbo jet with special equipment that allows the plane to be switched quickly from freight to passenger use and vice versa.

23. Project Options. Your midrange guess as to the amount of oil in a prospective field is 10 mil- lion barrels, but in fact there is a 50% chance that the amount of oil is 15 million barrels and a 50% chance of 5 million barrels. If the actual amount of oil is 15 million barrels, the present value of the cash flows from drilling will be $8 million. If the amount is only 5 million barrels, the present value will be only $2 million. It costs $3 million to drill the well. Suppose that a seismic test costing $100,000 can verify the amount of oil under the ground. Is it worth paying for the test? Use a decision tree to justify your answer. (LO10-4)

24. Project Options. A silver mine can yield 10,000 ounces of silver at a variable cost of $32 per ounce. The fixed costs of operating the mine are $40,000 per year. In half the years, silver can be sold for $48 per ounce; in the other years, silver can be sold for only $24 per ounce. Ignore taxes. (LO10-4)

a. What is the average cash flow you will receive from the mine if it is always kept in operation and the silver always is sold in the year it is mined?

b. Now suppose you can shut down the mine in years of low silver prices. What happens to the average cash flow from the mine?

25. Project Options. An auto plant that costs $100 million to build can produce a line of flexfuel cars that will produce cash flows with a present value of $140 million if the line is successful but only $50 million if it is unsuccessful. You believe that the probability of success is only about 50%. You will learn whether the line is successful immediately after building the plant. (LO10-4)

a. Would you build the plant? b. Suppose that the plant can be sold for $95 million to another automaker if the auto line is not

successful. Now would you build the plant? c. Illustrate the option to abandon in (b) using a decision tree.

26. Project Options. Explain why options to expand or contract production are most valuable when forecasts about future business conditions are most uncertain. (LO10-4)

27. Decision Trees. The box on page 314 describes Singapore Airlines option to buy additional A350 airliners. Draw a decision tree showing the future choices faced by the airline. (LO10-4)

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322 Part Two Value

b. At an oil price of $100, what level of annual sales, maintained over the life of the plant, is necessary for NPV break-even? (This will require trial and error unless you are familiar with more advanced features of Excel such as the Goal Seek command.)

c. At an oil price of $100, what is the accounting break-even level of sales in each year? Why does it change each year? Does this notion of break-even seem reasonable to you?

d. If each of the scenarios in the grid in part (a) is equally likely, what is the NPV of the facility? e. Why might the facility be worth building despite your answer to part (d)? (Hint: What real

option may the firm have to avoid losses in low-oil-price scenarios?)

CHALLENGE PROBLEM 28. Project Analysis. New Energy is evaluating a new biofuel facility. The plant would cost $4,000

million to build and has the potential to produce up to 40 million barrels of synthetic oil a year. The product is a close substitute for conventional oil and would sell for the same price. The market price of oil currently is fluctuating around $100 per barrel, but there is considerable uncertainty about future prices. Variable costs for the organic inputs to the production process are estimated at $82 per barrel and are expected to be stable. In addition, annual upkeep and maintenance expenses on the facility will be $100 million regardless of the production level. The plant has an expected life of 15 years, and it will be depreciated using MACRS and a 10-year recovery period. Salvage value net of cleanup costs is expected to be negligible.

Demand for the product is difficult to forecast. Depending on consumer acceptance, sales might range from 25 million to 35 million barrels annually. The discount rate is 12%, and New Energy’s tax bracket is 35%. (LO10-2)

a. Find the project NPV for the following combinations of oil price and sales volume. Which source of uncertainty seems most important to the success of the project?

Oil Price

Annual Sales $80/Barrel $100/Barrel $120/Barrel

25 million barrels 30 million barrels 35 million barrels

WEB EXERCISE 1. Can you guess Hewlett-Packard’s incremental cost for producing one computer? You probably

have that amount in your wallet or purse! This gives the company considerable operating lever- age. Let’s estimate the degree of operating leverage for HP (ticker symbol HPQ). Go to the annual income statement, which you can find at finance.yahoo.com. Assume that selling, general, admin- istrative, R&D, and depreciation expenses are fixed and cost of goods sold (which Yahoo! calls cost of revenue) are variable. Estimate the degree of operating leverage for HP for the last year (annual).

SOLUTIONS TO SELF-TEST QUESTIONS 10.1 Cash-flow forecasts for Finefodder’s new superstore:

Year 0 Years 1–12

Investment -5,400,000 1. Sales 16,000,000 2. Variable costs 13,280,000 3. Fixed costs 2,000,000 4. Depreciation 450,000 5. Pretax profi t (1 - 2 - 3 - 4) 270,000 6. Taxes (at 40%) 108,000 7. Profi t after tax 162,000 8. Cash fl ow from operations (4 + 7) 612,000 Net cash fl ow -5,400,000 612,000

Templates can be found in Connect.

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Chapter 10 Project Analysis 323

Break-even occurs when

PV(cash inflows) = investment

7.536 × (.1125 × sales - $1.033 million) = $5 million

Sales = $15.08 million

10.4 Break-even analysis finds the level of sales or revenue at which NPV  =  0. Sensitivity analysis changes these and other input variables to optimistic and pessimistic values and recalculates NPV.

10.5 Reworking Table 10.6 for the normal level of sales and 10% higher sales gives the following:

NPV = -$5.4 million + (7.5361 × $612,000) = -$787,907

which matches the value in Table 10.2 except for a minor rounding error in the annuity factor.

10.2 Both calculate how NPV depends on input assumptions. Sensitivity analysis changes inputs one at a time, whereas scenario analysis changes several variables at once. The changes should add up to a consistent scenario for the project as a whole.

10.3 With the lower initial investment, depreciation is also lower; it now equals $417,000 per year. Cash flow is now as follows:

1. Variable costs 81.25% of sales 2. Fixed costs $2 million 3. Depreciation $417,000 4. Pretax profi t (.1875 × sales) - $2.417 million 5. Tax (at 40%) .4 × (.1875 × sales - $2.417 million) 6. Profi t after tax .6 × (.1875 × sales - $2.417 million) 7. Cash fl ow (3 + 6) .6 × (.1875 × sales - $2.417 million) + $417,000

= .1125 × sales - $1.033 million

High Fixed Costs High Variable Costs

Normal 10% Higher Sales Normal 10% Higher Sales

Sales 16,000 17,600 16,000 17,600 - Variable costs 13,000 14,300 13,440 14,784 - Fixed costs 2,000 2,000 1,560 1,560 - Depreciation 450 450 450 450 = Pretax profi t 550 850 550 806

For the high-fixed-cost policy, profits increase by 54.5%, from $550,000 to $850,000. For the low-fixed-cost policy, profits increase by 46.5%. In both cases the percentage increase in profits equals DOL times the percentage increase in sales. This illustrates that DOL measures the sensitivity of profits to changes in sales.

10.6 See Figure 10.4 . Note that while technology A delivers the higher NPV if demand is high, technology B has the advantage of a higher salvage value if demand is unexpectedly low.

10.7 Abandonment options, options due to flexible production facilities, investment timing options.

FIGURE 10.4 Example of a decision tree for Widgeon Company

Stop project and sell equipment Salvageg value = $5 million

Continue NPV = $18 million

Stop project and sell equipment Salvage value = $1 million

Continue NPV = $20 million

Invest in technology A

Invest in technology B

Demand low

Demand high

Demand low

Demand high

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324 Part Two Value

MINICASE Maxine Peru, the CEO of Peru Resources, hardly noticed the plate of savory quenelles de brochet and the glass of Corton Char- lemagne ’94 on the table before her. She was absorbed by the engineering report handed to her just as she entered the executive dining room.

The report described a proposed new mine on the North Ridge of Mt. Zircon. A vein of transcendental zirconium ore had been discovered there on land owned by Ms. Peru’s company. Test bor- ings indicated sufficient reserves to produce 340 tons per year of transcendental zirconium over a 7-year period.

The vein probably also contained hydrated zircon gemstones. The amount and quality of these zircons were hard to predict, since they tended to occur in “pockets.” The new mine might come across one, two, or dozens of pockets. The mining engineer guessed that 150 pounds per year might be found. The current price for high- quality hydrated zircon gemstones was $3,300 per pound.

Peru Resources was a family-owned business with total assets of $45 million, including cash reserves of $4 million. The outlay required for the new mine would be a major commitment. Fortu- nately, Peru Resources was conservatively financed, and Ms. Peru believed that the company could borrow up to $9 million at an interest rate of about 8%.

The mine’s operating costs were projected at $900,000 per year, including $400,000 of fixed costs and $500,000 of variable costs. Ms. Peru thought these forecasts were accurate. The big question marks seemed to be the initial cost of the mine and the selling price of transcendental zirconium.

Opening the mine, and providing the necessary machinery and ore-crunching facilities, was supposed to cost $10 million, but cost overruns of 10% or 15% were common in the mining business. In

addition, new environmental regulations, if enacted, could increase the cost of the mine by $1.5 million.

There was a cheaper design for the mine, which would reduce its cost by $1.7 million and eliminate much of the uncertainty about cost overruns. Unfortunately, this design would require much higher fixed operating costs. Fixed costs would increase to $850,000 per year at planned production levels.

The current price of transcendental zirconium was $10,000 per ton, but there was no consensus about future prices. 9 Some experts were projecting rapid price increases to as much as $14,000 per ton. On the other hand, there were pessimists saying that prices could be as low as $7,500 per ton. Ms. Peru did not have strong views either way: Her best guess was that price would just increase with inflation at about 3.5% per year. (Mine operating costs would also increase with inflation.)

Ms. Peru had wide experience in the mining business, and she knew that investors in similar projects usually wanted a forecast nominal rate of return of at least 14%.

You have been asked to assist Ms. Peru in evaluating this proj- ect. Lay out the base-case NPV analysis, and undertake sensitivity, scenario, or break-even analyses as appropriate. Assume that Peru Resources pays tax at a 35% rate. For simplicity, also assume that the investment in the mine could be depreciated for tax purposes straight-line over 7 years.

What forecasts or scenarios should worry Ms. Peru the most? Where would additional information be most helpful? Is there a case for delaying construction of the new mine?

9 There were no traded forward or futures contracts on transcendental zir- conium. See Chapter 24.

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326

Introduction to Risk, Return, and the Opportunity Cost of Capital

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

11-1 Estimate the opportunity cost of capital for an “average-risk” project.

11-2 Calculate returns and standard deviation of returns for individual common stocks or for a stock portfolio.

11-3 Understand why diversification reduces risk.

11-4 Distinguish between specific risk, which can be diversified away, and market risk, which cannot.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

11 CHAPTE R

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327

P A

R T

TH R

E E

I n earlier chapters we skirted the issue of project risk; now it is time to confront it head-on. We can no longer be satisfied with vague statements like “The opportunity cost of capital depends on the risk of the

project.” We need to know how to measure risk, and

we need to understand the relationship between risk

and the cost of capital. These are the topics of the

next two chapters.

Think for a moment what the cost of capital for a

project means. It is the rate of return that sharehold-

ers could expect to earn if they invested in equally

risky securities. So one way to estimate the cost of

capital is to find securities that have the same risk as

the project and then estimate the expected rate of

return on these securities.

We start our analysis by looking at the rates of

return earned in the past from different investments,

concentrating on the extra return that investors have

received for investing in risky rather than safe securi-

ties. We then show how to measure the risk of a port-

folio, and we look again at past history to find out

how risky it is to invest in the stock market.

Finally, we explore the concept of diversification.

Most investors do not put all their eggs into one

basket—they diversify. Thus investors are not con-

cerned with the risk of each security in isolation;

instead, they are concerned with how much it con-

tributes to the risk of a diversified portfolio. We there-

fore need to distinguish between the risk that can be

eliminated by diversification and the risk that cannot

be eliminated.

Ri sk

Investing in risky assets is not the same as gambling. After reading this chapter, you should be able to explain the difference and understand the rewards for bearing risk in the stock market.

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328 Part Three Risk

11.1 Rates of Return: A Review When investors buy a stock or a bond, their return comes in two forms: (1) a dividend or interest payment and (2) a capital gain or a capital loss. For example, suppose you bought the stock of Ford at the beginning of 2013 when its price was $12.61 a share. By the end of the year the value of that investment had appreciated to $15.43, giving a capital gain of $15.43 − $12.61 = $2.82. In addition, in 2013 Ford paid a dividend of $.40 a share.

The percentage return on your investment was therefore

Percentage return = capital gain + dividend

initial share price (11.1)

= $2.82 + $.40

$12.61 = .255, or 25.5%

The percentage return can also be expressed as the sum of the dividend yield and percentage capital gain. The dividend yield is the dividend expressed as a percentage of the stock price at the beginning of the year:

Dividend yield = dividend

initial share price

= $.40

$12.61 = .032, or 3.2%

Similarly, the percentage capital gain is

Percentage capital gain = capital gain

initial share price

= $2.82

$12.61 = .224, or 22.4%

Thus the total return is the sum of 3.2% + 22.4% = 25.6%, which, apart from the rounding error, is the same as we calculated above.

Remember that in Chapter 5 we made a distinction between the nominal rate of return and the real rate of return. The nominal return measures how much more money you will have at the end of the year if you invest today. The return that we just calcu- lated for Ford stock is therefore a nominal return. The real rate of return tells you how much more you will be able to buy with your money at the end of the year. To convert from a nominal to a real rate of return, we use the following relationship:

1 + real rate of return = 1 + nominal rate of return

1 + inflation rate

In 2013 inflation was 1.5%. So we calculate the real rate of return on Ford stock as follows:

1 + real rate of return = 1.255

1.015 = 1.236

Therefore, the real rate of return equals .236, or 23.6%.

Suppose you buy a bond for $1,020 with a 15-year maturity paying an annual coupon of $80. A year later interest rates have dropped and the bond’s price has increased to $1,050. What are your nominal and real rates of return? Assume the inflation rate is 4%.

Self-Test 11.1

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Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 329

11.2 A Century of Capital Market History When you invest in a stock, you don’t know what return you will earn. But by look- ing at the history of security returns, you can get some idea of the return that investors might reasonably expect from investments in different types of securities and of the risks that they face. Let us look, therefore, at the risks and returns that investors have experienced in the past.

Market Indexes Investors can choose from an enormous number of different securities. For example, currently about 2,300 U.S. and foreign companies list their stocks on the New York Stock Exchange, and a further 2,600 stocks are traded on the NASDAQ stock market.

Financial analysts can’t track every stock, so they rely on market indexes to sum- marize the return on different classes of securities. The best-known stock market index in the United States is the Dow Jones Industrial Average, generally known as the Dow. The Dow tracks the performance of a portfolio that holds one share in each of 30 large firms. For example, suppose that the Dow starts the day at a value of 15,000 and then rises by 150 points to a new value of 15,150. Investors who own one share in each of the 30 companies make a capital gain of 150/15,000 = .01, or 1%. 1

The Dow Jones Industrial Average was first computed in 1896. Most people are used to it and expect to hear it on the 6 o’clock news. However, it is far from the best measure of the performance of the stock market. First, with only 30 large stocks, it is not representative of the performance of stocks generally. Second, investors don’t usu- ally hold an equal number of shares in each company. For example, in 2013 there were 10.1 billion shares in General Electric and 1.01 billion in UnitedHealth. So on average investors did not hold the same number of shares in the two firms. Instead, they held 10 times as many shares in General Electric as in UnitedHealth. It doesn’t make sense, therefore, to look at an index that measures the performance of a portfolio with an equal number of shares in the two firms.

The Standard & Poor’s Composite Index, better known as the S&P 500, includes the stocks of 500 major companies and is therefore a more comprehensive index than the Dow. Also, it measures the performance of a portfolio that holds shares in each firm in proportion to the number of shares that have been issued to investors. For example, the S&P portfolio would hold 10 times as many shares in General Electric as in UnitedHealth. Thus the S&P 500 shows the average performance of investors in the 500 firms.

Only a small proportion of the publicly traded companies are represented in the S&P 500. However, these firms are among the largest in the country, and they account for about 75% of the market value of traded stocks. Therefore, success for professional investors usually means “beating the S&P.”

Some stock market indexes, such as the Dow Jones Wilshire 5000, include an even larger number of stocks, while others focus on special groups of stocks such as the stocks of small companies. There are also stock market indexes for other countries, such as the Nikkei Index for Tokyo and the Financial Times (FT) Index for London. Morgan Stanley Capital International (MSCI) even computes a world stock market index. The Financial Times Company and Standard & Poor’s have combined to pro- duce their own world index.

The Historical Record The historical returns of stock or bond market indexes can give us an idea of the typi- cal performance of different investments. For example, Elroy Dimson, Paul Marsh,

market index Measure of the investment performance of the overall market.

Dow Jones Industrial Average Index of the investment performance of a portfolio of 30 “blue-chip” stocks.

1 Stock market indexes record the market value of the portfolio. To calculate the total return on the portfolio, we need to add in any dividends that are paid.

Standard & Poor’s Composite Index Index of the investment performance of a portfolio of 500 large stocks. Also called the S&P 500.

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330 Part Three Risk

and Mike Staunton have compiled measures of the investment performance of three portfolios of securities since 1900:

1. A portfolio of 3-month loans issued each week by the U.S. government. These loans are known as Treasury bills.

2. A portfolio of long-term Treasury bonds issued by the U.S. government and maturing in about 10 years.

3. A diversified portfolio of common stocks.

These portfolios are not equally risky. Treasury bills are about as safe an investment as you can make. Because they are issued by the U.S. government, you can be con- fident that you will get your money back. Their short-term maturity means that their prices are relatively stable. In fact, investors who wish to lend money for 3 months can achieve a certain payoff by buying 3-month bills. Of course, they can’t be sure what that money will buy; there is still some uncertainty about inflation.

Long-term Treasury bonds are also certain to be repaid when they mature, but the prices of these bonds fluctuate more as interest rates vary. When interest rates fall, the values of long-term bonds rise; when rates rise, the values of the bonds fall.

Common stocks are the riskiest of the three groups of securities. When you invest in common stocks, there is no promise that you will get your money back. As a part- owner of the corporation, you receive what is left over after the bonds and any other debts have been repaid.

Figure 11.1 shows the performance of the three groups of securities assuming that all dividends or interest income had been reinvested in the portfolios. You can see that the performance of the portfolios fits our intuitive risk ranking. Common stocks were the riskiest investment, but they also offered the greatest gains. One dollar invested at  the start of 1900 in a portfolio of common stocks would have grown to $33,940 by the start of 2014. At the other end of the spectrum, an investment in Treasury bills would have accumulated to only $74.

Table 11.1 shows the average of the annual returns from each of these portfolios. These returns are comparable to the return that we calculated for Ford. In other words, they include (1) dividends or interest and (2) any capital gains or losses.

The safest investment, Treasury bills, had the lowest rates of return—they averaged 3.9% a year. Long-term government bonds gave slightly higher returns than Treasury bills. This difference is called the maturity premium. Common stocks were in a class by themselves. Investors who accepted the risk of common stocks received on average

maturity premium Extra average return from investing in longversus short-term Treasury securities.

FIGURE 11.1 How an investment of $1 at the start of 1900 would have grown by the start of 2014 (index values plotted on log scale)

1

10

100

1,000

10,000

100,000

19 00

19 10

19 20

19 30

19 40

19 50

19 60

19 70

19 80

19 90

20 00

20 10

D o

lla rs

Equities Bonds Bills

$33,940

$224

$73.62

Start of year

Source: E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns (Princeton, NJ: Princeton University Press, 2002), with updates kindly provided by Triumph ’s authors.

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Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 331

an extra return of 7.6% a year over the return on Treasury bills. This compensation for taking on the risk of common stock ownership is known as the market risk premium:

Rate of return

on common stocks = interest rate on Treasury bills +

market risk premium

The historical record shows that investors have received a risk premium for hold- ing risky assets. Average returns on high-risk assets are higher than those on low-risk assets.

You may ask why we look back over such a long period to measure average rates of return. The reason is that annual rates of return for common stocks fluctuate so much that averages taken over short periods are extremely unreliable. In some years investors in common stocks had a disagreeable shock and received a substantially lower return than they expected. In other years they had a pleasant surprise and received a higher-than- expected return. By averaging the returns across both the rough years and the smooth, we should get a fair idea of the typical return that investors might justifiably expect.

While common stocks have offered the highest average returns, they have also been riskier investments. Figure 11.2 shows the 114 annual rates of return on com- mon stocks since 1900. The fluctuations in year-to-year returns on common stocks are remarkably wide. There were 2 years (1933 and 1954) when investors earned a return of more than 50%. However, Figure 11.2 shows that you can also lose money by investing in the stock market. The most dramatic case was the stock market crash of 1929–1932. Shortly after President Coolidge joyfully observed that stocks were “cheap at current prices,” stocks rapidly became even cheaper. By July 1932 the Dow Jones Industrial Average had fallen in a series of agonizing slides by 89%.

risk premium Expected return in excess of risk-free return as compensation for risk.

TABLE 11.1 Average rates of return on Treasury bills, government bonds, and common stocks, 1900–2013 (figures in percent per year)

Portfolio Average Annual Rate of Return

Average Premium (Extra return

versus Treasury bills)

Treasury bills 3.9 Treasury bonds 5.2 1.3 Common stocks 11.5 7.6

Source: Elroy Dimson, Paul Marsh, and Mike Staunton, Triumph of the Optimists: 101 Years of Global Equity Returns (Princeton, NJ: Princeton University Press, 2002), with updates kindly provided by Triumph ’s authors.

Arithmetic averages and compound annual

returns

BEYOND THE PAGE

brealey.mhhe.com/ch11-01

FIGURE 11.2 Rates of return on common stocks, 1900–2013

Source: E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns (Princeton, NJ: Princeton University Press, 2002), with updates kindly provided by Triumph ’s authors.

-60

-40

-20

0

20

40

60

80

1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Year

R at

e o

f re

tu rn

( %

)

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332 Part Three Risk

You don’t have to look that far back to see that the stock market is a risky place. Investors who bought at the stock market peak in March 2000 saw little but falling stock prices over the next 2½ years. By October 2002 the S&P 500 had declined by 49%, while the tech-heavy NASDAQ market fell by 78%. But this was not the end of the roller-coaster ride. After recovering sharply, share prices plunged 57% between October 2007 and March 2009 as the financial crisis unfolded.

Bond prices also fluctuate, but far less than stock prices. The worst year for inves- tors in our portfolio of Treasury bonds was 2009; their return that year was −14.9%.

Here are the average rates of return for common stocks and Treasury bills for four different periods:

What was the risk premium on stocks for each of these periods?

Self-Test 11.2

1900–1927 1928–1955 1956–1983 1984–2013

Stocks 11.0% 11.6% 11.0% 12.4% Treasury bills 4.9 1.0 5.6 4.0

Using Historical Evidence to Estimate Today’s Cost of Capital Think back now to Chapter 8, where we showed how firms calculate the present value of a new project by discounting the expected cash flows by the opportunity cost of capital. The opportunity cost of capital is the return that the firm’s share- holders are giving up by investing in the project rather than in comparable-risk alternatives.

Measuring the cost of capital is easy if the project is a sure thing. Since sharehold- ers can obtain a surefire payoff by investing in a U.S. Treasury bill, the firm should invest in a risk-free project only if it can at least match the rate of interest on such a loan. If the project is risky—and most projects are—then the firm needs to at least match the return that shareholders could expect to earn if they invested in securities of similar risk. It is not easy to put a precise figure on this, but our skim through history provides an idea of the average return an investor might expect from an investment in risky common stocks.

Suppose there is an investment project that you know —don’t ask how—has the same risk as an investment in a diversified portfolio of U.S. common stocks. We will say that it has the same degree of risk as the market portfolio.

Instead of investing in the project, your shareholders could invest directly in this market portfolio. Therefore, the opportunity cost of capital for your project is the return that the shareholders could expect to earn on the market portfolio. This is what they are giving up by investing money in your project.

The problem of estimating the project cost of capital boils down to estimating the currently expected rate of return on the market portfolio. One way to estimate the expected market return is to assume that the future will be like the past and that today’s investors expect to receive the average rates of return shown in Table 11.1 . In this case, you might judge that the expected market return today is 11.5%, the average of past market returns.

Unfortunately, this is not the way to do it. Investors are not likely to demand the same return each year on an investment in common stocks. For example, we know that the interest rate on safe Treasury bills varies over time. At their peak in 1981, Treasury

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Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 333

bills offered a return of 14%, over 10 percentage points above the 3.9% average return on bills shown in Table 11.1 .

What if you were called upon to estimate the expected return on common stocks in 1981? Would you have said 11.5%? That doesn’t make sense. Who would invest in the risky stock market for an expected return of 11.5% when you could get a safe 14% from Treasury bills?

A better procedure is to take the current interest rate on Treasury bills plus 7.6%, the average risk premium shown in Table 11.1 . In 1981, when the rate on Treasury bills was 14%, that would have given

Expected market

return (1981) = interest rate on Treasury bills (1981) + normal risk premium

= 14 + 7.6 = 21.6%

The first term on the right-hand side tells us the time value of money in 1981; the second term measures the compensation for risk. The expected return on an invest- ment provides compensation to investors both for waiting (the time value of money) and for worrying (the risk of the particular asset).

What about today? As we write this in early 2014, Treasury bills offer a return of about .1%. This suggests that investors in common stocks are looking for a return of 7.7%: 2

Expected market

return (2014) = interest rate on Treasury bills (2014) + normal risk premium

= 0.1 + 7.6 = 7.7%

These calculations assume that there is a normal, stable risk premium on the market portfolio, so the expected future risk premium can be measured by the average past risk premium. But even with more than 100 years of data, we can’t estimate the market risk premium exactly; nor can we be sure that investors today are demanding the same reward for risk that they were in the early 1900s. All this leaves plenty of room for argument about what the risk premium really is.

Many financial managers and economists believe that long-run historical returns are the best measure available. Others have a gut instinct that investors don’t need such a large risk premium to persuade them to hold common stocks. For example, surveys of financial economists and chief financial officers commonly suggest a risk premium that is 1% to 2% lower than the historical average. 3

We may be able to gain some further insights into the question by looking at the experience of other countries. Figure 11.3 shows that the United States is roughly average in terms of the risk premium. Danish common stocks come bottom of the league; the average risk premium in Denmark was only 5.1%. Top of the form is Germany, with a premium of 10.1%. Some of these variations between countries may reflect differences in risk. But remember how difficult it is to make precise estimates of what investors expected. You probably would not be too far out if you concluded that the expected risk premium was the same in each country.

2 In practice, things might be a bit more complicated. In 2014 short-term interest rates were unusually low and probably not appropriate for judging the required return on a long-term project. We will return to this problem in the next chapter.

3 Unfortunately, it is difficult to interpret these surveys precisely, because respondents define the risk premium in different ways. For example, see P. Fernandez, J. Aguirreamalloa, and P. Linares, “Market Risk Premium and Risk Free Rate Used for 51 Countries in 2013: A Survey with 6,237 Answers,” June 26, 2013, available at SSRN: http://ssrn.com/abstract  = 914160 ; and J. R. Graham and C. R. Harvey, “The Equity Risk Premium in 2013,” ssrn.com/abstract  = 2206538 .

The market risk premium

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334 Part Three Risk

11.3 Measuring Risk You now have some benchmarks. You know that the opportunity cost of capital for safe projects must be the rate of return offered by safe Treasury bills, and you know that the opportunity cost of capital for “average-risk” projects must be the expected return on the market portfolio. But you don’t know how to estimate the cost of capital for projects that do not fit these two simple cases. Before you can do this, you need to understand more about investment risk.

The average fuse time for army hand grenades is 5 seconds, but that average hides a lot of potentially relevant information. If you are in the business of throwing grenades, you need some measure of the variation around the average fuse time. 4 Similarly, if you are in the business of investing in securities, you need some measure of how far the returns may differ from the average.

One way to present the spread of possible investment returns is by using histograms, such as the ones in Figure 11.4 . The bars in each histogram show the number of years between 1900 and 2013 that the investment’s return fell within a specific range. Look first at the performance of common stocks. Their risk shows up in the wide spread of outcomes. For example, you can see that in one year the return was between +55% and +60%, but there was also one year that investors lost between 40% and 45%.

The corresponding histograms for Treasury bonds and bills show that unusually high or low returns are much less common. Investors in these securities could have been much more confident of the outcome than common stockholders.

Variance and Standard Deviation Investment risk depends on the dispersion or spread of possible outcomes. For example, Figure 11.4 showed that on past evidence there is greater uncertainty about the possi- ble returns from common stocks than about the returns from bills or bonds. Sometimes

4 We can reassure you; the variation around the standard fuse time is very small.

FIGURE 11.3 The risk premium in 18 countries, 1900–2013. For these 18 countries, the average return on common stocks has been 7.3% more than the interest rate on bills.

0

2

4

6

8

10

12

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( %

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23 )

Source: Author’s calculations using data from E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns (Princeton, NJ: Princeton University Press, 2002), with updates kindly provided by Triumph ’s authors.

Note: The data for Germany omit the hyperinfl ation years 1922 and 1923.

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Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 335

a picture like Figure 11.4 tells you all you need to know about (past) dispersion. But, in general, pictures do not suffice. The financial manager needs a numerical measure of dispersion. The standard measures are variance and standard deviation. More variable returns imply greater investment risk. This suggests that some measure of dispersion will provide a reasonable measure of risk, and dispersion is precisely what is measured by variance and standard deviation.

Here is a very simple example showing how variance and standard deviation are cal- culated. Suppose that you are offered the opportunity to play the following game: You start by investing $100. Then two coins are flipped. For each head that comes up your starting balance will be increased by 20%, and for each tail that comes up your starting balance will be reduced by 10%. Clearly there are four equally likely outcomes:

• Head + Head: You make  20 + 20 = 40% • Head + Tail: You make  20 − 10 = 10% • Tail   + Head: You make  − 10 + 20 = 10% • Tail   + Tail: You make  − 10 − 10 = −20%

variance Average value of squared deviations from mean. A measure of volatility.

standard deviation Square root of variance. Another measure of volatility.

FIGURE 11.4 Historical returns on major asset classes, 1900–2013

Common Stocks

0 2 4 6 8

10 12 14

- 45

to -

40

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Bonds

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Bills

0 10 20 30 40 50 60 70 80

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to 5

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6 0

Returns (%)

N u

m b

er o

f ye

ar s

Source: Author’s calculations using data from E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns (Princeton, NJ: Princeton University Press, 2002), with updates kindly provided by Triumph ’s authors.

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336 Part Three Risk

There is a chance of 1 in 4, or .25, that you will make 40%; a chance of 2 in 4, or .5, that you will make 10%; and a chance of 1 in 4, or .25, that you will lose 20%. The game’s expected return is therefore a weighted average of the possible outcomes:

Expected return = probability-weighted average of possible outcomes = (.25 × 40) + (.5 × 10) + (.25 × -20) = +10%

If you play the game a very large number of times, your average return should be 10%. Table 11.2 shows how to calculate the variance and standard deviation of the returns

on your game. Column 1 shows the four equally likely outcomes. In column 2 we cal- culate the difference between each possible outcome and the expected outcome. You can see that at best the return could be 30% higher than expected; at worst it could be 30% lower.

These deviations in column 2 illustrate the spread of possible returns. But if we want a measure of this spread, it is no use just averaging the deviations in column 2— the average is always going to be zero because the positive and negative deviations cancel out. To get around this problem, we square the deviations in column 2 before averaging them. These squared deviations are shown in column 3. The variance is the average of these squared deviations and therefore is a natural measure of dispersion:

Variance = average of squared deviations around the average (11.2)

= 1,800

4 = 450

When we squared the deviations from the expected return, we changed the units of measurement from percentages to percentages squared. Our last step is to get back to percentages by taking the square root of the variance. This is the standard deviation:

Standard deviation = square root of variance (11.3)

= "450 = 21% Because standard deviation is simply the square root of variance, it too is a natural

measure of risk. If the outcome of the game had been certain, the standard deviation would have been zero because there would then be no deviations from the expected outcome. The actual standard deviation is positive because we don’t know what will happen.

Now think of a second game: It is the same as the first except that each head means a 35% gain and each tail means a 25% loss. Again there are four equally likely outcomes:

• Head + Head: You gain 70% • Head + Tail: You gain 10% • Tail   + Head: You gain 10% • Tail   + Tail: You lose 50%

TABLE 11.2 The coin-toss game; calculating variance and standard deviation

(1) Percent Rate of Return

(2) Deviation from Expected Return

(3) Squared Deviation

+40 +30 900 +10 0 0 +10 0 0 -20 -30 900

Notes: 1. Variance  =  average of squared deviations  =  1,800/4  =  450.

2. Standard deviation  =  square root of variance = "450 = 21.2, about 21%.

How to calculate variance and standard

deviation

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Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 337

For this game, the expected return is 10%, the same as that of the first game, but it is riskier. For example, in the first game, the worst possible outcome is a loss of 20%, which is 30% worse than the expected outcome. In the second game the downside is a loss of 50%, or 60% below the expected return. This increased spread of outcomes shows up in the standard deviation, which is double that of the first game, 42% versus 21%. By this measure the second game is twice as risky as the first.

A Note on Calculating Variance When we calculated variance in Table 11.2 , we recorded separately each of the four possible outcomes. An alternative would have been to recognize that in two of the four possible cases the outcomes are the same. In other words, if you were to play the game a large number of times, you would find that on 50% of the occasions the deviation from the expected return is 0%, 25% of the time it is +30%, and the remaining 25% of the time it is −30%. This suggests a simple way to calculate variance: Just weight each squared deviation by its probability:

Variance = sum of squared deviations weighted by probabilities = .25 × 302 + .5 × 0 + .25 × (-30)2 = 450

Calculate the variance and standard deviation of the second (higher-risk) coin-tossing game.

Self-Test 11.3

Measuring the Variation in Stock Returns When estimating the spread of possible outcomes from investing in the stock market, most financial analysts start by assuming that the spread of returns in the past is a reasonable indication of what could happen in the future. Therefore, they calculate the standard deviation of past returns. To illustrate, suppose that you were presented with the data for stock market returns shown in Table 11.3 . The average return over the 6 years from 2008 to 2013 was 9.72%. This is just the sum of the returns over the 6 years divided by 6 (58.33/6 = 9.72%).

Column 2 in Table 11.3 shows the difference between each year’s return and the average return. For example, in 2013 the return of 33.06% on common stocks was

Year Rate of Return, % Deviation from

Average Return, % Squared Deviation

2008 −37.23 −46.96 2,204.88 2009 28.30 18.58 345.31 2010 17.16 7.44 55.40 2011 0.98 −8.74 76.47 2012 16.06 6.34 40.14 2013 33.06 23.34 544.74 Total 58.33 3,266.95

Average return = 58.33/6 = 9.72%

Variance = average of squared deviations = 3,266.95/6 = 544.49

Standard deviation = square root of variance = 23.33%

Note: Returns shown in the table are rounded to 2 decimal places. The squared deviation in the last column uses the actual returns, without rounding.

Source: Authors’ calculations using data from E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Global Equity Returns (Princeton, NJ: Princeton University Press, 2002), with updates kindly provided by Triumph ’s authors.

TABLE 11.3 The average return and standard deviation of stock market returns, 2008–2013

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338 Part Three Risk

above the 6-year average by 23.34%. In column 3 we square these deviations from the average. The variance is then the average of these squared deviations: 5

Variance = average of squared deviations

= 3,266.95

6 = 544.49

Since standard deviation is the square root of the variance,

Standard deviation = square root of variance

= "544.49 = 23.33% It is difficult to measure the risk of securities on the basis of just six past outcomes.

Therefore, Table 11.4 lists the annual standard deviations for our three portfolios of securities over the period 1900–2013. As expected, Treasury bills were the least vari- able security, and common stocks were the most variable. Treasury bonds hold the middle ground.

Of course, there is no reason to believe that the market’s variability should stay the same over many years. Indeed many people believe that in recent years the stock market has become more volatile due to irresponsible speculation by . . . (fill in here the name of your preferred guilty party). Figure 11.5 provides a chart of the volatility of the U.S. stock market for each year from 1900 to 2013. 6 Notice how volatility spiked upward

5 Technical note: When variance is estimated from a sample of observed returns, it is common to add the squared deviations and divide by N  − 1, rather than N, where N is the number of observations. This procedure adjusts the estimate for what is called the loss of a degree of freedom. We will ignore this fine point, emphasizing the interpretation of variance as an average squared deviation. In any event, the correction for the lost degree of freedom is negligible when there are plentiful observations. For example, with 100 years of data, the difference between dividing by 99 or 100 will affect the estimated variance by only 1% (i.e., a factor of 1.01). 6 We converted the weekly variance to an annual variance by multiplying by 52. In other words, the variance of annual returns is 52 times that of weekly returns. The longer you hold a security, the more risk you have to bear.

Portfolio Standard Deviation, %

Treasury bills 2.8 Long-term government bonds 8.9 Common stocks 19.9

Source: Authors’ calculations using data from Elroy Dimson, Paul Marsh, and Mike Staunton, Triumph of the Optimists: 101 Years of Global Equity Returns (Princeton, NJ: Princeton University Press, 2002), with updates kindly  provided by Triumph ’s authors .

TABLE 11.4 Standard deviation of returns, 1900–2013

FIGURE 11.5 Annualized standard deviation of weekly percent changes in the Dow Jones Industrial Average, 1900–2013

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Source: www.djaverages.com .

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Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 339

during the Great Crash of 1929. The past decade has also experienced unusually high volatility as the dot-com boom unwound in 2002 and as the financial crisis reached its climax in 2009. But recent years have also seen some of the most tranquil stock prices. Market volatility, it seems, may rise and fall, but there is little sign of an upward trend.

11.4 Risk and Diversification Diversification We can calculate our measures of variability equally well for individual securities and portfolios of securities. Of course, the level of variability over 100 years is less inter- esting for specific companies than for the market portfolio because it is a rare com- pany that faces the same business risks today as it did a century ago.

Table 11.5 presents estimated standard deviations for some well-known common stocks for a recent 5-year period. 7 The standard deviation of the market portfolio in these years was 18.9%, a shade below the long-term average. However, the standard deviation of the returns on most of our stocks was much higher than 18.9%. Most stocks are substantially more variable than the market portfolio; only a handful are less variable.

This raises an important question: The market portfolio is made up of individual stocks, so why isn’t its variability equal to the average variability of its components? The answer is that diversification reduces variability.

Selling umbrellas is a risky business; you may make a killing when it rains, but you are likely to lose your shirt in a heat wave. Selling ice cream is no safer; you do well in the heat wave, but business is poor in the rain. Suppose, however, that you invest in both an umbrella shop and an ice cream shop. By diversifying your investment across the two businesses, you make an average level of profit come rain or shine.

Portfolio diversification works because prices of different stocks do not move exactly together. Statisticians make the same point when they say that stock

7 We pointed out earlier that five annual observations are insufficient to give a reliable estimate of variability. Therefore, these estimates are derived from 60 monthly rates of return, and then the monthly variance is multi- plied by 12.

diversification Strategy designed to reduce risk by spreading the portfolio across many investments.

Stock Standard Deviation, %

Dow Chemical 59.6 U.S. Steel 59.3 Newmont Mining 38.6 General Electric 37.0 Amazon 35.0 Starbucks 34.4 Boeing 30.5 Google 29.4 Union Pacifi c 27.9 Disney 26.8 Intel 26.6 Pfi zer 21.2 IBM 19.5 S&P 500 18.9 Coca-Cola 17.8 Campbell Soup 17.4 ExxonMobil 16.8 Walmart 16.3 McDonald’s 14.3 Consolidated Edison 13.6

TABLE 11.5 Standard deviations for selected common stocks, May 2008– April 2013

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340 Part Three Risk

price changes are less than perfectly correlated. Diversification works best when the returns are negatively correlated, as is the case of our umbrella and ice cream businesses. When one business does well, the other does badly. Unfortu- nately, in practice, stocks that are negatively correlated are as rare as a summer snowstorm.

Asset versus Portfolio Risk The history of returns on different asset classes provides compelling evidence of a risk–return trade-off and suggests that the variability of the rates of return on each asset class is a useful measure of risk. However, volatility of returns can be a mislead- ing measure of risk for an individual asset held as part of a portfolio. To see why, consider the following example.

Suppose there are three equally likely outcomes, or scenarios, for the economy: a recession, normal growth, and a boom. An investment in an auto stock will have a rate of return of −8% in a recession, 5% in a normal period, and 18% in a boom. Auto firms are cyclical: They do well when the economy does well. In contrast, gold firms are often said to be countercyclical, meaning that they do well when other firms do poorly. Suppose that stock in a gold mining firm will provide a rate of return of 20% in a recession, 3% in a normal period, and −20% in a boom. These assumptions are summarized in Table 11.6 .

It appears that gold is the more volatile investment. The difference in return across the boom and bust scenarios is 40% (−20% in a boom versus +20% in a recession), compared to a spread of only 26% for the auto stock. In fact, we can confirm the higher volatility by measuring the variance or standard deviation of returns of the two assets. The calculations are set out in Table 11.7 .

Since all three scenarios are equally likely, the expected return on each stock is simply the average of the three possible outcomes. 8 For the auto stock the expected

8 If the probabilities were not equal, we would need to weight each outcome by its probability in calculating the expected outcome and the variance.

TABLE 11.6 Rate of return assumptions for two stocks Rate of Return, %

Scenario Probability Auto Stock Gold Stock

Recession 1/3 -8 +20 Normal 1/3 +5 +3 Boom 1/3 +18 -20

TABLE 11.7 Expected return and volatility for two stocks

*Variance = average of squared deviations from the expected value.

Auto Stock Gold Stock

Scenario Rate of

Return, %

Deviation from Expected Return, %

Squared Deviation

Rate of Return, %

Deviation from Expected Return, %

Squared Deviation

Recession -8 -13 169 +20 +19 361 Normal +5 0 0 +3 +2 4 Boom +18 +13 169 -20 -21 441 Expected return 1

3 (-8 + 5 + 18) = 5%

1 3

(+20 + 3 - 20) = 1%

Variance* 1 3

(169 + 0 + 169) = 112.7 1 3

(361 + 4 + 441) = 268.7

Standard deviation (="variance) "112.7 = 10.6% "268.7 = 16.4%

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Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 341

return is 5%; for the gold stock it is 1%. The variance is the average of the squared deviations from the expected return, and the standard deviation is the square root of the variance.

Suppose the probability of the recession or boom is .30, while the probabil- ity of a normal period is .40. Would you expect the variance of returns on these two investments to be higher or lower? Why? Confirm by calculating the standard deviation of the auto stock. (Refer to Section 11.3 if you are unsure of how to do this.)

Self-Test 11.4

The gold mining stock offers a lower expected rate of return than the auto stock and more volatility—a loser on both counts, right? Would anyone be willing to hold gold mining stocks in an investment portfolio? The answer is a resounding yes.

To see why, suppose you do believe that gold is a lousy asset, and therefore you hold your entire portfolio in the auto stock. Your expected return is 5% and your stan- dard deviation is 10.6%. We’ll compare that portfolio to a partially diversified one, invested 75% in autos and 25% in gold. For example, if you have a $10,000 portfolio, you could put $7,500 in autos and $2,500 in gold.

First, we need to calculate the return on this portfolio in each scenario. The port- folio return is the weighted average of returns on the individual assets with weights equal to the proportion of the portfolio invested in each asset. For a portfolio formed from only two assets,

Portfolio rate

of return = ¢ fraction of portfolioin first asset × rate of returnon first asset ≤ (11.4)

+ ¢ fraction of portfolioin second asset × rate of returnon second asset≤ For example, autos have a weight of .75 and a rate of return of −8% in the recession, and gold has a weight of .25 and a return of 20% in a recession. Therefore, the portfo- lio return in the recession is the following weighted average: 9

Portfolio return in recession = 3.75 × (-8%) 4 + (.25 × 20%) = -1%

Table 11.8 expands Table 11.6 to include the portfolio of the auto stock and the gold mining stock. The expected returns and volatility measures are summarized at the bottom of the table. The surprising finding is this: When you shift part of your funds from the auto stock to the more volatile gold mining stock, your portfolio vari- ability actually decreases. In fact, the volatility of the auto-plus-gold stock portfolio is considerably less than the volatility of either stock separately. This is the payoff to diversification.

We can understand this more clearly by focusing on asset returns in the two extreme scenarios, boom and recession. In the boom, when auto stocks do best, the poor return on gold reduces the performance of the overall portfolio. However, when auto stocks are stalling in a recession, gold shines, providing a substantial positive return that

9 Let’s confirm this. Suppose you invest $7,500 in autos and $2,500 in gold. If the recession hits, the rate of return on autos will be −8%, and the value of the auto investment will fall by 8% to $6,900. The rate of return on gold will be 20%, and the value of the gold investment will rise 20% to $3,000. The value of the total portfo- lio falls from its original value of $10,000 to $6,900 + $3,000 = $9,900, which is a rate of return of −1%. This matches the rate of return given by the formula for the weighted average.

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342 Part Three Risk

boosts portfolio performance. The gold stock offsets the swings in the performance of the auto stock, reducing the best-case return but improving the worst-case return. The inverse relationship between the returns on the two stocks means that returns are more stable when the gold mining stock is added to an all-auto portfolio.

A gold stock is really a negative-risk asset to an investor starting with an all-auto portfolio. Adding it to the portfolio reduces the volatility of returns. The incremental risk of the gold stock (that is, the change in overall risk when gold is added to the port- folio) is negative despite the fact that gold returns are highly volatile.

In Table 11.9 we consider several other potential portfolios, all formed by mixing our gold and auto stocks in varying proportions. Portfolio A is invested fully in the auto stock, portfolio B shifts 20% of the portfolio from the auto stock to gold, and so on, until we reach portfolio F, which is fully invested in gold. The table shows the rate of return of each portfolio in each scenario; the expected value and standard deviation of returns across the three scenarios appear in the last two columns. Notice that the standard deviation of portfolio A is 10.6%, which of course is just the standard devia- tion of the auto stock. When we shift 20% of the portfolio to more volatile gold, as in portfolio B, standard deviation actually falls. As we’ve seen, this is the benefit of diversification.

How much more can we reduce risk? The standard deviation of portfolio C, which has a 40% weight in gold, is even lower. But this is about the best we can do. Beyond this point, adding more gold increases standard deviation, to 5.6% for portfolio D and 11% for portfolio E. These portfolios are already heavily invested in gold, so adding more of it increases risk. Thus, the incremental risk of gold depends on where you are starting from. Portfolios A and B are dominated by the auto stock, so adding gold reduces volatility. But portfolios D and E are already dominated by gold, so adding more now increases volatility.

Figure 11.6 plots the expected return–standard deviation pairs of our six portfolios. The “extreme” portfolios, A and F, which are fully invested in either autos or gold, are at the two ends of the plot. When we “connect the dots” corresponding to each portfolio, we trace out the possible combinations of expected return and portfolio risk. This plot is called the investment opportunity frontier. The frontier dramatically illustrates the benefit of diversification. In our example, as portfolio C shows, risk can

investment opportunity frontier Plot of the combinations of expected return and standard deviation for various portfolio weights.

TABLE 11.8 Rates of return for two stocks and a portfolio with 75% invested in the auto stock and 25% in the gold stock

Rate of Return, %

Scenario Probability Auto Stock Gold Stock Portfolio Return, %*

Recession 1/3 -8 +20 -1.0 Normal 1/3 +5 +3 +4.5 Boom 1/3 +18 -20 +8.5 Expected return 5 1 4 Variance 112.7 268.7 15.2 Standard deviation 10.6 16.4 3.9

* Portfolio return = (.75 × auto stock return) + (.25 × gold stock return)

Portfolio Weights Portfolio Rate of Return

Gold Autos Recession Normal Boom

Expected Return

Standard Deviation

A 0.0 1.0 −8.0 5.0 18.0 5.0 10.6 B 0.2 0.8 −2.4 4.6 10.4 4.2 5.2 C 0.4 0.6 3.2 4.2 2.8 3.4 0.6 D 0.6 0.4 8.8 3.8 −4.8 2.6 5.6 E 0.8 0.2 14.4 3.4 −12.4 1.8 11.0 F 1.0 0.0 20.0 3.0 −20.0 1.0 16.4

TABLE 11.9 Risk and return on portfolios formed by mixing the auto and the gold stocks in varying proportions

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Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 343

be driven almost to zero. The great power of diversification in this case derives from the strong inverse relation between the gold and the auto stock. If the relationship were less strong, the investment opportunity frontier would have the same general shape, but it would not come so close to the vertical axis.

In general, the incremental risk of a stock depends on whether its returns tend to vary with or against the returns of the other assets in the portfolio. Incremental risk does not just depend on a stock’s volatility. If returns do not move closely with those of the rest of the portfolio, the stock generally will reduce the volatility of portfolio returns.

The degree to which two stocks move together can be measured by the correla- tion between their returns. If the gold and auto stocks in Table 11.7 moved in perfect lockstep, the correlation would be 1.0. If their returns were completely unrelated, the correlation would be zero. Because their returns actually move inversely, that is, one stock goes up when the other goes down, the correlation is negative. The lowest pos- sible correlation is −1.0, which indicates that returns move in perfect lockstep but in opposite directions. In our example the correlation between the gold and auto stocks was nearly this extreme at −.996. Unfortunately, in practice, negative correlations are rare because most stocks have a common dependence on the overall economy.

Table 11.10 shows correlations across a few major industries calculated from 5 years of monthly stock returns ending in 2012. You can find the correlation between any industry pair by picking off the number in the relevant row and column. Of course, each industry is perfectly correlated with itself, so every entry on the diagonal is exactly 1.

FIGURE 11.6 The investment opportunity frontier for the gold and auto stocks. Each point on the curve represents a feasible combination of expected return and volatility. The six labeled points correspond to the portfolios in Table 11.9.

0

1

2

3

4

5

6

0 5 10 15 20

Standard deviation (%)

E xp

ec te

d r

et u

rn (

% )

A

D

C

F

E

B

Agriculture Construction Machinery Autos Gold Utilities Telecom Retail

Agriculture 1.00 Construction 0.54 1.00 Machinery 0.58 0.88 1.00 Autos 0.51 0.78 0.85 1.00 Gold 0.09 0.25 0.30 0.12 1.00 Utilities 0.43 0.62 0.68 0.52 0.24 1.00 Telecom 0.49 0.80 0.84 0.75 0.25 0.78 1.00 Retail 0.42 0.79 0.78 0.78 0.15 0.49 0.79 1.00

Source: Authors’ calculations using monthly returns for the 5-year period ending December 2012, downloaded from the Fama-French data library: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/det_10_ind_port.html .

TABLE 11.10 Correlations across some major industries

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344

As we would expect, every correlation in the table is positive, but the correlations are highest between pairs of industries that are very sensitive to the business cycle. The maximum correlation in the table, .88, is between the machinery and construction industries. Correlations between these industries and less “cyclical” industries such as gold or agriculture are considerably lower; in fact, these two industries have the lowest correlation, .09. The real-life correlation between gold and autos is .12, quite low, but still not negative as in our example.

Excel provides built-in formulas that make calculating correlations as well as stan- dard deviations pretty easy. We show you how in the nearby box.

We can summarize as follows:

1. Investors care about the expected return and risk of their portfolio of assets. The risk of the overall portfolio can be measured by the volatility of returns, that is, the variance or standard deviation.

3. Row 11. We converted from monthly to annual standard deviation by multiplying by the square root of 12 (the number of months in a year). Annual variance is 12 times

monthly variance, so annual standard deviation is "12 times the monthly value.

4. Row 12. The correlation function, CORREL, takes as its arguments the entire series of returns on the two assets.

Spreadsheet Questions

1. Suppose Dow’s return in May had been −12.33% instead of −8.33%. Would you expect Dow’s standard deviation to be higher or lower than the value obtained in the spread- sheet? Reestimate standard deviation with the new value to confi rm your intuition.

2. Suppose again that Dow’s return in May had been −12.33% instead of −8.33%. Would you expect Dow’s cor - relation with the S&P 500 to be higher or lower than the value obtained in the spreadsheet? Reestimate correla- tion with the new value to confi rm your intuition.

Excel and most other spreadsheet programs provide built- in functions for calculating standard deviation and correla- tion. In columns B and C of the following spreadsheet, we have entered returns for the S&P 500 and Dow Chemical for 6 months in 2012. In practice, estimates based on only 6 months of data would be very unreliable, but our goal here is simply to illustrate the technique. Real-world estimates would be more likely to use 60 monthly returns or perhaps 52 weekly returns.

Here are some points to notice about the spreadsheet:

1. Columns B and C. These columns show monthly returns for the S&P 500 and Dow Chemical. Sometimes people mistakenly enter prices instead of returns and get nonsen- sical results.

2. Row 10. Footnote 5 (page 338) pointed out that in esti- mating standard deviation from a sample of observa- tions, it is common to make an adjustment for the loss of a “degree of freedom.” To do this, we would use the Excel formula STDEV rather than STDEVP. In some versions of Excel the formulas are STDEV.P (which does not correct for degrees of freedom) and STDEV.S (which does).

Solutions Spreadsheet Calculating Volatility

A B C D

1 Returns, percent Formula Used in

2 Month S&P 500 Dow Chemical Column C

3 Jun-12 3.96 2.48 4 May-12 −6.27 −8.33 5 Apr-12 −0.75 −2.20 6 Mar-12 3.13 4.10 7 Feb-12 4.06 0.00 8 Jan-12 4.36 16.53 9 Mean return 1.42 2.10 =AVERAGE(C3:C8) 10 Standard deviation (monthly) 3.85 7.57 =STDEVP(C3:C8) 11 Standard deviation, annualized 13.32 26.23 =C10*SQRT(12) 12 Correlation 0.75 =CORREL(C3:C8,B3:B8)

How to calculate correlation coefficients

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Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 345

2. The standard deviation of the returns of an individual security measures how risky that security would be if held in isolation. But an investor who holds a portfolio of securities is interested only in how each security affects the risk of the entire portfolio. The contribution of a security to the risk of the portfolio depends on how the security’s returns vary with the investor’s other holdings. Thus a security that is risky if held in isolation may nevertheless serve to reduce the variability of the portfolio if its returns do not move in lockstep with the rest of the portfolio.

3. You can calculate how risky a portfolio has been by collecting its historical returns and calculating the standard deviation or variance. The reduction in portfolio risk from diversification depends on the correlations between stocks in the portfolio. Portfolios of stocks all taken from one industry, for example, would not benefit much because the returns would be highly correlated. A portfolio diversified across different industries would benefit more because correlations would be lower.

Example 11.1 General Electric and Newmont Mining Our example of the auto and gold mining stocks was entirely fanciful, but we can make the same point by looking at two real firms, General Electric and Newmont Mining. For the 5 years ending in mid-2013, both firms had roughly equal stan- dard deviations, 10.7% a month for GE and 11.1% for Newmont. Panels a and b of Figure 11.7 contain histograms of monthly returns for the two firms, and consis- tent with their similar standard deviations, the histograms show pretty much equal dispersion.

Although both stocks had their ups and downs, they have not moved in lockstep. For example, in June 2010, GE’s return was −11.2% while Newmont’s stock price increased by 14.9%. Conversely, in July 2009, when Newmont fell by 8%, GE rose by 6%. In fact, the two stocks were nearly uncorrelated over this period, with a correla- tion coefficient of only .083. Because gains on one stock often offset losses on the other, you could have smoothed out your returns by diversifying between them.

Panel c shows the histogram of returns for a portfolio split equally between the two stocks. The histogram shows that the portfolio had less volatile returns than either of the two component stocks, with much higher frequency in the middle of

FIGURE 11.7 Monthly returns for General Electric and Newmont Mining

Rate of return (%)

0

5

10

15

20

25

- 35

to -

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to -

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to -

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to -

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to -

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to -

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- 5

to 0

0 to

5

5 to

1 0

10 to

1 5

15 to

2 0

20 to

2 5

25 to

3 0

O b

se rv

at io

n s

(a) Newmont Mining, standard deviation = 11.1%

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346 Part Three Risk

Market Risk versus Specific Risk Our examples illustrate that even a little diversification can provide a substantial reduc- tion in variability. Suppose you calculate and compare the standard deviations of ran- domly chosen one-stock portfolios, two-stock portfolios, five-stock portfolios, and so on. You can see from Figure 11.8 that diversification can cut the variability of returns by about a third. But you can get most of this benefit with relatively few stocks: The improvement is slight when the number of stocks is increased beyond, say, 20 or 30.

the distribution and the most extreme outcomes largely eliminated. The standard deviation of the portfolio is only 8.0%, considerably lower than the standard devia- tion of either component stock. Again, this is the benefit of diversification.

How diversification reduces risk

BEYOND THE PAGE

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An investor is currently fully invested in gold mining stocks. Which action would do more to reduce portfolio risk: diversification into silver mining stocks or into automotive stocks? Why?

Self-Test 11.5

- 35

to -

30

- 30

to -

25

- 25

to -

20

- 20

to -

15

- 15

to -

10

- 10

to -

5

- 5

to 0

0 to

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5 to

1 0

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1 5

15 to

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20 to

2 5

25 to

3 0

- 35

to -

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- 30

to -

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to -

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to -

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to 0

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1 0

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2 5

25 to

3 0

0

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20

25

O b

se rv

at io

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Rate of return (%)

(b) General Electric, standard deviation = 10.7%

(c) Portfolio, standard deviation = 8.0%

Rate of return (%)

0

5

10

15

20

25

O b

se rv

at io

n s

FIGURE 11.7 (continued)

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Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 347

Figure 11.8 also illustrates that no matter how many securities you hold, you cannot eliminate all risk. If the economy as a whole tanks, then most stocks, and even diversi- fied portfolios, are likely to plummet.

The risk that can be eliminated by diversification is called specific risk. The risk that you can’t avoid regardless of how much you diversify is generally known as mar- ket risk or systematic risk. Specific risk arises because many of the perils that surround an individual company are peculiar to that company and perhaps its direct competitors. Market risk stems from economywide perils that threaten all businesses. Market risk explains why stocks have a tendency to move together, so even well-diversified portfolios are exposed to market movements.

Figure 11.9 divides risk into its two parts—specific risk and market risk. If you have only a single stock, specific risk is very important; but once you have a portfolio of 30 or more stocks, diversification has done most of what it can to eliminate risk. For a reasonably well-diversified portfolio, only market risk matters.

11.5 Thinking about Risk How can you tell which risks are specific and diversifiable? Where do market risks come from? Here are three messages to help you think clearly about risk.

specific risk Risk factors affecting only that firm. Also called diversifiable risk.

market risk Economywide (macroeconomic) sources of risk that affect the overall stock market. Also called systematic risk.

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The importance of the market factor

FIGURE 11.8 The risk (variance) of portfolios containing different numbers of New York Stock Exchange stocks. The stocks were selected randomly from stocks in the Standard & Poor’s Composite Index, 2008–2012. Notice that diversification reduces risk rapidly at first and then more slowly.

0 5 10 15 20 25 30

Number of stocks R

is k

(v ar

ia n

ce )

FIGURE 11.9 Diversification eliminates specific risk. But there is some risk that diversification cannot eliminate. This is called market risk.

Number of stocks

R is

k (v

ar ia

n ce

)

10 1550

Specific risk

Market risk

20 25 30

Technical note: Risk here is measured by the variance. The total variance of a portfolio is the sum of the variance due to the market and the specifi c variance.

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348 Part Three Risk

Message 1: Some Risks Look Big and Dangerous but Really Are Diversifiable Managers confront risks “up close and personal.” They must make decisions about particular investments. The failure of such an investment could cost a promotion, bonus, or otherwise steady job. Yet that same investment may not seem risky to an investor who can stand back and combine it in a diversified portfolio with many other assets or securities.

Example 11.2 Wildcat Oil Wells You have just been promoted to director of exploration, Western Hemisphere, of MPS Oil. The manager of your exploration team in far-off Costaguana has appealed for $20 million extra to drill in an even steamier part of the Costaguanan jungle. The manager thinks there may be an “elephant” field worth $500 million or more hidden there. But the chance of finding it is at best 1 in 10, and yesterday MPS’s CEO sourly commented on the $100 million already “wasted” on Costaguanan exploration.

Is this a risky investment? For you it probably is; you may be a hero if oil is found and a goat otherwise. But MPS drills hundreds of wells worldwide; for the company as a whole, it’s the average success rate that matters. Geologic risks (is there oil or not?) should average out. The risk of a worldwide drilling program is much less than the apparent risk of any single wildcat well.

Back up one step, and think of the investors who buy MPS stock. The investors may hold other oil companies too, as well as companies producing steel, com- puters, clothing, cement, and breakfast cereal. They naturally—and realistically— assume that your successes and failures in drilling oil wells will average out with the thousands of independent bets made by the companies in their portfolio.

Therefore, the risks you face in Costaguana do not affect the rate of return investors demand for holding the stock of MPS Oil. Diversified investors in MPS stock will be happy if you find that elephant field, but they probably will not notice if you fail and lose your job. In any case, they will not demand a higher average rate of return for worrying about geologic risks in Costaguana.

Example 11.3 Fire Insurance Would you be willing to write a $100,000 fire insurance policy on your neighbor’s house? The neighbor is willing to pay you $100 for a year’s protection, and experi- ence shows that the chance of fire damage in a given year is substantially less than 1 in 1,000. But if your neighbor’s house is damaged by fire, you would have to pay up.

Few of us have deep enough pockets to insure our neighbors, even if the odds of fire damage are very low. Insurance seems a risky business if you think policy by policy. But a large insurance company, which may issue a million policies, is con- cerned only with average losses, which can be predicted with excellent accuracy.

Imagine a laboratory at IBM, late at night. One scientist speaks to another. “You’re right, Watson, I admit this experiment will consume all the rest of

this year’s budget. I don’t know what we’ll do if it fails. But if this yttrium– magnoosium alloy superconducts, the patents will be worth millions.”

Would this be a good or bad investment for IBM? Can’t say. But from the ultimate investors’ viewpoint this is not a risky investment. Explain why.

Self-Test 11.6

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Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 349

Message 2: Market Risks Are Macro Risks We have seen that diversified portfolios are not exposed to the specific risks of indi- vidual stocks but are exposed to the uncertain events that affect the entire securities market and the entire economy. These are macroeconomic, or “macro,” factors such as changes in interest rates, industrial production, inflation, foreign exchange rates, and energy costs. These factors affect most firms’ earnings and stock prices. When the relevant macro risks turn generally favorable, stock prices rise and investors do well; when the same variables go the other way, investors suffer.

You can often assess relative market risks just by thinking through exposures to the business cycle and other macro variables. The following businesses have substantial macro and market risks:

• Airlines. Because business travel falls during a recession, and individuals postpone vacations and other discretionary travel, the airline industry is subject to the swings of the business cycle. On the positive side, airline profits really take off when busi- ness is booming and personal incomes are rising.

• Machine tool manufacturers. These businesses are especially exposed to the busi- ness cycle. Manufacturing companies that have excess capacity rarely buy new machine tools to expand. During recessions, excess capacity can be quite high.

Here, on the other hand, are two industries with less-than-average macro exposures:

• Food companies. Companies selling staples, such as breakfast cereal, flour, and dog food, find that demand for their products is relatively stable in good times and bad.

• Electric utilities. Business demand for electric power varies somewhat across the business cycle, but by much less than demand for air travel or machine tools. Also, many electric utilities’ profits are regulated. Regulation cuts off upside profit potential but also gives the utilities the opportunity to increase prices when demand is slack.

Remember, investors holding diversified portfolios are mostly concerned with macroeconomic risks. They do not worry about microeconomic risks peculiar to a particular company or investment project. Micro risks wash out in diversified portfolios. Company managers may worry about both macro and micro risks, but only the former affect the cost of capital.

Which company of each of the following pairs would you expect to be more exposed to macro risks?

a. A luxury Manhattan restaurant or an established Burger Queen franchise? b. A paint company that sells through small paint and hardware stores to do-

it-yourselfers or a paint company that sells in large volumes to Ford, GM, and Chrysler?

Self-Test 11.7

Message 3: Risk Can Be Measured Delta Airlines clearly has more exposure to macro risks than food companies such as Kellogg or General Mills. These are easy cases. But is IBM stock a riskier invest- ment than ExxonMobil? That’s not an easy question to reason through. We can, how- ever, measure the risk of IBM and ExxonMobil by looking at how their stock prices fluctuate.

We’ve already hinted at how to do this. Remember that diversified investors are concerned with market risks. The movements of the stock market sum up the net effects of all relevant macroeconomic uncertainties. If the market portfolio of all

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350 Part Three Risk

L I S T I N G O F E Q UAT I O N S

11.1 Percentage return = capital gain + dividend

initial share price

11.2 Variance = average of squared deviations around the average

traded stocks is up in a particular month, we conclude that the net effect of mac- roeconomic news is positive. Remember, the performance of the market is barely affected by a firm-specific event. These cancel out across thousands of stocks in the market.

How do we measure the risk of a single stock, like IBM or ExxonMobil? We do not look at the stocks in isolation, because the risks that loom when you’re up close to a single company are often diversifiable. Instead we measure the individual stock’s sensitivity to the fluctuations of the overall stock market. We will show you how this works in the next chapter.

SUMMARY Over the past century the return on the Standard & Poor’s Composite Index of common stocks has averaged 7.6% a year higher than the return on safe Treasury bills. This is the risk premium that investors have received for taking on the risk of investing in stocks. Long-term bonds have offered a higher return than Treasury bills but less than stocks.

If the risk premium in the past is a guide to the future, we can estimate the expected return on the market today by adding that 7.6% expected risk premium to today’s interest rate on Treasury bills. This would be the opportunity cost of capital for an average-risk project, that is, one with the same risk as a typical share of common stock.

The spread of outcomes on different investments is commonly measured by the variance or standard deviation of the possible outcomes. The variance is the average of the squared deviations around the average outcome, and the standard deviation is the square root of the variance. The standard deviation of the returns on a market portfolio of common stocks has averaged around 20% a year.

The standard deviation of returns is generally higher on individual stocks than it is on the market. Because individual stocks do not move in exact lockstep, much of their risk can be diversified away. By spreading your portfolio across many investments, you smooth out the risk of your overall position. The risk that can be eliminated through diversification is known as specific risk.

Even if you hold a well-diversified portfolio, you will not eliminate all risk. You will still be exposed to macroeconomic changes that affect most stocks and the overall stock mar- ket. These macro risks combine to create market risk —that is, the risk that the market as a whole will slump.

Stocks are not all equally risky. But what do we mean by a “high-risk stock”? We don’t mean a stock that is risky if held in isolation; we mean a stock that makes an above-aver- age contribution to the risk of a diversified portfolio. In other words, investors don’t need to worry much about the risk that they can diversify away; they do need to worry about risk that can’t be diversified. This depends on the stock’s sensitivity to macroeconomic conditions.

How can one estimate the opportunity cost of capital for an “average-risk” project? (LO11-1)

How is the standard deviation of returns for individual common stocks or for a stock portfolio calculated? (LO11-2)

Why does diversification reduce risk? (LO11-3)

What is the difference between specific risk, which can be diversified away, and market risk, which cannot? (LO11-4)

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Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 351

11.3 Standard deviation = square root of variance

11.4 Portfolio rateof return = ¢ fraction of portfolioin first asset × rate of returnon first asset ≤

+ ¢ fraction of portfolioin second asset × rate of returnon second asset≤

QUESTIONS AND PROBLEMS 1. Stock Market History. Use the data in Tables 11.1 and 11.4 to answer these questions: (LO11-1)

a. What was the average rate of return on large U.S. common stocks from 1900 to 2013? b. What was the average risk premium on large stocks? c. What was the standard deviation of returns on the market portfolio?

2. Maturity Premiums. Investments in long-term government bonds produced a negative average return during the period 1977–1981. How should we interpret this? Did bond investors in 1977 expect to earn a negative maturity premium? What do these 5 years’ bond returns tell us about the normal future maturity premium? (LO11-1)

3. Risk Premiums. What will happen to the opportunity cost of capital if investors suddenly become especially conservative and less willing to bear investment risk? (LO11-1)

4. Risk Premium. If the stock market return next year turns out to be −20%, will our estimate of the “normal” risk premium increase or decrease? Does this make sense? (LO11-1)

5. Risk Premiums and Discount Rates. Top hedge fund manager Diana Sauros believes that a stock with the same market risk as the S&P 500 will sell at year-end at a price of $50. The stock will pay a dividend at year-end of $2. What price should she be willing to pay for the stock today? Assume that risk-free Treasury securities currently offer an interest rate of 2%. Use Table 11.1 to find a reasonable discount rate. (LO11-1)

6. Risk Premiums. Here are stock market and Treasury bill percentage returns between 2008 and 2012: (LO11-1)

Year Stock Market Return T-Bill Return

2008 −37.23 1.60 2009 28.30 0.10 2010 17.16 0.12 2011 0.98 0.04 2012 16.06 0.06

a. What was the risk premium on common stock in each year? b. What was the average risk premium? c. What was the standard deviation of the risk premium?

7. Rate of Return. A stock is selling today for $40 per share. At the end of the year, it pays a dividend of $2 per share and sells for $44. (LO11-2)

a. What is the total rate of return on the stock? b. What are the dividend yield and percentage capital gain? c. Now suppose the year-end stock price after the dividend is paid is $36. What are the divi-

dend yield and percentage capital gain in this case? d. Why is the dividend yield the same in parts (b) and (d)?

8. Real versus Nominal Returns. You purchase 100 shares of stock for $40 a share. The stock pays a $2 per share dividend at year-end. (LO11-2)

a. What is the rate of return on your investment if the end-of-year stock price is (i) $38; (ii) $40; (iii) $42?

b. What is your real (inflation-adjusted) rate of return if the inflation rate is 4%?

finance

®

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352 Part Three Risk

9. Real versus Nominal Returns. The Costaguanan stock market provided a rate of return of 95%. The inflation rate in Costaguana during the year was 80%. In the United States, in con- trast, the stock market return was only 12%, but the inflation rate was only 2%. Which country’s stock market provided the higher real rate of return? (LO11-2)

10. Real versus Nominal Returns. The inflation rate in the United States has averaged 3.1% a year since 1900. What was the average real rate of return on Treasury bills, Treasury bonds, and common stocks in that period? Use the data in Table 11.1 . (LO11-2)

11. Real versus Nominal Returns. Do you think it is possible for risk-free Treasury bills to offer a negative nominal interest rate? Might they offer a negative real expected rate of return? (LO11-2)

12. Market Indexes. The accompanying table shows annual stock prices on the Sulaco Stock Exchange in the republic of Costaguana for 2008–2013. Construct two stock market indexes, one using weights as in the Dow Jones Industrial Average and the other using weights as in the Standard & Poor’s Composite Index. (LO11-2)

Annual prices in Costaguanan pegos for trading on the Sulaco Stock Exchange (Only fi ve stocks were traded at the start of 2008)

San Tomé Mining,

184 million*

Sulaco Markets,

42 million*

National Central Railway,

64 million*

Minerva Shipping, 38 million*

Azuera Inc., 16 million*

2008 55.10 80.00 21.45 82.50 135.00 2009 58.15 144.62 24.04 115.52 151.22 2010 58.45 135.93 26.53 138.90 166.99 2011 52.43 74.61 23.53 121.02 149.42 2012 52.50 75.01 32.46 174.62 177.27 2013 54.82 67.22 34.48 164.48 165.52

* Number of shares outstanding.

13. Market Indexes. In February 2009, the Dow Jones Industrial Average was at a level of about 8,000. In February 2013, it was about 14,000. Would you expect the Dow in 2013 to be more or less likely to move up or down by more than 40 points in a day than in 2009? Does this mean the market was riskier in 2013 than it was in 2009? (LO11-2)

14. Scenario Analysis. Consider the following scenario analysis: (LO11-2)

Rate of Return

Scenario Probability Stocks Bonds

Recession 0.20 -5% +14% Normal economy 0.60 +15 +8 Boom 0.20 +25 +4

a. Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms?

b. Calculate the expected rate of return and standard deviation for each investment. c. Which investment would you prefer?

15. Scenario Analysis and Portfolio Risk. The common stock of Leaning Tower of Pita Inc., a restaurant chain, will generate payoffs to investors next year, which depend on the state of the economy, as follows: (LO11-2 and LO11-3)

Dividend Stock Price

Boom $8 $240 Normal economy 4 90 Recession 0 0

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Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 353

a. The company goes out of business if a recession hits. Calculate the expected rate of return and standard deviation of return to Leaning Tower of Pita shareholders. Assume for simplic- ity that the three possible states of the economy are equally likely. The stock is selling today for $80.

b. Who would view the stock of Leaning Tower of Pita as a risk-reducing investment—the owner of a gambling casino or a successful bankruptcy lawyer? Explain.

16. Scenario Analysis. The common stock of Escapist Films sells for $25 a share and offers the following payoffs next year:

Dividend Stock Price

Boom $0 $18 Normal economy 1 26 Recession 3 34

Calculate the expected return and standard deviation of Escapist. All three scenarios are equally likely. Then calculate the expected return and standard deviation of a portfolio half invested in Escapist and half in Leaning Tower of Pita (from Problem 15). Show that the portfolio standard deviation is lower than that of either stock. Explain why this happens. (LO11-3)

17. Portfolio Analysis. Use the data in the scenario analysis from Problem 14 and consider a port- folio with weights of .60 in stocks and .40 in bonds. (LO11-3)

a. What is the rate of return on the portfolio in each scenario? b. What are the expected rate of return and standard deviation of the portfolio? c. Would you prefer to invest in the portfolio, in stocks only, or in bonds only? Explain the

benefit of diversification.

18. Diversification. In which of the following situations would you get the largest reduction in risk by spreading your portfolio across two stocks? Why? (LO11-3)

a. The stock returns vary with each other. b. The stock returns are independent. c. The stock returns vary against each other.

19. Market Risk. Which firms of each pair below would you expect to have greater market risk? (LO11-4)

a. General Steel or General Food Supplies b. Club Med or General Cinemas

20. Risk and Return. A stock will provide a rate of return of either −18% or +26%. (LO11-2 and LO11-4)

a. If both possibilities are equally likely, calculate the stock’s expected return and standard deviation.

b. If Treasury bills yield 4% and investors believe that the stock offers a satisfactory expected return, what must the market risk of the stock be?

21. Specific versus Market Risk. Sassafras Oil is staking all its remaining capital on wildcat exploration off the Côte d’Huile. There is a 10% chance of discovering a field with reserves of 50 million barrels. If it finds oil, it will immediately sell the reserves to Big Oil at a price depending on the state of the economy. Thus the possible payoffs are as follows:

Value of Reserves,

per Barrel Value of Reserves, 50 Million Barrels

Value of Dryholes

Boom $4 $200,000,000 0 Normal economy 5 250,000,000 0 Recession 6 300,000,000 0

Is Sassafras Oil a risky investment for a diversified investor in the stock market—compared, say, to the stock of Leaning Tower of Pita, described in Problem 15? Explain. (LO11-4)

22. Diversification. Log in to Connect or ask your instructor for access to the materials for Chapter 11. You will find a spreadsheet containing 5 years of monthly rates of return on ExxonMobil (XOM), BP, and Walmart (WMT). (LO11-3)Templates can be found in Connect.

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354 Part Three Risk

a. What was the average return and standard deviation of returns for each firm? b. What was the correlation of returns between each pair of firms? Try using Excel’s CORREL

function, which calculates the correlation between two series of numbers. Which pair of firms exhibits the highest correlation of returns? Is this surprising?

c. Now imagine that you held an equally weighted portfolio of ExxonMobil and Walmart (that is, a portfolio with equal dollar investments in each stock). Compute the portfolio’s rate of return for each month, and calculate the standard deviation of the portfolio’s monthly rate of return. Is the portfolio standard deviation more or less than the average of the standard deviations of the two component stocks?

d. Repeat part (c), but this time calculate the results for a portfolio of BP and ExxonMobil. e. Comparing your answers to (c) and (d), which pair of firms provides greater benefits from

diversification? Relate your answer to the correlation coefficients you found in part (a).

WEB EXERCISES 1. Go to finance.yahoo.com , and find the monthly rates of return over a 2-year period for five

companies of your choice. Now assume you form each month an equally weighted portfolio of the five firms (i.e., a portfolio with equal investments in each firm). What is the rate of return each month on your portfolio? Compare the standard deviation of the monthly portfolio return to that of each firm and to the average standard deviation across the five firms. What do you conclude about portfolio diversification?

2. Return to the monthly returns of the five companies you chose in the previous question.

a. Using the Excel functions for average (AVERAGE) and sample standard deviation (STDEV), calculate the average and the standard deviation of the returns for each of the firms.

b. Using Excel’s correlation function (CORREL), find the correlations between each pair of five stocks. What are the highest and lowest correlations?

c. Try finding correlations between pairs of stocks in the same industry. Are the correlations higher than those you found in part (b)? Is this surprising?

3. A large mutual fund group such as Fidelity offers a variety of funds. Some, called sector funds, specialize in particular industries; others, known as index funds, simply invest in the market index. Log on to www.fidelity.com and look up the standard deviation of returns on the Fidelity Spartan 500 Index Fund, which replicates the S&P 500. Now find the standard deviation of fund returns for different industry (sector) funds. Are they larger or smaller than the index fund? How do you interpret your findings?

SOLUTIONS TO SELF-TEST QUESTIONS 11.1 The bond price at the end of the year is $1,050. Therefore, the capital gain on each bond is

$1,050 − $1,020 = $30. Your dollar return is the sum of the income from the bond, $80, plus the capital gain, $30, or $110. The rate of return is

Income plus capital gain

Original price =

80 + 30

1,020 = .108, or 10.8%

Real rate of return is

1 + nominal return

1 + inflation rate - 1 =

1.108

1.04 - 1 = .065, or 6.5%

11.2 The risk premium on stocks is the average return in excess of Treasury bills. It was 6.1% in period 1, 10.6% in period 2, 5.4% in period 3, and 8.4% in period 4.

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Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 355

11.3 Rate of Return Deviation Squared Deviation

+70% +60% 3,600 +10 0 0 +10 0 0 -50 -60 3,600

Variance = average of squared deviations = 7,200/4 = 1,800

Standard deviation = square root of variance = "1,800 = 42.4, about 42%

11.4 The standard deviation should decrease because there is now a lower probability of the more extreme outcomes. The expected rate of return on the auto stock is now

3.3 × (-8%) 4 + (.4 × 5%) + (.3 × 18%) = 5% The variance is

3.3 × (-8 - 5)2 4 + 3.4 × (5 - 5)2 4 + 3.3 × (18 - 5)2 4 = 101.4 The standard deviation is "101.4 = 10.07%, which is lower than the value assuming equal

probabilities of each scenario.

11.5 The gold mining stock’s returns are more highly correlated with the silver mining company than with a car company. As a result, the automotive firm will offer a greater diversification benefit. The power of diversification is lowest when rates of return are highly correlated, per- forming well or poorly in tandem. Shifting part of the portfolio from one such firm to another has little impact on overall risk.

11.6 The success of this project depends on the experiment. Success does not depend on the per- formance of the overall economy. The experiment creates a diversifiable risk. A portfolio of many stocks will embody “bets” on many such specific risks. Some bets will work out and some will fail. Because the outcomes of these risks do not depend on common factors, such as the overall state of the economy, the risks will tend to cancel out in a well-diversified portfolio.

11.7 a. The luxury restaurant will be more sensitive to the state of the economy because expense account meals will be curtailed in a recession. Burger Queen meals should be relatively recession-proof.

b. The paint company that sells to the auto producers will be more sensitive to the state of the economy. In a downturn, auto sales fall dramatically as consumers stretch the lives of their cars. In contrast, in a recession, more people “do it themselves,” which makes paint sales through small stores more stable and less sensitive to the economy.

SOLUTIONS TO SPREADSHEET QUESTIONS 1. If the return on Dow had been 12.33% in May, you should observe a higher standard devia-

tion, since the extreme (bad) performance in this month is now even more extreme. In fact, using this rate of return, the monthly standard deviation rises from 7.57% to 8.57%.

2. You should expect to observe a higher correlation. Dow falls more in this month, which is when the market also has its worst performance. The correlation increases from .75 to .82.

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356

Risk, Return, and Capital Budgeting

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

12-1 Measure and interpret the market risk, or beta, of a security.

12-2 Relate the market risk of a security to the rate of return that investors demand.

12-3 Understand why and how project risk determines the opportunity cost of capital.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

12 CHAPTE R

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357

I n Chapter 11 we began to come to grips with risk. We stressed the distinction between specific risk and market risk. Specific risk arises from events that affect only the individual firm or its immediate com-

petitors; it can be eliminated by diversification. But

regardless of how much you diversify, you cannot

avoid the macroeconomic events that create market

risk. This is why investors do not require a higher rate of

return to compensate for specific risk but do need a

higher return to persuade them to take on market risk.

How can you measure the market risk of a secu-

rity or a project? We will see that market risk is usu-

ally measured by beta, that is, by the sensitivity of the

investment’s returns to fluctuations in the market. We

will also see that the risk premium investors demand

should be proportional to beta. This relationship

between risk and return is a useful way to estimate

the return that investors expect from investing in com-

mon stocks.

Finally, we will distinguish the risk of the company’s

securities and the risk of an individual project. We will

also consider what managers should do when the

risk of the project is different from that of the com-

pany’s existing business.

Professor William F. Sharpe receiving the Nobel Prize in Economics. The prize was for Sharpe’s development of the capital asset pricing model. This model shows how risk should be measured and provides a formula relating risk to the opportunity cost of capital.

P A

R T

TH R

E E

Ri sk

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358 Part Three Risk

12.1 Measuring Market Risk Changes in interest rates, government spending, oil prices, foreign exchange rates, and other macroeconomic events affect almost all companies and the returns on almost all stocks. We can therefore assess the impact of “macro” news by tracking the rate of return on a market portfolio of all securities. If the market is up on a particular day, then the net impact of macroeconomic changes must be positive. We know the perfor- mance of the market reflects only macro events, because firm-specific events—that is, specific risks—average out when we look at the combined performance of thousands of companies and securities.

In principle the market portfolio should contain all assets in the world economy— not just stocks but bonds, foreign securities, real estate, and so on. In practice, how- ever, financial analysts make do with indexes of the stock market, such as the Standard & Poor’s Composite Index (the S&P 500). 1

Our task here is to define and measure the risk of individual common stocks. Because risk depends on exposure to macroeconomic events, we measure it as the sensitivity of a stock’s returns to fluctuations in returns on the market portfolio. This sensitivity is called the stock’s beta. Beta is often written as the Greek letter β .

Measuring Beta In the last chapter we looked at the variability of several individual securities. Dow Chemical had one of the highest standard deviations, and Consolidated Edison had the lowest. If you had held Dow Chemical on its own, your returns would have varied more than four times as much as they would have if you had held Con Ed. But wise investors don’t put all their eggs in just one basket: They reduce their risk by diversi- fication. An investor with a diversified portfolio will be interested in the effect each stock has on the risk of the entire portfolio.

Diversification can eliminate the risk that is unique to individual stocks but not the risk that the market as a whole may decline, carrying your stocks with it.

Some stocks are less affected than others by market fluctuations. Investment man- agers talk about “defensive” and “aggressive” stocks. Defensive stocks are not very sensitive to market fluctuations and therefore have low betas. In contrast, aggressive stocks amplify any market movements and have higher betas. If the market goes up, it is good to be in aggressive stocks; if it goes down, it is better to be in defensive stocks (and better still to leave your money in the bank).

Aggressive stocks have high betas, betas greater than 1.0. Their returns tend to respond more than one for one to returns on the overall market. The betas of defen- sive stocks are less than 1.0. The returns of these stocks vary less than one for one with market returns. The average beta of all stocks is—no surprises here—1.0 exactly.

Now we’ll show you how betas are measured.

market portfolio Portfolio of all assets in the economy. In practice a broad stock market index is used to represent the market.

1 We discussed the most popular stock market indexes in Section 11.2.

beta Sensitivity of a stock’s return to the return on the market portfolio.

Example 12.1 Measuring Beta for Turbot-Charged Seafoods Suppose we look back at the trading history of Turbot-Charged Seafoods and pick out 6 months when the return on the market portfolio was plus or minus 1%.

Month Market Return, % Turbot-Charged Seafoods Return, %

1 + 1 + .8 2 + 1 + 1.8 Average  =  .8% 3 + 1 - .2 4 - 1 - 1.8 5 - 1 + .2 Average  =   - .8 6 - 1 - .8

v

v

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Chapter 12 Risk, Return, and Capital Budgeting 359

As this example illustrates, we can break down common stock returns into two parts: the part explained by market returns and the firm’s beta, and the part due to news that is specific to the firm. Fluctuations in the first part reflect market risk; fluctuations in the second part reflect specific risk.

Of course, diversification can get rid of the specific risks. That’s why wise inves- tors, who don’t put all their eggs in one basket, will look to Turbot’s less-than-average beta and call its stock “defensive.”

FIGURE 12.1 This figure is a plot of the data presented in the table in Example 12.1. Each point shows the performance of Turbot- Charged Seafoods stock when the overall market is either up or down by 1%. On average, Turbot-Charged moves in the same direction as the market, but not as far. Therefore, Turbot-Charged’s beta is less than 1.0. We can measure beta by the slope of a line fitted to the points in the figure. In this case it is .8.

T u

rb o

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h ar

g ed

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( %

) 1.0-1.0 -0.8 -0.6 -0.4

-0.2

-2.0

2.0

1.5

1.0

0.5

0

-0.5

-1.0

-1.5

0.80.60.40.2

Market return (%)

Look at Figure 12.1 , where these observations are plotted. We’ve drawn a line through the average performance of Turbot when the market is up or down by 1%. The slope of this line is Turbot’s beta. You can see right away that the beta is .8, because on average Turbot stock gains or loses .8% when the market is up or down by 1%. Notice that a 2-percentage-point difference in the market return ( - 1 to + 1) generates on average a 1.6-percentage-point difference for Turbot share- holders ( - .8 to + .8). The ratio, 1.6/2  =  .8, is beta.

In 4 months, Turbot’s returns lie above or below the line in Figure 12.1 . The dis- tance from the line shows the response of Turbot’s stock returns to news or events that affected Turbot but did not affect the overall market. For example, in month 2, investors in Turbot stock benefited from good macroeconomic news (the market was up 1%) and also from some favorable news specific to Turbot. The market rise gave a boost of .8% to Turbot stock (beta of .8 times the 1% market return). Then firm-specific news gave Turbot stockholders an extra 1% return, for a total return that month of 1.8%.

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360

be negative if returns on the Dow and the market tended to move in opposition, one down when the other is up and one up when the other is down. Negative correlations are extremely rare in the stock market, however.

Spreadsheet Questions

1. Suppose that Dow’s return in January 2012 had been + 10%, and its return in May 2012 had been - 3%. Would you expect its beta to be more or less than the value obtained in the spreadsheet? Reestimate beta with these new data, and confi rm your intuition.

2. Suppose that Dow’s return in each month had been 1% higher than the values presented in the accompany- ing spreadsheet. Would Dow’s beta differ from the value obtained in the spreadsheet? Reestimate beta with these new data, and confi rm your intuition.

3. Suppose that you add 1 more month of data to your spreadsheet and fi nd that in July 2012, Dow was down 8.6% while the market was up 4.0%. Would you expect Dow’s beta to be more or less than the value obtained in the spreadsheet? Reestimate beta with this new data point, and confi rm your intuition.

Excel and most other spreadsheet programs provide built-in functions for computing a stock’s beta. In columns B and C of the following spreadsheet we have entered returns for Stan- dard & Poor’s 500 Index (the S&P 500) and Dow Chemical for 6 months in 2012. (In practice, estimates based on just 6 months would be very unreliable. Estimates of standard deviation and beta use at least 50 returns, usually 60 monthly returns for 5 years. Sometimes 1 or 2 years of weekly returns are used.)

This example uses the same data we looked at in the last chapter to estimate the volatility of Dow Chemical. Here, we focus on market risk (beta) rather than total volatility. Let’s walk through the spreadsheet.

1. Row 12. Use the SLOPE function to calculate beta. It’s important to enter the stock returns (C3:C8) fi rst, followed by the market returns (B3:B8).

2. Row 13. The correlation coefficient of .75 reveals that Dow and the market track each other closely, but not perfectly. Perfect tracking would mean that Dow returns are always above-average when the market return is above- average, and always below-average when the market return is below- average. In this case the correlation coefficient would be 1.0. Zero correlation means no tracking at all—in this case beta would also be zero. The correlation coefficient would

Solutions Spreadsheet Calculating Risk

You can find this spreadsheet in Connect.

A B C D 1 Returns, % Formula Used in 2 Month S&P 500 Dow Chemical Column C 3 Jun-12 3.96 2.48 4 May-12 - 6.27 - 8.33 5 Apr-12 - 0.75 - 2.20 6 Mar-12 3.13 4.10 7 Feb-12 4.06 0.00 8 Jan-12 4.36 16.53 9 10 Standard deviation (monthly) 3.85 7.57 = STDEVP(C3:C8) 11 Standard deviation,

annualized 13.32 26.23 = C10*SQRT(12)

12 Beta 1.47 = SLOPE(C3:C8,B3:B8) 13 Correlation 0.75 = CORREL(C3:C8,B3:B8)

Here are 6 months’ returns to stockholders in the Anchovy Queen restaurant chain:

Draw a figure like Figure 12.1 and check the slope of the fitted line. What is Anchovy Queen’s beta?

Self-Test 12.1

Month Market Return, % Anchovy Queen Return, % 1 + 1 + 2.0 2 + 1 + 0 3 + 1 + 1.0 4 - 1 - 1.0 5 - 1 + 0 6 - 1 - 2.0

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Chapter 12 Risk, Return, and Capital Budgeting 361

Real life doesn’t serve up numbers quite as convenient as those in our examples so far. However, the procedure for measuring real companies’ betas is exactly the same:

1. Observe rates of return, usually monthly or weekly, for the stock and the market. 2. Plot the observations as in Figure 12.1 . 3. Fit a line showing the average return to the stock at different market returns.

Beta is the slope of the fitted line. This may sound like a lot of work, but in practice computers do it for you. The

nearby box shows how to use the SLOPE function in Excel to calculate a beta. Here are two real examples.

Betas for Dow Chemical and Consolidated Edison Each point in Figure 12.2 a shows the return on Dow Chemical stock and the return on the market index in a different month. For example, the circled point shows that in September 2009, Dow Chemical’s stock price rose by 23.2%, whereas the market index rose by 3.6%. Notice that more often than not Dow outperformed the market when the index rose and underperformed the market when the index fell. Thus Dow was a relatively aggressive, high-beta stock.

We have drawn a line of best fit through the points in the figure. 2 The slope of this line is 2.34. For each extra 1% rise in the market, Dow’s stock price moved on average an extra 2.34%. For each extra 1% fall in the market, Dow’s stock price fell an extra 2.34%. Thus Dow’s beta was 2.34.

Of course, Dow’s stock returns are not perfectly related to market returns. For example, in September 2009, the point highlighted in Figure 12.2 a, Dow performed better than one would have predicted given the return on the market index. We know this because Dow’s return in that month lies above the upward-sloping line in the figure—the line that depends on the market returns and Dow’s beta. The vertical dis- tance from that beta line to Dow’s return in September 2009 shows the impact of firm- specific events that lifted Dow’s fortunes but not the fortunes of the average stock or the market overall. At other times, for example July 2012, Dow flew south when the market went north, or vice versa.

Thus the slope of the line in Figure 12.2 a measures beta and exposure to market risk. Firm-specific risk shows up in the scatter of points around the line: Wider scatter means more firm-specific risk.

Figure 12.2 b shows a similar plot of the monthly returns for Consolidated Edi- son. In contrast to Dow Chemical, Con Ed was a defensive, low-beta stock. It was not highly sensitive to market movements, usually lagging when the market rose, but doing better (or less badly) when the market fell. The slope of the line of best fit shows that on average an extra 1% change in the index resulted in an extra .17% change in the price of Con Ed stock. Thus Con Ed’s beta was .17.

Estimates of beta can be accessed easily, for example, at finance.yahoo.com , but you may find it interesting to look at Table 12.1 , which shows betas of several well-known stocks. Consolidated Edison had the lowest beta: Its stock return was .17 times as sensi- tive as the average stock to market movements. Dow Chemical was at the other extreme: Its return was 2.34 times as sensitive as the average stock to market movements.

Total Risk and Market Risk Dow Chemical tops our list of betas in Table 12.1 . It was also at the top of Table 11.5, which showed the total variability of the same group of stocks. But total risk is not the

2 The line of best fit is a regression line. The slope of the line can be calculated using ordinary least squares regression. The dependent variable is the return on the stock (Dow Chemical). The independent variable is the return on the market index, in this case the S&P 500.

BEYOND THE PAGE

brealey.mhhe.com/ch12-01

Beta estimates for U.S. stocks

BEYOND THE PAGE

brealey.mhhe.com/ch12-02

Comparing beta estimates

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362 Part Three Risk

same as market risk. Some of the most variable stocks have below-average betas, and vice versa.

Consider, for example, Newmont Mining. Newmont is the world’s largest gold pro- ducer. The company cites the many risks that the company faces as “gold and other metals’ price volatility, increased costs and variances in ore grade or recovery rates from those assumed in mining plans, as well as political and operational risks in the countries in which we operate and governmental regulation and judicial outcomes.”

These risks are considerable and are reflected in the high standard deviation of the returns on Newmont’s stock (see Table 11.5). But they are mostly firm-specific, not macro, risks. When the U.S. economy is booming, gold prices are just as likely to slump, and a mine in some distant part of the world may well be hit by political unrest. So, while Newmont stock has above-average total volatility, it has a relatively low beta.

FIGURE 12.2 (a) Each point in this figure shows the returns on Dow Chemical common stock and the overall market in a particular month between May 2008 and April 2013. Dow’s beta is the slope of the line fitted to these points. Dow has a very high beta of 2.34. (b) In this plot of 60 months’ returns for Con Ed and the overall market, the slope of the fitted line is much less than Dow’s beta in (a). Con Ed has a relatively low beta of .17.

-40

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-20

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0

10

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30

40

-40 -30 -20 -10 0 10 20 30 40

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July 2012

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(b)

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Chapter 12 Risk, Return, and Capital Budgeting 363

TABLE 12.1 Betas for selected common stocks, May 2008–April 2013

Beta

Dow Chemical 2.34 U.S. Steel 2.34 Ford 2.18 General Electric 1.66 Disney 1.22 Starbucks 1.21 Boeing 1.20 Union Pacifi c 1.14 Intel 1.01 Google 0.94 Amazon 0.82 Pfi zer 0.74 IBM 0.68 Coca-Cola 0.53 ExxonMobil 0.48 McDonald’s 0.37 Walmart 0.35 Newmont Mining 0.31 Consolidated Edison 0.17

Average Beta 1.04

Note: Betas are calculated from 5 years of monthly data.

Firm-specific risk is, of course, diversifiable and of no concern to an investor track- ing the performance of his or her fully diversified portfolio. Newmont’s CEO and financial managers are acutely interested in firm-specific risk, however, always hoping that the next return will plot above the beta line. Investors analyzing Newmont’s finan- cial performance will likewise watch total return, even if much of the risk in that return will, in the end, be diversified away.

12.2 What Can You Learn from Beta? You can learn a lot from beta. First, if you don’t know whether a stock is defensive or aggressive, you can check whether its beta has been less than or greater than 1.0. Second, you can predict the beta of a portfolio.

Portfolio Betas The beta of a portfolio is just an average of the betas in the portfolio, weighted by the investment in each security. For example, the beta of a two-stock portfolio is calcu- lated as:

Portfolio beta = (fraction of portfolio in stock 1 × beta of stock 1) (12.1)

+ (fraction of portfolio in stock 2 × beta of stock 2)

Thus a portfolio invested 50–50 in Dow Chemical and Consolidated Edison would have a beta of (.5  ×  2.34)  +  (.5  ×  .17)  =  1.26.

Suppose you formed a portfolio of the 19 stocks in Table 12.1 with an equal amount invested in each stock. You could predict the portfolio beta as a simple average of the betas listed in the table. If you decided to invest more money in some stocks than oth- ers, you would have to calculate a weighted average.

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364 Part Three Risk

Rosa Rugonis receives a bequest of $1 million and decides to invest it as fol- lows: $200,000 each in Ford, Starbucks, Union Pacific, and IBM, and $100,000 each in Newmont Mining and Walmart. Rosa is of course dangerously undi- versified. But what is her portfolio beta? Use the stock betas in Table 12.1 .

Self-Test 12.2

Example 12.2 How Risky Are Mutual Funds? You don’t have to be wealthy to own a diversified portfolio. You can buy shares in one of the more than 8,000 mutual funds in the United States.

Investors buy shares of the funds, and the funds use the money to buy portfolios of securities. The returns on the portfolios are passed through to the funds’ own- ers in proportion to their shareholdings. Therefore, the funds act like investment cooperatives, offering even the smallest investors diversification and professional management at low cost.

Panel a of Figure 12.3 shows the calculation of beta for both an individual stock, Intel, and a stock mutual fund, Vanguard’s Growth and Income (G&I) Fund. As in Figure  12.1 , each dot in the diagram shows the return in a particular month for the S&P 500 and a particular investment, either Intel or the mutual fund. The orange dots are for Intel, and the blue dots are for the mutual fund. As it turns out, both Intel and the G&I fund had identical betas in this period, 1.01, and a com- mon trend line describes their average relation with the market. At least during this period, both Intel and G&I displayed average sensitivity to market fluctuations, with betas of almost exactly 1. Therefore, if Intel and G&I had no specific risk, their returns would have been precisely as variable as the market’s. But they both do have specific risk, so their returns actually were more variable.

Intel’s returns exhibit a wide scatter, reflecting its considerable firm-specific risk. As a result, its total volatility is substantially greater than that of the market. Turn

FIGURE 12.3 a Betas of Intel and Vanguard’s Growth and Income Fund

R et

u rn

o n

in ve

st m

en t

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

Vanguard Growth and Income Fund Intel Corp

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

Return on S&P 500

(a)

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Chapter 12 Risk, Return, and Capital Budgeting 365

FIGURE 12.3 b The Vanguard 500 Portfolio is a fully diversified index fund designed to track the performance of the market. Note the fund’s beta (1.0) and the absence of specific risk. The fund’s returns lie almost precisely on the fitted line relating its returns to those of the S&P 500 portfolio.

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

R et

u rn

o n

V an

g u

ar d

’s S

& P

I n

d ex

F u

n d

Return on S&P 500

back to Table 11.5 and you will see that Intel’s standard deviation was 26.6% annu- ally, versus only 18.9% for the S&P 500. The G&I fund is highly diversified—it holds around 750 different stocks—so it has little specific risk and its dots cluster tightly around the trend line. Since its diversification is not complete (after all, the fund is attempting to beat the market, not precisely match it), its total volatility, 19.1%, still slightly exceeds the market’s but is considerably less than Intel’s; this is the benefit of diversification.

How did the G&I fund achieve a beta of almost exactly 1.0? By acquiring stocks with an average beta of 1.0. Remember, a portfolio beta equals the weighted- average beta of its component securities. The weights are the proportions invested in each security. If G&I were not a mutual fund (whose returns we can plot as in Figure 12.3) but a privately held portfolio, say a private pension fund, we could calculate its beta as the weighted-average beta of its holdings.

Figure 12.3 , panel b, shows the same sort of plot for Vanguard’s Index Trust 500 Portfolio mutual fund. Notice that this fund has a beta of 1.0 and only the tiniest residual of specific risk—the fitted line fits almost exactly because an index fund is designed to track the market as closely as possible. The managers of the fund do not attempt to pick good stocks but just work to achieve full diversification at very low cost. The index fund is fully diversified. Investors in this fund buy the market as a whole and don’t have to worry at all about specific risk.

By the way, knowing a mutual or pension fund’s beta will help you ask the right questions when a portfolio manager brags about “beating the market.” Suppose, for example, that in January 2014 you met the manager of a mutual fund that delivered a 35% rate of return in 2013, 3 percentage points above the 32% return on the S&P 500 in that year. Should you have congratulated the fund manager for her stock-picking prowess? It depends on the fund’s beta. Suppose the fund specialized in high-beta stocks with an average beta of 1.5. Then you should not have been impressed. An index fund constructed to have a beta of 1.5 would have earned about 32%  ×  1.5  =  48% in 2013, a great year for the stock market. So the mutual fund manager’s fund actually

(b)

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366 Part Three Risk

under performed by about 48  -  35  =  13 percentage points. 3 The mutual fund’s share- holders would have been better off in a high-beta index fund.

Of course, you cannot judge a mutual fund manager’s skill based on only 1 year’s performance. We simply point out that “beating the S&P” is child’s play for a high- beta portfolio in a bull market like 2013.

The Portfolio Beta Determines the Risk of a Diversified Portfolio You can also use beta to predict the total risk (standard deviation) of a diversified port- folio. Look back to Figure 11.9, which shows how the volatility of a portfolio return falls as more stocks are added and the portfolio becomes better diversified. The gain from diversification is rapid at first but slows down as specific risks are diversified away. With full diversification, only market risk remains.

OK, but how much market risk remains? It depends on the beta of the portfolio. Suppose you construct a diversified portfolio of stocks with betas of about .5, like Coca-Cola and ExxonMobil. The portfolio beta will also be .5. Most of the individual stocks’ specific risk would be diversified away. The market risk would remain, and the portfolio would end up half as variable as the market. If the standard deviation of the market is 20%, a fully diversified portfolio of stocks with betas of .5 has a standard deviation of .5  ×  20  =  10%. We show this outcome in Figure 12.4 . Suppose, on the other hand, you construct a fully diversified portfolio of stocks with betas of about 1.2, like Disney, Starbucks, and Boeing. In that case the portfolio standard deviation would be 1.2  ×  20  =  24%. 4

Of course, the average beta across all stocks must be 1.0. A fully diversified portfo- lio including all stocks will match the market and so have a beta of 1.0 and the same standard deviation as the market.

3  The predicted rate of return of 1.5  ×  32  =  48% is not quite right. We should have multiplied the beta of 1.5 by the risk premium earned on the market in 2013. The risk-free rate averaged about .5%, so the risk premium was 32  -  .5  =  31.5%. The predicted risk premium was therefore 1.5  ×  31.5  =  47.25%. The predicted return equals the interest rate plus the predicted risk premium, or .5  +  47.25  =  47.75%. Thus the underperformance was 47.75  -  35  =  12.75%. Our initial calculation was only .25% too high, but the error would be larger with a higher interest rate.

4  It can be difficult to achieve full diversification when constructing portfolios using stocks with very high or low betas. For example, a portfolio constructed from stocks with betas above 2, like Dow Chemical and U.S. Steel, could be concentrated in cyclical industries, and thus exposed to some undiversified industry risk in addi- tion to market risk.

FIGURE 12.4 The risk of a fully diversified portfolio depends on the portfolio beta. In this example, the portfolio beta is .5 and the standard deviation of the portfolio “bottoms out” at 10%, half the market standard deviation of 20%.

10%

20%

P o

rt fo

lio s

ta n

d ar

d d

ev ia

ti o

n

Market portfolio

Fully diversified portfolio with beta = .5

Diversification

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Chapter 12 Risk, Return, and Capital Budgeting 367

A wise and diversified investor does not judge the risk of individual stocks by their stand-alone volatility, but by their contributions to portfolio risk. By now you can see that the contributions depend on the stocks’ betas. In the next sections we will see how that observation leads to a model of risk and return and a way to estimate the opportu- nity cost of capital.

12.3 Risk and Return In Chapter 11 we looked at past returns on selected investments. The least risky invest- ment was U.S. Treasury bills. Since the return on Treasury bills is fixed, it is unaf- fected by what happens to the market. Thus the beta of Treasury bills is zero. The most risky investment that we considered was the market portfolio of common stocks. This has average market risk: Its beta is 1.0.

Wise investors don’t run risks just for fun. They are playing with real money and therefore require a higher average return from the market portfolio than from Treasury bills. The difference between the return on the market and the interest rate on bills is termed the market risk premium. Over the past century the average market risk premium has been 7.6% a year. Of course, there is plenty of scope for argument as to whether the past century constitutes a typical period, but we will just assume here that the normal risk premium is a nice round 7%; that is, 7% is the additional return that an investor could reasonably expect from investing in the stock market rather than Treasury bills.

In Figure 12.5 a we have plotted the risk and expected return from Treasury bills and the market portfolio. You can see that Treasury bills have a beta of zero and a risk- free return; we’ll assume that return is 3%. The market portfolio has a beta of 1.0, an expected risk premium of 7%, and an expected return of 3  +  7  =  10%.

Now, given these two benchmarks, what expected rate of return should an investor require from a portfolio that is equally divided between Treasury bills and the mar- ket? Halfway between, of course. Thus in Figure 12.5 b we have drawn a straight line through the Treasury bill return and the expected market return. The portfolio (marked with an X ) would have a beta of .5 and an expected return of 6.5%. This includes a risk premium of 3.5% above the Treasury bill return of 3%.

You can calculate this return as follows: Start with the difference between the expected market return r m and the Treasury bill rate r f . This is the expected market risk premium:

Market risk premium = rm - rf = 10% - 3% = 7%

Beta measures risk relative to the market. Therefore, the portfolio’s expected risk premium equals its beta times the market risk premium:

Risk premium = r - rf = b(rm - rf)

For example, with a beta of .5 and a market risk premium of 7%,

Risk premium = b(rm - rf) = .5 × 7% = 3.5%

market risk premium Risk premium of market portfolio. Difference between market return and return on risk-free Treasury bills.

Suppose you construct a portfolio from only 15 stocks with an average beta of 1.2. The market standard deviation is 20%. What can you say about the portfolio’s standard deviation? Is it 24%? Less? More? Why?

Self-Test 12.3

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368 Part Three Risk

The total expected rate of return is the sum of the risk-free rate and the risk premium:

Expected return = risk-free rate + risk premium (12.2)

r = rf + b(rm - rf)

= 3% + 3.5% = 6.5%

You could have calculated the expected rate of return in one step from this formula:

Expected return = r = rf + b(rm - rf)

= 3% + (.5 × 7%) = 6.5%

This basic relationship should hold not only for our portfolios of Treasury bills and the market but for any asset. This conclusion is known as the capital asset pricing model, or CAPM. The CAPM has a simple interpretation: The expected rates of return demanded by investors depend on two things: (1) compensation for the time value of money (the risk-free rate, r f ) and (2) a risk premium, which depends on beta and the market risk premium.

Note that the expected rate of return on an asset with β   =  1.0 is just the market return. With a risk-free rate of 3% and market risk premium of 7%,

r = rf + b(rm - rf)

= 3% + (1 × 7%) = 10%

capital asset pricing model (CAPM) Theory of the relationship between risk and return which states that the expected risk premium on any security equals its beta times the market risk premium.

FIGURE 12.5 (a) Here we begin the plot of expected rate of return against beta. The first benchmarks are Treasury bills (beta  =  0) and the market portfolio (beta  =  1.0). We assume a Treasury bill rate of 3% and a market return of 10%. The market risk premium is 10  -  3  =  7%. (b) A portfolio split evenly between Treasury bills and the market will have beta  =  .5 and an expected return of 6.5% (point X ). A portfolio invested 20% in the market and 80% in Treasury bills has beta  =  .2 and an expected rate of return of 4.4% (point Y ). Note that the expected rate of return on any portfolio mixing Treasury bills and the market lies on a straight line. The risk premium is proportional to the portfolio beta.

E xp

ec te

d r

et u

rn (

% )

3

Market portfolio

0

7% = market risk premium

Treasury bills

Beta

(a)

10

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% )

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3

X

Market portfolio

0

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10

.5.2 1.0

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(b)

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Chapter 12 Risk, Return, and Capital Budgeting 369

Why the CAPM Makes Sense The CAPM assumes that the stock market is composed of well-diversified investors— investors operating at the bottom of the portfolio risk curves illustrated in Figures 11.9 and 12.4 . The risks borne by such investors depend on their portfolio betas. This is real- istic in a market dominated by large institutions where even small fry can diversify at very low cost. The following example shows why this view of risk leads to the CAPM.

What are the risk premium and expected rate of return on a stock with β   =  1.5? Assume a Treasury bill rate of 6% and a market risk premium of 7%.

Self-Test 12.4

Example 12.3 How Would You Invest $1 Million? Have you ever daydreamed about receiving a $1 million check, no strings attached, from an unknown benefactor? Let’s daydream about how you would invest it.

We have two good candidates: Treasury bills, which offer an absolutely safe return, and the market portfolio (possibly via the Vanguard index fund discussed earlier in this chapter). The market has generated higher returns on average, but those returns have fluctuated a lot. (Look back to Figure 11.4.) So your investment policy is going to depend on your tolerance for risk.

If you’re a wimp, you may invest only a small part of your money in the market portfolio and lend the remainder to the government by buying Treasury bills. Sup- pose that you invest 20% of your money in the market portfolio and put the other 80% in U.S. Treasury bills. Then the beta of your portfolio will be a mixture of the beta of the market ( β market   =  1.0) and the beta of the T-bills ( β T-bills   =  0):

Beta of portfolio = ¢proportion in market

×

beta of market

≤ + ¢proportion in T-bills

×

beta of T-bills

≤ b = (.2 × bmarket) + (.8 × bT-bills)

= (.2 × 1.0) + (.8 × 0)

= .20

The fraction of funds that you invest in the market also affects your expected return. If you invest your entire million in the market portfolio, you earn the full mar- ket risk premium. But if you invest only 20% of your money in the market, your port- folio beta is .20 and you earn only 20% of the market risk premium.

Expected

risk premium on portfolio

= ¢proportion in market

×

market risk premium

≤ + ¢proportion in T-bills

×

risk premium on T-bills

≤ = (.2 × expected market risk premium) + (.8 × 0)

= .2 × expected market risk premium

= .2 × 7 = 1.4%

Notice that the portfolio risk premium equals the product of beta times the market risk premium.

The expected return on your portfolio is equal to the risk-free interest rate plus the expected risk premium:

Expected portfolio return = rportfolio = 3 + 1.4 = 4.4%

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370 Part Three Risk

How would you construct a portfolio with a beta of .25? What is the expected return to this strategy? Assume Treasury bills yield 6% and the market risk premium is 7%.

Self-Test 12.5

The expected return on this passive portfolio therefore gives a benchmark for the fair expected return on any other investment or asset with the same risk (beta). In Figure 12.5 b we show the beta and expected return on this portfolio by the letter Y.

The Security Market Line Example 12.3 illustrates a general point: By investing some proportion of your money in the market portfolio and lending (or borrowing) 5 the balance, you can obtain any combination of risk and expected return along the sloping line in Figure 12.6 . This line is known as the security market line.

The security market line describes the expected returns and risks from split- ting your overall portfolio between risk-free securities and the market. It also sets a standard for other investments. Investors will be willing to hold other securities only if they offer equally good prospects. Thus the required risk premium for any investment is given by the security market line:

Risk premium on investment = beta × expected market risk premium

5  Notice that the security market line extends above the market return at β   =  1.0. How would you generate a portfolio with, say, β   =  2.0? It’s easy, but it’s risky. Suppose you borrow $1 million and invest the loan plus $1 million in the market portfolio. That gives you $2 million invested and a $1 million liability. Your portfolio now has a beta of 2.0:

Beta of portfolio = (proportion in market × beta of market) + (proportion in loan × beta of loan)

b = (2 × bmarket) + (-1 × bloan)

= (2 × 1.0) + (-1 × 0) = 2 Notice that the proportion in the loan is negative because you are borrowing, not lending money.

By the way, borrowing from a bank or stockbroker would not be difficult or unduly expensive as long as you put up your $2 million stock portfolio as security for the loan.

Can you calculate the risk premium and the expected rate of return on this borrow-and-invest strategy?

security market line Relationship between expected return and beta.

FIGURE 12.6 The security market line shows how expected rate of return depends on beta. According to the capital asset pricing model, expected rates of return for all securities and all portfolios lie on this line.

E xp

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rf

0

Security market line

Beta

rm

1.0

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Chapter 12 Risk, Return, and Capital Budgeting 371

Look back to Figure 12.5 b, which suggests that an individual common stock with b   =   .5 must offer a 6.5% expected rate of return when Treasury bills yield 3% and the market risk premium is 7%. You can now see why this has to be so. If that stock offered a lower rate of return, nobody would buy even a little of it—they could get 6.5% just by investing 50–50 in Treasury bills and the market. And if nobody wants to hold the stock, its price has to drop. A lower price means a better buy for investors, that is, a higher rate of return. The price will fall until the stock’s expected rate of return is pushed up to 6.5%. At that price and expected return the CAPM holds.

If, on the other hand, our stock offered more than 6.5%, diversified investors would want to buy more of it. That would push the price up and the expected return down to the levels predicted by the CAPM.

This reasoning holds for stocks with any beta. That’s why the CAPM makes sense, and why the expected risk premium on an investment should be proportional to its beta.

Suppose you invest $400,000 in Treasury bills and $600,000 in the market portfolio. What is the return on your portfolio if bills yield 6% and the expected return on the market is 13%? What does the return on this portfolio imply for the expected return on individual stocks with betas of .6?

Self-Test 12.6

Using the CAPM to Estimate Expected Returns We can use the CAPM to calculate expected rates of return on individual stocks or other securities. We need three numbers: the risk-free interest rate, the expected mar- ket risk premium, and beta. Suppose the interest rate on Treasury bills is 3% and the expected market risk premium is 7%. We take betas from Table 12.1 . Table 12.2 puts these numbers together in the CAPM to get expected rates of return. Take Coca-Cola as an example:

Expected return on Coca-Cola = risk-free interest rate + beta × market risk premium r = rf + b × (rm - rf) = 3% + .53 × 7% = 6.7%

Dow Chemical and U.S. Steel had the highest betas in our sample of companies and the highest expected returns of about 19%. Ford was close behind, with an expected rate of return of about 18%. These high betas make sense for cyclical businesses com- ing through the recession of 2007–2009. For example, Ford was the only major U.S. auto manufacturer to escape bankruptcy. At the other extreme, Consolidated Edison, a regulated public utility, had a very low beta and a low CAPM expected rate of return.

The calculations in Table 12.2 are easy, but don’t assume that using the CAPM is a purely mechanical exercise. First, betas are estimates, not exact measurements. Coca- Cola’s beta of .53 is a best statistical estimate, but the true beta could be .4 or .6. If you want to round Coca-Cola’s beta to .50, that’s fine with us. Second, very high or very low betas tend not to repeat in the future. For example, we think that Ford’s beta will come down now that the company has regained financial health and profitability. Third, it’s difficult to pin down the expected future market risk premium. Fourth, the CAPM is widely used in practice, but it is not the last word in risk and return in the stock market, as we will now see.

How Well Does the CAPM Work? The basic idea behind the capital asset pricing model is that investors expect a reward for both waiting and worrying. The greater the worry, the greater the expected return. If you invest in a risk-free Treasury bill, you just receive the rate of interest. That’s the

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372 Part Three Risk

reward for waiting. When you invest in risky stocks, you can expect an extra return or risk premium for worrying. The capital asset pricing model states that this risk pre- mium is equal to the stock’s beta times the market risk premium.

How well does the CAPM work in practice? For example, do the returns on stocks with betas of .5 on average lie halfway between the return on the market portfolio and the interest rate on Treasury bills? Unfortunately, the evidence is conflicting. Let’s look back to the actual returns earned by investors in low-beta stocks and in high- beta stocks.

Imagine that in 1931 ten investors gathered together in a Wall Street bar and agreed to establish investment trust funds for their children. Each investor decided to follow a different strategy. Investor 1 opted to buy the 10% of the New York Stock Exchange stocks with the lowest estimated betas; investor 2 chose the 10% with the next-lowest betas; and so on, up to investor 10, who proposed to buy the stocks with the highest betas. They also planned that at the end of each year they would reestimate the betas of all NYSE stocks and reconstitute their portfolios. And so they parted with much cordiality and good wishes.

In time the 10 investors all passed away, but their children agreed to meet in early 2011 in the same bar to compare the performance of their portfolios. Figure 12.7 shows how they fared. Investor 1’s portfolio turned out to be much less risky than the market; its beta was only .50. However, investor 1 also realized the lowest return, 10.0% above the risk-free rate of interest. At the other extreme, the beta of investor 10’s portfolio was 1.54, about three times that of investor 1’s portfolio. But investor 10 was rewarded with the highest return, averaging 16.1% a year above the interest rate. So over this 80-year period returns did indeed increase with beta.

As you can see from Figure 12.7 , the market portfolio over the same 80-year period provided an average return of 12.3% above the interest rate 6 and (of course) had a beta

Beta Expected Return, %

Dow Chemical 2.34 19.4 U.S. Steel 2.34 19.4 Ford 2.18 18.3 General Electric 1.66 14.6 Disney 1.22 11.5 Starbucks 1.21 11.5 Boeing 1.20 11.4 Union Pacifi c 1.14 11.0 Intel 1.01 10.1 Google 0.94 9.6 Amazon 0.82 8.7 Pfi zer 0.74 8.2 IBM 0.68 7.8 Coca-Cola 0.53 6.7 ExxonMobil 0.48 6.4 McDonald’s 0.37 5.6 Walmart 0.35 5.4 Newmont Mining 0.31 5.2 Consolidated Edison 0.17 4.2

TABLE 12.2 Expected rates of return for selected companies

6  In Figure 12.7 the stocks in the “market portfolio” are weighted equally. Since the stocks of small firms have provided higher average returns than those of large firms, the risk premium on an equally weighted index is higher than that on a value-weighted index. This is one reason for the difference between the 12.3% market risk premium in Figure 12.7 and the 7.6% premium reported in Table 11.1.

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Chapter 12 Risk, Return, and Capital Budgeting 373

FIGURE 12.7 The capital asset pricing model states that the expected risk premium from any investment should lie on the security market line. The dots show the actual average risk premium from portfolios with different betas. The high-beta portfolios generated higher returns, just as predicted by the CAPM. But the high-beta portfolios plotted below the market line and the low-beta portfolios plotted above. A line fitted to the 10 portfolio returns would be “flatter” than the security market line.

Portfolio beta

Investor 1

Investor 10

Market portfolio

Security market line

2 3

4 5 6

7

8 9

0

2

4

6

8

10

12

14

16

18

A ve

ra g

e ri

sk p

re m

iu m

, 1 93

1– 20

10 (

% )

0 .4.2 .6 .8 1.0 1.2 1.4 1.8 21.6

MM

Source: This is an update of calculations that originally appeared in F. Black, “Beta and Return,” Journal of Portfolio Management 20 (Fall 1993), pp. 8–18. We are grateful to Adam Kolasinski for recalculating and extending the plots.

of 1.0. The CAPM predicts that the risk premium should increase in proportion to beta, so the returns of each portfolio should lie on the upward-sloping security market line in Figure 12.7 . Since the market provided a risk premium of 12.3%, investor 1’s portfolio, with a beta of .50, should have provided a risk premium of 6.1% and inves- tor 10’s portfolio, with a beta of 1.54, should have given a premium of 18.9%. You can see that, while high-beta stocks performed better than low-beta stocks, the difference was not as great as the CAPM predicts.

Figure 12.7 provides broad support for the CAPM, though it suggests that the line relating return to beta has been too flat. But recent years have been less kind to the CAPM. For example, if the 10 friends had invested their cash in 1966 rather than 1931, there would have been very little relation between their portfolio returns and beta. 7 Does this imply that there has been a fundamental change in the relation between risk and return in the last 40 years, or did high-beta stocks just happen to perform worse during these years than investors expected? It is hard to be sure.

There is little doubt that the CAPM is too simple to capture everything that is going on in the market. For example, look at Figure 12.8 . The orange line shows the cumula- tive difference between the returns on small-firm stocks and large-firm stocks. If you had bought the shares with the smallest market capitalizations and sold those with the largest capitalizations, this is how your wealth would have changed. You can see that small-cap stocks did not always do well, but over the long haul their owners have made substantially higher returns. Since the end of 1926 the average annual differ- ence between the returns on the two groups of stocks has been 3.8%. Now look at the blue line in Figure 12.8 , which shows the cumulative difference between the returns on value stocks and growth stocks. Value stocks here are defined as those with high ratios of book value to market value. Growth stocks are those with low ratios of book to market. Notice that value stocks have provided a higher long-run return than growth stocks. Since 1926 the average annual difference between returns on value and growth stocks has been 4.9%.

The superior performance of small-firm stocks and value stocks does not fit well with the CAPM, which predicts that beta is the only reason that expected returns differ. If investors expected the returns to depend on firm size or book-to-market ratios, then the simple version of the capital asset pricing model cannot be the whole truth.

What’s going on here? It is hard to say. Defenders of the capital asset pricing model emphasize that it is concerned with expected returns, whereas we can observe

7  During this later period, the returns to the first seven investors increased in line with beta. However, the highest-beta portfolios performed poorly.

The momentum factor

BEYOND THE PAGE

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374 Part Three Risk

only actual returns. Actual returns reflect expectations, but they also embody lots of “noise”—the steady flow of surprises that conceal whether on average investors have received the returns that they expected. Thus, when we observe that in the past small- firm stocks and value stocks have provided superior performance, we can’t be sure whether this was simply a coincidence or whether investors have required a higher expected return to hold these stocks.

Such debates have prompted headlines like “Is Beta Dead?” in the business press. It is not the first time that beta has been declared dead, but the CAPM remains the lead- ing model for estimating required returns. Only strong theories can have more than one funeral.

The CAPM is not the only model of risk and return. It has several brothers and sis- ters as well as second cousins. However, the CAPM captures in a simple way two fundamental ideas. First, almost everyone agrees that investors require some extra return for taking on risk. Second, investors appear to be concerned principally with the market risk that they cannot eliminate by diversification. That is why nearly three- quarters of financial managers use the capital asset pricing model to estimate the cost of capital. 8

12.4 The CAPM and the Opportunity Cost of Capital The discount rate for valuing a proposed capital investment project should be the opportunity cost of capital, defined as the expected rate of return that the company’s shareholders could achieve by investing on their own. But the CAPM tells us (con- firming common sense) that expected rates of return depend on risk, that is, on beta. Therefore the opportunity cost of capital for a proposed project should depend on the project’s beta. The project cost of capital is therefore its minimum acceptable expected rate of return, given its risk.

8  See J. R. Graham and C. R. Harvey, “The Theory and Practice of Corporate Finance: Evidence from the Field,” Journal of Financial Economics 61 (2001), pp. 187–243. A number of managers surveyed reported using more than one method to estimate the cost of capital. Seventy-three percent used the CAPM, while 39% stated they used the average historical stock return, and 34% used the CAPM with additional risk factors.

project cost of capital Minimum acceptable expected rate of return on a project given its risk.

FIGURE 12.8 The orange line shows the cumulative difference between the returns on small-firm and large-firm stocks from 1926 to 2013. The blue line shows the cumulative difference between the returns on high- book-to-market-value stocks and low-book-to-market-value stocks.

0.1

1

10

100

D o

lla rs

( lo

g s

ca le

)

Year

Small minus big

High minus low book-to-market

20 10

20 13

20 06

20 02

19 98

19 94

19 90

19 86

19 82

19 78

19 74

19 70

19 66

19 62

19 58

19 54

19 50

19 46

19 42

19 38

19 34

19 30

19 26

Source: mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html . Used by permission of Kenneth R. French.

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Chapter 12 Risk, Return, and Capital Budgeting 375

Example 12.4 Estimating the Opportunity Cost of Capital for a Project Suppose that Coke is contemplating an investment of $10 million to expand a warehouse. It has forecast cash flows and calculated an internal rate of return (IRR) of 6%. We assume, as in Table 12.2 , that the risk-free rate is 3% and the market risk premium is 7%. Should Coke invest?

To answer this question, you need to know the opportunity cost of capital r, defined as the expected rate of return that Coke’s shareholders could achieve if the $10 million were paid out to them to invest on their own. The CAPM says that the expected rate of return depends on the project beta.

Suppose that the project’s cash flows are an absolutely sure thing. Then beta  =  0 and the project cost of capital is

r = rf + b × (rm - rf) = 3% + 0 × 7% = 3%

If the project offers a 6% return when the opportunity cost of capital for the project is 3%, Coke should obviously go ahead. 9

What about the 6.7% rate of return for Coke in Table 12.2 ? It’s irrelevant if we are confident that the project is risk-free. Coke’s stock offers more than the risk-free rate because it is risky, with a beta of .53. Coke’s stockholders would all vote for Coke to invest on their behalf in a risk-free project earning 6% because the stockholders could get only 3% investing risk-free on their own. They can get 6.7% by buying additional Coke shares, but that is a separate decision.

Surefire projects rarely occur outside finance textbooks. So let’s think about the opportunity cost of capital if the project has the same risk as the market portfolio. In this case beta is 1.0 and the cost of capital is the expected rate of return on the market.

r = rf + b × (rm - rf) = 3% + 1.0 × 7% = 10%

Now that the project beta is 1.0, the project is no longer worth doing. The stockhold- ers would vote against the project at a 6% return because they could earn 10% at the same level of risk (same beta) by investing on their own in the market portfolio.

When its beta is 1.0, the project is no longer attractive because, as Figure 12.9 shows, its expected rate of return now lies below the security market line. The proj- ect offers a lower rate of return than investors can expect on equally risky invest- ments. Therefore it is negative-NPV.

9  In Chapter 8 we described some special cases where you should prefer projects that offer a lower internal rate of return than the cost of capital. We assume here that your project is a “normal” one and that you prefer high IRRs to low ones.

FIGURE 12.9 The expected return of this project is less than the expected return one could earn on stock market investments with the same market risk (beta). Therefore, the project’s expected return lies below the security market line and the project should be rejected.

E xp

ec te

d r

et u

rn (

% )

3

6 Project return = 6%

Project beta =1

0 Beta

10

Security market line

1.0

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376 Part Three Risk

If the CAPM holds, the security market line defines the opportunity cost of capital. If a project’s expected rate of return plots above the security market line, then it offers a higher expected rate of return than investors could get on their own at the same beta.

Walmart is planning an Internet subsidiary to compete head-to-head with Amazon. It argues that it can compete aggressively in Internet retail- ing because it has a low beta and its shareholders will be content with an expected rate of return of only 5.7%. Is the argument correct?

Self-Test 12.7

The Company Cost of Capital The cost of capital depends on the use to which the capital is put. It depends on the risk of the project—not on the risk of the company investing in the project. If a company has a low-risk project, it should discount project cash flows at a correspondingly low rate. If it has a high-risk project, it should discount at a correspondingly high rate.

That is the principle. But you can imagine the chaos in practice if a large company had to set a different discount rate for every one of thousands of investment projects. Therefore most companies estimate a company cost of capital, which depends on the average risk of its investments. Many companies use the company cost of capital for all capital-investment projects, which is fine provided that all projects are close enough to average risk. Others set the company cost of capital as a benchmark and adjust the discount rate up or down for riskier or safer projects.

Some companies set two or more discount rates for different types of projects. For example, several electric utilities have both regulated and “merchant” businesses. The regulated businesses are low-risk because they are not allowed to earn much more than a set rate of return. Their profit upside is limited, but so is the downside because they can pass most costs through to their customers and can petition to increase prices if their profits sag. (Consolidated Edison, which has the lowest beta in Table 12.2 , is mostly a regulated business.) Merchant electricity production, on the other hand, is unregulated and must sell power at fluctuating market prices. Merchant producers can make or lose a lot of money, depending on uncertain demand and costs of production. Companies with both regulated and merchant businesses typically set two costs of capital, one for regulated investments and one for merchant investments.

Many U.S. corporations use the CAPM to compute their company costs of capital. Expected rates of return like those computed for Table 12.2 are only the first step, however. This is because they are costs of equity, that is, expected rates of return on common stock. But most companies use debt as well as equity financing. They calcu- late the company cost of capital as a weighted average of the cost of debt and the cost of equity. We explain how this is done in the next chapter.

What Determines Project Risk? We have seen that the company cost of capital is the correct discount rate for projects that have the same risk as the company’s existing business but not for those projects that are safer or riskier than the company’s average. How do we know whether a proj- ect is unusually risky? Estimating project risk is never going to be an exact science, but here are two things to bear in mind.

First, we saw in Chapter 10 that operating leverage increases the risk of a project. When a large fraction of your costs is fixed, any change in revenues can have a dramatic effect on earnings. Therefore, projects that involve high fixed costs tend to have higher betas.

company cost of capital Opportunity cost of capital for investment in the firm as a whole. The company cost of capital is the appropriate discount rate for an average-risk investment project undertaken by the firm.

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Chapter 12 Risk, Return, and Capital Budgeting 377

Second, many people intuitively associate risk with the variability of earnings. But much of this variability reflects diversifiable risk. Lone prospectors in search of gold look forward to extremely uncertain future earnings, but whether they strike it rich is not likely to depend on the performance of the rest of the economy. These investments (like Newmont Mining) have a high standard deviation but a low beta.

What matters is the strength of the relationship between the firm’s earnings and the aggregate earnings of all firms. Cyclical businesses, whose revenues and earnings are strongly dependent on the state of the economy, tend to have high betas and a high cost of capital. By contrast, businesses that produce essentials, such as food, beer, and cosmetics, are less affected by the state of the economy. They tend to have low betas and a low cost of capital.

Don’t Add Fudge Factors to Discount Rates Risk to an investor arises because an investment adds to the spread of possible portfo- lio returns. To a diversified investor, risk is predominantly market risk. But in everyday usage risk simply means “bad outcome.” People think of the “risks” of a project as the things that can go wrong. For example,

• A geologist looking for oil worries about the risk of a dry hole. • A pharmaceutical manufacturer worries about the risk that a new drug which

reverses balding may not be approved by the Food and Drug Administration. • The owner of a hotel in a politically unstable part of the world worries about the

political risk of expropriation.

Managers sometimes add fudge factors to discount rates to account for worries such as these.

This sort of adjustment makes us nervous. First, the bad outcomes we cited appear to reflect diversifiable risks that would not affect the expected rate of return demanded by investors. Second, the need for an adjustment in the discount rate usually arises because managers fail to give bad outcomes their due weight in cash-flow forecasts. They then try to offset that mistake by adding a fudge factor to the discount rate. For example, if a manager is worried about the possibility of a bad outcome such as a dry hole in oil exploration, he or she may reduce the value of the project by using a higher discount rate. That’s not the way to do it. Instead, the possibility of the dry hole should be included in the calculation of the expected cash flows to be derived from the well. Suppose that there is a 50% chance of a dry hole and a 50% chance that the well will produce oil worth $20 million. Then the expected cash flow is not $20 million but (.5  ×  0)  +  (.5  ×  20)  =  $10 million. You should discount the $10 million expected cash flow at the opportunity cost of capital; it does not make sense to discount the $20  million using a fudged discount rate.

Expected cash-flow forecasts should already reflect the probabilities of all possible outcomes, good and bad. If the cash-flow forecasts are prepared prop- erly, the discount rate should reflect only the market risk of the project. It should not be fudged to offset errors or biases in the cash-flow forecast.

SUMMARY The contribution of a security to the risk of a diversified portfolio depends on its market risk. But not all securities are equally affected by fluctuations in the market. The sensitivity of a stock to market movements is known as beta. Stocks with a beta greater than 1.0 are particularly sensitive to market fluctuations. Those with a beta of less than 1.0 are not so sensitive to such movements. The average beta of all stocks is 1.0.

How can you measure and interpret the market risk, or beta, of a security? ( LO12-1 )

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378 Part Three Risk

The extra return that investors require for taking risk is known as the risk premium. The market risk premium —that is, the risk premium on the market portfolio —averaged 7.6% between 1900 and 2013. The capital asset pricing model states that the expected risk premium of an investment should be proportional to both its beta and the market risk premium. The expected rate of return from any investment is equal to the risk-free interest rate plus the risk premium, so the CAPM boils down to

r = rf + b(rm - rf)

The security market line is the graphical representation of the CAPM equation. The secu- rity market line relates the expected return investors demand of a security to its beta.

The opportunity cost of capital is the return that investors give up by investing in the proj- ect rather than in securities of equivalent risk. The CAPM implies that the opportunity cost of capital depends on the project’s beta. The company cost of capital is the expected rate of return demanded by investors in a company. It depends on the average risk of the com- pany’s assets and operations.

The opportunity cost of capital is determined by the use to which the capital is put. Therefore, required rates of return depend on the risk of the project, not on the risk of the firm’s existing business. The project cost of capital is the minimum acceptable expected rate of return on a project given its risk.

Your cash-flow forecasts should already factor in the chances of pleasant and unpleas- ant surprises. Potential bad outcomes should be reflected in the discount rate only to the extent that they affect beta.

What is the relationship between the market risk of a security and the rate of return that investors demand of that security? ( LO12-2 )

What determines the opportunity cost of capital for a project? ( LO12-3 )

L I S T I N G O F E Q UAT I O N S

12.1 Beta of portfolio = (fraction of portfolio in first stock × beta of first stock)

+ (fraction of portfolio in second stock × beta of second stock) 12.2 Expected return = risk-free rate + risk premium

r = rf + b(rm - rf)

QUESTIONS AND PROBLEMS 1. Diversifiable Risk. In light of what you’ve learned about market versus diversifiable (specific)

risks, explain why an insurance company has no problem in selling life insurance to individu- als but is reluctant to issue policies insuring against flood damage to residents of coastal areas. Why don’t the insurance companies simply charge coastal residents a premium that reflects the actuarial probability of damage from hurricanes and other storms? (LO12-1)

2. Specific versus Market Risk. Figure 12.10 plots monthly rates of return from 2009 to 2013 for the Snake Oil mutual fund. Was this fund fully diversified? Explain. (LO12-1)

3. Using Beta. Investors expect the market rate of return this year to be 14%. A stock with a beta of .8 has an expected rate of return of 12%. If the market return this year turns out to be 10%, what is your best guess as to the rate of return on the stock? (LO12-1)

4. Specific versus Market Risk. Figure 12.11 shows plots of monthly rates of return on three stocks versus the stock market index. (The plots are similar to those in Figure 12.2 but are taken from an earlier period.) The beta and standard deviation of each stock is given beside its plot. (LO12-1)

a. Which stock is safest for a diversified investor? b. Which stock is safest for an undiversified investor who puts all her funds in one of these stocks? c. Consider a portfolio with equal investments in each stock. What would this portfolio’s beta

have been?

finance

®

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Chapter 12 Risk, Return, and Capital Budgeting 379

FIGURE 12.10 Monthly rates of return for the Snake Oil mutual fund and the Standard & Poor’s Composite Index

FIGURE 12.11 Monthly rates of return for (a) Ford, (b) Disney, and (c) Newmont Mining, plus the market portfolio for the five years ending April 2010

S n

ak e

O il

re tu

rn (

% )

-20 -10 10 20

-20

20

-15

-10

-5

15

10

5

Market return (%)

3020100-10-20-30

-30

-20

-10

0

10

20

Beta = 2.53 Standard deviation = 77.4%

Market return (%)

F o

rd r

et u

rn (

% )

30

(a)

3020100-10-20-30

-30

-20

-10

0

10

20

Beta = 1.16 Standard deviation = 23.7%

Market return (%)

D is

n ey

r et

u rn

( %

)

30

(b)

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380 Part Three Risk

6. Portfolio Risk and Return. Suppose that the S&P 500, with a beta of 1.0, has an expected return of 10% and T-bills provide a risk-free return of 4%. (LO12-1)

a. How would you construct a portfolio from these two assets with an expected return of 8%? Specifically, what will be the weights in the S&P 500 versus T-bills?

b. How would you construct a portfolio from these two assets with a beta of .4? c. Find the risk premiums of the portfolios in (a) and (b), and show that they are proportional to

their betas.

7. Risk and Return. True or false? Explain or qualify as necessary. (LO12-2)

a. Investors demand higher expected rates of return on stocks with more variable rates of return. b. The capital asset pricing model predicts that a security with a beta of zero will provide an

expected return of zero. c. An investor who puts $10,000 in Treasury bills and $20,000 in the market portfolio will have

a portfolio beta of 2.0. d. Investors demand higher expected rates of return from stocks with returns that are highly

exposed to macroeconomic changes. e. Investors demand higher expected rates of return from stocks with returns that are very sen-

sitive to fluctuations in the stock market.

d. Consider a well-diversified portfolio made up of stocks with the same beta as Ford. What are the beta and standard deviation of this portfolio’s return? The standard deviation of the market portfolio’s return is 20%.

e. What is the expected rate of return on each stock? Use the capital asset pricing model with a market risk premium of 8%. The risk-free rate of interest is 4%.

5. Calculating Beta. Following are several months’ rates of return for Tumblehome Canoe Company. Prepare a plot like Figure 12.1 . What is Tumblehome’s beta? (LO12-1)

3020100-10-20-30

-30

-20

-10

0

10

20

Beta = .59 Standard deviation = 38.5%

Market return (%)

N ew

m o

n t

M in

in g

r et

u rn

( %

)

30

(c)

Month Market Return, % Tumblehome Return, %

1 0 +1 2 0 -1 3 -1 -2.5 4 -1 -0.5 5 +1 +2 6 +1 +1 7 +2 +4 8 +2 +2 9 -2 -2 10 -2 -4

FIGURE 12.11 (continued)

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Chapter 12 Risk, Return, and Capital Budgeting 381

8. Risk and Return. Suppose that the risk premium on stocks and other securities did in fact rise with total risk (that is, the variability of returns) rather than just market risk. Explain how inves- tors could exploit the situation to create portfolios with high expected rates of return but low levels of risk. (LO12-2)

9. CAPM and Valuation. You are considering acquiring a firm that you believe can generate expected cash flows of $10,000 a year forever. However, you recognize that those cash flows are uncertain. (LO12-2)

a. Suppose you believe that the beta of the firm is .4. How much is the firm worth if the risk- free rate is 4% and the expected rate of return on the market portfolio is 11%?

b. By how much will you overvalue the firm if its beta is actually .6?

10. CAPM and Expected Return. If the risk-free rate is 6% and the expected rate of return on the market portfolio is 13%, is a security with a beta of 1.25 and an expected rate of return of 16% overpriced or underpriced? (LO12-2)

11. Expected Returns. Consider the following two scenarios for the economy and the returns in each scenario for the market portfolio, an aggressive stock A, and a defensive stock D. (LO12-2)

Rate of Return

Scenario Market Aggressive Stock A Defensive Stock D

Bust -8% -10% -6% Boom 32 38 24

Company Beta

Cisco 1.22 Apple 1.44 Hershey .39 Coca-Cola .53

a. Find the beta of each stock. In what way is stock D defensive? b. If each scenario is equally likely, find the expected rate of return on the market portfolio and

on each stock. c. If the T-bill rate is 4%, what does the CAPM say about the fair expected rate of return on the

two stocks? d. Which stock seems to be a better buy on the basis of your answers to (a) through (c)?

12. CAPM and Valuation. A share of stock with a beta of .75 now sells for $50. Investors expect the stock to pay a year-end dividend of $2. The T-bill rate is 4%, and the market risk premium is 7%. If the stock is perceived to be fairly priced today, what must be investors’ expectation of the price of the stock at the end of the year? (LO12-2)

13. CAPM and Expected Return. A share of stock with a beta of .75 now sells for $50. Investors expect the stock to pay a year-end dividend of $2. The T-bill rate is 4%, and the market risk premium is 7%. (LO12-2)

a. Suppose investors believe the stock will sell for $52 at year-end. Is the stock a good or bad buy? What will investors do?

b. At what price will the stock reach an “equilibrium” at which it is perceived as fairly priced today?

14. CAPM and Expected Return. The following table shows betas for several companies. Calcu- late each stock’s expected rate of return using the CAPM. Assume the risk-free rate of interest is 5%. Use a 7% risk premium for the market portfolio. (LO12-2)

15. Portfolio Risk and Return. Suppose that the S&P 500, with a beta of 1.0, has an expected return of 13% and T-bills provide a risk-free return of 4%. (LO12-2)

a. What would be the expected return and beta of portfolios constructed from these two assets with weights in the S&P 500 of (i) 0; (ii) .25; (iii) .5; (iv) .75; (v) 1.0?

b. On the basis of your answer to (a), what is the trade-off between risk and return, that is, how does expected return vary with beta?

c. What does your answer to (b) have to do with the security market line relationship?

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382 Part Three Risk

16. Portfolio Risk and Return. According to the CAPM, would the expected rate of return on a security with a beta less than zero be more or less than the risk-free interest rate? Why would investors invest in such a security? (Hint: Look back to the auto and gold example in Chapter 11.) (LO12-1)

17. CAPM and Expected Return. Stock A has a beta of .5, and investors expect it to return 5%. Stock B has a beta of 1.5, and investors expect it to return 13%. Use the CAPM to find the mar- ket risk premium and the expected rate of return on the market. (LO12-2)

18. CAPM and Expected Return. If the expected rate of return on the market portfolio is 13% and T-bills yield 6%, what must be the beta of a stock that investors expect to return 10%? (LO12-2)

19. Risk and Return. True or false? Explain or qualify as necessary. (LO12-2)

a. The expected rate of return on an investment with a beta of 2.0 is twice as high as the expected rate of return of the market portfolio.

b. The contribution of a stock to the risk of a diversified portfolio depends on the market risk of the stock.

c. If a stock’s expected rate of return plots below the security market line, it is underpriced. d. A fully diversified portfolio with a beta of 2.0 is twice as volatile as the market portfolio. e. An undiversified portfolio with a beta of 2.0 is twice as volatile as the market portfolio.

20. CAPM and Expected Return. A mutual fund manager expects her portfolio to earn a rate of return of 11% this year. The beta of her portfolio is .8. If the rate of return available on risk-free assets is 4% and you expect the rate of return on the market portfolio to be 14%, what expected rate of return would you demand before you would be willing to invest in this mutual fund? Is this fund attractive? (LO12-2)

21. Required Rate of Return. Reconsider the mutual fund manager in Problem 20. How could you mix a stock index mutual fund with a risk-free position in Treasury bills (or a money market mutual fund) to create a portfolio with the same risk as the manager’s but with a higher expected rate of return? What is the rate of return on that portfolio? (LO12-2)

22. Required Rate of Return. In view of your answer to Problem 21, explain why a mutual fund must be able to provide an expected rate of return in excess of that predicted by the security market line for investors to consider the fund an attractive investment opportunity. (LO12-2)

23. CAPM. We Do Bankruptcies is a law firm that specializes in providing advice to firms in finan- cial distress. It prospers in recessions, when other firms are struggling. Consequently, its beta is negative, -.2. (LO12-2)

a. If the interest rate on Treasury bills is 5% and the expected return on the market portfolio is 15%, what is the expected return on the shares of the law firm according to the CAPM?

b. Suppose you invested 90% of your wealth in the market portfolio and the remainder of your wealth in the shares in the law firm. What would be the beta of your portfolio?

24. CAPM and Hurdle Rates. A project under consideration has an internal rate of return of 14% and a beta of .6. The risk-free rate is 4%, and the expected rate of return on the market portfolio is 14%. (LO12-3)

a. What is the required rate of return on the project? Should it be accepted? b. What is the required rate of return on the project if its beta is 1.6? Should the project be

accepted in this case? c. Why does your answer change?

25. CAPM and Cost of Capital. Suppose the Treasury bill rate is 4% and the market risk premium is 7%. (LO12-3)

a. What are the project costs of capital for new ventures with betas of .75 and 1.75?

b. Which of the following capital investments have positive NPVs?

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CHALLENGE PROBLEMS 30. Beta. Go to Connect and link to the material for Chapter 12, where you will find a spreadsheet

containing 5 years of monthly rates of return on Hershey (HSY), U.S. Steel (X), and the S&P 500. (LO12-1)

a. Calculate the beta of each firm. Use Excel’s SLOPE function, which fits a regression line through a scatter diagram of two series of numbers.

b. Does the relative magnitude of each beta make sense in terms of the business risk of the two firms? Explain.

31. Leverage and Portfolio Risk. Footnote 5 in the chapter asks you to consider a borrow-and- invest strategy in which you use $1 million of your own money and borrow another $1 million to invest $2 million in a market index fund. If the risk-free interest rate is 4% and the expected rate of return on the market index fund is 12%, what are the risk premium and expected rate of return on the borrow-and-invest strategy? Why is the risk of this strategy twice that of simply investing your $1 million in the market index fund? (LO12-2)

Templates can be found in Connect.

Chapter 12 Risk, Return, and Capital Budgeting 383

On the basis of the behavior of the firm’s stock, you believe that the beta of the firm is 1.4. Assuming that the rate of return available on risk-free investments is 4% and that the expected rate of return on the market portfolio is 12%, what is the net present value of the project? (LO12-3)

27. CAPM and Cost of Capital. Reconsider the project in Problem 26. What is the project IRR? What is the cost of capital for the project? Does the accept-reject decision using IRR agree with the decision using NPV? (LO12-3)

28. CAPM and Valuation. You are considering the purchase of real estate that will provide per- petual income that should average $50,000 per year. How much will you pay for the property if you believe its market risk is the same as the market portfolio’s? The T-bill rate is 5%, and the expected market return is 12.5%. (LO12-3)

29. Project Cost of Capital. Suppose Cisco is considering a new investment in the common stock of a chocolate company. What is the required rate of return for this venture? Explain why the expected return on Cisco stock is not the appropriate required return. Use the data in Prob- lem 14. (LO12-3)

26. CAPM and Valuation. You are a consultant to a firm evaluating an expansion of its current business. The cash-flow forecasts (in millions of dollars) for the project are as follows:

Project Beta Internal Rate of Return, %

P 1.0 14 Q 0 6 R 2.0 18 S 0.4 7 T 1.6 20

Years Cash Flow

0 -100 1–10 +  15

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384 Part Three Risk

SOLUTIONS TO SELF-TEST QUESTIONS 12.1 See Figure 12.12 . Anchovy Queen’s beta is 1.0.

12.2 Beta  =  1.11. This is a weighted average of the betas in Table 12.2 , with 20% weights on Ford, Starbucks, Union Pacific, and IBM, and 10% weights on Newmont Mining and Walmart.

12.3 More than 24%. Diversification across only 15 stocks is not enough to eliminate all specific risk.

12.4 r   =   r f   +   b ( r m   -   r f )  =  6  +  (1.5  ×  7)  =  16.5%

12.5 Put 25% of your money in the market portfolio and the rest in Treasury bills. The portfolio’s beta is .25 and its expected return is

rportfolio = (.75 × 6) + (.25 × 13) = 7.75%

The expected return also may be computed as

rf + b(rm - rf) = 6 + .25 × 7 = 7.75%

FIGURE 12.12 Each point shows the performance of Anchovy Queen stock when the market is up or down by 1%. On average, Anchovy Queen stock follows the market; it has a beta of 1.0.

A n

ch ov

y Q

u ee

n r

et u

rn (

% )

1.0-1.0 -0.8 -0.6 -0.4

-0.2

-2.0

2

1.5

1

.5

0

-0.5

-1.0

-1.5

0.80.60.40.2

Market return (%)

WEB EXERCISES 1. Betas and Expected Stock Returns. You can find estimates of stock betas by logging on

to finance.yahoo.com and looking at a company’s profile. Try comparing the stock betas of Google (GOOG), The Home Depot (HD), Du Pont (DD), Altria Group (MO), and Caterpillar (CAT). Once you have read Section 12.3, use the capital asset pricing model to estimate the expected return for each of these stocks. You will need a figure for the current Treasury bill rate. You can find this also on finance.yahoo.com by clicking on Bonds—Rates. Assume for your estimates a market risk premium of 7%.

2. Fund Betas. Log on to www.fidelity.com and look at the list of mutual funds that are managed by Fidelity. Some of these funds, such as the Aggressive Growth Fund, appear from their names to be high-risk. Others, such as the Balanced Fund, appear to be low-risk. Pick several apparent high- and low-risk funds and then check whether their betas really do match the fund’s name.

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Chapter 12 Risk, Return, and Capital Budgeting 385

SOLUTIONS TO SPREADSHEET QUESTIONS 1. We would expect beta to fall from the value obtained in the spreadsheet. Dow’s return in May

(when the market fell) is not as bad as originally assumed, and its return in January (when the market rose) is not as good as originally assumed. In both cases, Dow’s returns are less responsive to the market. In fact, beta falls from 1.47 to .80.

2. Dow’s beta is precisely the same as the original value. Increasing the assumed return in each month by a constant does not change the typical responsiveness of Dow to variation in the return of the market index.

3. If in the additional month of data Dow is down 8.6% while the market is up 4%, we would expect beta to fall. In this month, Dow’s stock moved in opposition to the market index. Add- ing this observation therefore reduces our estimate of Dow’s typical response to market move- ments. In fact, beta falls to 1.13.

12.6 r portfolio   =  (.4  ×  6)  +  (.6  ×  13)  =  10.2%. This portfolio’s beta is .6, since $600,000, which is 60% of the investment, is in the market portfolio. Investors in a stock with a beta of .6 would not buy it unless it also offered a rate of return of 10.2% and would rush to buy if it offered more. The stock price would adjust until the stock’s expected rate of return was 10.2%.

12.7 The argument is wrong. The beta of the Internet marketing project would be similar to Ama- zon’s beta, not Walmart’s. Use of Walmart’s low opportunity cost of capital would overvalue the project.

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386

The Weighted- Average Cost of Capital and Company Valuation

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

13-1 Calculate a firm’s capital structure.

13-2 Estimate the required rates of return on the securities issued by the firm.

13-3 Calculate the weighted-average cost of capital.

13-4 Understand when the weighted-average cost of capital is—or isn’t—the appropriate discount rate for a new project.

13-5 Use the weighted-average cost of capital to value a business given forecasts of its future cash flows.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

13 CHAPTE R

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387

P A

R T

TH R

E E

I n the previous chapter you learned how to use the capital asset pricing model to estimate the expected return on a company’s common stock. If the firm is financed wholly by common stock, then

the stockholders own all the firm’s assets and are

entitled to all the cash flows. In this case, the return

required by investors in the common stock equals the

company cost of capital.

Most companies, however, are financed by a mix-

ture of securities, including common stock, bonds,

preferred stock, or other securities. Each of these

securities has different risks, and therefore investors in

them look for different rates of return. In these circum-

stances, the company cost of capital is no longer the

same as the expected return on the common stock.

It depends on the expected return from all the securi-

ties that the company has issued.

The cost of capital also depends on taxes,

because interest payments made by a corporation

are tax-deductible expenses. Therefore, the company

cost of capital is usually calculated as a weighted

average of the after-tax cost of debt interest and the

“cost of equity,” that is, the expected rate of return on

the firm’s common stock. The weights are the frac-

tions of debt and equity in the firm’s capital structure.

Managers refer to the firm’s weighted-average cost of

capital, or WACC (rhymes with “quack”).

Managers use the weighted-average cost of capi-

tal to evaluate average-risk investment projects. “Aver-

age risk” means that the project’s risk matches the

risk of the firm’s existing assets and operations. This

chapter explains how the weighted-average cost of

capital is calculated in practice.

Managers calculating WACC can get bogged

down in formulas. We want you to understand why

WACC works, not just how to calculate it. Let’s start

with “Why?” We’ll listen in as a young financial man-

ager struggles to recall the rationale for project dis-

count rates.

Ri sk

Geothermal Corporation was founded to produce electricity from geothermal energy trapped under the earth. How should Geothermal determine its cost of capital?

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388 Part Three Risk

13.1 Geothermal’s Cost of Capital Jo Ann Cox, a recent graduate of a prestigious eastern business school, poured a third cup of black coffee and tried again to remember what she once knew about project hurdle rates. Why hadn’t she paid more attention in Finance 101? Why had she sold her finance text the day after passing the finance final?

Costas Thermopolis, her boss and CEO of Geothermal Corporation, had told her to prepare a financial evaluation of a proposed expansion of Geothermal’s produc- tion. She was to report at 9:00 Monday morning. Thermopolis, whose background was geophysics, not finance, not only expected a numerical analysis but also expected her to explain it to him.

Thermopolis had founded Geothermal in 1996 to produce electricity from geo- thermal energy trapped deep under Nevada. The company had pioneered this busi- ness and had obtained perpetual production rights for a large tract on favorable terms from the U.S. government. When the oil shock in 2007–2008 drove up energy prices worldwide, Geothermal became an exceptionally profitable company. It was currently reporting a rate of return on book assets of 25% per year.

Now, in 2014, energy prices were no longer high and production rights were no longer cheap. The proposed expansion would cost $30 million and should generate a perpetual after-tax cash flow of $4.5 million annually. The projected rate of return was 4.5/30 = .15, or 15%, much less than the profitability of Geothermal’s existing assets. However, once the new project was up and running, it would be no riskier than Geothermal’s present business.

Jo Ann realized that 15% was not necessarily a bad return—though of course 25% would have been better. Fifteen percent might still exceed Geothermal’s cost of capi- tal, that is, exceed the expected rate of return that outside investors would demand to invest money in the project. If the cost of capital was less than the 15% expected return, expansion would be a good deal and would generate net value for Geothermal and its stockholders.

Jo Ann remembered how to calculate the cost of capital for companies that used only common stock financing. Briefly she sketched the argument.

“I need the expected rate of return investors would require from Geothermal’s real assets—the wells, pumps, generators, etc. 1 That rate of return depends on the assets’ risk. However, the assets aren’t traded in the stock market, so I can’t observe how risky they have been. I can only observe the risk of Geothermal’s common stock.

“But if Geothermal issues only stock—no debt—then owning the stock means own- ing the assets, and the expected return demanded by investors in the stock must also be the cost of capital for the assets.” She jotted down the following identities:

Value of business = value of stock Risk of business = risk of stock

Rate of return on business = rate of return on stock Investors’ required return from business = investors’ required return from stock

If there were no company debt, this would be the right discount rate for Geothermal’s expansion plan.

Unfortunately, Geothermal had borrowed a substantial amount of money; its stock- holders did not have unencumbered ownership of Geothermal’s assets. The expansion project would also justify some extra debt finance. Jo Ann realized that she would have to look at Geothermal’s capital structure —its mix of debt and equity financing—and consider the expected rates of return required by debt as well as equity investors.

1 Investors will invest in the firm’s securities only if they offer the same expected return as other equally risky securities. When securities are properly priced, the return that investors can expect from their investments is therefore also the return that they require.

capital structure The mix of long-term debt and equity financing.

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Chapter 13 The Weighted-Average Cost of Capital and Company Valuation 389

“Holy Toledo, I’ve got it!” Jo Ann exclaimed. “If I bought all the securities issued by Geothermal, debt as well as equity, I’d own the entire business. That means . . .” She jotted again:

Value of business = value of portfolio of all the firm’s debt and equity securities

Risk of business = risk of portfolio

Rate of return on business = rate of return on portfolio

Investors’ required return on business

(company cost of capital) = investors’ required return on portfolio

“All I have to do is calculate the expected rate of return on a portfolio of all the firm’s securities. That’s easy. The debt’s yielding 8%, and Fred, that nerdy banker, says that equity investors want 14%. Suppose he’s right. The portfolio would contain 30% debt and 70% equity, so . . .”

Portfolio return = (.3 × 8%) + (.7 × 14%) = 12.2%

It was all coming back to her now. The company cost of capital is just a weighted average of returns on debt and equity, with weights depending on relative market val- ues of the two securities.

“But there’s one more thing. Interest is tax-deductible. If Geothermal pays $1 of interest, taxable income is reduced by $1, and the firm’s tax bill drops by 35 cents (assuming a 35% tax rate). The net cost is only 65 cents. So the after-tax cost of debt is not 8%, but .65 × 8 = 5.2%.

“Now I can finally calculate the weighted-average cost of capital:

WACC = (.3 × 5.2%) + (.7 × 14%) = 11.4%

“Looks like the expansion’s a good deal. Fifteen’s better than 11.4. But I sure need a break.”

13.2 The Weighted-Average Cost of Capital Jo Ann’s conclusions were important. It should be obvious by now that the choice of the discount rate can be crucial, especially when the project involves large capital expenditures or is long-lived.

Think again what the company cost of capital is, and what it is used for. We define it as the opportunity cost of capital for the firm’s existing assets; we use it to value new assets that have the same risk as the old ones. The company cost of capital is the

Geothermal had issued 22.65 million shares, now trading at $20 each. Thus share- holders valued Geothermal’s equity at $20 × 22.65  million = $453 million. In addi- tion, the company had issued bonds with market value currently equal to $194 million. The market value of the company’s debt and equity was therefore $194 + $453 = $647 million. Debt was 194/647 = .3, or 30% of the total.

“Geothermal’s worth more to investors than either its debt or its equity,” Jo Ann mused. “But I ought to be able to find the overall value of Geothermal’s business by adding up the debt and equity.” She sketched a rough balance sheet:

Assets Liabilities and Shareholders’ Equity

Market value of assets = value of Geothermal’s existing business $647 Market value of debt $194 (30%) Market value of equity 453 (70%) Total value $647 Total value $647 (100%)

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390 Part Three Risk

minimum acceptable rate of return when the firm expands by investing in average-risk projects.

We first introduced the opportunity cost of capital in Chapter 1. “Opportunity cost” is a shorthand reminder that when the firm invests rather than returning cash to share- holders, the shareholders lose the opportunity to invest in financial markets. If the corporation acts in the shareholders’ interests, it will invest their money only if it can find projects that offer higher rates of return than investors could achieve on their own. Therefore, the expected rates of return on investments in financial markets determine the cost of capital for corporate investments.

The company cost of capital is the opportunity cost of capital for the company as a whole. We discussed the company cost of capital in Chapter 12, but did not explain how to measure it when the firm has raised different types of debt and equity financing or how to adjust it for the tax-deductibility of interest payments. The weighted-average cost of capital formula handles these complications.

Calculating Company Cost of Capital as a Weighted Average When only common stock is outstanding, calculating the company cost of capital is straightforward, though not always easy. For example, a financial manager could esti- mate beta and calculate shareholders’ required rate of return using the capital asset pricing model (CAPM). This would be the expected rate of return investors require on the company’s existing assets and operations and also the expected return they will require on new investments that do not change the company’s market risk.

But most companies issue debt as well as equity. The company cost of capital is a weighted average of the returns demanded by debt and equity investors. The weighted average is the expected rate of return investors would demand on a portfolio of all the firm’s outstanding securities.

Let’s review Jo Ann Cox’s calculations for Geothermal. To avoid complications, we’ll ignore taxes for the next two or three pages. The total market value of Geother- mal, which we denote as V, is the sum of the values of the outstanding debt D and the equity  E. Thus firm value is V  =  D  +  E  = $194  million + $453  million = $647   million. Debt accounts for 30% of the value and equity accounts for the remaining 70%. If you held all the shares and all the debt, your investment in Geothermal would be V   =  $647  million. Between them, the debtholders and equityholders own all the firm’s assets. So V is also the value of these assets—the value of Geothermal’s exist- ing business.

Suppose that Geothermal’s equity investors require a 14% rate of return on their investment in the stock. What rate of return must a new project provide in order that all investors—both debtholders and stockholders—earn a fair rate of return? The debt- holders require a rate of return of r debt  = 8%. So each year the firm will need to pay interest of r debt  ×  D  = .08 × $194  million = $15.52 million. The shareholders, who have invested in a riskier security, require an expected return of r equity  = 14% on their investment of $453 million. Thus in order to keep shareholders happy, the company needs additional income of r equity  ×  E  =  .14 × $453  million = $63.42 million. To satisfy both the debtholders and the shareholders, Geothermal needs to earn $15.52  million + $63.42  million = $78.94 million. This is equivalent to earning a return of r assets  = 78.94/647 = .122, or 12.2%.

Figure 13.1 illustrates the reasoning behind our calculations. The figure shows the amount of income needed to satisfy the debt and equity investors. Notice that debt- holders account for 30% of Geothermal’s capital structure but receive less than 30% of its expected income. On the other hand, they bear less than a 30% share of risk, since they have first cut at the company’s income and also first claim on its assets if the com- pany gets in trouble. Shareholders expect a return of more than 70% of Geothermal’s income because they bear correspondingly more risk.

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Chapter 13 The Weighted-Average Cost of Capital and Company Valuation 391

However, if you buy all Geothermal’s debt and equity, you own its assets lock, stock, and barrel. You receive all the income and bear all the risks. The expected rate of return you’d require on this portfolio of securities is the same return you’d require from unencumbered ownership of the business. This rate of return—12.2%, ignoring taxes—is therefore the company cost of capital and the required rate of return from an expansion of the business.

The bottom line (still ignoring taxes) is

Company cost of capital = weighted average of debt and equity returns

The underlying algebra is simple. Debtholders need income of ( r debt  ×  D ), and the equity investors need expected income of ( r equity  ×  E ). The total income that is needed is ( r debt  ×  D ) + ( r equity  ×  E ). The amount of their combined existing investment in the company is V. So to calculate the return that is needed on the assets, we simply divide the income by the investment:

rassets = total income

value of investment

= (D × rdebt) + (E × requity)

V = aD

V × rdebtb + aEV × requityb

For Geothermal,

rassets = (.30 × 8%) + (.70 × 14%) = 12.2%

This figure is the expected return demanded by investors in the firm’s assets.

FIGURE 13.1 Geothermal’s debtholders account for 30% of the company’s capital structure, but they get a smaller share of expected income because their return is guaranteed by the company. Geothermal’s stockholders bear more risk and receive, on average, greater return. Of course, if you buy all the debt and all the equity, you get all the income.

Share of Capital Structure

Total = $647 (100%)

Share of Expected Income

Total = $78.9 (100%)

Debt $194 (30%)

Debt $15.5 (20%)

Equity $453 (70%)

Equity $63.4 (80%)

Hot Rocks Corp., one of Geothermal’s competitors, has issued long-term bonds with a market value of $50 million and an expected return of 9%. It has 4 million shares outstanding trading for $10 each. At this price the shares offer an expected return of 17%. What is the weighted-average cost of capi- tal for Hot Rocks’ assets and operations? Assume Hot Rocks pays no taxes.

Self-Test 13.1

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392 Part Three Risk

Use Market Weights, Not Book Weights The company cost of capital is the expected rate of return that investors demand from the company’s assets and operations. The cost of capital must be based on what investors are actually willing to pay for the company’s outstanding securities— that is, based on the securities’ market values.

Market values usually differ from the values recorded by accountants in the com- pany’s books. The book value of Geothermal’s equity reflects money raised in the past from shareholders or reinvested by the firm on their behalf. If investors recognize Geothermal’s excellent prospects, the market value of equity may be much higher than book, and the debt ratio will be lower when measured in terms of market values rather than book values.

Financial managers use book debt-to-value ratios for various purposes, and some- times they unthinkingly look to the book ratios when calculating weights for the com- pany cost of capital. That’s a mistake, because the company cost of capital measures what investors want from the company, and so depends on how they value the compa- ny’s securities. That value depends on future profits and cash flows, not on accounting history. Book values, while useful for many other purposes, measure only cumulative historical financing; they don’t generally measure market values accurately.

Here is a book balance sheet for Duane S. Burg Associates. Figures are in millions.

Unfortunately, the company has fallen on hard times. The 6 million shares are trading for only $4 apiece, and the market value of its debt securities is 20% below the face (book) value. Because of the company’s large cumulative losses, it will pay no taxes on future income.

Suppose shareholders now demand a 20% expected rate of return. The bonds are now yielding 14%. What is the weighted-average cost of capital?

Self-Test 13.2

Assets Liabilities and Shareholders’ Equity

Assets (book value) $75 Debt $25 Equity 50 $75 $75

Taxes and the Weighted-Average Cost of Capital So far our examples have ignored taxes. When you calculate a project’s NPV, you need to discount the cash flows after tax assuming that the project is wholly equity- financed. That is exactly the approach that we used in Chapter 9, when we valued Blooper’s investment in the magnoosium mine. Sometimes you may encounter com- panies that forecast cash flows before tax and then try to compensate for this by using a higher discount rate. It doesn’t work; there is no simple adjustment to the discount rate that will allow you to discount pretax cash flows.

Taxes are also important because most companies are financed by both equity and debt. The interest payments on this debt are deducted from income before tax is calcu- lated. Therefore, the cost to the company is reduced by the amount of this tax saving.

The interest rate on Geothermal’s debt is r debt  = 8%. However, with a corporate tax rate of T c  = .35, the government bears 35% of the cost of the interest payments. The government doesn’t send the firm a check for this amount, but the income tax that the

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Chapter 13 The Weighted-Average Cost of Capital and Company Valuation 393

firm pays is reduced by 35% of its interest expense. Therefore, Geothermal’s after-tax cost of debt is only 100 − 35 = 65% of the 8% pretax cost:

After-tax cost of debt = (1 - tax rate) × pretax cost = (1 - Tc) × rdebt = (1 - .35) × 8% = 5.2%

We can now adjust our calculation of Geothermal’s cost of capital to recognize the tax savings associated with interest payments:

Company cost of capital, after-tax = (.3 × 5.2%) + (.7 × 14%) = 11.4%

Now we’re back to the weighted-average cost of capital, or WACC. The general formula is

WACC = cD V

× (1 - Tc)rdebt d + aEV × requityb (13.1)

weighted-average cost of capital (WACC) Expected rate of return on a portfolio of all the firm’s securities, adjusted for tax savings due to interest payments.

Criss-Cross Industries has earnings before interest and taxes (EBIT) of $10 million. Interest payments are $2 million, and the corporate tax rate is 35%. Construct a simple income statement to show that the debt interest reduces the taxes the firm owes to the government. How much more tax would Criss-Cross pay if it were financed solely by equity?

Self-Test 13.3

Example 13.1 Weighted-Average Cost of Capital for Dow Chemical In Chapter 12 we showed how the capital asset pricing model can be used to esti- mate the expected return on Dow Chemical common stock. We will now use this estimate to figure out the company’s weighted-average cost of capital.

Step 1. Calculate the value of each security as a proportion of firm value. The company has outstanding 1,210 million shares, which in August 2013 had a market value of $38.74 each. The total market value of Dow’s equity was E  = 1,210 × $38.74 = $46,875 million. The company’s latest balance sheet showed that it had borrowed D  = $17,475 million and its bonds were currently selling close to par value. So the total value of Dow’s securities is V  =  D  +  E  = $17,475 + $46,875 = $64,350 million. Debt as a proportion of the total value is D / V  = $17,475/$64,350 = .27, and equity as a proportion of the total is $46,875/$64,350 = .73, or 73%.

Step 2. Determine the required rate of return on each security. In Chapter 12 we estimated that Dow’s shareholders required a return of 19.4%. The average yield on Dow’s debt was about 4.5%.

Step 3. Calculate a weighted average of the after-tax return on the debt and the return on the equity. 2 The weighted-average cost of capital is

WACC = cD V

× (1 - Tc)rdebt d + a EV × requityb = 3.27 × (1 - .35)4.5% 4 + (.73 × 19.4%) = 14.95%

2 Financial managers often use “equity” to refer to common stock, even though a firm’s equity strictly includes both common and preferred stock. We continue to use r equity to refer specifically to the expected return on the common stock.

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394 Part Three Risk

What If There Are Three (or More) Sources of Financing? We have simplified our discussion of the cost of capital by assuming the firm has only two classes of securities: debt and equity. Even if the firm has issued other classes of securities, our general approach to calculating WACC remains unchanged. We simply calculate the weighted-average after-tax return of each security type.

For example, suppose the firm also has outstanding preferred stock. Preferred stock has some of the characteristics of both common stock and fixed-income securities. Like bonds, preferred stock promises to pay a given, usually level, stream of divi- dends. Unlike bonds, however, there is no maturity date for the preferred stock. The promised dividends constitute a perpetuity as long as the firm stays in business. More- over, a failure to come up with the cash to pay the dividends does not push the firm into bankruptcy. Instead, any unpaid dividends simply cumulate; the common stock- holders do not receive dividends until the accumulated preferred dividends have been paid. Finally, unlike interest payments, preferred stock dividends are not considered tax-deductible expenses.

How would we calculate WACC for a firm with preferred stock as well as common stock and bonds outstanding? Using P to denote the value of preferred stock, we sim- ply generalize Equation 13.1 for WACC as follows:

WACC = cD V

× (1 - Tc)rdebt d + aPV × rpreferredb + a E

V × requityb (13.1a)

Wrapping Up Geothermal We now turn one last time to Jo Ann Cox and Geothermal’s proposed expansion. We want to make sure that she—and you—know how to use the weighted-average cost of capital.

Remember that the proposed expansion costs $30 million and should generate a perpetual cash flow of $4.5 million per year. A simple cash-flow worksheet might look like this: 3

3 For this example we ignore depreciation, a noncash but tax-deductible expense. (If the project were really per- petual, why depreciate?)

Calculate WACC for Hot Rocks (Self-Test 13.1) and Burg Associates (Self- Test 13.2) assuming the companies face a 35% corporate income tax rate.

Self-Test13.4

Revenue $10.00 million

− Operating expenses   − 3.08 = Pretax operating cash fl ow 6.92 − Tax at 35% − 2.42 After-tax cash fl ow $ 4.50 million

Note that these cash flows do not include the tax benefits of using debt. Geothermal’s managers and engineers forecast revenues, costs, and taxes as if the project were to be all-equity-financed. The interest tax shields generated by the project’s actual debt financing are not forgotten, however. They are accounted for by using the after-tax cost of debt in the weighted-average cost of capital.

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Chapter 13 The Weighted-Average Cost of Capital and Company Valuation 395

Project net present value is calculated by discounting expected cash flow (which is a perpetuity) at Geothermal’s 11.4% weighted-average cost of capital:

NPV = -30 + 4.5

.114 = +$9.5 million

Expansion will thus add $9.5 million to the net wealth of Geothermal’s owners.

Checking Our Logic Any project offering a rate of return more than 11.4% will have a positive NPV, assum- ing that the project has the same risk and financing as Geothermal’s business. A proj- ect offering exactly 11.4% would just break even; it would generate just enough cash to satisfy both debtholders and stockholders.

Let’s check that out. Suppose the proposed expansion had revenues of only $8.34 million and after-tax cash flows of $3.42 million:

Revenue $8.34 million

− Operating expenses − 3.08 = Pretax operating cash fl ow 5.26 − Tax at 35% − 1.84 After-tax cash fl ow $3.42 million

With an investment of $30 million, the internal rate of return on this perpetuity is exactly 11.4%:

Rate of return = 3.42

30 = .114, or 11.4%

and NPV is exactly zero:

NPV = -30 + 3.42

.114 = 0

When we calculated Geothermal’s weighted-average cost of capital, we recognized that the company’s debt ratio was 30%. When Geothermal’s analysts use the weighted- average cost of capital to evaluate the new project, they are assuming that the $30 mil- lion additional investment would support the issue of additional debt equal to 30% of the investment, or $9 million. The remaining $21 million is provided by the sharehold- ers either in the form of reinvested earnings or through the issue of additional shares.

The following table shows how the cash flows would be shared between the debt- holders and shareholders assuming still that the project has zero NPV. We start with the pretax operating cash flow of $5.26 million:

Cash fl ow before tax and interest $5.26 million

− Interest payment (.08 × $9  million) − .72 = Pretax cash fl ow 4.54 − Tax at 35% − 1.59 After-tax cash fl ow $2.95 million

Project cash flows before tax and interest are forecast to be $5.26 million. Out of this figure, Geothermal needs to pay interest of 8% of $9 million, which comes to $.72  million. This leaves a pretax cash flow of $4.54 million, on which the company must pay tax. Taxes equal .35 × 4.54 = $1.59 million. Shareholders are left with $2.95  million, just enough to give them the 14% return that they need on their $21  million investment. (Note that 2.95/21 = .14, or 14%.) Therefore, everything checks out.

If a project has zero NPV when the expected cash flows are discounted at the weighted-average cost of capital, then the project’s cash flows are just sufficient to give debtholders and shareholders the returns they require.

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396 Part Three Risk

13.3 Measuring Capital Structure We have explained the formula for calculating the weighted-average cost of capital. We will now look at some of the practical problems in applying that formula. Suppose that the financial manager of Big Oil has asked you to estimate the firm’s weighted- average cost of capital. Your first step is to work out Big Oil’s capital structure. But where do you get the data?

Financial managers usually start with the company’s accounts, which show the book value of debt and equity, whereas the weighted-average cost of capi- tal formula calls for their market values. A little work and a dash of judgment are needed to go from one to the other.

Table 13.1 shows the debt and equity issued by Big Oil. The firm has borrowed $200 million from banks and has issued a further $200 million of long-term bonds. These bonds have a coupon rate of 8% and mature at the end of 12 years. Finally, there are 100 million shares of common stock outstanding, each with a par value of $1. But the accounts also recognize that Big Oil has in past years plowed back into the firm $300 million of retained earnings. The total book value of the equity shown in the accounts is $100  million + $300  million = $400 million.

Notice that the right side of Table 13.1 contains long-term financing. Current liabil- ities have been subtracted on the left as an offset to current assets. Thus net working capital equals current assets minus current liabilities. We set up the balance sheet in this way in order to compute the weighted-average cost of capital, which is normally defined as the combined cost of long-term debt financing and equity. 4 Thus, the bal- ance sheet shows only sources of long-term financing on the right.

The figures shown in Table 13.1 are taken from Big Oil’s annual accounts and are therefore book values. Sometimes the differences between book values and market values are negligible. For example, consider the $200 million that Big Oil owes the bank. The interest rate on bank loans is usually linked to the general level of interest rates. Thus if interest rates rise, the rate charged on Big Oil’s loan also rises to main- tain the loan’s value. As long as Big Oil is reasonably sure to repay the loan, it is worth close to $200 million. Most financial managers most of the time are willing to accept the book value of bank debt as a fair approximation of its market value.

What about Big Oil’s long-term bonds? Since the bonds were originally issued, long-term interest rates have risen to 9%. 5 We can calculate the value today of each bond as follows: 6 There are 12 coupon payments of .08 × 200 = $16 million and then repayment of face value 12 years out. Thus the final cash payment to the bondholders is $216 million. All the bond’s cash flows are discounted back at the current interest rate of 9%:

PV = 16

1.09 +

16 (1.09)2

+

16 (1.09)3

+ c

+

216 (1.09)12

= $185.7

Therefore, the bonds are worth only $185.7 million, 93% of their face value. If you used the book value of Big Oil’s long-term debt rather than its market value,

you would be a little bit off in your calculation of the weighted-average cost of capital, but probably not seriously so.

The really big errors are likely to arise if you use the book value of equity rather than its market value. The $400 million book value of Big Oil’s equity measures the

4  Sometimes companies finance long-term investment with short-term debt, rolling over the short-term debt as it matures. In this case the permanent component of short-term debt could remain on the right side of the balance sheet, and the cost of short-term debt could be included in WACC.

5  If Big Oil’s bonds are traded, you can simply look up their price. (You can find prices for bond trades on www. finra.org/marketdata . ) But many bonds are not regularly traded, and in such cases you need to infer their price by calculating the bond’s value using the rate of interest offered by similar bonds.

6  We assume that coupon payments are annual. Most bonds in the United States actually pay interest twice a year.

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Chapter 13 The Weighted-Average Cost of Capital and Company Valuation 397

total amount of cash that the firm has raised from shareholders in the past or has retained and invested on their behalf. But perhaps Big Oil has been able to find proj- ects that were worth more than they originally cost, or perhaps the value of the assets has increased with inflation. Perhaps investors see great future investment opportuni- ties for the company. All these considerations determine what investors are willing to pay for Big Oil’s common stock.

Big Oil’s stock price is $12 a share. Thus the total market value of the stock is

Number of shares × share price = 100 million × $12 = $1,200 million

In Table 13.2 we show a market-value balance sheet for Big Oil. You can see that debt accounts for 24.3% of company value ( D / V  = .243) and equity accounts for 75.7% ( E / V  = .757). These are the proportions to use when calculating the weighted-average cost of capital. Notice that if you looked only at the book values shown in Table 13.1 , you would mistakenly conclude that debt and equity each accounted for 50% of value.

Assets Long-Term Liabilities and Equity

Net working capital $120 Bank debt $200 25.0% (= current assets −  current liabilities) Property, plant and 620 Long-term bonds 200 25.0 equipment (PP&E) (12-year maturity, 8% coupon) Other long-term assets 60 Common stock 100 12.5 (100 million shares, par value = $1) Retained earnings 300 37.5 $800 $800 100.0%

TABLE 13.1 Big Oil’s book (accounting) balance sheet (dollar values in millions)

Here is the capital structure shown in Executive Fruit’s book balance sheet:

Debt $4.1 million 45.0% Preferred stock 2.2 24.2 Common stock 2.8 30.8 Total $9.1 million 100.0%

Explain why the percentage weights given above should not be used in cal- culating Executive Fruit’s WACC.

Self-Test 13.5

Assets Liabilities and Equity

Net working capital $120.0 Bank debt $ 200.0 12.6% (= current assets −  current liabilities) Value of PP&E and other Long-term bonds long-term assets (including intangible assets) 1,465.7

(market value = 93% par value) 185.7 11.7

Total debt 385.7 24.3

Common stock (100 million shares, par value = $1) 1,200.0 75.7

Value $1,585.7 Value $1,585.7 100.0%

TABLE 13.2 Big Oil’s market- value balance sheet (dollar values in millions)

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398 Part Three Risk

13.4 Calculating the Weighted-Average Cost of Capital To calculate Big Oil’s weighted-average cost of capital, you first need the rate of return that investors require from each security.

The Expected Return on Bonds We know that Big Oil’s bonds offer a yield to maturity of 9%. As long as the company does not go belly-up, that is the rate of return investors can expect to earn from holding Big Oil’s bonds. If there is any chance that the firm may be unable to repay the debt, however, the yield to maturity of 9% represents the most favorable outcome and the expected return is lower than 9%.

For most large and healthy firms, the probability of bankruptcy is sufficiently low that financial managers are content to take the promised yield to maturity on the bonds as a measure of the expected return. But beware of assuming that the yield offered on the bonds of Fly-by-Night Corporation is the return that investors could expect to receive.

The Expected Return on Common Stock Estimates Based on the Capital Asset Pricing Model In the previ- ous chapter we showed you how to use the capital asset pricing model to estimate the expected rate of return on common stock. The capital asset pricing model tells us that investors demand a higher rate of return from stocks with high betas. The formula is

Expected returnon stock = risk-free

interest rate + ¢stock’sbeta × expected marketrisk premium ≤ Financial managers and economists measure the risk-free rate of interest by the

yield on Treasury debt securities. To measure the expected market risk premium, they usually look back at capital market history, which suggests that investors have received about an extra 7% a year from investing in common stocks rather than Trea- sury bills. 7 Yet wise financial managers use this evidence with considerable humil- ity, for who is to say whether investors in the past received more or less than they expected or whether investors today require a higher or lower reward for risk than their parents did?

Let’s suppose Big Oil’s common stock beta is estimated at .85, the risk-free interest rate ( r f ) is 6%, and the expected market risk premium ( r m  −  r f ) is 7%. Then the CAPM would put Big Oil’s cost of equity at

Cost of equity = requity = rf + b(rm - rf)

= 6% + .85(7%) = 12%

7  The Treasury bill rate is the customary measure of the risk-free rate of interest. There is a mismatch, how- ever, in using a short-term bill rate to calculate the cost of equity in a WACC. The WACC is used to discount cash flows that may arrive many years in the future. Discounting a distant future cash flow at a short-term rate doesn’t make sense, especially when monetary policy forces the short-term rate down close to zero. Therefore, financial managers calculating WACC usually estimate the cost of equity using a long-term Treasury bond rate. In this case, the market risk premium must be defined as the expected difference between the returns on the stock market and on long-term Treasury bonds. Notice in Table 11.1 that the average return on Treasury bonds has been 1.3 percentage points above the average return on bills. Suppose a financial manager uses a long-term bond yield to estimate the cost of equity. If the manager relies on history, he or she would use a market risk pre- mium that is 1.3 percentage points lower than the premium versus bills.

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Chapter 13 The Weighted-Average Cost of Capital and Company Valuation 399

Estimates Based on the Dividend Discount Model Whenever you are given an estimate of the expected return on a common stock, always look for ways to check whether it is reasonable. One check on the estimates provided by the CAPM can be obtained from the dividend discount model (DDM). In Chapter 7 we showed you how to use the constant-growth DDM formula to estimate the return that inves- tors expect from different common stocks. Remember the formula: If dividends are expected to grow indefinitely at a constant rate g, then the price of the stock is equal to

P0 = DIV1

requity - g

where P 0 is the current stock price, DIV 1 is the forecast dividend at the end of the year, and r equity is the expected return from the stock. We can rearrange this formula to pro- vide an estimate of r equity :

requity = DIV1

P0 + g (13.2)

In other words, the expected return on equity is equal to the dividend yield (DIV 1 / P 0 ) plus the expected perpetual growth rate in dividends ( g ).

This constant-growth dividend discount model is widely used in estimating expected rates of return on common stocks of public utilities. Utility stocks have a fairly stable growth pattern and are therefore tailor-made for the constant-growth formula.

Remember that the constant-growth formula will get you into trouble if you apply it to firms with very high current rates of growth. Such growth cannot be sustained indefinitely. Using the formula in these circumstances will lead to an over- estimate of the expected return.

Beware of False Precision Do not expect estimates of the cost of equity to be precise. In practice you can’t know whether the capital asset pricing model fully explains expected returns or whether the assumptions of the dividend discount model hold exactly. Even if your formulas were right, the required inputs would be noisy and subject to error. Thus a financial analyst who can confidently locate the cost of equity in a band of 2 or 3 percentage points is doing pretty well. In this endeavor it is perfectly okay to conclude that the cost of equity is, say, “about 15%” or “somewhere in a range from 14% to 16%.” 8

Sometimes accuracy can be improved by estimating the cost of equity or WACC for an industry or a group of comparable companies. This cuts down the “noise” that plagues single-company estimates. Suppose, for example, that Jo Ann Cox is able to identify three companies with investments and operations similar to Geothermal’s. The average WACC for these three companies would be a valuable check on her esti- mate of WACC for Geothermal alone.

8  The calculations in this chapter have been done to one or two decimal places just to avoid confusion from rounding.

Jo Ann Cox decides to check whether Fred, the nerdy banker, was correct in claiming that Geothermal’s cost of equity is 14%. She estimates Geother- mal’s beta at 1.20. The risk-free interest rate is 6%, and the long-run average market risk premium is 7.6%. What is the expected rate of return on Geother- mal’s common stock, assuming of course that the CAPM is true? Recalculate Geothermal’s weighted-average cost of capital.

Self-Test 13.6

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400 Part Three Risk

Or suppose that Geothermal is contemplating investment in oil refining. For this venture, Geothermal’s existing WACC is probably not right; it needs a discount rate reflecting the risks of the refining business. It could therefore try to estimate WACC for a sample of oil refining companies. If too few “pure-play” refining companies were available—most oil companies invest in production and marketing as well as refining—an industry WACC for a sample of large oil companies could be a useful check or benchmark.

The Expected Return on Preferred Stock Preferred stock that pays a fixed annual dividend can be valued from the perpetuity formula:

Price of preferred = dividend rpreferred

where r preferred is the appropriate discount rate for the preferred stock. Therefore, we can infer the required rate of return on preferred stock by rearranging the valuation formula to

rpreferred = dividend

price of preferred (13.3)

For example, if a share of preferred stock sells for $20 and pays a dividend of $2 per share, the expected return on preferred stock is r preferred  = $2/$20 = 10%, which is simply the dividend yield.

Adding It All Up Once you have worked out Big Oil’s capital structure and estimated the expected return on its securities, you require only simple arithmetic to calculate the weighted- average cost of capital. Table 13.3 summarizes the necessary data. Now all you need to do is plug the data in Table 13.3 into the weighted-average cost of capital formula:

WACC = cD V

× (1 - Tc)rdebt d + aEV × requityb = 3.243 × (1 - .35)9% 4 + (.757 × 12%) = 10.5%

Suppose that Big Oil needs to evaluate a project with the same risk as its existing busi- ness. If the project would also support a 24.3% debt ratio, the 10.5% weighted-average cost of capital is the appropriate discount rate for the cash flows. 9

Real-Company WACCs Big Oil is entirely hypothetical. Therefore you might be interested in looking at Table 13.4 , which gives some estimates of the weighted-average cost of capital for a sample of real companies. As you do so, remember that any estimate of the cost of capi- tal for a single company can be way off the true cost. You should always try to check your estimate by looking at the cost of capital for a group of similar companies.

9 Notice that Ford’s WACC is about average despite its very high cost of equity. This results from the company’s very high debt ratio. Should Ford use a WACC of 9.5% when valuing a proposal to expand its operations? The answer is yes if a 79% debt ratio really is a sensible target capital structure. But if you believe that this debt ratio does not constitute a desirable long-term capital structure for Ford, then you would need to recalculate WACC with a lower ratio.

Security Type Capital Structure Required Rate of Return

Debt D  =  $ 385.7 D / V  = .243 r debt  = .09, or 9% Common stock E  = $1,200.0 E / V  = .757 r equity  = .12, or 12% Total V  = $1,585.7

Note: Corporate tax rate =  T c  = .35.

TABLE 13.3 Data needed to calculate Big Oil’s weighted- average cost of capital (dollar values in millions)

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Chapter 13 The Weighted-Average Cost of Capital and Company Valuation 401

13.5 Interpreting the Weighted-Average Cost of Capital

When You Can and Can’t Use WACC The weighted-average cost of capital is the rate of return that the firm must expect to earn on its average-risk investments in order to provide an adequate expected return to all its security holders. Strictly speaking, the weighted- average cost of capital is an appropriate discount rate only for a project that is a car- bon copy of the firm’s existing business. But often it is used as a companywide benchmark discount rate; the benchmark may be adjusted upward for unusu- ally risky projects and downward for unusually safe ones.

There is a good musical analogy here. Most of us, lacking perfect pitch, need a well-defined reference point, like middle C, before we can sing on key. But anyone who can carry a tune gets relative pitches right. Businesspeople have good intuition about relative risks, at least in industries they are used to, but not about absolute risk or required rates of return. Therefore, they set a company- or industrywide cost of capital as a benchmark. This is not the right hurdle rate for everything the company does, but judgmental adjustments can be made for more risky or less risky ventures.

Some Common Mistakes One danger with the weighted-average formula is that it tempts people to make logical errors. Think back to your estimate of the cost of capital for Big Oil:

WACC = cD V

× (1 - Tc)rdebt d + aEV × requityb = 3.243 × (1 - .35)9% 4 + (.757 × 12%) = 10.5%

Expected Return on Equity, %

Interest Rate on Debt, %

Proportion of Equity

( E / V )

Proportion of Debt

( D / V ) WACC, %

Dow Chemical 19.4 5.74 0.70 0.30 14.7 U.S. Steel 19.4 6.70 0.41 0.59 10.5 Ford 18.3 6.30 0.38 0.62 9.5 General Electric 14.6 4.87 0.93 0.07 13.8 Disney 11.5 5.13 0.91 0.09 10.8 Starbucks 11.5 5.18 0.99 0.01 11.4 Boeing 11.4 5.13 0.90 0.10 10.6 Union Pacifi c 11.0 5.13 0.89 0.11 10.2 Intel 10.1 5.08 0.89 0.11 9.4 Google 9.6 4.92 0.99 0.01 9.5 Amazon 8.7 4.98 0.98 0.02 8.6 Pfi zer 8.2 4.92 0.83 0.17 7.3 IBM 7.8 4.92 0.89 0.11 7.3 Coca-Cola 6.7 5.18 0.92 0.08 6.4 ExxonMobil 6.4 4.42 0.98 0.02 6.3 McDonald’s 5.6 5.13 0.87 0.13 5.3 Walmart 5.4 4.92 0.85 0.15 5.1 Newmont Mining 5.2 5.74 0.72 0.28 4.8 Consolidated Edison 4.2 5.18 0.62 0.38 3.9

Notes: 1. Expected return on equity is taken from Table 12.2. 2. Interest rate on debt is calculated from yields on similarly rated bonds. 3. D is the book value of the fi rm’s debt, and E is the market value of equity. 4. WACC = ( D / V ) × (1 − .35) ×  r debt  + ( E / V ) ×  r equity .

TABLE 13.4 Calculating the weighted-average cost of capital for selected companies

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402 Part Three Risk

Now you might be tempted to say to yourself: “Aha! Big Oil has a good credit rating. It could easily push up its debt ratio to 50%. If the interest rate is 9% and the required return on equity is 12%, the weighted-average cost of capital would be

WACC = 3.50 × (1 - .35)9% 4 + (.50 × 12%) = 8.9% At a discount rate of 8.9%, we can justify a lot more investment.”

That reasoning will get you into trouble. First, if Big Oil increased its borrowing, the lenders would almost certainly demand a higher rate of interest on the debt. Sec- ond, as the borrowing increased, the risk of the common stock would also increase and therefore the stockholders would demand a higher return.

There are actually two costs of debt finance. The explicit cost of debt is the rate of interest that bondholders demand. But there is also an implicit cost, because borrowing increases the required return to equity. When you jumped to the conclu- sion that Big Oil could lower its weighted-average cost of capital to 8.9% by borrowing more, you were recognizing only the explicit cost of debt and not the implicit cost.

Jo Ann Cox’s boss has pointed out that Geothermal proposes to finance its expansion entirely by borrowing at an interest rate of 8%. He argues that this is therefore the appropriate discount rate for the project’s cash flows. Is he right?

Self-Test 13.7

How Changing Capital Structure Affects Expected Returns We will illustrate how changes in capital structure affect expected returns by focusing on the simplest possible case, where the corporate tax rate T c is zero.

Think back to our earlier example of Geothermal. Geothermal, you may remember, has the following market-value balance sheet:

Assets Liabilities and Shareholders’ Equity

Assets = value of Geothermal’s existing business $647 Debt $194 (30%)

Equity 453 (70%) Total value $647 Value $647 (100%)

Geothermal’s debtholders require a return of 8%, and the shareholders require a return of 14%. Since we assume here that Geothermal pays no corporate tax, its weighted- average cost of capital is simply the expected return on the firm’s assets:

WACC = rassets = (.3 × 8%) + (.7 × 14%) = 12.2%

This is the return you would expect if you held all Geothermal’s securities and there- fore owned all its assets.

Now think what will happen if Geothermal borrows an additional $97 million and uses the cash to buy back and retire $97 million of its common stock. The revised market-value balance sheet is:

Assets Liabilities and Shareholders’ Equity

Assets = value of Geothermal’s existing business $647 Debt $291 (45%)

Equity 356 (55%) Total value $647 Value $647 (100%)

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Chapter 13 The Weighted-Average Cost of Capital and Company Valuation 403

If there are no corporate taxes, the change in capital structure does not affect the total cash that Geothermal pays out to its security holders and it does not affect the risk of those cash flows. Therefore, if investors require a return of 12.2% on the total pack- age of debt and equity before the financing, they must require the same 12.2% return on the package afterward. The weighted-average cost of capital is therefore unaffected by the change in the capital structure.

Is that surprising? After all, the required return on debt is lower than the required return on equity, so you might expect the additional borrowing to reduce the weighted- average cost of capital. The reason that it does not do so is that the return on the indi- vidual securities changes. Since the company has more debt than before, the debt is riskier and debtholders are likely to demand a higher return. Increasing the amount of debt also makes the equity riskier and increases the return that shareholders require. We will return to this point in Chapter 16.

What Happens When the Corporate Tax Rate Is Not Zero We have shown that when there are no corporate taxes, the weighted-average cost of capital is unaffected by a change in capital structure. Unfortunately, taxes can compli- cate the picture. 10 For the moment, just remember:

• The weighted-average cost of capital is the right discount rate for average- risk capital investments.

• The weighted-average cost of capital is the return the company needs to earn after tax in order to satisfy all its security holders.

• If the firm increases its debt ratio, both the debt and the equity will become more risky. The debtholders and equityholders require a higher return to compensate for increased risk.

13.6 Valuing Entire Businesses Investors routinely buy and sell shares of common stock. Companies frequently buy and sell entire businesses. Do the discounted cash-flow formulas that we used in Chap- ter 7 to value Blue Skies’ stock also work for entire businesses?

Sure! As long as the company’s debt ratio is expected to remain fairly constant, you can treat the company as one big project and discount its cash flows by the weighted- average cost of capital. The result is the combined value of the company’s debt and equity. If you want to know just the value of the equity, you must remember to subtract the value of the debt from the company’s total value.

Suppose that you are interested in buying Establishment Industry’s concatenator manufacturing operation. The problem is to figure out what it is worth. Table 13.5 sets out your forecasts for the next 6 years. Row 8 shows the expected cash flow from operations. This is equal to the expected profit after tax plus depreciation. Remember, depreciation is not a cash outflow, and therefore you need to add it back when calculat- ing the operating cash flow. Row 9 in the table shows the forecast investment in fixed assets and net working capital.

The operating cash flow less investment expenditures is the amount of cash that the business can pay out to investors after paying for all investments necessary for growth. This is the concatenator division’s free cash flow (row 10 in the table). Notice that the free cash flow is negative in the early years. Is that a bad sign? Not really. The business

10  There’s nothing wrong with our formulas and examples, provided that the tax deductibility of interest payments doesn’t change the aggregate risk of the debt and equity investors. However, if the tax savings from deducting interest are treated as safe cash flows, the formulas get more complicated. If you really want to dive into the tax- adjusted formulas showing how WACC changes with capital structure, we suggest Chapter 19 in R. A. Brealey, S. C. Myers, and F. Allen, Principles of Corporate Finance, 11th ed. (New York: Irwin/McGraw-Hill, 2014).

free cash flow Cash flow that is not required for investment in fixed assets or working capital and is therefore available to investors.

Valuing the concatenator business

BEYOND THE PAGE

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404 Part Three Risk

is running a cash deficit not because it is unprofitable but because it is growing so fast. Rapid growth is good news, not bad, as long as the business is earning more than the cost of capital on its investments.

The forecast cash flows in Table 13.5 do not include a deduction for debt inter- est. But we will not forget that acquisition of the concatenator business will support additional debt. We will recognize that fact by discounting the free cash flows by the weighted-average cost of capital, which reflects both the firm’s capital structure and the tax deductibility of its interest payments.

Suppose that a sensible capital structure for the concatenator operation is 60% equity and 40% debt. 11 You estimate that the required rate of return on the equity is 12% and that the business could borrow at an interest rate of 5%. The weighted-aver- age cost of capital is therefore

WACC = cD V

× (1 - Tc)rdebt d + aEV × requityb = 3.4 × (1 - .35)5% 4 + (.6 × 12%) = 8.5%

Calculating the Value of the Concatenator Business The value of the concatenator operation is equal to the discounted value of the free cash flows (FCFs) out to a horizon year plus the forecast value of the business at the horizon, also discounted back to the present. That is,

PV = FCF1

1 + WACC +

FCF2 (1 + WACC)2

+ c

+

FCFH (1 + WACC)H

+

PVH (1 + WACC)H

(''''''''')'''''''''* ('')''*

PV (free cash flows) + PV (horizon value)

Of course, the concatenator business will continue to grow after the horizon, but it’s not practical to forecast free cash flow year by year to infinity. PV H stands in for the value of free cash flows in periods H  + 1,  H  + 2, and so on.

Horizon years are often chosen arbitrarily. Sometimes the boss tells everybody to use 10 years because that’s a nice round number. We have picked year 5 as the horizon year because the business is expected to settle down to steady growth of 5% a year from then on.

11  By this we mean that it makes sense to finance 40% of the present value of the business by debt. Remember that we use market-value weights to compute WACC. Debt as a proportion of book value may be more or less than 40%.

Year

1 2 3 4 5 6

1. Sales 1,200.0 1,440.0 1,728.0 1,987.2 2,285.3 2,513.8 2. Costs 1,020.0 1,224.0 1,468.8 1,689.1 1,942.5 2,136.7 3. EBITDA *  = 1 − 2 180.0 216.0 259.2 298.1 342.8 377.1

4. Depreciation 86.4 103.7 124.4 143.1 137.1 120.7 5. Profi t before tax = 3 − 4 93.6 112.3 134.8 155.0 205.7 256.4 6. Tax at 35% 32.8 39.3 47.2 54.3 72.0 89.7 7. Profi t after tax = 5 − 6 60.8 73.0 87.6 100.8 133.7 166.7 8. Operating cash fl ow = 4 + 7 147.2 176.7 212.0 243.8 270.8 287.3 9. Investment in fi xed assets and net

working capital 180.0 247.7 297.2 298.6 87.4 −16.5

10. Free cash fl ow = 8 − 9 −32.8 −71.0 −85.2 −54.8 183.4 303.8

* EBITDA = earnings before interest, taxes, depreciation, and amortization.

TABLE 13.5 Forecasts of operating cash flow and investment for the concatenator manufacturing division (thousands of dollars). Rapid expansion means that free cash flow is negative in the early years, because investment outstrips the cash flow from operations. Free cash flow turns positive when growth slows down.

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Chapter 13 The Weighted-Average Cost of Capital and Company Valuation 405

There are several common formulas or rules of thumb for estimating horizon value. Let’s try the constant-growth formula that we introduced in Chapter 7:

Horizon value = free cash flow in year 6

r - g =

303.8

.085 - .05 = $8,680 thousand

We now have all we need to calculate the value of the concatenator business today. We add up the present values of the free cash flows in the first 5 years and that of the horizon value:

PV (business) = PV (free cash flows years 1–5) + PV (horizon value)

= -32.8

1.085 +

-71.0 (1.085)2

+

-85.2 (1.085)3

+

-54.8 (1.085)4

+

183.4 (1.085)5

+

8,680 (1.085)5

= $5,697.5 thousand

Notice that when we use the weighted-average cost of capital to value a company, we are asking, “What is the combined value of the company’s debt and equity?” If you need to value the equity, you must subtract the value of any outstanding debt. Suppose that the concatenator business has been partly financed with $2,279,000 of debt, 40% of the overall value of about $5,697,500. Then the equity in the business is worth only $5,697,500 − $2,279,000 = $3,418,500.

Managers often use rules of thumb to check their estimates of horizon value. Suppose you observe that the value of the debt plus equity of a typical mature concatenator producer is 15 times its EBITDA. (EBITDA is defined at line 3 of Table 13.5 .) If your operation sold in year 5 at a similar multiple of EBITDA, how would your estimate of the present value of the operation change?

Self-Test 13.8

SUMMARY They need a standard discount rate for average-risk projects. An “average-risk” project is one that has the same risk as the firm’s existing assets and operations.

The weighted-average cost of capital can still be used as a benchmark. The benchmark may be adjusted up for unusually risky projects and down for unusually safe ones.

Here’s the WACC formula one more time:

WACC = cD V

× (1 - Tc)rdebt d + aEV × requityb The WACC is the expected rate of return on the portfolio of debt and equity securities issued by the firm. The required rate of return on each security is weighted by its proportion of the firm’s total market value (not book value). Since interest payments reduce the firm’s income tax bill, the required rate of return on debt is measured after tax, as r debt  × (1 −  T c ).

Capital structure is the proportion of each source of financing in total market value. The WACC formula is usually written assuming the firm’s capital structure includes just two

Why do firms compute weighted-average costs of capital? ( LO13-4)

What about projects that are not average? ( LO13-4 )

How do firms compute weighted-average costs of capital? ( LO13-3 )

How do firms measure capital structure? ( LO13-1 )

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406 Part Three Risk

classes of securities, debt and equity. If there is another class, say preferred stock, the formula expands to include it. In other words, we would estimate r preferred , the rate of return demanded by preferred stockholders, determine P/V, the fraction of market value accounted for by preferred, and add rpreferred  ×  P / V to the equation. Of course the weights in the WACC formula always add up to 1. In this case D / V  +  P / V  +  E / V  = 1.

The cost of debt ( r debt ) is the market interest rate demanded by bondholders. In other words, it is the rate that the company would pay on new debt issued to finance its investment proj- ects. The cost of preferred ( r preferred ) is just the preferred dividend divided by the market price of a preferred share.

The tricky part is estimating the cost of equity ( r equity ), the expected rate of return on the firm’s shares. Financial managers use the capital asset pricing model to estimate expected return. But for mature, steady-growth companies, it can also make sense to use the con- stant-growth dividend discount model. Remember, estimates of expected return are less reliable for a single firm’s stock than for a sample of comparable-risk firms. Therefore, managers also consider WACCs calculated for industries.

The rates of return on debt and equity will change. For example, increasing the debt ratio will increase the risk borne by both debt and equity investors and cause them to demand higher returns. However, this does not necessarily mean that the overall WACC will increase, because more weight is put on the cost of debt, which is less than the cost of equity. In fact, if we ignore taxes, the overall cost of capital will stay constant as the frac- tions of debt and equity change. This is discussed further in Chapter 16.

Just think of the business as a very large project. Forecast the business’s operating cash flows (after-tax profits plus depreciation), and subtract the future investments in plant and equipment and in net working capital. The resulting free cash flows can then be discounted back to the present at the weighted-average cost of capital. Of course, the cash flows from a company may stretch far into the future. Financial managers therefore typically produce detailed cash flows only up to some horizon date and then estimate the remaining value of the business at the horizon.

How are the costs of debt and equity calculated? ( LO13-3 )

What happens when capital structure changes? ( LO13-4 )

Can WACC be used to value an entire business? ( LO13-5 )

L I S T I N G O F E Q UAT I O N S

13.1 WACC = cD V

× (1 - Tc)rdebt d + aEV × requityb

13.1a WACC = cD V

× (1 - Tc)rdebt d + aPV × rpreferredb + a E

V × requityb

13.2 requity = DIV1

P0 + g

13.3 rpreferred = dividend

price of preferred

QUESTIONS AND PROBLEMS 1. Capital Structure. In 2013 Caterpillar Inc. had about 648 million shares outstanding. Their

book value was $27 per share, and the market price was $83.50 per share. The company’s bal- ance sheet shows that the company had $25.7 billion of long-term debt, which was currently selling near par value. (LO13-1)

a. What was Caterpillar’s book debt-to-value ratio? b. What was its market debt-to-value ratio? c. Which of these two measures should you use to calculate the company’s cost of capital?

finance

®

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Chapter 13 The Weighted-Average Cost of Capital and Company Valuation 407

2. Capital Structure. Here is a simplified balance sheet for Epicure Pizza (figures in $ millions):

Assets Liabilities and

Shareholders’ Equity

Current assets 80 Current liabilities 60 Fixed assets 125 Long-term debt 65 Equity 80 Total 205 Total 205

Note: There are 16 million shares outstanding.

Epicure shares are currently priced at $12 each. (LO13-1)

a. You wish to calculate Epicure’s WACC. What is the relevant figure for the company’s debt ratio?

b. You now realize that since Epicure issued its debt, interest rates have fallen substantially. Do you need to revise your measure of the debt ratio upward or downward?

3. Cost of Debt. Olympic Sports has two issues of debt outstanding. One is a 9% coupon bond with a face value of $20 million, a maturity of 10 years, and a yield to maturity of 10%. The coupons are paid annually. The other bond issue has a maturity of 15 years, with coupons also paid annually, and a coupon rate of 10%. The face value of the issue is $25 million, and the issue sells for 94% of par value. The firm’s tax rate is 35%. (LO13-2)

a. What is the before-tax cost of debt for Olympic? b. What is Olympic’s after-tax cost of debt?

4. Cost of Equity. Bunkhouse Electronics is a recently incorporated firm that makes electronic entertainment systems. Its earnings and dividends have been growing at a rate of 30%, and the current dividend yield is 2%. Its beta is 1.2, the market risk premium is 8%, and the risk-free rate is 4%. (LO13-2)

a. Calculate two estimates of the firm’s cost of equity. b. Which estimate seems more reasonable to you? Why?

5. Cost of Debt. Micro Spinoffs Inc. issued 20-year debt a year ago at par value with a coupon rate of 8%, paid annually. Today, the debt is selling at $1,050. If the firm’s tax bracket is 35%, what is its percentage after-tax cost of debt? (LO13-2)

6. Cost of Preferred Stock. Pangbourne Whitchurch has preferred stock outstanding. The stock pays a dividend of $4 per share, and sells for $40. What is the percentage cost of the preferred stock? (LO13-2)

7. Cost of Equity. Reliable Electric is a regulated public utility, and it is expected to provide steady dividend growth of 5% per year for the indefinite future. Its last dividend was $5 per share; the stock sold for $60 per share just after the dividend was paid. What is the company’s percentage cost of equity? (LO13-2)

8. WACC. Here is some information about Stokenchurch Inc.: Beta of common stock = 1.2 Treasury bill rate = 4% Market risk premium = 7.5% Yield to maturity on long-term debt = 6% Book value of equity = $440  million Market value of equity = $880  million Long-term debt outstanding = $880  million Corporate tax rate = 35% What is the company’s WACC? (LO13-3)

9. WACC. Reactive Industries has the following capital structure. Its corporate tax rate is 35%. What is its WACC? (LO13-3)

Security Market Value Required Rate of Return

Debt $20 million 6% Preferred stock 10 million 8 Common stock 50 million 12

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408 Part Three Risk

10. WACC. The common stock of Buildwell Conservation & Construction Inc. (BCCI) has a beta of .9. The Treasury bill rate is 4%, and the market risk premium is estimated at 8%. BCCI’s capital structure is 30% debt, paying a 5% interest rate, and 70% equity. Buildwell pays tax at 40%. (LO13-3)

a. What is BCCI’s cost of equity capital? b. What is its WACC? c. If BCCI is presented with a project with an internal rate of return of 12%, should it accept

the project?

11. Calculating WACC. The total book value of WTC’s equity is $10 million, and book value per share is $20. The stock has a market-to-book ratio of 1.5, and the cost of equity is 15%. The firm’s bonds have a face value of $5 million and sell at a price of 110% of face value. The yield to maturity on the bonds is 9%, and the firm’s tax rate is 40%. Find the company’s WACC. (LO13-3)

12. WACC. Nodebt Inc. is a firm with all-equity financing. Its equity beta is .80. The Treasury bill rate is 4%, and the market risk premium is expected to be 10%. (LO13-3)

a. What is Nodebt’s asset beta? b. What is Nodebt’s WACC?

13. WACC. Look at the following book-value balance sheet for University Products Inc. The pre- ferred stock currently sells for $15 per share and pays a dividend of $2 a share. The common stock sells for $20 per share and has a beta of .8. There are 1 million common shares outstand- ing. The market risk premium is 10%, the risk-free rate is 6%, and the firm’s tax rate is 40%. (LO13-3)

BOOK-VALUE BALANCE SHEET (Figures in $ millions)

Assets Liabilities and Net Worth

Cash and short-term securities $ 1 Bonds, coupon = 8%, paid annually (maturity = 10 years, current yield

to maturity = 9%) $10 Accounts receivable 3 Preferred stock (par value $20 per

share) 2 Inventories 7 Common stock (par value $.10) 0.1 Plant and equipment 21 Additional paid-in stockholders’

equity 9.9 Retained earnings 10

Total $32 $32

a. What is the market debt-to-value ratio of the firm? b. What is University’s WACC?

14. Company versus Project Discount Rates. Geothermal’s WACC is 11.4%. Executive Fruit’s WACC is 12.3%. Now Executive Fruit is considering an investment in geothermal power production. (LO13-4)

a. Should it discount project cash flows at 12.3%? b. What would be a better discount rate for this investment?

15. Project Discount Rate. The total market value of Okefenokee Real Estate Company’s equity is $6 million, and the total value of its debt is $4 million. The treasurer estimates that the beta of the stock currently is 1.2 and that the expected risk premium on the market is 10%. The Trea- sury bill rate is 4%, and investors believe that Okefenokee’s debt is essentially free of default risk. (LO13-4)

a. What is the required rate of return on Okefenokee stock? b. Estimate the WACC assuming a tax rate of 40%. c. Estimate the discount rate for an expansion of the company’s present business. d. Suppose the company wants to diversify into the manufacture of rose-colored glasses. The

beta of optical manufacturers with no debt outstanding is 1.4. What is the required rate of return on Okefenokee’s new venture? (You should assume that the risky project will not enable the firm to issue any additional debt.)

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Chapter 13 The Weighted-Average Cost of Capital and Company Valuation 409

16. Project Discount Rate. Universal Foods has a debt-to-value ratio of 40%, its debt is currently selling on a yield of 6%, and its cost of equity is 12%. The corporate tax rate is 40%. The com- pany is now evaluating a new venture into home computer systems. The internal rate of return on this venture is estimated at 13.4%. WACCs of firms in the personal computer industry tend to average around 14%. (LO13-4)

a. What is Universal’s WACC? b. Will Universal make the correct decision if it discounts cash flows on the proposed venture

at the firm’s WACC? c. Should the new project be pursued?

17. Company Valuation. Icarus Airlines is proposing to go public, and you have been given the task of estimating the value of its equity. Management plans to maintain debt at 30% of the company’s present value, and you believe that at this capital structure the company’s debthold- ers will demand a return of 6% and stockholders will require 11%. The company is forecasting that next year’s operating cash flow (depreciation plus profit after tax at 40%) will be $68 mil- lion and that investment expenditures will be $30 million. Thereafter, operating cash flows and investment expenditures are forecast to grow in perpetuity by 4% a year. (LO13-5)

a. What is the total value of Icarus? b. What is the value of the company’s equity?

18. Company Valuation. You need to estimate the value of Laputa Aviation. You have the follow- ing forecasts (in millions of dollars) of its profits and of its future investments in new plant and working capital:

From year 5 onward, EBITDA, depreciation, and investment are expected to remain unchanged at year-4 levels. Laputa is financed 50% by equity and 50% by debt. Its cost of equity is 15%, its debt yields 7%, and it pays corporate tax at 40%. (LO13-5)

a. Estimate the company’s total value. b. What is the value of Laputa’s equity?

Year

1 2 3 4

Earnings before interest, taxes, depreciation, and amortization (EBITDA) 80 100 115 120 Depreciation 20 30 35 40 Pretax profi t 60 70 80 80 Tax at 40% 24 28 32 32 Investment 12 15 18 20

CHALLENGE PROBLEMS 19. Changes in Capital Structure. Look back at Section 13.4. Suppose Big Oil is excused from

paying taxes. It starts from the financing mix in Table 13.3 , and then borrows an additional $200 million from the bank. It then pays out a special $200 million dividend, leaving its assets and operations unchanged. What happens to Big Oil’s WACC, still assuming it pays no taxes? What happens to the cost of equity? (LO13-1)

20. Changes in Capital Structure. Look at our calculation of Big Oil’s WACC in Section 13.4. (LO13-2)

a. Suppose Big Oil is excused from paying taxes. What would be its WACC? b. Now suppose that, after the tax rate has fallen to zero, Big Oil makes a large stock issue and

uses the proceeds to pay off all its debt. What would be the cost of equity after the issue?

21. Interpreting WACC. An analyst at Dawn Chemical notes that its cost of debt is far below that of equity. He concludes that it is important for the firm to maintain the ability to increase its borrowing because if it cannot borrow, it will be forced to use more expensive equity to finance some projects. This might lead it to reject some projects that would have seemed attractive if evaluated at the lower cost of debt. Comment on this reasoning. (LO13-4)

Templates can be found in Connect.

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410 Part Three Risk

22. WACC and Taxes. “The after-tax cost of debt is lower when the firm’s tax rate is higher; there- fore, the WACC falls when the tax rate rises. Thus, with a lower discount rate, the firm must be worth more if its tax rate is higher.” Explain why this argument is wrong. (LO13-5)

WEB EXERCISE 1. Estimate the weighted-average cost of capital for Home Depot, Altria, Caterpillar, Intel, and

Du Pont. You can estimate the expected stock returns for these companies by using the betas shown on finance.yahoo.com . You can also use Yahoo! Finance to find the relative proportions of equity and debt for each company. Remember, though, to use the market value of the equity, not its book value. Finding the yield on the debt is a little trickier. One possibility it to log on to www.bondsonline.com to find the current level of Treasury yields and the yield spreads (i.e., the extra yield for bonds with different ratings). An alternative is to look at the yields shown in the bonds section of Yahoo! Finance. Note: As we write this, Moody’s ratings for the five com- panies vary from Baa for Altria, to A for Home Depot, Caterpillar, Intel, and Du Pont.

SOLUTIONS TO SELF-TEST QUESTIONS 13.1 Hot Rocks’ 4 million common shares are worth $40 million. Its market-value balance sheet is:

Assets Liabilities and Shareholders’ Equity

Assets $90 Debt $50 (56%) Equity 40 (44%)

Value $90 Value $90

WACC = (.56 × 9%) + (.44 × 17%) = 12.5%

We use Hot Rocks’ pretax return on debt because the company pays no taxes.

13.2 Burg’s 6 million shares are now worth only 6  million × $4 = $24 million. The debt is selling for 80% of book, or $20 million. The market-value balance sheet is:

Assets Liabilities and Shareholders’ Equity

Assets $44 Debt $20 (45%) Equity 24 (55%)

Value $44 Value $44

WACC = (.45 × 14%) + (.55 × 20%) = 17.3%

Note that this question ignores taxes.

13.3 Compare the two income statements, one for Criss-Cross Industries and the other for a firm with identical EBIT but no debt in its capital structure. (All figures in millions.)

Criss-Cross Firm with No Debt

EBIT $10.0 $10.0 Interest expense 2.0 0.0 Taxable income 8.0 10.0 Taxes owed 2.8 3.5 Net income 5.2 6.5 Total income accruing to debt- & equityholders 7.2 6.5

Notice that Criss-Cross pays $.7 million less in taxes than its debt-free counterpart. Accord- ingly, the total income available to debt- plus equityholders is $.7 million higher.

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Chapter 13 The Weighted-Average Cost of Capital and Company Valuation 411

13.4 For Hot Rocks,

WACC = 3.56 × 9 × (1 - .35) 4 + (.44 × 17) = 10.8% For Burg Associates,

WACC = 3.45 × 14 × (1 - .35) 4 + (.55 × 20) = 15.1% 13.5 WACC measures the expected rate of return demanded by debt and equity investors in the

firm (plus a tax adjustment capturing the tax-deductibility of interest payments). Thus the calculation must be based on what investors are actually paying for the firm’s debt and equity securities. In other words, it must be based on market values.

13.6 From the CAPM:

requity = rf + bequity(rm - rf)

= 6% + 1.20(7.6%) = 15.1%

WACC = .3(1 - .35)8% + .7(15.1%) = 12.13%

13.7 Jo Ann’s boss is wrong. The ability to borrow at 8% does not mean that the cost of capital is 8%. The firm could not finance a stand-alone project with 8% debt. This analysis ignores the side effects of the borrowing, for example, that at the higher indebtedness of the firm the equity will be riskier and, therefore, the equityholders will demand a higher rate of return on their investment.

13.8 Estimated horizon value for the concatenator business is 15 × year-5 EBITDA = 15 × 342.8 = $5,142 thousand. PV (horizon value) is $5,142/(1.085) 5 = $3,149.7 thousand. Adding in the PV of free cash flows for years 1 to 5 gives a present value for the business of $3,344.9 thousand.

MINICASE Bernice Mountaindog was glad to be back at Sea Shore Salt. Employees were treated well. When she had asked a year ago for a leave of absence to complete her degree in finance, top man- agement promptly agreed. When she returned with an honors degree, she was promoted from administrative assistant (she had been secretary to Joe-Bob Brinepool, the president) to treasury analyst.

Bernice thought the company’s prospects were good. Sure, table salt was a mature business, but Sea Shore Salt had grown steadily at the expense of its less well known competitors. The company’s brand name was an important advantage, despite the difficulty most customers had in pronouncing it rapidly.

Bernice started work on January 2, 2014. The first 2 weeks went smoothly. Then Mr. Brinepool’s cost of capital memo (see Figure  13.2 ) assigned her to explain Sea Shore Salt’s weighted- average cost of capital to other managers. The memo came as a surprise to Bernice, so she stayed late to prepare for the questions that would surely come the next day.

Bernice first examined Sea Shore Salt’s most recent balance sheet, summarized in Table 13.6 . Then she jotted down the follow- ing additional points:

• The company’s bank charged interest at current market rates, and the long-term debt had just been issued. Book and market values could not differ by much.

• But the preferred stock had been issued 35 years ago, when interest rates were much lower. The preferred stock, originally issued at a book value of $100 per share, was now trading for only $70 per share.

• The common stock traded for $40 per share. Next year’s earnings per share would be about $4 and dividends per share probably $2. (Ten million shares of common stock are outstanding.) Sea Shore Salt had traditionally paid out 50% of earnings as dividends and plowed back the rest.

• Earnings and dividends had grown steadily at 6% to 7% per year, in line with the company’s sustainable growth rate:

Sustainable growth rate =

return on equity ×

plowback ratio

= 4/30 × .5

= .067, or 6.7%

Sea Shore Salt’s beta had averaged about .5, which made sense, Bernice thought, for a stable, steady-growth business. She made a quick cost of equity calculation by using the capital asset pricing model (CAPM). With current interest rates of about 7%, and a mar- ket risk premium of 7%,

CAPM cost of equity = rE = rf + b(rm - rf)

= 7% + .5(7%) = 10.5%

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412 Part Three Risk

FIGURE 13.2 Mr. Brinepool’s cost of capital memo

The rates of return on the bank loan and bond issue are of course just the interest rates we pay. However, interest is tax-deductible, so the after-tax interest rates are lower than shown above. For example, the after-tax cost of our bank financing, given our 35% tax rate, is 8(1 - .35) = 5.2%.

The rate of return on preferred stock is 6%. Sea Shore Salt pays a $6 dividend on each $100 preferred share.

Our target rate of return on equity has been 16% for many years. I know that some newcomers think this target is too high for the safe and mature salt business. But we must all aspire to superior profitability.

Once this background is absorbed, the calculation of Sea Shore Salt's weighted-average cost of capital (WACC) is elementary:

WACC = 8(1 - .35)(.20) + 7.75(1 - .35)(.133) + 6(.167) + 16(.50) = 10.7%

The official corporate hurdle rate is therefore 10.7%.

If you have further questions about these calculations, please direct them to our new Treasury Analyst, Ms. Bernice Mountaindog. It is a pleasure to have Bernice back at Sea Shore Salt after a year's leave of absence to complete her degree in finance.

This memo states and clarifies our company's long-standing policy regarding hurdle rates for capital investment decisions. There have been many recent questions, and some evident confusion, on this matter.

Sea Shore Salt evaluates replacement and expansion investments by discounted cash flow. The discount or hurdle rate is the company's after-tax weighted-average cost of capital.

The weighted-average cost of capital is simply a blend of the rates of return expected by investors in our company. These investors include banks, bondholders, and preferred stock investors in addition to common stockholders. Of course many of you are, or soon will be, stockholders of our company.

The following table summarizes the composition of Sea Shore Salt's financing.

Sea Shore Salt Company Spring Vacation Beach, Florida

CONFIDENTIAL MEMORANDUM

DATE: January 15, 2014 TO: S.S.S. Management FROM: Joe-Bob Brinepool, President SUBJECT: Cost of Capital

Amount (in millions) Percent of Total Rate of Return

Bank loan $120 20% 8% Bond issue 80 13.3 7.75 Preferred stock 100 16.7 6 Common stock 300 50 16

$600 100%

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Chapter 13 The Weighted-Average Cost of Capital and Company Valuation 413

This cost of equity was significantly less than the 16% decreed in Mr. Brinepool’s memo. Bernice scanned her notes apprehen- sively. What if Mr. Brinepool’s cost of equity was wrong? Was there some other way to estimate the cost of equity as a check on the CAPM calculation? Could there be other errors in his calculations?

Bernice resolved to complete her analysis that night. If neces- sary, she would try to speak with Mr. Brinepool when he arrived at his office the next morning. Her job was not just finding the right number. She also had to figure out how to explain it all to Mr. Brinepool.

TABLE 13.6 Sea Shore Salt’s balance sheet, taken from the company’s 2013 balance sheet (figures in $millions)

Assets Liabilities and Net Worth

Working capital $200 Bank loan $120

Plant and equipment 360 Long-term debt 80 Other assets 40 Preferred stock 100

Common stock, including retained earnings 300 Total $600 Total $600

Notes: 1. At year-end 2013, Sea Shore Salt had 10 million common shares outstanding. 2. The company had also issued 1 million preferred shares with book value of $100 per share. Each share receives

an annual dividend of $6.

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414

Introduction to Corporate Financing

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

14-1 Explain why managers should assume that the securities they issue are fairly priced.

14-2 Summarize the changing ways that U.S. firms have financed their growth.

14-3 Interpret shareholder equity accounts in the firm’s financial statements.

14-4 Describe voting procedures for the election of a firm’s board of directors and other matters.

14-5 Describe the major classes of securities sold by the firm.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

14 CHAPTE R

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415

P A

R T

F O

U R

U p to this point we have concentrated almost exclusively on the firm’s capital expenditure decisions. Now we move to the other side of the balance sheet to look at how the firm can finance

those capital expenditures. To put it crudely, you have

learned how to spend money; now you must learn

how to raise it. In the next few chapters, therefore, we

assume that the firm has already decided on which

investment projects to accept, and we focus on the

best way to finance these projects.

You will find that in some ways financing decisions

are more complicated than investment decisions.

You’ll need to learn about the wide variety of securi-

ties that companies can issue. But there are also ways

in which financing decisions are easier than invest-

ment decisions. For example, financing decisions do

not have the same degree of finality as investment

decisions. When Ford Motor Company decides to

issue a bond, it knows that it can buy it back later if

second thoughts arise. It would be far more difficult

for Ford to dismantle or sell an auto factory that is no

longer needed.

In later chapters we will look at some of the clas-

sic finance problems, such as how much firms should

borrow and what dividends they should pay their

shareholders. In this chapter we set the scene with a

brief overview of the types of long-term finance.

We begin our discussion of financing with a basic

conceptual point. It is easier to make shareholders

wealthier through your investment decisions than by

your financing decisions. As we explain, competition

between investors makes it difficult to find misvalued

securities.

We then introduce you to the principal sources

of finance, and we show how they are used by cor-

porations. It is customary to classify these sources of

finance as debt or equity. However, we will see that a

simple division of sources of finance into debt and

equity would miss the enormous variety of financing

instruments that companies use today.

Fi n

a n

c in

g

GM and Chrysler went bankrupt, but Ford managed to raise and keep enough financing to survive the recent financial crisis and recession. It’s time to start learning about financing.

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416 Part Four Financing

14.1 Creating Value with Financing Decisions Smart investment decisions make shareholders wealthier. So do smart financing deci- sions. For example, if your company can borrow at 3% when the going rate is 4%, you have done your shareholders a good turn.

Unfortunately, this is more easily said than done. The problem is that competition in financial markets is more intense than in most product markets. In product mar- kets, companies regularly find competitive advantages that allow positive-NPV invest- ments. For example, a company may have only a few competitors that specialize in the same line of business in the same geographic area. Or it may be able to capitalize on patents or technology or on customer recognition and loyalty. All this opens up the opportunity to make superior profits and find projects with positive NPVs.

But there are few protected niches in financial markets. You can’t patent the design of a new security. Moreover, in these markets you always face fast-moving competi- tion, including all the other corporations seeking funds, to say nothing of the state, local, and federal governments, financial institutions, individuals, and foreign firms and governments that also come to New York, London, or Tokyo for financing. The investors who supply financing are numerous, and they are smart. Most likely, these investors can assess values of securities at least as well as you can.

Of course, when you borrow, you would like to pay less than the going rate of interest. But if the loan is a good deal for your shareholders, it must be a bad deal for the lenders. So what are the chances that your firm could consistently trick investors into overpaying for its securities? Pretty slim. In general, firms should assume that financing will be raised on fair terms—in other words, that the securities they issue sell for their true values.

But what do we mean by true value? It is a potentially slippery phrase. True value does not mean ultimate future value—we do not expect investors to be fortune-tellers. It means a price that incorporates all the information currently available to investors. We came across this idea in Chapter 7, when we introduced the concept of efficient capital markets and showed how difficult it is for investors to obtain consistently supe- rior performance. In an efficient capital market all securities are fairly priced given the information available to investors. In that case the sale of securities at their market price can never be a positive-NPV transaction.

All this means that it’s harder to make or lose money by smart or stupid financing strategies. It is difficult to make money—that is, to find cheap financing—because the investors who supply the financing demand fair terms. At the same time, it’s harder to lose money because competition among investors prevents any one of them from demanding more than fair terms.

Just remember as you read the following chapters: There are few free lunches on Wall Street .  .  . and few easy answers for the financial manager who must make corporate financing decisions.

14.2 Patterns of Corporate Financing Firms have three broad sources of cash: They can plow back part of their profits, or they can raise money from external sources by an issue of either shares or debt. Look, for example, at Figure 14.1 , which shows how FedEx and Dow Chemical have gen- erated cash. In each panel the green line shows the percentage yearly addition to the firm’s capital that was provided by the sale of shares. The orange line shows the addi- tion that came from new issues of long- or short-term debt, and the blue line shows the contribution from internally generated funds (defined as depreciation plus earnings that are not paid out as dividends 1 ).

1  Remember that depreciation is a noncash expense. This means that it is treated as an expense even though it does not represent a use of cash. Therefore, we add it back to earnings to find the cash flow generated by the firm.

internally generated funds Cash reinvested in the firm: depreciation plus earnings not paid out as dividends.

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Chapter 14 Introduction to Corporate Financing 417

There are both some similarities and some differences in our two examples. Let’s start with the similarities. By far the largest source of cash for both companies came from plowing back profits. The gap between this internally generated cash and the cash that the company needs is called the financial deficit . To make up the deficit, the company must either sell new equity or borrow. Neither FedEx nor Dow raised signifi- cant amounts of cash by selling new shares. In fact, as often as not they used cash to buy back shares that had been issued in earlier years. In Figure 14.1 these repurchases show up as negative issues of common stock. (Dow did make an issue of preferred stock in 2009. This is not shown in Figure 14.1 .).

financial deficit Difference between the cash companies need and the amount generated internally.

FIGURE 14.1 Sources of funds for FedEx and Dow Chemical

S o

u rc

es o

f fu

n d

s ($

m ill

io n

s)

Year

(a) FedEx

-2,000

-1,000

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Internally generated

Net common stock issues

Net debt issues

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(b) Dow Chemical

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Internally generated

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Net debt issues

Year

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418 Part Four Financing

Instead of issuing equity, both companies have made occasional large new issues of debt, but they have done so for somewhat different reasons. For example, FedEx bought Kinko’s in early 2004 for $2.4 billion in cash. To help prepare for this pur- chase, FedEx sold $1.9 billion of short-term debt, called commercial paper, at the end of 2003. It then issued a package of 1-, 3-, and 5-year unsecured notes and used the proceeds to pay off the commercial paper. Much of this increased borrowing was also subsequently repaid over the next 4 years. Figure 14.1 a shows the spike in FedEx’s debt issuance in 2003 as well as the negative net debt issues in subsequent years.

FedEx’s debt issue was needed to offset a temporary increase in expenditures. In contrast, Dow Chemical’s large debt issues in 2002 and 2009 coincided with a period of operating losses. Thus, the debt issues in those years largely substituted for internal funds.

Figure 14.2 shows the net effect of these financing decisions on the debt ratios of the two companies. Debt ratios here are measured in two ways: using the book value of the equity or its market value. For most of this period FedEx’s steady accumulation of internal funds resulted in a fairly continuous decline in the debt ratio. By contrast, Dow’s periodic large issues of debt to make up for shortfalls in profitability left it with much higher debt ratios.

There is nothing particularly remarkable about the financial structure of either FedEx or Dow. Some companies, such as Google, rely almost entirely on internal

FIGURE 14.2 Ratio of debt to debt plus equity for FedEx and Dow Chemical

(a) FedEx

Year

(b) Dow Chemical

0

10

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60

70

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D eb

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( %

)

Ratio computed using market values

Ratio computed using book values

Year

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Chapter 14 Introduction to Corporate Financing 419

funds and have no debt. Others, such as Marriott, are at the opposite extreme. Mar- riott has $2.5 billion of long-term debt, and the book value of its equity is negative at − $1.3 billion. 2

Figure 14.3 shows how corporate America as a whole has financed its investments. Notice again the importance of internal funds. Over the 18-year period, internally gen- erated cash covered 92% of corporate capital requirements. The gap was more than made up by borrowing. 3 Equity issues in each year were negative; firms used some of their new cash to buy back stock.

Are Firms Issuing Too Much Debt? We have seen that rather than sell additional common stock, firms have on average issued debt and used part of the proceeds to buy back some of their stock. Has this policy resulted in an increase in the proportion of debt that companies use?

Figure 14.4 provides some long-term perspective on the question. If all U.S. manu- facturing corporations were merged into a single gigantic firm, this would be its ratio of debt to total capital. Debt ratios are lower when computed from market rather than book values. This is because the market value of equity is substantially greater than book value for most firms. Debt ratios using either measure increased until about 1990, but since then they have largely jiggled around with no strong upward or down- ward trend. 4

Should we be worried that book debt ratios are higher today than they were 50 years ago? It is true that high debt ratios mean that more companies are likely to fall into financial distress when a serious recession hits the economy. Undoubtedly GM, Chrysler, American Airlines, and the many other companies that faced insolvency in the recent recession would all have been in a stronger position if they had carried less debt. But it does not always follow that less risk is better. Finding the optimal debt ratio is like finding the optimal speed limit; we can agree that accidents at 30 miles per

2  In other words, Marriott’s accumulated losses exceed the total cumulative amount that it has raised from shareholders. 3  The type of debt that firms use varies from year to year. For example, in 2009 the financial crisis led firms to repay bank debt and to issue instead huge amounts of corporate bonds. These variations do not show up in Figure 14.3 . 4  The rise in debt ratios in the first part of the period was not due to stock repurchases, since these were rela- tively uncommon until the mid-1980s.

FIGURE 14.3 Sources of funds for U.S. nonfinancial corporations, 1995–2012

Year

Internal funds Net equity issues Debt issues

-100

-50

0

50

100

150

1 9

9 5

1 9

9 7

1 9

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2 0

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P er

ce n

t o

f to

ta l s

o u

rc es

Source: Board of Governors of the Federal Reserve System, Division of Research and Statistics, “Financial Accounts of the United States,” Table F.102, at www.federalreserve.gov/releases/z1/current/data.htm .

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420 Part Four Financing

hour are less dangerous, other things being equal, than accidents at 60 miles per hour, but we do not therefore set the national speed limit at 30. Speed has benefits as well as risks. So does debt, as we will see in Chapter 16.

a. Which of the following sources of financing is most important for U.S. cor- porations as a whole: internal funds, net new borrowing, or stock issues?

b. Figure 14.3 indicates that net equity issues are negative for U.S. corpora- tions as a whole. How is that possible? Don’t U.S. corporations ever issue common stock?

Self-Test 14.1

FIGURE 14.4 The ratio of debt to debt plus equity for the nonfinancial corporate sector

0

10

20

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60

19 55

19 57

19 59

19 61

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D eb

t ra

ti o

( %

)

Market debt ratio Book debt ratio

Year

Source: Board of Governors of the Federal Reserve System, Division of Research and Statistics, “Financial Accounts of the United States,” Table B.102 at www.federalreserve.gov/releases/z1/current/data.htm .

14.3 Common Stock We will now look more closely at the different sources of finance, starting with com- mon stock. We will stick with our example of Dow Chemical.

Most major corporations are far too large to be owned by one investor. For example, you would need to lay your hands on nearly $47 billion if you wanted to own the whole of Dow. Dow is owned by about 580,000 different investors, each of whom holds a number of shares of common stock. These investors are therefore known as shareholders, or stockholders. At the end of 2012 Dow had outstanding 1,203 billion shares of common stock. Thus, if you were to buy one Dow share, you would own 1/1,203,000,000, or about .00000008%, of the company. Of course, a large pension fund might hold many thousands of Dow shares.

The 1.203 billion shares held by investors are the only shares that have been issued by Dow, but many companies have issued more shares that they later bought back from investors. These repurchased shares are held in the company’s treasury and are known as treasury stock . The shares held by investors are said to be issued and outstanding shares . By contrast, treasury shares are said to be issued but not outstanding. 5

5  Dow bought back shares from investors in the past, but by 2012 it had resold all these treasury shares to inves- tors. There were no shares left in the company’s treasury.

treasury stock Stock that has been repurchased by the company and is held in its treasury.

issued shares Shares that have been issued by the company.

outstanding shares Shares that have been issued by the company and are held by investors.

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Chapter 14 Introduction to Corporate Financing 421

If Dow wishes to raise more money, it can sell more shares. However, there is a limit to the number that it can issue without the approval of the current sharehold- ers. The maximum number of shares that can be issued is known as the authorized share capital —for Dow, this is 1.5 billion shares. Since Dow has already issued 1.203 billion shares, it can issue nearly 300 million more without shareholders’ approval.

Table 14.1 shows how the investment by Dow’s common stockholders is recorded in the company’s books. The price at which each share is recorded is known as its par value . In Dow’s case each share has a par value of $2.50. Thus the total par value of the issued shares is 1.203 billion shares  ×  $2.50 per share  =  $3.008 billion. Par value has little economic significance. 6

The price at which new shares are sold to investors almost always exceeds par value. The difference is entered into the company’s accounts as additional paid-in capital , or capital surplus. For example, if Dow sold an additional 1 million shares at $30 a share, the par value of the common stock would increase by 1 million  ×  $2.50  =   $2.5 million and additional paid-in capital would increase by 1  million  ×  ($30  −  $2.50)  =   $27.5 million. You can see from this example that the funds raised from the stock issue are divided between par value and additional paid-in capital. Since the choice of par value in the first place was immaterial, so is the allocation between par value and additional paid-in capital.

Besides buying new stock, shareholders also indirectly contribute new capital to the firm whenever profits that could be paid out as dividends are instead plowed back into the company. Table 14.1 shows that retained earnings , the cumulative value of such reinvested profits, are $18.495 billion.

Any money that Dow spent to buy Treasury stock would also be shown on the bal- ance sheet. Such money has been returned to stockholders and is therefore deducted from the stockholders’ equity.

The sum of the par value, additional paid-in capital, and retained earnings, less repurchased stock and some miscellaneous other adjustments, is known as the net common equity of the firm. It equals the total amount contributed directly by share- holders when the firm issued new stock and indirectly when it plowed back part of its earnings. The book value of Dow’s net common equity is $16.877 billion. With 1.203 billion shares outstanding this is equivalent to 16.877/1.203  =  $14.03 a share. But the market value of Dow’s stock is nearly $39, much higher than its book value. Evidently investors believe that Dow’s assets are worth much more than they origi- nally cost.

authorized share capital Maximum number of shares that the company is permitted to issue.

6  Some companies issue shares with no par value, in which case the stock is listed in the accounts at an arbi- trarily determined figure.

par value Value of security shown in the company’s accounts.

additional paid-in capital Difference between issue price and par value of stock. Also called capital surplus.

retained earnings Cumulative value of reinvested profits.

Common shares ($2.50 par value per share) $ 3,008 Additional paid-in capital 3,281 Retained earnings 18,495 Treasury shares at cost — Other (7,907) Net common equity 16,877 Note: Authorized shares 1,500 Issued shares, of which 1,203 Outstanding shares 1,203 Treasury shares 0

TABLE 14.1 Book value of common stockholders’ equity of Dow Chemical, December 31, 2012 (figures in $ millions)

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422 Part Four Financing

Ownership of the Corporation A corporation is owned by its common stockholders. As we saw in Chapter 2, over 40% of the stock is held by individual U.S. investors and nonprofit organizations. The remainder belongs to financial institutions such as mutual funds, pension funds, and insurance companies. Their holdings are summarized again in Figure 14.5 .

What do we mean when we say that the stockholders own the corporation? First, the stockholders are entitled to whatever profits are left over after the lenders have received their due. Usually the company pays out part of these profits as dividends and plows back the remainder into new investments. Shareholders hope that these invest- ments will enable the company to earn higher profits and pay higher dividends in the future.

Second, shareholders have the ultimate control over how the company is run. This does not mean that shareholders can do whatever they like. For example, the bank that lends to the company may place restrictions on how much extra borrowing the company can undertake. However, the contract with the bank can never restrict all the actions that the company might wish to undertake. The shareholders retain the residual rights of control over these decisions.

Generic Products has had one stock issue in which it sold 100,000 shares to the public at $15 per share. Can you fill in the following table?

Self-Test 14.2

Common shares ($1 par value per share) _________ Additional paid-in capital _________ Retained earnings _________ Net common equity $4,500,000

FIGURE 14.5 Holdings of corporate equities, December 31, 2012

Source: Board of Governors of the Federal Reserve System, Division of Research and Statistics, “Financial Accounts of the United States,” Table L.213, at www.federalreserve.gov/releases/z1/current/data.htm .

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Chapter 14 Introduction to Corporate Financing 423

Occasionally, the company must get shareholder approval before it can take certain actions. For example, it needs shareholder agreement to increase the authorized capital or to merge with another company. On most other matters, shareholder control boils down to the right to vote on appointments to the board of directors.

The board of directors is supposed to represent the shareholders’ interests. The board appoints and oversees management and must vote to approve important finan- cial decisions, including major capital investments, payment of dividends, share repur- chase programs, and new stock issues.

For public companies, the board usually includes the CEO, perhaps one or two other members of top management, and outside directors, who are not employees. The New York and NASDAQ stock exchanges require that a majority of the board consist of independent outside directors. Independent directors have “no material relation- ship” with the company aside from their service as directors and their ownership of the company’s shares. The board compensation committee, which approves compensation for managers, must be entirely composed of independent directors.

The CEO has traditionally also served as the chair of the board. The chair has extra influence, since he or she can set the agenda, which guides the board’s deliberations. Some companies appoint a nonexecutive chair, thus separating the roles of chair and CEO and reducing the CEO’s influence. Nonexecutive chairs are common in some other countries, including Canada and the United Kingdom.

Voting Procedures For many U.S. companies, the entire board of directors comes up for reelection every year. However, approximately 50% of large companies have classified boards, in which only one-third of the directors come up for reelection each year. Share- holder activists complain that such staggered elections make it more difficult for a dissident group of shareholders to replace the board and therefore help to entrench management. Staggered elections appear to protect management, deter proxy con- tests, and reduce the degree to which CEO compensation is linked to firm perfor- mance. In recent years many companies have been pressured by their shareholders to declassify their boards; declassification has generally resulted in an increase in stock price.

In most companies stockholders elect directors by a system of majority voting . In this case each director is voted on separately, and stockholders can cast one vote for each share they own. In some companies directors are elected by cumulative voting . The directors are then voted on jointly, and the stockholders can, if they choose, cast all their votes for just one candidate. For example, suppose that there are five directors to be elected and you own 100 shares. You therefore have a total of 5  ×  100  =  500 votes. Under majority voting you can cast a maximum of 100 votes for any one can- didate. With a cumulative voting system you can cast all 500 votes for your favorite candidate. Cumulative voting makes it easier for a minority group of the stockholders to elect a director to represent their interests. That is why minority groups devote so much effort to campaigning for cumulative voting.

On many issues a simple majority of the votes cast is enough to carry the day, but there are some decisions that require a “supermajority” of, say, 75% of those eligible to vote. For example, a supermajority vote is sometimes needed to approve a merger. This makes it difficult for the firm to be taken over and therefore helps to protect the incumbent management.

Shareholders can either vote in person or appoint a proxy to vote. The issues on which they are asked to vote are rarely contested, particularly in the case of large pub- licly traded firms. Occasionally, however, there are proxy contests in which outsiders compete with the firm’s existing management and directors for control of the corpora- tion. But the odds are stacked against the outsiders, for the insiders can get the firm to pay all the costs of presenting their case and obtaining votes.

majority voting Voting system in which each director is voted on separately.

cumulative voting Voting system in which all votes that one shareholder is allowed to cast can be cast for one candidate for the board of directors.

proxy contest Takeover attempt in which outsiders compete with management for shareholders’ votes.

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424 Part Four Financing

Classes of Stock Most companies in the United States issue just one class of common stock. But a few, such as Ford Motor and Google, have issued two classes of shares with different voting rights. For example, suppose that a firm needs fresh capital, but its management does not want to give up its controlling interest. The existing shares could be labeled “class A,” and then “class B” shares with limited voting rights could be issued to outside investors.

In some countries it is fairly common for firms to issue two classes of stock with different voting rights. That may be a good thing if the controlling shareholders then use their influence to improve profitability. However, you can see the dangers here. If an idle or incompetent management has a large block of votes, it may use these votes to stay in control. Or if another corporation has a controlling stake, it may exercise its influence to gain a business advantage.

14.4 Preferred Stock Usually when investors talk about equity or stock, they are referring to common stock. But Dow Chemical has also issued 4 million shares of preferred stock , and this too is part of the company’s equity. The sum of Dow’s common equity and preferred stock is known as its net worth .

For most companies preferred stock is much less important than common stock. However, it can be a useful method of financing in mergers and certain other special situations.

Like debt, preferred stock promises a series of fixed payments to the investor, and with relatively few exceptions preferred dividends are paid in full and on time. Nev- ertheless, preferred stock is legally an equity security. This is because payment of a preferred dividend is within the discretion of the directors. The only obligation is that no dividends can be paid on the common stock until the preferred dividend has been paid. 7 If the company goes out of business, the preferred stockholders get in the queue after the debtholders but before the common stockholders.

Preferred stock rarely confers full voting privileges. This is an advantage to firms that want to raise new money without sharing control of the firm with the new share- holders. However, if there is any matter that affects their place in the queue, preferred stockholders usually get to vote on it. Most issues also provide the holder with some voting power if the preferred dividend is skipped.

Companies cannot deduct preferred dividends when they calculate taxable income. Like common stock dividends, preferred dividends are paid from after-tax income. For most industrial firms this is a serious deterrent to issuing preferred. However, regulated public utilities can take tax payments into account when they negotiate with regulators the rates they charge customers. So they can effectively pass the tax disadvantage of preferred on to the consumer. Preferred stock also has a particular attraction for banks, for regulators allow banks to lump preferred in with common stock when calculating whether they have sufficient equity capital.

Preferred stock does have one tax advantage. If one corporation buys another’s stock, only 30% of the dividends it receives is taxed. This rule applies to dividends on both common and preferred stock, but it is most important for preferred, for which returns are dominated by dividends rather than capital gains.

Suppose that your firm has surplus cash to invest. If it buys a bond, the interest will be taxed at the company’s tax rate of 35%. If it buys a preferred share, it owns an asset like a bond (the preferred dividends can be viewed as “interest”), but the effective tax rate is only 30% of 35%, .30  ×  .35  =  .105, or 10.5%. It is no surprise that most pre- ferred shares are held by corporations.

preferred stock Stock that takes priority over common stock in regard to dividends.

net worth Book value of common stockholders’ equity plus preferred stock.

7  These days this obligation is usually cumulative. In other words, before the common stockholders get a cent, the firm must pay any preferred dividends that have been missed in the past.

Alibaba and dual-class shares

BEYOND THE PAGE

brealey.mhhe.com/ch14-01

Voting rights and private benefits

BEYOND THE PAGE

brealey.mhhe.com/ch14-02

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Chapter 14 Introduction to Corporate Financing 425

If you invest your firm’s spare cash in a preferred stock, you will want to make sure that when it is time to sell the stock, it won’t have plummeted in value. One problem with garden-variety preferred stock that pays a fixed dividend is that the preferred’s market prices go up and down as interest rates change (because present values fall when rates rise). So one ingenious banker thought up a wrinkle: Why not link the divi- dend on the preferred stock to interest rates so that it goes up when interest rates rise and vice versa? The result is known as floating-rate preferred . If you own floating- rate preferred, you know that any change in interest rates will be counterbalanced by a change in the dividend payment, so the value of your investment is protected.

floating-rate preferred Preferred stock paying dividends that vary with short-term interest rates.

A company in a 35% tax bracket can buy a bond yielding 10% or a preferred stock of the same firm that is priced to yield 8%. Which will provide the higher after-tax yield?

Self-Test 14.3

14.5 Corporate Debt When they borrow money, companies promise to make regular interest payments and to repay the principal (that is, the original amount borrowed). However, corporations have limited liability. By this we mean that the promise to repay the debt is not always kept. If the company gets into deep water, the company has the right to default on the debt and to hand over its assets to the lenders.

Clearly it will choose bankruptcy only if the value of the assets is less than the amount of the debt. In practice, when companies go bankrupt, this handover of assets is far from straightforward. For example, when Lehman Brothers filed for bankruptcy, the bankruptcy court was faced with 65,000 claims from creditors. The cost of shep- herding Lehman through bankruptcy will exceed $2 billion.

Because lenders are not regarded as owners of the firm, they don’t normally have any voting power. Also, the company’s payments of interest are regarded as a cost and are therefore deducted from taxable income. Thus interest is paid out of before-tax income, whereas dividends on common and preferred stock are paid out of after-tax income. This means that the government provides a tax subsidy on the use of debt, which it does not provide on stock. We cover debt and taxes in Chapter 16.

Debt Comes in Many Forms Some orderly scheme of classification is essential to cope with the almost endless vari- ety of debt issues. We will walk you through the major distinguishing characteristics.

Interest Rate The interest payment, or coupon, on most long-term loans is fixed at the time of issue. If a $1,000 bond is issued with a coupon of 10%, the firm continues to pay $100 a year regardless of how interest rates change. You may also encounter zero-coupon bonds. In this case the firm does not make a regular interest payment. It just makes a single payment at maturity. Obviously, investors pay less for zero-coupon bonds.

Most loans from a bank and some long-term loans carry a floating interest rate. For example, your firm may be offered a loan at “1 percent over prime.” The prime rate is the benchmark interest rate charged by banks to large customers with good to excellent credit. (But the largest and most creditworthy corporations can, and do, borrow at less than prime.) The prime rate is adjusted up and down with the general level of interest rates. When the prime rate changes, the interest on your floating-rate loan also changes.

prime rate Benchmark interest rate charged by banks.

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426 Part Four Financing

Floating-rate loans are not always tied to the prime rate. Often they are tied to the rate at which international banks lend to one another. This is known as the London Interbank Offered Rate, or LIBOR.

Would you expect the price of a 10-year floating-rate bond to be more or less sensitive to changes in interest rates than the price of a 10-year maturity fixed-rate bond?

Self-Test 14.4

Maturity Funded debt is any debt repayable more than 1 year from the date of issue. Debt due in less than a year is termed unfunded and is carried on the balance sheet as a current liability. Unfunded debt is often described as short-term debt, and funded debt is described as long-term, although it is clearly artificial to call a 364-day debt short-term and a 366-day debt long-term (except in leap years).

There are corporate bonds of nearly every conceivable maturity. For example, in 2014, the French utility company EDF issued bonds that do not mature for 100 years. Some British banks have issued perpetuities—that is, bonds which may survive for- ever. At the other extreme we find firms borrowing literally overnight.

Repayment Provisions Long-term loans are commonly repaid in a steady, regular way, perhaps after an initial grace period. For bonds that are publicly traded, this is done by means of a sinking fund . Each year the firm puts aside a sum of cash into a sinking fund that is then used to buy back the bonds. When there is a sinking fund, investors are prepared to lend at a lower rate of interest. They know that they are more likely to be repaid if the company sets aside some cash each year than if the entire loan has to be repaid on one specified day.

Suppose that a company issues a 6%, 30-year bond at a price of $1,000. Five years later interest rates have fallen to 4%, and the price of the bond has risen dramatically. If you were the company’s treasurer, wouldn’t you like to be able to retire the bonds and issue some new bonds at the lower interest rate? Well, with some bonds, known as callable bonds , the company does have the option to buy them back for the call price. 8 Of course, holders of these callable bonds know that the company will wish to buy the issue back if interest rates fall, and therefore the price of the bond will not rise above the call price.

Figure 14.6 shows the risk of a call to the bondholder. The blue line is the value of a 30-year, 6% “straight,” that is, noncallable, bond; the orange line is the value of a bond with the same coupon rate and maturity but callable at $1,060 (i.e., 106% of face value). At very high interest rates the risk that the company will call the bonds is neg- ligible, and the values of the two bonds are nearly identical. As rates fall, the straight bond continues to increase steadily in value, but since the capital appreciation of the callable bond is limited by the call price, its capital appreciation will lag behind that of the straight bond.

A callable bond gives the company the option to retire the bonds early. But some bonds give the investor the right to demand early repayment. During the 1990s many loans to Asian companies gave the lenders a repayment option. When the Asian crisis struck in 1997, these companies were faced by a flood of lenders demanding their money back. Needless to say, companies that were already struggling to survive did not appreciate this additional burden.

funded debt Debt with more than 1 year remaining to maturity.

sinking fund Fund established to retire debt before maturity.

8  Sometimes callable bonds specify a period during which the firm is not allowed to call the bond if the purpose is simply to issue another bond at a lower interest rate.

callable bond Bond that may be repurchased by the issuing firm before maturity at a specified call price.

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Chapter 14 Introduction to Corporate Financing 427

Country and Currency These days capital markets know few national boundaries and many large firms in the United States borrow abroad. For example, an American company may choose to finance a new plant in Switzerland by borrowing Swiss francs from a Swiss bank, or it may expand its Dutch operation by issuing a bond in Holland. Also many foreign companies come to the United States to borrow dollars, which are then used to finance their operations throughout the world.

In addition to these national capital markets, there is an international capital market centered mainly in London. Banks from all over the world have branches in London. They include such giants as Citicorp, UBS, Deutsche Bank, Mitsubishi UFJ, HSBC, and BNP Paribas. One reason they are there is to collect deposits in the major curren- cies. For example, suppose an Arab sheikh has just received payment in dollars for a large sale of oil to the United States. Rather than depositing the check in the United States, he may choose to open a dollar account with a bank in London. Dollars held in a bank outside the United States came to be known as eurodollars . Similarly, yen held outside Japan were termed euroyen, and so on.

The London bank branch that is holding the sheikh’s dollar deposit may temporar- ily lend those dollars to a company, in the same way that a bank in the United States may relend dollars that have been deposited with it. Thus a company can either borrow dollars from a bank in the United States or borrow dollars from a bank in London. 9

If a firm wants to make an issue of long-term bonds, it can choose to do so in the United States. Alternatively, it can sell the bonds to investors in several coun- tries. Because these international issues have usually been marketed by the London

eurodollars Dollars held on deposit in a bank outside the United States.

9 Because the Federal Reserve requires banks in the United States to keep interest-free reserves, there is in effect a tax on dollar deposits in the United States. Overseas dollar deposits are free of this tax, and therefore banks can afford to charge the borrower slightly lower interest rates.

Suppose Dow Chemical is considering two issues of 20-year maturity cou- pon bonds; one issue will be callable, the other not. For a given coupon rate, will the callable or noncallable bond sell at the higher price? If the bonds are both to be sold to the public at face value, which bond must have the higher coupon rate?

Self-Test 14.5

FIGURE 14.6 Prices of callable versus straight debt. When interest rates fall, bond prices rise. But the price of the callable bond (orange line) is limited by the call price.

Straight bond

Callable bond

B o

n d

p ri

ce (

$) Interest rate (%)

2,000

1,600

1,200

800

400

0

1,800

1,400

1,000

600

200

2 8 1814 1612106

Call price = $1,060

4

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428 Part Four Financing

branches of international banks, they have traditionally been known as eurobonds . A eurobond may be denominated in dollars, yen, or any other currency. Unfortunately, when the single European currency was established it was called the euro. It is easy, therefore, to confuse a eurobond (a bond that is sold internationally) with a bond that is denominated in euros.

Public versus Private Placements Publicly issued bonds are sold to any- one who wishes to buy, and once they have been issued, they can be freely traded in the securities markets. In a private placement , the issue is sold directly to a small number of banks, insurance companies, or other investment institutions. Privately placed bonds cannot be resold to individuals in the United States and can be resold only to other qualified institutional investors. However, there is increasingly active trading among these investors.

We will have more to say about the difference between public issues and private placements in the next chapter.

A Debt by Any Other Name The word debt sounds straightforward, but companies enter into a number of financial arrangements that look suspiciously like debt yet are treated differently in the accounts. Some of these obligations are easily identifiable. For example, accounts payable are simply obligations to pay for goods that have already been delivered and are therefore like a short-term debt.

Other arrangements are not so easy to spot. For example, instead of borrowing money to buy equipment, many companies lease or rent it on a long-term basis. In this case the firm promises to make a series of payments to the lessor (the owner of the equipment). This is just like the obligation to make payments on an outstanding loan. What if the firm can’t make the payments? The lessor can then take back the equip- ment, which is precisely what would happen if the firm had borrowed money from the lessor, using the equipment as collateral for the loan.

Postretirement health benefits and pension promises can also be huge liabilities. For example, at the start of 2013 Ford faced an estimated $18.7 billion deficit on its pension plan. That is a debt which the company will eventually need to pay.

There is nothing underhanded about these obligations. They are clearly shown on the company’s balance sheet as a liability. Sometimes, however, companies go to con- siderable lengths to ensure that investors do not know how much they have borrowed. For example, Enron was able to borrow $658 million by setting up special-purpose entities (SPEs), which raised cash by a mixture of equity and debt and then used that debt to help fund the parent company. None of this debt showed up on Enron’s balance sheet.

eurobond Bond that is marketed internationally.

private placement Sale of securities to a limited number of investors without a public offering.

lease Long-term rental agreement.

Example 14.1 The Terms of Apple’s Bond Issue In May 2013 Apple made a huge $17 billion issue of debt. Part of this issue was in the form of 30-year bonds. Now that you are familiar with some of the jargon, you might like to look at Table 14.2 , which summarizes the terms of Apple’s bond issue. We have added some explanatory notes.

Innovations in bond design

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Innovation in the Debt Market We have discussed domestic bonds and eurobonds, fixed-rate and floating-rate loans, secured and unsecured loans, senior and junior loans (in Chapter 7), and much more. You might think that this gives you all the choice you need. Yet issuers are always try- ing to devise new types of bonds that they hope will appeal to a particular clientele of investors. Just to give you a flavor of the inventiveness of financial managers, here are some examples of innovative bonds.

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Chapter 14 Introduction to Corporate Financing 429

Mortality Bonds Managers of life insurance companies agonize about the pos- sibility of a pandemic or other disaster that results in a sharp increase in the death rate. In 2009 the Swiss insurance company Swiss Re sought to protect itself against this danger by issuing €75 million of mortality bonds. Swiss Re’s bonds offer a tempting yield, but if mortality rates in the United States and United Kingdom exceed a pre- determined threshold, the investors’ funds are used to pay Swiss Re’s life insurance obligations. So the investors are in a way betting that people will die on schedule.

Asset-Backed Bonds Instead of borrowing money directly, companies some- times bundle a group of loans and then sell the cash flows from these loans. This issue is known as an asset-backed bond. For example, automobile loans, student loans, and credit card receivables have all been bundled together and remarketed as asset-backed bonds. However, by far the most common application has been in the field of mortgage lending.

Suppose your company has made a large number of mortgage loans to buyers of homes or commercial real estate. However, you don’t want to wait until the loans are paid off; to get your hands on the money now, you can sell mortgage pass-through certificates backed by the mortgage loans. The holders of these certificates are buy- ing a share of the payments made by the underlying pool of mortgages. For example, if interest rates fall and the mortgages are repaid early, holders of the pass-through certificates are also repaid early. That is not generally popular with these holders, for they get their money back just when they don’t want it—when interest rates are low.

Sometimes, instead of issuing one class of pass-through certificates, companies have issued several different classes of security, known as collateralized debt obliga- tions (or CDOs ) . For example, any mortgage payments might be used first to pay off

Comment Description of Bond

1. Interest of 3.85% will be payable on May 4 and November 4 of each year. Thus every 6 months each note will pay inter- est of (.0385/2)  ×  $1,000  =  $19.25.

ISSUE Apple Inc. 3.85% Notes

2. Investors will be repaid the $1,000 face value in 2043. DUE May 4, 2043 3. Moody’s bond rating is Aa, the second-highest-quality rating. RATING—Aa 4. A trustee is appointed to look after investors’ interest. TRUSTEE Issued under an indenture between Apple and

The Bank of New York Mellon Trust Company 5. The bonds are registered. The registrar keeps a record of

who owns the bonds. REGISTERED Issued in registered, book-entry form

6. The company is not obliged to repay any of the bonds on a regular basis before maturity.

SINKING FUND None

7. The company has the option to buy back the notes. The redemption price is the greater of $1,000 or a price that is determined by the value of an equivalent Treasury bond.

CALLABLE in whole or in part at any time

8. The notes are senior debt, ranking equally with all Apple’s other unsecured senior debt.

SENIORITY

9. The notes are not secured; that is, no assets have been set aside to protect the noteholders in the event of default. How- ever, if Apple sets aside assets to protect any other bond- holders, the notes will also be secured by these assets. This is termed a negative pledge clause.

SECURITY The notes are unsecured. However, “if Apple shall incur, assume or guarantee any Debt, . . . it will secure . . . the debt securities then outstanding equally and ratably with . . . such Debt.”

10. The principal amount of the issue was $3 billion. The notes were sold at 99.418% of their principal value. After deduct- ing the payment to the underwriters, the company received $987.18 per bond.

OFFERED $3,000,000,000 at 99.418% (proceeds to Company 99.42%)

11. The book runners are the managing underwriters to the issue and maintain the book of securities sold.

JOINT BOOK-RUNNING MANAGERS Goldman, Sachs; Deutsche Bank Securities

TABLE 14.2 Apple’s Debt Issue

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430 Part Four Financing

the class of security holders called senior investors and only then will other, junior classes start to be repaid.

By 2007 over half of the new issues of CDOs involved exposure to subprime mort- gages. Because the mortgages were packaged together, senior investors in these CDOs were protected against the risk of default on any particular mortgage. However, even the senior tranches were exposed to the risk of an economy-wide slump in the housing market that would lead to widespread defaults

Economic catastrophe struck in the summer of 2007, when the investment bank Bear Stearns revealed that two of its hedge funds had invested heavily in CDOs that became nearly worthless when mortgage default rates rose. Bear Stearns was rescued with help from the Federal Reserve, but the incident signaled the start of the credit crunch and the collapse of the CDO market. In 2008 new issues of CDOs fell by nearly 90%.

There is a great variety of potential security designs. As long as you can convince investors of its attractions, you can issue a callable, subordinated, floating-rate bond denominated in euros. Rather than combining features of existing securities, you may be able to create an entirely new one. We can imagine a copper mining company issu- ing preferred shares on which the dividend fluctuates with the world copper price. We know of no such security, but it is perfectly legal to issue it and—who knows?—it might generate considerable interest among investors.

Variety is intrinsically good. People have different tastes, levels of wealth, rates of tax, and so on. Why not offer them a choice? Of course, the problem is the expense of designing and marketing new securities. But if you can think of a new security that will appeal to investors, you may be able to issue it on especially favorable terms and thus increase the value of your company.

14.6 Convertible Securities We have seen that companies sometimes have the option to repay an issue of bonds before maturity. There are also cases in which investors have an option. The most dra- matic case is provided by a warrant , which is nothing but an option. Companies often issue warrants and bonds in a package.

warrant Right to buy shares from a company at a stipulated price before a set date.

Example 14.2 Warrants Macaw Bill wishes to make a bond issue, which could include some warrants as a “sweetener.” Each warrant might allow you to purchase one share of Macaw stock at a price of $50 any time during the next 5 years. If Macaw’s stock performs well, that option could turn out to be very valuable. For instance, if the stock price at the end of the 5 years is $80, then you pay the company $50 and receive in exchange a share worth $80. Of course, an investment in warrants also has its perils. If the price of Macaw stock fails to rise above $50, then the warrants expire worthless.

A convertible bond gives its owner the option to exchange the bond for a prede- termined number of common shares. The convertible bondholder hopes that the com- pany’s share price will zoom up so that the bond can be converted at a big profit. But if the shares zoom down, there is no obligation to convert; the bondholder remains just that. Not surprisingly, investors value this option to keep the bond or exchange it for shares, and therefore a convertible bond sells at a higher price than a comparable bond that is not convertible.

convertible bond Bond that the holder may exchange for a specified amount of another security.

Tesla Motors convertible bond

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Chapter 14 Introduction to Corporate Financing 431

The convertible is like a package of a bond and a warrant. But there is an important difference: When the owners of a convertible wish to exercise their options to buy shares, they do not pay cash—they just exchange the bond for shares of the stock.

Companies may also issue convertible preferred stock. In this case the investor receives preferred stock with fixed dividend payments but has the option to exchange this preferred stock for the company’s common stock. The preferred stock issued by Dow Chemical is convertible into common stock.

These examples do not exhaust the options encountered by the financial manager. In fact, once you read Chapter 23 and learn how to analyze options, you will find that they are all around you.

SUMMARY Managers want to raise money at the lowest possible cost, but their ability to find cheap financing is limited by the intense competition between investors. As a result of this com- petition, securities are likely to be fairly priced given the information available to investors. Such a market is said to be efficient.

Internally generated cash is the principal source of company funds. In recent years, net equity issues have often been negative; that is, companies have repurchased more equity than they have issued. At the same time companies have issued large quantities of debt. However, large levels of internally generated funds in this period allowed book equity to increase despite the share repurchases, so the ratio of long-term debt to book value of equity was fairly stable.

The stockholders’ equity account breaks down the book value of equity into par value, additional paid-in capital, retained earnings, and treasury stock. For most purposes, the allocation among the first three categories is not important. These accounts also show the total number of shares issued as well as shares repurchased by the company.

Most companies use a majority voting system in which each director is voted on sep- arately and stockholders cast one vote for each share they own. Less commonly, firms employ cumulative voting, which means that all directors are voted on jointly and stock- holders may cast all their votes for just one candidate. Many companies have classified boards, in which case only a third of directors come up for reelection each year. How- ever, companies have increasingly moved to declassify their boards so that all directors are voted on each year.

The CEO is almost always a director, often joined by a few other top managers. But for U.S. public companies a majority of the board must be independent outside directors. Members of the compensation committee, which sets executive compensation, must all be independent directors.

A company can issue a variety of securities such as common stock, preferred stock, and bonds. The common stockholders own the company. By this we mean that they are enti- tled to whatever profits are left over after other investors have been paid and that they have the ultimate control over how the company is run. Because shareholdings in the United States are usually widely dispersed, managers get to make most of the decisions. Managers may be given strong financial incentives to perform well, and their actions are monitored by the board of directors.

Why should firms assume that the securities they issue are fairly priced? (LO14-1)

What are recent trends in firms’ use of different sources of finance? (LO14-2)

What information is contained in the shareholders’ equity account in the firm’s financial statements? (LO14-3)

What procedures are used for elections to a firm’s board of directors and other matters put to shareholders? (LO14-4)

Who are the members of the company’s board of directors? ( LO14-4 )

What are the major classes of securities issued by firms to raise capital? (LO14-5)

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Why do companies issue convertibles?

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432 Part Four Financing

4. Equity Accounts. The authorized share capital of the Alfred Cake Company is 100,000 shares. The equity is currently shown in the company’s books as follows: (LO14-3)

Preferred stock offers a fixed dividend but the company has the discretion not to pay it. It can’t, however, then pay a dividend on the common stock. Despite its name, preferred stock is not a popular source of finance, but it is useful in special situations.

When companies issue bonds, they promise to make a series of interest payments and to repay the principal. However, this liability is limited. Stockholders have the right to default on their obligation and to hand over the assets to the debtholders. Unlike dividends on common stock and preferred stock, the interest payments on debt are regarded as a cost and therefore they are paid out of before-tax income. Here are some forms of debt:

• Fixed-rate and floating-rate debt. • Funded (long-term) and unfunded (short-term) debt. • Callable and sinking-fund debt. • Domestic bonds and eurobonds. • Publicly traded debt and private placements.

The fourth source of finance consists of options and optionlike securities. The sim- plest option is a warrant, which gives its holder the right to buy a share from the firm at a set price by a set date. Warrants are often sold in combination with other securities. Convertible bonds give their holder the right to convert the bond to shares. They therefore resemble a package of straight debt and a warrant.

QUESTIONS AND PROBLEMS 1. Financing Decisions. True or false? (LO14-1)

a. Smart financial managers know that good financing decisions create as much value for the firm as good investment decisions.

b. Competition between investors means that companies can generally sell their securities for more than they are worth.

2. Sources of Finance. Fill in the blanks in the following passage by choosing the most appropri- ate term from the following list: debt issues, higher, internally generated cash, lower, risen, financial deficit, fallen, negative, stayed roughly constant. ( Note: A term may be used more than once.) (LO14-2)

By far the largest source of cash for most companies comes from _______ . The gap between this cash and the cash that companies need is called the _______. On average, equity issues have been _______; in other words, companies have used the cash from _______ and retained earnings to buy back their stock. Debt ratios can be measured using either market values or book values. Generally, book debt ratios are _______ than market-value ratios. In the 30 or so years before 1990 both debt ratios have on average _______, but since then they have _______.

3. Equity Accounts. Match each of the following terms with the correct definition: (LO14-3)

finance

®

a. additional paid-in capital b. issued and outstanding c. retained earnings d. treasury stock e. authorized share capital f. par value

A. The price at which each share is recorded in the company’s books

B. Held by investors C. Cumulative amount of profits that have been plowed back D. The difference between the amount of cash raised by an

equity issue and the par value of the issue E. The maximum number of shares that can be issued

without shareholder approval F. The amount that the company has spent buying back stock

that it has not subsequently resold

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Chapter 14 Introduction to Corporate Financing 433

Common stock ($1 par value) $ 60,000 Additional paid-in capital 10,000 Retained earnings 30,000 Common equity $100,000 Treasury stock (2,000 shares) 5,000 Net common equity $95,000

a. How many shares are issued? b. How many shares are outstanding? c. How many more shares can be issued without the approval of shareholders?

5. Equity Accounts. Common Products has just made its first issue of stock. It raised $2 million by selling 200,000 shares of stock to the public. These are the only shares outstanding. The par value of each share was $2. Fill in the following table: (LO14-3)

Common shares (par value) _________ Additional paid-in capital _________ Retained earnings _________ Net common equity $2,500,000

6. Equity Accounts. (LO14-3)

a. Rework Table 14.1 , supposing that Dow Chemical now issues 10 million shares at $30 a share. Which of the figures would change?

b. What would happen to Table 14.1 if instead Dow bought back 10 million shares at $30 per share?

7. Voting for Directors. If there are 10 directors to be elected and a shareholder owns 100 shares, indicate the maximum number of votes that he or she can cast for a favorite candidate under: (LO14-4)

a. Majority voting b. Cumulative voting

8. Voting for Directors. The shareholders of the Pickwick Paper Company need to elect five directors. There are 400,000 shares outstanding. How many shares do you need to own to ensure that you can elect at least one director if the company has: (LO14-4)

a. Majority voting? b. Cumulative voting? ( Hint: How many votes in total will be cast? How many votes are required to ensure that at least one-fifth of votes are cast for your choice?)

9. Preferred Stock. True or false? (LO14-5)

a. A company’s equity includes both common and preferred stock. b. The sum of common equity and preferred stock is known as net worth. c. As its name implies, preferred stock is a more important source of financing than common

equity. d. A corporation pays tax on only 30% of the common or preferred dividends it receives from

other corporations. e. Because of the tax advantage, a large fraction of preferred shares is held by corporations.

10. Corporate Bonds. Look at the terms of the Apple bond issue in Section 14.5. (LO14-5)

a. Does the company have a call option? b. How much interest is paid on each Apple bond in a year? c. What was the total amount that the underwriters were paid for their services? d. Can Apple issue secured debt that would come ahead of this issue? e. Does Apple’s bond receive Moody’s highest credit rating? f. Are the bonds repaid in one lump or by installments? g. Are Apple’s bonds funded or unfunded debt?

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434 Part Four Financing

11. Preferred Stock. Preferred stock of financially strong firms sometimes sells at lower yields than the bonds of those firms. For weaker firms, the preferred stock has a higher yield. What might explain this pattern? (LO14-5)

12. Corporate Bonds. Other things equal, will the following provisions increase or decrease the yield to maturity at which a firm can issue a bond? (LO14-5)

a. The borrower has the option to repay the loan before maturity. b. The bond is convertible into shares. c. The bond is a private placement.

13. Corporate Bonds. Fill in the blanks by choosing the appropriate term from the following list: lease, funded, floating-rate, eurobond, convertible, subordinated, call, sinking fund, prime rate, private placement, public issue, senior, unfunded, eurodollar rate, warrant, debentures, term loan. (LO14-5)

a. Debt maturing in more than 1 year is often called _______ debt. b. An issue of bonds that is sold simultaneously in several countries is traditionally

called a(n) _______ . c. If a lender ranks behind the firm’s general creditors in the event of default, the loan is said to

be _______ . d. In many cases a firm is obliged to make regular contributions to a(n) _______ , which is then

used to repurchase bonds. e. Some bonds give the firm the right to repurchase or _______ the bonds at specified prices. f. The benchmark interest rate that banks charge to their customers with good credit is gener-

ally termed the _______. g. The interest rate on bank loans is often tied to short-term interest rates. These loans are usu-

ally called _______loans. h. Where there is a(n) _______, securities are sold directly to a small group of institutional

investors. These securities cannot be resold to individual investors. i. In the case of a(n) _______, debt can be freely bought and sold by individual investors. j. A long-term rental agreement is called a(n) _______. k. A(n) _______ bond can be exchanged for shares of the issuing corporation. l. A(n) _______ gives its owner the right to buy shares in the issuing company at a predeter-

mined price.

WEB EXERCISES 1. Pick two companies [Caterpillar (CAT) and Union Pacific (UNP) could be good candidates],

and compare their sources of funds and financial structures. You can find summary cash-flow statements and balance sheets on finance.yahoo.com , but you may also find it useful to go to the companies’ websites. What factors might explain the difference in the companies’ financing patterns?

2. In Figure 14.3 we summarized the sources and uses of funds for U.S. nonfinancial corporations. The data for this figure can be found on www.federalreserve.gov/releases/z1/current/data. htm . Look at Table F.102 for the latest year. Find “total internal funds” (which appeared in row 9 at the time we last looked) and “net funds raised in markets” (row 38). What proportion of the funds that companies needed in the latest year was generated internally, and how much had to be raised on the financial markets? Is this the usual pattern? Now look at “net new equity issues” (row 39). Were companies on average issuing new equity or buying their shares back?

3. Construct a table similar to Table 14.1 for a company of your choice by looking up its annual report on the web. What is the difference between the company’s outstanding and issued shares? Explain. Has the company in the past raised more money by issuing new shares or by plowing back earnings? Is that typical of U.S. public companies (see Section 14.2)?

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Chapter 14 Introduction to Corporate Financing 435

SOLUTIONS TO SELF-TEST QUESTIONS 14.1 a. Internal funds are most important, followed by net new borrowing. Net equity issues are in

last place. b. Stock repurchases have exceeded issues.

14.2 Par value of common shares must be $1  ×  100,000  shares  =  $100,000. Additional paid-in capital is ($15  −  $1)  ×  100,000  =  $1,400,000. Since book value is $4,500,000, retained earn- ings must be $3,000,000. Therefore, the accounts look like this:

Common shares ($1 par value per share) $ 100,000 Additional paid-in capital 1,400,000 Retained earnings 3,000,000 Net common equity $4,500,000

14.3 The corporation’s after-tax yield on the bonds is 10%  −  (.35  ×  10%)  =  6.5%. The after-tax yield on the preferred is 8%  −  [.35  ×  (.30  ×  8%)]  =  7.16%. The preferred stock provides the higher after-tax rate despite its lower before-tax rate.

14.4 Because the coupon on floating-rate debt adjusts periodically to current market conditions, the bondholder is less vulnerable to changes in market yields. The coupon rate paid by the bond is not locked in for as long a period of time. Therefore, prices of floaters should be less sensitive to changes in market interest rates.

14.5 The callable bond will sell at a lower price. Investors will not pay as much for the callable bond since they know that the firm may call it away from them if interest rates fall. Thus they know that their capital gains potential is limited, which makes the bond less valuable. If both bonds are to sell at face value, the callable bond must pay a higher coupon rate as compensa- tion to the investor for the firm’s right to call the bond.

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436

How Corporations Raise Venture Capital and Issue Securities

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

15-1 Understand how venture capital works.

15-2 Understand how firms make initial public offerings and the costs of such offerings.

15-3 Understand how established firms make subsequent public issues of securities.

15-4 Describe how companies may make private placements of securities.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

15 CHAPTE R

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437

P A

R T

F O

U R

B ill Gates and Paul Allen founded Microsoft in 1975, when both were around 20 years old. Eleven years later Microsoft shares were sold to the public for $21 a share and immediately zoomed

to $35. The largest shareholder was Bill Gates, whose

shares in Microsoft then were worth $350 million.

In 1976 two college dropouts, Steve Jobs and Steve

Wozniak, sold their most valuable possessions, a van

and a couple of calculators, and used the cash to

start manufacturing computers in a garage. In 1980,

when Apple Computer went public, the shares were

offered to investors at $22 and jumped to $36. At that

point, the shares owned by the company’s two found-

ers were worth $414 million.

In 1996 two Stanford computer science students,

Larry Page and Sergey Brin, decided to collaborate

to develop a web search engine. To help turn their

idea into a commercial product, the two friends

succeeded in raising almost $1 million from several

wealthy investors. They also raised cash from two ven-

ture capital firms that specialized in helping young

start-up businesses. Google went public in 2004 at a

price of $85 a share, putting a value on the enterprise

of $23 billion.

Such stories illustrate that the most important asset

of a new firm may be a good idea. But that is not all

you need. To take an idea from the drawing board

to a prototype and through to large-scale operations

requires ever greater amounts of capital.

This chapter proceeds as follows: First we describe

how venture capital firms provide equity capital and

advice to help young companies over their awkward

adolescent period, before they are large and success-

ful enough to “go public” in an initial public offering

or IPO. Then we describe how IPOs are accomplished.

A company’s initial public offering is seldom its last.

We saw in Chapter 14 that internally generated cash

is not usually sufficient for capital investment and

other cash requirements. Established companies

make up the deficit by issuing more debt or equity.

The remainder of this chapter looks at these debt

and equity issues. You will learn about the costs and

pros and cons of general cash offers, rights issues,

and private placements.

Fi n

a n

c in

g

Trading opens on NASDAQ for shares in Facebook.

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438 Part Four Financing

15.1 Venture Capital You have taken the big step. With a couple of friends, you have formed a corpora- tion to open a chain of fast-food outlets, offering innovative combinations of national dishes such as sushi with sauerkraut, curry Bolognese, and chow mein with Yorkshire pudding. Breaking into the fast-food business costs money, but, after pooling your sav- ings and borrowing to the hilt from the bank, you have raised $100,000 and purchased 1 million shares in the new company. At this zero-stage investment, your company’s assets are $100,000 plus the idea for your new product.

That $100,000 is enough to get the business off the ground, but if the idea takes off, you will need more capital to pay for new restaurants. Many start-ups continue to grow with funds provided directly by managers or by their friends and families. Some thrive using bank loans and reinvested earnings. But you will probably need to find an investor who is prepared to back an untried company in return for part of the profits. Equity capital in young businesses is known as venture capital, which is provided by specialist venture capital firms, wealthy individuals, investment institutions such as pension funds, and sometimes mature corporations on the hunt for new technology or new products. Specialist venture capital (or “VC”) firms are the most likely source if your start-up is high-risk and high-tech.

Most entrepreneurs are able to spin a plausible yarn about their company. But it is as hard to convince a venture capitalist to invest in your business as it is to get a first novel published. Your first step is to prepare a business plan. This describes your prod- uct, the potential market, the production method, and the resources—time, money, employees, plant, and equipment—needed for success. It helps if you can point to the fact that you are prepared to put your money where your mouth is. By staking all your savings in the company, you signal your faith in the business.

The venture capital company knows that the success of a new business depends on the effort its managers put in. Therefore, it will try to structure any deal so that you have a strong incentive to work hard. For example, if you agree to accept a modest salary (and look forward instead to increasing the value of your investment in the com- pany’s stock), the venture capital company knows you will be committed to working hard. However, if you insist on a watertight employment contract and a fat salary, you won’t find it easy to raise venture capital.

You will have a hard time persuading a venture capitalist to give you several years of financing all at once. You will get only enough to reach the next key milestone or checkpoint. That gives the venture capitalist the opportunity to evaluate progress and decide whether investing in the next stage is worthwhile.

Suppose the first milestone for your restaurant chain is demonstrated profitability at the first two outlets. You budget an additional $500,000 investment to get to this milestone. Then you convince your friendly VC to buy 1 million new shares for $.50 each. This will give the VC one-half ownership of the firm: It owns 1 million shares, and you and your friends also own 1 million shares. Because the venture capitalist is paying $500,000 for a claim to half your firm, it is placing a $1 million value on the business. After this first-stage financing, your company’s balance sheet looks like this:

venture capital Money invested to finance a new firm.

FIRST-STAGE MARKET-VALUE BALANCE SHEET (Figures in $ millions)

Assets Liabilities and Shareholders’ Equity

Cash from new equity $ .5 New equity from venture capital $ .5 Other assets .5 Your original equity .5 Value $1.0 Value $1.0

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Chapter 15 How Corporations Raise Venture Capital and Issue Securities 439

Suppose that 2 years later your business has grown to the point at which it needs a further injection of equity. This second-stage financing might involve the issue of a further 1 million shares at $1 each. Some of these shares might be bought by the origi- nal VC firm and some by other venture capital firms. The balance sheet after the new financing would then be as follows:

Why might the venture capital company prefer to put up only part of the funds up front? Would this affect the amount of effort put in by you, the entrepre- neur? Is your willingness to accept only part of the venture capital that will eventually be needed a good signal of the likely success of the venture?

Self-Test 15.1

SECOND-STAGE MARKET-VALUE BALANCE SHEET (Figures in $ millions)

Assets Liabilities and Shareholders’ Equity

Cash from new equity $1 New equity from second-stage fi nancing $1 Other assets 2 Equity from fi rst stage 1 Your original equity 1 Value $3 Value $3

Notice that the value of the initial 1 million shares owned by you and your friends has now been marked up to $1 million. Does this begin to sound like a money machine? It was so only because you have made a success of the business and new investors are prepared to pay $1 to buy a share in the business. When you started out, it wasn’t clear that sushi and sauerkraut would catch on. If it hadn’t caught on, the venture capital firm could have refused to put up more funds.

You are not yet in a position to cash in on your investment, but your gain is real. The second-stage investors have paid $1 million for a one-third share in the com- pany. (There are now 3 million shares outstanding, and the second-stage investors hold 1 million shares.) At least these impartial observers—who are willing to back up their opinions with a large investment—must have decided that the company was worth at least $3 million. Your one-third share is therefore also worth $1 million.

Venture Capital Companies Some young companies grow with the aid of equity investment provided by wealthy individuals known as angel investors. Many others raise capital from specialist venture capital firms, which pool funds from a variety of investors, seek out fledgling compa- nies to invest in, and then work with these companies as they try to grow. In addition, some large technology firms such as Intel and Johnson & Johnson act as corporate venturers by providing capital to new and innovative companies. In a recent develop- ment, young companies have also used the web to raise money from small investors. This development, known as crowdfunding, is described in the nearby box.

Most venture capital funds are organized as limited private partnerships with a fixed life of about 10 years. Pension funds and other investors are the limited partners. The management company, which is the general partner, is responsible for making and overseeing the investments and, in return, receives a fixed fee as well as a share of the profits. You will find that these venture capital partnerships are often lumped together with similar partnerships that provide funds for companies in distress or that buy out whole companies and then take them private. The general term for these activities is private equity investing.

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U.S. venture capital

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Finance in Practice Every Crowd Has a Silver Lining was heavily oversubscribed; more than 26,000 individuals pledged a total of $2.3 million. Many of these pledges were for less than $25; others were much more substantial.

Crowdfunding may be used by entrepreneurs seeking to raise millions of dollars for a new enterprise, but more often it is a method for individuals to raise a few thousand dollars. In contrast to traditional venture capital projects, a relatively small proportion of projects are high-tech and many are for artistic activities or movie production. The payoff for investors may be in cash, but many crowdfunded projects instead offer samples of the product. For example, the smallest backers of the 3Doodler were simply promised a listing in the product’s Hall of Fame; more substantial backers were offered sample products.

A new way for entrepreneurs to fi nance start-ups has emerged. It is known as crowdfunding, which uses the Inter- net to raise money directly from a crowd of individuals.

WobbleWorks is a small toy and robotics fi rm that was founded in Boston in 2011 by two entrepreneurs. The com- pany needed capital to develop the 3Doodler, a pen that could be used to produce 3-D plastic images. The compa- ny’s solution was to advertise for backers on Kickstarter, a website for young enterprises that seek to raise capital from a large number of individuals. Possible backers were given about a month to decide whether they wished to support the 3Doodler project and how much they wished to invest. This particular concept proved enormously popular, and the offer

440

Venture capital firms are not passive investors. They are usually represented on each company’s board of directors, they help to recruit senior managers for the company, and they provide ongoing advice. This advice can be especially valuable to businesses in their early years and helps them to bring their products more quickly to market.

For every 10 first-stage venture capital investments, only 2 or 3 may survive as suc- cessful, self-sufficient businesses, and only 1 may pay off big. From these statistics come two rules of success in venture capital investment. First, don’t shy away from uncertainty; accept a low probability of success. But don’t buy into a business unless you can see the chance of a big, public company in a profitable market. There’s no sense taking a big risk unless the reward is big if you win. Second, cut your losses; identify losers early, and if you can’t fix the problem—by replacing management, for example—don’t throw good money after bad. There’s an old saying in the venture capital business: “The secret of success in VC is not picking winners, but shutting down the losers before you spend too much money on them.”

Very few new businesses are big winners, but those that do win can be very profit- able. So venture capitalists keep sane by reminding themselves of the success stories— those who got in on the ground floor of firms like Google, Microsoft, and FedEx. 1

15.2 The Initial Public Offering For many successful start-ups there comes a time when they need more capital than can comfortably be provided by a small number of individuals or venture capitalists. At this point one solution is to sell the business to a larger firm. But many entrepre- neurs do not fit easily into a corporate bureaucracy and would prefer instead to remain the boss. In this case, the company may choose to raise money by selling shares to the public. A firm goes public when it sells its first issue of shares in a general offering to investors. This first sale of stock is called an initial public offering, or IPO.

An IPO is termed a primary offering when new shares are sold to raise additional cash for the company. It is a secondary offering when the company’s founders and the venture capitalist cash in on some of their gains by selling shares. A secondary offer therefore is no more than a sale of shares from the early investors in the firm to new investors, and the cash raised in a secondary offer does not flow to the company. Of course, IPOs can be and commonly are both primary and secondary: The firm raises new cash at the same time that some of the already existing shares in the firm are sold to the public.

1 Fortunately, the successes seem to have outweighed the failures. Cambridge Associates estimated that the aver- age annual return on venture capital funds was 20% for the 30 years ending in March 2013.

initial public offering (IPO) First offering of stock to the general public.

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Chapter 15 How Corporations Raise Venture Capital and Issue Securities 441

Some of the biggest secondary offerings have involved governments selling off stock in nationalized enterprises. For example, the U.S. Treasury raised $20 billion by selling its holdings in General Motors common and preferred stock. But even this huge issue was dwarfed by the $70 billion that was raised in the same year by the sale of the Brazilian state-owned oil company Petrobras.

We have seen that companies may make an IPO to raise new capital or to enable the existing shareholders to cash out, but there can be other benefits. For example, the company’s stock price provides a readily available yardstick of performance and allows the firm to reward the management team with stock options.

While there are advantages to having a market for your shares, we should not give the impression that firms everywhere aim to go public. In many countries it is com- mon for businesses to remain privately owned. Even in the United States many firms choose to remain as private, unlisted companies. They include some very large opera- tions, such as Koch Industries, Bechtel, Cargill, and Levi Strauss. Also, you should not think of the issue process in the United States as a one-way street; public firms often go into reverse and return to being privately owned. For a somewhat extreme example, consider the food service company Aramark. It began life in 1936 as a pri- vate company and went public in 1960. In 1984 the management bought out the com- pany and took it private, and it remained private until 2001, when it had its second public offering. But the experiment did not last long, for 5 years later Aramark was the object of yet another buyout that took the company private once again. In Decem- ber 2013 Aramark went public for a third time.

Managers often chafe at the red tape involved in running a public company and at the unrelenting pressure from shareholders to report increasing earnings. These com- plaints have become more vocal since the passage of the Sarbanes-Oxley Act. This act has sought to prevent a repeat of the corporate scandals that brought about the collapse of Enron and WorldCom, but a consequence has been an increased reporting burden on small public companies and a rise in the number of companies reverting to private ownership.

Arranging a Public Issue Once a firm decides to go public, the first task is to select the underwriters. Under- writers are investment banking firms that act as financial midwives to a new issue. Usually they play a triple role—first providing the company with procedural and financial advice, then buying the stock, and finally reselling it to the public. A small IPO may have only one underwriter, but larger issues usually require a syndi- cate of underwriters that buy the issue and resell it.

In the typical underwriting arrangement, called a firm commitment, the underwriters buy the securities from the firm and then resell them to the public. The underwriters receive payment in the form of a spread —that is, they are allowed by the company to sell the shares at a slightly higher price than they paid for them. But the underwriters also accept the risk that they won’t be able to sell the stock at the agreed offering price. If that happens, they will be stuck with unsold shares and must get the best price they can for them. In the more risky cases, the underwriter may not be willing to enter into a firm commitment and handles the issue on a best efforts basis. In this case the under- writer agrees to sell as much of the issue as possible but does not guarantee the sale of the entire issue.

Before any stock can be sold to the public, the company must register the issue with the Securities and Exchange Commission (SEC). This involves preparation of a detailed and sometimes cumbersome registration statement, which contains informa- tion about the proposed financing and the firm’s history, existing business, and plans for the future. The SEC does not evaluate the wisdom of an investment in the firm, but it does check the registration statement for accuracy and completeness. The firm

underwriter Firm that buys an issue of securities from a company and resells it to the public.

spread Difference between public offer price and price paid by underwriter.

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Largest U.S. private companies

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442 Part Four Financing

must also comply with the “blue-sky” laws of each state, so named because they seek to protect the public against firms that fraudulently promise the blue sky to investors. 2

The first part of the registration statement is distributed to the public in the form of a preliminary prospectus. One function of the prospectus is to warn investors about the risks involved in any investment in the firm. Some investors have joked that if they read prospectuses carefully, they would never dare buy any new issue. The appendix to this chapter provides a streamlined version of a possible prospectus for your restaurant business.

The company and its underwriters also need to set the issue price. To gauge how much the stock is worth, they may undertake discounted cash-flow calculations like those described in Chapter 7. They also look at the price-earnings ratios of the shares of the firm’s principal competitors.

Before settling on the issue price, the underwriters generally arrange a “roadshow,” which gives the underwriters and the company’s management an opportunity to talk to potential investors. These investors may then offer their reaction to the issue, suggest what they think is a fair price, and indicate how much stock they would be prepared to buy. This allows the underwriters to build up a book of likely orders. Although inves- tors are not bound by their indications, they know that if they want to maintain a good relationship with the underwriters, they must be careful not to renege on their expres- sions of interest.

The managers of the firm are eager to secure the highest possible price for their stock, but the underwriters are likely to be cautious because they will be left with any unsold stock if they overestimate investor demand. As a result, underwriters typically try to underprice the initial public offering. Underpricing, they argue, is needed to tempt investors to buy stock and to reduce the cost of marketing the issue to custom- ers. Underpricing represents a cost to the existing owners since the new investors are allowed to buy shares in the firm at a favorable price.

Sometimes new issues are dramatically underpriced. For example, when the pro- spectus for the IPO of eBay was first published, the underwriters indicated that the company would sell 3.5 million shares at a price between $14 and $16 each. However, the enthusiasm for eBay’s web-based auction system was such that the underwriters increased the issue price to $18. The next morning dealers were flooded with orders to buy eBay; over 4.5 million shares traded, and the stock closed the day at a price of $47.375.

The experience of eBay is not typical, but it is common to see the stock price increase significantly from the issue price in the days following the sale. For example, one study of 7,900 new issues between 1980 and 2013 found an average first-day price rise of 18.0%. 3 Such immediate price jumps suggest that investors would have been prepared to pay much more than they did for the shares.

2 Sometimes states go beyond blue-sky laws in their efforts to protect their residents. When Apple Computer Inc. made its first public issue, the Massachusetts state government decided the offering was too risky for its residents and therefore banned the sale of the shares to investors in the state. The state relented later, after the issue was out and the price had risen. Massachusetts investors obviously did not appreciate this “protection.”

prospectus Formal summary that provides information on an issue of securities.

underpricing Issuing securities at an offering price set below the true value of the security.

3 These figures are provided on Jay Ritter’s home page, bear.cba.ufl.edu/ritter .

Example 15.1 Underpricing of IPOs Suppose an IPO is a secondary issue and the firm’s founders sell part of their hold- ing to investors. Clearly, if the shares are sold for less than their true worth, the founders will suffer an opportunity loss.

But what if the IPO is a primary issue that raises new cash for the company? Do the founders care whether the shares are sold for less than their market value? The following example illustrates that they do care.

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Twitter’s IPO prospectus

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Hot IPOs

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Chapter 15 How Corporations Raise Venture Capital and Issue Securities 443

Unfortunately, underpricing does not mean that anyone can become wealthy by buying stock in IPOs. If an issue is underpriced, everybody will want to buy it and the underwriters will not have enough stock to go around. You are therefore likely to get only a small share of these hot issues. If it is overpriced, other investors are unlikely to want it and the underwriter will be only too delighted to sell it to you. This phenom- enon is known as the winner’s curse. 4 It implies that, unless you can spot which issues are underpriced, you are likely to receive a small proportion of the cheap issues and a large proportion of the expensive ones. Since the dice are loaded against uninformed investors, they will play the game only if there is substantial underpricing on average.

4 The highest bidder in an auction is the participant who places the highest value on the auctioned object. There- fore, it is likely that the winning bidder has an overly optimistic assessment of true value. Winning the auction suggests that you have overpaid for the object—this is the winner’s curse. In the case of IPOs, your ability to “win” an allotment of shares may signal that the stock is overpriced.

Suppose Cosmos.com has 2 million shares outstanding and now offers a further 1 million shares to investors at $50. On the first day of trading the share price jumps to $80, so the shares that the company sold for $50 million are now worth $80 million. The total market capitalization of the company is 3  million  ×  $80  =  $240 million.

The value of the founders’ shares is equal to the total value of the company less the value of the shares that have been sold to the public—in other words, $240 million -  $80 million  =  $160 million. The founders might justifiably rejoice at their good for- tune. However, if the company had issued shares at a higher price, it would have needed to sell fewer shares to raise the $50 million that it needs and the founders would have retained a larger share of the company. For example, suppose that the outside investors, who put up $50 million, received shares that were worth only $50 million. In that case the value of the founders’ shares would be $240 million  -  $50 million  =  $190 million.

The effect of selling shares below their true value is to transfer $30 million of value from the founders to the investors who buy the new shares.

Example 15.2 Underpricing and the Winner’s Curse Suppose that an investor will earn an immediate 10% return on underpriced IPOs and lose 5% on overpriced IPOs. But because of high demand, you may get only half the shares you bid for when the issue is underpriced. Suppose you bid for $1,000 of shares in two issues, one overpriced and the other underpriced. You are awarded the full $1,000 of the overpriced issue but only $500 worth of shares in the underpriced issue. The net gain on your two investments is (.10  ×  $500)  -  (.05  × $1,000)  =  0. Your net profit is zero, despite the fact that, on average, the IPOs are underpriced (10% underpricing versus 5% overpricing). You have suffered the win- ner’s curse: You “win” a larger allotment of shares when they are overpriced.

What is the percentage profit earned by an investor who can identify the underpriced issues in Example 15.2? Who are such investors likely to be?

Self-Test 15.2

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444 Part Four Financing

The costs of a new issue are termed flotation costs. Underpricing is not the only flotation cost. In fact, when people talk about the cost of a new issue, they often think only of the direct costs of the issue. For example, preparation of the registration state- ment and prospectus involves management, legal counsel, and accountants, as well as underwriters and their advisers. There is also the underwriting spread. (Remember, underwriters make their profit by selling the issue at a higher price than they paid for it.) For most issues of $20 million to $80 million, the spread is 7%.

Look at the blue bars (corresponding to IPOs) in Figure 15.1 . These show the direct costs of going public. For all but the smallest IPOs the underwriting spread and admin- istrative costs are likely to absorb 7% to 8% of the proceeds from the issue. For the very largest IPOs, these direct costs may amount to only 5% of the proceeds.

flotation costs The costs incurred when a firm issues new securities to the public.

Example 15.3 Costs of an IPO The largest U.S. IPO was the $19.7 billion sale of stock by the credit card company Visa in 2008. A syndicate of 45 underwriters acquired a total of 446.6 million Visa shares for $42.768 each and then resold them to the public at an offering price of $44. The underwriters’ spread was therefore $44 -  $42.768  =  $1.232. The firm also paid a total of $45.5 million in legal fees and other costs. 5 Therefore, the direct costs of the Visa issue were as follows:

5 These figures do not capture all administrative costs. For example, they do not include management time spent on the issue.

Direct Expenses

Underwriting spread (446.6  million  ×  $1.232)  =  $550.2 million Other expenses 45.5 Total direct expenses $595.7 million

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The JOBS Act

FIGURE 15.1 Total direct costs as a percentage of gross proceeds, 2004–2008. The total direct costs for initial public offerings (IPOs), seasoned equity offerings (SEOs), convertible bonds, and straight bonds are composed of underwriter spreads and other direct expenses.

0

2

4

6

8

10 IPOs

SEOs

Convertibles

Bonds

Le ss

th an

25 0 25

0–

60 0 60

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Source: We are grateful to Nickolay Gantchev for undertaking these calculations, which update tables in Immoo Lee, Scott Lochhead, Jay Ritter, and Quanshui Zhao, “The Costs of Raising Capital,” Journal of Financial Research 19 (Spring 1996), pp. 59–74. Used with permission. Updates courtesy of Nickolay Gantchev.

The total amount of money raised by the issue was 446.6  million  ×  $44  =  $19,650 million. Of this sum 3% was absorbed by direct expenses (that is, 595.7/19,650  =  .030).

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Chapter 15 How Corporations Raise Venture Capital and Issue Securities 445

Other New-Issue Procedures Almost all IPOs in the United States use the bookbuilding method. In other words, the underwriters build up a book of likely orders, buy the issue from the company at a dis- count, and then resell it to investors. This method is in some ways like an auction, since potential buyers indicate how many shares they are prepared to buy at given prices. However, the indications are not binding and are used only as a guide to fix the price of the issue. The advantage of the bookbuilding method is that it allows underwriters to give preference to those investors whose bids are most helpful in setting the issue price and to offer them a reward in the shape of underpricing. But critics of the method point to the dangers of allowing the underwriters to decide who is allotted stock.

Stock can also be issued in an open auction. In this case, investors are invited to submit their bids, stating both an offering price and how many shares they wish to buy. The securities are then sold to the highest bidders. Most governments, including the U.S. Treasury, sell their bonds by auction. In the United States, auctions of common stock are fairly rare. However, in 2004 Google simultaneously raised eyebrows and $1.7 billion in the world’s largest IPO to be sold by auction.

The Underwriters We have described underwriters as playing a triple role—providing advice, buying a new issue from the company, and reselling it to investors. Underwriters don’t just help the company to make its initial public offering; they are called in whenever a company wishes to raise cash by selling securities to the public.

Successful underwriting requires considerable experience and financial muscle. If a large issue fails to sell, the underwriters may be left with a loss of several hundred million dollars and some very red faces. Underwriting in the United States is therefore dominated by the major investment banking firms, which specialize in underwriting new issues, dealing in securities, and arranging mergers.

They include such giants as JPMorgan Chase, Morgan Stanley, Goldman Sachs, and Bank of America Merrill Lynch. Large foreign banks, such as Deutsche Bank, Credit Suisse, UBS, and Barclays, are also heavily involved in underwriting securities that are sold internationally.

Underwriting is not always fun. In April 2008 the British bank HBOS offered its shareholders two new shares at a price of £2.75 for each five shares that they

Suppose that the underwriters acquired Visa shares for $45 and sold them to the public at an offering price of $47. If all other features of the offer were unchanged (and investors still valued the stock at $56.50 a share), what would have been the direct costs of the issue and the costs of underpricing? What would have been the total costs (direct costs plus underpricing) as a propor- tion of the market value of the shares?

Self-Test 15.3

In addition to these direct costs, there was the cost of underpricing. By the end of the first day’s trading Visa’s stock price had risen to $56.50, so investors valued Visa shares at 446.6  ×  $56.50  =  $25,233 million. In other words, Visa sold stock for $25,233  -  $19,650  =  $5,583 million less than its market value. This was the cost of underpricing.

Managers commonly focus only on the direct costs of an issue. But, when we add in the cost of underpricing, the total cost of the Visa issue as a proportion of the market value of the shares was ($595.7  +  $5,583)/$25,233  =  .24, or 24%.

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446 Part Four Financing

currently held. 6 The underwriters to the issue guaranteed that at the end of 8 weeks they would buy any new shares that the stockholders did not want. At the time of the offer HBOS shares were priced at about £5, so the underwriters felt confident that they would not have to honor their pledge. Unfortunately, they reckoned without the turbulent market in bank shares that year. The bank’s shareholders worried that the money they were asked to provide would largely go to bailing out the bondholders and depositors. By the end of the 8 weeks the price of HBOS stock had slumped below the issue price, and the underwriters were left with 932 million unwanted shares worth £3.6 billion and a lot of egg on their faces.

Companies get to make only one IPO, but underwriters are in the business all the time. Wise underwriters, therefore, realize that their reputation is on the line and will not handle an issue unless they believe the facts have been presented fairly to investors. If a new issue goes wrong and the stock price crashes, the underwriters can find them- selves very unpopular with their clients. For example, in 1999 the software company VA Linux went public at $30 a share. The next day trading opened at $299 a share, but then the price began to sag. Within 2 years it had fallen below $2. Disgruntled VA Linux investors sued the underwriters for overhyping the issue. VA Linux investors were not the only ones to feel aggrieved. Investment banks soon found themselves embroiled in a major scandal as evidence emerged that they had deliberately over- sold many of the issues that they underwrote during the dot-com boom years. There was further embarrassment when it emerged that several well-known underwriters had engaged in “spinning”—that is, allocating stock in popular new issues to managers of their important corporate clients. The underwriter’s seal of approval for a new issue no longer seemed as valuable as it once had.

15.3 General Cash Offers by Public Companies After the initial public offering a successful firm will continue to grow, and from time to time it will need to raise more money by issuing stock or bonds. An issue of addi- tional stock by a company whose stock already is publicly traded is called a seasoned offering. Any issue of securities needs to be formally approved by the firm’s board of directors. If a stock issue requires an increase in the company’s authorized capital, it also needs the consent of the stockholders.

Public companies can issue securities either by making a general cash offer to inves- tors at large or by making a rights issue, which is limited to existing shareholders. In the latter case, the company offers the shareholders the opportunity, or right, to buy more shares at an “attractive” price. For example, if the current stock price is $100, the company might offer investors an additional share at $50 for each share they hold.

Because the “attractive” offer is shared by and limited to all existing shareholders, it has no effect on their wealth. Suppose that before the issue an investor has one share worth $100 and $50 in the bank. If the investor takes up the offer of a new share, that $50 of cash is transferred from the investor’s bank account to the company’s. The investor now has two shares that are a claim on the original assets worth $100 and on the $50 cash that the company has raised. So the two shares are worth a total of $150, or $75 each. The investor’s wealth is unchanged.

6 This arrangement is known as a rights issue. We describe rights issues later in the chapter.

seasoned offering Sale of securities by a firm that is already publicly traded.

rights issue Issue of securities offered only to current stockholders.

Example 15.4 Rights Issues We have already come across one example of a rights issue—the offer by the British bank HBOS, which ended up in the hands of its underwriters. Let us look more closely at another issue.

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Chapter 15 How Corporations Raise Venture Capital and Issue Securities 447

In some countries the rights issue is the most common or only method for issuing stock, but in the United States rights issues are now very rare. We therefore will con- centrate on the mechanics of the general cash offer.

General Cash Offers and Shelf Registration When a public company makes a general cash offer of debt or equity, it essentially follows the same procedure used when it first went public. This means that it must first register the issue with the SEC and draw up a prospectus. 7 Before settling on the issue price, the underwriters will usually contact potential investors and build up a book of likely orders. The company will then sell the issue to the underwriters, and they in turn will offer the securities to the public.

Companies do not need to prepare a separate registration statement every time they issue new securities. Instead, they are allowed to file a single registration statement covering financing plans for up to 2 years into the future. The actual issues can then be sold to the public with scant additional paperwork, whenever the firm needs cash or thinks it can issue securities at an attractive price. This is called shelf registration — the registration is put “on the shelf,” to be taken down, dusted off, and used as needed.

Think of how you might use shelf registration when you are a financial manager. Sup- pose that your company is likely to need up to $200 million of new long-term debt over the next year or so. It can file a registration statement for that amount. It now has approval to issue up to $200 million of debt, but it isn’t obliged to issue any. Nor is it required to work through any particular underwriters—the registration statement may name the underwriters the firm thinks it may work with, but others can be substituted later.

Now you can sit back and issue debt as needed, in bits and pieces if you like. Sup- pose JPMorgan comes across an insurance company with $10 million ready to invest in corporate bonds, priced to yield, say, 7.3%. If you think that’s a good deal, you say OK and the deal is done, subject to only a little additional paperwork. JPMorgan then resells the bonds to the insurance company, hoping for a higher price than it paid for them.

Here is another possible deal. Suppose you think you see a window of opportu- nity in which interest rates are “temporarily low.” You invite bids for $100 million of bonds. Some bids may come from large investment bankers acting alone, others from ad hoc syndicates. But that’s not your problem; if the price is right, you just take the best deal offered.

general cash offer Sale of securities open to all investors by an already-public company.

7 The procedure is similar when a company makes an international issue of bonds or equity, but as long as these issues are not sold publicly in the United States, they do not need to be registered with the SEC.

shelf registration A procedure that allows firms to file one registration statement for several issues of the same security.

In September 2013 the British bank Barclays needed to raise £5.8 billion. It did so by offering its existing shareholders the right to buy one new share for every four that they currently held. The new shares were priced at £1.85 each, almost 40% below the preannouncement price.

Before the issue, Barclays had 12.68 billion shares outstanding, which were priced at £2.85 each. So investors valued the company at 12.68  ×  £2.85  =  £36.14 billion. The new issue increased the total number of shares by (1/4)  ×  12.68  =  3.17 billion and therefore raised 3.17  billion  ×   £1.85  =   £5.86 billion. Thus the issue increased the total value of the company to 36.14  +   5.86  =   £42.00 billion and reduced the value of each share to 42.00/15.85  =  £2.65.

Suppose that just before the issue you held four shares of Barclays plus £1.85 in cash. Your total wealth would be £13.25. If you decide to take up the rights issue, you would have to lay out all your cash to buy the one new share to which you are entitled, and you would end up with five shares worth 5  ×  £2.65  =  £13.25. You would have gotten what you paid for.

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448 Part Four Financing

Thus shelf registration offers several advantages:

1. Securities can be issued in dribs and drabs without incurring excessive costs. 2. Securities can be issued on short notice. 3. Security issues can be timed to take advantage of “market conditions” (although

any financial manager who can reliably identify favorable market conditions could make a lot more money by quitting and becoming a bond or stock trader instead).

4. The issuing firm can make sure that underwriters compete for its business.

Not all companies eligible for shelf registration actually use it for all their pub- lic issues. Sometimes they believe they can get a better deal by making one large issue through traditional channels, especially when the security to be issued has some unusual feature or when the firm believes it needs the investment banker’s counsel or stamp of approval on the issue. Thus shelf registration is less often used for issues of common stock than for garden-variety corporate bonds.

Costs of the General Cash Offer Whenever a firm makes a cash offer, it incurs substantial administrative costs. Also, the firm needs to compensate the underwriters by selling them securities below the price that they expect to receive from investors. Look back at Figure 15.1 , which shows the average underwriting spread and administrative costs for several types of security issues in the United States.

You can see that issue costs are higher for equity than for debt securities. This partly reflects the extra administrative costs of an equity issue. In addition, the under- writers demand extra compensation for the greater risk they take in buying and resell- ing equity.

Market Reaction to Stock Issues Because stock issues usually throw a sizable number of new shares onto the market, it is widely believed that they must temporarily depress the stock price. If the proposed issue is very large, this price pressure may, it is thought, be so severe as to make it almost impossible to raise money.

This belief in price pressure implies that a new issue depresses the stock price tem- porarily below its true value. However, that view doesn’t appear to fit very well with the notion of market efficiency. If the stock price falls solely because of increased sup- ply, then that stock would offer a higher return than comparable stocks and investors would be attracted to it as ants to a picnic.

Economists who have studied new issues of common stock have generally found that the announcement of the issue does result in a decline in the stock price. For industrial issues in the United States this decline amounts to about 3%. 8 While this may not sound overwhelming, such a price drop can be a large fraction of the money raised. Suppose that a company with a market value of equity of $5 billion announces its intention to issue $500 million of additional equity and thereby causes the stock price to drop by 3%. The loss in value is .03  ×  $5 billion, or $150 million. That’s 30% of the amount of money raised (.30  ×  $500  million  =  $150  million).

What’s going on here? Is the price of the stock simply depressed by the prospect of the additional supply? Possibly, but here is an alternative explanation.

Suppose managers (who have better information about the firm than outside inves- tors) know that their stock is undervalued. If the company sells new stock at this low

8 See, for example, P. Asquith and D. W. Mullins, “Equity Issues and Offering Dilution,” Journal of Financial Economics 15 (January–February 1986), pp. 61–90; R. W. Masulis and A. N. Korwar, “Seasoned Equity Offer- ings: An Empirical Investigation,” Journal of Financial Economics 15 (January–February 1986), pp. 91–118; and W. H. Mikkelson and M. M. Partch, “Valuation Effects of Security Offerings and the Issuance Process,” Journal of Financial Economics 15 (January–February 1986), pp. 31–60.

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Chapter 15 How Corporations Raise Venture Capital and Issue Securities 449

price, it will give the new shareholders a good deal at the expense of the old sharehold- ers. In these circumstances managers might be prepared to forgo the new investment rather than sell shares at too low a price.

If managers know that the stock is overvalued, the position is reversed. If the com- pany sells new shares at the high price, it will help its existing shareholders at the expense of the new ones. Managers might be prepared to issue stock even if the new cash were just put in the bank.

Of course investors are not stupid. They can predict that managers are more likely to issue stock when they think it is overvalued, and therefore they mark the price of the stock down accordingly. The tendency for stock prices to decline at the time of an issue may have nothing to do with increased supply. Instead, the stock issue may simply be a signal that well-informed managers believe the market has overpriced the stock. 9

15.4 The Private Placement Whenever a company makes a public offering, it must register the issue with the SEC. It could avoid this costly process by selling the issue privately. There are no hard- and-fast definitions of a private placement, but the SEC has insisted that the security should be restricted largely to knowledgeable investors.

One disadvantage of a private placement is that the investor cannot easily resell the security. This is less important to institutions such as life insurance companies, which invest huge sums of money in corporate debt for the long haul. In 1990 the SEC relaxed its restrictions on who could buy unregistered issues. Under Rule 144a large financial institutions can trade unregistered securities among themselves.

As you would expect, it costs less to arrange a private placement than to make a public issue. That might not be so important for the very large issues where costs are less significant, but it is a particular advantage for companies making smaller issues.

Another advantage of the private placement is that the debt contract can be custom- tailored for firms with special problems or opportunities. Also, if the firm wishes later to change the terms of the debt, it is much simpler to do this with a private placement where only a few investors are involved.

Therefore, it is not surprising that private placements occupy a particular niche in the corporate debt market, namely, loans to small and medium-size firms. These are the firms that face the highest costs in public issues, that require the most detailed investigation, and that may require specialized, flexible loan arrangements.

We do not mean that large, conventional firms should rule out private placements. Enormous amounts of capital are sometimes raised by this method. For example, in 2013, Sprint, the telecommunications company, borrowed $6.5 billion in a private placement. Nevertheless, the advantages of private placement—avoiding registration costs and establishing a direct relationship with the lender—are generally more impor- tant to smaller firms.

Of course these advantages are not free. Lenders in private placements have to be compensated for the risks they face and for the costs of research and negotiation. They also have to be compensated for holding an asset that is not easily resold. All these fac- tors are rolled into the interest rate paid by the firm. It is difficult to generalize about the differences in interest rates between private placements and public issues, but a typical yield differential is on the order of half a percentage point.

9 This explanation was developed in S. C. Myers and N. S. Majluf, “Corporate Financing and Investment Deci- sions When Firms Have Information That Investors Do Not Have,” Journal of Financial Economics 13 (1984), pp. 187–222.

private placement Sale of securities to a limited number of investors without a public offering.

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450 Part Four Financing

SUMMARY Infant companies raise venture capital to carry them through to the point at which they can make their first public issue of stock. Venture capital firms try to structure the financ- ing to avoid conflicts of interest. If both the entrepreneur and the venture capital investors have an important equity stake in the company, they are likely to pull in the same direction. The entrepreneur’s willingness to take that stake also signals management’s confidence in the company’s future. In addition, most venture capital is provided in stages that keep the firm on a short leash and force it to prove at each stage that it deserves the additional funds.

The initial public offering or IPO is the first sale of shares in a general offering to inves- tors. The sale of the securities is usually managed by an underwriting firm that buys the shares from the company and resells them to the public. The underwriter helps to prepare a prospectus, which describes the company and its prospects. Underwriting firms have expertise in such sales because they are in the business all the time, whereas the company raises capital only occasionally. The costs of an IPO include direct costs, such as legal and administrative fees, as well as the underwriting spread —the difference between the price the underwriter pays to acquire the shares from the firm and the price the public pays the underwriter for those shares. Another major implicit cost is the underpricing of the issue—that is, shares are typically sold to the public somewhat below the true value of the security. This discount is reflected in abnormally high average returns to new issues on the first day of trading.

There are always economies of scale in issuing securities. It is cheaper to go to the market once for $100 million than to make two trips for $50 million each. Consequently, firms “bunch” security issues. This may mean relying on short-term financing until a large issue is justified. Or it may mean issuing more than is needed at the moment to avoid another issue later.

A seasoned offering may depress the stock price. The extent of this price decline var- ies, but for issues of common stocks by industrial firms the fall in the value of the existing stock may amount to a significant proportion of the money raised. The likely explanation for this pressure is the information the market reads into the company’s decision to issue stock.

Shelf registration often makes sense for debt issues by blue-chip firms. Shelf registra- tion reduces the time taken to arrange a new issue, it increases flexibility, and it may cut underwriting costs. It seems best suited for debt issues by large firms that are happy to switch between investment banks. It seems least suited for issues of unusually risky securi- ties or for issues by small companies that most need a close relationship with an invest- ment bank.

In private placements, the firm places the newly issued securities with a small number of large institutions. These arrangements avoid registration expenses, may be tailored to the special needs of the issuer, and, in the case of debt, allow for a more direct relationship with the lender. However, buyers need to be compensated for the fact that such issues are not easily resold. Private placements are well-suited for small, risky, or unusual firms, but the advantages are not worth as much to blue-chip borrowers.

How do venture capital firms design successful deals? (LO15-1)

How do firms make initial public offerings, and what are the costs of such offerings? (LO15-2)

What are some of the significant issues that arise when established firms make a general cash offer of securities? (LO15-3)

How do companies make private placements? (LO15-4)

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Chapter 15 How Corporations Raise Venture Capital and Issue Securities 451

QUESTIONS AND PROBLEMS 1. Venture Capital. True or false? (LO15-1)

a. Venture capital companies know that managers are more likely to work hard if they can be assured of a good steady salary.

b. Venture capital companies generally advance the money in stages. c. Venture capital companies are generally passive investors and are happy to let the companies

in which they are invested get on with the job. d. Some young companies grow with the aid of equity investment provided by wealthy indi-

viduals known as angel investors.

2. Venture Capital. Complete the passage using the following terms: limited partners, venture capital, private, underwriters, general partners, private equity, corporate venturers, partner- ships, private, angel investors. ( Note: Not all terms will be used.) (LO15-1) Equity capital in young businesses is known as _____, and it is provided by specialist firms, wealthy individuals (known as _____), and large technology companies that act as _____. Ven- ture capital funds are organized as _____. The management companies are the _____, and pen- sion funds and other investors are the _____. Venture capital partnerships are often lumped together with similar partnerships that buy whole companies and take them _____. The general term for these firms is _____ companies.

3. Venture Capital. (LO15-1)

a. “A signal is credible only if it is costly.” Explain why an entrepreneur’s willingness to invest in her company’s equity is a credible signal. Is a willingness to accept only part of the ven- ture capital that will eventually be needed also a credible signal?

b. “When managers take their reward in the form of increased leisure or executive jets, the cost is borne by the shareholders.” Explain how venture capital financing tackles this problem.

4. Stock Issues. True or false? (LO15-1–LO15-3)

a. Venture capitalists typically provide first-stage financing sufficient to cover all development expenses. Second-stage financing is provided by stock issued in an IPO.

b. Underpricing in an IPO is a problem only when the original investors are selling part of their holdings.

c. Stock price generally falls when the company announces a new issue of shares. This is attributable to the information released by the decision to issue.

5. IPO Costs. Moonscape has just completed an initial public offering. The firm sold 3 million shares at an offer price of $8 per share. The underwriting spread was $.50 a share. The price of the stock closed at $12 per share at the end of the first day of trading. The firm incurred $100,000 in legal, administrative, and other costs. (LO15-2)

a. What were flotation costs as a fraction of funds raised? b. Were flotation costs for Moonscape higher or lower than is typical for IPOs of this size (see

Figure 15.1 )?

6. IPO Costs. When Microsoft went public, the company sold 2 million new shares (the primary issue). In addition, existing shareholders sold .8 million shares (the secondary issue) and kept 21.1 million shares. The new shares were offered to the public at $21, and the underwriters received a spread of $1.31 a share. At the end of the first day’s trading the market price was $35 a share. (LO15-2)

a. How much money did the company receive before paying its portion of the direct costs? b. How much did the existing shareholders receive from the sale of their shares? c. If the issue had been sold to the underwriters for $30 a share, how many shares would the

company have needed to sell to raise the same amount of cash? d. How much better off would the existing shareholders have been?

finance

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452 Part Four Financing

a. What is the average underpricing of this sample of IPOs? b. What is the average initial return on my “portfolio” of shares purchased from the four IPOs

I bid on? Calculate this average initial return, weighting by the amount of money invested in each issue.

c. “You have just encountered the problem of the winners’ curse.” True or false?

8. IPO Costs. Look at the illustrative new-issue prospectus in the appendix. (LO15-2)

a. Is this issue a primary offering, a secondary offering, or both? b. What are the direct costs of the issue as a percentage of the total proceeds? c. Are these direct costs more than the average for an issue of this size? d. Suppose that on the first day of trading the price of Hotch Pot stock is $15 a share. What are

the total costs of the issue as a percentage of the market price? e. After paying her share of the expenses, how much will the firm’s president, Emma Lucullus,

receive from the sale? f. What will be the value of the shares that Emma Lucullus retains in the company?

9. Underpricing. In some U.K. IPOs any investor may be able to apply to buy shares. Mr. Bean has observed that on average these stocks are underpriced by about 9%, and for some years he has followed a policy of applying for a constant proportion of each issue. He is therefore disap- pointed and puzzled to find that this policy has not resulted in a profit. Explain to him why this is so. (LO15-2)

10. Issue Methods. After each of the following issue methods, we have listed two types of issue. Choose the one more likely to employ that method. (LO15-4)

a. Rights issue (initial public offer / further sale of an already publicly traded stock) b. Private placement (issue of existing stock / bond issue by an industrial company) c. Shelf registration (initial public offer / bond issue by a large industrial company)

11. Issue Methods. (LO15-4)

a. Is a private placement more likely to be used for issues of seasoned stock or seasoned bonds by an industrial company?

b. Is a rights issue more likely to be used for an initial public offering or for subsequent issues of stock?

c. Is shelf registration more likely to be used for issues of unseasoned stocks or bonds by a large industrial company?

12. Issue Methods. Each of the terms listed below on the left is associated with one of the events on the right. Can you match them up? (LO15-3)

a. shelf registration A. The underwriter agrees to buy the issue from the company at a b. firm commitment fixed price. c. rights issue B. The company offers to sell stock to existing stockholders. C. Several issues of the same security may be sold under the same

registration.

13. Issue Methods. For each of the following pairs of issues, state which issue is likely to involve the lower proportionate underwriting and administrative costs. (LO15-3)

a. A large issue or a small issue b. A bond issue or a common stock issue c. A small private placement of bonds or a small general cash offer of bonds

7. IPO Costs. Having heard about IPO underpricing, I put in an order to my broker for 1,000 shares of every IPO he can get for me. After 3 months, my investment record is as follows: (LO15-2)

IPO Shares Allocated to Me Price per Share Initial Return

A 500 $10 7% B 200 20 12 C 1,000 8 - 2 D 0 12 23

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Chapter 15 How Corporations Raise Venture Capital and Issue Securities 453

14. Private Placements. You need to choose between making a public offering and arranging a private placement. In each case the issue involves $10 million face value of 10-year debt. You have the following data for each: (LO15-4)

• A public issue: The interest rate on the debt would be 8.5%, and the debt would be issued at face value. The underwriting spread would be 1.5%, and other expenses would be $80,000.

• A private placement: The interest rate on the private placement would be 9%, but the total issuing expenses would be only $30,000.

a. What is the difference in the proceeds to the company net of expenses? b. Other things being equal, which is the better deal? c. What other factors beyond the interest rate and issue costs would you wish to consider

before deciding between the two offers?

15. Issue Methods. Match each of the following terms with the correct definition: (LO15-3)

a. shelf registration A. Sale of stock by a company to raise new cash b. seasoned issue B. The difference between the issue price and the price paid by c. primary issue the underwriters d. secondary issue C. State rules governing the issue of securities e. best efforts D. Underwriter’s agreement to sell as much of an issue as f. underwriters’ spread possible g. blue-sky laws E. Sale of securities by existing investors h. registration statement F. Sale of additional stock by a public company G. Registration statement covering possible further issues of

securities H. Document filed with SEC providing details of a new issue

16. Issue Methods. Young Corporation stock currently sells for $30 per share. There are 1 million shares currently outstanding. The company announces plans to raise $3 million by offering shares to the public at a price of $30 per share. (LO15-3)

a. If the underwriting spread is 6%, how many shares will the company need to issue in order to be left with net proceeds of $3 million?

b. If other administrative costs are $60,000, what is the dollar value of the total direct costs of the issue?

c. If the share price falls by 3% at the announcement of the plans to proceed with a seasoned offering, what is the dollar cost of the announcement effect?

17. Issue Methods. The market value of the research firm Fax Facts is $600 million. The firm issues an additional $100 million of stock, but as a result the stock price falls by 2%. What is the cost of the price drop to existing shareholders as a fraction of the funds raised? (LO15-3)

18. Underwriting. Each of the terms listed below on the left is associated with one of the events on the right. Can you match them up? (LO15-3)

a. best efforts A. Investors indicate to the underwriter how many shares they would b. bookbuilding like to buy in a new issue, and these indications are used to help set c. shelf registration the price. B. The underwriter accepts responsibility only to try to sell the issue. C. Several tranches of the same security may be sold under the same

registration. (A “tranche” is a batch, a fraction of a larger issue.)

19. Rights Issues. Associated Breweries is planning to market unleaded beer. To finance the ven- ture, it proposes to make a rights issue with a subscription price of $10. One new share can be purchased for each two shares held. The company currently has outstanding 100,000 shares priced at $40 a share. Assuming that the new money is invested to earn a fair return, give values for the following: (LO15-3)

a. Number of new shares b. Amount of new investment c. Total value of company after the issue d. Total number of shares after the issue e. Share price after the issue

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454 Part Four Financing

20. Rights Issues. Pandora Box Company Inc. makes a rights issue at a subscription price of $5 a share. One new share can be purchased for every five shares held. Before the issue there were 10 million shares outstanding and the share price was $6. (LO15-3)

a. What is the total amount of new money raised? b. What is the expected stock price after the rights are issued? c. By what percentage would the total value of the company need to fall before shareholders

would be unwilling to take up their rights? d. Suppose that you initially own 100 shares plus $100 in the bank. If you take up your rights

issue, what will be your total wealth after the issue is completed? e. Suppose that the company now decides to issue the new stock at $4 instead of $5 a share.

How many new shares would it have needed to raise the same sum of money? f. What is the expected stock price under this new arrangement after the rights are issued? g. If you take up your rights issue under this new arrangement, what will be your total wealth

after the issue is completed? h. Which arrangement makes you better off: the first, the second, or neither?

WEB EXERCISES 1. In the appendix to this chapter we provide a flavor of an IPO prospectus, and to see an actual

prospectus, you can scan the icon in the margin on page 442 to see Twitter’s prospectus. Try finding a prospectus for a recent IPO. We suggest that you first log on to finance.yahoo .com and click on the Investing tab to find a recent IPO by a U.S. company. Now log on to the SEC’s huge database at www.sec.gov/edgar/searchedgar/webusers.htm . Edgar can be a bit complicated, but the final IPO prospectus should be shown as Form 424B4. On the basis of this prospectus, do you think the stock looks like an attractive investment? Which parts of the statement appear most useful? Which seem the least useful? What were the direct expenses of the issue?

2. We describe underpricing as part of the costs of a new issue. Jay Ritter’s home page ( bear.cba. ufl.edu/ritter ) is a mine of information on IPO underpricing. Look up his table of underpricing by year. Is underpricing less of a problem now than in the boom IPO years of 1998–2000? Now look at Jay Ritter’s table of “money-left-on-the-table.” Which company provided the greatest 1-day dollar gains to investors?

CHALLENGE PROBLEM 21. Venture Capital. Here is a difficult question: Pickwick Electronics is a new high-tech company

financed entirely by 1 million ordinary shares, all of which are owned by George Pickwick. The firm needs to raise $1 million now for stage 1 and, assuming all goes well, a further $1 million at the end of 5 years for stage 2. First Cookham Venture Partners is considering two possible financing schemes:

• Buying 2 million shares now at their current valuation of $1. • Buying 1 million shares at the current valuation and investing a further $1 million at the end

of 5 years at whatever the shares are worth.

The outlook for Pickwick is uncertain, but as long as the company can secure the additional finance for stage 2, it will be worth either $2 million or $12 million after completing stage 2. (The company will be valueless if it cannot raise the funds for stage 2.) Show the possible payoffs for Mr. Pickwick and First Cookham, and explain why one scheme might be preferred. Assume an interest rate of zero. (LO15-1)

Template can be found in Connect.

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Chapter 15 How Corporations Raise Venture Capital and Issue Securities 455

SOLUTIONS TO SELF-TEST QUESTIONS 15.1 Unless the firm can secure second-stage financing, it is unlikely to succeed. If the entrepre-

neur is going to reap any reward on his own investment, he needs to put in enough effort to get further financing. By accepting only part of the necessary venture capital, management increases its own risk and reduces that of the venture capitalist. This decision would be costly and foolish if management lacked confidence that the project would be successful enough to get past the first stage. A credible signal by management is one that only managers who are truly confident can afford to provide. (Words are cheap. So just saying that you are confident is not a credible signal.)

15.2 If an investor can distinguish between overpriced and underpriced issues, she will bid only on the underpriced ones. In this case she will purchase only issues that provide a 10% gain. However, the ability to distinguish these issues requires considerable insight and research. The return to the informed IPO participant may be viewed as a return on the resources expended to become informed.

15.3 Underwriting spread = 446.6  million  ×  $2 $ 893.2 million Other expenses 45.5 Total direct expenses $ 938.7 million Underpricing  =  446.6  million  ×  ($56.50  -  $47) 4,242.7 Total expenses $ 5,181.4 million Market value of issue  =  446.6  ×  $56.50 $ 25,232.9 million

Expenses as a proportion of market value  =  $5,181.4/25,232.9  =  .205, or 20.5%.

MINICASE Mutt.Com was founded in 2011 by two graduates of the Univer- sity of Wisconsin with help from Georgina Sloberg, who had built up an enviable reputation for backing new start-up businesses. Mutt.Com ’s user-friendly system was designed to find buyers for unwanted pets. Within 3 years the company was generating rev- enues of $3.4 million a year and, despite racking up sizable losses, was regarded by investors as one of the hottest new e-commerce businesses. The news that the company was preparing to go public therefore generated considerable excitement.

The company’s entire equity capital of 1.5 million shares was owned by the two founders and Ms. Sloberg. The initial public offering involved the sale of 500,000 shares by the three existing shareholders, together with the sale of a further 750,000 shares by the company in order to provide funds for expansion.

The company estimated that the issue would involve legal fees, auditing, printing, and other expenses of $1.3 million, which would be shared proportionately between the selling shareholders and the company. In addition, the company agreed to pay the underwriters a spread of $1.25 per share (this cost also would be shared).

The roadshow had confirmed the high level of interest in the issue, and indications from investors suggested that the entire issue could be sold at a price of $24 a share. The underwriters, however, cautioned about being too greedy on price. They pointed out that indications from investors were not the same as firm orders. Also, they argued, it was much more important to have a successful issue

than to have a group of disgruntled shareholders. They therefore suggested an issue price of $18 a share.

That evening Mutt.Com ’s financial manager decided to run through some calculations. First, she worked out the net receipts to the company and the existing shareholders assuming that the stock was sold for $18 a share. Next, she looked at the various costs of the IPO and tried to judge how they stacked up against the typical costs for similar IPOs. That brought her up against the question of underpricing. When she had raised the matter with the underwriters that morning, they had dismissed the notion that the initial day’s return on an IPO should be considered part of the issue costs. One of the members of the underwriting team had asked: “The under- writers want to see a high return and a high stock price. Would Mutt.Com prefer a low stock price? Would that make the issue less costly?” Mutt.Com ’s financial manager was not convinced but felt that she should have a good answer. She wondered whether under- pricing was only a problem because the existing shareholders were selling part of their holdings. Perhaps the issue price would not matter if they had not planned to sell.

Is the initial day’s return on the IPO a real cost to the firm? How much would that cost be if the stock is offered at $18 but actu- ally could be sold for $24? How would you respond to the under- writer’s questions, “Would Mutt.Com prefer a low stock price? Would that make the issue less costly?”

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456 Part Four Financing

APPENDIX Hotch Pot’s New-Issue Prospectus 10

10 Real prospectuses would be much longer than our simple example.

Price to Public Underwriting

Discount Proceeds to Company*

Proceeds to Selling Shareholders †

Per share $12.00 $1.30 $10.70 $10.70 Total † $9,600,000 $1,040,000 $5,350,000 $3,210,000

* Before deducting expenses payable by the Company estimated at $400,000, of which $250,000 will be paid by the Company and $150,000 by the Selling Stockholders. †  The Company and the Selling Shareholders have granted to the Underwriters options to purchase up to 120,000 additional shares at the initial public offering price less the underwriting discount, solely to cover overallotment.

Prospectus 800,000 Shares Hotch Pot Inc. Common Stock ($.01 par value)

Of the 800,000 shares of Common Stock offered hereby, 500,000 shares are being sold by the Com- pany and 300,000 shares are being sold by the Selling Stockholders. See “Principal and Selling Stockholders.” The Company will not receive any of the proceeds from the sale of shares by the Selling Stockholders.

Before this offering there has been no public market for the Common Stock. These securities involve a high degree of risk. See “Certain Factors.”

THESE SECURITIES HAVE NOT BEEN APPROVED OR DISAPPROVED BY THE SECU- RITIES AND EXCHANGE COMMISSION NOR HAS THE COMMISSION PASSED ON THE ACCURACY OR ADEQUACY OF THIS PROSPECTUS. ANY REPRESENTATION TO THE CONTRARY IS A CRIMINAL OFFENSE.

The Common Stock is offered, subject to prior sale, when, as, and if delivered to and accepted by the Underwriters and subject to approval of certain legal matters by their counsel and by counsel for the Company and the Selling Shareholders. The Underwriters reserve the right to withdraw, cancel, or modify such offer and reject orders in whole or in part.

Silverman Pinch Inc. April 1, 2014

No person has been authorized to give any information or to make any representations, other than as contained therein, in connection with the offer contained in this Prospectus, and, if given or made, such information or representations must not be relied upon. This Prospectus does not constitute an offer of any securities other than the registered securities to which it relates or an offer to any person in any jurisdiction where such an offer would be unlawful. The delivery of this Prospectus at any time does not imply that information herein is correct as of any time subsequent to its date.

IN CONNECTION WITH THIS OFFERING, THE UNDERWRITER MAY OVERALLOT OR EFFECT TRANSACTIONS WHICH STABILIZE OR MAINTAIN THE MARKET PRICE OF THE COMMON STOCK OF THE COMPANY AT A LEVEL ABOVE THAT WHICH MIGHT OTHERWISE PREVAIL IN THE OPEN MARKET. SUCH STABILIZING, IF COMMENCED, MAY BE DISCONTINUED AT ANY TIME.

Prospectus Summary The following summary information is qualified in its entirety by the detailed information and finan- cial statements appearing elsewhere in this Prospectus.

The Company: Hotch Pot Inc. operates a chain of 140 fast-food outlets in the United States offer- ing unusual combinations of dishes.

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Chapter 15 How Corporations Raise Venture Capital and Issue Securities 457

Selected Financial Data [ The Prospectus typically includes a summary income statement and balance sheet. ]

The Offering: Common Stock offered by the Company 500,000 shares; Common Stock offered by the Selling Stockholders 300,000 shares; Common Stock to be outstanding after this offer- ing 3,500,000 shares.

Use of Proceeds: For the construction of new restaurants and to provide working capital.

The Company Hotch Pot Inc. operates a chain of 140 fast-food outlets in Illinois, Pennsylvania, and Ohio. These restaurants specialize in offering an unusual combination of foreign dishes.

The Company was organized in Delaware in 2004.

Use of Proceeds The Company intends to use the net proceeds from the sale of 500,000 shares of Common Stock offered hereby, estimated at approximately $5 million, to open new outlets in midwest states and to provide additional working capital. It has no immediate plans to use any of the net proceeds of the offering for any other specific investment.

Dividend Policy The Company has not paid cash dividends on its Common Stock and does not anticipate that divi- dends will be paid on the Common Stock in the foreseeable future.

Certain Factors Investment in the Common Stock involves a high degree of risk. The following factors should be carefully considered in evaluating the Company:

Substantial Capital Needs The Company will require additional financing to con- tinue its expansion policy. The Company believes that its relations with its lenders are good, but there can be no assurance that additional financing will be available in the future.

Competition The Company is in competition with a number of restaurant chains supplying fast food. Many of these companies are substantially larger and better capitalized than the Company.

Capitalization The following table sets forth the capitalization of the Company as of December 31, 2013, and as adjusted to reflect the sale of 500,000 shares of Common Stock by the Company.

Actual As Adjusted (in thousands)

Long-term debt $ — $ — Stockholders’ equity 30 35 Common stock—$.01 par value, 3,000,000 shares outstanding, 3,500,000 shares outstanding, as adjusted

Paid-in capital 1,970 7,315 Retained earnings 3,200 3,200 Total stockholders’ equity 5,200 10,550 Total capitalization $5,200 $10,550

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458 Part Four Financing

Certain Transactions At various times between 2004 and 2013 First Cookham Venture Partners invested a total of $1.5 million in the Company. In connection with this investment, First Cookham Venture Partners was granted certain rights to registration under the Securities Act of 1933, including the right to have their shares of Common Stock registered at the Company’s expense with the Securities and Exchange Commission.

Principal and Selling Stockholders The following table sets forth certain information regarding the beneficial ownership of the Company’s voting Common Stock as of the date of this prospectus by (i) each person known by the Company to be the beneficial owner of more than 5% of its voting Common Stock, and (ii) each director of the Company who beneficially owns voting Common Stock. Unless otherwise indicated, each owner has sole voting and dispositive power over his shares.

Emma Lucullus Emma Lucullus established the Company in 2004 and has been its Chief Execu- tive Officer since that date.

Ed Lucullus Ed Lucullus has been employed by the Company since 2004.

Executive Compensation The following table sets forth the cash compensation paid for services rendered for the year 2013 by the executive officers:

Management’s Analysis of Results of Operations and Financial Condition Revenue growth for the year ended December 31, 2013, resulted from the opening of ten new restau- rants in the Company’s existing geographic area and from sales of a new range of desserts, notably crepe suzette with custard. Sales per customer increased by 20% and this contributed to the improve- ment in margins.

During the year the Company borrowed $600,000 from its banks at an interest rate of 2% above the prime rate.

Business Hotch Pot Inc. operates a chain of 140 fast-food outlets in Illinois, Pennsylvania, and Ohio. These restaurants specialize in offering an unusual combination of foreign dishes. 50% of company’s rev- enues derived from sales of two dishes, sushi and sauerkraut and curry bolognese. All dishes are prepared in three regional centers and then frozen and distributed to the individual restaurants.

Management The following table sets forth information regarding the Company’s directors, executive officers, and key employees:

Name Age Position

Emma Lucullus 28 President, Chief Executive Officer, & Director Ed Lucullus 33 Treasurer & Director

Name Capacity Cash Compensation

Emma Lucullus President and Chief Executive Officer $130,000 Ed Lucullus Treasurer $ 95,000

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Chapter 15 How Corporations Raise Venture Capital and Issue Securities 459

Lock-Up Agreements The holders of the Common Stock have agreed with the Underwriter not to sell, pledge, or otherwise dispose of their shares, other than as specified in this Prospectus, for a period of 180 days after the date of the Prospectus without the prior consent of Silverman Pinch.

Description of Capital Stock The Company’s authorized capital stock consists of 10,000,000 shares of voting Common Stock.

As of the date of this Prospectus, there are 4 holders of record of the Common Stock. Under the terms of one of the Company’s loan agreements, the Company may not pay cash divi-

dends on Common Stock except from net profits without the written consent of the lender.

Underwriting Subject to the terms and conditions set forth in the Underwriting Agreement, the Underwriter, Sil- verman Pinch Inc., has agreed to purchase from the Company and the Selling Stockholders 800,000 shares of Common Stock.

There is no public market for the Common Stock. The price to the public for the Common Stock was determined by negotiation between the Company and the Underwriter and was based on, among other things, the Company’s financial and operating history and condition, its prospects, and the prospects for its industry in general, the management of the Company, and the market prices of secu- rities for companies in businesses similar to that of the Company.

Legal Matters The validity of the shares of Common Stock offered by the Prospectus is being passed on for the Company by Cameron, Merkel, and Sarkozy and for the Underwriter by Harper Berlusconi.

Legal Proceedings Hotch Pot was served in January 2014 with a summons and complaint in an action commenced by a customer who alleges that consumption of the Company’s products caused severe nausea and loss of feeling in both feet. The Company believes that the complaint is without foundation.

Experts The consolidated financial statements of the Company have been so included in reliance on the reports of Hooper Firebrand, independent accountants, given on the authority of that firm as experts in auditing and accounting.

Financial Statements [ Text and tables omitted. ]

Shares Benefi cially Owned prior to Offering

Shares Benefi cially Owned after Offering

Name of Benefi cial Owner Number Percent

Shares to Be Sold Number Percent

Emma Lucullus 400,000 13.3 25,000 375,000 12.9 Ed Lucullus 400,000 13.3 25,000 375,000 12.9 First Cookham Venture Partners 1,700,000 66.7 250,000 1,450,000 50.0 Hermione Kraft 200,000 6.7 — 200,000 6.9

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460

Debt Policy

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

16-1 Show why capital structure does not affect firm value in perfect capital markets.

16-2 Calculate interest tax shields and explain why the U.S. tax system encourages debt finance.

16-3 Describe the costs of financial distress and explain the trade-off theory of capital structure.

16-4 Explain the benefits (and sometimes costs) of financial slack and how the target level of financial slack influences debt policy.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

16 CHAPTE R

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461

P A

R T

F IV

E

A firm’s basic financial resource is the stream of cash flows produced by its assets and operations. When the firm is financed entirely by common stock, all those cash flows belong to the

stockholders. When it issues both debt and equity, the

firm splits the cash flows into two streams, a relatively

safe stream that goes to the debtholders and a more

risky one that goes to the stockholders.

The firm’s mix of securities is known as its capital

structure. Look at Table 16.1 . You can see that in some

industries companies borrow much more heavily

than in others. Most high-tech firms, such as Intel and

Microsoft, rely almost wholly on equity finance. So do

most biotech, software, and Internet companies. At

the other extreme, corporations in the chemical, food,

and hotel industries rely much more on debt finance.

Capital structure is not immutable. Firms can

change their capital structure, sometimes almost over-

night. Shareholders want management to choose

the mix of securities that maximizes firm value. But is

there an optimal capital structure? We must consider

the possibility that no combination has any greater

appeal than any other. Perhaps the really impor-

tant decisions concern the company’s assets, and

decisions about capital structure are mere details—

matters to be attended to but not worried about.

In the first part of the chapter we look at examples

in which capital structure doesn’t matter, and we

point out some tempting financial fallacies that you

should be prepared to resist. After that we put back

some of the things that do make a difference, such as

taxes, bankruptcy, and the signals that your financing

decisions may send to investors. We then draw up a

checklist for financial managers who need to decide

on the firm’s capital structure.

The appendix to the chapter contains a brief dis-

cussion of what happens when firms cannot pay

their debts and enter bankruptcy proceedings.

D e

b t a

n d

P a

yo u

t P o

lic y

River Cruises is reviewing its capital structure. More debt would increase the expected return on its shares, but would it add value?

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462 Part Five Debt and Payout Policy

16.1 How Borrowing Affects Value in a Tax-Free Economy

It is after the ball game and the pizza man is delivering a pizza to Yogi Berra. “Should I cut it into four slices as usual, Yogi?” asks the pizza man. “No,” replies Yogi, “Cut it into eight; I’m hungry tonight.”

If you understand why more slices won’t sate Yogi’s appetite, you will have no diffi- culty understanding when a company’s choice of capital structure does not increase the underlying value of the firm.

Think of a simple balance sheet, with all entries expressed as current market values:

Assets Liabilities and Stockholders’ Equity

Value of cash fl ows from the fi rm’s real assets and operations

Market value of debt Market value of equity

Value of fi rm Value of fi rm

The right- and left-hand sides of a balance sheet are always equal. (Balance sheets have to balance!) Therefore, if you add up the market values of all the firm’s debt and equity securities, you can calculate the value of all the future cash flows from the firm’s real assets and operations.

In fact, the value of those cash flows determines the value of the firm and therefore determines the aggregate value of all the firm’s outstanding debt and equity securities. If the firm changes its capital structure, say, by using more debt and less equity financ- ing, overall value should not change.

Think of the left-hand side of the balance sheet as the size of the pizza; the right- hand side determines how it is sliced. A company can slice its cash flow into as many parts as it likes, but the value of those parts will always sum back to the value of the unsliced cash flow. (Of course, we have to make sure that none of the cash-flow stream is lost in the slicing. We cannot say “The value of a pizza is independent of how it is sliced” if the slicer is also a nibbler.)

The basic idea here (the value of a pizza does not depend on how it is sliced) has various applications. Yogi Berra got friendly chuckles for his misapplication. Franco Modigliani and Merton Miller received Nobel Prizes for applying it to corporate financing. Modigliani and Miller, always referred to as “MM,” showed in 1958 that the value of a firm does not depend on how its cash flows are “sliced.” More precisely,

capital structure The mix of long-term debt and equity financing.

Industry Debt Ratio

Communications equipment 0 .03 Internet information providers 0 .04 Integrated oil and gas 0.08 Software 0 .18 Semiconductors 0 .20 Pharmaceutical and biotechnology 0 .28 Appliances 0 .31 Gas utilities 0.40 Aerospace 0 .42 Railroads 0 .44 Chemicals 0 .50 Food 0 .63 Hotels 0 .68

Note: Debt to total capital ratio  =   D /( D   +   E ), where D and E are the book values of long-term debt and equity. Source: Compustat.

TABLE 16.1 Median ratios of long-term debt to total capital, 2012

Industry debt ratios in 2013

BEYOND THE PAGE

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Chapter 16 Debt Policy 463

they demonstrated the following proposition: When there are no taxes and capital markets function well, the market value of a company does not depend on its capital structure. In other words, financial managers cannot increase value by changing the mix of securities used to finance the company.

Of course, this MM proposition rests on some important simplifying assumptions. For example, capital markets have to be “well functioning.” This means that investors can trade securities without restrictions and can borrow or lend on the same terms as the firm. It also means that capital markets are efficient, so securities are fairly priced given the information available to investors. (We discussed market efficiency in Chap- ter 7.) MM’s proposition also assumes that there are no distorting taxes, and it ignores the costs encountered if a firm borrows too much and lands in financial distress.

The firm’s capital structure decision does matter if these assumptions are not true or if other practical complications are encountered. But the best way to start thinking about capital structure is to work through MM’s argument. To keep things as simple as possible, we will ignore taxes until further notice.

MM’s Argument—A Simple Example Cleo, the president of River Cruises, is reviewing that firm’s capital structure with Antony, the financial manager. Table 16.2 shows the current position. The company has no debt, and all its operating income is paid as dividends to the shareholders. The expected earnings and dividends per share are $1.25, but this figure is by no means certain—it could turn out to be more or less than $1.25. For example, earnings could fall to $.75 in a slump or they could jump to $1.75 in a boom.

The price of each share is $10. The firm expects to produce a level stream of earn- ings and dividends in perpetuity. No growth is forecast, so stockholders’ expected return is equal to the dividend yield—that is, the expected dividend per share divided by the price, $1.25/$10.00  =  .125, or 12.5%.

Cleo has come to the conclusion that shareholders would be better off if the company had equal proportions of debt and equity. She therefore proposes to issue $500,000 of debt at an interest rate of 10% and to use the proceeds to repurchase 50,000 shares. This is called a restructuring. Notice that the $500,000 raised by the new borrowing does not stay in the firm. It goes right out the door to shareholders in order to repur- chase and retire 50,000 shares. Therefore, the assets and investment policy of the firm are not affected. Only the financing mix changes.

What would MM say about this new capital structure? Suppose the change is made. Operating income is the same, so the value of the “pie” is fixed at $1 million. With $500,000 in new debt outstanding, the remaining common shares must be worth $500,000, that is, 50,000 shares at $10 per share. The total value of the debt and equity is still $1 million.

restructuring Process of changing the firm’s capital structure without changing its real assets.

TABLE 16.2 River Cruises is entirely equity-financed. Although it expects to have an income of $125,000 in perpetuity, this income is not certain. This table shows the return to the stockholder under different assumptions about operating income. We assume no taxes.

Data

Number of shares 100,000 Price per share $10 Market value of shares $1 million

State of the Economy

Slump Normal Boom

Operating income $75,000 125,000 175,000 Earnings per share $.75 1.25 1.75 Return on shares 7.5% 12.5% 17.5%

Expected outcome

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464 Part Five Debt and Payout Policy

Since the value of the firm is the same, common shareholders are no better or worse off than before. River Cruises shares still trade at $10 each. The overall value of River Cruises’ equity falls from $1 million to $500,000, but shareholders have also received $500,000 in cash.

Antony points all this out: “The restructuring doesn’t make our stockholders any richer or poorer, Cleo. Why bother? Capital structure doesn’t matter.”

Suppose River Cruises issues $350,000 of new debt (rather than $500,000) and uses the proceeds to repurchase and retire common stock. How does this affect price per share? How many shares will be left outstanding?

Self-Test 16.1

TABLE 16.3 River Cruises is wondering whether to issue $500,000 of debt at an interest rate of 10% and repurchase 50,000 shares. This table shows the return to the shareholder under different assumptions about operating income. Returns to shareholders are higher than they were in Table 16.2 in normal and boom times but lower in slumps.

Data

Number of shares 50,000 Price per share $10 Market value of shares $500,000 Market value of debt $500,000

Outcomes

State of the Economy

Slump Normal Boom

Operating income $75,000 125,000 175,000 Interest $50,000 50,000 50,000 Equity earnings $25,000 75,000 125,000 Earnings per share $.50 1.50 2.50 Return on shares 5% 15%

Expected outcome

25%

How Borrowing Affects Earnings per Share Cleo is unconvinced. She prepares Table 16.3 and Figure 16.1 to show how borrow- ing $500,000 could increase earnings per share. Comparison of Tables 16.2 and 16.3 shows that “normal” earnings per share increase to $1.50 (versus $1.25) after the restructuring. Table 16.3 also shows more “upside” (earnings per share of $2.50 versus $1.75) and more “downside” ($.50 versus $.75).

The orange line in Figure 16.1 shows how earnings per share would vary with oper- ating income under the firm’s current all-equity financing. It is therefore simply a plot of the data in Table 16.2 . The blue line shows how earnings per share would vary if the company moves to equal proportions of debt and equity. It is therefore a plot of the data in Table 16.3 .

Cleo reasons as follows: “It is clear that debt could either increase or reduce the return to the equityholder. In a slump the return to the equityholder is reduced by the use of debt, but otherwise it is increased. We could be heading for a recession but it doesn’t look likely. Maybe we could help our shareholders by going ahead with the debt issue.”

As financial manager, Antony replies as follows: “I agree that borrowing will increase earnings per share as long as there’s no slump. But we’re not really doing anything for shareholders that they can’t do on their own. Suppose River Cruises does not borrow. In that case an investor could go to the bank, borrow $10, and then invest $20 in two shares. Such an investor would put up only $10 of her own money. Table 16.4 shows how the payoffs on this $10 investment vary with River Cruises’ operating income. You can see that these payoffs are exactly the same as the investor

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Chapter 16 Debt Policy 465

would get by buying one share in the company after the restructuring. (Compare the last two lines of Tables 16.3 and 16.4 .) It makes no difference whether shareholders borrow directly or whether River Cruises borrows on their behalf. Therefore, if River Cruises goes ahead and borrows, it will not allow investors to do anything that they could not do already, and so it cannot increase the value of the firm.

“We can run the same argument in reverse and show that investors also won’t be any worse off after the restructuring. Imagine an investor who owns two shares in the company before the restructuring. If River Cruises borrows money, there is some chance that the return on the shares will be lower than before. If that possibility is not to our investor’s taste, he can buy one share in the restructured company and also invest $10 in the firm’s debt. Table 16.5 shows how the payoff on this investment var- ies with River Cruises’ operating income. You can see that these payoffs are exactly the same as the investor got before the restructuring. (Compare the last lines of Tables 16.2 and 16.5 .) By lending half of his capital (by investing in River Cruises’ debt), the investor exactly offsets the company’s borrowing. So if River Cruises goes ahead and borrows, it won’t stop investors from doing anything that they could previously do.”

FIGURE 16.1 Borrowing increases River Cruises’ earnings per share (EPS) when operating income is greater than $100,000 but reduces it when operating income is less than $100,000. Expected EPS rises from $1.25 to $1.50.

Operating income ($)

E ar

n in

g s

p er

s h

ar e

($ )

2.00 Equal proportions debt and equity

All equity

Expected operating income = $125,000

Expected EPS with debt and equity

Expected EPS with all equity

1.75

1.50

1.25

1.00

.75

.50

.25

50,000 100,000 150,000

TABLE 16.4 Individual investors can replicate River Cruises’ borrowing by borrowing on their own. In this example we assume that River Cruises has not restructured. However, the investor can put up $10 of her own money, borrow $10 more, and buy two shares at $10 apiece. This generates the same rates of return as in Table 16.3 .

State of the Economy

Slump Normal Boom

Earnings on two shares $1.50 2.50 3.50 Less interest at 10% $1.00 1.00 1.00 Net earnings on investment $0.50 1.50 2.50 Return on $10 investment 5% 15% 25%

Expected outcome

TABLE 16.5 Individual investors can also undo the effects of River Cruises’ borrowing. Here the investor buys one share for $10 and lends out $10 more. Compare these rates of return to the original returns of River Cruises in Table 16.2 .

State of the Economy

Slump Normal Boom

Earnings on one share $0.50 1.50 2.50 Plus interest at 10% $1.00 1.00 1.00 Net earnings on investment $1.50 2.50 3.50 Return on $20 investment 7.5% 12.5% 17.5%

Expected outcome

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466 Part Five Debt and Payout Policy

This recreates MM’s original argument. 1 As long as investors can borrow or lend on their own account on the same terms as the firm, they are not going to pay more for a firm that has borrowed on their behalf. The value of the firm after the restructuring must be the same as before. In other words, the value of the firm must be unaf- fected by its capital structure.

This conclusion is widely known as MM’s proposition I. It is also called the MM debt-irrelevance proposition, because it shows that under ideal conditions the firm’s debt policy shouldn’t matter to shareholders.

1  There are many more general—and technical—proofs of the MM proposition. We will not pursue them here.

MM’s proposition I (debt-irrelevance proposition) The value of a firm is unaffected by its capital structure.

Suppose that River Cruises had issued $750,000 of debt, using the proceeds to buy back stock.

a. What would be the impact of a $50,000 change in operating income on earnings per share?

b. Show how a conservative investor could “undo” the change in River Cruises’ capital structure by varying the investment strategy shown in Table 16.5 . Hint: The investor will have to lend $3 for every dollar invested in River Cruises’ stock.

Self-Test 16.2

How Borrowing Affects Risk and Return Figure  16.2 summarizes the implications of MM’s debt irrelevance proposition for River Cruises. The upper circles represent firm value; the lower circles, expected, or “normal,” operating income. Restructuring does not affect the size of the circles, because the amount and risk of operating income are unchanged. Thus if the firm raises $500,000 in debt and uses the proceeds to repurchase and retire shares, the remaining shares must be worth $500,000, and the total value of debt and equity must stay at $1 million.

The two bottom circles in Figure 16.2 are also the same size. But notice that the bottom right circle shows that shareholders can expect to earn more than half of River Cruises’ normal operating income. They get more than half of the expected income “pie.” Does that mean shareholders are better off? MM say no. Why? Because share- holders bear more risk.

Look again at Tables 16.2 and 16.3 . Restructuring does not affect operating income, regardless of the state of the economy. Therefore, debt financing does not affect the operating risk or, equivalently, the business risk of the firm. But with less equity outstanding, a change in operating income has a greater impact on earnings per share. Suppose operating income drops from $125,000 to $75,000. Under all-equity financ- ing, there are 100,000 shares; so earnings per share fall by $.50. With 50% debt, there are only 50,000 shares outstanding; so the same drop in operating income reduces earnings per share by $1.

You can see now why the use of debt finance is known as financial leverage and a firm that has issued debt is described as a levered firm. The debt increases the uncer- tainty about percentage stock returns. If the firm is financed entirely by equity, a decline of $50,000 in operating income reduces the return on the shares by 5 percentage points. If the firm issues debt, then the same decline of $50,000 in operating income reduces the return on the shares by 10 percentage points. (Compare Tables 16.2 and 16.3 .) In other words, the effect of leverage is to double the magnitude of the upside and downside in the return on River Cruises’ shares. If borrowing doubles the upside and downside returns for River Cruises’ stock, what happens to beta? It also doubles. For example, if beta is .33 (1/3) with 100% equity, it is .67 (2/3) with 50% debt and 50% equity.

operating risk (business risk) Risk in firm’s operating income.

financial leverage Debt financing to amplify the effects of changes in operating income on the returns to stockholders.

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Chapter 16 Debt Policy 467

Debt finance does not affect operating risk but it does add financial risk. With only half the equity to absorb the same amount of operating risk, risk per share must double.  2

Consider now the implications of MM’s proposition I for the expected return on River Cruises’ stock. Before the proposed debt issue, the expected stream of earnings and divi- dends per share is $1.25. Since investment in the shares is risky, the shareholders require a return of 12.5%, or 2.5% above the interest rate. So the share price (which for a perpetu- ity is equal to the expected dividend divided by the required return) is $1.25/.125  =  $10. The good news is that after the debt issue, expected earnings and dividends rise to $1.50. The bad news is that the risk of the shares has now doubled. So instead of being content with a return of 2.5% above the interest rate, shareholders now demand a return of 5% more than the interest rate—that is, a required return of 10  +  5  =  15%. The benefit from the rise in dividends is exactly canceled out by the rise in the required return. The share price after the debt issue is $1.50/.15  =  $10, exactly the same as before.

2  Think back to Section 10.3, where we showed that fixed costs increase the variability in a firm’s profits. These fixed costs create operating leverage. It is exactly the same with debt. Debt interest is a fixed cost, and therefore debt magnifies the variability of profits after interest. These fixed interest charges create financial leverage.

financial risk Risk to shareholders resulting from the use of debt.

FIGURE 16.2 “Slicing the pie” for River Cruises. The circles on the left assume the company has no debt. The circles on the right reflect the proposed restructuring. The restructuring splits firm value (top circles) 50–50. Shareholders get more than 50% of expected, or “normal,” operating income (bottom circles), but only because they bear financial risk. Note that restructuring does not affect total firm value or operating income.

All-equity financing

Firm value

After restructuring

$1 million equity value

$500,000 debt

$500,000 equity value

Expected income Equity income = operating income = $125,000

Debt interest = $50,000

Equity income = $75,000

Current Structure: All Equity

Proposed Structure: Equal Debt and Equity

Expected earnings per share $1.25 $1.50 Share price $10 $10 Expected return on share 12.5% 15.0%

Thus leverage increases the expected return to shareholders, but it also increases the risk. The two effects cancel, leaving shareholder value unchanged.

16.2 Debt and the Cost of Equity What is River Cruises’ cost of capital? With all-equity financing, the answer is easy. Stockholders pay $10 per share and expect earnings per share of $1.25. If the earnings per share are paid out in a perpetual stream, the expected return is $1.25/10  =  .125, or

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468 Part Five Debt and Payout Policy

12.5%. This is the cost of equity capital, r equity , and also r assets , the expected return and cost of capital for the firm’s assets.

Since the restructuring does not change operating earnings or firm value, it should not change the cost of capital either. Suppose the restructuring takes place. Also, by a grand stroke of luck you simultaneously become a billionaire and buy all the out- standing debt and equity of River Cruises. What rate of return should you expect on this investment? Your answer should be 12.5%, because once you own all the debt and equity, you will effectively own all the assets and receive all the operating income.

You will indeed get 12.5%. Table 16.3 shows expected earnings per share of $1.50 and a share price that is unchanged at $10. Therefore, the expected return on equity is $1.50/$10  =  .15, or 15% ( r equity   =  .15). The return on debt is 10% ( r debt   =  .10). Your overall return is

(.5 × .10) + (.5 × .15) = .125 = rassets

There is obviously a general principle here: The appropriate weighted average of r debt and r equity takes you to r assets , the opportunity cost of capital for the company’s assets. The formula is

rassets = (rdebt × D/V) + (requity × E/V)

where D and E are the amounts of outstanding debt and equity and V equals overall firm value, the sum of D and E. Remember that D, E, and V are market values, not book values.

This formula does not quite match the weighted-average cost of capital (WACC) formula presented in Chapter 13 because at this point we are still ignoring taxes. 3 Don’t worry, we’ll get to WACC in a moment. First let’s look at the implications of MM’s debt-irrelevance proposition for the cost of equity.

MM’s proposition I states that the firm’s choice of capital structure does not affect the firm’s operating income or the value of its assets. So r assets , the expected return on the package of debt and equity, is unaffected.

However, we have just seen that leverage does increase the risk of the equity and the return that shareholders demand. To see how the expected return on equity varies with leverage, we simply rearrange the formula for the company cost of capital as follows:

requity = rassets + D

E (rassets - rdebt) (16.1)

which in words says that

Expected

return on equity

=

expected return

on assets + C debt-equity

ratio

× £expectedreturn on assets

-

expected return on

debt ≥S

This is MM’s proposition II. It states that the expected rate of return on the com- mon stock of a levered firm increases in proportion to the debt-equity ratio ( D/E ), expressed in market values. Note that r equity   =   r assets if the firm has no debt.

3  See Sections 13.1 and 13.2.

MM’s proposition II The required rate of return on equity increases as the firm’s debt-equity ratio increases.

Example 16.1 River Cruises’ Cost of Equity We can check out MM’s proposition II for River Cruises. Before the decision to borrow,

requity = rassets = expected operating income market value of all securities

= 125,000

1,000,000 = .125, or 12.5%

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Chapter 16 Debt Policy 469

We pointed out in Chapter 13 that you can think of a debt issue as having an explicit cost and an implicit cost. The explicit cost is the rate of interest charged on the firm’s debt. But debt also increases financial risk and causes shareholders to demand a higher return on their investment. Once you recognize this implicit cost, debt is no cheaper than equity—the return that investors require on their assets is unaf- fected by the firm’s borrowing decision. Be sure to remember this point whenever you hear some layperson say “Debt is cheaper than equity.”

When the firm issues debt, why does r assets , the company cost of capital, remain fixed while the expected return on equity, r equity , changes? Why is it not the other way around?

Self-Test 16.3

If the firm goes ahead with its plan to borrow, the expected return on assets, r assets , is still 12.5%. So the expected return on equity is

requity = rassets + D E

(rassets - rdebt)

= .125 + 500,000 500,000

(.125 - .10)

= .15, or 15%

FIGURE 16.3 MM’s proposition II with a fixed interest rate on debt. The expected return on River Cruises’ equity rises in line with the debt-equity ratio. The weighted average of the expected returns on debt and equity is constant, equal to the expected return on assets.

Debt-equity ratio, D/E

R at

es o

f re

tu rn

( %

)

18

16

14

12

10

8

6

4

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.60

requity = expected return on equity

rdebt = return on debt

rassets = expected return on assets

The implications of MM’s proposition II are shown in Figure 16.3 . No matter how much the firm borrows, the expected return on the package of debt and equity, r assets , is unchanged, but the expected rate of return on the separate parts of the package does change. How is this possible? Because the proportions of debt and equity in the pack- age are also changing. More debt means that the cost of equity increases, but at the same time the amount of equity is less.

In Figure 16.3 we have drawn the rate of interest on the debt as constant no mat- ter how much the firm borrows. That is not wholly realistic. It is true that most large, conservative companies could borrow a little more or less without noticeably affect- ing the interest rate that they pay. But at higher debt levels lenders become concerned that they may not get their money back and they demand higher rates of interest. Figure 16.4 modifies Figure 16.3 to take account of this. You can see that as the firm borrows more, the risk of default increases and the firm has to pay higher rates of

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470 Part Five Debt and Payout Policy

interest. Proposition II continues to predict that the expected return on the package of debt and equity does not change. However, the slope of the r equity line now tapers off as D/E increases. Why? Essentially because holders of risky debt begin to bear part of the firm’s operating risk. As the firm borrows more, more of that risk is transferred from stockholders to bondholders.

No Magic in Financial Leverage MM’s propositions boil down to a simple warning: There is no magic in financial leverage. Financial managers who ignore this warning can be sucked into serious prac- tical mistakes. Here are two examples of tempting fallacies.

Debt Is Not Cheap Financing Your surfactants business is under pressure from overseas producers. Claxon Drywall, a consultant, argues that you should double your planned capital investment in order to modernize plant and equipment and cut produc- tion costs. You point out that the expanded investment offers only a 9% return and is negative-NPV when forecast cash flows are discounted at your company’s normal 11% cost of capital.

Drywall responds condescendingly: “Look, banks will be happy to lend you the money at 5%, and NPV at 5% is strongly positive. And there’s no financial risk—your operating cash flows will service the bank debt with a large safety cushion. There’s no reason for your shareholders to worry or demand a higher rate of return. Your overall cost of capital will go down.”

You quickly see Drywall’s mistakes. First, he is confusing the cost of debt, which depends on the firm’s creditworthiness, with the opportunity cost of capital, which depends on the risk of the proposed capital investment. Second, he naively thinks that substituting “cheap” debt for “expensive” equity will bring down the overall cost of capital. (Drywall is not invoking the tax advantages of debt, which we cover below.) Third, Drywall thinks that financial risk is the risk that the firm will not be able to ser- vice its debt. That’s wrong: Substituting debt for equity financing creates financial risk even if the risk of default is zero.

Notice that the risk of default never arose in our calculations for River Cruises. The company’s operating income covered interest even when the economy slumped. Borrowing money nevertheless created financial risk because it concentrated the com- pany’s operating risk on a smaller equity investment. For example, it doubled the vola- tility of net income and increased River Cruises’ beta from .33 to .67.

Beware of Hidden Debt A law firm ( not Dewey, Cheatem, and Howe) is expanding rapidly and must move to new office space. Business is good, and the firm is encouraged to purchase an entire building for $10 million. The building offers

FIGURE 16.4 MM’s proposition II when debt is not risk-free. As the debt- equity ratio increases, debtholders demand a higher expected rate of return to compensate for the risk of default. The expected return on equity increases more slowly when debt is risky because the debtholders take on part of the risk. The expected return on the package of debt and equity, r assets , remains constant.

Debt-equity ratio, D/E

R at

es o

f re

tu rn

( %

)

18

16

14

12

10

8

6

Risk-free debt Risky debt4

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.60

requity = expected return on equity

rdebt = return on debt

rassets = expected return on assets

How the cost of capital changes with leverage

BEYOND THE PAGE

brealey.mhhe.com/ch16-02

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Chapter 16 Debt Policy 471

first-class office space, convenient to the firm’s most important corporate clients, and provides space for future expansion.

Claxon Drywall appears again and encourages the firm not to buy the building but to sign a long-term lease for the building instead. “With lease financing, you’ll save $10 million. You won’t have to put up any equity investment,” Drywall explains.

The senior law partner asks about the terms of the lease. “I’ve taken the liberty to check,” Drywall says. “The lease will provide 100% financing. It will commit you to 20 fixed annual payments of $950,000, with the first payment due immediately.”

“The initial payment of $950,000 sounds like a down payment to me,” the senior partner observes sourly.

“Good point,” Drywall says amiably, “but you’ll still save $9,050,000 up front. You can earn a handsome rate of return on that money. For example, I understand you are considering branch offices in London and Brussels. The $9 million would pay the costs of setting up the new offices, and the cash flows from the new offices should more than cover the lease payments.”

You can immediately see the dangers here. Committing to the lease amounts to tak- ing on de facto debt of $9,050,000 after the first lease payment. (The lease payments are fixed obligations, just like debt service.) Is that prudent borrowing? Could the law firm make the lease payments if its business declined and a group of partners left?

It turns out that the 20 fixed payments of $950,000 would give the lessor an 8% rate of return. 4 That’s the effective cost of debt embedded in the lease. 5 When Drywall says that the firm could cover the lease payments by opening branch offices, he is effec- tively arguing that investments in the branch offices are worthwhile if they offer a rate of return higher than 8%.

Drywall is again confusing the cost of debt, in this case 8%, with the opportunity cost of capital, which depends on the risk of investing in the branch offices.

What would MM say to the senior partner? First, they would ask whether the pro- posed branch offices have positive NPVs when forecast cash flows are discounted at the opportunity cost of capital. They would not object to borrowing $9,050,000 by way of the lease if the firm can use the money, if it can cover the lease payments with a reasonable safety cushion, and if 8% is a fair market rate for that amount of de facto borrowing. But they would caution that the extra borrowing will not reduce the overall company cost of capital. And they would insist that 8% is not the correct discount rate for cash flows from the new offices. Discounting at 8% implicitly assumes that there is magic in financial leverage. There is none.

MM would also suggest that we move on and think about debt and taxes.

16.3 Debt, Taxes, and the Weighted-Average Cost of Capital The MM propositions suggest that debt policy should not matter. Yet financial manag- ers do worry about debt policy, and for good reasons. Now we are ready to see why.

If debt policy were completely irrelevant, actual debt ratios would vary randomly from firm to firm and from industry to industry. Yet almost all airlines, utilities, and real estate development companies rely heavily on debt. And so do many firms in capital-intensive industries like steel, aluminum, chemicals, and mining. On the other hand, it is rare to find a biotech or software company that is not predominantly

4  The present value of a 20-year annuity due of $950,000 is $10,073,000 at 8%. Or you can say that the present value at 8% of the 19 year-end payments is $9,123,000. With the initial payment of $950,000, the present value of all lease payments, again, is $10,073,000. Either way, the lessor earns slightly more than 8% on his or her money. 5  We caution that leases are more complicated than implied here. For example, the lease would transfer owner- ship of the building and the law firm would lose depreciation tax shields.

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472 Part Five Debt and Payout Policy

equity-financed. Glamorous growth companies seldom use much debt, despite rapid expansion and often heavy requirements for capital.

The explanation of these patterns lies partly in the things that we have so far left out of our discussion. Now we will put all these things back in, starting with taxes.

Debt and Taxes at River Cruises Debt financing has one important advantage: The interest that the company pays is a tax-deductible expense, but equity income is subject to corporate tax.

To see the tax advantage of debt, let’s look again at River Cruises. The left column of Table 16.6 assumes that the company has no debt. We now assume expected pretax income is $192,308, so expected income after tax at 35% remains $125,000. The right column shows what happens if the company borrows $500,000 at 10%.

Notice that the combined income of the debtholders and equityholders is higher by $17,500 when the firm is levered. This is because the interest payments are tax- deductible. Thus every dollar of interest reduces taxes by $.35. The total amount of tax savings is simply .35  ×  interest payments. In the case of River Cruises, the interest tax shield is .35  ×  $50,000  =  $17,500 each year. In other words, the “pie” of after-tax income that is shared by debt and equity investors increases by $17,500 relative to the zero-debt case. Since the debtholders receive no more than the going rate of interest, all the benefit of this interest tax shield is captured by the shareholders.

The interest tax shield is a valuable asset. Let’s see how much it could be worth. Suppose that River Cruises plans to replace its bonds when they mature and to keep “rolling over” the debt indefinitely. It therefore looks forward to a permanent stream of tax savings of $17,500 per year.

If the debt is really fixed and permanent, and if River Cruises is confident that it will earn enough taxable income to cover the interest deductions, then the interest tax shields are a safe perpetuity. Suppose that the risk of the tax shields is the same as the interest payments generating them. Then we can discount at the 10% interest rate demanded by debt investors. The present value is

PV interest tax shield = $17,500

.10 = $175,000

This simple calculation is a common rule of thumb. The rule takes the projected interest tax shield and divides by the cost of debt, as if the interest tax shield were per- petual and just as safe as the debt. 6

Unfortunately, the rule almost always overstates the value of interest tax shields. First, the firm may not borrow permanently. Second, it may run into future losses and not pay income taxes. If that happens, there are no taxes for interest to shield. Third, the formula assumes that the amount of debt is fixed regardless of how well the firm performs. It’s more reasonable to assume that the firm will rebalance its capital structure over time to keep its debt ratio more or less constant. If the firm

interest tax shield Tax savings resulting from deductibility of interest payments.

6  Notice that the PV in this case equals the tax rate times the amount of debt outstanding. If the tax rate is T C , the annual interest tax shield is T C   ×   r debt   ×   D. The tax shield is a perpetuity, so the PV calculation divides T C   ×   r debt   ×   D by r debt , and PV tax shield  =   T C   ×   D.

Zero Debt $500,000 Debt

Expected operating income $192,308 $192,308 Debt interest at 10% 0 50,000 Before-tax income 192,308 142,308 Tax at 35% 67,308 49,808 After-tax income 125,000 92,500 Combined debt and equity income  =   after-tax income  +  interest 125,000 142,500

TABLE 16.6 River Cruises expects to earn $125,000 (now after tax at 35%) if there is no debt. But the total amount earned by debt and equity investors increases to $142,500 if there is $500,000 of debt. The increase of $17,500 occurs because interest is a tax-deductible expense. The interest tax shield reduces taxes by $17,500.

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Chapter 16 Debt Policy 473

thrives and its value increases, it can borrow more. If the firm hits hard times and its value decreases, it can gradually pay down debt to a more comfortable level. Rebal- ancing means future debt and interest tax shields are no longer fixed amounts; they vary with the firm’s performance, and therefore should be discounted at a rate higher than the cost of debt.

Suppose that River Cruises will rebalance its debt in each and every future period, always keeping its debt ratio constant. In this case the debt levels and interest tax shields fluctuate along with River Cruises’ market value and are about as risky. This suggests a more conservative rule of thumb: Because the tax shields have the same risk as the rest of the firm, discount them at the same rate investors would use for operating income, which is 12.5% in our example. 7

PV interest tax shield = $17,500

.125 = $140,000

Even this more conservative PV calculation demonstrates that interest tax shields can add significant value for the firm and its shareholders.

7  The annual interest tax shield is T C   ×   r debt   ×   D, as in footnote 6. But this PV calculation divides T C   ×   r debt   ×   D by r assets , so PV interest tax shield  =   T C   ×   D   ×  ( r debt / r assets ).

Suppose River Cruises borrows only $300,000. Use the rules of thumb for valuing PV interest tax shield to answer the following questions:

a. What is the PV of interest tax shields if this borrowing is fixed and permanent?

b. What is this PV if River Cruises borrows permanently but rebalances its debt every future period to maintain a constant debt-to-value ratio?

c. The latter calculation is probably still too high. Why?

Self-Test 16.4

How Interest Tax Shields Contribute to the Value of Stockholders’ Equity MM’s proposition I amounts to saying that “the value of the pizza does not depend on how it is sliced.” The pizza is the firm’s assets, and the slices are the debt and equity claims. If we hold the pizza constant, then a dollar more of debt means a dollar less of equity value.

But there is really a third slice—the government’s. MM would still say that the value of the pizza—in this case the company value before taxes—is not changed by slicing. But anything the firm can do to reduce the size of the government’s slice obvi- ously leaves more for the others. One way to do this is to borrow money. This reduces the firm’s tax bill and increases the cash payments to the investors. The value of their investment goes up by the present value of the tax savings.

In a no-tax world, MM’s proposition I states that the value of the firm is unaffected by capital structure. But MM also modified proposition I to recognize corporate taxes:

Value of levered firm = value if all-equity-financed + present value of tax shield

This formula is illustrated in Figure 16.5 . It implies that borrowing increases firm value and shareholders’ wealth.

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474 Part Five Debt and Payout Policy

Corporate Taxes and the Weighted-Average Cost of Capital We have shown that when there are corporate taxes, debt provides the company with a valuable tax shield. Few companies explicitly calculate the present value of inter- est tax shields associated with a particular borrowing policy. The tax shields are not forgotten, however, because they show up in the discount rate used to evaluate capital investments.

Since debt interest is tax-deductible, the government in effect pays 35% of the inter- est cost. So to keep its investors happy, the firm has to earn the after-tax rate of interest on its debt plus the return required by shareholders. Once we recognize the tax benefit of debt, the weighted-average cost of capital formula (see Chapter 13 for a review if you need one) becomes

WACC = (1 - Tc)rdebt a DD + Eb + requity a E

D + E b

Notice that when we allow for the tax advantage of debt, the weighted-average cost of capital depends on the after-tax rate of interest (1  −   T c )  ×   r debt .

Example 16.2 WACC and Debt Policy We can use the weighted-average cost of capital formula to see how leverage affects River Cruises’ cost of capital if the company pays corporate tax. When a company has no debt, the weighted-average cost of capital and the return required by shareholders are identical. For River Cruises, the WACC with all-equity financing is 12.5%, and the value of the all-equity firm is $1 million, just as in the no- tax examples earlier in this chapter.

Now we calculate River Cruises’ WACC with D   =  $500,000 of debt. If we use the more conservative rule of thumb 8 for the PV of the interest tax shields (see foot- note 7), then company value V   =   D   +   E increases by .35 × $500,000 × (.10/.125) = $140,000 to $1,140,000. The equity value E is $1,140,000  −  $500,000  =  $640,000.

8  Recall that the more conservative rule of thumb assumes that the firm rebalances future debt levels to keep its debt ratio constant. This rule of thumb is the right match for a WACC calculation, because use of WACC as a discount rate for long-lived assets also assumes constant debt ratios. For a more detailed analysis of the assump- tions implicit in formulas for WACC and the cost of equity, see Chapter 19 in R. A. Brealey, S. C. Myers, and F. Allen, Principles of Corporate Finance, 11th ed. (New York: McGraw-Hill Irwin), 2014.

FIGURE 16.5 The heavy blue line shows how the interest tax shields affect the market value of the firm. Additional borrowing decreases corporate income tax payments and increases the cash flows available to investors. Thus market value increases.

Debt ratio

M ar

ke t

va lu

e

PV tax shield

Value if all-equity- financed

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Chapter 16 Debt Policy 475

The right column in Table 16.6 shows equity income of $92,500 after interest and taxes, so the expected rate of return to shareholders is 92,500/640,000  =  14.45%  ( r equity   =   .1445). The interest rate is 10% ( r debt   =   .10), and the corporate tax rate is 35% ( T C   =  .35). This is all the information we need to see how taxes affect River Cruises’ WACC:

WACC = (1 - TC)rdebt a DD + Eb + requity a E

D + E b (16.2)

= (1 - .35).10 a 500,000 1,140,000

b + .1445 a 640,000 1,140,000

b = .1096, or about 11% Thus interest tax shields increase the total value of River Cruises ( V   =   D   +   E ) by $140,000 and reduce its WACC from 12.5% to about 11%.

Figure 16.6 repeats Figure 16.3 , except for the impact of interest tax shields. As the firm borrows more, the cost of equity rises, just as in Figure 16.3 , although in this case to 14.45% instead of 15%. 9 But the after-tax cost of debt is only 6.5%. At bor- rowing of $500,000, the equity is worth $640,000, and the debt-equity ratio is D / E   =  500,000/640,000  =  .78. Figure 16.6 shows that WACC at this level of debt is 10.96%, the same as we calculated just above.

9  The reason why r equity falls to 14.45% from its value of 15% in the no-tax case is that interest tax shields increase firm value and reduce D / E from 500,000/500,000  =  1.0 in the no-tax case to 500,000/640,000  =  .78. By the way, MM’s proposition II works fine for the cost of equity as long as current and future debt-to-equity ratios are held constant. In this example,

requity = rassets + (D/E) × (rassets - rdebt) = .125 + .78 × (.125 - .10) = .1445, or 14.45%

FIGURE 16.6 Changes in River Cruises’ cost of capital with increased leverage when there are corporate taxes. The after-tax cost of debt is assumed to be constant at (1  −  .35)10%  =  6.5%. With increased borrowing the cost of equity rises, but the weighted-average cost of capital (WACC) declines.

Debt-equity ratio, D/E

R at

es o

f re

tu rn

( %

)

16

14

12 12.5

10

8

14.45%

10.96%

6.5% 6

4

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.78 0.0

requity = expected return on equity

WACC

(1 - Tc) × rdebt = after-tax expected return on debt

The Implications of Corporate Taxes for Capital Structure If borrowing provides an interest tax shield, the implied optimal debt policy appears to be embarrassingly extreme: All firms should borrow to the hilt. This maximizes firm value and minimizes the weighted-average cost of capital.

MM were not that fanatical about it. No one would expect the gains to apply at extreme debt ratios. For example, if a firm borrows heavily, all its operating income may go to pay interest. At this point, there are no corporate taxes to be paid and therefore no tax shields on additional debt. There is no point in such firms borrowing any more.

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476 Part Five Debt and Payout Policy

There may also be some tax disadvantages to borrowing, for bondholders have to pay personal income tax on any interest they receive. The top rate of tax on bond interest is about 40%. On the other hand, stockholders currently are taxed at only 20% on both dividends and capital gains. Capital gains have the additional advantage that they are not taxed until the stock is sold. (The delay reduces the present value of the tax payment.)

All this suggests that there may come a point at which the tax savings from debt level off and may even decline. But it doesn’t explain why highly profitable companies with large tax bills often thrive with little or no debt. There are clearly factors besides taxes to consider. One such factor is the likelihood of financial distress.

16.4 Costs of Financial Distress Financial distress occurs when promises to creditors are broken or honored with dif- ficulty. Sometimes financial distress leads to bankruptcy. Sometimes it means only skating on thin ice.

As we will see, financial distress is costly. Investors know that levered firms may run into financial difficulty, and they worry about the costs of financial distress. That worry is reflected in the current market value of the levered firm’s securities. Even the most blue-chip firms are concerned about how their debt is perceived by investors. They want to maintain ready access to debt markets and to avoid the higher costs of debt that lenders are apt to demand at the first signs of financial weakness. Therefore they want to maintain a good credit rating. Thus you may hear a CFO say, “We want to maintain a single-A debt rating” or “We want to be a strong triple-B.” But even high- rated firms sometimes fall into financial distress. For example, Eastman Kodak, which had a triple-A rating in the 1980s, fell into financial distress in the 21st century and filed for bankruptcy in 2012.

Even if the firm is not now in financial distress, investors factor the potential for future distress into their assessment of current value. This means that the overall value of the firm is

Overall market value =

value if all-equity- financed +

PV tax shield -

PV costs of financial distress

The present value of the costs of financial distress depends both on the probability of distress and on the magnitude of the costs encountered if distress occurs.

Figure 16.7 shows how the trade-off between the tax benefits of debt and the costs of distress determines optimal capital structure. Think of a firm like River Cruises, which starts with no debt but considers moving to higher and higher debt levels, hold- ing its assets and operations constant. At moderate debt levels the probability of financial distress is trivial, and therefore the tax advantages of debt dominate. But at some point additional borrowing causes the probability of financial distress to increase rapidly, and the potential costs of distress begin to take a substantial bite out of firm value. The theoretical optimum is reached when the present value of tax savings from further borrowing is just offset by increases in the present value of costs of distress.

This is called the trade-off theory of optimal capital structure. The theory says that managers will try to increase debt levels to the point where the value of additional interest tax shields is exactly offset by the additional costs of financial distress.

Now let’s take a closer look at financial distress.

Bankruptcy Costs In principle, bankruptcy is merely a legal mechanism for allowing creditors (that is, lenders) to take over the firm when the decline in the value of its assets triggers a default on outstanding debt. If the company cannot pay its debts, the company is

costs of financial distress Costs arising from bankruptcy or distorted business decisions before bankruptcy.

trade-off theory Debt levels are chosen to balance interest tax shields against the costs of financial distress.

Does MM apply to banks?

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Chapter 16 Debt Policy 477

turned over to the creditors, who become the new owners; the old stockholders are left with nothing. In this case, bankruptcy is not the cause of the decline in the value of the firm. It is the result.

In practice, of course, anything involving courts and lawyers cannot be free. The fees involved in a bankruptcy proceeding are paid out of the remaining value of the firm’s assets. Creditors end up with what is left after paying the lawyers and other court expenses. If there is a possibility of bankruptcy, the current market value of the firm is reduced by the present value of these potential costs.

It is easy to see how increased leverage affects the costs of financial distress. The more the firm owes, the higher the chance of default and therefore the greater the expected value of the associated costs. This reduces the current market value of the firm.

Creditors foresee the costs and realize that if default occurs, the bankruptcy costs will come out of the value of the firm. For this they demand compensation in advance in the form of a higher promised interest rate. This reduces the possible payoffs to stockholders and reduces the current market value of their shares.

Suppose investors foresee $2 million of legal costs if the firm defaults on its bonds. How does this affect the value of the firm’s bonds if bankruptcy occurs? How does the possibility of default affect the interest rate demanded by bondholders today? How does this possibility affect today’s value of the firm’s common stock?

Self-Test 16.5

FIGURE 16.7 The trade-off theory of capital structure. The curved blue line shows how the market value of the firm at first increases as the firm borrows but finally decreases as the costs of financial distress become more and more important. The optimal capital structure balances the costs of financial distress against the value of the interest tax shields generated by borrowing.

PV costs of financial distress

Optimal debt ratio

Debt ratio M

ar ke

t va

lu e

PV tax shield

Value if all-equity- financed

We summarize bankruptcy procedures in the appendix to this chapter. Here we will focus only on Chapter 11 of the bankruptcy code, which is the route usually taken by large firms that need help to climb out of financial distress. The purpose of Chapter 11 is to nurse the firm back to health and enable it to face the world again. This requires approval of a reorganization plan for who gets what; under the plan each class of creditors needs to give up its claim in exchange for new securities or a mixture of new securities and cash. The challenge is to design a new capital structure that will satisfy the creditors and allow the firm to solve the business problems that got it into trouble in the first place. Sometimes it proves possible to satisfy both demands and the patient emerges fit and healthy. Often, however, the proceedings involve costly delays and legal tangles, and the business continues to deteriorate.

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478 Part Five Debt and Payout Policy

Bankruptcy costs can add up fast. The failed energy giant Enron paid nearly $800 million in legal, accounting, and other professional fees during the time that it spent in bankruptcy. As we write this in the fall of 2013, the costs of sorting out the 65,000 claims on the assets of Lehman Brothers have already reached $2.2 billion.

Of course, these are exceptional cases, for only the largest firms can lay their hands on a billion dollars when bankrupt. But daunting as such numbers may seem, bank- ruptcy costs average only about 3% of the value of a firm in the year before bank- ruptcy. 10 The proportion is typically higher for small firms than for large ones; it seems that there are significant economies of scale in going bankrupt.

Thus far we have discussed only the direct (that is, legal and administrative) costs of bankruptcy. The indirect costs reflect the difficulties of running a company while it is going through bankruptcy. When Eastern Airlines entered bankruptcy in 1989, it was in severe financial trouble, but it still had some valuable, profit-making routes and some readily salable assets such as planes and terminal facilities. These assets were more than sufficient to repay in full its liabilities of $3.7 billion. However, the bank- ruptcy judge was determined to keep Eastern flying. Unfortunately, Eastern’s losses continued to pile up. After the airline spent nearly 2 years under the “protection” of the bankruptcy court, the judge called it a day, the assets were sold off, and the creditors received less than $900 million. The unsuccessful attempt at resuscitation had cost Eastern’s creditors $2.8 billion.

We don’t know how much these indirect costs add to the expenses of bankruptcy. We suspect it is a significant number, particularly when bankruptcy proceedings are prolonged. Perhaps the best evidence is the reluctance of creditors to force a firm into bankruptcy. In principle, they would be better off to end the agony and seize the assets as soon as possible. But, instead, creditors often overlook defaults in the hope of nursing the firm over a difficult period. They do this in part to avoid the costs of bankruptcy. There is an old financial saying, “Borrow $1,000 and you’ve got a banker. Borrow $10,000,000 and you’ve got a partner.”

Costs of Bankruptcy Vary with Type of Asset Suppose your firm’s only asset is a large downtown hotel, mortgaged to the hilt. A recession hits, occupancy rates fall, and the mortgage payments cannot be met. The lender takes over and sells the hotel to a new owner and operator. The stock is worth- less and you use the firm’s stock certificates for wallpaper.

What is the cost of bankruptcy? In this example, probably very little. The value of the hotel is, of course, much less than you hoped, but that is due to the lack of guests, not to bankruptcy. Bankruptcy does not damage the hotel itself. The direct bankruptcy costs are restricted to items such as legal and court fees, real estate commissions, and the time the lender spends sorting things out.

Suppose we repeat the story of Heartbreak Hotel for Fledgling Electronics. Every- thing is the same, except for the underlying assets. Fledgling is a high-tech going con- cern, and much of its value reflects investors’ belief that its research team will come up with profitable ideas. Fledgling is a “people business”; its most important assets go down in the elevator and into the parking lot every night.

If Fledgling gets into trouble, the stockholders may be reluctant to put up money to cash in on those profitable ideas—why should they put up cash which will simply go to pay off the banks? Failure to invest is likely to be much more serious for Fledgling than for a company like Heartbreak Hotel.

If Fledgling finally defaults on its debt, the lender would find it much more difficult to cash in by selling the assets. In fact, if trouble comes, many of those assets may drive into the sunset and never come back.

10  See, for example, L. A. Weiss, “Bankruptcy Resolution: Direct Costs and Violation of Priority of Claims,” Journal of Financial Economics 27 (October 1990), pp. 285–314.

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Chapter 16 Debt Policy 479

Some assets, like good commercial real estate, can pass through bankruptcy and reorganization largely unscathed; the values of other assets are likely to be consider- ably diminished. The losses are greatest for intangible assets that are linked to the continuing prosperity of the firm. That may be why debt ratios are low in the biotech industry, where company values depend on continued success in research and develop- ment. It may also explain the low debt ratios in many service companies, whose main asset is their skilled labor. The moral of these examples is this: Do not think only about whether borrowing is likely to bring trouble. Think also of the value that may be lost if trouble comes.

For which of the following companies would the costs of financial distress be most serious? Why?

• A 3-year-old biotech company. So far the company has no products approved for sale, but its scientists are hard at work developing a breakthrough drug.

• An oil production company with 50 producing wells and 20 million barrels of proven oil reserves.

Self-Test 16.6

Financial Distress without Bankruptcy Not every firm that gets into trouble goes bankrupt. As long as the firm can scrape up enough cash to pay the interest on its debt, it may be able to postpone bankruptcy for many years. Eventually the firm may recover, pay off its debt, and escape bankruptcy altogether.

A narrow escape from bankruptcy does not mean that costs of financial distress are avoided. When a firm is in trouble, suppliers worry that they may not be paid, potential customers fear that the firm will not be able to honor its warranties, 11 and employees start slipping out for job interviews. The firm’s bondholders and stockholders both want it to recover, but in other respects their interests may be in conflict. In times of financial distress the security holders are like many political parties—united on generalities but threatened by squabbling on any specific issue. Financial distress is costly when these conflicts get in the way of running the business. Stockholders are tempted to forsake the usual objective of maximizing the overall market value of the firm and to pursue narrower self-interest instead. They are tempted to play games at the expense of their creditors. These games add to the costs of financial distress.

Think of a company—call it Double-R Nutting—which is teetering on the brink of bankruptcy. It has large debts and large losses. Double-R’s assets have little value, and if its debts were due today, Double-R would default, leaving the firm bankrupt. The debtholders would perhaps receive a few cents on the dollar, and the shareholders would be left with nothing.

But suppose the debts are not due yet. That grace period explains why Double- R’s shares still have value. There could be a stroke of luck that will rescue the firm and allow it to pay off its debts with something left over. That’s a long shot—unless firm value increases sharply, the stock will be valueless. But the owners have a secret weapon: They control investment and operating strategy.

The First Game: Bet the Bank’s Money Suppose Double-R has the opportunity to take a wild gamble. If it does not come off, the shareholders will be no worse off; the company will probably go under anyway. But if the gamble does

11  In an attempt to stave off Chrysler’s bankruptcy, the U.S. government sought to reassure the firm’s customers by backing the warranties on its vehicles.

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480 Part Five Debt and Payout Policy

succeed, there will be more than enough assets to pay off the debt and the surplus will go into the shareholders’ pockets. You can see why management might want to take the chance. In taking the gamble, they are essentially betting the debtholders’ money, but if Double-R does hit the jackpot, the equityholders get most of the loot.

This was essentially the situation facing Federal Express while it was still strug- gling in 1974. It had only $5,000 left in its checking account but needed $24,000 for its weekly jet fuel payment. Fred Smith took the incentive to gamble literally. He took the firm’s remaining $5,000 and boarded a plane for Las Vegas, where he won $27,000. When asked how he had mustered the nerve to do this, he replied, “What dif- ference did it make? Without the funds for the fuel companies, we couldn’t have flown anyway.” 12 The effects of such distorted incentives to take on risk are usually not this blatant, but the results can be the same.

These kinds of risk-shifting strategies are costly for the bondholders and for the firm as a whole. Why are they associated with financial distress? Because the tempta- tion to follow such strategies is strongest when the odds of default are high. A healthy firm would never invest in Double-R’s lousy gamble, since it would be gambling with its own money, not the bondholders’. A healthy firm’s creditors would not be vulner- able to this type of game.

The Second Game: Don’t Bet Your Own Money We have just seen how shareholders, acting in their narrow self-interest, may take on risky, unprofitable projects. These are errors of commission. We will now illustrate how conflicts of inter- est may also lead to errors of omission.

Suppose Double-R uncovers a relatively safe project with a positive NPV. Unfor- tunately, the project requires a substantial investment. Double-R will need to raise this extra cash from its shareholders. Although the project has a positive NPV, the profits may not be sufficient to rescue the company from bankruptcy. If that is so, all the profits from the new project will be used to help pay off the company’s debt, and the shareholders will get no return on the cash they put up. Although it is in the firm’s interest to go ahead with the project, it is not in the owners’ interest, and the project will be passed up. A recent example of this problem occurred during the financial cri- sis when many banks, threatened with failure, discovered that their shareholders were reluctant to come to the rescue. The shareholders faced a debt overhang problem: Any cash that they contributed would simply be used to get existing debtholders and the government off the hook.

These examples illustrate a general point. The value of any investment opportunity to the firm’s stockholders is reduced because project benefits must be shared with the bondholders. Thus it may not be in the stockholders’ self-interest to contribute fresh equity capital even if that means forgoing positive-NPV opportunities.

These two games illustrate potential conflicts of interest between stockholders and debtholders. The conflicts, which theoretically affect all levered firms, become much more serious when firms are staring bankruptcy in the face. If the probability of default is high, managers and stockholders will be tempted to take on exces- sively risky projects. At the same time, stockholders may refuse to contribute more equity capital even if the firm has safe, positive-NPV opportunities. Stock- holders would rather take money out of the firm than put new money in.

The company knows that lenders will demand a higher rate of interest if they are worried that games will be played at their expense. So to reassure lenders that its intentions are honorable, the firm will commonly agree to loan covenants. For exam- ple, it may promise to limit future borrowing and not to pay excessive dividends. Of

12  Roger Frock, Changing How the World Does Business, FedEx’s Incredible Journey to Success: The Inside Story (San Francisco: Berrett-Koehler Publishers, 2006).

risk shifting Firms threatened with default are tempted to shift to riskier investments.

debt overhang Firms threatened with default may pass up positive-NPV projects because bondholders capture part of the value added.

loan covenant Agreement between firm and lender requiring the firm to fulfill certain conditions to safeguard the loan.

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Chapter 16 Debt Policy 481

course, no amount of fine print can cover every possible game that the company might play. For instance, no contract can ensure that companies will accept all positive-NPV investments and reject negative ones.

We do not mean to leave the impression that managers and stockholders always suc- cumb to temptation unless restrained. Usually they refrain voluntarily, not only because of a sense of fair play but also on pragmatic grounds: A firm or individual that makes a killing today at the expense of a creditor will be coldly received when the time comes to borrow again. Aggressive game playing is done only by firms in extreme financial dis- tress (and sometimes by out-and-out crooks). Firms limit borrowing precisely because they don’t wish to land in distress and be exposed to the temptation to play.

Suppose lenders foresee possible future risk-shifting and debt-overhang problems.

a. How do the lenders respond today? b. How should the company respond today if the lenders’ concerns are valid?

Is there an argument for moving to a lower debt ratio?

Self-Test 16.7

We have now completed our review of the building blocks of the trade-off theory of optimal capital structure. In the next section we will sum up that theory and briefly cover a competing “pecking order” theory.

16.5 Explaining Financing Choices

The Trade-Off Theory Financial managers often think of the firm’s debt-equity decision as a trade-off between interest tax shields and the costs of financial distress. Of course, there is con- troversy about how valuable interest tax shields are and what kinds of financial trouble are most threatening, but these disagreements are only variations on a theme. Thus Figure 16.7 illustrates the debt-equity trade-off.

This trade-off theory predicts that target debt ratios will vary from firm to firm. Companies with safe, tangible assets and plenty of taxable income to shield ought to have high target ratios. Unprofitable companies with risky, intangible assets ought to rely primarily on equity financing.

All in all, this trade-off theory of capital structure tells a comforting story. It avoids extreme predictions and rationalizes moderate debt ratios. But what are the facts? Can the trade-off theory of capital structure explain how companies actually behave?

The answer is yes and no. On the yes side, the trade-off theory successfully explains many of the industry differences in capital structure that we encountered in Table 16.1 . For example, high-tech growth companies, whose assets are risky and mostly intan- gible, normally use relatively little debt. Utilities or hotels can and do borrow heavily because their assets are tangible and relatively safe.

On the no side, there are other things the trade-off theory cannot explain. It cannot explain why some of the most successful companies thrive with little debt. Apple, Google and Microsoft are almost entirely equity-financed. They have some debt out- standing, but the debts are tiny fractions of the value of their common stock. Moreover, their holdings of cash and short-term investments are several times their outstanding debt. For example, at the end of 2013 Google’s outstanding debt was about $7 billion, its cash holdings about $55 billion, and the market value of its common stock about $370 billion.

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482 Part Five Debt and Payout Policy

Granted, these companies’ most valuable assets are intangible, and intangible assets and conservative capital structures should go together. But they pay large amounts in corporate taxes. They could borrow enough to save millions of tax dollars without raising a whisker of concern about possible financial distress.

Apple, Google, and Microsoft illustrate an odd fact about real-life capital struc- tures: The most profitable companies generally borrow the least. Here the trade-off theory fails, for it predicts exactly the reverse. Under the trade-off theory, high prof- its should mean more debt-servicing capacity and more taxable income to shield and therefore should result in a higher debt ratio.

Rank these industries in order of predicted debt ratios under the trade-off theory of capital structure: (a) Internet software; (b) auto manufacturing; (c) regulated electric utilities.

Self-Test 16.8

Apple’s debt issue

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A Pecking Order Theory There is an alternative theory which could explain why profitable companies borrow less. It is based on asymmetric information —managers know more than outside inves- tors about the profitability and prospects of the firm. Thus investors may not be able to assess the true value of a new issue of securities by the firm. They may be especially reluctant to buy newly issued common stock, because they worry that the new shares will turn out to be overpriced.

Such worries can explain why the announcement of a stock issue can drive down the stock price. 13 If managers know more than outside investors, they will be tempted to time stock issues when their companies’ stock is overpriced —in other words, when the managers are relatively pessimistic. On the other hand, optimistic managers will see their companies’ shares as underpriced and decide not to issue. You can see why investors would learn to interpret the announcement of a stock issue as a “pessimistic manager” signal and mark down the stock price accordingly. You can also see why optimistic financial managers—and most managers are optimistic!—would view a common stock issue as a relatively expensive source of financing.

All these problems are avoided if the company can finance with internal funds, that is, with earnings retained and reinvested. But if external financing is required, the path of least resistance is debt, not equity. Issuing debt seems to have a trifling effect on stock prices. There is less scope for debt to be misvalued and therefore a debt issue is a less worrisome signal to investors.

These observations suggest a pecking order theory of capital structure. It goes like this:

1. Firms prefer internal finance. Reinvesting internally generated cash does not send adverse signals that could lower the stock price.

2. If external finance is required, firms issue debt first and issue equity only as a last resort. This pecking order arises because an issue of debt is less likely than an equity issue to be interpreted by investors as a bad omen.

In this story, there is no clear target debt-equity mix, because there are two kinds of equity, internal and external. The first is at the top of the pecking order, and the second is at the bottom. The pecking order explains why the most profitable firms gen- erally borrow less; it is not because they have low target debt ratios but because they don’t need outside money. Less profitable firms issue debt because they do not have

13  We described this “announcement effect” in Chapter 15.

pecking order theory Firms prefer to issue debt rather than equity if internal finance is insufficient.

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Chapter 16 Debt Policy 483

sufficient internal funds for their capital investment program and because debt is first in the pecking order for external finance.

The pecking order theory does not deny that taxes and financial distress can be important factors in the choice of capital structure. However, the theory says that these factors are less important than managers’ preference for internal over external funds and for debt financing over new issues of common stock.

For most U.S. corporations, internal funds finance the majority of new investment, and most external financing comes from debt. These aggregate financing patterns are consistent with the pecking order theory. Yet the pecking order seems to work best for mature firms. Fast-growing high-tech firms often resort to a series of common stock issues to finance their investments. Of course you wouldn’t expect the pecking order to apply to firms with extremely valuable growth opportunities. Such firms have good reasons to issue stock; they are credible issuers. Stock issues by growth firms do not send the same pessimistic signal as issues by mature firms.

The Two Faces of Financial Slack Other things equal, it’s better to be at the top of the pecking order than at the bottom. Firms that have worked down the pecking order and need external equity may end up living with excessive debt or bypassing good investments because shares can’t be sold at what managers consider a fair price.

When asked about what factors are uppermost in their minds when they think about debt policy, financial managers commonly mention the tax advantage of debt and the importance of maintaining the firm’s credit rating. But they place even greater emphasis on the need to retain flexibility so that the company has access to funds for pursuing new projects when they come along. 14 In other words, they place a high value on financial slack. Having financial slack means having cash, marketable securities, and ready access to the debt markets or to bank financing. Ready access basically requires conservative financing so that potential lenders see the company’s debt as a safe investment.

In the long run, a company’s value rests more on its capital investment and operating decisions than on financing. Therefore, you want to make sure your firm has sufficient financial slack so that financing is quickly available for good investments. Financial slack is most valuable to firms with plenty of positive-NPV growth opportunities. That is another reason why growth companies usually aspire to conservative capital structures.

However, there is also a dark side to financial slack. Too much of it may encourage managers to take it easy, expand their perks, or empire-build with cash that should be paid back to stockholders. Michael Jensen has stressed this free-cash-flow problem: the tendency of managers with ample free cash flow (or unnecessary financial slack) to plow too much cash into mature businesses or ill-advised acquisitions. “The problem,” Jensen says, “is how to motivate managers to disgorge the cash rather than investing it below the cost of capital or wasting it in organizational inefficiencies.” 15

If that’s the problem, then maybe debt is an answer. Scheduled interest and princi- pal payments are contractual obligations of the firm. Debt forces the firm to pay out cash. Perhaps the best debt level would leave just enough cash in the bank, after debt service, to finance all positive-NPV projects, with not a penny left over.

We do not recommend this degree of fine-tuning, but the idea is valid and important. For some firms, the threat of financial distress may have a good effect on managers’ incentives. After all, skating on thin ice can be useful if it makes the skater concen- trate. Likewise, managers of highly levered firms are more likely to work harder, run a leaner operation, and think more carefully before they spend money.

14  J. R. Graham and C. R. Harvey, “The Theory and Practice of Corporate Finance: Evidence from the Field,” Journal of Financial Economics 61 (2001), pp. 187–243.

financial slack Ready access to cash or debt financing.

15  M. C. Jensen, “Agency Costs of Free Cash Flow, Corporate Finance and Takeovers,” American Economic Review 26 (May 1986), p. 323.

free-cash-flow problem Companies with ample cash flow are tempted to overinvest and to operate inefficiently. Companies facing this problem may benefit from the discipline imposed by more debt and higher debt-service requirements.

Sealed Air Corporation

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484 Part Five Debt and Payout Policy

SUMMARY The goal is to maximize the overall market value of all the securities issued by the firm. Think of the financial manager as taking all the firm’s real assets and selling them to inves- tors as a package of securities. Some financial managers choose the simplest package possible: all-equity financing. Others end up issuing dozens of types of debt and equity securities. The financial manager must try to find the particular combination that maximizes the market value of the firm. If firm value increases, common stockholders will benefit.

But capital structure does not necessarily affect firm value. Modigliani and Miller’s (MM’s) famous debt-irrelevance proposition states that firm value can’t be increased by changing capital structure. Therefore, the proportions of debt and equity financing don’t matter. Financial leverage does increase the expected rate of return to shareholders, but the risk of their shares increases proportionally. MM show that the extra return and extra risk balance out, leaving shareholders no better or worse off.

Of course, MM’s argument rests on simplifying assumptions. For example, it assumes efficient, well-functioning capital markets and ignores taxes and costs of financial distress. But even if these assumptions are incorrect in practice, MM’s proposition is important. It exposes logical traps that financial managers sometimes fall into, particularly the idea that debt is “cheap financing” because the explicit cost of debt (the interest rate) is less than the cost of equity. Debt has an implicit cost too, because increased borrowing increases finan- cial risk and the cost of equity. When both costs are considered, debt is not cheaper than equity. MM show that if there are no corporate income taxes, the firm’s weighted-average cost of capital does not depend on the amount of debt financing.

Debt interest is a tax-deductible expense. Thus borrowing creates an interest tax shield. The present value of future interest tax shields can be very large, a substantial fraction of the value of outstanding debt. Of course, interest tax shields are valuable only for compa- nies that are making profits and paying taxes.

The more firms borrow, the higher the odds of financial distress. The costs of financial distress can be broken down as follows:

• Direct bankruptcy costs, primarily legal and administrative costs. • Indirect bankruptcy costs, reflecting the difficulty of managing a company when it is

in bankruptcy proceedings. • Financial decisions that are distorted by the threat of default and bankruptcy, includ-

ing poor investment decisions caused by the conflicts of interest between debthold- ers and stockholders. The conflicts create potential risk-shifting and debt-overhang problems.

Combining interest tax shields and costs of financial distress leads to a trade-off theory of optimal capital structure. The trade-off theory says that financial managers should increase debt to the point where the value of additional interest tax shields is just offset by addi- tional costs of possible financial distress.

The trade-off theory says that firms with safe, tangible assets and plenty of taxable income should operate at high debt levels. Less profitable firms, or firms with risky, intan- gible assets, ought to borrow less.

The pecking order theory says that firms prefer internal financing (that is, earnings retained and reinvested) over external financing. If external financing is needed, they prefer to issue debt rather than issue new shares. The pecking order theory says that the amount of debt a firm issues will depend on its need for external financing. The theory also suggests that financial managers should try to maintain at least some financial slack, that is, a reserve of ready cash or unused borrowing capacity.

On the other hand, too much financial slack may lead to slack managers. High debt lev- els (and the threat of financial distress) can create strong incentives for managers to work harder, conserve cash, and avoid negative-NPV investments.

What is the goal of the capital structure decision? What is the financial manager trying to do? When would capital structure not matter? (LO16-1)

How do corporate income taxes modify MM’s leverage-irrelevance proposition? (LO16-2)

If interest tax shields are valuable, why don’t all taxpaying firms borrow as much as possible? (LO16-3)

What’s the pecking order theory? (LO16-4)

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Chapter 16 Debt Policy 485

Sorry, there are no simple answers for capital structure decisions. Debt may be better than equity in some cases, worse in others. But there are at least four dimensions for the finan- cial manager to think about.

• Taxes. How valuable are interest tax shields? Is the firm likely to continue paying taxes over the full life of a debt issue? Safe, consistently profitable firms are most likely to stay in a taxpaying position.

• Risk. Financial distress is costly even if the firm survives it. Other things equal, financial distress is more likely for firms with high business risk. That is why risky firms typically issue less debt.

• Asset type. If distress does occur, the costs are generally greatest for firms whose value depends on intangible assets. Such firms generally borrow less than firms with safe, tangible assets.

• Financial slack. How much is enough? More slack makes it easy to finance future investments, but it may weaken incentives for managers. More debt, and therefore less slack, increases the odds that the firm may have to issue stock to finance future investments.

Is there a rule for finding optimal capital structure? ( LO16-3, LO16-4)

L I S T I N G O F E Q UAT I O N S

16.1 requity = rassets + D

E (rassets - rdebt)

16.2 WACC  =  (1  −   T c ) r debt a DD + Eb   +   r equity a E

D + E b

QUESTIONS AND PROBLEMS 1. Debt Irrelevance. True or false? MM’s leverage-irrelevance proposition says: (LO16-1)

a. The value of the firm does not depend on the fraction of debt versus equity financing. b. As financial leverage increases, the value of the firm increases by just enough to offset the

additional financial risk absorbed by equity. c. The cost of equity increases with financial leverage only when the risk of financial distress

is high. d. If the firm pays no taxes, the weighted-average cost of capital does not depend on the debt

ratio.

2. Debt Irrelevance. River Cruises (see Section 16.1) is all-equity-financed with 50,000 shares. It now proposes to issue $250,000 of bonds and use the proceeds to repurchase 25,000 shares. Suppose an investor currently holds 500 shares in the company but is unhappy with its decision to borrow $250,000. Which of the following modifications to her own investment portfolio would offset the effects of the firm’s additional borrowing? (LO16-1)

a. Borrow $250 on her own account and use the cash to buy additional River Cruises’ shares. b. Raise $250 by selling River Cruises’ shares and use the cash to buy the company’s debt. c. Keep her current holding of River Cruises’ shares and borrow $250 to invest in the

company’s bond issue.

3. Leverage and Earnings. River Cruises (see Section 16.1) is all-equity-financed. Suppose it now issues $250,000 of debt at an interest rate of 10% and uses the proceeds to repurchase 25,000 shares. Assume that the firm pays no taxes and that debt finance has no impact on firm value. Rework Table 16.3 by selecting values for (a) to (j) below to show how earnings per share and share return vary with operating income after the financing. (LO16-1)

finance

®

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486 Part Five Debt and Payout Policy

Current Data

Number of shares 100,000 Price per share $10 Market value of shares $1 million

Outcomes State of the Economy Slump Normal Boom Profi ts before interest $75,000 $125,000 $175,000 Interest (a) (a) (a) Equity earnings (b) (c) (d) Earnings per share (e) (f) (g) Return on shares (h) (i) (j) ↑

Expected outcome

4. Leverage and P/E Ratios. River Cruises (see Section 16.1) is all-equity-financed with 100,000 shares. It now proposes to issue $250,000 of debt at an interest rate of 10% and use the proceeds to repurchase 25,000 shares. Profits before interest are expected to be $125,000. (LO16-1)

a. What is the ratio of price to expected earnings for River Cruises before it borrows the $250,000? b. What is the ratio after it borrows?

5. Debt Irrelevance. What’s wrong with the following arguments? (LO16-1)

a. As the firm borrows more and debt becomes risky, both stock- and bondholders demand higher rates of return. Thus by reducing the debt ratio we can reduce both the cost of debt and the cost of equity, making everybody better off.

b. Moderate borrowing doesn’t significantly affect the probability of financial distress or bankruptcy. Consequently, moderate borrowing won’t increase the expected rate of return demanded by stockholders.

c. A capital investment opportunity offering a 10% internal rate of return is an attractive proj- ect if it can be 100% debt-financed at an 8% interest rate.

d. The more debt the firm issues, the higher the interest rate it must pay. That is one important reason that firms should operate at conservative debt levels.

6. Leverage and Earnings. Reliable Gearing currently is all-equity-financed. It has 10,000 shares of equity outstanding, selling at $100 a share. The firm is considering a capital restructuring. The low-debt plan calls for a debt issue of $200,000 with the proceeds used to buy back stock. The high-debt plan would exchange $400,000 of debt for equity. The debt will pay an interest rate of 10%. The firm pays no taxes. (LO16-1)

a. What will be the debt-to-equity ratio if it borrows $200,000? b. If earnings before interest and tax (EBIT) are $110,000, what will be earnings per share

(EPS) if Reliable borrows $200,000? c. What will EPS be if it borrows $400,000?

7. Leverage and the Cost of Capital. The common stock and debt of Northern Sludge are valued at $70 million and $30 million, respectively. Investors currently require a 16% return on the common stock and an 8% return on the debt. If Northern Sludge issues an additional $10 mil- lion of common stock and uses this money to retire debt, what happens to the expected return on the stock? Assume that the change in capital structure does not affect the risk of the debt and that there are no taxes. (LO16-1)

8. Leverage and the Cost of Capital. “Increasing financial leverage increases both the cost of debt ( r debt ) and the cost of equity ( r equity ). So the overall cost of capital cannot stay constant.” This problem is designed to show that the speaker is confused. Buggins Inc. is financed equally by debt and equity, each with a market value of $1 million. The cost of debt is 5%, and the cost of equity is 10%. The company now makes a further issue of debt and uses the proceeds to repurchase equity. This causes the cost of debt to rise to 6% and the cost of equity to rise to 12%. Assume the firm pays no taxes. (LO16-1)

a. How much debt does the company now have? b. How much equity does it now have? c. What is the overall cost of capital?

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Chapter 16 Debt Policy 487

9. Leverage and the Cost of Capital. Astromet is financed entirely by common stock and has a beta of 1.0. The firm pays no taxes. The stock has a price-earnings multiple of 10 and is priced to offer a 10% expected return. The company decides to repurchase half the common stock and substitute an equal value of debt. Assume that the debt yields a risk-free 5%. Calculate the following: (LO16-1)

a. The beta of the common stock after the refinancing b. The required return and risk premium on the common stock before the refinancing c. The required return and risk premium on the common stock after the refinancing d. The required return on the debt e. The required return on the company (i.e., stock and debt combined) after the refinancing

If EBIT remains constant:

f. What is the percentage increase in earnings per share after the refinancing? g. What is the new price-earnings multiple? ( Hint: Has anything happened to the stock price?)

10. Leverage and the Cost of Capital. Hubbard’s Pet Foods is financed 80% by common stock and 20% by bonds. The expected return on the common stock is 12%, and the rate of interest on the bonds is 6%. Assume that the bonds are default-free and that there are no taxes. Now assume that Hubbard’s issues more debt and uses the proceeds to retire equity. The new financing mix is 60% equity and 40% debt. If the debt is still default-free, what happens to the following? (LO16-1)

a. The expected rate of return on equity b. The expected return on the package of common stock and bonds

11. Leverage and the Cost of Capital. “MM totally ignore the fact that as you borrow more, you have to pay higher rates of interest.” Explain carefully whether this is a valid objection. (LO16-1)

12. Leverage and the Cost of Capital. A firm currently has a debt-equity ratio of 1/2. The debt, which is virtually riskless, pays an interest rate of 6%. The expected rate of return on the equity is 12%. What would happen to the expected rate of return on equity if the firm reduced its debt- equity ratio to 1/3? Assume the firm pays no taxes. (LO16-1)

13. Tax Shields. River Cruises (see Section 16.1) is all-equity-financed with 100,000 shares. It now proposes to issue $250,000 of debt at an interest rate of 10% and to use the proceeds to repur- chase 25,000 shares. Suppose that the corporate tax rate is 35%. Calculate the dollar increase in the combined after-tax income of its debtholders and equityholders if profits before interest are: (LO16-2)

a. $75,000 b. $100,000 c. $175,000

14. Tax Shields. Establishment Industries borrows $800 million at an interest rate of 7.6%. Estab- lishment will pay tax at an effective rate of 35%. What is the present value of interest tax shields if: (LO16-2)

a. It expects to maintain this debt level into the far future? b. It expects to repay the debt at the end of 5 years? c. It expects to maintain a constant debt ratio once it borrows the $800 million and rassets = 10%?

15. Tax Shields. What is an interest tax shield? How does it increase the size of the “pie” for after- tax income stockholders? Explain. ( Hint: Construct a simple numerical example showing how financial leverage affects the total cash flow available to debt and equity investors. Be sure to hold earnings before interest constant.) (LO16-2)

16. Leverage and the Cost of Capital. Dusit is financed 30% by debt yielding 8%. Investors require a return of 15% on Dusit’s equity. (LO16-2)

a. What is the company’s weighted-average cost of capital if the corporate tax rate is 35%? b. What would be the company’s cost of capital if it were exempted from corporate tax?

17. Financial Slack. True or false? (LO16-4)

a. Financial slack means having cash in the bank or ready access to the debt markets. b. Financial slack is most valuable to firms with few investment opportunities. c. Managers with excessive financial slack may be tempted to spend it on poor investments.

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488 Part Five Debt and Payout Policy

18. Taxes and the Cost of Capital. Here is Establishment Industries’ market-value balance sheet (figures in $ millions):

The debt is yielding 7%, and the cost of equity is 14%. The tax rate is 35%. Investors expect this level of debt to be permanent. (LO16-2)

a. What is Establishment’s WACC? b. How would the market-value balance sheet change if Establishment retired all its debt?

19. Taxes and the Cost of Capital. Here are book- and market-value balance sheets of the United Frypan Company:

Net working capital $ 550 Debt $ 800 Long-term assets 2,150 Equity 1,900 Value of fi rm $2,700 $2,700

Book-Value Balance Sheet

Net working capital $ 20 Debt $ 40 Long-term assets 80 Equity 60

$ 100 $ 100

Market-Value Balance Sheet

Net working capital $ 20 Debt $ 40 Long-term assets 140 Equity 120

$ 160 $ 160

Assume that MM’s theory holds except for taxes. There is no growth, and the $40 of debt is expected to be permanent. Assume a 35% corporate tax rate. (LO16-2)

a. How much of the firm’s value is accounted for by the debt-generated tax shield? b. What is United Frypan’s after-tax WACC if r debt   =  8% and r equity   =  15%? c. Now suppose that Congress passes a law that eliminates the deductibility of interest for tax

purposes after a grace period of 5 years. What will be the new value of the firm, other things equal? Assume an 8% borrowing rate.

20. Financial Distress. True or false? (LO16-3)

a. If the probability of default is high, managers and stockholders will be tempted to take on excessively risky projects.

b. If the probability of default is high, stockholders may refuse to contribute equity even if the firm has safe, positive-NPV opportunities.

c. When a company borrows, the expected costs of bankruptcy come out of the lenders’ pock- ets and do not affect the market value of the shares.

21. Theories of Capital Structure. Fill in the missing entries by choosing from the following terms: safe tangible assets, less, pecking order theory, capital, taxable income to shield, interest tax shields, financial distress, trade-off theory, more, risky assets. (Note: Not all terms will be used.) (LO16-3) Managers will try to increase debt levels to the point where the value of _______ is exactly offset by the additional costs of _______ . This is known as the _______ of capital structure. The theory predicts that companies with _______ and plenty of _______ ought to borrow _______ .

22. Costs of Financial Distress. What are the drawbacks of operating a firm that is close to bank- ruptcy? Give some examples. (LO16-3)

23. Costs of Financial Distress. The Salad Oil Storage Company (SOS) has financed a large part of its facilities with long-term debt. There is a significant risk of default, but the company is not on the ropes yet. (LO16-3)

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Chapter 16 Debt Policy 489

a. Explain why SOS stockholders could lose by investing in a positive-NPV project financed by an equity issue.

b. Explain why SOS stockholders could gain by investing in a highly risky, negative-NPV project.

24. Costs of Financial Distress. For which of the following firms would you expect the costs of financial distress to be highest? Explain briefly. (LO16-3)

a. A computer software company that depends on skilled programmers to produce new products

b. A shipping company that operates a fleet of modern oil tankers

25. Trade-Off Theory. Smoke and Mirrors currently has EBIT of $25,000 and is all-equity- financed. EBIT is expected to stay at this level indefinitely. The firm pays corporate taxes equal to 35% of taxable income. The discount rate for the firm’s projects is 10%. (LO16-3)

a. What is the market value of the firm? b. Now assume the firm issues $50,000 of debt paying interest of 6% per year, using the pro-

ceeds to retire equity. The debt is expected to be permanent. What will happen to the total value of the firm (debt plus equity)?

c. Recompute your answer to (b) under the following assumptions: The debt issue raises the probability of bankruptcy. The firm has a 30% chance of going bankrupt after 3 years. If it does go bankrupt, it will incur bankruptcy costs of $200,000. The discount rate is 10%.

d. Should the firm issue the debt under these new assumptions?

26. Pecking Order Theory. What is the pecking order theory of optimal capital structure? If the theory is correct, what types of firms would you expect to operate at high debt levels? (LO16-4)

27. Pecking Order Theory. Alpha Corp. and Beta Corp. both produce turbo encabulators. Both companies’ assets and operations are growing at the same rate, and their annual capital expen- ditures are about the same. However, Alpha Corp. is the more efficient producer and is consis- tently more profitable. According to the pecking order theory, which company should have the higher debt ratio? (LO16-4)

28. Financial Slack. Scan the Beyond the Page icon in the margin on page 483 to read about Sealed Air’s restructuring. What was the value of financial slack to Sealed Air before its restructuring? What does the success of the restructuring say about optimal capital structure? Would you rec- ommend that all firms restructure as Sealed Air did? (LO16-4)

CHALLENGE PROBLEMS 29. Taxes. MM’s proposition I suggests that in the absence of taxes it makes no difference whether

the firm borrows on behalf of its shareholders or whether they borrow directly. However, if there are corporate taxes, this is no longer the case. Construct a simple example to show that with taxes it is better for the firm to borrow than for the shareholders to do so. (LO16-2)

30. Taxes. MM’s proposition I, when modified to recognize corporate taxes, suggests that there is a tax advantage to firm borrowing. If there is a tax advantage to firm borrowing, there is also a tax disadvantage to retaining and lending large amounts of cash. Explain why. (LO16-2)

31. Tax Shields and WACC. River Cruises’ management now understands that the trade-off theory of optimal capital structure implies managers will increase debt as long as the value of additional interest tax shields exceeds the additional costs of potential financial distress. This trade-off gives rise to the hump-shaped curve in Figure 16.7 , where the value of the firm is maximized at the optimal debt level. What will the curve of WACC as a function of debt level look like? (LO16-2)

a. Start with a no-tax economy. Continue to assume that River Cruises’ required return on assets is 12.5% and return on debt is 10%. In a spreadsheet, calculate r equity , WACC, and r debt for debt-equity ratios ranging from 0 to 2.5 in increments of .1. Does WACC vary with the D / E ratio? Compare your plot to Figure 16.3 .

b. Now assume the corporate tax rate is 35%. Repeat part (a). What happens to WACC as D / E increases? What seems to be the optimal capital structure?

Templates can be found in Connect.

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490 Part Five Debt and Payout Policy

c. What considerations are missing that would affect the optimal capital structure seemingly implied by part (b)?

32. Costs of Financial Distress. Let’s go back to the Double-R Nutting Company. Suppose that Double-R’s bonds have a face value of $50. Its current market-value balance sheet is:

WEB EXERCISES 1. Log on to finance.yahoo.com and click the Key Statistics link for Pfizer (PFE) and Coca-Cola

(KO). Construct the debt ratio, debt/(debt  +  equity), for both firms. Now calculate their debt ratios by using the market value of equity but assuming that book value of debt approximates its market value. How does debt as a proportion of firm value change as you switch from book to market values?

2. On finance.yahoo.com find the profiles for PepsiCo (PEP) and IBM (IBM), and then look at each firm’s annual balance sheet and income statement under Financials. Calculate the present value of the interest tax shield contributed by each company’s long-term debt. Now suppose that each issues $3 billion more of long-term debt and uses the proceeds to repurchase equity. How would the interest tax shield change? In each case assume that the debt is fixed and permanent.

Assets Liabilities and Equity Net working capital $20 Bonds outstanding $25 Fixed assets 10 Common stock 5 Total assets $30 Total liabilities and shareholders’ equity $30

Who would gain or lose from the following maneuvers? (LO16-3)

a. Double-R pays a $10 cash dividend. b. Double-R halts operations, sells its fixed assets for $6, and converts net working capital into

$20 cash. It invests its $26 in Treasury bills. c. Double-R encounters an investment opportunity requiring a $10 initial investment with

NPV  =  $0. It borrows $10 to finance the project by issuing more bonds with the same secu- rity, seniority, and so on, as the existing bonds.

d. Double-R finances the investment opportunity in part (c) by issuing more common stock.

33. Trade-Off Theory. Ronald Masulis 16 has analyzed the stock price impact of exchange offers of debt for equity or vice versa. In an exchange offer, the firm offers to trade freshly issued securi- ties for seasoned securities in the hands of investors. Thus a firm that wanted to move to a higher debt ratio could offer to trade new debt for outstanding shares. A firm that wanted to move to a more conservative capital structure could offer to trade new shares for outstanding debt securities.

Masulis found that debt-for-equity exchanges were good news (stock price increased on announcement) and equity-for-debt exchanges were bad news. (LO16-3)

a. Explain whether these results are consistent with the trade-off theory of capital structure? b. Are the results consistent with the evidence that investors regard announcements of (i) stock

issues as bad news, (ii) stock repurchases as good news, and (iii) debt issues as no news or, at most, trifling disappointments? Say why or why not.

34. Pecking Order Theory. Construct a simple example to show that a firm’s existing stockhold- ers gain if it can sell overpriced stock to new investors and invest the cash in a zero-NPV project. Who loses from these actions? If investors are aware that managers are likely to issue stock when it is overpriced, what will happen to the stock price when the issue is announced? (LO16-4)

35. Pecking Order Theory. When companies announce an issue of common stock, the share price typically falls. When they announce an issue of debt, there is typically only a negligible change in the stock price. Can you explain why? (LO16-4)

16  R. W. Masulis, “The Effects of Capital Structure Change on Security Prices: A Study of Exchange Offers,” Journal of Financial Economics 8 (June 1980), pp. 139–177, and “The Impact of Capital Structure Change on Firm Value,” Journal of Finance 38 (March 1983), pp. 107–126.

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Chapter 16 Debt Policy 491

SOLUTIONS TO SELF-TEST QUESTIONS 16.1 Price per share will stay at $10, so with $350,000, River Cruises can repurchase 35,000 shares,

leaving 65,000 outstanding. The remaining value of equity will be $650,000. Overall firm value stays at $1 million. Shareholders’ wealth is unchanged: They start with shares worth $1 million, receive $350,000, and retain shares worth $650,000.

16.2 a. Data

Number of shares 25,000 Price per share $10 Market value of shares $250,000 Market value of debt $750,000

State of the Economy

Slump Normal Boom

Operating income, dollars 75,000 125,000 175,000 Interest, dollars 75,000 75,000 75,000 Equity earnings, dollars 0 50,000 100,000 Earnings per share, dollars 0 2.00 4.00 Return on shares 0% 20% 40%

Every change of $50,000 in operating income leads to a change in the return to equityholders of 20%. This is double the swing in equity returns when debt was only $500,000. b. The stockholder should lend out $3 for every $1 invested in River Cruises’ stock. For

example, he could buy one share for $10 and then lend $30. The payoffs are:

State of the Economy Slump Normal Boom

Earnings on one share, dollars 0 2.00 4.00 Plus interest at 10%, dollars 3.00 3.00 3.00 Net earnings, dollars 3.00 5.00 7.00 Return on $40 investment 7.5% 12.5% 17.5%

16.3 Business risk is unaffected by capital structure. As the financing mix changes, whatever equity is outstanding must absorb the fixed business risk of the firm. The less equity, the more risk absorbed per share. Therefore, as capital structure changes, r assets is held fixed while r equity adjusts.

16.4 Interest tax shields are .35  ×  .10  ×  300,000  =  $10,500 per year.

a. Discount the perpetuity at the cost of debt. PV  =  10,500/.10  =  $105,000. b. In this case the tax shields are about as risky as operating earnings. Discount at 12.5%.

PV  =  10,500/.125  =  $84,000. c. The company can’t be sure that it will have enough taxable income to exploit interest tax

shields in all future years.

16.5 In bankruptcy bondholders will receive $2 million less. This lowers the expected cash flow from the bond and reduces its present value. Therefore, the bonds will be priced lower and must offer a higher interest rate. This higher rate is paid by the firm today. It comes out of stockholders’ income. Thus common stock value falls.

16.6 The biotech company. Its assets are all intangible. If bankruptcy threatens and the best scien- tists accept job offers from other firms, there may not be much value remaining for the biotech company’s debt and equity investors. On the other hand, bankruptcy would have little or no effect on the value of 50 producing oil wells and of the oil reserves still in the ground.

16.7 a. Lenders will demand a higher interest rate and possibly additional covenants or other restrictions on borrowing.

b. The possibility of distorted future investment and operating decisions reduces the value of the firm today. The reduction in value is a cost of financial distress and a reason for a more conservative debt policy.

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16.8 The electric utility has the most stable cash flow. It also has the highest reliance on tangible assets that would not be impaired by a bankruptcy. It should have the highest debt ratio. The software firm has the least dependence on tangible assets and the most on assets that have value only if the firm continues as an ongoing concern. It probably also has the most unpre- dictable cash flows. It should have the lowest debt ratio.

MINICASE In March 2015 the management team of Londonderry Air (LA) met to discuss a proposal to purchase five shorthaul aircraft at a total cost of $25 million. There was general enthusiasm for the invest- ment, and the new aircraft were expected to generate an annual cash flow of $4 million for 20 years.

The focus of the meeting was on how to finance the purchase. LA had $20 million in cash and marketable securities (see table), but Ed Johnson, the chief financial officer, pointed out that the company needed at least $10 million in cash to meet normal out- flow and as a contingency reserve. This meant that there would be a cash deficiency of $15 million, which the firm would need to cover either by the sale of common stock or by additional borrowing. While admitting that the arguments were finely balanced, Mr. John- son recommended an issue of stock. He pointed out that the airline industry was subject to wide swings in profits and the firm should be careful to avoid the risk of excessive borrowing. He estimated that in market value terms the long-term debt ratio was about 59% and that a further debt issue would raise the ratio to 62%.

Mr. Johnson’s only doubt about making a stock issue was that investors might jump to the conclusion that management believed the stock was overpriced, in which case the announcement might prompt an unjustified selloff by investors. He stressed therefore that the company needed to explain carefully the reasons for the issue. Also, he suggested that demand for the issue would be enhanced if at the same time LA increased its dividend payment. This would pro- vide a tangible indication of management’s confidence in the future.

These arguments cut little ice with LA’s chief executive. “Ed,” she said, “I know that you’re the expert on all this, but everything

you say flies in the face of common sense. Why should we want to sell more equity when our stock has fallen over the past year by nearly a fifth? Our stock is currently offering a dividend yield of 6.5%, which makes equity an expensive source of capital. Increasing the dividend would simply make it more expensive. What’s more, I don’t see the point of paying out more money to the stockholders at the same time that we are asking them for cash. If we hike the dividend, we will need to increase the amount of the stock issue; so we will just be paying the higher dividend out of the shareholders’ own pockets. You’re also ignoring the question of dilution. Our equity currently has a book value of $12 a share; it’s not playing fair by our existing shareholders if we now issue stock for around $10 a share.

“Look at the alternative. We can borrow today at 6%. We get a tax break on the interest, so the after-tax cost of borrowing is .65  ×  6  =  3.9%. That’s about half the cost of equity. We expect to earn a return of 15% on these new aircraft. If we can raise money at 3.9% and invest it at 15%, that’s a good deal in my book.

“You finance guys are always talking about risk, but as long as we don’t go bankrupt, borrowing doesn’t add any risk at all.

“Ed, I don’t want to push my views on this—after all, you’re the expert. We don’t need to make a firm recommendation to the board until next month. In the meantime, why don’t you get one of your new business graduates to look at the whole issue of how we should finance the deal and what return we need to earn on these planes?”

Evaluate Mr. Johnson’s arguments about the stock issue and dividend payment as well as the reply of LA’s chief executive. Who is correct? What is the required rate of return on the new planes?

* The yield to maturity on LA debt currently is 6%. † LA has 10 million shares outstanding, with a market price of $10 a share. LA’s equity beta is estimated at 1.25, the market risk premium is 8%, and the Treasury bill rate is 3%.

Balance Sheet

Bank debt $ 50 Cash $ 20 Other current liabilities 20 Other current assets 20 10% bond, due 2032* 100 Fixed assets 250 Stockholders’ equity† 120

Total liabilities $290 Total assets $290

Income Statement

Gross profi t $57.5 Depreciation 20.0 Interest 7.5 Pretax profi t 30.0 Tax 10.5 Net profi t 19.5 Dividend 6.5

Summary financial statements for Londonderry Air, 2014 (Figures are book values, in millions of dollars.)

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Chapter 16 Debt Policy 493

Bankruptcy Procedures

Firms that issue debt always bear a risk that when the debt comes due, they will not be able to pay their creditors. At that point, the firm may be forced into bankruptcy. We conclude this chapter with a brief overview of the bankruptcy process.

A corporation that cannot pay its debts will often try to come to an informal agreement with its creditors. This is known as a workout. A workout may take several forms. For example, the firm may negotiate an extension, that is, an agreement with its creditors to delay payments. Or the firm may negotiate a composition, in which the firm makes partial payments to its creditors in exchange for relief of its debts.

The advantage of a negotiated agreement is that the costs and delays of formal bankruptcy are avoided. However, the larger the firm and the more complicated its capital structure, the less likely it is that a negotiated settlement can be reached.

If the firm cannot get an agreement, then it may have no alternative but to file for bankruptcy. 17

Under the federal bankruptcy system the firm has a choice of procedures. In about two-thirds of the cases a firm will file for, or be forced into, bankruptcy under Chapter 7 of the 1978 Bankruptcy Reform Act. Then the firm’s assets are liquidated —that is, sold—and the proceeds are used to pay creditors.

Secured creditors have first priority to the collateral pledged for their loans. Then come unsecured creditors in the following rank order: First come claims for expenses that arise after bankruptcy is filed, such as attorneys’ fees or employee compensation earned after the filing. If such postfiling claims did not receive priority, no firm in bankruptcy proceedings could continue to operate. Next come claims for wages and employee benefits earned in the period immediately prior to the filing. Taxes are next in line, together with debts to some government agencies such as the Small Busi- ness Administration or the Pension Benefit Guarantee Corporation. Finally come general unsecured claims such as unsecured trade debt.

The alternative to a liquidation is a reorganization, which keeps the firm as a going concern and usually compensates creditors with new securities in the reorganized firm. Such reorganizations are generally in the shareholders’ interests—they have little to lose if things deteriorate further and everything to gain if the firm recovers. Almost all large firms opt for a reorganization rather than a liquidation.

Firms attempting reorganization seek refuge under Chapter 11 of the Bankruptcy Reform Act. Chapter 11 is designed to keep the firm alive and operating and to protect the value of its assets while a plan of reorganization is worked out. During this period, other proceedings against the firm are halted and the company is operated by existing management or by a court-appointed trustee.

The responsibility for developing a plan of reorganization may fall on the debtor firm. If no trustee is appointed, the firm has 120 days to present a plan to creditors. If this deadline is not met, or if a trustee is appointed, anyone can submit a plan—the trustee, for example, or a committee of creditors.

The reorganization plan is basically a statement of who gets what; each class of creditors gives up its claim in exchange for new securities. (Sometimes creditors receive cash as well.) The problem is to design a new capital structure for the firm that will (1) satisfy the creditors and (2) allow the firm to solve the business problems that got the firm into trouble in the first place. Sometimes only a plan of baroque complexity can satisfy these two requirements.

The reorganization plan goes into effect if it is accepted by creditors and confirmed by the court. Acceptance requires approval by a majority of each class of creditor. Once a plan is accepted, the court normally approves it, provided that each class of creditors has approved it and that the creditors will be better off under the plan than if the firm’s assets were liquidated and distributed. The court may, under certain conditions, confirm a plan even if one or more classes of creditors vote against it. This is known as a cram-down.

The interests of the different classes of creditors do not always coincide. For example, junior creditors may threaten to slow the process as a way of extracting concessions from senior creditors. The senior creditors may take less than 100 cents on the dollar and give something to junior creditors in order to expedite the process and reach an agreement.

Chapter 11 proceedings are often successful, and the patient emerges fit and healthy. But in other cases cure proves impossible and the assets are liquidated. Sometimes the firm may emerge from

workout Agreement between a company and its creditors establishing the steps the company must take to avoid bankruptcy.

17  Occasionally creditors will allow the firm to petition for bankruptcy after it has reached an agreement with the creditors. This is known as a prepackaged bankruptcy. The court simply approves the agreed workout plan.

bankruptcy The reorganization or liquidation of a firm that cannot pay its debts.

liquidation Sale of bankrupt firm’s assets.

reorganization Restructuring of financial claims on failing firm to allow it to keep operating.

APPENDIX

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494 Part Five Debt and Payout Policy

Chapter 11 for a brief period before it is once again submerged by disaster and back in bankruptcy. For example, TWA came out of bankruptcy at the end of 1993 and was back again less than 2 years later and then for a third time in 2001, prompting jokes about “Chapter 33.” TWA has plenty of com- pany in this regard. In recent years, about 80% of large firms have emerged from bankruptcy pro- ceedings with a second life, but nearly one-third of those reorganized firms met with failure within 5 years. 18 Among other notable “serial failures” are Planet Hollywood, Grand Union, Memorex, Continental Airlines, and Harvard Industries.

The Choice between Liquidation and Reorganization Here is an idealized view of the bankruptcy decision. Whenever a payment is due to creditors, man- agement checks the value of the firm. If the firm is worth more than the promised payment, the firm pays up (if necessary, raising the cash by an issue of shares). If not, the equity is worthless, and the firm defaults on its debt and petitions for bankruptcy. If in the court’s judgment the assets of the bankrupt firm can be put to better use elsewhere, the firm is liquidated and the proceeds are used to pay off the creditors. Otherwise, the creditors simply become the new owners and the firm continues to operate.

In practice, matters are rarely so simple. For example, we observe that firms often petition for bankruptcy even when the equity has a positive value. Moreover, the bankruptcy court may decide to keep the firm on life support even when the assets could be used more efficiently elsewhere. There are several reasons for this.

First, although the reorganized firm is legally a new entity, it is entitled to any tax-loss carry- forwards belonging to the old firm. If the firm is liquidated rather than reorganized, any tax-loss carry-forwards disappear. Thus there is an incentive to continue in operation even if assets are better used by another firm.

Second, if the firm’s assets are sold off, it is easy to determine what is available to pay the credi- tors. However, when the company is reorganized, it needs to conserve cash as far as possible. There- fore, claimants are generally paid in a mixture of cash and securities. This makes it less easy to judge whether they have received their entitlement. For example, each bondholder may be offered $300 in cash and $700 in a new bond which pays no interest for the first 2 years and a low rate of interest thereafter. A bond of this kind in a company that is struggling to survive may not be worth much, but the bankruptcy court usually looks at the face value of the new bonds and may therefore regard the bondholders as paid in full.

Senior creditors who know they are likely to get a raw deal in a reorganization are likely to press for a liquidation. Shareholders and junior creditors prefer a reorganization. They hope that the court will not interpret the pecking order too strictly and that they will receive some crumbs.

Third, although shareholders and junior creditors are at the bottom of the pecking order, they have a secret weapon: They can play for time. Bankruptcies of large companies often take several years before a plan is presented to the court and agreed to by each class of creditor. When they use delaying tactics, the junior claimants are betting on a turn of fortune that will rescue their investment. On the other hand, the senior creditors know that time is working against them, so they may be prepared to accept a smaller payoff as part of the price for getting a plan accepted. Also, prolonged bankruptcy cases are costly. (While their cases are extreme, we’ve seen that the Enron and Lehman bankruptcies have generated $800 million and over $2 billion, respectively, in legal and administrative costs.) Senior claimants may see their money seeping into lawyers’ pockets and therefore decide to settle quickly.

Fourth, while a reorganization plan is being drawn up, the company is allowed to buy goods on credit and borrow money. Postpetition creditors (those who extend credit to a firm already in bank- ruptcy proceedings) have priority over the old creditors, and their debt may even be secured by assets that are already mortgaged to existing debtholders. This also gives the prepetition creditors an incen- tive to settle quickly, before their claim on assets is diluted by the new debt.

Finally, profitable companies may file for Chapter 11 bankruptcy to protect themselves against “burdensome” suits. For example, in 1982 Manville Corporation was threatened by 16,000 dam- age suits alleging injury from asbestos. Manville filed for bankruptcy under Chapter 11, and the bankruptcy judge agreed to put the damage suits on hold until the company was reorganized. This took 6 years. Of course, legislators worry that these actions are contrary to the original intent of the bankruptcy acts.

18  “The Firms That Can’t Stop Failing,” The Economist, September 7, 2002.

Chapter 55

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Chapter 16 Debt Policy 495

The U.S. bankruptcy system is often described as debtor-friendly. In some other countries, the bankruptcy regime is designed to recover as much cash as possible for the lenders. While critics of Chapter 11 complain about the costs of saving businesses that are not worth saving, commentators elsewhere bemoan the fact that their bankruptcy laws are causing the breakup of potentially healthy businesses.

Appendix Questions 1. Bankruptcy. True or false?

a. When a company becomes bankrupt, it is usually in the interests of the equityholders to seek a liquidation rather than a reorganization.

b. A reorganization plan must be presented for approval by each class of creditor. c. The Internal Revenue Service has first claim on the company’s assets in the event of

bankruptcy. d. In a reorganization, creditors may be paid off with a mixture of cash and securities. e. When a company is liquidated, one of the most valuable assets to be sold is often the tax-loss

carry-forward.

2. Bankruptcy. Explain why equity can sometimes have a positive value even when companies petition for bankruptcy.

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496

Payout Policy

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

17-1 Describe how dividends are paid and shares are repurchased.

17-2 Explain why dividend increases and repurchases are good news for investors and why dividend cuts are bad news.

17-3 Explain why payout policy would not affect shareholder value in perfect and efficient financial markets.

17-4 Show how market imperfections, especially the different tax treatment of dividends and capital gains, can affect payout policy.

17-5 Understand how payout policy varies over the life cycle of the firm.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

17 CHAPTE R

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497

P A

R T

F IV

E

S hareholders invest in the corporation when they buy newly issued shares and when the corporation reinvests earnings on the share- holders’ behalf. The shareholders do not usually

demand a prompt cash return on this investment.

Some long-established companies have never paid

a cash dividend. Sooner or later, however, most cor-

porations do pay out cash to their shareholders. They

pay dividends, or they use cash to buy back previ-

ously issued shares.

How much should a corporation pay out in a

given year? Should the payout come as dividends or

share repurchases? The answers to these two ques-

tions are the corporation’s payout policy.

We start the chapter with a discussion of how divi-

dends are paid and how firms repurchase their stock.

We explain why dividend increases usually convey

good news to investors, and why dividend cuts con-

vey bad news. Then we explain why payout policy

should not affect shareholder wealth in an ideal

world with perfect and efficient financial markets.

That leads us to the real-world complications that

could favor one payout policy over another. Taxes,

which favor repurchases, are probably at the head

of the list.

We close with a discussion of total cash payout

and how it is likely to change over the life cycle of the

firm. Young, growing firms pay out little or nothing—

they are raising cash from investors, not returning it.

Mature firms pay out more and more as they age

and investment opportunities shrink. A generous

payout by aging firms is welcomed by investors, who

worry that managers will otherwise waste free cash

flow on empire-building and negative-NPV projects.

D e

b t a

n d

P a

yo u

t P o

lic y

In 2013 Union Pacific paid out $1.3 billion in dividends and used a further $2.2 billion to repurchase stock. How do companies decide on the payout to shareholders?

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498 Part Five Debt and Payout Policy

17.1 How Corporations Pay Out Cash to Shareholders Corporations pay out cash to their shareholders in two ways. They can pay a cash divi- dend or repurchase some outstanding shares. Figure 17.1 shows annual repurchases and dividends in the United States since 1980. You can see that stock repurchases were rare before the mid-1980s but have since become far more common. In 2013, some of the more active stock repurchasers included Home Depot ($17 billion), AT&T ($11 billion), GE ($10 billion), and PepsiCo ($10 billion). The repurchase champion, however, is ExxonMobil, which bought back more than $191 billion of its shares in the 8 years ending in 2012.

Most mature, profitable companies pay cash dividends. By contrast, growth com- panies typically pay small or no dividends. The no-dividend group includes household names such as Amazon, Facebook, eBay, and Google. The no-dividend group also includes companies that used to pay dividends but have fallen on hard times and been forced to cut back dividends to conserve cash. An example is Ford Motor Company, which paid regular dividends for decades but cut its dividend to zero in 2006.

Here is a table of payout practices for U.S. firms from 2003 to 2012:

FIGURE 17.1 Dividends and stock repurchases in the United States, 1980–2012 (figures in $ billions)

Pay Dividend?

Yes No

Repurchase? Yes 15% 11% No 19% 55%

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How companies pay out cash

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Dividends and repurchases You can see that firms are not obliged to choose between dividends and repurchase.

On average, in any year, 15% of the firms both paid a dividend and also repurchased shares. The fraction that paid dividends but did not repurchase was 19%. The cor- responding fraction for repurchases but no dividends was 11%. But 55% neither paid dividends nor repurchased shares.

Source: Compustat, www.compustat.com.

Repurchases

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

19 80

19 82

19 84

19 86

19 88

19 90

19 92

19 94

19 96

19 98

20 00

20 02

20 04

20 06

20 08

20 10

20 12

D o

lla rs

, b ill

io n

s

Dividends

Year

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Chapter 17 Payout Policy 499

How Firms Pay Dividends In August 2013, Union Pacific’s board of directors met and decided to authorize a quarterly cash dividend of $.79 per share. Some of Union Pacific’s shareholders may have welcomed the cash, but others preferred to reinvest the dividend in the company. To help these investors, Union Pacific offered an automatic dividend reinvestment plan, or DRIP. If a shareholder belonged to this plan, his or her dividends were auto- matically used to buy additional shares. 1

Who receives the Union Pacific dividend? That may seem an obvious question, but shares trade constantly, and the firm’s records of who owns its shares are never fully up to date. So corporations have to specify a particular day’s roster of shareholders who qualify to receive each dividend. Union Pacific announced that it would send a dividend check on October 1 (the payment date ) to all shareholders recorded in its books on August 30 (the record date ).

On August 28, two days before the record date, Union Pacific stock began to trade ex-dividend. Investors who bought shares on or after that date did not have their pur- chases registered by the record date and were not entitled to the dividend. Other things equal, a stock is worth less if you miss out on the dividend. So when a stock “goes ex-dividend,” its price falls by about the amount of the dividend.

Figure  17.2 illustrates the sequence of the key dividend dates. This sequence is the same whenever companies pay a dividend (though of course the actual dates will differ).

cash dividend Payment of cash by the firm to its shareholders.

1 Often the new shares in an automatic dividend investment plan are issued at a small discount of around 5% from the market price; the firm offers this sweetener because it saves the underwriting costs of a regular share issue. Sometimes 10% or more of total dividends are reinvested under such plans.

ex-dividend Without dividend. Buyer of a stock after the ex-dividend date does not receive the most recently declared dividend.

Mick Milekin buys 100 shares of Junk Bombs Inc. on Tuesday, June 2. The company has declared a dividend of $1 per share payable on June 30 to share- holders of record as of Wednesday, June 3. If the ex-dividend date is June 1, is Mick entitled to the dividend? When will the checks go out in the mail?

Self-Test 17.1

FIGURE 17.2 The key dates for Union Pacific’s quarterly dividend August 1, 2013

Declaration date Ex-dividend date Record date Payment date

August 28 August 30 October 1 Union Pacific

declares regular quarterly dividend of $.79 per share.

Shares start to trade ex-dividend.

Dividend will be paid to share-

holders registered on this date.

Dividend checks are mailed to shareholders.

Limitations on Dividends Suppose that an unscrupulous board decided to sell all the firm’s assets and distribute the money as dividends. That would not leave anything in the kitty to pay the firm’s debts.

State law helps to protect the firm’s creditors against excessive dividend payments. For example, most states prohibit a company from paying dividends if doing so would make the company insolvent. 2 Also, companies are not allowed to pay a dividend if it

2 The statutes define insolvency in different ways. In some cases, it just means an inability to meet immediate obligations; in other cases, it means a deficiency of assets compared with all outstanding fixed liabilities.

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500 Part Five Debt and Payout Policy

cuts into legal capital. Legal capital is generally defined as the par value of the out- standing shares. 3

Banks and other lenders may also demand dividend restrictions, particularly if they are worried about the borrower’s creditworthiness. We mentioned that Ford eliminated its dividend in 2006. Ford had lost billions and had been forced to borrow heavily to finance its recovery plan. Its loan agreements prohibited dividends. Thus Ford was only able to start paying dividends again in 2012 when its health had improved.

Stock Dividends and Stock Splits Union Pacific’s dividend was in cash, but companies sometimes declare stock dividends. For example, the firm could declare a stock dividend of 10%. In this case it would send each shareholder 1 additional share for each 10 that the shareholder owns.

A stock dividend is very much like a stock split. In both cases the shareholder is given a fixed number of new shares for each one held. For example, in a two-for-one stock split, each investor would receive one additional share for each share already held. The investor ends up with two shares rather than one. A two-for-one stock split is therefore like a 100% stock dividend. Both result in a doubling of the number of outstanding shares, but they do not affect the company’s assets, profits, or total value. 4

More often than not, however, the announcement of a stock split does result in a rise in the market price of the stock, even though investors are aware that the company’s business is not affected. Perhaps low-priced shares are particularly favored by inves- tors, or maybe investors take the decision as a signal of management’s confidence in the future. 5

3 Where there is no par value, legal capital consists of part or all of the receipts from past share issues.

stock dividends and splits Distributions of additional shares to a firm’s stockholders.

4 Unusually high stock prices can make trading difficult for some individual investors who are accustomed to buying shares in round lots of 100 shares each. So a corporation with stock that is selling for, say, $240 per share could use a six-for-one split to pull the price down into a more convenient “trading range” of around $40. It seems that sometimes individual investors may favor stocks with low prices and that companies respond to this change in demand by splitting their stock. See M. Baker, R. Greenwood, and J. Wurgler, “Catering through Nominal Share Prices,” Journal of Finance 64 (December 2009), pp. 2559–2590. 5 See E. F. Fama, L. Fisher, M. Jensen, and R. Roll, “The Adjustment of Stock Prices to New Information,” International Economic Review 10 (February 1969), pp. 1–21. For evidence that companies which split their stock have above-average earnings prospects, see P. Asquith, P. Healy, and K. Palepu, “Earnings and Stock Splits,” Accounting Review 64 (July 1989), pp. 387–403.

Example 17.1 Stock Dividends and Splits Amoeba Products has issued 2 million shares currently selling at $15 each. Thus investors place a total market value on Amoeba of $30 million. The company now declares a 50% stock dividend. This means that each shareholder will receive one new share for every two shares that are currently held. So the total number of Amoeba shares will increase from 2 million to 3 million. The company’s assets are not changed by this paper transaction and are still worth $30 million. The value of each share after the stock dividend is therefore $30/3  =  $10.

If Amoeba split its stock three for two, the effect would be the same. 6 In this case two shares would split into three. (Amoeba’s motto is “Divide and conquer.”) So each shareholder has 50% more shares with the same total value. Other things equal, share price must decline by a third.

6 The distinction between stock dividends and stock splits is a technical one. A stock dividend is shown on the balance sheet as a transfer from retained earnings to par value and additional paid-in capital. A split is shown as a proportional reduction in the par value of each share. Neither affects the total book value of stockholders’ equity.

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Chapter 17 Payout Policy 501

Sometimes companies with very low stock prices use reverse splits to increase price per share. Citigroup, for example, announced a 1-for-10 reverse split in 2011. Citi had survived the financial crisis of 2007–2009, but its stock had fallen from precrisis levels of around $50 per share to a little above $4. The reverse split gave each shareholder 1 new share for every 10 old shares. Suddenly Citi stock was trading above $40. Of course, shareholders who purchased the stock precrisis remembered that the 10 shares they gave up in the split used to be worth $500.

Stock Repurchases Another way for the firm to hand back cash to its stockholders is to repurchase some of its shares. For example, 2 weeks before announcing its dividend increase, Union Pacific announced that it had spent $463 million in the latest quarter on repurchases. The company can keep these reacquired shares in its treasury and resell them if it needs money later. The shares can also be issued to managers who exercise stock options.

There are four main ways to implement a stock repurchase:

1. Open-market repurchase. The firm announces that it plans to buy stock in the secondary market, just like any other investor. This is by far the most common method. There are limits on how many of its own shares a firm is allowed to purchase on a given day, so repurchases are spread out over several months or years.

2. Tender offer. The firm offers to buy back a stated number of shares at a fixed price. If enough shareholders accept the offer, the deal is done.

3. Auction. The firm states a range of prices at which it is prepared to repurchase. Shareholders submit offers declaring how many shares they are prepared to sell at each price, and the firm calculates the lowest price at which it can buy the desired number of shares.

4. Direct negotiation. The firm may negotiate repurchase of a block of shares from a major shareholder. The most notorious examples are greenmail transactions, in which the target of an attempted takeover buys out the hostile bidder. “Greenmail” means that the shares are repurchased at a generous price that makes the bidder happy to leave the target alone.

17.2 The Information Content of Dividends and Repurchases In 2004 a survey asked senior executives about their firms’ dividend policies. Figure 17.3 summarizes the executives’ responses. Three features stand out:

1. Managers are reluctant to make dividend changes that may have to be reversed, and they are willing to raise new financing if necessary to maintain payout.

2. Managers “smooth” dividends and hate to cut them back. Dividends tend to follow the growth in long-run, sustainable earnings. Transitory fluctuations in earnings rarely affect dividend payouts.

3. Managers focus more on dividend changes than on absolute levels. Thus paying a $2 dividend is an important financial decision if last year’s dividend was $1, but it’s no big deal if last year’s dividend was $2.

From these replies you can see why an announcement of a dividend increase is good news for investors. Investors know that managers are reluctant to cut dividends and therefore will not increase them unless they are confident that the payment can be maintained. Therefore the declaration of a dividend increase has information content; it signals managers’ confidence in the future.

It is no surprise, therefore, to find that the announcement of a dividend increase prompts a small rise in the stock price and that a dividend cut results in a fall. For

stock repurchase Firm distributes cash to stockholders by repurchasing shares.

information content of dividends Dividend increases convey managers’ confidence about future cash flow and earnings. Dividend cuts convey lack of confidence and therefore are bad news.

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502 Part Five Debt and Payout Policy

example, Healy and Palepu found that announcement of a company’s first dividend caused an immediate price increase of 4% on average. 7 Amihud and Li found that during the 1990s the announcement of a dividend increase (by companies already pay- ing a regular dividend) caused, on average, an immediate price rise of about .5%. A dividend cut resulted in a fall in price of about 2%. 8 Notice that investors do not get excited about the level of a company’s dividend; they worry about the change, which they view as an indicator of management’s confidence in the future.

Seasoned financial managers understand the information content of dividends and take care not to change dividends in a way that sends false signals to investors. But some dividend changes do not have any information content. For example, not all dividend cuts are bad news; if investors are convinced that there is a good reason for the cut, the stock price may emerge unscathed. The nearby box explains how investors went along with a dividend cut by JPMorgan Chase in 2009. Also, dividend cuts don’t convey bad news when the information is already out and investors realize that the dividend cut is coming, as the following example illustrates.

7 P. Healy and K. Palepu, “Earnings Information Conveyed by Dividend Initiations and Omissions,” Journal of Financial Economics 21 (1988), pp. 149–175. 8 Y. Amihud and K. Li, “The Declining Information Content of Dividend Announcements and the Effect of Insti- tutional Holdings,” Journal of Financial and Quantitative Analysis 41 (2006), pp. 637–660. Amihud and Li also found that the information content of dividend announcements was much larger during the 1960s and 1970s.

Example 17.2 BP’s Dividend Suspension BP announced on June 16, 2010, that it planned to suspend dividends at least through the end of the year. The suspension freed up roughly $7.8 billion in cash, which could be used for the compensation fund that BP agreed to set up in the wake of the Gulf oil spill. Yet the announcement of the dividend cut barely moved BP’s stock price. This cut was widely anticipated, so it wasn’t new information. It was a response to a bad event that had already happened and knocked down BP’s stock price. It was not interpreted as a signal of fresh bad news about BP.

FIGURE 17.3 A survey of financial executives suggested that their firms were reluctant to cut the dividend and tried to maintain a smooth series of payments.

Executives who agree or strongly agree

0 10 20 30 40 6050 70 80 90 100

88.2%

77.9%

66.7%

89.6%

93.8%Try to avoid reducing the dividend

Try to maintain a smooth dividend stream

Look at the current dividend level

Reluctant to make a change that may have to be reversed

Consider the change in dividend

Rather than reducing dividends, raise new funds to undertake a profitable project

The cost of external capital is lower than that of a dividend cut

65.4%

42.8%

Firm’s policy:

Source: A. Brav, J. R. Graham, C. R. Harvey, and R. Michaely, “Payout Policy in the 21st Century,” Journal of Financial Economics 77 (September 2005), pp. 483–527.

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503

There is also information content in stock repurchases. Repurchases can be signals of managers’ optimism and may indicate their view that the company’s shares are underpriced by investors. Investors may also applaud repurchases if they worry that the cash would otherwise be frittered away on unprofitable investments. (Of course, investors would be less thrilled if their favorite growth company suddenly announced a repurchase program because its managers could not think of anything better to do with the cash.) But announcement of a share repurchase program is not a commitment to continue repurchases in later years. So news about a planned repurchase is less strongly positive than the announcement of a dividend increase.

Many large, mature corporations, for example, ExxonMobil, pay regular cash divi- dends and repurchase shares year in and year out. For them, repurchases are routine, one part of an overall payout strategy, and periodic announcements of repurchase programs convey less information.

17.3 Dividends or Repurchases? The Payout Controversy It seems clear that a change in payout may provide information about management’s confidence in the firm and so may affect the stock price. But this change in stock price would happen anyway as the information eventually seeped out through other chan- nels. Can payout policy change the underlying value of the firm’s common stock, or is it just a signal about that value?

This can be a difficult question to tackle because payout decisions are often inter- twined with other financing or investment decisions. Some firms pay low dividends because management is optimistic about the firm’s future and wishes to retain earn- ings for expansion. In this case the payout decision is a by-product of the firm’s capital budgeting decision. Another firm might finance capital expenditures largely by bor- rowing. This frees up cash that can be paid out to shareholders. In this case, the payout decision is a by-product of the borrowing decision.

We wish to isolate payout policy from other problems of financial management. The precise question we should ask is: What is the effect of a change in dividend pay- out given the firm’s capital budgeting and borrowing decisions?

One nice feature of economics is that it can accommodate not just two but three opposing points of view. And so it is with payout policy. On one side there is a group that believes high dividends increase value. On the other side there is a group that believes that high dividends bring high taxes and therefore reduce firm value. And in the center there is a middle-of-the-road party that believes payout policy makes no dif- ference. Let’s start with the middle-of-the-roaders.

Finance in Practice Good News: J.P. Morgan Cuts Its Dividend to a Nickel J.P. Morgan Chase, however, acted from a position of

relative strength. It remained profi table when other large U.S. banks were announcing horrifi c losses. Its CEO James Dimon explained that the dividend cut would save $5 billion a year and prepare it for a worst-case recession. It would also “put the bank in a position to pay back more quickly the $25 billion that it took from the government under the Troubled Asset Relief Program.” J.P. Morgan has said it was encouraged to take the money and didn’t need it.

Thus investors interpreted the dividend cut as a signal of confi dence, not of distress.

Source: R. Sidel and M. Rieker, “J.P. Morgan Makes 87% Cut in its Dividend to a Nickel,” The Wall Street Journal, February 24, 2009, pp. C1, C3.

On February 23, 2009, J.P. Morgan cut its quarterly divi- dend from 38¢ to a nickel (5¢) per share. The cut was a sur- prise to investors, but the bank’s share price increased by  about 5%.

Usually dividend cuts or omissions are bad news, because investors infer trouble. Investors take the cut as a signal of a cash or earnings shortfall—and they are usually right. Man- agers know that cuts will be treated as bad news, so they usually put off cuts until enough bad news accumulates to force them to act. For example, General Motors, which lost $39 billion in 2007 and $31 billion in 2008, continued paying quarterly dividends of 25¢ per share until June 2008, when it cut its dividend to zero.

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Repurchase motives

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504 Part Five Debt and Payout Policy

Franco Modigliani and Merton Miller (MM), who proved that debt policy doesn’t matter in perfect financial markets, founded the middle-of-the-road party when they proved that dividend decisions also don’t matter in perfect financial markets. 9 MM would admit that payout policy may matter in practice, not just because of the infor- mation content of dividends and repurchases but also because of taxes and market imperfections. But understanding when and why payout policy does not matter will help us to understand when it may matter.

We start with a simple example illustrating MM’s argument.

Dividends or Repurchases? An Example Suppose a corporation decides to pay out cash to shareholders. Does it matter whether the cash is paid out by dividends or repurchases?

Panel A of Table  17.1 shows the market value of Hewlard Pocket’s assets and equity. The firm is worth $1.1 million. With 100,000 shares outstanding, price per share is $11. This is the price just before the ex-dividend date.

Panel B shows what happens after Pocket pays out a dividend of $1 per share, $100,000 in total. The cash account falls to $50,000, and the market value of the firm falls from $1.1 million to $1 million. Since there are 100,000 shares, price per share falls from $11 to $10.

The shareholders neither gain nor lose as a result of the dividend because the cash dividend exactly compensates them for the fall in share price. Suppose that you own 1,000 shares worth $11,000 before the dividend. After the dividend you still have $11,000: $10,000 in stock plus $1,000 in cash.

Panel C shows what happens if Pocket pays no dividend but instead pays out $100,000 by repurchasing shares. It repurchases 9,091 shares at $11, leaving 100,000  −   9,091  =   90,909 shares outstanding. (Notice that the price stays at $11. Firm value is $1 million and price per share  =  $1,000,000/90,909  =  $11.)

Suppose again that you own 1,000 shares worth $11,000 before the repurchase. If you sell the shares back to Pocket, you get $11,000 in cash. If you don’t sell, your

9 M. H. Miller and F. Modigliani, “Dividend Policy, Growth and the Valuation of Shares,” Journal of Business 34 (October 1961), pp. 411–433.

Assets Liabilities and Shareholders’ Equity

A. Original balance sheet

Cash $ 150,000 Debt $ 0 Other assets 950,000 Equity 1,100,000 Value of fi rm $1,100,000 Value of fi rm $1,100,000 Shares outstanding  =  100,000 Price per share  =  $1,100,000/100,000  =  $11

B. After cash dividend of $1 per share

Cash $ 50,000 Debt $ 0 Other assets 950,000 Equity 1,000,000 Value of fi rm $1,000,000 Value of fi rm $1,000,000 Shares outstanding  =  100,000 Price per share  =  $1,000,000/100,000  =  $10

C. After $100,000 stock repurchase program

Cash $ 50,000 Debt $ 0 Other assets 950,000 Equity 1,000,000 Value of fi rm $1,000,000 Value of fi rm $1,000,000 Shares outstanding  =  90,909 Price per share  =  $1,000,000/90,909  =  $11

TABLE 17.1 Hewlard Pocket’s market value balance sheets illustrate the effects of dividends vs. repurchases.

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Chapter 17 Payout Policy 505

shares are still worth $11,000. It doesn’t matter whether you sell or not—your wealth is the same. You are also exactly as well off with the repurchase as with the cash dividend.

Our example therefore confirms MM’s argument by demonstrating that the choice between cash dividends and repurchases doesn’t matter for shareholder wealth. (Some tax and other complications are still to come, of course.)

You may hear a claim that repurchases increase stock price. That’s not quite right, as our example illustrates. A repurchase avoids the fall in stock price that would occur on the ex-dividend date if the cash spent on repurchases was used instead to pay divi- dends. (Compare panels B and C in Table 17.1 . Notice that with the repurchase the price per share stays at $11 instead of dropping to $10 ex-dividend.) Repurchases also reduce the number of outstanding shares, so future earnings per share increase.

What would Table 17.1 look like if the dividend changes to $1.50 per share and the share repurchase to $150,000?

Self-Test 17.2

Repurchases and the Dividend Discount Model Now here is a problem that often causes confusion: We stated in Chapter 7 that the value of a share of stock equals the discounted value of future dividends. Does this dividend discount model still work if the firm distributes cash by repurchases instead of divi- dends? The answer is yes, but you have to be careful to forecast dividends per share.

Let’s start again with Table 17.1 , panel B. Hewlard Pocket has just paid a dividend of $1 a share, and its 100,000 shares are now selling for $10 each. We add two assump- tions. First assume that the firm is expected to generate earnings of $100,000 per year, with no growth or decline ( g   =  0), and to pay out all earnings to stockholders. The stock price in panel B is ex-dividend, so the next payout of $100,000 ($1 per share) will come next period. Second, assume that the cost of equity is r   =  .10 (10%). We can apply the constant-growth dividend discount model from Chapter 7:

P0 = DIV1 r - g

=

$1

.10 - 0 = $10

Now suppose that Pocket announces that henceforth it will pay out exactly 50% of earnings as cash dividends and 50% as repurchases. This means that next year’s expected dividend is only DIV 1   =  $.50. On the other hand, the repurchases will reduce the number of shares outstanding, increasing earnings and dividends per share in year 2 and later years. It turns out that the $.50 reduction in the dividend will be exactly offset by 5% growth in earnings and dividends per share.

Let’s see how this works. Pocket will use $50,000 (50% of earnings) to repurchase shares in year 1. With that $50,000 and an ex-dividend stock price of $10.50 ($11 minus the $.50 dividend), it can repurchase $50,000/$10.50  =  4,762 shares. The number of shares outstanding therefore will fall from 100,000 to 95,238. Thus the expected earn- ings per share in year 2 increase from $1 to $100,000/95,238  =  $1.05 per share. The growth rate is 5%. Dividends per share in year 2 will also grow by 5% to $.525. And if you carry this example forward to year 3 and beyond, you will find that using 50% of earnings to repurchase shares continues to generate a growth rate in earnings and dividends per share of 5% per year.

You can probably see where this leads. The effect of the reduction in cash dividends is exactly offset by the growth in earnings and dividends per share. Again we use the dividend discount model, this time with the lower dividend of $.50 and 5% growth:

P0 = DIV1 r - g

=

$.50

.10 - .05 = $10

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506 Part Five Debt and Payout Policy

This result illustrates a general point: The dividend discount model is not upset by repurchases as long as you are careful to forecast earnings and dividends per share. But such forecasts may be difficult in practice because share repurchase programs are often volatile and erratic. If you are valuing a company that is likely to make frequent repurchases, it can be fiddly to keep track of the changing number of shares and the dividends per share. In such cases you should consider using an alternative approach. This involves two steps:

Step 1. Calculate equity market capitalization (the value of all outstanding shares) by forecasting and discounting the free cash flow that will be paid out to all current and future shareholders either as dividends or by stock repurchases.

Step 2. Calculate price per share by dividing market capitalization by the number of shares currently outstanding. That way you don’t have to worry about how payout is split between dividends and repurchases.

In our example, you would forecast total payout of $100,000 per year and market capitalization of $100,000/.10  =  $1 million after dividends and repurchases in the cur- rent period. Price per share would be $1,000,000/100,000  =  $10. (If we had started this example in panel C of Table 17.1 , the number of shares would be 90,909 and price per share would be $1,000,000/90,909  =  $11. The total market capitalization of the firm would still be $1,000,000.)

Dividends and Share Issues Our Hewlard Pocket example showed that shareholders are no better or worse off if the company pays less in dividends and uses the cash that is saved to repurchase stock. But maybe companies can increase value by paying out more to shareholders either as dividends or through stock repurchases. Let’s check.

Suppose that Pocket’s cash holding is not surplus. Instead, the company has set aside $100,000 to buy a new fan pump. However, Pocket’s president has read that the value of a stock is equal to the discounted stream of dividends. So he reasons that the company could increase the value of its stock by paying out that $100,000 as an extra dividend. The president’s heart is in the right place. Unfortunately, his head isn’t. To understand why, think about the effect of this proposed change in dividend policy given the firm’s capital budgeting and borrowing decisions.

If Pocket buys its much-needed fan pump, the cash expended needs to be replaced. If borrowing is fixed, the money must come from the sale of $100,000 in new shares. After Pocket pays the additional $100,000 dividend and replaces the cash by selling new shares, the company value is unchanged. But since the new stockholders are putting up $100,000, they will demand to receive shares worth $100,000. Because the total value of the company is the same, the value of the old stockholders’ stake in the company falls by this $100,000. The old shareholders now have an extra $100,000 of cash in their pockets, but they have given up a stake in the firm to those investors who buy the newly issued shares. Thus the extra dividend that the old stockholders receive just offsets the loss in the value of the shares that they hold. In other words, Pocket is simply recycling cash: It pays out extra cash to its current investors (the dividend), but simultaneously takes back the same amount (through the share issue). To suggest that this makes investors better off is like advising the cook to cool the kitchen by leaving the refrigerator door open.

Does it make any difference to the old stockholders that they receive an extra divi- dend payment plus an offsetting capital loss? It might if that were the only way they could get their hands on the cash. But as long as there are efficient capital markets, they can raise cash by selling shares. Thus Pocket’s old shareholders can “cash in” either by persuading the management to pay a higher dividend or by selling some of their shares. In either case there will be the same transfer of ownership and value from the old to the new stockholders. Because investors do not need dividends to convert their shares to cash, they will not pay higher prices for firms with higher dividend payouts. In other words, payout policy will have no impact on the value of the firm.

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Chapter 17 Payout Policy 507

We have seen that MM’s irrelevance argument holds both for increases in dividends and for reductions (always remembering that capital investment and borrowing are held constant). As our examples illustrate, payout policy is a trade-off between cash dividends and the issue or repurchase of common stock. In a perfect capital market, payout policy would have no impact on firm value. Of course, our examples of divi- dend irrelevance have ignored taxes, issue costs, and a variety of other real-world com- plications. We will turn to these intricacies shortly, but before we do, we note that the crucial assumption in our proof is that the sale or purchase of shares occurs at a fair price. The shares that Pocket buys back for $100,000 must be worth $100,000; those that it sells to raise $100,000 must also be worth that figure. In other words, dividend irrelevance assumes efficient capital markets.

17.4 Why Dividends May Increase Value MM’s conclusions follow from their assumptions of perfect and efficient capital mar- kets. However, nobody claims their model is an exact description of the real world. Thus the impact of payout policy finally boils down to arguments about imperfections and inefficiencies.

Those who believe that dividends are good argue that some investors have a natural preference for high-payout stocks. For example, some financial institutions are legally restricted from holding stocks lacking established dividend records. Trusts and endow- ment funds may prefer high-dividend stocks because dividends are regarded as spend- able “income,” whereas capital gains are only “additions to principal.”

In addition, there is a natural clientele of investors, including the elderly, who look to their stock portfolios for a steady source of cash to live on. In principle this cash can be generated from stocks paying no dividends at all; the investors can just sell off a small fraction of their holdings from time to time. But that can be inconvenient and lead to transaction costs.

Behavioral psychology may also help to explain why some investors prefer to receive regular dividends rather than sell small amounts of stock. We are all liable to succumb to temptation. Some of us may hanker after fattening foods, while others may be dying for a drink. We could seek to control these cravings by willpower, but that can be a painful struggle. Instead, it may be easier to set simple rules for ourselves (“cut out chocolate,” or “wine only with meals”). In just the same way, we may wel- come the self-discipline that comes from limiting our spending to dividend income.

All this may well be true, but it does not follow that you can increase the value of your firm by increasing dividend payout. Smart managers already have recognized that there is a clientele of investors who would be prepared to pay a premium for high- payout stocks. There are natural clienteles for high-payout stocks, but it does not follow that any particular firm can benefit by increasing its dividends. The high- dividend clienteles already have plenty of high-dividend stocks to choose from.

Suppose that the CEO of a software company announces at a press conference a plan to enter the market for mint toothpaste. When you ask why, the CEO points out that millions of people buy mint toothpaste. You would doubt the CEO’s business san- ity. Does the world need another mint toothpaste manufacturer? So why should you believe that because there is a clientele of investors who like high payouts, your com- pany can increase value by manufacturing a high payout? That clientele was probably satisfied long ago.

Perhaps the most persuasive argument in favor of a high-payout policy is that it mitigates free-cash-flow problems. Suppose a company has plenty of cash but few profitable investment opportunities. Shareholders may fear that the money will be plowed back into building a larger empire rather than a more profitable one. In such cases, generous dividends or share repurchases deprive the managers of excess cash and encourage a more careful, value-oriented investment policy. Dividends provide

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508

more discipline than repurchases because financial managers rarely cut dividends except under great duress.

The nearby box describes how Apple decided to initiate dividends and repurchases in order to reduce its “cash mountain.”

The Altria Group pays a generous cash dividend. Suppose an investor in Altria does not need a regular income. What could she do? If there were no trading costs, would she have any reason to care about Altria’s payout policy? What if there is a brokerage fee on the purchase of new shares? What if Altria has a divi- dend reinvestment plan that allows the investor to buy shares at a 5% discount?

Self-Test 17.3

Finance in Practice Apple’s Cash Mountain On March 19, 2012, Apple announced that it would pay a

quarterly dividend of $2.65 per share and spend $10 billion for share buybacks. It forecasted $45 billion in payout over the following three years. Apple’s stock price jumped by $15.53 to $601 by the close of trading on the announcement day. Apple’s dividend yield went from zero to (2.65  ×  4)/601  =  1.8%.

Was Apple’s payout sufficiently generous? Analysts’ opin- ions varied. “A pretty vanilla return-of-cash program” (A. M. Sacconaghi, Bernstein Research). “It’s not too piddling, and on the other hand not so large to signal that growth prospects are not what they thought” (David A. Rolfe, Wedgewood Part- ners). Bill Choi (Janney Montgomery Scott) pointed out that income-oriented mutual funds would now be more comfort- able holding Apple stock.

Source: N. Wingfi eld, “Flush with Cash, Apple Declares a Dividend and Buy- back,” The New York Times, March 20, 2012, pp. B1, B9.

The fi gure below shows how Apple’s holdings of cash and mar- ketable securities have grown over the past decade. By the start of 2012, Apple Inc. had accumulated cash and long-term secu- rities of about $100 billion. Steve Jobs, the architect of Apple’s explosive growth, had preferred to keep the war chest of cash for investment or possible acquisitions. Jobs’s fi scal conserva- tism may seem quaint when Apple’s forecasted income for 2012 was over $40 billion. But Jobs could remember tough times for Apple; the company was near bankruptcy when Jobs took over in 1997. Apple had paid cash dividends in the early 1990s, but was forced to stop in 1995 as its cash reserves dwindled.

After Jobs died in October 2011, the pressure from inves- tors for payout steadily increased. “They have a ridicu- lous amount of cash,” said Douglas Skinner, a professor of accounting at the Chicago Booth School of Business. “There is no feasible acquisition that Apple could do that would need that much cash.”

The growth in Apple’s holdings of cash and marketable securities, 2002–2011

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80

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Year ending September

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Chapter 17 Payout Policy 509

17.5 Why Dividends May Reduce Value The low-dividend creed is simple. Companies can convert dividends into capital gains by shifting their payout policy. If dividends are taxed more heavily than capital gains, such financial alchemy should be welcomed by any taxpaying investor. Firms should pay the lowest cash dividend they can get away with. Surplus cash should be used to repurchase shares.

Table 17.2 illustrates this. It assumes that dividends are taxed at a rate of 40% but that capital gains are taxed at only 20%. The stocks of firms A and B are equally risky, and investors demand an expected after-tax rate of return of 10% on each. Investors expect A to be worth $112.50 per share next year. The share price of B is expected to be only $102.50, but a $10 dividend is also forecast, so the total pretax payoff is the same, $112.50.

Both stocks offer the same pretax dollar payoff. But to provide the same after-tax rate of return, B must sell for less than A, $97.78 rather than $100. The reason is obvi- ous: Investors are willing to pay more for stock A because its return comes in the form of low-taxed capital gains. After tax, both stocks offer the same 10% expected return despite the fact that B’s pretax return is higher.

Suppose the management of firm B eliminates the $10 dividend and uses the cash to repurchase stock instead. We saw earlier that a stock repurchase is equivalent to a cash dividend, but now we need to recognize that it is treated differently by the tax authorities. Stockholders who sell shares back to their firm pay tax only on any capital gains realized in the sale. By substituting a repurchase for a dividend, B’s new policy would reduce the taxes paid by stockholders, and its stock price should rise. 10

10 The tax authorities have rules intended to prevent tax avoidance by substitution of repurchases for dividends. These rules are not applied to public corporations. But a private corporation that eliminates dividends and repur- chases shares on a regular basis may find the repurchases reclassified as dividends for tax purposes.

Firm A Firm B

Next year’s price $112.50 $102.50 Dividend $ 0 $ 10.00 Total pretax payoff $112.50 $112.50 Today’s stock price $100 $ 97.78 Capital gain $ 12.50 $ 4.72

Before-tax rate of return (%) 12.5 100

= .125 = 12.5% 14.72 97.78

= .1505 = 15.05%

Tax on dividend at 40% $0 .40  ×  $10  =  $4.00 Tax on capital gain at 20% .20  ×  $12.50  =  $2.50 .20  ×  $4.72  =  $.94 Total after-tax income (dividends plus capital gains less taxes) (0  +  12.50)  −  2.50  =  $10.00

(10  +  4.72) −  (4.00  +  .94)  =  $9.78

After-tax rate of return (%) 10 100

= .10 = 10% 9.78 97.78

= .10 = 10%

TABLE 17.2 Effects of a shift in dividend policy when dividends are taxed more heavily than capital gains. The high-payout stock (firm B) must sell at a lower price in order to provide the same after-tax return.

Look again at Table 17.2 . What would happen to the price and pretax rate of return on stock B if the tax on capital gains were eliminated?

Self-Test 17.4

Taxation of Dividends and Capital Gains under Current Tax Law If dividends are taxed more heavily than capital gains, why should any firm ever pay a cash dividend? If cash is to be distributed to stockholders, isn’t share repurchase the best channel for doing so?

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510 Part Five Debt and Payout Policy

In the United States, the case for low dividends was strongest before 1986. The top rate of tax on dividends was then 50%, while realized capital gains were taxed at 20%. However, the top tax rate is now 20% on both dividends and capital gains.

There is, however, one way that tax law still favors capital gains. Taxes on divi- dends have to be paid immediately, but taxes on capital gains can be deferred until shares are sold and the capital gains are realized. Stockholders can choose when to sell their shares and thus when to pay the capital gains tax. 11 The longer they wait, the less the present value of the capital gains tax liability. 12 Thus the effective capital gains tax rate can be less than the statutory rate.

The distinction between dividends and capital gains is less important for pension funds, endowments, and some other financial institutions that operate free of all taxes and therefore have no reason to prefer capital gains to dividends or vice versa. Only corporations have a tax reason to prefer dividends. They pay corporate income tax on only 30% of any dividends received. 13 Thus the effective tax rate on dividends received by large corporations is 30% of 35% (the marginal rate of corporate income tax), or 10.5%. But they have to pay a 35% tax on the full amount of any capital gain.

The implications of these tax rules for payout policy are pretty simple. Capital gains have advantages to many investors, but they are far less advantageous than they were 30 or 40 years ago. Consequently, it is less easy today to make convincing arguments in favor of one kind of payout rather than another.

17.6 Payout Policy and the Life Cycle of the Firm MM said that payout policy does not affect shareholder value. Shareholder value is driven by investment policy, including exploitation of growth opportunities, and to some extent by debt policy (as we saw in the previous chapter). In MM’s analysis, payout is a residual, a by-product of other financial decisions. The firm should make investment and financing decisions and then distribute whatever cash is left over. If payout is a residual, then payout decisions should evolve over the life cycle of the firm.

Young growth firms have plenty of profitable investment opportunities. During this time it is efficient to retain and reinvest all operating cash flow. Why pay out cash to investors if the firm then has to replace the cash by borrowing or issuing more shares? Retaining cash avoids the costs of issuing securities and minimizes shareholders’ taxes. Investors are not worried about wasteful overinvestment because investment opportunities are good, and managers’ compensation is tied to stock price.

As the firm matures, positive-NPV projects become scarcer relative to cash flow. The firm begins to accumulate cash. Now investors begin to worry about free-cash- flow problems, for example, overinvestment or excessive perks. The investors pressure management to start paying out cash. Sooner or later, the managers comply— otherwise, stock price stagnates. The payout may come as share repurchases, but initiating a regu- lar cash dividend sends a stronger and more reassuring signal of financial discipline. The commitment to financial discipline can outweigh the tax costs of dividends. (The middle-of-the-road party argues that the tax costs of paying cash dividends may not be that large, particularly in recent years, when U.S. personal tax rates on dividends and capital gains have been low.) Regular dividends may also be attractive to some types of investors, for example, retirees who depend on dividends for living expenses.

11 If the stock is willed to your heirs, capital gains escape taxation altogether. 12 Suppose the discount rate is 6%, and an investor in a 15% capital gains tax bracket has a $100 capital gain. If the stock is sold today, the capital gains tax will be $15. If sale is deferred 1 year, the tax due on that $100 gain still will be $15, but by virtue of delaying the sale for a year, the present value of the tax falls to $15/1.06  =  $14.15. The effective tax rate falls to 14.15%. The longer the sale is deferred, the lower the effective tax rate. 13 The percentage of dividend income on which tax is paid depends on the firm’s ownership share in the company paying the dividend. If the share is less than 20%, taxes are paid on 30% of dividends received.

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U.S. tax rates, 1960–2013

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Chapter 17 Payout Policy 511

As the firm ages, more and more payout is called for. The payout may come as higher dividends or larger repurchases. Sometimes the payout comes as the result of a takeover. Shareholders are bought out, and the firm’s new owners generate cash by selling assets and restructuring operations. We discuss takeovers in Chapter 21.

The life cycle of the firm is not always predictable. It’s not always obvious when the firm is “mature” and ready to start paying cash back to shareholders. The following three questions can help the financial manager decide:

1. Is the company generating positive free cash flow after making all investments with positive NPVs, and is the positive free cash flow likely to continue?

2. Is the firm’s debt ratio prudent? 3. Are the company’s holdings of cash a sufficient cushion for unexpected setbacks

and a sufficient war chest for unexpected opportunities?

If the answer to all three questions is yes, then the free cash flow is surplus and payout is called for.

SUMMARY Dividends come in many forms. The most common is the regular cash dividend, but sometimes companies pay a stock dividend. A firm is not free to pay dividends at will. For example, it may have accepted restrictions on dividends as a condition for borrow - ing money.

Dividends do not go up and down with every change in the firm’s earnings. Instead, managers aim for smooth dividends and increase dividends gradually as earnings grow.

Corporations also distribute cash by repurchasing shares. Stock repurchases have grown rapidly in recent years, but they do not replace dividends. Mature firms that pay dividends also repurchase shares. On the other hand, thousands of U.S. corporations pay no divi- dends at all. When they pay out cash, they do so exclusively through repurchases.

Managers do not increase dividends unless they are confident that the firm will generate enough earnings to cover the payout. Announcement of a dividend conveys the manag- ers’ confidence to investors. Dividend cuts convey lack of confidence. Managers generally avoid them unless their firms are in trouble. This information content of dividends is the main reason that stock prices respond to dividend changes.

Repurchases are usually also good news. For example, announcement of a repurchase program can reveal managers’ view that their company’s stock is a “good buy” at the cur- rent price.

Cash payouts by dividends and repurchases can also reassure investors who worry that managers might otherwise spend the money on empire-building and negative-NPV projects.

If we hold the company’s investment policy and capital structure constant, then payout policy is a trade-off between cash dividends and the issue or repurchase of common stock. In an ideally simple and perfect world, the choice would have no effect on mar- ket value. An increased cash dividend would require more shares issued or fewer shares repurchased. The increased cash in shareholders’ wallets would be exactly offset by a lower share price. This is the MM dividend-irrelevance proposition.

How are dividends paid, and how do companies decide how much to pay? (LO17-1)

How are repurchases used to distribute cash to shareholders? (LO17-1)

Why are dividend increases and repurchases usually good news for investors? Why are dividend cuts bad news? (LO17-2)

Why would payout policy not affect firm value in an ideal world? (LO17-3)

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512 Part Five Debt and Payout Policy

QUESTIONS AND PROBLEMS 1. How Corporations Pay Dividends. Cash Cow International paid a regular quarterly dividend

of $.075 a share. (LO17-1)

a. Match each of the following dates to the correct term:

i. May 7 A. Record date

ii. June 6 B. Payment date

iii. June 7 C. Ex-dividend date

iv. June 11 D. Last with-dividend date

v. July 2 E. Declaration date

b. On one of these dates the stock price is likely to fall by about the amount of the dividend. Which date?

c. The stock price in early January was $27. What was the prospective dividend yield? d. The annual earnings per share were forecast at around $1.90. What was the percentage pay-

out ratio?

2. How Corporations Pay Dividends. True or false? (LO17-1)

a. A corporation cannot pay a dividend if its legal capital is impaired or if it is insolvent. b. The effective tax rate on capital gains can be less than the stated rate. c. Managers and investors are more concerned with dividend changes than dividend levels. d. Future stock price will be higher when a corporation distributes cash by repurchases rather

than cash dividends. e. Stock dividends increase the number of shares that investors own and therefore increase

shareholder wealth. f. By increasing the number of shares, stock dividends dilute each shareholder’s interest in the

company and therefore reduce wealth.

3. How Corporations Pay Dividends. Suppose that you own 1,000 shares of Nocash Corp. and the company is about to pay a 25% stock dividend. The stock currently sells at $100 per share. (LO17-1)

a. What will be the number of shares that you hold after the stock dividend is paid? b. What will be the total value of your equity position after the stock dividend is paid? c. What will be the number of shares that you hold if the firm splits five for four instead of pay-

ing the stock dividend?

4. Stock Repurchases. True or false? (LO17-1)

a. A company can keep repurchased stock in its treasury and reissue it later. b. The most common method for repurchasing stock is by auction. c. A greenmail transaction is one in which the target of a possible takeover buys back stock

from the potential bidder.

In the United States, individual investors currently pay tax on dividend income at a top rate of 20%. The top capital gains rate is also 20%, but the investor pays no tax on capital gains until his or her shares are actually sold. The longer the wait before the sale, the lower the present value of the tax. Thus capital gains have a tax advantage for investors. The advan- tage was much greater in the 1970s and early 1980s, when the top tax rate on dividends was 50% and the top rate on capital gains only 20%.

If dividend income is taxed more heavily than capital gains, investors should demand a higher pretax rate of return on high-dividend stocks. Instead of paying high dividends, corporations should shift to repurchases.

Young, rapidly growing firms are usually raising cash from investors, not distributing it. Such firms rarely pay dividends, although they may repurchase from time to time. Mature firms that generate positive free cash flow make regular payouts, often by repurchases as well as dividends. Commitment to a regular dividend can reassure investors who worry about free-cash-flow problems, that is, about overinvestment and inefficient operations

How might differences in the tax treatment of dividends and capital gains affect payout policy? (LO17-4)

How does payout policy normally evolve over the life cycle of the firm? (LO17-5)

finance

®

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Chapter 17 Payout Policy 513

a. What price is Payout stock selling for today? b. What price will it sell for tomorrow? Ignore taxes.

6. Stock Repurchases. The stock of Payout Corp. (see Problem 5) will go ex-dividend tomorrow. The dividend will be $.50 per share, and there are 20,000 shares of stock outstanding. Now sup- pose that Payout announces its intention to repurchase $10,000 worth of stock instead of paying out the dividend. (LO17-1)

a. What effect will the repurchase have on an investor who currently holds 100 shares and sells 1 of those shares back to the company in the repurchase?

b. Compare the effects of the repurchase to the effects of the cash dividend that you worked out in Problem 5.

7. How Corporations Pay Dividends. Here are several “facts” about typical corporate dividend policies. Which are true and which are false? (LO17-1)

a. The vast majority of companies pay out cash each year in the form of a dividend or a stock repurchase.

b. Companies decide each year’s dividend by looking at their capital expenditure requirements and then distributing whatever cash is left over.

c. Managers and investors seem more concerned with dividend changes than with dividend levels.

d. Managers often increase dividends temporarily when earnings are unexpectedly high for a year or two.

e. Companies undertaking substantial share repurchases usually finance them with an offset- ting cut in cash dividends.

f. A company that declares a 10% stock dividend gives each shareholder 1 additional share for each 10 shares that he or she currently owns.

8. Information Content. Which of the following newspaper headlines would have the greatest positive impact on stock price? Explain. (LO17-2)

a. “Growler Corporation announces a $1 increase in its regular dividend.” b. “Growler Corporation announces a $1 special one-off dividend.” c. “Growler Corporation unexpectedly wins a lawsuit and collects cash amounting to $1 per

Growler share. Growler plans to use the cash in a stock buyback program.”

9. Information Content of Dividends. Why are dividend increases typically good news for inves- tors and dividend cuts bad news? Explain briefly. (LO17-2)

10. Payout Policy. Mr. Milquetoast is enthusiastic about the prospects for Facebook. He wants to invest $100,000 in the stock, but hesitates because Facebook has never paid a dividend. He needs to generate $5,000 per year in cash for living expenses. What should Mr. Milquetoast do? (LO17-3)

11. Payout Policy. Surf & Turf Hotels is a mature business, although it pays no cash dividends. Next year’s earnings are forecast at $56 million. There are 10 million outstanding shares. The company has traditionally used 50% of earnings to repurchase shares of stock and reinvested the remaining earnings. With reinvestment, the company has generated steady growth averaging 5% per year. Assume the cost of equity is 12%. (LO17-3)

a. Calculate Surf & Turf’s current stock price, using the constant-growth DCF model from Chap- ter 7. ( Hint: Take the easy route and start by calculating the total value of outstanding equity.)

b. Now Surf & Turf’s CFO announces a switch from repurchases to a regular cash dividend. Next year’s dividend will be $2.80 per share. The CFO reassures investors that the company will

Assets Liabilities and Equity

Cash $100,000 Equity $1,000,000 Fixed assets 900,000

d. Most companies that distribute cash to investors do so either by paying dividends or by repurchase. It is very rare to find a company paying out cash by both methods.

5. How Corporations Pay Dividends. The stock of Payout Corp. will go ex-dividend tomorrow. The dividend will be $.50 per share, and there are 20,000 shares of stock outstanding. The market-value balance sheet for Payout is shown in the following table. (LO17-1)

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514 Part Five Debt and Payout Policy

continue to pay out 50% of earnings and reinvest 50%. All future payouts will come as divi- dends, however. What would you expect to happen to Surf & Turf’s stock price? Ignore taxes.

12. Payout Policy. Consolidated Pasta is currently expected to pay annual dividends of $10 a share in perpetuity on the 1 million shares that are outstanding. Shareholders require a 10% rate of return from Consolidated stock. (LO17-3) a. What is the price of Consolidated stock? b. What is the total market value of its equity?

Consolidated now decides to increase next year’s dividend to $20 a share, without changing its investment or borrowing plans. Thereafter the company will revert to its policy of distributing $10 million a year. c. How much new equity capital will the company need to raise to finance the extra dividend

payment? d. What will be the total present value of dividends paid each year on the new shares that the

company will need to issue? e. What will be the transfer of value from the old shareholders to the new shareholders? f. Is this figure more than, less than, or the same as the extra dividend that the old shareholders

will receive?

13. Payout Policy. Respond to the following two statements: (LO17-3)

a. “MM say that investors are equally happy with a dollar of dividends and a dollar of capital gains. That’s crazy. Everyone knows that dividends are stable and capital gains risky. I’ll take the dividend any day.”

b. “Safer companies tend to pay more generous dividends. Therefore a company can reduce the risk of its shares by increasing dividend payout.”

14. Payout Policy. You own 2,000 shares of Patriot Corporation, which is about to double its divi- dend from $.75 to $1.50 per share. You do not need the extra dividend income, but you don’t want to sell out. What would you do to offset the dividend increase? (LO17-3)

15. Payout Policy. Go back to the first Hewlard Pocket balance sheet. Pocket needs to hold on to $50,000 of cash for a future investment. Nevertheless it decides to pay a cash dividend of $2 per share, and to replace the cash with a new issue of shares. After the dividend is paid and the new stock is issued: (LO17-3) a. What will be the price per share? b. What will be the total value of the company? c. What will be the total value of the stock held by new investors? d. What will be the wealth of the existing investors including the dividend payment?

16. Payout Policy. Go back again to the first Hewlard Pocket balance sheet. Now assume that Pocket wins a lawsuit and is paid $100,000 in cash. The market value of the equity rises by that amount, and Pocket decides to pay out $2 per share instead of $1 per share. (LO17-3) a. What will be Pocket’s stock price if the payout comes as a cash dividend? b. What will be Pocket’s stock price if the payout comes as a share repurchase?

17. Payout Policy. House of Haddock has 5,000 shares outstanding and the stock price is $100. The company is expected to pay a dividend of $20 per share next year, and thereafter the dividend is expected to grow indefinitely by 5% a year. The president, George Mullet, now makes a surprise announcement: He says that the company will henceforth distribute half the cash in the form of dividends and the remainder will be used to repurchase stock. (LO17-3) a. What is the total value of the company before the announcement? b. What is the total value after the announcement? c. What is the value of one share before the announcement? d. What is the new growth rate in the dividend stream? (Check your estimate of share value by

discounting this stream of dividends per share.)

18. Payout Policy. We stated in Section 17.3 that MM’s proof of dividend irrelevance assumes that any new shares are sold at a fair price. Consider the case in Problem 15 in which Hewlard Pocket pays the higher dividend of $2 a share and replaces the cash by issuing new stock. Sup- pose that the new shares are sold in a public issue at $8 a share, which is below the market price after the $2 dividend is paid. What is the loss suffered by the existing shareholders? Is dividend policy still irrelevant? Why or why not? (LO17-3)

19. Payout Policy. “Many companies use stock repurchases to increase earnings per share. For example, suppose that a company is in the following position: (LO17-3)

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Chapter 17 Payout Policy 515

a. If each stock is priced at $100, what are the expected net returns on each stock to (i) a pen- sion fund that does not pay taxes, (ii) a corporation paying tax at 35%, and (iii) an individual with an effective tax rate of 15% on dividends and 10% on capital gains?

b. Suppose that investors pay 50% tax on dividends and 20% tax on capital gains. If stocks are priced to yield an 8% return after tax, what would A, B, and C each sell for? Assume the expected dividend is a level perpetuity.

22. Payout Policy and Taxes. For each of the following U.S. investors, state whether the investor has a tax reason to (a) prefer the company’s payout to be in the form of dividends, (b) prefer payout to be in the form of repurchases, or (c) have no preference: (LO17-4)

a. A pension fund b. An individual investor in the top income tax bracket c. A corporation d. An endowment for a charity or university

23. Payout Policy and Taxes. Good Values Inc. is all-equity-financed. The total market value of the firm currently is $100,000, and there are 2,000 shares outstanding. Ignore taxes. (LO17-4)

a. The firm has declared a $5 per share dividend. The stock will go ex-dividend tomorrow. At what price will the stock sell today?

b. At what price will the stock sell tomorrow? c. Now assume that the tax rate on all dividend income is 30% and the tax rate on capital gains

is zero. At what price will the stock sell, taking account of the taxation of dividends?

Now suppose that instead of paying a dividend, Good Values plans to repurchase $10,000 worth of stock. d. What will be the stock price before the repurchase? e. What will it be after the repurchase? f. Does the existence of taxes tend to favor dividends or repurchases?

24. Payout Policy and Taxes. Investors require an after-tax rate of return of 10% on their stock investments. Assume that the tax rate on dividends is 30% while capital gains escape taxation. A firm will pay a $2 per share dividend 1 year from now, after which it is expected to sell at a price of $20. (LO17-4)

a. Find the current price of the stock. b. Find the expected before-tax rate of return for a 1-year holding period. c. Now suppose that the dividend will be $3 per share. If the expected after-tax rate of return

is still 10% and investors still expect the stock to sell at $20 in 1 year, at what price must the stock now sell?

d. What is the before-tax rate of return? e. Is this smaller or larger than your answer to part (b)?

“The company now repurchases 200,000 shares at $200 a share. The number of shares declines to 800,000 shares, and earnings per share increase to $12.50. Assuming the price-earnings ratio stays at 20, the share price must rise to $250.” Discuss.

20. Payout Policy and Taxes. What is the tax reason for not paying generous cash dividends? (LO17-4)

21. Payout Policy and Taxes. The expected pretax return on three stocks is divided between divi- dends and capital gains in the following way: (LO17-4)

Stock Expected Dividend Expected Capital Gain

A $ 0 $10 B 5 5 C 10 0

Net profi t $10 million

Number of shares before repurchase 1 million Earnings per share $10 Price-earnings ratio 20 Share price $200

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516 Part Five Debt and Payout Policy

a. What will be the subsequent price per share if the firm pays a dividend? b. What will be the subsequent price per share if the firm repurchases stock? c. If total earnings of the firm are $2,000 a year, find earnings per share if the firm pays a

dividend. d. Now find earnings per share if the firm repurchases stock. e. Find the price-earnings ratio if the firm pays a dividend. f. Find the price-earnings ratio if the firm repurchases stock. g. Adherents of the “dividends-are-good” school sometimes point to the fact that stocks with

high dividend payout ratios tend to sell at above-average price-earnings multiples. Is Big Industries’ P/E ratio higher if it pays a dividend?

h. Looking back at your answers to parts (a) to (f), do you think that the difference in P/E sup- ports the “dividends-are-good” case?

25. Payout Policy and Taxes. Prowler Corporation wants to increase its debt ratio without chang- ing its operations or capital investment outlays. Obviously Prowler will have to increase bor- rowing, but how should it reduce equity? What would you recommend? (LO17-4)

26. Life Cycle and Payout Policy. MM show that in an idealized setting, firm value is not affected by payout policy. Yet we observe that more mature firms regularly pay higher dividends than do younger ones. Is this purely happenstance, or is there a real-world violation of the MM assump- tions that may explain this pattern? (LO17-5)

27. Life Cycle and Payout Policy. In Section 17.2, we report results of a survey about corporate dividend policy. How might the tendencies documented in that survey result in more mature firms exhibiting systematically higher dividend payout ratios? (LO17-5)

28. Life Cycle and Payout Policy. Would you predict that mature or younger firms make greater use of repurchases relative to dividends? Why might one of these payout tools be better suited to younger firms? (LO17-5)

CHALLENGE PROBLEM 29. Payout Policy. Big Industries has the following market-value balance sheet. The stock currently

sells for $20 a share, and there are 1,000 shares outstanding. The firm will either pay a $1 per share dividend or repurchase $1,000 worth of stock. Ignore taxes. (LO17-3)

Assets Liabilities and Equity

Cash $ 2,000 Debt $10,000 Fixed assets 28,000 Equity 20,000

WEB EXERCISES 1. Go to finance.yahoo.com . Under the Investing tab, choose Industries. Find the dividend yield

and payout ratio of the typical firm in the biotech industry and the electric utilities industry. Which is higher? Can you come up with a good explanation for the difference?

2. Log on to the market data center of The Wall Street Journal online, online.wsj.com , to find a list of dividend declarations. What is the meaning of each event? What is the typical interval between each event?

SOLUTIONS TO SELF-TEST QUESTIONS 17.1 The ex-dividend date is June 1. Therefore, Mick buys the stock ex-dividend and will not

receive the dividend. The checks will be mailed on June 30.

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Chapter 17 Payout Policy 517

17.2

Assets Liabilities and Equity

After cash dividend Cash $ 0 Debt $ 0 Other assets 950,000 Equity 950,000 Value of fi rm $950,000 Value of fi rm $950,000 Shares outstanding  =  100,000 Price per share  =  $950,000/100,000  =  $9.50 After stock repurchase Cash $ 0 Debt $ 0 Other assets 950,000 Equity 950,000 Value of fi rm $950,000 Value of fi rm $950,000 Shares outstanding  =  86,364 Price per share  =  $950,000/86,364  =  $11

If a dividend is paid, the stock price falls by the amount of the dividend. If the company instead uses the cash for a share repurchase, the stock price remains unchanged at $11 but, with fewer shares left outstanding, the market value of the firm falls by the same amount as it would have if the dividend had been paid.

17.3 An investor who prefers a zero-dividend policy can reinvest any dividends received. This will cause the value of the shares held to be unaffected by payouts. The price drop on the ex-dividend date is offset by the reinvestment of the dividends. However, if the investor had to pay brokerage fees on the newly purchased shares, she would be harmed by a high-payout policy since part of the proceeds of the dividends would go toward paying the broker. On the other hand, if the firm offers a dividend reinvestment plan (DRIP) with a 5% discount, she is better off with a high-dividend policy. The DRIP is like a “negative trading cost.” She can increase the value of her stock by 5% of the dividend just by participating in the DRIP. Of course, her gain is at the expense of shareholders that do not participate in the DRIP.

17.4 The price of the stock will equal the after-tax cash flows discounted by the required (after-tax) rate of return:

P = 102.50 + 10 × (1 - .4)

1.10 = 98.64

Notice that the after-tax proceeds from the stock would increase by the amount that previously went to pay capital gains taxes, .20  ×  $4.72  =  $.944. The present value of this tax saving is $.944/1.10  =  $.86. Therefore, the price increases to $97.78  +  $.86  =  $98.64. The pretax rate of return falls to (102.50  −  98.64  +  10)/98.64  =  .1405, or 14.05%, but the after-tax rate of return remains at 10%.

MINICASE George Liu, the CEO of Penn Schumann, was a creature of habit. Every month he and Jennifer Rodriguez, the company’s chief financial officer, met for lunch and an informal chat at Pierre’s. Nothing was ever discussed until George had finished his favorite escalope de foie gras chaude. At their last meeting in March he had then toyed thoughtfully with his glass of Chateau Haut-Brion Blanc before suddenly asking, “What do you think we should be doing about our payout policy?”

Penn Schumann was a large and successful pharmaceutical company. It had an enviable list of highly profitable drugs, many of which had 5 or more further years of patent protection. Earnings in the latest 4 years had increased rapidly, but it was difficult to see that such rates of growth could continue. The company had tradi- tionally paid out about 40% of earnings as dividends, though the

figure in 2014 was only 35%. Penn was spending over $4 billion a year on R&D, but the strong operating cash flow and conservative dividend policy had resulted in a buildup of cash. Penn’s recent income statements, balance sheets, and cash-flow statements are summarized in Tables 17.3 to 17.5 .

The problem, as Mr. Liu explained, was that Penn’s dividend policy was more conservative than that of its main competitors. “Share prices depend on dividends,” he said. “If we raise our divi- dend, we’ll raise our share price, and that’s the name of the game.” Ms. Rodriguez suggested that the real issue was how much cash the company wanted to hold. The current cash holding was more than adequate for the company’s immediate needs. On the other hand, the research staff had been analyzing a number of new compounds with promising applications in the treatment of liver diseases. If

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518 Part Five Debt and Payout Policy

2014

Net income 4,792 Depreciation 928 Decrease (increase) in receivables (376) Decrease (increase) in inventories 493 Increase (decrease) in payables 612 Total cash from operations 6,449 Capital expenditures (2,063) Increase (decrease) in short-term debt (1,063) Increase (decrease) in long-term debt (135) Dividends paid (1,678) Cash provided by fi nancing activities (2,876) Net increase in cash 1,510

TABLE 17.5 Penn Schumann Inc. statement of cash flows (figures in $ millions)

2014 2013

Revenue 16,378 13,378 Costs 8,402 7,800 Depreciation 928 850 EBIT 7,048 4,728 Interest 323 353 Tax 1,933 1,160 Net income 4,792 3,215 Dividends 1,678 1,350 Earnings per share ($) 8.91 6.23 Dividends per share ($) 3.12 2.62

TABLE 17.4 Penn Schumann Inc. income statement (figures in $ millions)

2014 2013

Cash and short-term investments 7,061 5,551 Receivables 2,590 2,214 Inventory 1,942 2,435 Total current assets 11,593 10,200 Property, plant, & equipment 21,088 19,025 Less accumulated depreciation 5,780 4,852 Net fi xed assets 15,308 14,173 Total assets 26,901 24,373 Payables 6,827 6,215 Short-term debt 1,557 2,620 Total current liabilities 8,384 8,835 Long-term debt 3,349 3,484 Shareholders’ equity 15,168 12,054 Total liabilities and equity 26,901 24,373 Note: Shares outstanding, millions 538 516 Market price per share ($) 105 88

TABLE 17.3 Penn Schumann Inc. balance sheet (figures in $ millions)

this research were to lead to a marketable product, Penn would need to make a large investment. In addition, the company might require cash for possible acquisitions in the biotech field. “What worries me,” Ms. Rodriguez said, “is that investors don’t give us credit for this and think that we are going to fritter away the cash on negative-NPV investments or easy living. I don’t think we should commit to paying out high dividends, but perhaps we could use some of our cash to repurchase stock.”

“I don’t know where anyone gets the idea that we fritter away cash on easy living,” replied Mr. Liu, as he took another sip of wine, “but I like the idea of buying back our stock. We can tell shareholders that we are so confident about the future that we believe buying our own stock is the best investment we can make.” He scribbled briefly on his napkin. “Suppose we bought back 50 million shares at $105. That would reduce the shares outstanding to 488 million. Net income last year was nearly $4.8 billion, so earnings per share would increase to $9.84. If the price-earnings multiple stays at 11.8, the stock price should rise to $116. That’s an increase of over 10%.” A smile came over Mr. Liu’s face. “Wonderful, he exclaimed, “here comes my homard à la nage. Let’s come back to this idea over dessert.”

Evaluate the arguments of Jennifer Rodriguez and George Liu. Do you think the company is holding too much cash? If you do, how do you think it could be best paid out?

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520

Long-Term Financial Planning

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

18-1 Describe the contents and uses of a financial plan.

18-2 Construct a simple financial planning model.

18-3 Estimate the effect of growth on the need for external financing.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

18 CHAPTE R

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521

P A

R T

S IX

I t’s been said that a camel looks like a horse designed by a committee. If a firm made every decision piecemeal, it would end up with a finan- cial camel. That is why smart financial managers

consider the overall effect of future investment and

financing decisions.

Think back to Chapter 1, where we discussed the

job of the financial manager. The manager must

consider what investments the firm should under-

take and how the firm should raise the cash to

pay for those investments. By now you know a fair

amount about how to make investment decisions

that increase shareholder value and about the dif-

ferent securities that the firm can issue. But because

new investments need to be paid for, those decisions

cannot be made independently. They must add up

to a sensible whole. That’s why financial planning

is needed. The financial plan allows managers to

think about the implications of alternative financial

strategies and to tease out any inconsistencies in

the firm’s goals.

Financial planning also helps managers avoid

some surprises and consider how they should react

to surprises that cannot be avoided. In Chapter 10

we stressed that good financial managers insist on

understanding what makes projects work and what

could go wrong with them. The same approach

should be taken when investment and financing

decisions are considered as a whole.

Finally, financial planning helps establish goals to

motivate managers and provide standards for mea-

suring performance.

We start the chapter by summarizing what finan-

cial planning involves, and we describe the contents

of a typical financial plan. We then discuss the use

of financial models in the planning process. Finally,

we examine the relationship between a firm’s growth

and its need for new financing.

Fi n

a n

c ia

l A n

a ly

si s

a n

d P

la n

n in

g

Financial planners don’t guess the future; they prepare for it.

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522 Part Six Financial Analysis and Planning

18.1 What Is Financial Planning? Firms must plan for both the short term and the long term. Short-term planning rarely looks further ahead than the next 12 months. It seeks to ensure that the firm has enough cash to pay its bills and that short-term borrowing and lending are arranged to the best advantage. We discuss short-term planning in the next chapter.

Here we are concerned with long-term planning, where a typical planning horizon is 5 years, although some firms look out 10 years or more. For example, it can take at least 10 years for an electric utility to design, obtain approval for, build, and test a major generating plant.

Long-term financial planning focuses on the firm’s long-term goals, the invest- ment that will be needed to meet those goals, and the finance that must be raised. But you can’t think about these things without also tackling other important issues. For example, you need to consider possible dividend policies, for the more that is paid out to shareholders, the more external financing that will be needed. You also need to think about what is an appropriate debt ratio for the firm. A conservative capital structure may mean greater reliance on new share issues. The financial plan is used to enforce consistency in the way that these questions are answered and to highlight the choices that the firm needs to make. Finally, by establishing a set of consistent goals, the plan enables subsequent evaluation of the firm’s performance in meeting those goals.

Financial Planning Focuses on the Big Picture Many of the firm’s capital expenditures are proposed by plant managers. But the final budget must also reflect strategic plans made by senior management. Positive-NPV opportunities occur in those businesses where the firm has a real competitive advan- tage. Strategic plans need to identify such businesses and look to expand them. The plans also seek to identify businesses to sell or liquidate as well as businesses that should be allowed to run down. Of course, these decisions are not the sole province of the financial manager. The company’s chief executive together with specialists in functional areas, such as marketing, production, and human resources, will be closely involved in the planning process. The final plan will also be subject to the approval of the board of directors.

Strategic planning involves capital budgeting on a grand scale. In this process, you need to look at the investment by each line of business and avoid getting bogged down in details. Of course, some individual projects are large enough to have significant individual impact. For example, the telecom giant Verizon has spent billions of dollars to deploy fiber-optic-based broadband technology to its residential customers; you can bet that this project was explicitly analyzed as part of its long-range financial plan. Normally, however, planners do not work on a project-by-project basis. Smaller proj- ects are aggregated into a unit that is treated as a single project.

At the beginning of the planning process the corporate staff might ask each division to submit three alternative business plans covering the next 5 years:

1. A best-case or aggressive growth plan calling for heavy capital investment and rapid growth of existing markets.

2. A normal growth plan in which the division grows with its markets but not significantly at the expense of its competitors.

3. A plan of retrenchment if the firm’s markets contract. This is planning for lean economic times.

The plan will contain a summary of capital expenditures, working capital require- ments, and strategies to raise funds for these investments.

planning horizon Time horizon for a financial plan.

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Chapter 18 Long-Term Financial Planning 523

Why Build Financial Plans? Firms spend considerable energy, time, and resources building elaborate financial plans. What do they get for this investment?

Contingency Planning Planning is not just forecasting. Forecasting concen- trates on the most likely outcomes, but planners need to worry about unlikely events as well as likely ones. If you think ahead about what could go wrong, then you are less likely to ignore the danger signals and you can respond faster to trouble.

Companies have developed a number of ways of asking “what-if” questions about both individual projects and the overall firm. For example, as we saw in Chapter 10, managers often work through the consequences of their decisions under different sce- narios. One scenario might envisage high interest rates contributing to a slowdown in world economic growth and lower commodity prices. A second scenario might involve a buoyant domestic economy, high inflation, and a weak currency.

The idea is to formulate responses to inevitable surprises. What will you do, for example, if sales in the first year turn out to be 10% below forecast? A good financial plan should help you adapt as events unfold.

Considering Options Planners need to think whether there are opportunities for the company to exploit its existing strengths by moving into a wholly new area. Often they may recommend entering a market for “strategic” reasons—that is, not because the immediate investment has a positive net present value but because it establishes the firm in a new market and creates options for possibly valuable follow-on investments.

For example, Verizon’s costly fiber-optic initiative would never be profitable strictly in terms of its most common current uses. But the new technology gives Veri- zon options to offer services that may be highly valuable in the future, such as the rapid delivery of an array of home entertainment services. The justification for the huge investment lies in these potential growth options.

Forcing Consistency Financial plans draw out the connections between the firm’s plans for growth and the financing requirements. For example, a forecast of 25% growth might require the firm to issue securities to pay for necessary capital expenditures, while a 5% growth rate might enable the firm to finance capital expendi- tures by using only reinvested profits.

Financial plans should help to ensure that the firm’s goals are mutually consistent. For example, the chief executive might say that she is shooting for a profit margin of 10% and sales growth of 20%, but financial planners need to think whether the higher sales growth may require price cuts that will reduce profit margin.

Moreover, a goal that is stated in terms of accounting ratios is not operational unless it is translated back into what that means for business decisions. For example, a higher profit margin can result from higher prices, lower costs, or a move into new, high-margin products. Why then do managers define objectives in this way? In part, such goals may be a code to communicate real concerns. For example, a target profit margin may be a way of saying that in pursuing sales growth, the firm has allowed costs to get out of control.

The danger is that everyone may forget the code and the accounting targets may be seen as goals in themselves. No one should be surprised when lower-level managers focus on the goals for which they are rewarded. For example, when Volkswagen set a goal of 6.5% profit margin, some VW groups responded by developing and promot- ing expensive, high-margin cars. Less attention was paid to marketing cheaper mod- els, which had lower profit margins but higher sales volume. As soon as this became apparent, Volkswagen announced that it would de-emphasize its profit margin goal and would instead focus on return on investment. It hoped that this would encourage managers to get the most profit out of every dollar of invested capital.

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524 Part Six Financial Analysis and Planning

18.2 Financial Planning Models Financial planners often use a financial planning model to help them explore the conse- quences of alternative strategies. These models range from simple models, such as the one presented later in this chapter, to models that incorporate hundreds of equations.

Financial planning models support the financial planning process by making it easier and cheaper to construct forecast financial statements. The models automate an important part of planning that would otherwise be boring, time-consuming, and labor-intensive.

Programming these financial planning models used to consume large amounts of computer time and high-priced talent. These days standard spreadsheet programs such as Excel can be used to solve complex financial planning problems.

Components of a Financial Planning Model A completed financial plan for a large company is a substantial document. A smaller corporation’s plan would have the same elements but less detail. For the smallest busi- nesses, financial plans may be entirely in the financial managers’ heads. The basic elements of the plans will be similar, however, for firms of any size.

Financial plans include three components: inputs, the planning model, and outputs. The relationship among these components is represented in Figure 18.1 . Let’s look at them in turn.

Inputs The inputs to the financial plan consist of the firm’s current financial state- ments and its forecasts about the future. Usually, the principal forecast is the likely growth in sales, since many of the other variables such as labor requirements and inventory levels are tied to sales. These forecasts are only in part the responsibility of the financial manager. Obviously, the marketing department will play a key role in forecasting sales. In addition, because sales will depend on the state of the overall economy, large firms will seek forecasting help from firms that specialize in preparing macroeconomic and industry forecasts.

The Planning Model The financial planning model calculates the implications of the manager’s forecasts for profits, new investment, and financing. The model con- sists of equations relating output variables to forecasts. For example, the equations can show how a change in sales is likely to affect costs, working capital, fixed assets, and financing requirements. The financial model could specify that the total cost of goods produced may increase by 80 cents for every $1 increase in total sales, that accounts receivable will be a fixed proportion of sales, and that the firm will need to increase fixed assets by 8% for every 10% increase in sales.

Outputs The output of the financial model consists of financial statements such as income statements, balance sheets, and statements describing sources and uses of cash. These statements are called pro formas, which means that they are forecasts based on the inputs and the assumptions built into the plan. Usually the output of financial models also includes many of the financial ratios we discussed in Chapter 4. These ratios indicate whether the firm will be financially fit and healthy at the end of the planning period.

pro formas Projected or forecast financial statements.

FIGURE 18.1 The components of a financial plan

Outputs Projected financial statements (pro formas). Financial ratios. Sources and uses of cash.

Planning Model Equations specifying key relationships.

Inputs Current financial statements. Forecasts of key variables such as sales or interest rates.

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Chapter 18 Long-Term Financial Planning 525

Percentage of Sales Models We can illustrate the basic components of a planning model with a very simple exam- ple. In the next section we will start to add some complexity.

Suppose that Executive Cheese has prepared the simple balance sheet and income statement shown in Table 18.1 . The firm’s financial planners forecast that total sales next year will increase by 10% from this year’s level. They expect that costs will be a fixed proportion of sales, so they too will increase by 10%. Almost all the fore- casts for Executive Cheese are proportional to the forecast of sales. Such models are therefore called percentage of sales models. The result is the pro forma, or fore- cast, income statement in Table 18.2 , which shows that next year’s income will be $200  ×  1.10  =  $220.

Executive Cheese has no spare capacity, and in order to sustain this higher level of output, it must increase plant and equipment by 10%, or $200. Therefore, the left-hand side of the balance sheet, which lists total assets, must increase to $2,200. What about the right-hand side? The firm must decide how it intends to finance its new assets. Suppose that it decides to maintain a fixed debt-equity ratio. Then both debt and equity would grow by 10%, as shown in the pro forma balance sheet in Table 18.2 . Notice that this implies that the firm must issue $80 in additional debt. On the other hand, no equity needs to be issued. The 10% increase in equity can be accomplished by retain- ing $120 of earnings.

This raises a question, however. If income is forecast at $220, why does equity increase by only $120? The answer is that the firm must be planning to pay a dividend of $220  -  $120  =  $100. Notice that this dividend payment is not chosen indepen- dently but is a consequence of the other decisions. Given the company’s need for funds and its decision to maintain the debt-equity ratio, dividend policy is completely deter- mined. Any other dividend payment would be inconsistent with the two conditions that (1) the right-hand side of the balance sheet increase by $200 and (2) both debt and equity increase in the same proportion. For this reason we call dividends the balancing item, or plug. The balancing item is the variable that adjusts to make the sources of funds equal to the uses.

Of course, most firms would be reluctant to vary dividends simply because they have a temporary need for cash; instead, they like to maintain a steady progression of

percentage of sales model Planning model in which sales forecasts are the driving variables and most other variables are proportional to sales.

balancing item Variable that adjusts to maintain the consistency of a financial plan. Also called plug.

TABLE 18.1 Financial statements of Executive Cheese Company for past year

INCOME STATEMENT

Sales $1,200 Costs 1,000 Net income $ 200

BALANCE SHEET (Year-end)

Assets $2,000 Debt $ 800 Equity 1,200

Total $2,000 Total $2,000

TABLE 18.2 Pro forma financial statements of Executive Cheese

PRO FORMA INCOME STATEMENT

Sales $1,320 Costs 1,100 Net income $ 220

PRO FORMA BALANCE SHEET (Year-end)

Assets $2,200 Debt $ 880 Equity 1,320

Total $2,200 Total $2,200

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526 Part Six Financial Analysis and Planning

dividends. In this case Executive Cheese could commit to some other dividend pay- ment and allow the debt-equity ratio to vary. The amount of debt would therefore become the balancing item.

Example 18.1 Balancing Item Suppose the firm commits to a dividend level of $180 and raises any extra money it needs by an issue of debt. In this case the amount of debt becomes the balancing item. With the dividend set at $180, reinvested earnings would be only $40, so the firm would have to issue $160 in new debt to help pay for the additional $200 of assets. Table 18.3 , panel A, is the new balance sheet.

Now suppose instead that the firm commits to the $180 dividend but decides that it will issue at most $100 in new debt. In that case, new equity issues become the balancing item. With $40 of earnings reinvested and $100 of new debt, an additional $60 of equity needs to be raised to support the total addition of $200 to the firm’s assets. Table 18.3 , panel B, is the resulting balance sheet.

Suppose that the firm decides to maintain its debt-equity ratio at 800/1,200  =  2/3. It is committed to increasing assets by 10% to support the forecast increase in sales, and it strongly believes that a dividend payment of $180 is in the best interests of the firm. What must be the balancing items? What is the implication for the firm’s financing activities in the next year?

Self-Test 18.1

Is one of these plans better than the others? It’s hard to give a simple answer. The choice of dividend payment depends partly on how investors will interpret the decision. If last year’s dividend was only $50, investors might regard a dividend payment of $100 as a sign of a confident management; if last year’s dividend was $150, investors might not be so content with a payment of $100. The alternative of paying $180 in dividends and making up the shortfall by issuing more debt leaves the company with a debt- equity ratio of 77%. That is unlikely to make your bankers edgy, but you may worry about how long you can continue to finance expansion predominantly by borrowing.

Our example shows how experiments with a financial model, including changes in the model’s balancing item, can raise important financial questions. But the model does not answer these questions. Financial models ensure consistency between growth assumptions and financing plans, but they do not identify the best financing plan.

An Improved Model Now that you have grasped the idea behind financial planning models, we can move on to a more sophisticated example.

Table 18.4 shows the financial statements for Executive Fruit Company in 2014. Judging by these figures, the company is ordinary in almost all respects. Its earnings before interest and taxes were 10% of sales revenue. Net income was $96,000 after payment of taxes and 10% interest on $400,000 of long-term debt. The company paid out two-thirds of its net income as dividends.

TABLE 18.3 Pro forma balance sheets. A: Dividends are fixed, and debt is the balancing item. B: Dividends and debt are fixed, and equity issues are the balancing item.

Panel A Panel B

Assets $2,200 Debt $ 960 Assets $2,200 Debt $ 900 Equity 1,240 Equity 1,300

Total $2,200 Total $2,200 Total $2,200 Total $2,200

Executive Fruit

BEYOND THE PAGE

brealey.mhhe.com/ch18-01

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Chapter 18 Long-Term Financial Planning 527

Next to each item on the financial statements in Table  18.4 we have entered a comment about the relationship between that variable and sales. In most cases, the comment gives the value of each item as a percentage of sales. This may be useful for forecasting purposes. For example, it would be reasonable to assume that cost of goods sold will remain at 90% of sales even if sales grow by 10% next year. Similarly, it is reasonable to assume that net working capital will remain at 10% of sales.

On the other hand, the fact that long-term debt was 20% of sales in 2014 does not mean that we should assume that this ratio will continue to hold next year. Many alter- native financing plans with varying combinations of debt issues, equity issues, and dividend payouts may be considered without affecting the firm’s operations.

Now suppose that you are asked to prepare pro forma financial statements for Exec- utive Fruit for 2015. You are told to assume that (1) sales and operating costs are expected to be up 10% over 2014, (2) interest rates will remain at their current level, (3) the firm will stick to its traditional dividend policy of paying out two-thirds of earnings, and (4) Executive will need 10% more fixed assets and net working capital next year to support the higher sales volume.

In Table 18.5 we present the resulting first-stage pro forma calculations for Execu- tive Fruit. These calculations show what would happen if the size of the firm increases along with projected sales, but at this preliminary stage the plan does not specify a particular mix of new security issues.

Without any security issues, the balance sheet will not balance: Assets increase to $1,100,000, while debt plus shareholders’ equity amounts to only $1,036,000. Some- how the firm will need to raise an extra $64,000 to help pay for the increase in assets that is necessary to support the higher projected level of sales in 2015. In this first pass, external financing is the balancing item. Given the firm’s growth forecasts and its divi- dend policy, the financial plan calculates how much money the firm needs to raise but does not yet specify how those funds will be raised.

In the second-stage pro forma, the firm must decide on the financing mix that best meets its needs for additional funds. It must choose some combination of new debt or new equity that supports the contemplated acquisition of additional assets. For exam- ple, it could issue $64,000 of equity or debt, or it could choose to maintain its long- term debt-equity ratio at two-thirds by issuing both debt and equity.

TABLE 18.4 Financial statements for Executive Fruit Co., 2014 (figures in $ thousands)

INCOME STATEMENT, 2014

Comment

Revenue $2,000 Cost of goods sold 1,800 90% of sales EBIT 200 Difference = 10% of sales Interest 40 10% of debt Earnings before taxes 160 EBIT - interest State and federal tax 64 40% of (EBIT - interest) Net income $ 96 EBIT - interest - taxes Dividends $ 64 Payout ratio = 2/3 Additions to retained earnings $ 32 Net income - dividends

BALANCE SHEET (Year-end, 2014)

Assets Net working capital $ 200 10% of sales Fixed assets 800 40% of sales Total assets $1,000 50% of sales Liabilities and shareholders’ equity Long-term debt $ 400 Shareholders’ equity 600 Total liabilities and shareholders’ equity $1,000 Equals total assets

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528 Part Six Financial Analysis and Planning

Table 18.6 shows the second-stage pro forma balance sheet if the required funds are raised by issuing $64,000 of debt. Therefore, in Table 18.6 , debt is treated as the balancing item. Notice that while the plan requires the firm to specify a financing plan consistent with its growth projections, it does not provide guidance as to the best financing mix.

Table  18.7 sets out the firm’s sources and uses of funds. It shows that working capital must be increased by $20,000 and fixed assets by $80,000 compared with their level a year earlier. The firm reinvested $36,000 of this year’s profits, so $64,000 must be raised in the capital markets. Under the financing plan presented in Table 18.6 , the firm borrows the entire $64,000.

We have spared you the trouble of actually calculating the figures necessary for Tables 18.5 through 18.7 . The calculations do not take more than a few minutes for this simple example, provided you set up the calculations correctly and make no arith- metic mistakes. If that time requirement seems trivial, remember that in reality you probably would be asked for five similar sets of statements covering each year from 2015 to 2019. Probably you would be asked for alternative projections under different

TABLE 18.5 First-stage pro forma statements for Executive Fruit Co., 2015 (figures in $ thousands)

PRO FORMA INCOME STATEMENT, 2015

Comment

Revenue $2,200 10% higher Cost of goods sold 1,980 10% higher EBIT 220 10% higher Interest 40 Unchanged Earnings before taxes 180 EBIT - interest State and federal tax 72 40% of (EBIT - interest) Net income $ 108 EBIT - interest - taxes Dividends $ 72 2/3 of net income Additions to retained earnings $ 36 Net income - dividends

PRO FORMA BALANCE SHEET (Year-end, 2015)

Assets Net working capital $ 220 10% higher Fixed assets 880 10% higher Total assets $ 1,100 10% higher Liabilities and shareholders’ equity Long-term debt $ 400 Temporarily held fi xed Shareholders’ equity 636 Increased by earnings

reinvested during year Total liabilities and shareholders’ equity $1,036 Sum of debt plus equity Required external fi nancing $ 64 Balancing item or plug

(= $1,100 - $1,036)

TABLE 18.6 Second-stage pro forma balance sheet for Executive Fruit Co., year-end 2015 (figures in $ thousands)

Comment

Assets Net working capital $ 220 10% higher Fixed assets 880 10% higher Total assets $1,100 10% higher Liabilities and shareholders’ equity Long-term debt $ 464 16% higher (new borrowing = $64;

this is the balancing item) Shareholders’ equity 636 Increased by reinvested earnings Total liabilities and shareholders’ equity $1,100 Again equals total assets

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Chapter 18 Long-Term Financial Planning 529

assumptions (for example, 5% instead of 10% growth rate of revenue) or different financial strategies (for example, freezing dividends at their 2015 level of $64,000). This would be far more time-consuming. Moreover, actual plans will have many more line items than this simple one. Building a model and letting the computer toil in your place have obvious attractions.

Spreadsheet 18.1 is the spreadsheet we used for the Executive Fruit model. Col- umn E contains the values that appear in Table 18.4 . Columns F and G are pro forma statements using the growth rate given in cell B3. The spreadsheet recognizes that additional debt issued in one year will result in increased interest expenses in the fol- lowing year. For example, interest expense in 2016 is 10% of the debt outstanding at the end of 2015.

Column H presents the formulas used to obtain each value in column G. Notice that we assume the firm will maintain its dividend payout ratio at 2/3 and that debt will be the balancing item, increasing in each year by required external financing (row 24). Required external financing in 2016 equals total assets required to support that year’s sales (cell G17) minus the previous year’s assets (cell F17) minus earnings reinvested during the year (cell G11). Shareholders’ equity (cell G21) equals its previous value plus reinvested earnings.

TABLE 18.7 Statement of sources and uses of funds for Executive Fruit, 2015 (figures in $ thousands)

Sources Uses

Reinvested earnings $ 36 Investment in working capital $ 20 New borrowing 64 Investment in fi xed assets 80 Total sources $100 Total uses $100

You can find this spreadsheet in Connect.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

A. Model inputs

Growth rate

Tax rate

Interest rate

NWC/sales ratio

Fixed assets/sales

COGS/sales

Payout ratio

Notes:

(a): Long-term debt, the balancing item, increases by required external financing.

(b): Shareholders’ equity equals its value in the previous year plus reinvested earnings.

Income Statement Revenue

Cost of goods sold

EBIT

Interest expense

Earnings before taxes

Taxes

Net income

Dividends

Addn. to retained earnings

Balance Sheet (year-end) Assets

Net working capital

Fixed assets

Total assets

Liabilities and equity

Long-term debt (note a)

Shareholders’ equity (note b)

Total liab. & share. equity

Required external financing

.10

0.4

0.1

0.1

0.4

0.9

2/3

Base year 2014

Formula for column G2015 2016

BA C D

2,000

1,800

200

40

160

64

96

64

32

200

800

1,000

400

600

1,000

2,200.0

1,980.0

220.0

40.0

180.0

72.0

108.0

72.0

36.0

220.0

880.0

1,100.0

464.0

636.0

1,100.0

64.0

2,420.0

2,178.0

242.0

46.4

195.6

78.2

117.4

78.2

39.1

242.0

968.0

1,210.0

534.9

675.1

1,210.0

70.9

E F G

=F3*(1+$B3)

=G3*$B$8

=G3-G4

=$B$5*F20

=G5-G6

=$B$4*G7

=G7-G8

=G9*$B$9

=G9-G10

=$B$6*G3

=$B$7*G3

=G15+G16

=F20+G24

=F21+G11

=G20+G21

=G17-F17-G11

H

SPREADSHEET 18.1 Executive Fruit spreadsheet

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530 Part Six Financial Analysis and Planning

Now that the spreadsheet is set up, it is easy to explore the consequences of vari- ous assumptions. For example, you can change the assumed growth rate (cell B3) or experiment with different policies, such as changing the dividend payout ratio or forc- ing debt or equity finance (or both) to absorb the required external financing.

a. Suppose that Executive Fruit is committed to a 10% growth rate and to paying out two-thirds of its profits as dividends. However, it now also wishes to maintain its debt-equity ratio at 2/3. What are the implications for external financing in 2015?

b. If the company is prepared to reduce dividends paid in 2015 to $60,000, how much external financing would be needed?

Self-Test 18.2

Example 18.2 What Happens if the Growth Rate Changes? Let’s use the spreadsheet to explore the effect of sales growth on the need for exter- nal financing. We can alter the assumed growth rate in cell B3 and see the effect on required external financing in cell F24. For example, we saw in Spreadsheet 18.1 that when the growth rate was 10%, required external financing was $64,000. In our model, assets are proportional to sales, so when we assume a higher growth rate of sales, assets also increase at a faster rate. The additional funds necessary to pay for those additional assets imply greater external financing.

Table 18.8 shows how required external financing responds to a change in the growth rate. Notice that at a 3.33% growth rate, required external financing is zero. At higher growth rates, the firm requires external financing; at lower rates, rein- vested earnings exceed the addition to assets and there is a surplus of funds from internal sources; this shows up as negative required external financing. Later in the chapter, we will explore the limits to internal growth more systematically.

TABLE 18.8 Required external financing for Executive Fruit. Higher growth rates require greater amounts of external capital.

Growth Rate, % Required External Financing, $ Thousands

0 -32 2 -12.8 3.33 0 5 16 10 64 15 112 20 160

18.3 Planners Beware

Pitfalls in Model Design The Executive Fruit model is still too simple for practical application. You probably have already noticed several ways to improve it. For example, we ignored depreciation of fixed assets. Depreciation is important because it provides a tax shield. If Execu- tive Fruit deducts depreciation before calculating its tax bill, it could plow back more money into new investments and would need to borrow less. We’ve also simplified the firm’s borrowing plans, ignoring short-term debt and assuming that the firm will be

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Chapter 18 Long-Term Financial Planning 531

able to issue small amounts of long-term debt as needed at a fixed interest rate regard- less of changes in its leverage.

You would certainly want to make these obvious improvements. But beware: There is always the temptation to make a model bigger and more detailed. You may end up with an exhaustive model that is too cumbersome for routine use.

Excessive detail gets in the way of the intended use of corporate planning mod- els, which is to project the financial consequences of a variety of strategies and assumptions. The fascination of detail, if you give in to it, distracts attention from crucial decisions like stock issues and dividend policy and allocation of capital by business area.

The Assumption in Percentage of Sales Models When forecasting Executive Fruit’s capital requirements, we assumed that both fixed assets and working capital increase proportionately with sales. For example, the orange line in Figure 18.2 shows that net working capital is a constant 10% of sales.

Percentage of sales models are useful first approximations for financial planning. However, in reality, assets may not be proportional to sales. For example, we will see in Chapter 19 that important components of working capital such as inventories and cash balances will generally rise less than proportionately with sales. Suppose that Executive Fruit looks back at past variations in sales and estimates that on average a $1 rise in sales requires only a $.075 increase in net working capital. The blue line in Figure 18.2 shows the level of working capital that would now be needed for different levels of sales. To allow for this in the Executive Fruit model, we would need to set net working capital equal to ($50,000  +  .075  ×  sales).

A further complication is that fixed assets such as plant and equipment are typically not added in small increments as sales increase. Instead, the picture is more likely to resemble Figure 18.3 . If Executive Fruit’s factories are operating at less than full capacity (point A, for example), then the firm can expand sales without any additional investment in plant. Ultimately, however, if sales continue to increase, say beyond point B, Executive Fruit will need to add new capacity. This is shown by the occasional large changes to fixed assets in Figure 18.3 . These “lumpy” changes to fixed assets need to be recognized when devising the financial plan. If there is considerable excess capacity, even rapid sales growth may not require big additions to fixed assets. On the other hand, if the firm is already operating at capacity, even small sales growth may call for large investment in plant and equipment.

FIGURE 18.2 Net working capital as a function of sales. The orange line shows net working capital equal to .10  ×  sales. The blue line depicts net working capital as $50,000  +  .075  ×  sales, so that it increases less than proportionately with sales.

Sales ($ thousands)

N et

w o

rk in

g c

ap it

al (

$ th

o u

sa n

d s)

200

(b) (a)

50

2,000

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532 Part Six Financial Analysis and Planning

The Role of Financial Planning Models Models such as the one that we constructed for Executive Fruit help the financial man- ager to avoid surprises. If the planned rate of growth will require the company to raise external financing, the manager can start planning how best to do so.

We commented earlier that financial planners are concerned about unlikely events as well as likely ones. For example, Executive Fruit’s manager may wish to consider how the company’s capital requirement would change if profit margins come under pressure and the company generated less cash from its operations. Planning models make it easy to explore the consequences of such events.

Example 18.3 Required External Funds and Excess Capacity Suppose that Carter Tools has $50 million invested in fixed assets and generates sales of $60 million. The company is currently working at 80% of capacity. Suppose that a 50% increase in sales is forecast. How much investment in fixed assets would be required?

Sales can increase without the need for new investments in fixed assets until the company is at 100% of capacity. Therefore, sales can increase to $60  million  × 100/80  =  $75 million before the firm reaches full capacity given its current level of fixed assets. At full capacity, therefore, the ratio of assets to sales would be $50  million/$75  million  =  2⁄3.

The 50% increase in forecast sales would imply a sales level of $60  million  × 1.5  =   $90  million. To support this level of sales, the company needs at least $90  million  ×  2⁄3  =  $60 million of fixed assets. This calls for a $10 million investment in additional fixed assets.

Suppose that at its current level of assets and sales, Carter Tools in Example 18.3 is working at 75% of capacity.

a. How much can sales expand without any further investment in fixed assets?

b. How much investment in fixed assets would be required to support a 50% expansion in sales?

Self-Test 18.3

FIGURE 18.3 If factories are operating below full capacity, sales can increase without investment in fixed assets (point A ). Beyond some sales level (point B ), new capacity must be added.

Sales

A B

Fi xe

d a

ss et

s

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Chapter 18 Long-Term Financial Planning 533

However, there are limits to what you can learn from planning models. Although they help to trace through the consequences of alternative plans, they do not tell you which plan is best. For example, we saw that Executive Fruit is proposing to grow its sales and earnings per share. Is that good news for shareholders? Well, not necessar- ily; it depends on the opportunity cost of the additional capital that the company needs to achieve that growth. In 2015 the company proposes to invest $100,000 in fixed assets and working capital. Table 18.5 showed that this extra investment is expected to generate $12,000 of additional net income, equivalent to a return of 12% on the new investment. 1 If the cost of that capital is less than 12%, the new investment will have a positive NPV and will add to shareholder wealth. But suppose that the cost of capital is higher at, say, 15%. In this case Executive Fruit’s investment makes shareholders worse off, even though the company is recording steady growth in earnings per share and dividends. Executive Fruit’s planning model tells us how much money the firm must raise to fund the planned growth, but it cannot tell us whether that growth con- tributes to shareholder value. Nor can it tell us whether the company should raise the cash by issuing new debt or equity.

1 We assume this additional income is a perpetuity.

Which of the following questions will a financial plan help to answer?

a. Is the firm’s assumption for asset growth consistent with its plans for debt and equity issues and dividend policy?

b. Will accounts receivable increase in direct proportion to sales? c. Will the contemplated debt-equity mix maximize the value of the firm?

Self-Test 18.4

18.4 External Financing and Growth Financial plans force managers to be consistent in their goals for growth, investments, and financing. The nearby box describes how one company was brought to its knees in part by fundamental inconsistences between its growth strategy and its financing plans.

Financial models, such as the one that we have developed for Executive Fruit, can help managers trace through the financial consequences of their growth plans and avoid such disasters. But there is a danger that the complexities of a full-blown finan- cial model can obscure the basic issues. Therefore, managers also use some simple rules of thumb to draw out the relationship between a firm’s growth objectives and its requirement for external financing.

Recall that in 2014 Executive Fruit ended the year with $1,000,000 of fixed assets and net working capital, and it had $2,000,000 of sales. In other words, each dollar of sales required $.50 of net assets. The company forecasts that sales in 2015 will increase by $200,000. Therefore, if the ratio of net assets to sales remains constant, assets in 2015 will need to rise by $.50  ×  $200,000  =  $100,000. 2 Part of this increase can be financed by reinvested earnings, which in 2015 are $36,000. So the amount of external financing needed is

Required external financing =

net assets

sales ×

increase in sales -

reinvested earnings

= .50 × $200,000 - 36,000 = $64,000

Sometimes it is useful to write this calculation in terms of growth rates. Executive Fruit’s forecast increase in sales is equivalent to a rise of 10%. So, if net assets are a

2 However, remember our earlier warning that the ratio of net assets to sales may change as the firm grows.

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534

constant proportion of sales, the higher sales volume will also require a 10% addition to net assets. Thus

New investment = growth rate × initial assets

$100,000 = .10 × $1,000,000

Part of the funds to pay for the new assets is provided by reinvested earnings. The remainder must come from external financing. Therefore,

Required external financing = new investment - reinvested earnings (18.1) = (growth rate × assets) - reinvested earnings

This simple equation highlights that the amount of external financing depends on the firm’s projected growth. The faster the firm grows, the more it needs to invest and therefore the more it needs to raise new capital.

In the case of Executive Fruit,

Required external financing = (.10 × $1,000,000) - $36,000

= $100,000 - $36,000 = $64,000

If Executive Fruit’s assets remain a constant percentage of sales, then the company needs to raise $64,000 to produce a 10% addition to sales.

The sloping line in Figure 18.4 illustrates how required external financing increases with the growth rate. At low growth rates, the firm generates more funds than neces- sary for expansion. In this sense, its requirement for further external funds is negative. It may choose to use its surplus earnings to pay off some of its debt or buy back its stock. In fact, the vertical intercept in Figure 18.4 , at zero growth, is the negative of the

Finance in Practice The Collapse of Vivendi: A Failure in Planning reluctant to extend further credit, and its bonds were down- graded to junk status. By July 2002 the share price had fallen to less than 10% of its level 2 years earlier. With the company facing imminent bankruptcy, M. Messier was ousted and the new management set about slashing costs and selling assets to reduce the debt burden. *

Vivendi’s problems were exacerbated by considerable waste and ostentatious extravagance, but its brush with bankruptcy was a result of a lack of fi nancial planning. The company’s goals for growth were unsustainable, and it had few options for surviving a decline in operating cash fl ow.

*The rise and fall of Vivendi is chronicled in J. Johnson and M. Orange, The Man Who Tried to Buy the World: Jean-Marie Messier and Vivendi Universal (Portfolio, 2003).

In 1994 39-year-old Jean-Marie Messier became CEO of the French company Générale des Eaux. He immediately set out to transform it from a sleepy water and sewage business into a multinational media and telecommunications group. The company, now renamed Vivendi, entered into a series of major acquisitions, including a $42 billion purchase of Seagram, owner of Universal Studios. To fi nance its expan- sion, Vivendi increased its borrowing to $35 billion, and it increased its leverage further by repurchasing 104 million shares for $6.3 billion. Confi dent that its share price would rise, the company raised the stakes even more by selling a large number of put options on its own stock.

Vivendi’s strategy made it very vulnerable to any decline in operating cash fl ow. As profi ts began to evaporate, the company faced a severe cash shortage. Its banks were

FIGURE 18.4 External financing and growth

R eq

u ir

ed e

xt er

n al

f u

n d

s

Projected growth rate

0

Internal growth rate

Required external funds

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Chapter 18 Long-Term Financial Planning 535

addition to retained earnings. When growth is zero, no funds are needed for expansion, so all that addition is surplus.

As the firm’s projected growth rate increases, more funds are needed to pay for the necessary investments. Therefore, the plot in Figure 18.4 is upward-sloping. For high rates of growth the firm must issue new securities to pay for new investments.

Where the sloping line crosses the horizontal axis, external financing is zero: The firm is growing as fast as possible without resorting to new security issues. This is called the internal growth rate. The growth rate is “internal” because it can be main- tained without resorting to additional external sources of capital.

Notice that if we set required external financing to zero, we can solve Equation 18.1 for the internal growth rate as

Internal growth rate = reinvested earnings

assets

Thus the firm’s rate of growth without additional external sources of capital will equal the ratio of reinvested earnings to assets. This means that a firm with a high volume of reinvested earnings relative to its assets can generate a higher growth rate without needing to raise more capital.

We can gain more insight into what determines the internal growth rate by mul- tiplying the top and bottom of the expression for internal growth by net income and equity as follows:

Internal growth rate = reinvested earnings

net income ×

net income

equity ×

equity

assets

= plowback ratio × return on equity × equity

assets (18.2)

A firm can achieve a higher growth rate without raising external capital if (1) it plows back a high proportion of its earnings, (2) it has a high return on equity (ROE), and (3) it has a low debt-to-asset ratio.

internal growth rate Maximum rate of growth without external financing.

Example 18.4 Internal Growth for Executive Fruit Executive Fruit has chosen a plowback ratio of 1⁄3. Equity outstanding at the start of 2015 is 600, and outstanding assets are 1,000. Executive Fruit’s return on equity 3 is ROE  =  16.67%, and its ratio of equity to assets is 600/1,000  =  .60. If it is unwilling to raise new capital, its maximum growth rate is

Internal growth rate = plowback ratio × ROE × equity assets

= 1 3

× .1667 × .60 = .033, or 3.33%

Look back at Table 18.8 and you will see that at this growth rate, external financing is in fact zero. This growth rate is much lower than the 10% growth Executive Fruit projects, which explains its need for external financing.

3 Actually, calculating ROE to find the internal growth rate can be a bit tricky. Executive Fruit is forecasting a growth rate of 10% and an ROE of 108/600  =  18%, but if it grows more slowly, sales, net income and ROE will be lower. In other words, ROE may depend on the growth rate. We saw in Table 18.8 that a growth rate of 3.33% implies external financing of zero; we will choose the ROE corresponding to the internal growth rate of 3.33%. If you input .0333 as the growth rate in the Executive Fruit spreadsheet (Spreadsheet 18.1), you will find that net income in 2015 is $100,000 while equity outstanding at the beginning of 2015 (end of 2014) is $600,000, which implies an ROE of 100/600  =  .1667. Notice that although it is common to calculate ROE by dividing income by either end-of-year or year-average shareholders’ equity, neither of those conventions will work in this applica- tion. To find the internal growth rate, we need to view ROE as analogous to the rate of return on a stock, that is, as money earned during the year per dollar of shareholders’ equity at the start of the year.

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536 Part Six Financial Analysis and Planning

Instead of focusing on the maximum growth rate that can be supported without any external financing, firms also may be interested in the growth rate that can be sus- tained without additional equity issues. Of course, if the firm is able to issue enough debt, virtually any growth rate can be financed. It makes more sense to assume that the firm has settled on an optimal capital structure that it will maintain even as equity is augmented by reinvested earnings. The firm issues only enough debt to keep its debt- equity ratio constant. The sustainable growth rate is the highest growth rate the firm can maintain without increasing its financial leverage. It turns out that the sustainable growth rate depends only on the plowback ratio and return on equity: 4

Sustainable growth rate = plowback ratio × return on equity (18.3)

You may remember this formula from Chapter 7, where we first used it when we looked at the valuation of the firm and the dividend discount model.

4 Here is a proof: Required equity issues = growth rate × assets - reinvested earnings - new debt issues

We find the sustainable growth rate by setting required new equity issues to zero and solving for growth:

Sustainable growth rate = reinvested earnings + new debt issues

assets

= reinvested earnings + new debt issues

debt + equity

However, because both debt and equity are growing at the same rate, new debt issues must equal reinvested earnings multiplied by the ratio of debt to equity, D/E. Therefore, we can write the sustainable growth rate as

Sustainable growth rate = reinvested earnings × (1 + D/E)

debt + equity

= reinvested earnings × (1 + D/E)

equity × (1 + D/E) =

reinvested earnings

equity

= reinvested earnings

net income ×

net income

equity = plowback × ROE

sustainable growth rate Steady rate at which a firm can grow without changing leverage; plowback ratio  ×  return on equity.

Example 18.5 Sustainable Growth Rate Executive Suites Inc. currently has an equity-to-asset ratio of .8. Its ROE is 18%. The firm currently reinvests one-third of its earnings back into the firm. Moreover, if it plans to keep leverage unchanged, it will issue an additional 20 cents of debt for every 80 cents of reinvested earnings. Given this policy, its maximum growth rate is

Sustainable growth rate = plowback ratio × ROE

= 1/3 × .18 = .06, or 6%

If the firm is willing to plow back a higher proportion of its earnings, it can issue more debt without increasing its leverage. Both the greater reinvested profits and the additional debt issues would allow it to grow more rapidly. You can confirm in the following Self-Test problem [see part (b)] that if the firm increases its plowback ratio, its sustainable growth rate will be higher.

Suppose Executive Suites reduces the dividend payout ratio to 25%. Calcu- late its growth rate assuming (a) that no new debt or equity will be issued and (b) that the firm maintains its debt-to-equity ratio at .25.

Self-Test 18.5

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Chapter 18 Long-Term Financial Planning 537

SUMMARY Most firms take financial planning seriously and devote considerable resources to it. The tangible product of the planning process is a financial plan describing the firm’s financial strategy and projecting its future consequences by means of pro forma balance sheets, income statements, and statements of sources and uses of funds. The plan establishes financial goals and is a benchmark for evaluating subsequent performance. Usually it also describes why that strategy was chosen and how the plan’s financial goals are to be achieved.

Planning, if it is done right, forces the financial manager to think about events that could upset the firm’s progress and to devise strategies to be held in reserve for counterattack when unfortunate surprises occur. Planning is more than forecasting, because forecast- ing deals with the most likely outcome. Planners also have to think about events that may occur even though they are unlikely.

In long-range, or strategic, planning, the planning horizon is usually 5 years or more. This kind of planning deals with aggregate decisions; for example, the planner would worry about whether the division should commit to heavy capital investment and rapid growth, but not whether the division should choose machine tool A versus tool B. In fact, planners must be constantly on guard against the fascination of detail, because giving in to it means slighting crucial issues like investment strategy, debt policy, and the choice of a target dividend payout ratio.

The plan is the end result. The process that produces the plan is valuable in its own right. Planning forces the financial manager to consider the combined effects of all the firm’s investment and financing decisions. This is important because these decisions inter- act and should not be made independently.

There is no theory or model that leads straight to the optimal financial strategy. Conse- quently, financial planning proceeds by trial and error. Many different strategies may be projected under a range of assumptions about the future before one strategy is finally chosen. The dozens of separate projections that may be made during this trial-and-error process generate a heavy load of arithmetic and paperwork. Firms have responded by developing corporate planning models to forecast the financial consequences of speci- fied strategies and assumptions about the future. One very simple starting point may be a percentage of sales model, in which many key variables are assumed to be directly pro- portional to sales. Planning models are efficient and widely used. But remember that there is not much finance in them. Their primary purpose is to produce accounting statements. The models do not search for the best financial strategy but only trace out the consequences of a strategy specified by the model user.

Higher growth rates will lead to greater need for investments in fixed assets and working capital. The internal growth rate is the maximum rate at which the firm can grow if it relies entirely on reinvested profits to finance its growth, that is, the maximum rate of growth without requiring external financing. The sustainable growth rate is the rate at which the firm can grow without changing its leverage ratio or issuing new equity.

What are the contents and uses of a financial plan? (LO18-1)

How are financial planning models constructed? (LO18-2)

What is the effect of growth on the need for external financing? (LO18-3)

L I S T I N G O F E Q UAT I O N S

18.1 Required external financing  =  growth rate  ×  assets  -  reinvested earnings

18.2 Internal growth rate = plowback ratio × return on equity × equity

assets

18.3 Sustainable growth rate  =  plowback ratio  ×  return on equity

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538 Part Six Financial Analysis and Planning

QUESTIONS AND PROBLEMS 1. Financial Planning. True or false? Explain. (LO18-1)

a. Financial planning should attempt to minimize risk. b. The primary aim of financial planning is to obtain better forecasts of future cash flows and

earnings. c. Financial planning is necessary because financing and investment decisions interact and

should not be made independently. d. Firms’ planning horizons rarely exceed 3 years. e. Individual capital investment projects are not considered in a financial plan unless they are

very large. f. Financial planning requires accurate and consistent forecasting. g. Financial planning models should include as much detail as possible.

2. Financial Models. What are the dangers and disadvantages of using a financial model? Discuss. (LO18-1)

3. Using Financial Plans. Corporate financial plans are often used as a basis for judging subse- quent performance. What can be learned from such comparisons? What problems might arise, and how might you cope with such problems? (LO18-1)

4. Financial Targets. Managers sometimes state a target growth rate for sales or earnings per share. Do you think that either makes sense as a corporate goal? If not, why do you think that managers focus on them? (LO18-1)

5. Percentage of Sales Models. Percentage of sales models usually assume that costs, fixed assets, and working capital all increase at the same rate as sales. When do you think that these assumptions do not make sense? Would you feel happier using a percentage of sales model for short-term or long-term planning? (LO18-2)

6. Relationships among Variables. Comebaq Computers is aiming to increase its market share by slashing the price of its new range of personal computers. Are costs and assets likely to increase or decrease as a proportion of sales? Explain. (LO18-2)

7. Balancing Items. What are the possible choices of balancing items when using a financial plan- ning model? Discuss whether some are generally preferable to others. (LO18-2)

8. Building Financial Models. How would Executive Fruit’s financial model change if the divi- dend payout ratio were cut to 1/3? Use the revised model to generate a new financial plan for 2015 assuming that debt is the balancing item. Show how the financial statements given in Table 18.6 would change. What would be required external financing? (LO18-2)

9. Percentage of Sales Models. Here are the abbreviated financial statements for Planner’s Peanuts:

INCOME STATEMENT, 2015

Sales $2,000 Cost 1,500 Net income $ 500

BALANCE SHEET, YEAR-END

2014 2015 2014 2015

Assets $2,500 $3,000 Debt $ 833 $1,000 Equity 1,667 2,000

Total $2,500 $3,000 Total $2,500 $3,000

If sales increase by 20% in 2016 and the company uses a strict percentage of sales planning model (meaning that all items on the income and balance sheet also increase by 20%), what must be the balancing item? What will be its value? (LO18-2)

10. Building Financial Models. The following tables contain financial statements for Dynastat- ics Corporation. Although the company has not been growing, it now plans to expand and will increase net fixed assets (that is, assets net of depreciation) by $200,000 per year for the next 5 years, and it forecasts that the ratio of revenues to total assets will remain at 1.50. Annual depre- ciation is 10% of net fixed assets at the beginning of the year. Fixed costs are expected to remain at $56,000 and variable costs at 80% of revenue. The company’s policy is to pay out two-thirds of net income as dividends and to maintain a book debt ratio of 25% of total capital. (LO18-2)

finance

®

Templates can be found in Connect.

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Chapter 18 Long-Term Financial Planning 539

a. Find Eagle’s required external funds if it maintains a dividend payout ratio of 70% and plans a growth rate of 15% in 2016.

b. If Eagle chooses not to issue new shares of stock, what variable must be the balancing item? What will its value be?

c. Now suppose that the firm plans instead to increase long-term debt only to $1,100 and does not wish to issue any new shares of stock. Why must the dividend payment now be the bal- ancing item? What will its value be?

a. Produce a set of financial statements for 2016. Assume that net working capital will equal 50% of fixed assets.

b. Now assume that the balancing item is debt and that no equity is to be issued. Prepare a completed pro forma balance sheet for 2016. What is the projected debt ratio for 2016?

11. Using Percentage of Sales. Eagle Sports Supply has the following financial statements. Assume that Eagle’s assets are proportional to its sales. (LO18-2)

INCOME STATEMENT, 2015 (Figures in $ thousands)

Revenue $1,800 Fixed costs 56 Variable costs (80% of revenue) 1,440 Depreciation 80 Interest (8% of beginning-of-year debt) 24 Taxable income 200 Taxes (at 40%) 80 Net income $ 120 Dividends $80 Addition to retained earnings $40

BALANCE SHEET, YEAR-END (Figures in $ thousands)

2015

Assets Net working capital $ 400 Fixed assets 800 Total assets $1,200 Liabilities and shareholders’ equity Debt $ 300 Equity 900 Total liabilities and

shareholders’ equity $1,200

INCOME STATEMENT, 2015

Sales $950 Costs 250 Interest 50 Taxes 150 Net income $500

BALANCE SHEET, YEAR-END

2014 2015 2014 2015

Assets $2,700 $3,000 Debt $ 900 $1,000 Equity 1,800 2,000

Total $2,700 $3,000 Total $2,700 $3,000

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540 Part Six Financial Analysis and Planning

12. Feasible Growth Rates. (LO18-3)

a. What is the internal growth rate of Eagle Sports (see Problem 11) if the dividend payout ratio is fixed at 70% and the equity-to-asset ratio is fixed at 2/3?

b. What is the sustainable growth rate?

13. Growth Rates. Find the sustainable and internal growth rates for a firm with the following ratios: asset turnover  =  1.40; profit margin  =  5%; payout ratio  =  25%; equity/assets  =  .60. (LO18-3)

14. Required External Financing. If Planner’s Peanuts dividend payout ratio in Problem 9 is fixed at 50%, calculate the required total external financing for growth rates in 2016 of 15%, 20%, and 25%. (LO18-3)

15. Feasible Growth Rates. What is the maximum possible growth rate for Planner’s Peanuts (see Problem 9) if the payout ratio remains at 50% and: (LO18-3)

a. No external debt or equity is to be issued? b. The firm maintains a fixed debt ratio but issues no equity?

16. Required External Financing. Executive Fruit’s financial manager believes that sales in 2015 could rise by as much as 20% or by as little as 5%. (LO18-3)

a. Recalculate the first-stage pro forma financial statements ( Table 18.5 ) under these two assump- tions. How does the rate of growth in revenues affect the firm’s need for external funds?

b. Assume any required external funds will be raised by issuing long-term debt and that any surplus funds will be used to retire such debt. Prepare the completed (second-stage) pro forma balance sheet.

17. Sustainable Growth. Plank’s Plants had net income of $2,000 on sales of $50,000 last year. The firm paid a dividend of $500. Total assets were $100,000, of which $40,000 was financed by debt. (LO18-3)

a. What is the firm’s sustainable growth rate? b. If the firm grows at its sustainable growth rate, how much debt will be issued next year? c. What would be the maximum possible growth rate if the firm did not issue any debt

next year?

18. Sustainable Growth. A firm has decided that its optimal capital structure is 100% equity- financed. It perceives its optimal dividend policy to be a 40% payout ratio. Asset turnover is sales/assets  =  .8, the profit margin is 10%, and the firm has a target growth rate of 5%. (LO18-3)

a. Is the firm’s target growth rate consistent with its other goals? b. If not, by how much does it need to increase asset turnover to achieve its goals? c. How much would it need to increase the profit margin instead?

19. Internal Growth. Go-Go Industries is growing at 30% per year. It is all-equity-financed and has total assets of $1 million. Its return on equity is 25%. Its plowback ratio is 40%. (LO18-3)

a. What is the internal growth rate? b. What is the firm’s need for external financing this year? c. By how much would the firm increase its internal growth rate if it reduced its payout ratio

to zero? d. By how much would such a move reduce the need for external financing? What do you

conclude about the relationship between dividend policy and requirements for external financing?

20. Sustainable Growth. A firm’s profit margin is 10%, and its asset turnover ratio is .6. It has no debt, has net income of $10 per share, and pays dividends of $4 per share. What is the sustain- able growth rate? (LO18-3)

21. Internal Growth. An all-equity-financed firm plans to grow at an annual rate of at least 10%. Its return on equity is 18%. What is the maximum possible dividend payout rate the firm can maintain without resorting to additional equity issues? (LO18-3)

22. Internal Growth. Suppose the firm in the previous question has a debt-equity ratio of 1/3. What is the maximum dividend payout ratio it can maintain without resorting to any external financing? (LO18-3)

23. Internal Growth. A firm has an asset turnover ratio of 2.0. Its plowback ratio is 50%, and it is all-equity-financed. What must its profit margin be if it wishes to finance 10% growth using only internally generated funds? (LO18-3)

Templates can be found in Connect.

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Chapter 18 Long-Term Financial Planning 541

24. Internal Growth. If the profit margin of the firm in the previous problem is 6%, what is the maximum payout ratio that will allow it to grow at 8% without resorting to external financing? (LO18-3)

25. Internal Growth. If the profit margin of the firm in Problem 23 is 6%, what is the maximum possible growth rate that can be sustained without external financing? (LO18-3)

CHALLENGE PROBLEMS 26. Spreadsheet Problem. Use Spreadsheet 18.1 to answer the following questions about Execu-

tive Fruit. (LO18-2)

a. What would be the required external financing if the growth rate is 15% and the dividend payout ratio is 60%?

b. Given the assumptions in part (a), what would be the amount of debt and equity issued if the firm wants to maintain its debt-equity ratio at a level of 2/3?

c. What formulas would you put in cells H20 and H21 (as well as the corresponding cells in columns F and G) of Spreadsheet 18.1 to maintain the debt-equity ratio at 2/3 while forcing the balance sheet to balance (that is, forcing debt  +  equity  =  total assets)?

27. Using Percentage of Sales. The 2015 financial statements for Growth Industries are presented below. Sales and costs in 2016 are projected to be 20% higher than in 2015. Both current assets and accounts payable are projected to rise in proportion to sales. The firm is currently operating at full capacity, so it plans to increase fixed assets in proportion to sales. What external financ- ing will be required by the firm? Interest expense in 2016 will equal 10% of long-term debt out- standing at the start of the year. The firm will maintain a dividend payout ratio of .40. (LO18-3)

Templates can be found in Connect.

INCOME STATEMENT, 2015

Sales $200,000 Costs 150,000 EBIT $ 50,000 Interest expense 10,000 Taxable income $ 40,000 Taxes (at 35%) 14,000 Net income $ 26,000 Dividends $10,400 Addition to retained earnings $15,600

BALANCE SHEET, YEAR-END, 2015

Assets Liabilities

Current assets Current liabilities Cash $ 3,000 Accounts payable $ 10,000 Accounts receivable 8,000 Total current liabilities $ 10,000 Inventories 29,000 Long-term debt 100,000 Total current assets $ 40,000 Stockholders’ equity Net plant and equipment 160,000 Common stock plus additional

paid-in capital 15,000 Retained earnings 75,000

Total assets $200,000 Total liabilities plus stockholders’ equity $200,000

28. Capacity Use and External Financing. Now suppose that the fixed assets of Growth Indus- tries (from the previous problem) are operating at only 75% of capacity. What is the required external financing over the next year? (LO18-3)

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542 Part Six Financial Analysis and Planning

29. Capacity Use and External Financing. If Growth Industries from Problem 27 is operating at only 75% of capacity, how much can sales grow before the firm will need to raise any external funds? Assume that once fixed assets are operating at capacity, they will need to grow thereafter in direct proportion to sales. (LO18-3)

30. Internal Growth. We will see in Chapter 19 that for many firms, cash and inventory needs may grow less than proportionally with sales. When we recognize this fact, will the firm’s internal growth rate be higher or lower than the level predicted by the following formula? (LO18-3)

Internal growth rate = reinvested earnings

assets

Templates can be found in Connect.

WEB EXERCISES 1. Log on to finance.yahoo.com, and compare Wendy’s International (WEN) and McDonald’s

(MCD) internal growth rates and sustainable growth rates by using recent annual data. (Note that the internal growth rate is calculated by using the earnings reinvested in the firm in the current year, not total retained earnings from the balance sheet.) Yahoo also shows the earnings growth that analysts are forecasting for each firm. Are the forecasts supported by the past per- formance of each firm?

2. Go to finance.yahoo.com . Find the (annual) balance sheet and income statement for American Electric Power (AEP). Suppose the company plans on 4% revenue growth over the next year. Under a percentage of sales approach, where assets and costs (except for depreciation) are pro- portional to sales, find AEP’s required external funding over the next year. Assume that it will maintain the same dividend payout ratio as in the current year and that its average tax rate will be the same next year as it was in the most recent year.

3. Log on to biz.yahoo.com, and click on Industries. The industry browser provides some finan- cial ratios for different sectors. What is the sustainable rate of growth for each sector if the firms maintain their plowback ratio and return on equity? ( Note: Although Yahoo does not report the plowback ratio, you can work it out from the P/E and dividend yield.) Do you think that those industries with a high return on equity can continue to earn such a high return on new investment?

SOLUTIONS TO SELF-TEST QUESTIONS 18.1 Total assets will rise to $2,200. The debt-equity ratio is to be maintained at 2/3. Therefore,

debt rises by $80 to $880, and equity rises by $120 to $1,320. Net income will be $220. (See Table 18.2 .) If the dividend is fixed at $180, reinvested earnings will be $40. Therefore, the firm needs to issue $120  -  $40  =  $80 of new equity and $80 of new debt.

18.2 a. The total amount of external financing is unchanged, since the dividend payout is unchanged. The $100,000 increase in total assets will now be financed by a mixture of debt and equity. If the debt-equity ratio is to remain at 2/3 , the firm will need to increase equity by $60,000 and debt by $40,000. Since reinvested earnings already increase shareholders’ equity by $36,000, the firm would issue an additional $24,000 of new equity and $40,000 of debt.

b. If dividends are reduced from $72,000 to $60,000, then required external funds fall by $12,000, from $64,000 to $52,000.

18.3 a. The company currently runs at 75% of capacity given the current level of fixed assets. Sales can increase until the company is at 100% of capacity; therefore, sales can increase to $60  million  ×  (100/75)  =  $80 million.

b. If sales were to increase by 50% to $90 million, new fixed assets would need to be added. The ratio of assets to sales when the company is operating at 100% of capacity [from part (a)] is $50  million/$80  million  =  5/8. Therefore, to support sales of $90 million, the com- pany needs at least $90  million  ×  5/8  =  $56.25 million of fixed assets. This calls for a $6.25 million investment in additional fixed assets.

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Chapter 18 Long-Term Financial Planning 543

18.4 a. This question is answered by the planning model. Given assumptions for asset growth, the model will show the need for external financing, and this value can be compared to the firm’s plans for such financing.

b. Such a relationship may be assumed and built into the model. However, the model does not help to determine whether it is a reasonable assumption.

c. Financial models do not shed light on the best capital structure. They can tell us only whether contemplated financing decisions are consistent with asset growth.

18.5 a. The equity-to-asset ratio is .8. If the payout ratio were reduced to 25%, the maximum growth rate assuming no external financing would be .75  ×  18%  ×  .8  =  10.8%.

b. If the firm also can issue enough debt to maintain its equity-to-asset ratio unchanged, the sustainable growth rate will be .75  ×  18%  =  13.5%.

MINICASE Garnett Jackson, the founder and CEO of Tech Tune-Ups, stared out the window as he finished his customary peanut butter and jelly sandwich, contemplating the dilemma currently facing his firm. Tech Tune-Ups is a start-up firm, offering a wide range of computer services to its clients, including online technical assis- tance, remote maintenance and backup of client computers through the Internet, and virus prevention and recovery. The firm has been highly successful in the 2 years since it was founded; its reputa- tion for fair pricing and good service is spreading, and Mr. Jackson believes the firm is in a good position to expand its customer base rapidly. But he is not sure that the firm has the financing in place to support that rapid growth.

Tech Tune-Ups’ main capital investments are its own powerful computers, and its major operating expense is salary for its consul- tants. To a reasonably good approximation, both of these factors grow in proportion to the number of clients the firm serves.

Currently, the firm is a privately held corporation. Mr. Jackson and his partners, two classmates from his undergraduate days, have contributed $250,000 in equity capital, largely raised from their parents and other family members. The firm has a line of credit with a bank that allows it to borrow up to $400,000 at an interest rate of 8%. So far, the firm has used $200,000 of its credit line. If and when the firm reaches its borrowing limit, it will need to raise equity capital and will probably seek funding from a venture capi- tal firm. The firm is growing rapidly, requiring continual invest- ment in additional computers, and Mr. Jackson is concerned that it is approaching its borrowing limit faster than anticipated.

Mr. Jackson thumbs through past financial statements and esti- mates that each of the firm’s computers, costing $10,000, can sup- port revenues of $80,000 per year but that the salary and benefits paid to each consultant using one of the computers is $70,000. Sales revenue in 2014 was $1.2 million, and sales are expected to grow at a 20% annual rate in the next few years. The firm pays taxes at a rate of 35%. Its customers pay their bills with an average delay of 3 months, so accounts receivable at any time are usually around 25% of that year’s sales.

Mr. Jackson and his co-owners receive minimal formal salary from the firm, instead taking 70% of profits as a “dividend,” which accounts for a substantial portion of their personal incomes. The remainder of the profits are reinvested in the firm. If reinvested profits are not suffi- cient to support new purchases of computers, the firm borrows the required additional funds using its line of credit with the bank.

Mr. Jackson doesn’t think Tech Tune-Ups can raise venture funding until after 2016. He decides to develop a financial plan to determine whether the firm can sustain its growth plans using its line of credit and reinvested earnings until then. If not, he and his partners will have to consider scaling back their hoped-for rate of growth, negotiate with their bankers to increase the line of credit, or consider taking a smaller share of profits out of the firm until further financing can be arranged.

Mr. Jackson wiped the last piece of jelly from the keyboard and settled down to work.

Can you help Mr. Jackson develop a financial plan? Do you think his growth plan is feasible?

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544

Short-Term Financial Planning

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

19-1 Understand why the firm needs to invest in net working capital.

19-2 Show how long-term financing policy affects short-term financing requirements.

19-3 Trace a firm’s sources and uses of cash and evaluate its need for short-term borrowing.

19-4 Develop a short-term financing plan that meets the firm’s need for cash.

19-5 Identify several major sources of short-term financing.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

19 CHAPTE R

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545

M uch of this book is devoted to long-term financial decisions such as capital bud-geting and the choice of capital structure. These decisions are called long-term for two reasons.

First, they usually involve long-lived assets or liabilities.

Second, they are not easily reversed and thus may

commit the firm to a particular course of action for

several years.

Short-term financial decisions generally involve

short-lived assets and liabilities, and usually they are

easily reversed. Compare, for example, a 60-day bank

loan for $50 million with a $50 million issue of 20-year

bonds. The bank loan is clearly a short-term deci-

sion. The firm can repay it 2 months later and be right

back where it started. A firm might conceivably issue

a 20-year bond in January and retire it in March, but

it would be extremely inconvenient and expensive to

do so. In practice, such a bond issue is a long-term

decision, not only because of the bond’s 20-year

maturity but also because the decision to issue it

cannot be reversed on short notice.

A financial manager responsible for short-term

financial decisions does not have to look far into

the future. The decision to take the 60-day bank loan

could properly be based on cash-flow forecasts for

the next few months only. The bond issue decision

will normally reflect forecast cash requirements 5, 10,

or more years into the future.

Short-term financial decisions do not involve many

of the difficult conceptual issues encountered else-

where in this book. In a sense, short-term decisions

are easier than long-term decisions—but they are not

less important. A firm can identify extremely valuable

capital investment opportunities, find the precise

optimal debt ratio, follow the perfect dividend policy,

and yet founder because no one bothers to raise the

cash to pay this year’s bills. Hence the need for short-

term planning.

We start by showing how long-term financing deci-

sions, introduced in the previous chapter, affect the

firm’s short-term financial planning problem. Next

we review the components of working capital and

describe the cash conversion cycle that dictates the

types and amount of working capital a firm might

maintain. We demonstrate how financial managers

forecast month-by-month cash requirements or sur-

pluses and how they develop short-term financing

strategies. We conclude with an examination of vari-

ous sources of short-term finance.

Short-term financial planning ensures that you have enough cash on hand to pay the bills.

P A

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Fi

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P la

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546 Part Six Financial Analysis and Planning

19.1 Links between Long-Term and Short-Term Financing When you plan your personal finances, you have to choose which factors are central to your decision making and which are merely distractions. Often, this will depend on your time horizon. For example, at very long horizons such as for retirement planning, you don’t think too carefully about when you will need to purchase your next car. At shorter horizons, covering perhaps the next 3 to 5 years, specific big-ticket items such as that potential car purchase need to be accounted for explicitly. At the shortest hori- zons, your planning might involve details down to the balances you maintain in your checking account.

It is the same with firms. When formulating long-term financial plans such as those considered in the previous chapter, firms may plan year by year. They often will be content with rules of thumb that relate average levels of fixed and short-term assets to annual sales, and not worry so much about seasonal variations in these relation- ships. In such cases, the likelihood that accounts receivable rise as sales peak in the Christmas season would be a needless detail that would distract from more important strategic decisions. But these considerations become crucial when firms focus on their near-term needs for cash and working capital. Short-term financing issues are concep- tually easier than those involved in capital budgeting, but woe to the firm that takes them for granted.

Short-term financing needs are tied to the firm’s long-term decisions. For example, businesses require capital—that is, money invested in plant, machinery, inventories, accounts receivable, and all the other assets it takes to run a company efficiently. Typically, these assets are not purchased all at once but are obtained gradually over time as the firm grows. The total cost of these assets is called the firm’s total capital requirement.

Figure  19.1 illustrates the growth in the firm’s total capital requirements. The upward-sloping line shows that as the business grows, it is likely to need additional fixed assets and current assets. You can think of this trendline as showing the base level of capital that is required. In addition to this base capital requirement, there may be seasonal fluctuations in the business that require an additional investment in current assets. Thus the wavy line in the illustration shows that the total capital requirement peaks late in each year. In practice, there would also be week-to-week and month-to-month fluctuations in the capital requirement, but these are not shown in Figure 19.1 .

FIGURE 19.1 The firm’s total capital requirement grows over time. It also exhibits seasonal variation around the trend.

Seasonal component of required assets

December 2012 December 2013

To ta

l c ap

it al

r eq

u ir

em en

t

Time

The base level of fixed assets

and current assets

December 2014

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Chapter 19 Short-Term Financial Planning 547

The total capital requirement can be met through either long- or short-term financing. When long-term financing does not cover the total capital requirement, the firm must raise short-term capital to make up the difference. When long-term financing more than covers the total capital requirement, the firm has surplus cash available for short-term investment. Thus the difference between the long-term financing raised and the total capital requirement determines whether the firm is a short-term borrower or lender.

The three panels in Figure 19.2 illustrate this. Each depicts a different long-term financing strategy. The “relaxed strategy” in panel a implies a permanent short-term cash surplus. This surplus will be invested in marketable securities. The “restrictive” policy illustrated in panel c implies a permanent need for short-term borrowing. Finally, panel b illustrates an intermediate strategy: The firm has spare cash that it can lend out during the part of the year when total capital requirements are relatively low, but it is a borrower during the rest of the year when capital requirements are relatively high.

What is the best level of long-term financing relative to the total capital require- ment? It is hard to say. We can make several practical observations, however:

1. Matching maturities. When financial managers are asked the most important reason for choosing short-term rather than long-term debt, they generally say that they try

FIGURE 19.2 Alternative approaches to long- versus short-term financing: (a) relaxed strategy, where the firm is always a short-term lender; (b) middle-of-the-road policy; (c) restrictive policy, where the firm is always a short-term borrower Excess capital =

investment in cash and marketable securities

Long-term financing

Asset requirements

D o

lla rs

Time

(a)

Firm holds marketable securities

Firm is a short-term borrower in this region

D o

lla rs

Time

(b)

Short-term borrowing

D o

lla rs

Time

(c)

Long-term financing

Asset requirements

Long-term financing

Asset requirements

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548 Part Six Financial Analysis and Planning

4 L. Pinkowitz and R. Williamson, “The Market Value of Cash,” Journal of Applied Corporate Finance 19 (2007), pp. 74–81.

to “match” the maturities of the firm’s assets and liabilities. 1 That is, they finance long-lived assets like plant and machinery with long-term borrowing and equity. Short-term assets like inventory and accounts receivable are financed with short- term bank loans or by issuing short-term debt such as commercial paper.

2. Permanent working capital requirements. Most firms have a permanent investment in net working capital (current assets less current liabilities). By this we mean that they plan to have at all times a positive amount of working capital. This is financed from long-term sources. This is an extension of the maturity-matching principle. Since the working capital is permanent, it is funded with long-term sources of financing.

3. The advantages of liquidity. Current assets can be converted into cash more easily than can long-term assets. So firms with large holdings of current assets enjoy greater liquidity. Of course, some current assets are more liquid than others. Inventories are converted into cash only when the goods are produced, sold, and paid for. Receivables are more liquid; they become cash as customers pay their outstanding bills. Short-term securities can generally be sold if the firm needs cash on short notice and are therefore more liquid still.

Some firms choose to hold more liquidity than others. For example, many high-tech companies, such as Intel and Cisco, hold huge amounts of short-term securities. On the other hand, firms in old-line manufacturing industries—such as chemicals, paper, or steel—manage with a far smaller reservoir of liquidity. 2 Why is this? One reason is that companies with rapidly growing profits may generate cash faster than they can redeploy it in new positive-NPV investments. This produces a surplus of cash that can be invested in short-term securities.

There are some advantages to holding a large reservoir of cash, particularly for smaller firms that face relatively high costs to raise funds on short notice. For example, biotech firms require large amounts of cash if their drugs succeed in gaining regula- tory approval. Therefore, these firms generally have substantial cash holdings to fund their possible investment needs.

Financial managers of firms with a surplus of long-term financing and with cash in the bank don’t have to worry about finding the money to pay next month’s bills. They would feel more comfortable under the relaxed strategy illustrated in Figure  19.2 a than the restrictive strategy in panel c. But there are also costs to having surplus cash. Holdings of marketable securities are at best a zero-NPV investment for a taxpaying firm. 3 Also, managers of firms with large cash surpluses may be tempted to run a less tight ship. The box nearby describes how the fashion company L. A. Gear was able to use its cash to survive 6 years of large losses and to employ a variety of radical, though ultimately unsuccessful, strategies to stave off bankruptcy. For shareholders, it may be best for firms with excess cash to go on a diet and use the money to retire some of their long-term securities. Indeed, we saw in Chapter 17 that Apple reduced its cash mountain by starting to pay dividends and repurchasing its stock.

Pinkowitz and Williamson looked at the value that investors place on a firm’s cash and found that on average shareholders valued a dollar of cash at $1.20. 4 Investors

1 A survey by Graham and Harvey found that 63% of managers believed that maturity matching was the most important factor in their choice of debt maturity. See J. R. Graham and C. R. Harvey, “The Theory and Practice of Corporate Finance: Evidence from the Field,” Journal of Financial Economics 61 (2001) pp. 187–243. 2 Look back at Table 4.8. You can see that the firms in the computer and electronic industry are among those with the highest quick ratios. 3 Why do we say at best zero NPV? Not because we worry that the Treasury bills may be overpriced. Instead, we worry that when the firm holds Treasury bills, the interest income is subject to double taxation, first at the corporate level and then again at the personal level when the income is passed through to investors as dividends. The extra layer of taxation can make corporate holdings of Treasury bills a negative-NPV investment even if the bills would provide a fair rate of interest to an individual investor.

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Chapter 19 Short-Term Financial Planning 549

placed a particularly high value on liquidity in the case of firms with plenty of growth opportunities. At the other extreme, Pinkowitz and Williamson found that when a firm was likely to face financial distress, a dollar of cash within the firm was often worth less than a dollar to the shareholders.

19.2 Working Capital Much of short-term financial planning focuses on the variation in working capital. Short-term or current assets and liabilities such as cash, accounts receivable, invento- ries, and accounts payable vary considerably as firms move through a cycle in which raw materials are purchased, goods are produced and sold, and customers pay their bills. In order to plan for this variation, it is best to begin by considering the various compo- nents of working capital and the factors that determine the level of each component.

The Components of Working Capital Short-term, or current, assets and liabilities are collectively known as working capital. Table 19.1 gives a breakdown of current assets and liabilities for all manufacturing corporations in the United States in 2013. Total current assets were $2,356 billion, and total current liabilities were $1,714 billion.

Current Assets One important current asset is accounts receivable. Accounts receiv- able arise because companies do not usually expect customers to pay for their purchases immediately. These unpaid bills are a valuable asset that companies expect to be able to turn into cash in the near future. The bulk of accounts receivable consists of unpaid bills from sales to other companies and are known as trade credit. The remainder arises from the sale of goods to the final consumer. These are known as consumer credit.

Another important current asset is inventory. Inventories may consist of raw materi- als, work in process, or finished goods awaiting sale and shipment. Table 19.1 shows that firms in the United States have about the same amount invested in inventories as in accounts receivable.

The remaining current assets are cash and marketable securities. The cash consists partly of dollar bills, but most of the cash is in the form of bank deposits. These may be demand deposits (money in checking accounts that the firm can pay out immedi- ately) and time deposits (money in savings accounts that can be paid out only with a delay). The principal marketable security is commercial paper (short-term unsecured debt sold by other firms). Other securities include Treasury bills, which are short-term debts sold by the U.S. government, and state and local government securities. Large firms usually invest directly in these securities; smaller firms may invest through a money market mutual fund that holds a package of short-term securities.

In managing their cash, companies face much the same problem you do. There are always advantages to holding large amounts of ready cash—there is less risk of running

Current Assets Current Liabilities

Cash $ 336 Short-term loans $ 202 Marketable securities 175 Accounts payable 528 Accounts receivable 701 Accrued income taxes 35 Inventories 749 Current payments due on long-term debt 158 Other current assets 395 Other current liabilities 791 Total $2,356 Total $1,714

Notes: Net working capital (current assets − current liabilities) = $2,356 − $1,714 = $642 billion. Column sums subject to rounding error. Source: U.S. Department of Commerce, Quarterly Financial Report for Manufacturing, Mining and Trade Corporations, September 2013, www.census.gov/prod/www/abs/qfr-mm.html .

TABLE 19.1 Current assets and liabilities, U.S. manufacturing corporations, second quarter 2013 (figures in $ billions)

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550

out of cash and having to borrow more on short notice. On the other hand, there is a cost to holding idle cash balances rather than putting the money to work earning interest.

Now take a look at Figure 19.3 , which shows the relative importance of current assets in different industries. For example, current assets constitute over half of the total assets of aerospace companies, while they account for only 20% of the assets of oil companies. For some companies “current assets” means principally inventory; for others it means accounts receivable or cash and securities. For example, you can see that inventory accounts for the majority of the current assets of retail firms, receivables are more important for oil companies, and cash and short-term securities make up the bulk of the current assets of computer and electronic companies.

Current Liabilities We have seen that a typical company’s principal current asset consists of unpaid bills. One firm’s credit must be another’s debit. Therefore, it is not surprising that a company’s principal current liability generally consists of accounts payable —that is, outstanding payments due to other companies.

Finance in Practice The Rise and Fall of L. A. Gear The second table shows L. A. Gear’s capital structure.

Notice that after 1991 the company had almost no short-term bank debt, so that it was largely free from the discipline that is exerted whenever a company has to approach its bank for a loan to be renewed. As losses cumulated, common equity dwindled and the debt ratio climbed to 92%. Yet even in 1996 the company’s cash holdings were over eight times that year’s interest payments.

Because the company could liquidate its inventories and receivables and had no maturing debt, it was able to survive 6 years of large losses and to try a variety of radical new strategies, including a new emphasis on performance ath- letic shoes and then on children’s shoes. All these strategies were ultimately unsuccessful. A company with large fi xed assets that are not so easily liquidated would have found it less easy to survive so long.

Source: Data from H. DeAngelo, L. DeAngelo, and K. H. Wruck, “Asset Liquidity, Debt Covenants, and Managerial Discretion in Financial Distress: The Collapse of L. A. Gear,” Journal of Financial Economics 64 (April 2002), pp. 3–34.

Fashion company L. A. Gear was one of the stars of the 1980s. Teenie boppers loved its pink sequined sneakers and its silver and gold lamé workout shoes. Investors preferred the 1300% growth in the company’s stock price in the space of 4 years. But as the company failed to react to changes in fashion during the 1990s, sales and profi ts fell away rapidly. In January 1998 L. A. Gear fi led for Chapter 11 bankruptcy. The decline of L. A. Gear illustrates how a company’s liquid assets can provide the fi nancial slack that allows it to evade market discipline and survive repeated losses.

The fi rst table below summarizes the changes in L. A. Gear’s profi tability and its assets. The fi rst two rows of the table show that after 1990 L. A. Gear’s sales declined sharply and the fi rm produced losses for the rest of its life. The remaining rows show the company’s assets. Since L. A. Gear farmed out shoe and clothing production, it had few fi xed assets and owned largely cash, receivables, and inventory. As sales declined, two things happened. First, the company was able to reduce its inventory of fi nished goods. Second, customers paid off their outstanding bills. Thus, despite mak- ing steady losses, the company’s holdings of cash and short- term securities initially increased.

Sales, Income, and Assets of L. A. Gear 1989–1996 (fi gures in $ millions)

1989 1990 1991 1992 1993 1994 1995 1996

Sales 617 820 619 430 398 416 297 196 Net income 55 31 −66 −72 −33 −22 −51 −62 Cash & securities 0 3 1 84 28 50 36 34 Receivables 101 156 112 56 73 77 47 24 Inventory 140 161 141 62 110 58 52 33 Current assets 257 338 297 230 220 194 138 93

1989 1990 1991 1992 1993 1994 1995 1996

Bank debt 37 94 20 0 4 1 1 0 Long-term debt 0 0 0 0 50 50 50 50 Preferred stock 0 0 100 100 100 100 108 116 Common equity 168 206 132 88 47 18 −41 −111

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Chapter 19 Short-Term Financial Planning 551

The other major current liability consists of short-term borrowing. We will have more to say about this later in the chapter.

Working Capital and the Cash Conversion Cycle The difference between current assets and current liabilities is known as net working capital, but financial managers often refer to the difference simply (but imprecisely) as working capital. Usually current assets exceed current liabilities—that is, firms have positive net working capital. For U.S. manufacturing companies, current assets are on average about 40% higher than current liabilities.

To see why firms need net working capital, imagine a small company, Simple Sou- venirs, that makes small novelty items for sale at gift shops. It buys raw materials such as leather, beads, and rhinestones for cash, processes them into finished goods such as wallets or costume jewelry, and then sells these goods on credit. Figure 19.4 shows the whole cycle of operations.

If you prepare the firm’s balance sheet at the beginning of the process, you see cash (a current asset). If you delay a little, you find the cash replaced first by inventories

net working capital Current assets minus current liabilities. Often called working capital.

FIGURE 19.3 Current assets as a percentage of total assets in different industries

0

10

20

30

40

50

60

Ae ro

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Inventories

Accounts receivable

Cash & securities

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Industry

Source: U.S. Department of Commerce, Quarterly Financial Report for Manufacturing, Mining and Trade Corpora- tions, September 2013, www.census.gov/prod/www/abs/qfr-mm.html .

FIGURE 19.4 Simple cycle of operations

Finished goods inventory

Receivables Raw materials

inventory

Cash

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552 Part Six Financial Analysis and Planning

of raw materials and then by inventories of finished goods (also current assets). When the goods are sold, the inventories give way to accounts receivable (another current asset), and finally, when the customers pay their bills, the firm takes out its profit and replenishes the cash balance.

The components of working capital constantly change with the cycle of operations, but the amount of working capital is fixed. This is one reason why net working capital is a useful summary measure of current assets or liabilities.

Figure 19.5 depicts four key dates in the production cycle that influence the firm’s investment in working capital. The firm starts the cycle by purchasing raw materials, but it does not pay for them immediately. This delay is the accounts payable period. The firm processes the raw material and then sells the finished goods. The delay between the initial investment in inventories and the sale date is the inventory period. Some time after the firm has sold the goods, its customers pay their bills. The delay between the date of sale and the date at which the firm is paid is the accounts receiv- able period.

The top part of Figure 19.5 shows that the total delay between initial purchase of raw materials and ultimate payments from customers is the sum of the inventory and accounts receivable periods: First the raw materials must be purchased, processed, and sold, and then the bills must be collected. However, the net time that the company is out of cash is reduced by the time it takes to pay its own bills. The length of time between the firm’s payment for its raw materials and the collection of payment from the customer is known as the firm’s cash conversion cycle. To summarize,

Cash conversion cycle = (inventory period + receivables period)

- accounts payable period

The longer the production process, the more cash the firm must keep tied up in inventories. Similarly, the longer it takes customers to pay their bills, the higher the value of accounts receivable. On the other hand, if a firm can delay paying for its own materials, it may reduce the amount of cash it needs. In other words, accounts payable reduce net working capital.

In Chapter 4 we showed you how the firm’s financial statements can be used to estimate the inventory period, also called days’ sales in inventory:

Inventory period = inventory

annual cost of goods sold/365

The denominator in this equation is the firm’s daily output. The ratio of inventory to daily output measures the average number of days from the purchase of the inventories to the final sale.

cash conversion cycle Period between firm’s payment for materials and collection on its sales.

FIGURE 19.5 Cash conversion cycle

Raw materials purchased

Payment for raw materials

Sale of finished goods

Cash collected on sales

Accounts receivable

period

Accounts payable period

Inventory period

Cash conversion cycle

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Chapter 19 Short-Term Financial Planning 553

We can estimate the accounts receivable period and the accounts payable period in a similar way: 5

Accounts receivable period = accounts receivable

annual sales/365

Accounts payable period = accounts payable

annual cost of goods sold/365

Of course, the cash conversion cycle is much shorter in some businesses than in others. For example, look at Table 19.2 , which shows the average length of the cycle for the sample of industries that we looked at earlier.

5 Because inventories are valued at cost, we divide inventory levels by cost of goods sold rather than sales rev- enue to obtain the inventory period. This way, both numerator and denominator are measured by cost. The same reasoning applies to the accounts payable period. On the other hand, because accounts receivable are valued at product price, we divide average receivables by daily sales revenue to find the receivables period.

Example 19.1 Cash Conversion Cycle The following table provides the information necessary to compute the cash con- version cycle for manufacturing firms in the United States in mid-2013. We can use the table to answer four questions: How long on average does it take U.S. manu- facturing firms to produce and sell their product? How long does it take to collect bills? How long does it take to pay bills? And what is the cash conversion cycle?

These data can be used to calculate the cash conversion cycle for U.S. manufacturing firms in 2013 (figures in $ billions)

Income Statement Data Balance Sheet Data

Sales $6,660 Inventory $749 Cost of goods sold 6,120 Accounts receivable 701 Accounts payable 528

Note: Cost of goods sold includes selling, general, and administrative expenses. Source: U.S. Department of Commerce, Quarterly Financial Report for Manufacturing, Mining and Trade Corporations, September 2013, Tables 1.0 and 1.1.

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Cash conversion cycle

Industry Inventory

Period

Accounts Receivable

Period

Accounts Payable Period

Cash Conversion

Cycle

Food 40.7 29.1 24.4 45.4 Paper 40.6 40.0 32.5 48.0 Oil/coal 14.0 22.7 22.8 13.9 Chemicals 49.6 47.9 35.9 61.6 Pharmaceuticals 57.8 51.2 35.7 73.2 Iron/steel 57.2 39.5 32.6 64.1 Computers & electronics 35.9 44.1 33.7 46.3 Aerospace 148.0 50.9 34.1 164.8 Motor vehicles 24.9 25.8 40.2 10.5 Retail 39.7 8.2 25.8 22.2 Clothing 50.8 3.3 28.9 25.2 Broadcasting 43.0 62.9 17.6 88.4

Source: U.S. Department of Commerce, Quarterly Financial Report for Manufacturing, Mining and Trade Corporations, September 2013, www.census.gov/prod/www/abs/qfr-mm.html .

TABLE 19.2 Average cash conversion cycle (days) for selected industries, 2013

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554 Part Six Financial Analysis and Planning

The delays in collecting cash are given by the inventory and receivables periods. The delay in paying bills is given by the payables period. The net delay in collecting payments is the cash conversion cycle. We calculate these periods as follows:

Inventory period = inventory

annual cost of goods sold/365

= 749

6,120/365 = 44.7 days

Receivables period = accounts receivable

annual sales/365

= 701

6,660/365 = 38.4 days

Payables period = accounts payable

annual cost of goods sold/365

= 528

6,120/365 = 31.5 days

The cash conversion cycle is

Inventory period + receivables period - payables period

= 44.7 + 38.4 - 31.5 = 51.6 days

It is therefore taking U.S. manufacturing companies an average of just over 7 weeks from the time they lay out money on inventories to collect payment from their customers.

a. Would you expect Tiffany, which sells fine jewelry, or Target, which sells a wide range of household goods at attractive prices, to have the higher cash conversion cycle? Why?

b. Use the following data to calculate the cash conversion cycle of each firm (all values are in millions of dollars). What factor has the greatest impact on the difference in their conversion cycles?

Self-Test 19.1

Tiffany Target

Sales 3,794 73,301 Cost of goods sold 1,631 50,568 Inventories 2,234 7,903 Accounts receivable 254 5,841 Accounts payable 326 11,037

The Working Capital Trade-Off Of course the cash conversion cycle is not cast in stone. To a large extent it is within management’s control. Working capital can be managed. For example, accounts receivable are affected by the terms of credit the firm offers to its customers. You can cut the amount of money tied up in receivables by getting tough with customers who are slow in paying their bills. (You may find, however, that in the future they take their business elsewhere.) Similarly, the firm can reduce its investment in inventories of raw

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Chapter 19 Short-Term Financial Planning 555

materials. (Here the risk is that it may one day run out of inventories and production will grind to a halt.)

These considerations show that investment in working capital has both costs and benefits. For example, the cost of the firm’s investment in receivables is the interest that could have been earned if customers had paid their bills earlier. The firm also forgoes interest income when it holds idle cash balances rather than putting the money to work in marketable securities. The cost of holding inventory includes not only the opportunity cost of capital but also storage and insurance costs and the risk of spoilage or obsoles- cence. All of these carrying costs encourage firms to hold current assets to a minimum.

While carrying costs discourage large investments in current assets, a low level of current assets makes it more likely that the firm will face shortage costs. For example, if the firm runs out of inventory of raw materials, it may have to shut down produc- tion. Similarly, a producer holding a small finished goods inventory is more likely to be caught short, unable to fill orders promptly. There are also disadvantages to holding small “inventories” of cash. If the firm runs out of cash, it may have to sell securities and incur unnecessary trading costs. The firm may also maintain too low a level of accounts receivable. If the firm tries to minimize accounts receivable by restricting credit sales, it may lose customers. An important job of the financial manager is to strike a bal- ance between the costs and benefits of current assets, that is, to find the level of current assets that minimizes the sum of carrying costs and shortage costs.

In Chapter 4 we pointed out that when managers review the performance of each part of their business, they often deduct the cost of the capital employed from its prof- its. This measure is known as residual income or economic value added (EVA), which is the term coined by the consulting firm Stern Stewart. Firms that employ EVA to measure performance have often discovered that they can make large savings on work- ing capital. Herman Miller Corporation, the furniture manufacturer, found that after it introduced EVA, employees became much more conscious of the cash tied up in inventories. One sewing machine operator commented:

We used to have these stacks of fabric sitting here on the tables until we needed them. . . . We were going to use the fabric anyway, so who cares that we’re buying it and stacking it up there? Now no one has excess fabric. They only have stuff we’re working on today. And it’s changed the way we connect with suppliers, and we’re having [them] deliver fabric more often. 6

The company also started to look at how rapidly customers paid their bills. It found that any time an item was missing from an order, the customer would delay payment until all the pieces had been delivered. When the company cleared up the problem of missing items, it made its customers happier and it collected the cash faster. 7

We will look more carefully at the costs and benefits of working capital in the next two chapters.

carrying costs Costs of maintaining current assets, including opportunity cost of capital.

shortage costs Costs incurred from shortages in current assets.

6 A. Ehrbar, EVA: The Real Key to Creating Wealth (New York: John Wiley & Sons, 1998), pp. 130–131. 7 A. Ehrbar and G. Bennett Stewart III, “The EVA Revolution,” Journal of Applied Corporate Finance 12 ( Summer 1999), pp. 18–31.

How will the following affect the size of the firm’s optimal investment in current assets?

a. The interest rate rises from 6% to 8%. b. A just-in-time inventory system is introduced that reduces the risk of

inventory shortages. c. Customers pressure the firm for a more lenient credit sales policy.

Self-Test 19.2

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556 Part Six Financial Analysis and Planning

19.3 Tracing Changes in Cash and Working Capital Table 19.3 compares 2013 and 2014 year-end balance sheets for Dynamic Mattress Company. Table 19.4 shows the firm’s income statement for 2014. Note that Dynam- ic’s cash balance increased from $4 million to $5 million in 2014. What caused this increase? Did the extra cash come from Dynamic Mattress Company’s additional long-term borrowing? From reinvested earnings? From cash released by reducing inventory? Or perhaps it came from extra credit extended by Dynamic’s suppliers. (Note the increase in accounts payable.)

The correct answer? All of the above. There is rarely any point in linking a particu- lar source of funds with a particular use. Instead, as we saw in Chapter 3, financial analysts trace the sources and uses of cash in the statement of cash flows like the one shown in Table  19.5 . The positive entries in that table correspond to activities that generated cash and the negative ones to activities that absorbed cash. So we see that Dynamic generated cash through the following means:

1. By far, the biggest cash generator was Dynamic’s operations. Net income was $12 million, but that entry understates the cash flow from operations because it reflected a $4 million charge for depreciation. Remember, depreciation is not a cash outlay, so it must be added back when computing operating cash flow.

2. Dynamic reduced inventory, which freed up $1 million of cash. 3. It also increased accounts payable, in effect borrowing $7 million from its suppliers. 4. Finally, Dynamic issued $7 million of long-term debt.

Dynamic used cash for the following purposes:

1. It allowed accounts receivable to expand by $5 million, in effect lending this amount to its customers.

Assets 2013 2014 Liabilities and Shareholders’ Equity 2013 2014

Current assets Current liabilities Cash $ 4 $ 5 Bank loans $ 5 $ 0 Marketable securities 0 5 Accounts payable 20 27 Inventory 26 25 Total current liabilities $25 $ 27 Accounts receivable 25 30 Long-term debt 5 12 Total current assets $55 $ 65 Net worth (equity and retained earnings) 65 76 Fixed assets Total liabilities and owners’ equity $95 $115 Gross investment $56 $ 70 Less depreciation 16 20 Net fi xed assets $40 $ 50 Total assets $95 $115

TABLE 19.3 Year-end balance sheets for Dynamic Mattress Company (figures in $ millions)

Sales $350 Operating costs 321 Depreciation 4 EBIT 25 Interest 1 Pretax income 24 Tax at 50% 12 Net income $ 12

Note: Dividend = $1  million; reinvested earnings = $11  million.

TABLE 19.4 2014 income statement for Dynamic Mattress Company (figures in $ millions)

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Dynamic Mattress

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Chapter 19 Short-Term Financial Planning 557

2. It invested $14 million in fixed assets. This shows up as the increase in gross fixed assets in the balance sheet in Table 19.3 .

3. It paid a $1 million dividend. (Note: The $11 million increase in Dynamic’s equity is due to reinvested earnings: $12 million of net income less the $1 million dividend.)

4. It purchased $5 million of marketable securities. 5. It repaid a $5 million bank loan.

Cash fl ows from operating activities: Net income $ 12.0 Depreciation 4.0 Decrease (increase) in accounts receivable −5.0 Decrease (increase) in inventories 1.0 Increase (decrease) in accounts payable 7.0 Net cash fl ow from operating activities $ 19.0 Cash fl ows from investing activities: Investment in fi xed assets −$14.0 Cash fl ows from fi nancing activities: Dividends −$1.0 Sale (purchase) of marketable securities −5.0 Increase (decrease) in long-term debt 7.0 Increase (decrease) in bank loans −5.0 Net cash fl ow from fi nancing activities −$4.0 Increase in cash balance $ 1.0

TABLE 19.5 2014 statement of cash flows for Dynamic Mattress Company (figures in $ millions)

How will the following affect cash and net working capital?

a. The firm takes out a short-term bank loan and uses the funds to pay off some of its accounts payable.

b. The firm uses cash on hand to buy raw materials. c. The firm repurchases outstanding shares of stock. d. The firm sells long-term bonds and puts the proceeds in its bank account.

Self-Test 19.3

19.4 Cash Budgeting The financial manager’s task is to forecast future sources and uses of cash. These fore- casts serve two purposes. First, they alert the financial manager to future cash needs. Second, the cash-flow forecasts provide a standard, or budget, against which subse- quent performance can be judged.

There are several ways to produce a quarterly cash budget. Many large firms have developed elaborate “corporate models”; others use a spreadsheet program to plan their cash needs. The procedures of smaller firms may be less formal. But no matter what method is chosen, there are three common steps to preparing a cash budget:

Step 1. Forecast the sources of cash. The largest inflow of cash comes from pay- ments by the firm’s customers.

Step 2. Forecast uses of cash. Step 3. Calculate whether the firm is facing a cash shortage or surplus.

The financial plan sets out a strategy for investing cash surpluses or financing any deficit. We will illustrate these issues by continuing the example of Dynamic Mattress.

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558 Part Six Financial Analysis and Planning

But unless customers pay cash on delivery, sales become accounts receivable before they become cash. Cash flow comes from collections on accounts receivable.

Most firms keep track of the average time it takes customers to pay their bills. From this they can forecast what proportion of a quarter’s sales is likely to be converted into cash in that quarter and what proportion is likely to be carried over to the next quarter as accounts receivable. This proportion depends on the lags with which customers pay their bills. For example, if customers wait 1 month to pay their bills, then on average one-third of each quarter’s bills will not be paid until the following quarter. If the payment delay is 2 months, then two-thirds of quarterly sales will be collected in the following quarter.

Forecast Sources of Cash Most of Dynamic’s cash inflow comes from the sale of mattresses. We therefore start with a sales forecast by quarter for 2015: 8

8 For simplicity, we present a quarterly forecast. However, most firms would forecast by month instead of by quarter. Sometimes weekly or even daily forecasts are made.

Quarter: First Second Third Fourth

Sales ($ millions) 87.5 78.5 116 131

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

A. Accounts receivable Receivables (beginning of period)

Sales

Collections

On sales in current period (80%)

On sales in previous period (20%)a

Total collections

Receivables (end of period) = rows 4+5–9

B. Cash budget Sources of cash Collections of accounts receivable (row 9)

Other

Total collections

Uses of cash Payments of accounts payable

Labor & other expenses

Capital expenses

Taxes, interest, and dividends

Total uses

Net cash inflow = sources – uses

C. Short-term financing requirements Cash at start of period

+ Net cash inflow (from row 24)

= Cash at end of periodb

Minimum operating balance

Cumulative financing requiredc (row 30–29)

30.0

87.5

70.0

15.0

85.0

32.5

85.0

1.5

86.5

65.0

30.0

32.5

4.0

131.5

–45.0

5.0

–45.0

–40.0

5.0

45.0

Quarter: First

B

32.5

78.5

62.8

17.5

80.3

30.7

80.3

0.0

80.3

60.0

30.0

1.3

4.0

95.3

–15.0

–40.0

–15.0

–55.0

5.0

60.0

Second

C

30.7

116.0

92.8

15.7

108.5

38.2

108.5

12.5

121.0

55.0

30.0

5.5

4.5

95.0

26.0

–55.0

26.0

–29.0

5.0

34.0

Third

D

38.2

131.0

104.8

23.2

128.0

41.2

128.0

0.0

128.0

50.0

30.0

8.0

5.0

93.0

35.0

–29.0

35.0

6.0

5.0

–1.0

Fourth

EASPREADSHEET 19.1 Dynamic Mattress’s cash budget for 2015 (figures in $ millions)

You can find this spreadsheet in Connect.

a Sales in the fourth quarter of the previous year were $75 million. b Firms cannot literally hold a negative amount of cash. This line shows the amount of cash the fi rm will have to raise to pay its bills. c A negative sign indicates that no short-term fi nancing is required. Instead the fi rm has a cash surplus.

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Chapter 19 Short-Term Financial Planning 559

Suppose that 80% of sales are collected in the immediate quarter and the remaining 20% in the next. Panel A of Spreadsheet 19.1 shows forecast collections under this assumption.

In the first quarter, for example, collections from current sales are 80% of $87.5 million, or $70 million. But the firm also collects 20% of the previous quarter’s sales, or .20 × $75  million = $15  million. Therefore, total collections are $70  million + $15  million = $85  million.

Dynamic started the first quarter with $30 million of accounts receivable. The quarter’s sales of $87.5 million were added to accounts receivable, but $85 million of collections were subtracted. Therefore, as Spreadsheet 19.1 shows, Dynamic ended the quarter with accounts receivable of $30  million + $87.5  million − $85  million = $32.5  million. The general formula is

Ending accounts receivable = beginning accounts receivable + sales - collections

Panel B of Spreadsheet 19.1 shows forecast sources and uses of cash for Dynamic Mattress. Collection of receivables is the main source, but it is not the only one. Per- haps the firm plans to dispose of some land or expects a tax refund or payment of an insurance claim. All such items are included as “other” sources. It is also possible that the firm may raise additional capital by borrowing or selling stock, but we don’t want to prejudge that question. Therefore, for the moment we just assume that Dynamic will not raise further long-term finance.

Forecast Uses of Cash There always seem to be many more uses for cash than there are sources. Panel B of Spreadsheet 19.1 shows how Dynamic expects to use cash. For simplicity, we con- dense the uses into four categories:

1. Payments of accounts payable. Dynamic has to pay its bills for raw materials, parts, electricity, and so on. The cash-flow forecast assumes all these bills are paid on time, although Dynamic could probably delay payment to some extent. Delayed payment is sometimes called stretching your payables. Stretching is one source of short-term financing, but for most firms it is an expensive source, because by stretching they lose discounts given to firms that pay promptly. (This is discussed in more detail in Chapter 20.)

2. Labor, administrative, and other expenses. This category includes all other regular business expenses.

3. Capital expenditures. Note that Dynamic Mattress plans a major outlay of cash in the first quarter to pay for a long-lived asset.

4. Taxes, interest, and dividend payments. This includes interest on currently outstanding long-term debt and dividend payments to stockholders.

The forecast net inflow of cash (sources minus uses) is shown in row 24. Note the large negative figure for the first quarter: a $45 million forecast outflow. There is a smaller forecast outflow in the second quarter and then substantial cash inflows in the second half of the year.

The Cash Balance So far, Dynamic Mattress does not know how much it will have to borrow or, for that matter, if it will have to borrow at all. These calculations are presented in panel C, which shows how much financing Dynamic will have to raise if its cash-flow forecasts are right. It starts the year with $5 million in cash. There is a $45 million cash outflow in the first quarter, which in the absence of external financing would create a $40 million cash shortfall at the end of the period (row 29). This deficit is carried to the beginning of the next quarter (cell C27). At the very least, Dynamic must obtain $40 million of additional financing just to cover the forecast cash deficit. This would leave the firm with a forecast cash balance of exactly zero at the start of the second quarter.

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560 Part Six Financial Analysis and Planning

Calculate Dynamic Mattress’s quarterly cash receipts, net cash inflow, and cumulative short-term financing required if customers pay for only 60% of pur- chases in the current quarter and pay the remaining 40% in the following quarter.

Self-Test 19.4

However, most financial managers would regard a planned cash balance of zero as driving too close to the edge of the cliff. They establish a minimum operating cash balance to absorb unexpected cash inflows and outflows. We assume in Spreadsheet 19.1 that Dynamic’s minimum operating cash balance is $5 million. That means it has to raise $45 million instead of $40 million in the first quarter and $15 million more in the second quarter. Thus its cumulative financing requirement is $60 million in the second quarter. Fortunately, this is the peak; the cumulative requirement declines in the third quarter when its $26 million net cash inflow reduces its cumulative financ- ing requirement to $34 million. (Notice that cumulative short-term financing falls by the net cash inflow in that quarter from row 24.) In the final quarter Dynamic is out of the woods. Its $35 million net cash inflow is enough to eliminate short-term financ- ing and actually increase cash holdings above the $5 million minimum acceptable balance.

Before moving on, we offer two general observations about this example:

1. The large cash outflows in the first two quarters do not necessarily spell trouble for Dynamic Mattress. In part they reflect the capital investment made in the first quarter: Dynamic is spending $32.5 million, but it should be acquiring an asset worth that much or more. The cash outflows also reflect low sales in the first half of the year; sales recover in the second half. 9 If this is a predictable seasonal pattern, the firm should have no trouble borrowing to help it get through the slow months.

2. Spreadsheet 19.1 is only a best guess about future cash flows. It is a good idea to think about the uncertainty in your estimates. For example, you could undertake a sensitivity analysis, in which you inspect how Dynamic’s cash requirements would be affected by a shortfall in sales or by a delay in collections.

9 Maybe people buy more mattresses late in the year when the nights are longer.

Our next step will be to develop a short-term financing plan that addresses the fore- cast requirements in the most economical way possible. Before presenting such a plan, however, we should pause briefly to point out that short-term financial planning, like long-term planning, is best done on a computer. Spreadsheet 19.2 presents the formula view of Spreadsheet 19.1. Examine the entries and note which items are inputs (for example, rows 18 to 21) and which are calculated from equations. The formulas also indicate the links from one panel to another. For example, collections of receivables are calculated in panel A, row 9, and passed through as inputs in panel B, row 14. Similarly, net cash inflow in panel B, row 24, is passed along to panel C, row 28.

Once the spreadsheet is set up, it becomes easy to explore the consequences of many “what-if” questions. For example, Self-Test 19.4 asked you to recalculate the quarterly cash receipts, net cash inflow, and cumulative short-term financing required if the firm’s collections on accounts receivable slow down. You can obviously do this by hand, but it is quicker and easier to do it in a spreadsheet—especially when there might be dozens of scenarios that you need to work through!

You can find this spreadsheet in Connect.

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Chapter 19 Short-Term Financial Planning 561

19.5 A Short-Term Financing Plan Dynamic’s cash budget defines its problem. Its financial manager must find short-term financing to cover the firm’s forecast cash requirements. There are dozens of sources of short-term financing, but for simplicity we will consider only two: obtaining bank loans or stretching payables.

We assume that Dynamic can borrow up to $40 million from its bank at an interest rate of 8% per year, or 2% per quarter. It can borrow and repay the loan whenever it wants to, but it may not exceed its credit limit.

Alternatively, Dynamic can raise capital by putting off paying its bills. The finan- cial manager believes that Dynamic can defer the following amounts in each quarter:

SPREADSHEET 19.2 Dynamic Mattress’s cash budget (formula view)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

A. Accounts receivable Receivables (beginning of period)

Sales

Collections

On sales in current period (80%)

On sales in previous period (20%)

Total collections

Receivables (end of period)

B. Cash budget Sources of cash Collections of accts receivable

Other

Total sources

Uses Payments of accounts payable

Labor & other expenses

Capital expenses

Taxes, interest, and dividends

Total uses

Net cash inflow = sources - uses

C. Short-term financing requirements Cash at start of period

+ Net cash inflow

= Cash at end of period

Minimum operating balance

Cumulative financing required

30

87.5

=0.8*B5

=0.2*75

=B7+B8

=B4+B5-B9

=B9

1.5

=B14+B15

65

30

32.5

4

=SUM(B18:B21)

=B16-B22

5

=B24

=B27+B28

5

=B30-B29

Quarter: First

B

Second

C

Third

D

Fourth

EA

=B10

78.5

=0.8*C5

=0.2*B5

=C7+C8

=C4+C5-C9

=C9

0

=C14+C15

60

30

1.3

4

=SUM(C18:C21)

=C16-C22

=B29

=C24

=C27+C28

=B30

=C30-C29

=C10

116

=0.8*D5

=0.2*C5

=D7+D8

=D4+D5-D9

=D9

12.5

=D14+D15

55

30

5.5

4.5

=SUM(D18:D21)

=D16-D22

=C29

=D24

=D27+D28

=C30

=D30-D29

=D10

131

=0.8*E5

=0.2*D5

=E7+E8

=E4+E5-E9

=E9

0

=E14+E15

50

30

8

5

=SUM(E18:E21)

=E16-E22

=D29

=E24

=E27+E28

=D30

=E30-E29

Quarter: First Second Third Fourth

Amount deferrable ($ millions) 52 48 44 40

That is, $52 million can be saved in the first quarter by not paying bills in that quar- ter. ( Note: Spreadsheet 19.1 was prepared assuming these bills are paid in the first quarter.) If deferred, these payments must be made in the second quarter. Similarly, $48 million of the second quarter’s bills can be deferred to the third quarter, and so on.

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562 Part Six Financial Analysis and Planning

Stretching payables is often costly, however, even if no ill will is incurred. 10 This is because many suppliers offer discounts for prompt payment, so Dynamic loses the dis- count if it pays late. In this example we assume the lost discount is 5% of the amount deferred. In other words, if a $52 million payment is delayed in the first quarter, the firm must pay 5% more, or $54.6 million, in the next quarter. This is like borrowing at an annual interest rate of over 20% (because 1.05 4  − 1 = .216, or 21.6%).

Dynamic Mattress’s Financing Plan With these two options, the short-term financing strategy is obvious: Use the lower- cost bank loan first. Stretch payables only if you can’t borrow enough from the bank.

Spreadsheet 19.3 shows the resulting plan. Panel A (cash requirements) sets out the cash that needs to be raised in each quarter. Panel B (cash raised) describes the various sources of financing the firm plans to use. Panels C and D describe how the firm will use net cash inflows when they turn positive. Panel E keeps track of the bank loan.

In the first quarter the plan calls for borrowing the full amount available from the bank ($40 million). In addition, the firm sells the $5 million of marketable securities it held at the end of 2014. Thus under this plan it raises the necessary $45 million in the first quarter.

In the second quarter, an additional $15 million must be raised to cover the net cash outflow predicted in Spreadsheet 19.1. In addition, $.8 million must be raised to pay interest on the bank loan. Therefore, the plan calls for Dynamic to maintain its bank borrowing and to stretch $15.8 million in payables. Notice that in the first two quarters, when net cash flow from operations is negative, the firm maintains its cash balance at the minimum acceptable level. Additions to cash balances are zero. Similarly, repayments of outstanding debt are zero. In fact outstanding debt rises in each of these quarters.

10 In fact, ill will is likely to be incurred. Firms that stretch payments risk being labeled as credit risks. Since stretching is so expensive, suppliers reason that customers will resort to it only when they cannot obtain credit at reasonable rates elsewhere. Suppliers naturally are reluctant to act as the lender of last resort.

You can find this spreadsheet in Connect.

SPREADSHEET 19.3 Dynamic Mattress’s financing plan (figures in $ millions)

1

2

3

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5

6

7

8

9

10

11

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14

15

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22

A. Cash requirements Cash required for operationsa

Interest on bank loanb

Interest on stretched payablesc

Total cash required

B. Cash raised in quarter Bank loan

Stretched payables

Securities sold

Total cash raised

C. Repayments Of stretched payables

Of bank loan

D. Addition to cash balances

E. Bank loan Beginning of quarter

End of quarter

45.00

0.00

0.00

45.00

40.00

0.00

5.00

45.00

0.00

0.00

0.00

0.00

40.00

15.00

0.80

0.00

15.80

0.00

15.80

0.00

15.80

0.00

0.00

0.00

40.00

40.00

–26.00

0.80

0.79

–24.41

0.00

0.00

0.00

0.00

15.80

8.61

0.00

40.00

31.39

–35.00

0.63

0.00

–34.37

0.00

0.00

0.00

0.00

0.00

31.39

2.98

31.39

0.00

Quarter: First

B

Second

C

Third

D

Fourth

EA

a A negative cash requirement implies positive cash fl ow from operations. This row is derived from row 24 of Spreadsheet 19.1. b The interest rate on the bank loan is 2% per quarter applied to the bank loan outstanding at the start of the quarter. Thus the interest due in the second quarter is .02 × $40  million = $.8 million. c The “interest” cost of the stretched payables is 5% of the amount of payment deferred. For example, in the third quarter, 5% of the $15.8 million stretched in the second quarter is about $.8 million.

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Chapter 19 Short-Term Financial Planning 563

In the third and fourth quarters, the firm generates a cash-flow surplus, so the plan calls for Dynamic to pay off its debt. First it pays off stretched payables, as it is required to do, and then it uses any remaining cash-flow surplus to pay down its bank loan. In the third quarter, all of the net cash inflow is used to reduce outstanding short-term borrowing. In the fourth quarter, the firm pays off its remaining short-term borrowing and uses the extra $2.98 million to increase its cash balances.

Revise Dynamic Mattress’s short-term financial plan assuming it can borrow up to $45 million through its bank loan. Assume that the firm will still sell its $5 million of short-term securities in the first quarter.

Self-Test 19.5

Evaluating the Plan Does the plan shown in Spreadsheet 19.3 solve Dynamic’s short-term financing problem? No—the plan is feasible, but Dynamic can probably do better. The most glaring weak- ness of this plan is its reliance on stretching payables, an extremely expensive financing device. Remember that it costs Dynamic 5% per quarter to delay paying bills—more than a 20% per year effective annual interest rate. This first plan should merely stimulate the financial manager to search for cheaper sources of short-term borrowing.

The financial manager would ask several other questions as well. For example:

1. Does Dynamic need a larger reserve of cash or marketable securities to guard against, say, its customers stretching their payables (thus slowing down collections on accounts receivable)?

2. Does the plan yield satisfactory current and quick ratios? 11 Its bankers may be worried if these ratios deteriorate.

3. Are there hidden costs to stretching payables? Will suppliers begin to doubt Dynamic’s creditworthiness?

4. Does the plan for 2015 leave Dynamic in good financial shape for 2016? (Here the answer is yes, since Dynamic will have paid off all short-term borrowing by the end of the year.)

5. Should Dynamic try to arrange long-term financing for the major capital expenditure in the first quarter? This seems sensible, following the rule of thumb that long-term assets deserve long-term financing. It would also dramatically reduce the need for short-term borrowing. A counterargument is that Dynamic is financing the capital investment only temporarily by short-term borrowing. By year-end, the investment is paid for by cash from operations. Thus Dynamic’s initial decision not to seek immediate long-term financing may reflect a preference for ultimately financing the investment with retained earnings.

6. Perhaps the firm’s operating and investment plans can be adjusted to make the short- term financing problem easier. Is there any easy way of deferring the first quarter’s large cash outflow? For example, suppose that the large capital investment in the first quarter is for new mattress-stuffing machines to be delivered and installed in the first half of the year. The new machines are not scheduled to be ready for full-scale use until August. Perhaps the machine manufacturer could be persuaded to accept 60% of the purchase price on delivery and 40% when the machines are installed and operating satisfactorily.

Short-term financing plans must be developed by trial and error. You lay out one plan, think about it, and then try again with different assumptions on financ- ing and investment alternatives. You continue until you can think of no further improvements.

11 These ratios are discussed in Chapter 4.

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564 Part Six Financial Analysis and Planning

19.6 Sources of Short-Term Financing Dynamic solved the greater part of its cash shortage by borrowing from a bank. Banks offer various types of loans, and one type may make more sense for you than another. Also, banks are not the only source of short-term borrowing. For example, firms may obtain loans from finance companies, which specialize in lending to businesses and individuals. Unlike banks, finance companies obtain funds through selling securities rather than through deposits. Firms may also raise money by selling their own short- term debt directly to investors. Let’s look at some of these alternative sources of short- term financing.

Bank Loans The simplest and most common source of short-term finance is a loan from a bank. Companies sometimes wait until they need the money before they apply for a bank loan, but in the majority of cases the firm will arrange a revolving line of credit that permits it to borrow from the bank up to an agreed limit. The company can borrow and repay whenever it wants until the agreement expires. In return, the company will agree to pay the bank a commitment fee of up to .5% on any unused amount.

Many bank loans have durations of only a few months. For example, a firm may need a loan to cover a seasonal increase in inventories, and the loan is then repaid as the goods are sold. Such a loan is described as self-liquidating; in other words, the sale of goods provides the cash to repay the loan. However, banks also make term loans, which last for several years.

Some bank loans are too large for a single lender. In these cases the borrower may pay an arrangement fee to a lead bank, which then parcels out the loan or credit line among a syndicate of banks. For example, when the mining company BHP Billiton needed to raise $45 billion to finance its (ultimately unsuccessful) takeover bid for Potash, six banks from around the world agreed to provide the money.

Most short-term bank loans are made at a fixed rate of interest, which is often quoted as a discount. For example, if the interest rate on a 1-year loan is stated as a discount of 5%, the borrower receives $100 − $5 = $95 and undertakes to pay $100 at the end of the year. The return on such a loan is not 5% but 5/95 = .0526, or 5.26%.

For longer-term bank loans the interest rate is usually linked to the general level of interest rates. A common benchmark is the London Interbank Offered Rate (LIBOR), which is the interest rate at which the major international banks borrow dollars from one another. 12 Thus, if the rate is set at “1% over LIBOR,” the borrower may pay 5% in the first 3 months when LIBOR is 4%, 6% in the next 3 months when LIBOR is 5%, and so on.

Figure 19.6 shows the 3-month LIBOR rate and the equivalent Treasury bill rate. The difference between these rates, usually called the TED spread, indicates the finan- cial strength of the banking sector. When banks are in trouble, the rates at which they are prepared to lend to each other will naturally increase. While the TED spread was below .5% for the early part of the decade, at the height of the financial crisis it spiked to 4.65%.

Secured Loans If a bank is concerned about a firm’s credit risk, the firm will need to provide security or collateral for the loan. Sometimes this security will include both current and fixed assets. However, if the bank is lending on a short-term basis, the collateral is generally restricted to liquid assets such as receivables, inventories, or securities. For example, a

revolving line of credit Agreement by a bank that a company may borrow at any time up to an established limit.

12 Occasionally, the interest rate is linked to the bank’s prime rate or to the federal funds rate, which is the inter- est rate at which banks in the United States lend excess reserves to each other.

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Chapter 19 Short-Term Financial Planning 565

firm may decide to borrow short-term money secured by its accounts receivable. When its customers pay their bills, it can use the cash collected to repay the loan.

Banks will not usually lend the full value of the assets that are used as security. So a firm that puts up $100,000 of receivables as security may find that the bank is prepared to lend only $75,000. The safety margin (or haircut, as it is called) is likely to be even larger in the case of loans that are secured by inventory.

Accounts Receivable Financing When a loan is secured by receivables, the firm assigns the receivables to the bank. If the firm fails to repay the loan, the bank can collect the receivables from the firm’s customers and use the cash to pay off the debt. However, the firm is still responsible for the loan even if the receivables ultimately cannot be collected. The risk of default on the receivables is therefore borne by the firm.

An alternative procedure is to sell the receivables at a discount to a financial institu- tion known as a factor and let it collect the money. In other words, some companies solve their financing problem by borrowing on the strength of their current assets; others solve it by selling their current assets. Once the firm has sold its receivables, the factor bears all the responsibility for collecting on the accounts. Therefore, the factor plays three roles: It administers collection of receivables, takes responsibility for bad debts, and provides finance.

FIGURE 19.6 Interest rates on 3-month Treasury bills and LIBOR. The orange line shows how the spread between the two rates (the TED spread) leapt up during the banking crisis.

0

1

2

3

4

5

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A ug

-9 9

A ug

-0 0

A ug

-0 1

A ug

-0 2

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-0 3

A ug

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A ug

-0 5

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A ug

-0 9

A ug

-1 0

A ug

-1 1

A ug

-1 2

A ug

-1 3

P er

ce n

t

3-month LIBOR

3-month T-bill

Spread

Example 19.2 Factoring To illustrate factoring, suppose that the firm sells its accounts receivable to a fac- tor at a 2% discount. This means that the factor pays 98 cents for each dollar of accounts receivable. If the average collection period is 1 month, then in a month the factor should be able to collect $1 for every 98 cents it paid today. Therefore, the implicit interest rate is 2/98 = 2.04% per month, which corresponds to an effec- tive annual interest rate of (1.0204) 12  − 1 = .274, or 27.4%.

While factoring would appear from this example to be an expensive source of financing for the firm, part of the apparently steep interest rate represents payment for the assumption of default risk and for the cost of running the credit operation.

Inventory Financing Banks also lend on the security of inventory, but they are choosy about the inventory they will accept. They want to make sure that they can

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566

identify and sell it if you default. Automobiles and other standardized nonperishable commodities are good security for a loan; work in progress and ripe strawberries are poor collateral.

Banks need to monitor companies to be sure they don’t sell their assets and run off with the money. Consider, for example, the story of the great salad oil swindle. Fifty-one banks and companies made loans of nearly $200 million to the Allied Crude Vegetable Oil Refining Corporation in the belief that these loans were secured by valu- able salad oil. Unfortunately, they did not notice that Allied’s tanks contained false compartments which were mainly filled with seawater. When the fraud was discov- ered, the president of Allied went to jail and the 51 lenders stayed out in the cold look- ing for their $200 million. The nearby box presents a similar story that illustrates the potential pitfalls of secured lending. Here, too, the loans were not as “secured” as they appeared: The supposed collateral did not exist.

To protect themselves against this sort of risk, lenders often insist on field ware- housing. An independent warehouse company hired by the bank supervises the inven- tory pledged as collateral for the loan. As the firm sells its product and uses the revenue to pay back the loan, the bank directs the warehouse company to release the inventory back to the firm. If the firm defaults on the loan, the bank keeps the inventory and sells it to recover the debt.

Commercial Paper When banks lend money, they provide two services. They match up would-be borrow- ers and lenders, and they check that the borrower is likely to repay the loan. Banks recover the costs of providing these services by charging borrowers on average a higher interest rate than they pay to lenders. These services are less necessary for large, well-known companies that regularly need to raise large amounts of cash. Such companies have increasingly found it profitable to bypass the bank and to sell short- term debt, known as commercial paper, directly to large investors.

In the United States commercial paper has a maximum maturity of 270 days; longer maturities would require registration with the Securities and Exchange Commission. However, most paper matures in 60 days or less. Commercial paper is not secured, but companies generally back their issue of paper by arranging a special backup line of

commercial paper Short-term unsecured notes issued by firms.

Finance in Practice The Hazards of Secured Bank Lending came to check that their loans were safe. Sometimes a sus- picious banker would ask to inspect a particular container. Friedrich would then explain that it was away on exercise, fl y the banker across the country in a light plane, and point to a container well out in the bush. The container would of course be empty, but the banker had no way to know that.

Six years after Friedrich was appointed CEO, his massive fraud was uncovered. But a few days before a warrant could be issued, Friedrich disappeared. Although he was eventu- ally caught and arrested, he shot himself before he could come to trial. Investigations revealed that Friedrich was oper- ating under an assumed name, having fl ed from his native Germany, where he was wanted by the police. Many rumors continued to circulate about Friedrich. He was variously alleged to have been a plant of the CIA and the KGB, and the NSC was said to have been behind an attempted coun- tercoup in Fiji. For the banks there was only one hard truth: Their loans to the NSC, which had appeared so well secured, would never be repaid.

Source: Adapted from T. Sykes, The Bold Riders (St. Leonards, NSW, Austra- lia: Allen & Unwin, 1994), chap. 7.

The National Safety Council of Australia’s Victoria Division had been a sleepy outfi t until John Friedrich took over. Under its new management, NSC members trained like comman- dos and were prepared to go anywhere and do anything. They saved people from drowning, fought fi res, found lost bushwalkers, and went down mines. Their lavish equipment included 22 helicopters, 8 aircraft, and a mini-submarine. Soon the NSC began selling its services internationally.

Unfortunately the NSC’s paramilitary outfi t cost millions of dollars to run—far more than it earned in revenue. Fried- rich bridged the gap by borrowing $A236 million of debt. The banks were happy to lend because the NSC’s debt appeared well secured. At one point the company showed $A107 mil- lion of receivables (that is, money owed by its customers), which it pledged as security for bank loans. Later checks revealed that many of these customers did not owe the NSC a cent. In other cases banks took comfort in the fact that their loans were secured by containers of valuable rescue gear. There were more than 100 containers stacked around the NSC’s main base. Only a handful contained any equipment, but these were the ones that the bankers saw when they

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Chapter 19 Short-Term Financial Planning 567

SUMMARY Short-term financial planning is concerned with the management of the firm’s short-term, or current, assets and liabilities. The most important current assets are cash, marketable securities, inventory, and accounts receivable. The most important current liabilities are bank loans and accounts payable. The difference between current assets and current liabili- ties is called net working capital.

Net working capital arises from lags between the time the firm obtains the raw materials for its product and the time it finally collects its bills from customers. The cash conversion cycle is the length of time between the firm’s payment for materials and the date that it gets paid by its customers. The cash conversion cycle is partly within management’s control. For example, it can choose to have a higher or lower level of inventories. Management needs to trade off the benefits and costs of investing in current assets. Higher investments in current assets entail higher carrying costs but lower expected shortage costs.

The nature of the firm’s short-term financial planning problem is determined by the amount of long-term capital it raises. A firm that issues large amounts of long-term debt or com- mon stock, or that retains a large part of its earnings, may find that it has permanent excess cash. Other firms raise relatively little long-term capital and end up as permanent short- term debtors. Most firms attempt to find a golden mean by financing all fixed assets and part of current assets with equity and long-term debt. Such firms may invest cash surpluses during part of the year and borrow during the rest of the year.

The starting point for short-term financial planning is an understanding of sources and uses of cash. Firms forecast their net cash requirement by forecasting collections on accounts receivable, adding other cash inflows, and subtracting all forecast cash outlays. If the fore- cast cash balance is insufficient to cover day-to-day operations and to provide a buffer against contingencies, the firm will need to find additional finance.

The search for the best short-term financial plan inevitably proceeds by trial and error. The financial manager must explore the consequences of different assumptions about cash requirements, interest rates, limits on financing from particular sources, and so on. Firms commonly use computerized financial models to help in this process.

Why do firms need to invest in net working capital? (LO19-1)

How does long-term financing policy affect short-term financing requirements? (LO19-2)

How does the firm’s sources and uses of cash relate to its need for short-term borrowing? (LO19-3)

How do firms develop a short-term financing plan that meets their need for cash? (LO19-4)

credit with a bank. This guarantees that they can find the money to repay the paper, and the risk of default is therefore small.

Since investors are reluctant to buy paper that does not have the highest credit rat- ing, companies cannot rely on the commercial paper market to provide them with short-term capital if their credit standing deteriorates. For example, when the rating services downrated the commercial paper of Ford and General Motors, both compa- nies were forced to reduce sharply the amount of paper that they had issued and to rely instead on the long-term debt market. Ford Credit had $42 billion of commercial paper outstanding at the end of 2000; by 2009 at the height of the crisis it had cut that amount to $6.4 billion.

Recent years have not been kind to the commercial paper market. When Lehman Brothers went bankrupt in 2008, it defaulted on its outstanding commercial paper. The commercial paper market seized up; many companies either found it impossible to issue commercial paper or were obliged to pay very high rates of interest. The resulting inter- ruption of credit to the corporate sector was a major cause of the recession that followed the financial crisis. Even before the crisis, however, all was not well. In 2001 two large California utilities, Pacific Gas & Electric and Southern California Edison, became the first companies for 10 years to default on their nonfinancial commercial paper.

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568 Part Six Financial Analysis and Planning

5. Cash Conversion Cycle. Will the following increase or decrease the cash conversion cycle? (LO19-1)

a. Customers are given a larger discount for cash transactions. b. The inventory turnover ratio falls from 8 to 6. c. New technology streamlines the production process. d. The firm adopts a policy of reducing outstanding accounts payable. e. The firm starts producing more goods in response to customers’ advance orders instead of

producing for inventory. f. A temporary glut in the commodity market induces the firm to stock up on raw materials

while prices are low.

6. Cash Conversion Cycle. A firm is considering several policy changes to increase sales. It will increase the variety of goods it keeps in inventory, but this will increase inventory by $10,000. It will offer more liberal sales terms, but this will result in average receivables increasing by $65,000. These actions are expected to increase sales by $800,000 per year, and cost of goods will remain at 80% of sales. Because of the firm’s increased purchases for its own production needs, average payables will increase by $35,000. What effect will these changes have on the firm’s cash conversion cycle? (LO19-1)

A major source of short-term financing is bank loans. Often, firms pay a regular fee for a line of credit that allows them to borrow from the bank up to an agreed amount. Other important sources of short-term finance are commercial paper, secured loans such as accounts receivable or inventory financing, and factoring.

What are some of the major sources of short-term financing? (LO19-5)

QUESTIONS AND PROBLEMS 1. Working Capital Management. How would each of the following six different transactions

affect Dynamic Mattress’s (i) cash and (ii) net working capital? (LO19-1)

a. Paying out a $2 million cash dividend b. A customer paying a $2,500 bill resulting from a previous sale c. Paying $5,000 previously owed to one of its suppliers d. Borrowing $1 million long-term and investing the proceeds in inventory e. Borrowing $1 million short-term and investing the proceeds in inventory f. Selling $5 million of marketable securities for cash

2. Cash Conversion Cycle. Will each of the following events increase or decrease the cash con- version cycle? (LO19-1)

a. Higher financing rates induce the firm to reduce its level of inventory. b. The firm obtains a new line of credit that enables it to avoid stretching payables to its suppliers. c. The firm factors its accounts receivable. d. A recession occurs, and the firm’s customers increasingly stretch their payables.

3. Managing Working Capital. A new computer system allows your firm to more accurately monitor inventory and anticipate future inventory shortfalls. As a result, the firm feels more able to pare down its inventory levels. Will the new system increase or decrease (a) working capital and (b) the cash conversion cycle? (LO19-1)

4. Cash Conversion Cycle. Calculate the accounts receivable period, accounts payable period, inventory period, and cash conversion cycle for the following firm: (LO19-1)

Income statement data: Sales 5,000 Cost of goods sold 4,200 Balance sheet data: Inventory 550 Accounts receivable 110 Accounts payable 270

finance

®

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Chapter 19 Short-Term Financial Planning 569

8. Short-Term Financial Plans. Fill in the blanks in the following statements. (LO19-3) a. A firm has a cash surplus when its _____ exceeds its _____. The surplus is normally invested

in _____. b. In developing the short-term financial plan, the financial manager starts with a(n) _____

budget for the next year. This budget shows the _____ generated or absorbed by the firm’s operations and also the minimum _____ needed to support these operations. The financial manager may also wish to invest in _____ as a reserve for unexpected cash requirements.

9. Sources and Uses of Cash. How would each of the following events affect the firm’s balance sheet? State whether each change is a source or use of cash. (LO19-3)

a. An automobile manufacturer increases production in response to a forecast increase in demand. Unfortunately, the demand does not increase.

b. Competition forces the firm to give customers more time to pay for their purchases. c. The firm sells a parcel of land for $100,000. The land was purchased 5 years earlier for

$200,000. d. The firm repurchases its own common stock. e. The firm pays its quarterly dividend. f. The firm issues $1 million of long-term debt and uses the proceeds to repay a short-term

bank loan.

10. Short-Term Financial Policy. What will be the effect of each of the following transactions on cash, net working capital, and the current ratio? Assume that the current ratio is above 1.0. (LO19-4)

a. The firm borrows $1,000 in a short-term loan from its bank and pays $500 in accounts payable. b. The firm factors $1,000 in receivables at a 4% discount. c. The firm issues $1,000 in long-term bonds and uses the proceeds to pay $800 in payables

and purchase $200 in marketable securities.

11. Forecasting Collections. Here is a forecast of sales by National Bromide for the first 4 months of 2015 (figures in thousands of dollars):

Month: 1 2 3 4

Cash sales 15 24 18 14 Sales on credit 100 120 90 70

7. Sources and Uses of Cash. Create the statement of cash flows from the following entries: (LO19-3)

Net income $1,500 Dividends 900 Additions to inventory 120 Additions to receivables 150 Depreciation 90 Reduction in payables 550 Net issuance of long-term debt 300 Sale of fi xed assets 60

On average, 50% of credit sales are paid for in the current month, 30% in the next month, and the remainder in the month after that. What are the expected cash collections in months 3 and 4? (LO19-4)

12. Forecasting Payments. If a firm pays its bills with a 30-day delay, what fraction of its pur- chases will be paid for in the current quarter? In the following quarter? What if its payment delay is 60 days? (LO19-4)

13. Short-Term Planning. Paymore Products places orders for goods equal to 75% of its sales forecast in the next quarter. What will orders be in each quarter of the year if the sales forecasts for the next five quarters are as follows: (LO19-4)

Quarter in Coming Year Following Year

First Second Third Fourth First Quarter

Sales forecast $372 $360 $336 $384 $384

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570 Part Six Financial Analysis and Planning

14. Forecasting Payments. Calculate Paymore’s cash payments (from Problem 13) to its suppliers under the assumption that the firm pays for its goods with a 1-month delay. Therefore, on aver- age, two-thirds of purchases are paid for in the quarter that they are purchased, and one-third are paid in the following quarter. (LO19-4)

15. Forecasting Collections. Now suppose that Paymore’s customers (from Problem 13) pay their bills with a 2-month delay. What is the forecast for Paymore’s cash receipts in each quarter of the coming year? Assume that sales in the last quarter of the previous year were $336. (LO19-4)

16. Forecasting Net Cash Flow. Assuming that Paymore’s labor and administrative expenses (from Problem 13) are $65 per quarter and that interest on long-term debt is $40 per quarter, work out the net cash inflow for Paymore for the coming year using a table like Spreadsheet 19.1, panel B. (LO19-4)

17. Short-Term Financing Requirements. Suppose that Paymore’s cash balance (from Problem 13) at the start of the first quarter is $40 and its minimum acceptable cash balance is $30. Work out the short-term financing requirements for the firm in the coming year using a table like Spreadsheet 19.1, panel C. The firm pays no dividends. (LO19-4)

18. Short-Term Financing Plan. Now assume that Paymore (from Problem 13) can borrow up to $100 from a line of credit at an interest rate of 2% per quarter. Prepare a short-term financing plan. Use Spreadsheet 19.3 to guide your answer. (LO19-4)

19. Short-Term Plan. Recalculate Dynamic Mattress’s financing plan (Spreadsheet 19.3) assum- ing that the firm wishes to maintain a minimum cash balance of $10 million instead of $5 mil- lion. Assume the firm can convince the bank to extend its line of credit to $45 million. (LO19-4)

20. Sources and Uses of Cash. The accompanying tables show Dynamic Mattress’s year-end 2012 balance sheet and its income statement for 2013. Use these tables (and Table 19.3) to work out a statement of sources and uses of cash for 2013. (LO19-4)

YEAR-END BALANCE SHEET FOR 2012 (Figures in $ millions)

Assets Liabilities

Current assets Current liabilities Cash 4 Bank loans 4 Marketable securities 2 Accounts payable 15 Inventory 20 Total current liabilities 19 Accounts receivable 22 Long-term debt 5 Total current assets 48 Net worth (equity and retained earnings) 60 Fixed assets Gross investment 50 Less depreciation 14 Total liabilities and net worth 84 Net fi xed assets 36 Total assets 84

INCOME STATEMENT FOR 2013 (Figures in $ millions)

Sales 300 Operating costs −285

15 Depreciation −2 EBIT 13 Interest −1 Pretax income 12 Tax at 50% −6 Net income 6

Note: Dividend = $1 million, and reinvested earnings = $5 million.

Templates can be found in Connect.

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Chapter 19 Short-Term Financial Planning 571

21. Factoring. A firm sells its $1,000,000 receivables to a factor for $960,000. The average collec- tion period is 1 month. What is the effective annual rate on this arrangement? (LO19-5)

22. Factoring. A firm sells its accounts receivables to a factor at a 1.5% discount. The average collection period is 1 month. What is the implicit effective annual interest rate on the factoring arrangement? What is the implicit effective annual interest rate if the average collection period is 1.5 months? (LO19-5)

23. Lines of Credit. The chapter notes that firms commonly pay commitment fees to banks when obtaining a line of credit. Yet when the line is first taken out, it commonly is not drawn down (i.e., the firm does not initiate any borrowing from its line). Why do these firms pay for some- thing that seems to be not currently needed? (LO19-5)

CHALLENGE PROBLEMS 24. Impact of Long-Term Financing. Suppose that Dynamic Mattress issued $5 million of addi-

tional long-term debt and used the proceeds to add to its cash balances. Recalculate its short- term financing plan (Spreadsheet 19.3) now that it has raised $5 million of additional long-term financing. (LO19-2)

25. Cash Budget. The following data are from the budget of Ritewell Publishers. Half the com- pany’s sales are transacted on a cash basis. The other half are paid for with a 1-month delay. The company pays all of its credit purchases with a 1-month delay. Credit purchases in January were $30, and total sales in January were $180. (LO19-4)

February March April

Sources of cash Collections on current sales Collections on accounts receivable Total sources of cash Uses of cash Payments of accounts payable Cash purchases Labor and administrative expenses Capital expenditures Taxes, interest, and dividends Total uses of cash Net cash infl ow Cash at start of period 100 + Net cash infl ow = Cash at end of period + Minimum operating cash balance 100 100 100 = Cumulative short-term fi nancing required

February March April

Total sales 200 220 180 Cash purchases 70 80 60 Credit purchases 40 30 40 Labor and administrative expenses 30 30 30 Taxes, interest, and dividends 10 10 10 Capital expenditures 100 0 0

Complete the following cash budget:

Templates can be found in Connect.

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572 Part Six Financial Analysis and Planning

19.2 a. An increase in the interest rate will increase the cost of carrying current assets. The effect is to reduce the optimal level of such assets.

b. The just-in-time system lowers the expected level of shortage costs and reduces the amount of goods the firm ought to be willing to keep in inventory.

c. If the firm decides that more lenient credit terms are necessary to avoid lost sales, it must then expect customers to pay their bills more slowly. Accounts receivable will increase.

19.3 a. This transaction merely substitutes one current liability (short-term debt) for another (accounts payable). Neither cash nor net working capital is affected.

b. This transaction will increase inventory at the expense of cash. Cash falls but net working capital is unaffected.

c. The firm will use cash to buy back the stock. Both cash and net working capital will fall. d. The proceeds from the sale will increase both cash and net working capital.

WEB EXERCISES 1. Log on to finance.yahoo.com and find the condensed balance sheets and income statements for

Merck (MRK) and Consolidated Edison (ED). Calculate the net working capital and the cash conversion cycle, discussed in Section 19.2, for each firm. By how much would the investment in working capital fall if each firm could reduce its cash conversion cycle by 1 day?

2. We mentioned that the interest rate on longer-term bank loans is not usually fixed for the term of the loan but is adjusted up or down as the general level of interest rates changes. Often the inter- est rate is linked to the London Interbank Offered Rate (LIBOR), which is the interest rate at which major international banks lend to one another. Two alternatives are to link it to the federal funds rate or the bank’s prime rate. Suppose you are offered the choice of a 3-year loan at 1.5% above 3-month LIBOR, at the bank’s prime rate, or at 1.25% above federal funds. Which would you prefer? Log on to www.bloomberg.com to find current rates.

SOLUTIONS TO SELF-TEST QUESTIONS 19.1 One would expect Tiffany’s to have the longer conversion cycle. It holds an inventory of

expensive jewelry that can take a long time to sell. Target’s wares are “priced to sell.” In fact, the calculations below show that the difference in the two firms’ cash conversion cycles is driven primarily by their extremely different inventory periods.

Tiffany Target

Sales 3,794 73,301 COGS 1,631 50,568 Inventories 2,234 7,903 Accounts receivable 254 5,841 Accounts payable 326 11,037 Inventory period 499.9 57.0 Receivables period 24.4 29.1 Payables period 73.0 79.7 Cash conversion cycle 451.3 6.5

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Chapter 19 Short-Term Financial Planning 573

19.4

19.5 The major change in the plan is the substitution of the extra $5 million of borrowing from the bank in the second quarter and the corresponding reduction in the stretched payables. This substitution is advantageous because the bank loan is a cheaper source of funds. Notice that the cash balance at the end of the year is higher under this plan than in the original plan.

Quarter: First Second Third Fourth

Cash requirements 1. Cash required for operations 45 15 -26  -35 2. Interest on line of credit 0 0.8 0.9 0.6 3. Interest on stretched payables 0 0 0.5 0 4. Total cash required 45 15.8 -24.6 -34.4 Cash raised 5. Bank loan 40 5 0 0 6. Stretched payables 0 10.8 0 0 7. Securities sold 5 0 0 0 8. Total cash raised 45 15.8 0 0 Repayments 9. Of stretched payables 0 0 10.8 0 10. Of bank loan 0 0 13.8 31.2 Increase in cash balances 11. Addition to cash balances 0 0 0 3.2 Bank loan 12. Beginning of quarter 0 40 45 31.2 13. End of quarter 40 45 31.2 0

Quarter: First Second Third Fourth

Accounts receivable Receivables (beginning of period) 30.0 35.0 31.4 46.4 Sales 87.5 78.5 116.0 131.0 Collections* 82.5 82.1 101.0 125.0 Receivables (end of period) 35.0 31.4 46.4 52.4 Cash budget Sources of cash Collections of accounts receivable 82.5 82.1 101.0 125.0 Other 1.5 0.0 12.5 0.0 Total sources 84.0 82.1 113.5 125.0 Uses Payments of accounts payable 65.0 60.0 55.0 50.0 Labor and administrative expenses 30.0 30.0 30.0 30.0 Capital expenses 32.5 1.3 5.5 8.0 Taxes, interest, and dividends 4.0 4.0 4.5 5.0 Total uses 131.5 95.3 95.0 93.0 Net cash infl ow −47.5 −13.2 18.5 32.0 Short-term fi nancing requirements Cash at start of period 5.0 −42.5 −55.7 −37.2 + Net cash infl ow −47.5 −13.2 18.5 32.0 = Cash at end of period −42.5 −55.7 −37.2 −5.2 Minimum operating balance 5.0 5.0 5.0 5.0 Cumulative short-term fi nancing required 47.5 60.7 42.2 10.2

* Sales in fourth quarter of the previous year totaled $75 million.

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574 Part Six Financial Analysis and Planning

MINICASE Capstan Autos operated an East Coast dealership for a major Japa- nese car manufacturer. Capstan’s owner, Sidney Capstan, attributed much of the business’s success to its no-frills policy of competitive pricing and immediate cash payment. The business was basically a simple one—the firm imported cars at the beginning of each quarter and paid the manufacturer at the end of the quarter. The revenues from the sale of these cars covered the payment to the manufac- turer and the expenses of running the business, as well as providing Sidney Capstan with a good return on his equity investment.

By the fourth quarter of 2018 sales were running at 250 cars a quarter. Since the average sale price of each car was about $20,000, this translated into quarterly revenues of 250 × $20,000 = $5  mil- lion. The average cost to Capstan of each imported car was $18,000. After paying wages, rent, and other recurring costs of $200,000 per quarter and deducting depreciation of $80,000, the company was left with earnings before interest and taxes (EBIT) of $220,000 a quarter and net profits of $140,000.

The year 2019 was not a happy year for car importers in the United States. Recession led to a general decline in auto sales, while the fall in the value of the dollar shaved profit margins for many deal- ers in imported cars. Capstan more than most firms foresaw the dif- ficulties ahead and reacted at once by offering 6 months’ free credit while holding the sale price of its cars constant. Wages and other costs were pared by 25% to $150,000 a quarter, and the company effectively eliminated all capital expenditures. The policy appeared successful. Unit sales fell by 20% to 200 units a quarter, but the com- pany continued to operate at a satisfactory profit (see table).

The slump in sales lasted for 6 months, but as consumer con- fidence began to return, auto sales began to recover. The compa- ny’s new policy of 6 months’ free credit was proving sufficiently

popular that Sidney Capstan decided to maintain the policy. In the third quarter of 2019 sales had recovered to 225 units; by the fourth quarter they were 250 units; and by the first quarter of the next year they had reached 275 units. It looked as if by the second quarter of 2020 the company could expect to sell 300 cars. Earnings before interest and tax were already in excess of their previous high, and Sidney Capstan was able to congratulate himself on weathering what looked to be a tricky period. Over the 18-month period the firm had earned net profits of over half a million dollars, and the equity had grown from just over $1.5 million to about $2 million.

Sidney Capstan was first and foremost a superb salesman and always left the financial aspects of the business to his financial manager. However, there was one feature of the financial statements that disturbed Sidney Capstan—the mounting level of debt, which by the end of the first quarter of 2020 had reached $9.7 million. This unease turned to alarm when the financial manager phoned to say that the bank was reluctant to extend further credit and was even questioning its current level of exposure to the company.

Mr. Capstan found it impossible to understand how such a suc- cessful year could have landed the company in financial difficul- ties. The company had always had good relationships with its bank, and the interest rate on its bank loans was a reasonable 8% a year (or about 2% a quarter). Surely, Mr. Capstan reasoned, when the bank saw the projected sales growth for the rest of 2020, it would realize that there were plenty of profits to enable the company to start repaying its loans.

Mr. Capstan kept coming back to three questions: Was his com- pany really in trouble? Could the bank be right in its decision to withhold further credit? And why was the company’s indebtedness increasing when its profits were higher than ever?

SUMMARY INCOME STATEMENT (All fi gures except unit sales in $ thousands)

Year: 2018 2019 2020

Quarter: 4 1 2 3 4 1

1. Number of cars sold 250 200 200 225 250 275 2. Unit price 20 20 20 20 20 20 3. Unit cost 18 18 18 18 18 18 4. Revenues (1 × 2) 5,000 4,000 4,000 4,500 5,000 5,500 5. Cost of goods sold (1 × 3) 4,500 3,600 3,600 4,050 4,500 4,950 6. Wages and other costs 200 150 150 150 150 150 7. Depreciation 80 80 80 80 80 80 8. EBIT (4 - 5 - 6 - 7) 220 170 170 220 270 320 9. Net interest 4 0 76 153 161 178 10. Pretax profi t (8 - 9) 216 170 94 67 109 142 11. Tax (.35 × 10) 76 60 33 23 38 50 12. Net profi t (10 - 11) 140 110 61 44 71 92

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Chapter 19 Short-Term Financial Planning 575

SUMMARY BALANCE SHEETS (Figures in $ thousands)

End of 3rd Quarter 2018

End of 1st Quarter 2020

Cash 10 10 Receivables 0 10,500 Inventory 4,500 5,400 Total current assets 4,510 15,910 Fixed assets, net 1,760 1,280 Total assets 6,270 17,190 Bank loan 230 9,731 Payables 4,500 5,400 Total current liabilities 4,730 15,131 Shareholders’ equity 1,540 2,059 Total liabilities plus equity 6,270 17,190

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576

Working Capital Management

LEARNING OBJECTIVES

After reading this chapter, you should be able to:

20-1 Describe the usual steps in a firm’s credit management policy.

20-2 Measure the implicit interest rate on credit sales.

20-3 Describe how firms assess the probability that a customer will pay its bills.

20-4 Decide whether it makes sense to grant credit to customers.

20-5 Cite the costs and benefits of holding inventories and cash balances.

20-6 Compare the different techniques that firms use to make and receive payments.

20-7 Compare alternatives for investing excess funds over short horizons.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

20 CHAPTE R

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577

P A

R T

S IX

M ost of this book is devoted to long-term financial decisions such as capital bud-geting and the choice of capital structure. In the previous chapter, we started our analysis of

short-term planning decisions by looking at how firms

ensure that they have enough cash to pay their bills.

It is now time to look more closely at the manage-

ment of short-term assets and liabilities, known col-

lectively as working capital.

There are four principal types of current assets.

All need to be managed. We begin with accounts

receivable. Companies frequently sell goods on

credit, so it may be weeks or even months before they

receive payment. The unpaid bills show up in the bal-

ance sheet as accounts receivable. We will explain

how the company’s credit manager sets the terms

of payment, decides which customers should be

offered credit, and ensures that they pay promptly.

The second major short-term asset is inventory. To

do business, firms need reserves of raw materials, work

in progress, and finished goods. But these inventories

can be expensive to store, and they tie up capital.

Inventory management involves a trade-off between

these costs and benefits. In manufacturing compa-

nies, the production manager is most likely to make

this judgment without direct input from the financial

manager. Therefore, we spend less time on this topic

than on the management of the other components

of working capital.

Our next task is to discuss the firm’s cash balances.

The first problem is to decide how much cash the

firm should retain and, therefore, how much can be

invested in interest-bearing securities. The second

is to ensure that cash payments are handled effi-

ciently. You want to collect payments as quickly as

possible and put them to work earning interest. We

will describe some of the techniques that firms use to

move money around efficiently.

Finally, we describe some of the firm’s choices for

how to invest excess funds in a variety of short-term

securities, which are the fourth major component of

working capital.

Fi n

a n

c ia

l A n

a ly

si s

a n

d P

la n

n in

g

Amazon’s warehouses are stacked with over $7 billion of inventory. What are the benefits and costs of this inventory?

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578 Part Six Financial Analysis and Planning

20.1 Accounts Receivable and Credit Policy We start our tour of current assets with the firm’s accounts receivable. When one com- pany sells goods to another, it does not usually expect to be paid immediately. The unpaid bills, or trade credit, compose the bulk of accounts receivable. The remainder is made up of consumer credit, bills awaiting payment by the final customer.

Credit management involves the following five steps:

1. You must establish the terms of sale on which you propose to sell your goods. For example, how long will you give customers to pay their bills? Will you offer a discount for immediate payment?

2. You must decide what evidence you require that the customer owes you money. For example, is a signed receipt enough, or do you insist on a formal IOU?

3. You must determine which customers are likely to pay their bills. This is called credit analysis.

4. You must decide on credit policy. How much credit will you extend to each customer? How much risk are you prepared to take on marginally creditworthy prospects?

5. Finally, you have to collect the money when it becomes due. What do you do about reluctant payers or deadbeats?

We discuss these topics in turn.

Terms of Sale Whenever you sell goods, you need to set the terms of sale. For example, if you are sup- plying goods to a wide variety of irregular customers, you may require cash on delivery (COD). And if you are producing goods to the customer’s specification or incurring heavy delivery costs, then it may be sensible to ask for cash before delivery (CBD).

In many other cases, payment is not made until after delivery, so the buyer receives credit. Each industry seems to have its own typical credit arrangements. These arrange- ments have a rough logic. For example, the seller will naturally demand earlier pay- ment if its customers are financially less secure, if their accounts are small, or if the goods are perishable or quickly resold.

When you buy goods on credit, the supplier will state a final payment date. To encourage you to pay before the final date, it is common to offer a cash discount for prompt settlement. For example, a manufacturer may require payment within 30 days but offer a 5% discount to customers who pay within 10 days. These terms would be referred to as 5/10, net 30:

Similarly, if a firm sells goods on terms of 2/30, net 60, customers receive a 2% dis- count for payment within 30 days or else must pay in full within 60 days. If the terms are simply net 30, then customers must pay within 30 days of the invoice date and no discounts are offered for early payment.

trade credit Bills awaiting payment from one company to another.

consumer credit Bills awaiting payment from the final customer to a company.

terms of sale Credit, discount, and payment terms offered on a sale.

5 10, net 30

percent discount for early payment

number of days that discount is available

number of days before payment is due

Suppose that a firm sells goods on terms of 2/10, net 20. On May 1 you buy goods from the company with an invoice value of $20,000. How much would you need to pay if you took the cash discount? What is the latest date on which the cash discount is available? By what date should you pay for your purchase if you decide not to take the cash discount?

Self-Test 20.1

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Chapter 20 Working Capital Management 579

For many items that are bought regularly, it is inconvenient to require separate pay- ment for each delivery. A common solution is to pretend that all sales during the month in fact occur at the end of the month (EOM). Thus goods may be sold on terms of 8/10, EOM, net 60. This allows the customer a cash discount of 8% if the bill is paid within 10 days of the end of the month; otherwise, the full payment is due within 60 days of the invoice date.

A firm that buys on credit is in effect borrowing from its supplier. It saves cash today but will have to pay later. This is an implicit loan from the supplier. Of course, if it is free, a loan is always worth having. But if you pass up a cash discount, then the loan may prove to be very expensive. For example, a customer who buys on terms of 3/10, net 30, may decide to forgo the cash discount and pay on the thirtieth day. The customer obtains an extra 20 days’ credit by deferring payment from 10 to 30 days after the sale but pays about 3% more for the goods. This is equivalent to bor- rowing money at a rate of 74.3% a year. To see why, consider an order of $100. If the firm pays within 10 days, it gets a 3% discount and pays only $97. If it waits the full 30 days, it pays $100. The extra 20 days of credit increase the payment by the fraction 3/97 =  .0309, or 3.09%. Therefore, the implicit interest charged to extend the trade credit is 3.09% per 20 days. There are 365/20 = 18.25 twenty-day periods in a year, so the effective annual rate of interest on the loan is (1.0309) 18.25  − 1 = .743, or 74.3%.

The general formula for calculating the implicit annual interest rate for customers who do not take the cash discount is

Effective annual rate = a1 + discount discounted price

b365/extra days credit - 1 (20.1) The discount divided by the discounted price is the percentage increase in price paid by a customer who forgoes the discount. In our example, with terms of 3/10, net 30, the percentage increase in price is 3/97 = .0309, or 3.09%. This is the implicit rate of interest per period. The period of the loan is the number of extra days of credit that you can obtain by forgoing the discount. In our example, this is 20 days. To annualize this rate, we compound the per-period rate by the number of periods in a year.

Of course any firm that delays payment beyond day 30 gains a cheaper loan but damages its reputation for creditworthiness.

Example 20.1 Trade Credit Rates What is the implied interest rate on trade credit if the discount for early payment is 5/10, net 60?

The cash discount in this case is 5% and customers who choose not to take the discount receive an extra 60 − 10 = 50 days credit. So the effective annual interest is

Effective annual rate = a1 + discount discounted price

b365/extra days credit - 1

= a1 + 5 95

b365/50 - 1 = .454, or 45.4% In this case the customer who does not take the discount is effectively borrowing money at an annual interest rate of 45.4%.

You might wonder why the effective interest rate on trade credit is typically so high. At such steep effective rates, most purchasers will choose to pay early and receive the discount. Those who don’t are probably strapped for cash. It makes sense to charge these firms a high rate of interest.

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580 Part Six Financial Analysis and Planning

Credit Agreements The terms of sale define the amount of any credit but not the nature of the contract. Repetitive sales are almost always made on open account and involve only an implicit contract. There is simply a record in the seller’s books and a receipt signed by the buyer.

Sometimes you might want a clear commitment from the buyer before you deliver the goods. In this case the common procedure is to arrange a commercial draft. This is simply jargon for an order to pay. 1 It works as follows: The seller prepares a draft ordering payment by the customer and sends this draft to the customer’s bank. If immediate payment is required, the draft is termed a sight draft; otherwise, it is known as a time draft. Depending on whether it is a sight or a time draft, the customer either tells the bank to pay up or acknowledges the debt by adding the word “accepted” and a signature. Once accepted, a time draft is like a postdated check and is called a trade acceptance. This trade acceptance is then forwarded to the seller, who holds it until the payment becomes due.

If your customer’s credit is shaky, you may ask the customer to arrange for a bank to accept the time draft. In this case, the bank guarantees the customer’s debt, and the draft is called a banker’s acceptance. Banker’s acceptances are often used in overseas trade. They are actively bought and sold in the money market, the market for short- term high-quality debt.

Credit Analysis There are a number of ways to find out whether customers are likely to pay their debts, that is, to carry out credit analysis. The most obvious indication is whether they have paid promptly in the past. Prompt payment is usually a good omen, but beware of the customer who establishes a high credit limit on the basis of small payments and then disappears, leaving you with a large unpaid bill.

If you are dealing with a new customer, you will probably check with a credit agency. Dun & Bradstreet, which is by far the largest of these agencies, provides credit ratings on a huge number of domestic and foreign firms. In addition to its rating ser- vice, Dun & Bradstreet provides on request a full credit report on a potential customer.

Credit agencies usually report the experience that other firms have had with your customer, but you can also get this information by contacting those firms directly or through a credit bureau.

Your bank can also make a credit check. It will contact the customer’s bank and ask for information on the customer’s average bank balance, access to bank credit, and general reputation.

In addition to checking with your customer’s bank, it might make sense to discover what everybody else in the financial community thinks about your customer’s credit standing. Does that sound expensive? Not if your customer is a public company. You just look at the Moody’s or Standard & Poor’s rating for the customer’s bonds. 2 You can also compare prices of these bonds with the prices of other firms’ bonds. (Of course the comparisons should be between bonds of similar maturity, coupon, and so on.)

open account Agreement whereby sales are made with no formal debt contract.

1 For example, a check is an example of a draft. Whenever you write a check, you are ordering the bank to make a payment.

credit analysis Procedure to determine the likelihood a customer will pay its bills.

2 We described bond ratings in Chapter 6, Section 6.6.

What would be the effective annual interest rate in Example 20.1 if the terms of sale were 5/10, net 50? Why is the rate higher?

Self-Test 20.2

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Chapter 20 Working Capital Management 581

If you don’t wish to rely on the judgment of others, you can do your own homework. Ideally this would involve a detailed analysis of the company’s business prospects and financing, but this is usually too expensive. Therefore, credit analysts concentrate on the company’s financial statements, using rough rules of thumb to judge whether the firm is a good credit risk. The rules of thumb are based on financial ratios. Chapter 4 described how these ratios are calculated and interpreted.

Numerical Credit Scoring Analyzing credit risk is like detective work. You have a lot of clues—some important, some fitting into a neat pattern, others contradic- tory. You must weigh these clues to come up with an overall judgment.

When the firm has a small, regular clientele, the credit manager can easily handle the process informally and make a judgment about what are often termed the five Cs of credit:

1. The customer’s character. 2. The customer’s capacity to pay. 3. The customer’s capital. 4. The collateral provided by the customer. 3 5. The condition of the customer’s business.

When the company is dealing directly with consumers or with a large number of small trade accounts, some streamlining is essential. In these cases it may make sense to use a scoring system to prescreen credit applications.

If you apply for a credit card or a bank loan, you will probably be asked to complete a questionnaire that provides details about your job, home, and financial health. This infor- mation is then used to calculate an overall credit score. 4 If you do not make the grade on the score, you are likely to be refused credit or subjected to a more detailed analysis. In a similar way, banks and the credit departments of industrial firms also use mechanical credit-scoring systems to assess the financial health of potential commercial customers.

Suppose that you are given the task of developing a credit-scoring system that will help to decide when it makes sense to extend credit to the firm’s customers. You start by comparing the financial statements of companies that went bankrupt over a 40-year period with those of surviving firms. Figure 20.1 shows what you find. Panel a illus- trates that, as early as 4 years before they went bankrupt, failing firms were earning a much lower return on assets (ROA) than firms that survived. Panel b shows that on average they also had a high ratio of liabilities to assets, and panel c shows that EBITDA (earnings before interest, taxes, depreciation, and amortization) was low rel- ative to the firms’ total liabilities. Thus bankrupt firms were less profitable (low ROA), were more highly leveraged (high ratio of liabilities to assets), and generated relatively little cash (low ratio of EBITDA to liabilities). In each case, these indicators of the firms’ financial health steadily deteriorated as bankruptcy approached.

William Beaver, Maureen McNichols, and Jung-Wu Rhie studied these firms and concluded that these variables could be used together to estimate the likelihood of bankruptcy. The chance of failing during the next year relative to the odds of not failing was best estimated by the following equation: 5

Log(relative chance of failure) = -6.445 - 1.192 × ROA + 2.307 × liabilities

assets -.346 ×

EBITDA

liabilities

3 For example, the customer can offer bonds as collateral. These bonds can then be seized by the seller if the customer fails to pay. 4 The most commonly used consumer credit score is the FICO score developed by Fair Isaac Corp., which uses data provided by any one of three credit bureaus—Experian, Trans Union, or Equifax. 5 See W. H. Beaver, M. F. McNichols, and J.-W. Rhie, “Have Financial Statements Become Less Informative? Evidence from the Ability of Financial Ratios to Predict Bankruptcy,” Review of Accounting Studies 10 (2005), pp. 93–122.

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582 Part Six Financial Analysis and Planning

FIGURE 20.1 Financial ratios of failing and nonfailing firms

Source: W. H. Beaver, M. F. McNichols, and J.-W. Rhie, “Have Financial Statements Become Less Informative? Evidence from the Ability of Financial Ratios to Predict Bankruptcy,” Review of Accounting Studies 10 (2005), pp. 93–122.

Years before bankruptcy

(a)

R et

u rn

o n

a ss

et s

(% )

-20

-15

-10

-5

0

5

10

3 2 14

Failing firms Nonfailing firms

Failing firms Nonfailing firms

0

4 3 1

10

20

30

40

50

60

70

80

2

90

100

Years before bankruptcy

T o

ta l l

ia b

ili ti

es a

s %

o f

as se

ts

(b)

-10

-5

0

4 3 2 1

5

10

15

20

25

30

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40

Failing firms Nonfailing firms

Years before bankruptcy

E B

IT D

A a

s %

o f

to ta

l l ia

b ili

ti es

(c)

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Chapter 20 Working Capital Management 583

A variety of similar techniques have been used to develop credit-scoring systems. The model that we have just described uses the technique of hazard analysis. An early and still widely used approach, the famous Z -score model developed by Edward Altman uses multiple discriminant analysis to separate the creditworthy sheep from the impecunious goats. 6 His analysis suggested that a firm’s financial ratios could be combined as follows into a summary measure of creditworthiness, now commonly known as a Z score: 7

Z = 3.3 × EBIT

total assets + 1.0 ×

sales

total assets + .6 ×

market value of equity

total book debt +

1.4 × retained earnings

total assets + 1.2 ×

working capital

total assets

Altman found that most bankrupt firms had Z scores below 2.7 before they went bank- rupt, while most nonbankrupt firms had Z scores above this level.

6 See E. I. Altman, “Financial Ratios and the Prediction of Corporate Bankruptcy,” Journal of Finance 23 ( September 1968), pp. 589–609. 7 EBIT is earnings before interest and taxes. E. I. Altman, “Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy,” Journal of Finance 23 (September 1968), pp. 589–609.

Example 20.2 The Z -Score Model Consider a firm with the following financial ratios:

EBIT Total assets

= .12 Sales

Total assets = 1.4

Market value of equity Total book debt

= .9

Retained earnings Total assets

= .4 Working capital

Total assets = .12

The firm’s Z score is

(3.3 × .12) + (1.0 × 1.4) + (.6 × .9) + (1.4 × .4) + (1.2 × .12) = 3.04

This score is above the cutoff level for predicting bankruptcy, and it would there- fore be considered favorably in an evaluation of the firm’s creditworthiness.

The nearby box describes how statistical scoring systems can provide timely first- cut estimates of creditworthiness. These assessments can streamline the credit deci- sion and free up labor for other, less mechanical tasks.

The Credit Decision You have taken the first three steps toward an effective credit operation. In other words, you have fixed your terms of sale; you have decided whether to sell on open account or to ask your customers to sign an IOU; and you have established a procedure for estimating the probability that each customer will pay up. Your next step is to decide on credit policy.

If there is no possibility of repeat orders, the credit decision is relatively simple. Figure 20.2 summarizes your choice. On the one hand, you can refuse credit and pass up the sale. In this case you make neither profit nor loss. The alternative is to offer credit. If you offer credit and the customer pays, you benefit by the profit margin on the sale. If the customer defaults, you lose the cost of the goods delivered. The decision to offer credit depends on the probability of payment. You should grant credit if the expected profit from doing so is greater than the profit from refusing.

credit policy Standards set to determine the amount and nature of credit to extend to customers.

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You should grant credit if the expected profit from doing so is positive.

The overriding factor in a small-business credit score is your personal credit history. Specifi cally, the system looks at whether you pay your personal bills on time. The later you pay, the fewer points you get, and the more bills you pay late, the more your score gets knocked down.

The next key input is how much credit you’ve already got access to and balances on your accounts. If lines of credit are maxed out, lenders worry that there is little room to maneuver if the business runs into trouble. Other major red fl ags include bankruptcies, debts turned over to a collection agency, liens, and even overdue child-support payments. You can even get penalized for shopping too hard for credit.

Finally, specifi c business characteristics are weighed. They include the size of the company, its age, the industry in which it does business, and whether it’s a corporation, part- nership, or sole proprietorship. A sole prop gets fewer points than a partnership, and a partnership gets fewer points than a corporation. After all, if you’re a sole proprietor and you get hit by a bus, all bets are off on your business. By the same token, a manufacturer gets higher points than bars or restau- rants because it’s less likely to go under quickly.

To hear bankers tell it, credit scoring is the best thing to hap- pen to small-business borrowers since the invention of com- pound interest. Forget haggling over things like how well your business is doing or what your competitors are up to. Just hand in some predetermined data about yourself and your company, let the computer crunch the numbers, and voilà: Out comes a “credit score” that predicts the chances that you’ll actually pay off the loan. Score high enough, and you get approved, sometimes within minutes.

Scoring is already ubiquitous in consumer lending, and 22 of the 25 biggest players in the small-business loan mar- ket use the system, according to Fair, Isaac & Co., a pio- neer in the development of credit-scoring software. Almost any loan of $50,000 or less issued by a national fi nancial services company will have gone through a credit-scoring system.

Credit-scoring models assign points for up to 20 factors. The more points you get, the better credit risk you repre- sent. The best-known credit-scoring models are provided by Fair, Isaac. The score on its Small Business Scoring Service ranges from 50 to 350, with most small businesses falling into the 150 to 250 area. While lenders set their own cutoff points, if you score above 220, that’s generally good, while scores below 170 are considered high risk.

Finance in Practice Credit Scoring: What Your Lender Won’t Tell You

Source: V. M. Kahn, “Credit Scoring: What Your Lender Won’t Tell You,” Busi- nessWeek, May 22, 2000, p. F30. Used with permission of Bloomberg L.P. Copyright © 2011. All rights reserved.

Suppose that the probability that the customer will pay up is p. If the customer does pay, you receive additional revenues (REV) and you deliver goods that you incurred costs to produce; your net gain is the present value of REV − COST. Unfortunately, you can’t be certain that the customer will pay; there is a probability (1 −  p ) of default. Default means you receive nothing but still incur the additional costs of the delivered goods. The expected profit 8 from the two sources of action is therefore as follows:

8 Notice that we use the present values of costs and revenues. This is because there sometimes are significant lags between costs incurred and revenues generated. Also, while we follow convention in referring to the “expected profit” of the decision, it should be clear that our equation for expected profit is in fact the net present value of the decision to grant credit. As we emphasized in Chapter 1, the manager’s task is to add value, not to maximize accounting profits.

Action Expected Profi t

Refuse credit: 0 Grant credit: p  × PV(REV − COST) − (1 −  p ) × PV(COST)

FIGURE 20.2 If you refuse credit, you make neither profit nor loss. If you offer credit, there is a probability p that the customer will pay and you will make REV − COST and there is a probability (1 −  p ) that the customer will default and you will lose COST.

REV - COST

- COST

Offer credit

Refuse credit

0

Customer defaults (1- p)

Customer pays (p)

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Chapter 20 Working Capital Management 585

Example 20.3 The Credit Decision Consider the case of the Cast Iron Company. On each nondelinquent sale Cast Iron receives revenues with a present value of $1,200 and incurs costs with a pres- ent value of $1,000. Therefore, the company’s expected profit if it offers credit is

p × PV(REV - COST) - (1 - p) × PV(COST) = p × 200 - (1 - p) × 1,000

If the probability of collection is 5/6, Cast Iron can expect to break even:

Expected profit = 5/6 × 200 - (1 - 5/6) × 1,000 = 0

Thus Cast Iron’s policy should be to grant credit whenever the chances of collec- tion are better than 5 out of 6.

In this last example, the net present value of granting credit is positive if the prob- ability of collection exceeds 5/6. In general, this break-even probability can be found by setting the net present value of granting credit equal to zero and solving for p. It turns out that the formula for the break-even probability is simply the ratio of the pres- ent value of costs to revenues:

p × PV(REV - COST) - (1 - p) × PV(COST) = 0

Break-even probability of collection, then, is

p = PV(COST)

PV(REV)

and the break-even probability of default is

(1 - p) = 1 - PV(COST)/PV(REV) = PV(PROFIT)/PV(REV)

In other words, the break-even probability of default is simply the profit margin on each sale. If the default probability is larger than the profit margin, you should not extend credit.

Think what this implies. Companies that operate on low profit margins should be cautious about granting credit to high-risk customers. Firms with high margins can afford to deal with more doubtful ones.

What is the break-even probability of collection if the present value of the rev- enues from the sale is $1,100 rather than $1,200? Why does the break-even probability increase? Use your answer to decide whether firms that sell high- profit-margin or low-margin goods should be more willing to issue credit.

Self-Test 20.3

So far we have ignored the possibility of repeat orders. But one of the reasons for offering credit today is that you may get yourself a good, regular customer.

Suppose Cast Iron has been asked to extend credit to a new customer. You can find little information on the firm, and you believe that the probability of payment is no better than .8. If you grant credit, the expected profit on this order is

Expected profit on initial order = p × PV(REV - COST) - (1 - p) × PV(COST)

= (.8 × 200) - (.2 × 1,000) = -$40

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586 Part Six Financial Analysis and Planning

You decide to refuse credit. This is the correct decision if there is no chance of a repeat order. But now consider

future periods. If the customer does pay up, there will be a reorder next year. Having paid once, the customer will seem less of a risk. For this reason, any repeat order is very profitable.

Think back to Chapter 10, and you will recognize that the credit decision bears many similarities to our earlier discussion of real options. By granting credit now, the firm retains the option to grant credit on an entire sequence of potentially profitable repeat sales. This option can be very valuable and can tilt the decision toward granting credit. Even a dubious prospect may warrant some initial credit if there is a chance that the company will develop into a profitable steady customer.

Example 20.4 Credit Decisions with Repeat Orders To illustrate, let’s look at an extreme case. Suppose that if a customer pays up on the first sale, you can be sure you will have a regular and completely reliable cus- tomer. In this case, the value of such a customer is not the profit on one order but an entire stream of profits from repeat purchases. For example, suppose that the customer will make one purchase each year from Cast Iron. If the discount rate is 10% and the profit on each order is $200 a year, then the present value of a perpet- ual stream of business from a good customer is not $200 but $200/.10 = $2,000. There is a probability p that Cast Iron will secure a good customer with a value of $2,000. There is a probability of (1 -  p ) that the customer will default, resulting in a loss of $1,000. So, once we recognize the benefits of securing a good and perma- nent customer, the expected profit from granting credit is

Expected profit = (p × 2,000) - (1 - p) × 1,000

This is positive for any probability of collection above .33. Thus the break-even probability falls from 5/6 to 1/3. If one sale may lead to profitable repeat sales, the firm should be inclined to grant credit on the initial purchase.

How will the break-even probability vary with the discount rate? Try a rate of 20% in Example 20.4. What is the intuition behind your answer?

Self-Test 20.4

Of course, real-life situations are generally far more complex than our simple exam- ples. Customers are not all good or all bad. Many pay late consistently; you get your money, but it costs more to collect and you lose a few months’ interest. And estimating the probability that a customer will pay up is far from an exact science. Then there is uncertainty about repeat sales. There may be a good chance that the customer will give you further business, but you can’t be sure of that and you can’t know for how long she or he will continue to buy from you.

Like almost all financial decisions, credit allocation involves a strong dose of judg- ment. Our examples are intended as reminders of the issues involved rather than as cookbook formulas. Here are the basic things to remember:

1. Maximize profit. As credit manager your job is not to minimize the number of bad accounts; it is to maximize profits. You are faced with a trade-off. The best

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Chapter 20 Working Capital Management 587

that can happen is that the customer pays promptly; the worst is default. In the one case the firm receives the full additional revenues from the sale less the additional costs; in the other it receives nothing and loses the costs. You must weigh the chances of these alternative outcomes. If the margin of profit is high, you are justified in a liberal credit policy; if it is low, you cannot afford many bad debts.

2. Concentrate on the dangerous accounts. You should not expend the same effort on analyzing all credit decisions. If an application is small or clear-cut, your decision should be largely routine; if it is large or doubtful, you may do better to move straight to a detailed credit appraisal. Most credit managers don’t make credit decisions on an order-by-order basis. Instead, they set a credit limit for each customer. The sales representative is required to refer the order for approval only if the customer exceeds this limit.

3. Look beyond the immediate order. Sometimes it may be worth accepting a relatively poor risk as long as there is a likelihood that the customer will grow into a regular and reliable buyer. (This is why credit card companies are eager to sign up college students even though few students can point to an established credit history.) New businesses must be prepared to incur more bad debts than established businesses because they have not yet formed relationships with low-risk customers. This is part of the cost of building up a good customer list.

Collection Policy It would be nice if all customers paid their bills by the due date. But they don’t, and since you may also “stretch” your payables, from time to time, you can’t altogether blame them.

Slow payers impose two costs on the firm. First, they require the firm to spend more resources in collecting payments. They also force the firm to invest more in working capital. Recall from Chapter 4 that accounts receivable are proportional to the average collection period (also known as days’ sales in receivables):

Accounts receivable = daily sales × average collection period

When your customers stretch payables, you end up with a longer collection period and a greater investment in accounts receivable. That’s why you need a collection policy.

The credit manager keeps a record of payment experiences with each customer. In addition, the manager monitors overdue payments by drawing up a schedule of the aging of receivables. The aging schedule classifies accounts receivable by the length of time they are outstanding. This may look roughly like Table 20.1 . The table shows that customer A, for example, is fully current: There are no bills outstanding for more than a month. Customer Z, however, might present problems, as there are $15,000 in bills that have been outstanding for more than 3 months.

collection policy Procedures to collect and monitor receivables.

aging schedule Classification of accounts receivable by time outstanding.

Customer’s Name

Less than 1 Month 1–2 Months 2–3 Months

More than 3 Months Total Owed

A $ 10,000 $ 0 $ 0 $ 0 $ 10,000 B 8,000 3,000 0 0 11,000 • • • • • • • • • • • • • • • • • • Z 5,000 4,000 6,000 15,000 30,000

Total $200,000 $40,000 $15,000 $43,000 $298,000

TABLE 20.1 An aging schedule of receivables

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588 Part Six Financial Analysis and Planning

When a customer is in arrears, the usual procedure is to send a statement of account and to follow this at intervals with increasingly insistent letters, telephone calls, or fax messages. If none of these has any effect, most companies turn the debt over to a collection agency or an attorney.

Large firms can reap economies of scale in record keeping, billing, and so on, but the small firm may not be able to support a fully fledged credit operation. However, it can obtain some scale economies by farming out part of the job to a factor. The factor and its client’s firm agree on credit limits for each customer, and the client notifies each customer that the factor has purchased the debt (i.e., the trade credit). The factor then takes on the responsibility (and risk) of collecting the bills and pays the invoice value to the client minus a fee of 1% or 2%.

Factoring is fairly prevalent in Europe but accounts for only a small proportion of debt collection in the United States. It is most common in industries such as cloth- ing and toys. These are characterized by many small producers and retailers that do not have long-term relationships with each other. Because a factor may be employed by a number of manufacturers, it sees a larger proportion of the transactions than any single firm and therefore is better placed to judge the creditworthiness of each customer. 9

There is always a potential conflict of interest between the collection depart- ment and the sales department. Sales representatives commonly complain that they no sooner win new customers than the collection department frightens them off with threatening letters. The collection manager, on the other hand, bemoans the fact that the sales force is concerned only with winning orders and does not care whether the goods are subsequently paid for. This conflict is another example of the agency prob- lem introduced in Chapter 1. Good collection policy balances conflicting goals. The company wants cordial relations with its customers. It also wants them to pay their bills on time.

There are instances of cooperation between sales managers and the financial man- agers who worry about collections. For example, the specialty chemicals division of a major pharmaceutical company actually made a business loan to an important cus- tomer that had been suddenly cut off by its bank. The pharmaceutical company bet that it knew its customer better than the customer’s bank did—and the pharmaceuti- cal company was right. The customer arranged alternative bank financing, paid back the pharmaceutical company, and became an even more loyal customer. It was a nice example of financial management supporting sales.

It is not common for suppliers to make business loans in this way, but they lend money indirectly whenever they allow a delay in payment. Trade credit can be an important source of funds for indigent customers that cannot obtain a bank loan. But that raises an important question: If the bank is unwilling to lend, does it make sense for you, the supplier, to continue to extend trade credit? Here are two possible reasons that it may make sense: First, as in the case of our pharmaceutical company, you may have more information than the bank about the customer’s business. Second, you need

9 This point is made in S. L. Mian and C. W. Smith, Jr., “Accounts Receivable Management Policy: Theory and Evidence,” Journal of Finance 47 (March 1992), pp. 169–200.

Suppose a customer who buys goods on terms 1/10, net 45, always forgoes the cash discount and pays on the 45th day after sale. If the firm typically buys $10,000 of goods a month, spread evenly over the month, what will the aging schedule look like?

Self-Test 20.5

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Chapter 20 Working Capital Management 589

to look beyond the immediate transaction and recognize that your firm may stand to lose some profitable future sales if the customer goes out of business. 10

20.2 Inventory Management The second important current asset is inventory. Inventories may consist of raw materials, work in process, or finished goods awaiting sale and shipment. Firms are not obliged to carry these inventories. For example, they could buy materials day by day, as needed. But then they would pay higher prices for ordering in small lots, and they would risk produc- tion delays if the materials were not delivered on time. They can avoid that risk by ordering more than the firm’s immediate needs. Similarly, firms could do away with inventories of finished goods by producing only what they expect to sell tomorrow. But this also could be a dangerous strategy. A producer with only a small inventory of finished goods is more likely to be caught short and unable to fill orders if demand is unexpectedly high. Moreover, a large inventory of finished goods may allow longer, more economical production runs.

But there are also costs to holding inventories that must be set against these ben- efits. These are called carrying costs. For example, money tied up in inventories does not earn interest; storage and insurance must be paid for; and there may be a risk of spillage or obsolescence. Therefore, production managers need to strike a sensible bal- ance between the benefits of holding inventory and the costs.

10 Of course, banks also need to recognize the possibility of continuing business from the firm. The question therefore is whether suppliers have a greater stake in the firm’s continuing prosperity. For some evidence on the determinants of the supply and demand for trade credit, see M. A. Petersen and R. G. Rajan, “Trade Credit: Theories and Evidence,” Review of Financial Studies 10 (Fall 1997), pp. 661–692.

Example 20.5 Inventory Management Here is a simple inventory problem. Akron Wire Products uses 255,000 tons a year of wire rod. Suppose that it orders Q tons at a time from the manufacturer. Just before delivery, its inventories of wire have run down to zero. Just after delivery, it has an inventory of Q tons. Thus, Akron’s inventory of wire rod roughly follows the sawtooth pattern in Figure 20.3 .

There are two costs to holding this inventory. First, there are carrying costs, such as the cost of storage, and the cost of the capital that is tied up in inventory. Sup- pose these costs work out to an annual figure of about $55 per ton. The second type of cost is the order cost. Each order that Akron places with the manufacturer involves a fixed handling and delivery charge of $450.

BEYOND THE PAGE

brealey.mhhe.com/ch20-01

How Akron’s inventory costs change with

order size

FIGURE 20.3 A simple inventory rule. The company waits until inventories of materials are exhausted and then reorders a constant quantity.

In ve

n to

ry le

ve l

Time

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590 Part Six Financial Analysis and Planning

In calculating the economic order quantity for Akron Wire, we made several unreal- istic assumptions. For instance, most firms do not use up their inventory of raw mate- rial at a constant rate, and they would not wait until stocks had completely run out before replenishing them. But this simple model does capture some essential features of inventory management:

• Optimal inventory levels involve a trade-off between carrying costs and order costs. • Carrying costs include the cost of storing goods as well as the cost of capital tied up

in inventory. • A firm can manage its inventories by waiting until they reach some minimum level

and then replenishing them by ordering a predetermined quantity. • When carrying costs are high and order costs are low, it makes sense to place more

frequent orders and maintain higher levels of inventory. If order costs are high, you will want to make larger and therefore less frequent orders.

• Inventory levels do not rise in direct proportion to sales. As sales increase, the opti- mal inventory level rises, but less than proportionately.

FIGURE 20.4 As the inventory order size increases, order costs fall and inventory carrying costs rise. Total costs are minimized when the saving in order costs equals the increase in carrying costs.

Here, then, is the kernel of the inventory problem: As Akron increases its order size, the number of orders falls but average inventory rises. Figure 20.4 shows that cost related to the number of orders declines, though at a decreasing rate, while carrying cost related to inventory size rises. It is worth increasing order size as long as the decline in order cost outweighs the rise in carrying cost. The optimal inven- tory policy is one in which these two effects exactly offset each other. In our exam- ple, this occurs when the firm places about 250 orders a year (roughly one order every working day) and the size of each order is Q  = 2,043 tons. The optimal order size (2,043 tons in our example) is known as the economic order quantity, or EOQ. 11

11 When the firm uses up materials at a constant rate, as in our example, there is a simple formula for calculating the economic order quantity (EOQ). It is

Optimal order size = Q = Å 2 × sales × cost per order

carrying cost

In our example, Q = Å 2 × 255,000 × 450

55 = 2,043 tons.

Optimal order size

Order costs

Carrying costs

0

50 50

0

70 0

90 0

90 0

1, 10

0

1, 30

0

1, 50

0

1, 70

0

1, 90

0

2, 04

3

2, 20

0

2, 40

0

2, 60

0

2, 80

0

3, 00

0

3, 20

0

3, 40

0

3, 60

0

3, 80

0

4, 00

0

4, 20

0

4, 40

0

4, 60

0

4, 80

0

100

150

200

250

300

Order size (tons)

C o

st s

($ t

h o

u sa

n d

s)

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Corporations today get by with lower levels of inventory than they used to. Thirty years ago, inventories held by U.S. companies accounted for 12% of firm assets. Today the figure is about 8%. One way that companies have reduced inventory levels is by moving to a just-in-time approach. Just-in-time was pioneered by Toyota in Japan. Toyota keeps inventories of auto parts to a minimum by ordering supplies only as they are needed. Thus deliveries of components to its plants are made throughout the day at intervals as short as 1 hour. Toyota is able to operate successfully with such low inven- tories only because it has a set of plans to ensure that strikes, traffic snarl-ups, or other hazards don’t halt the flow of components and bring production to a standstill. Many companies in the United States have learned from Toyota’s example and have pared their investment in inventories.

Firms are also finding that they can reduce their inventories of finished goods by producing their goods to order. For example, Dell Computer discovered that it did not need to keep a large stock of finished machines. Its customers are able to use the Inter- net to specify what features they want on their PC. The computer is then assembled to order and shipped to the customer. 12

20.3 Cash Management Short-term securities pay interest; cash doesn’t. So why do corporations and individu- als hold billions of dollars in cash and demand deposits? Why, for example, don’t you take all your cash and invest it in interest-bearing securities? The answer of course is that cash gives you more liquidity than do securities. You can use it to buy things. It is hard enough to get New York cab drivers to give you change for a $20 bill, but try asking them to split a Treasury bill.

When you have only a small proportion of your wealth in cash, a little extra can be extremely useful; when you have a substantial holding, any additional liquidity is not worth much. Therefore, as financial manager you want to hold cash balances up to the point where the marginal value of the liquidity is equal to the value of the interest forgone.

In choosing between cash and short-term securities, the financial manager faces a task like that of the production manager. After all, cash is just another raw material that you need to do business, and there are costs and benefits to holding large “inventories” of cash. If the cash were invested in securities, it would earn interest. On the other hand, you can’t use those securities to pay the firm’s bills. If you had to sell them every time you needed to pay a bill, you could incur heavy transaction costs. The financial manager must trade off the cost of keeping an inventory of cash (the lost interest) against the benefits (the saving on transaction costs).

For very large firms, the transaction costs of buying and selling securities are trivial compared with the opportunity cost of holding idle cash balances. Suppose that the interest rate is 3% per year, or roughly 3/365 = .0082% per day. Then the daily interest earned on $1 million is .000082 × $1,000,000 = $82. Even at a cost of $50 per trans- action, which is generous, it pays to buy Treasury bills today and sell them tomorrow rather than to leave $1 million idle overnight.

A corporation such as Walmart, with $470 billion of annual sales, has an average daily cash flow of $470,000,000,000/365 = $1,287 million. Firms of this size end up buying or selling securities once a day, every day, unless by chance they have only a small positive cash balance at the end of the day.

Banks have developed a variety of ways to help such firms invest idle cash. For example, they may provide sweep programs, in which the bank automatically

just-in-time approach System of inventory management that requires minimal inventories of materials and very frequent deliveries by suppliers.

12 These examples of just-in-time and build-to-order production are taken from T. Murphy, “JIT When ASAP Isn’t Good Enough,” Ward’s Auto World, May 1999, pp. 67–73; R. Schreffler, “Alive and Well,” Ward’s Auto World, May 1999, pp. 73–77; “A Long March: Mass Customization,” The Economist, July 14, 2001, pp. 63–65.

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592 Part Six Financial Analysis and Planning

“sweeps” surplus funds into a higher-interest account. Why then do these large firms hold any significant amounts of cash in non-interest-bearing accounts? For two rea- sons: First, cash may be left in accounts to compensate banks for the services they provide. Second, large corporations may have literally hundreds of accounts with doz- ens of different banks. It is often less expensive to leave idle cash in some of these accounts than to monitor each account daily and make daily transfers between them.

One major reason for the proliferation of bank accounts is decentralized manage- ment. If you give a subsidiary operating freedom to manage its own affairs, you must also give it the right to spend and receive cash. Good cash management nevertheless implies some degree of centralization. You cannot maintain your desired inventory of cash if all the subsidiaries in the group are responsible for their own private pools of cash. And you certainly want to avoid situations in which one subsidiary is investing its spare cash at 8% while another is borrowing at 10%. It is not surprising, therefore, that even in highly decentralized companies there is generally central control over cash balances and bank relations.

Check Handling and Float Traditionally, most large bills in the United States have been paid with checks. But check handling is a cumbersome and labor-intensive task, and it can take several days for a check to clear. Suppose, for example, that you renew your auto insurance by writ- ing a check for $600, which you mail to your insurance company. A day or so later the insurance company receives your check and deposits it in its bank account. But this money isn’t available to the company immediately. The company’s bank won’t actually have the money in hand until it sends the check to your bank and receives pay- ment. Since the bank has to wait, it makes the insurance company wait too—usually 1 or 2 business days. Until the check has been presented and cleared, that $600 will continue to sit in your bank account.

Checks that have been mailed but not yet cleared are known as float. In our exam- ple, float provided you with an extra $600 in your bank account while your check went first to the insurance company, then to the company’s bank, and finally to your own bank. This may make float seem like a marvelous invention, but unfortunately it can also work in reverse. Every time someone writes you a check, you have to wait several days after depositing it before you may spend the money.

Changes in federal law in the last several years have helped to speed up collections. The Check Clearing for the 21st Century Act, usually known as “Check 21,” allows banks to send digital images of checks to one another rather than sending the checks themselves. So fewer cargo planes and trucks need to crisscross the country to take bundles of checks from one bank to another. The cost of processing checks is also being reduced by a technological innovation known as check conversion. In this case, when you write a check, the details of your bank account and the amount of the pay- ment are automatically captured at the point of sale, your check is handed back to you, and your bank account is immediately debited.

Firms that receive a large volume of paper checks have devised a number of ways to ensure that the cash becomes available as quickly as possible. For example, a retail chain may arrange for each branch to deposit receipts in a collection account at a local bank. Surplus funds are then periodically transferred electronically to a concentration account at one of the company’s principal banks. There are two reasons that concentra- tion banking allows the company to gain quicker use of its funds. First, because the store is nearer to the bank, transfer times are reduced. Second, since the customer’s check is likely to be drawn on a local bank, the time taken to clear the check is also reduced.

Concentration banking is often combined with a lock-box system. In this case the firm’s customers are instructed to send their payments to a regional post-office box. The local bank then takes on the administrative chore of emptying the box and depos- iting the checks in the company’s local deposit account.

concentration account Customers make payments to a regional collection center, which then transfers funds to an account at a principal bank.

lock-box system System whereby customers send payments to a post- office box and a local bank collects and processes checks.

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Chapter 20 Working Capital Management 593

Other Payment Systems There are a variety of ways besides checks that you can pay for larger purchases or send payments to another location. Some of the more important payment methods are set out in Table 20.2 .

Figure 20.5 compares use of these payment systems around the world. Payment patterns vary widely across countries. For example, look at the bottom (blue) portion of the bars in the figure. Checks are virtually unheard of in Switzerland. Most pay- ments there are made by debit cards or credit transfer. By contrast, Americans love to write checks. In 2012, U.S. individuals and firms made about 18 billion payments by check. But even in the United States, check writing is steadily giving way to electronic payments. The number of checks written fell by more than 50% between 2003 and 2012. Over 50% of U.S. households now use direct payment for recurring expendi- tures, and nearly three-quarters of employees are paid by direct deposit.

In fact, the use of checks continues to decline around the world as the market share of credit and debit cards continues to grow. In addition, mobile phone technology and

Example 20.6 Lock-Box Systems Suppose that you are thinking of opening a lock box. The local bank shows you a map of mail delivery times. From that and knowledge of your customers’ locations, you come up with the following data:

On this basis, the lock box would reduce float by

150 items per day × $1,200 per item × (1.2 + .8) days saved = $360,000

Invested at .02% per day, that gives a daily return of

.0002 × $360,000 = $72

The bank’s charge for operating the lock-box system depends on the number of checks processed. Suppose that the bank charges $.26 per check. That works out to 150 × $.26 = $39 per day. You are ahead by $72 − $39 = $33 per day, plus whatever your firm saves from not having to process the checks itself.

Average number of daily payments to lock box  = 150 Average size of payment = $1,200 Rate of interest per day = .02% Saving in mailing time = 1.2 days Saving in processing time = .8 day

How will the following conditions affect the price that a firm should be willing to pay for a lock-box service?

a. The average size of its payments increases. b. The number of payments per day increases (with no change in average

size of payments). c. The interest rate increases. d. The average mail time saved by the lock-box system increases. e. The processing time saved by the lock-box system increases.

Self-Test 20.6

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594 Part Six Financial Analysis and Planning

the Internet are encouraging the development of new infant payment systems. Here are just two examples:

• Electronic bill presentment and payment (or EBPP) allows companies to bill cus- tomers and receive payments through the Internet. Already in Finland, two out of three people regard the Internet as the most typical medium for paying bills.

• Stored value cards (or e-money) let you transfer funds to a card that can be used pretty much as electronic cash. For example, Hong Kong’s Octopus card system, which was developed to pay for travel fares, has become a widely used electronic cash system throughout the territory.

Electronic Funds Transfer As we’ve just noted, throughout the world payments are increasingly being made elec- tronically. The most familiar forms of electronic payment are the credit card and debit card, but there are three other important ways that money can travel electronically. It can do so by direct payment, direct deposit, or wire transfer.

Direct payment systems (also known as direct debit systems) are used for recur- ring expenditures, such as utility bills, insurance premiums, and mortgage or loan

Check When you write a check, you are instructing your bank to pay a specifi ed sum on demand to the particular fi rm or person named on the check. Credit card A credit card, such as a Visa or MasterCard, gives you a line of credit that allows you to make purchases up to a stated limit. At the end of each month, either you pay the credit card company for these purchases or you will be charged interest on any outstanding balance. Charge card (or travel and entertainment card) A charge card may look like a credit card and you can spend money with it like a credit card. But with a charge card the day of reckoning comes at the end of each month, when you must pay for all purchases that you have made. In other words, you must pay off your entire balance every month. Debit card A debit card allows you to have your purchases from a store charged directly to your bank account. The deduction is usually made electronically and is immediate. Often, debit cards may also be used to make withdrawals from a cash machine (ATM). Credit transfer With a credit transfer you ask your bank to set up a standing order to make a regular set payment to a supplier. For example, standing orders are often used to make regular fi xed mortgage payments. Direct payment A direct payment (also called direct debit) is an instruction to your bank to allow a company to collect varying amounts from your account, as long as you have been given advance notice of the collection amounts and dates. For example, an electric utility company may ask you to set up a direct debit that allows it to receive automatic payment of your electricity bills from your bank account.

TABLE 20.2 Small face- to-face purchases are commonly paid for in cash, but here are some of the other ways that you can pay your bills.

Source: Bank for International Settlements, “Statistics on Payment and Settlement Systems in the CPSS Countries,” www.bis.org/publ , January 2013.

FIGURE 20.5 How purchases are paid for: percentage of total volume of cashless transactions (Data exclude small usage of card-based e-money)

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Chapter 20 Working Capital Management 595

payments. For example, if you have taken out a student loan, you may have autho- rized the lender to take the payment directly from your bank account each month. The student loan company simply needs to provide its bank with a file showing details of each student, the amount to be debited, and the date. The payment then travels electronically through the Automated Clearing House (ACH) system. You are saved from the chore of writing regular checks, and the firm knows exactly when the cash is coming in and avoids the labor-intensive process of handling thousands of checks.

The Automated Clearing House system also allows money to flow in the reverse direction. Thus, while a direct payment transaction provides an automatic debit, a direct deposit constitutes an automatic credit. Direct deposits are used to make bulk payments such as wages or dividends. Again the company provides its bank with a file of instruc- tions. The bank then debits the company’s account and transfers the cash via the Auto- mated Clearing House to the bank accounts of the firm’s employees or shareholders. ACH transactions have grown dramatically in recent years. You can see from Table 20.3 that the total value of these transactions in the United States has overtaken that of checks.

The third method of electronic payment is wire transfer. Most large-value payments between companies are made electronically through Fedwire or CHIPS (Clearing House Interbank Payments System). Fedwire is operated by the Federal Reserve and connects nearly 9,000 financial institutions to the Fed and so to each other. 13 CHIPS, the other electronic payment system, is owned by the banks and used mainly for cross- border payments. Wire transfers allow fast and secure movement of very large sums of money. For example, suppose bank A wires the Fed to transfer $10 million from its account with the Fed to the account of bank B. Bank A’s account is immediately reduced by $10 million, and bank B’s is increased at the same time. Table 20.3 shows that although the number of payments by Fedwire and CHIPS is relatively small, the average value of each payment is about $5  million, and the total value of payments going through the two systems is nearly $1,000 trillion a year ($1,000,000,000,000,000). Thus, while these systems account for a far smaller number of transactions than do checks, they are much more important in terms of value.

These electronic payment systems have several advantages:

• Record keeping and routine transactions are easy to automate when money moves electronically.

• The marginal cost of transactions is very low. For example, a transfer using Fedwire typically costs about $20, while it costs only a few cents to make each ACH payment.

• Float is reduced. For example, cash managers at Occidental Petroleum found that one plant was paying out about $8 million a month several days early to avoid any risk of late fees if checks were delayed in the mail. The solution was obvious: The plant’s managers switched to paying large bills electronically; that way they could ensure payments arrived exactly on time.

International Cash Management Cash management in domestic firms is child’s play compared with that in large mul- tinational corporations operating in dozens of different countries, each with its own currency, banking system, and legal structure.

Automated Clearing House (ACH) An electronic network for cash transfers in the United States.

13 Fedwire is a real-time, gross settlement system, which means that each transaction over Fedwire is settled individually and immediately. With a net settlement system, transactions are put into a pot and periodically netted off before being settled. CHIPS is an example of a net system that settles at frequent intervals.

Number of Payments, millions Value of Payments, $ trillions

Checks 18,300 26 ACH 16, 750 37 Fedwire 131 599 CHIPS 60 365

TABLE 20.3 Use of payment systems in the United States, 2012

Source: www.federalreserve.gov , www.nacha.org , and www.chips.org .

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596 Part Six Financial Analysis and Planning

A single centralized cash management system is an unattainable ideal for these com- panies, although they are edging toward it. For example, suppose that you are treasurer of a large multinational company with operations throughout Europe. You could allow the separate businesses to manage their own cash, but that would be costly and would almost certainly result in each one accumulating little hoards of cash. The solution is to set up a regional system. In this case the company establishes a local concentration account with a bank in each country. Any surplus cash is swept daily into central multicurrency accounts in London or another European banking center. This cash is then invested in marketable securities or used to finance any subsidiaries that have a cash shortage.

Payments can also be made out of the regional center. For example, to pay wages in each European country, the company just needs to send its principal bank a computer file with details of the payments to be made. The bank then finds the least costly way to transfer the cash from the company’s central accounts and arranges for the funds to be credited on the correct day to the employees in each country.

Most large multinationals have several banks in each country, but the more banks they use, the less control they have over their cash balances. So development of regional cash management systems favors banks that can offer a worldwide branch network. These banks can also afford the high costs of setting up computer systems for handling cash payments and receipts in different countries.

20.4 Investing Idle Cash: The Money Market When firms have excess funds, they can invest the surplus in a variety of securities in the money market, the market for short-term financial assets. Larger firms usually invest directly in these securities. However, smaller firms often park their spare cash in a money market mutual fund, which holds a portfolio of money market investments.

Only fixed-income securities with maturities less than 1 year are considered to be part of the money market. In fact, however, most instruments in the money market have considerably shorter maturity. Limiting maturity has two advantages for the cash man- ager. Recall from Chapter 6 that risk due to interest rate fluctuations increases with maturity. Very short-term securities, therefore, have almost no interest rate risk. Second, it is far easier to gauge the risk of default over short horizons. One need not worry as much about deterioration in financial strength over a 90-day horizon as over the 30-year life of a bond. These considerations imply that high-quality money market securities are a safe “parking spot” to keep idle balances until they are converted back to cash.

Most money market securities are also highly marketable or liquid, meaning that it is easy and cheap to sell the asset for cash. This property, too, is an attractive feature of securities used as temporary investments until cash is needed.

Some of the important instruments of the money market are:

Treasury bills. Treasury bills are issued weekly by the U.S. government and mature in 4 weeks, 3 months, 6 months, and 12 months. They are the safest and most liquid money market instrument.

Commercial paper. This is short-term, usually unsecured, debt of large and well- known companies. While maturities can range up to 270 days before registration with the SEC is required, most commercial paper is issued with maturities of less than 2 months. Because there is no active trading in commercial paper, it has low marketability. Therefore, it would not be an appropriate investment for a firm that could not hold it until maturity. Moody’s, Standard & Poor’s, and Fitch rate com- mercial paper in terms of the default risk of the issuer.

Certificates of deposit. CDs are time deposits at banks, usually in denominations greater than $100,000. Unlike demand deposits (checking accounts), time deposits cannot be withdrawn from the bank on demand: The bank pays interest and principal only at the maturity of the deposit. However, short-term CDs (with maturities less than 3 months) are actively traded, so a firm can easily sell the security if it needs cash.

money market Market for short-term financial assets.

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Chapter 20 Working Capital Management 597

Repurchase agreements. Also known as repos, repurchase agreements are, in effect, collateralized loans. A government bond dealer sells Treasury securities to an investor, with an agreement to repurchase them at a later date at a higher price. The increase in price serves as implicit interest, so the investor in effect is lending money to the dealer, first giving money to the dealer and later getting it back with interest. The bills serve as collateral for the loan: If the dealer fails, and cannot buy back the bill, the investor can keep it. Repurchase agreements are usually very short-term, with maturities of only a few days.

Interest rates on short-term loans (loans of less than 1 year) are often quoted on a so- called discount basis. For example, a $95,000 loan might require repayment of $100,000 in 1 year. On a discount basis, the rate would be quoted as the discount from face value, in this case 5%. The actual interest rate is a bit higher than this. You pay interest of $5,000 on a $95,000 loan, so the interest rate is $5,000/$95,000 = .0526, or 5.26%. You should be aware that rates in the money market also are typically quoted on a discount basis.

Example 20.7 Money Market Rates A Treasury bill with face value $100,000 and maturity 6 months is sold for $98,000. The rate on this bill on a discount basis would be quoted as 4%. The actual dis- count from face value over 6 months is therefore 2%. The effective annual yield on this half-year investment can be found by solving

98,000 × (1 + r)1/2 = 100,000

which implies that r  = .0412, or 4.12%.

Yields on Money Market Investments When we value long-term debt, it is important to take account of default risk. Almost any- thing may happen in 30 years, and even today’s most respectable company may get into trouble eventually. Therefore, corporate bonds offer higher yields than Treasury bonds.

Short-term debt is not risk-free either. During the financial crisis seven companies stopped payments on their commercial paper. They included Lehman Brothers, which defaulted on a record $3 billion of paper. Fortunately, such examples are exceptions; in general, the dan- ger of default is less for money market securities issued by corporations than for corporate bonds. There are two reasons for this. First, as we pointed out above, the range of pos- sible outcomes is smaller for short-term investments. Even though the distant future may be clouded, you can usually be confident that a particular company will survive for at least the next month. Second, for the most part only well-established companies can borrow in the money market. If you are going to lend money for just a few days, you can’t afford to spend too much time in evaluating the loan. Thus, you will consider only blue-chip borrowers.

Despite the high quality of money market investments, there are often signifi- cant differences in yield between corporate and U.S. government securities. Why is this? One answer is the risk of default. Another is that the investments have different degrees of liquidity, or “moneyness.” Investors like Treasury bills because they are easily turned into cash on short notice. Securities that cannot be converted so quickly and cheaply into cash need to offer relatively high yields.

During times of market turmoil investors may place a higher value on having ready access to cash. On these occasions the yield on illiquid securities can increase dramati- cally. This happened in 2007, when banks across the world revealed huge losses in the U.S. subprime mortgage market. Fearful that some banks would be forced into sales of their positions, investors shrank from illiquid securities, and there was a “flight to qual- ity.” The spread between the yields on commercial paper and Treasury bills increased to over 100 basis points (1.00%), four times its level at the beginning of the year.

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598 Part Six Financial Analysis and Planning

The International Money Market In addition to the domestic money market, there is also an international market for short- term dollar investments, which is known as the eurodollar market. Eurodollars have noth- ing to do with the euro, the currency of the European Monetary Union (EMU). They are simply dollars deposited in a bank in Europe. For example, suppose that an American auto producer buys 1,000 ounces of palladium from GlencoreXstrata, the European min- ing giant. It pays for the purchase with a check for $1.5 million drawn on JPMorgan Chase. GlencoreXstrata then deposits the check with its account at Barclays Bank in London. As a result, Barclays has an asset in the form of a $1.5 million credit in its account with JPMorgan Chase. It also has an offsetting liability in the form of a dollar deposit. Since that dollar deposit is placed in Europe, it is called a eurodollar deposit. 14

Just as there is both a domestic U.S. money market and a eurodollar market, so there is both a domestic Japanese money market and a market in London for euroyen. So if a U.S. corporation wishes to make a short-term investment in yen, it can deposit the yen with a bank in Tokyo or it can make a euroyen deposit in London. Similarly, there is both a domestic money market in the euro area as well as a money market for euros in London. And so on.

Major international banks in London lend dollars to one another at the London Interbank Offered Rate (LIBOR). Similarly, they lend yen to each other at the yen LIBOR interest rate, and they lend euros at the euro interbank offered rate, or Euribor. These interest rates are used as a benchmark for pricing many types of short-term loans in the United States and in other countries. For example, a corporation in the United States may issue a floating-rate note with interest payments tied to dollar LIBOR.

14 GlencoreXstrata could equally well deposit the check with the London branch of a U.S. bank or a Japanese bank. It would still have made a eurodollar deposit.

SUMMARY The first step in credit management is to set normal terms of sale. This means that you must decide the length of the payment period and the size of any cash discounts. In most industries these conditions are fairly standardized.

Your second step is to decide the form of the contract with your customer. Most domes- tic sales are made on open account. In this case the only evidence that the customer owes you money is the entry in your ledger and a receipt signed by the customer. Sometimes, you may require a more formal commitment before you deliver the goods. For example, the supplier may arrange for the customer to provide a trade acceptance.

The third task is to assess each customer’s creditworthiness. When you have made an assessment of the customer’s credit standing, the fourth step is to establish sensible credit policy. Finally, once the credit policy is set, you need to establish a collection policy to identify and pursue slow payers.

The effective interest rate for customers who buy goods on credit rather than taking the discount for quicker payment is

a1 + discount discounted price

b365/extra days credit - 1 C redit analysis is the process of deciding which customers are likely to pay their bills. There are various sources of information: your own experience with the customer, the experience of other creditors, the assessment of a credit agency, a check with the custom- er’s bank, the market value of the customer’s securities, and an analysis of the customer’s financial statements. Firms that handle a large volume of credit information often use a formal system for combining the various sources into an overall credit score.

What are the usual steps in credit management? (LO20-1)

How do we measure the implicit interest rate on credit? (LO20-2)

How do firms assess the probability that a customer will pay? (LO20-3)

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Chapter 20 Working Capital Management 599

L I S T I N G O F E Q UAT I O N

20.1 Effective annual rate = a1 + discount discounted price

b365/extra days credit - 1

Credit policy refers to the decision to extend credit to a customer. The job of the credit man- ager is not to minimize the number of bad debts; it is to maximize profits. This means that you need to weigh the odds that the customer will pay, providing you with a profit, against the odds that the customer will default, resulting in a loss. Remember not to be too shortsighted when reckoning the expected profit. It is often worth accepting the marginal applicant if there is a chance that the applicant may become a regular and reliable customer.

If credit is granted, the next problem is to set a collection policy. This requires tact and judgment. You want to be firm with the truly delinquent customer, but you don’t want to offend the good one by writing demanding letters just because a check has been delayed in the mail. You will find it easier to spot troublesome accounts if you keep a careful aging schedule of outstanding accounts.

The benefit of higher inventory levels is the reduction in order costs associated with restocking and the reduced chances of running out of material. The costs are the carrying costs, which include the cost of space, insurance, spoilage, and the opportunity cost of the capital tied up in inventory. Cash provides liquidity, but it doesn’t pay interest. Securities pay interest, but you can’t use them to buy things. As financial manager you want to hold cash up to the point where the incremental or marginal benefit of liquidity is equal to the cost of holding cash, that is, the interest that you could earn on securities.

When you mail a check, it may take several days before it is presented and cleared. During this time the money will continue to sit in your bank account. Checks that have been mailed but not yet cleared are known as float. Unfortunately, float also works in reverse. Every time someone writes you a check, there is a delay before the money ends up in your bank account. Compa- nies that receive a large volume of checks employ techniques such as lock-box banking and concentration accounts to speed up the process of depositing and clearing checks.

Check usage is on the decline. Instead, money increasingly travels electronically. For example, your mortgage payment will probably be taken directly from your bank account each month, and your salary will probably be paid directly into your account. Large-value payments between companies are made electronically by means of the Fedwire and CHIPS systems. The number of payments going through these two systems is quite small, but their value is huge.

Firms can invest idle cash in the money market, the market for short-term financial assets. These assets tend to be short-term, low-risk, and highly liquid, making them ideal instru- ments in which to invest funds for short periods of time before cash is needed. The most important money market instruments are Treasury bills, commercial paper, certificates of deposit and repurchase agreements.

How do firms decide whether it makes sense to grant credit to a customer? (LO20-4)

What are the costs and benefits of holding inventories and cash? (LO20-5)

What are some of the ways that companies receive and make payments? (LO20-6)

Where do firms invest excess funds until they are needed to pay bills? (LO20-7)

QUESTIONS AND PROBLEMS 1. Terms of Sale. Complete the passage below by selecting the appropriate terms from the follow-

ing list (some terms may be used more than once): acceptance, open, commercial, trade, the United States, his or her own, draft, account, bank, banker’s, the customer’s. (LO20-1)

Most goods are sold on _____ _____ . In this case the only evidence of the debt is a record in the seller’s books and a signed receipt. An alternative is for the seller to arrange a(n) _____ _____ ordering payment by the customer. In order to obtain the goods, the customer must acknowledge this order and sign the document. This signed acknowledgment is known as a(n) _____ _____ . Sometimes the seller may also ask _____ _____ bank to sign the document. In this case it is known as a(n) _____ _____ .

finance

®

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600 Part Six Financial Analysis and Planning

2. Payment Lag. The lag between the purchase date and the date on which payment is due is known as the terms lag. The lag between the due date and the date on which the buyer actually pays is termed the due lag, and the lag between the purchase and actual payment dates is the pay lag. Thus

Pay lag = terms lag + due lag

Would the following events likely increase or decrease each of these lags? (LO20-1)

a. The company imposes a service charge on late payers. b. A recession causes customers to be short of cash. c. The company changes its terms from net 10 to net 20.

3. Trade Credit Rates. Company X sells on a 1/20, net 60, basis. Company Y buys goods with an invoice of $1,000. (LO20-2)

a. How much can company Y deduct from the bill if it pays on day 20? b. How many extra days of credit can company Y receive if it passes up the cash discount? c. What is the effective annual rate of interest if Y pays on the due date rather than day 20?

4. Trade Credit Rates. A firm currently offers terms of sale of 3/20, net 40. What effect will the following actions have on the implicit interest rate charged to customers that pass up the cash discount? Will the implicit interest rate increase or decrease? (LO20-2)

a. The terms are changed to 4/20, net 40. b. The terms are changed to 3/30, net 40. c. The terms are changed to 3/20, net 30.

5. Trade Credit and Receivables. A firm offers terms of 3/15, net 30. Currently, two-thirds of all customers take advantage of the trade discount; the remainder pay bills at the due date. (LO20-2)

a. What will be the firm’s typical value for its accounts receivable period? (See Chapter 19, Section 19.2, for a review of the accounts receivable period.)

b. What is the average investment in accounts receivable if annual sales are $20 million? c. What would likely happen to the firm’s accounts receivable period if it changed its terms to

4/15, net 30?

6. Credit Analysis. Financial ratios were described in Chapter 4. If you were the credit manager, to which financial ratios would you pay most attention? (LO20-3)

7. Terms of Sale. For each pair below, is firm A or firm B more likely to grant the longer credit period? (LO20-4)

a. Firm A sells hardware; firm B sells bread. b. Firm A’s customers have an inventory turnover ratio of 10; firm B’s customers have a turn-

over of 15. c. Firm A sells mainly to electric utilities; firm B sells to fashion boutiques.

8. Terms of Sale. Microbiotics currently sells all of its frozen dinners cash on delivery but believes it can increase sales by offering supermarkets 1 month of free credit. The price per carton is $50, and the cost per carton is $40. (LO20-4)

a. If unit sales will increase from 1,000 cartons to 1,060 per month, what is the expected profit from offering the credit? The interest rate is 1% per month, and all customers will pay their bills.

b. What if the interest rate is 1.5% per month? c. What if the interest rate is 1.5% per month but the firm can offer the credit only as a special

deal to new customers, while old customers will continue to pay cash on delivery?

9. Credit Decision/Repeat Sales. Locust Software sells computer training packages to its busi- ness customers at a price of $101. The cost of production (in present value terms) is $96. Locust sells its packages on terms of net 30 and estimates that about 7% of all orders will be uncollect- ible. An order comes in for 20 units. The interest rate is 1% per month. (LO20-4)

a. Should the firm extend credit if this is a one-time order? What is the expected profit of extending credit? The sale will not be made unless credit is extended.

b. What is the break-even probability of collection? c. Now suppose that if a customer pays this month’s bill, it will place an identical order in each

month indefinitely and can be safely assumed to pose no risk of default. Should credit be extended?

d. What is the break-even probability of collection in the repeat-sales case?

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10. Credit Decision. Look back at Example 20.3. Cast Iron’s costs have increased from $1,000 to $1,050. Assuming that there is no possibility of repeat orders and that the probability of successful collection from the customer is p  = .95, answer the following: (LO20-4)

a. What is the expected profit of granting credit? Should Cast Iron grant or refuse credit? b. What is the break-even probability of collection?

11. Credit Decision. The Branding Iron Company sells its irons for $60 apiece wholesale. Produc- tion cost is $50 per iron. There is a 25% chance that a prospective customer will go bankrupt within the next half-year. The customer orders 1,000 irons and asks for 6 months’ credit. What is the expected profit of accepting the order? Should Branding Iron accept the order? Assume the discount rate is 8% per year, there is no chance of a repeat order, and the customer will either pay in full or not pay at all. (LO20-4)

12. Credit Policy. As treasurer of the Universal Bed Corporation, Aristotle Procrustes is worried about his bad debt ratio, which is currently running at 6%. He believes that imposing a more stringent credit policy might reduce sales by 5% and reduce the bad debt ratio to 4%. If the cost of goods sold is 80% of the selling price, what is the impact of changing credit policy on expected profit? Should Mr. Procrustes adopt the more stringent policy? (LO20-4)

13. Credit Decision/Repeat Sales. Surf City sells its network browsing software for $15 per copy to computer software distributors and allows its customers 1 month to pay their bills. The cost of the software is $10 per copy. The industry is very new and unsettled, however, and the probabil- ity that a new customer granted credit will go bankrupt within the next month is 25%. The firm is considering switching to a cash-on-delivery credit policy to reduce its exposure to defaults on trade credit. The discount rate is 1% per month. (LO20-4)

a. What is the impact on the firm’s expected profits of switching to a cash-on-delivery policy? If it switches, sales will fall by 40%.

b. How would your answer change if a customer that is granted credit and pays its bills can be expected to generate repeat orders with negligible likelihood of default for each of the next 6 months? Similarly, customers that pay cash also will generate on average 6 months of repeat sales.

14. Credit Policy. A firm currently makes only cash sales. It estimates that allowing trade credit on terms of net 30 would increase sales from 100 to 110 units per month. The price per unit is $101, and the cost (in present value terms) is $80. The interest rate is 1% per month. (LO20-4)

a. What would be the NPV of a change in the firm’s credit policy? b. How would your answer to (a) change if 5% of all customers will fail to pay their bills under

the new credit policy? c. What if 5% of only the new customers fail to pay their bills? The current customers take

advantage of the 30 days of free credit but remain safe credit risks.

15. Cash Management. Suppose that the rate of interest increases from 4% to 8% per year. Would firms’ cash balances go up or down relative to sales? Explain. (LO20-5)

16. Float. On January 25, Coot Company has $250,000 deposited with a local bank. On January 27, the company writes and mails checks of $20,000 and $60,000 to suppliers. At the end of the month, Coot’s financial manager deposits a $45,000 check received from a customer in the morning mail and picks up the end-of-month account summary from the bank. The manager notes that only the $20,000 payment of the 27th has cleared the bank. What is the company’s available balance with its bank? (LO20-6)

17. Float. Most banks now allow you to pay your bills over the Internet. You log on to your account to tell the bank which payments it should send out on your behalf. Whereas most banks charge you for writing paper checks, they do not charge for this Internet bill-paying service and, in fact, do not even charge you for their cost of postage. Why are the banks willing to provide this service to you for no fee? (LO20-6)

18. Float. General Products writes checks that average $20,000 daily. These checks take an average of 6 days to clear. It receives payments that average $22,000 daily. It takes 3 days before these checks are available to the firm. What would be the annual savings if General Products could obtain access to the payments it receives within 2 days? The interest rate is 6% per year. (LO20-6)

19. Lock Boxes. Anne Teak, the financial manager of a furniture manufacturer, is considering oper- ating a lock-box system. She forecasts that 400 payments a day will be made to lock boxes with

Templates can be found in Connect.

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602 Part Six Financial Analysis and Planning

an average payment size of $2,000. The bank’s charge for operating the lock boxes is $.40 a check. The interest rate is .015% per day. (LO20-6)

a. If the lock box makes the cash available 2 days earlier, what is the net daily advantage of the system? Is it worthwhile to adopt the system?

b. What minimum reduction in the time required to collect and process each check is needed to justify use of the lock-box system?

20. Cash Management. Complete the passage below by choosing the appropriate terms from the following list: lock-box banking, Fedwire, concentration banking. (LO20-6)

Firms can increase their cash resources by speeding up collections. One way to do this is to arrange for payments to be made to regional offices that pay the checks into local banks. This is known as  _____ . Surplus funds are then transferred from the local banks to one of the company’s main banks. Transfers can be made electronically through the _____ system. Another technique is to arrange for a local bank to collect the checks directly from a post office. This is known as _____ .

21. Lock Boxes. Sherman’s Sherbet currently takes about 6 days to collect and deposit checks from customers. A lock-box system could reduce this time to 4 days. Collections average $15,000 daily. The interest rate is .02% per day. (LO20-6)

a. By how much will the lock-box system reduce float? b. What is the daily interest savings of the system? c. Suppose the lock-box service is offered for a fixed monthly fee instead of payment per

check. What is the maximum monthly fee that Sherman’s should be willing to pay for this service? (Assume a 30-day month.)

22. Lock Boxes. The financial manager of JAC Cosmetics is considering opening a lock box in Pittsburgh. Checks cleared through the lock box will amount to $300,000 per month. The lock box will make cash available to the company 3 days earlier. (LO20-6)

a. Suppose that the bank offers to run the lock box for a $25,000 compensating balance. How much does the lock box contribute to profits?

b. Suppose that the bank offers to run the lock box for a fee of $.10 per check cleared instead of a compensating balance. What must the average check size be for the fee alternative to be less costly? Assume an interest rate of 6% per year.

c. Why did you need to know the interest rate to answer (b) but not to answer (a)?

23. Collection Policy. Major Manufacturing currently has one bank account located in New York to handle all of its collections. The firm keeps an additional cash balance with the bank of $300,000 to pay for these services. It is considering opening a bank account with West Coast National Bank to speed up collections from its many California-based customers. Major estimates that the West Coast account would reduce collection time by 1 day on the $1 million a day of business that it does with its California-based customers. If it opens the account, it can reduce the balance with its New York bank to $200,000 since it will do less business in New York. However, West Coast will require an additional cash balance of $200,000. What would be the profitability of the new account? (LO20-6)

24. Money Markets. A Treasury bill with face value $100,000 and maturity 3 months sells for $99,000. What would be the rate quoted on this bill on a discount basis? What would be its effective annual rate? (LO20-7)

25. Money Markets. What happens to the spread between commercial paper rates and Treasury bill rates when there is a “flight to quality”? Why is commercial paper considered less liquid than Treasury bills? (LO20-7)

CHALLENGE PROBLEMS 26. Credit Analysis. Use the data in Example 20.3. Now suppose, however, that 10% of Cast Iron’s

customers are slow payers and that slow payers have a probability of 30% of defaulting on their bills. If it costs $5 to determine whether a customer has been a prompt or slow payer in the past, should Cast Iron undertake such a check? (What are the expected savings and expected profit from the credit check? The answers will depend on both the probability of uncovering a slow payer and the savings from denying slow payers credit.) (LO20-3)

27. Credit Analysis. Look back at Problem 26, but now suppose that if a customer defaults on a payment, you can eventually collect about half the amount owed to you. Will you be more or

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Chapter 20 Working Capital Management 603

less tempted to pay for a credit check once you account for the possibility of partial recovery of debts? (LO20-3)

28. Credit Analysis. Galenic Inc. is a wholesaler for a range of pharmaceutical products. Before deducting any losses from bad debts, Galenic operates on a profit margin of 5%. For a long time the firm has employed a numerical credit-scoring system based on a small number of key ratios. This has resulted in a bad debt ratio of 1%.

Galenic has recently commissioned a detailed statistical study of the payment record of its cus- tomers over the past 8 years and, after considerable experimentation, has identified five variables that could form the basis of a new credit-scoring system. On the evidence of the past 8 years, Galenic calculates that for every 10,000 accounts it would have experienced the following default rates:

By refusing credit to firms with a poor credit score (worse than 80), Galenic calculates that it would reduce its bad debt ratio to 60/9,160, or just under .7%. While this may not seem like a big deal, Galenic’s credit manager reasons that this is equivalent to a decrease of one-third in the bad debt ratio and would result in a significant improvement in the profit margin. (LO20-3)

a. What is Galenic’s current profit margin, allowing for bad debts? b. Assuming that the firm’s estimates of default rates are right, by how much would the new

credit-scoring system affect profits? c. Why might you suspect that Galenic’s estimates of default rates will not be realized in practice? d. Suppose that one of the variables in the proposed new scoring system is whether the cus-

tomer has an existing account with Galenic (new customers are more likely to default). Would you be more or less likely to accept the proposal? ( Hint: Think about repeat sales.)

29. Credit Policy. Jim Khana, the credit manager of Velcro Saddles, is reappraising the company’s credit policy. Velcro sells on terms of net 30. Cost of goods sold is 85% of sales. Velcro classi- fies customers on a scale of 1 to 4. During the past 5 years, the collection experience for the four groups of customers was as follows:

The average interest rate was 15%. What is the expected profit for each group in Velcro’s credit policy? Should the firm deny credit to any of its customers? Which groups? What other factors should be taken into account before changing this policy? (LO20-4)

Classifi cation

Defaults as Percentage

of Sales

Average Collection Period in Days for

Nondefaulting Accounts

1 0 45 2 2 42 3 10 50 4 20 85

Number of Accounts

Credit Score under Proposed System Defaulting Paying Total

Better than 80 60 9, 100 9,160 Worse than 80 40 800 840 Total 100 9, 900 10,000

WEB EXERCISES For Exercises 1 to 4, obtain financial statements for the firms either from the company websites or from a service such as finance.google.com or finance.yahoo.com .

1. Look at the financial statements of Ann Inc. (ANN) and The Buckle Inc. (BKE), two fashion- clothing retailers. Compare the inventory level and turnover of each. What might explain the differences you uncover?

2. Check out the recent performance of a nice coffee shop with attached free reading rooms: Barnes & Noble Inc. (BKS). BKS is sometimes characterized as an “inventory business.” In what way is this the case?

Templates can be found in Connect.

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604 Part Six Financial Analysis and Planning

3. Compare and contrast the accounts receivable turnover and days’ sales outstanding for Keurig Green Mountain (GMCR) and the casino and gaming firm Wynn Resorts (WYNN). Read the business description for information that may explain the level of each company’s investment in accounts receivable.

4. Calculate the Z score for Ford (F) over the last 3 years. What do you think has happened to its bond rating over this period?

5. When credit managers need a credit check on a small business, they often look up the Dun & Bradstreet report on the company. You can see a sample Comprehensive Report by logging on to www.dnb.com . On the basis of this report, would you be prepared to extend credit to this company? Why or why not?

6. Credit scoring is widely used to rate applicants for personal loans. Several websites provide a free calculator that you can use to estimate your FICO score. Try varying some of the inputs and see how your credit rating changes. How much would the rating change if you missed a loan payment?

7. Log on to the web page of a major bank such as Wells Fargo ( www.wellsfargo.com ) or Bank of America ( www.bankofamerica.com ). How do these banks help corporations to manage their cash? For example, check out each bank’s Treasury management services. Among their offer- ings, you will find lock-box services as well as electronic check processing.

SOLUTIONS TO SELF-TEST QUESTIONS 20.1 To get the cash discount, you have to pay the bill within 10 days, that is, by May 11. With the

2% discount, the amount that needs to be paid by May 11 is $20,000 × .98 = $19,600. If you forgo the cash discount, you do not have to pay your bill until May 21, but on that date the amount due is $20,000.

20.2 The cash discount in this case is 5%, and customers who choose not to take the discount receive an extra 50 − 10 = 40 days credit. So the effective annual interest is

Effective annual rate = a1 + discount discounted price

b365/extra days credit - 1

= a1 + 5 95

b365/40 - 1 = .597, or 59.7% In this case the customer who does not take the discount is effectively borrowing money at an

annual interest rate of 59.7%. This is higher than the rate in Example 20.1 because fewer days of credit are obtained by forfeiting the discount.

20.3 The present value of costs is still $1,000. Present value of revenues is now $1,100. The break- even probability is defined by

p × 100 - (1 - p) × 1,000 = 0

which implies that p  = .909. The break-even probability is higher because the profit margin is now lower. The firm cannot afford as high a bad debt ratio as before since it is not making as much on its successful sales. We conclude that high-margin goods will be offered with more liberal credit terms.

20.4 The higher the discount rate the less important are future sales. Because the present value of repeat sales is lower, the break-even probability on the initial sale is higher. For instance, we saw that the break-even probability was 1/3 when the discount rate was 10%. When the discount rate is 20%, the present value of a perpetual flow of repeat sales falls to $200/.20 = $1,000, and the break-even probability increases to 1/2:

1/2 × $1,000 - 1/2 × $1,000 = 0

20.5 The customer pays bills 45 days after the invoice date. Because goods are purchased daily, at any time there will be bills outstanding with “ages” ranging from 1 to 45 days. At any time, the customer will have 30 days’ worth of purchases, or $10,000, outstanding for a period of up to 1 month and have 15 days’ worth of purchases, or $5,000, outstanding for between 1 month and 45 days. The aging schedule will appear as follows:

Age of Account Amount

<1 month $10,000 1–2 months 5,000

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Chapter 20 Working Capital Management 605

20.6 The benefit of the lock-box system, and the price the firm should be willing to pay for the system, is higher when:

a. Payment size is higher (since interest is earned on more funds). b. Payments per day are higher (since interest is earned on more funds). c. The interest rate is higher (since the cost of float is higher). d. Mail time saved is higher (since more float is saved). e. Processing time saved is higher (since more float is saved).

MINICASE George Stamper, a credit analyst with Micro-Encapsulators Corp. (MEC), needed to respond to an urgent e-mail request from the southeast sales office. The local sales manager reported that she had an opportunity to clinch an order from Miami Spice (MS) for 50 encapsulators at $10,000 each. She added that she was particu- larly keen to secure this order since MS was likely to have a con- tinuing need for 50 encapsulators a year and could therefore prove a very valuable customer. However, orders of this size to a new cus- tomer generally required head office agreement, and it was there- fore George’s responsibility to make a rapid assessment of MS’s creditworthiness and to approve or disapprove the sale.

Mr. Stamper knew that MS was a medium-size company with a patchy earnings record. After growing rapidly in the 1980s, MS had encountered strong competition in its principal markets and earn- ings had fallen sharply. Mr. Stamper was not sure exactly to what extent this was a bad omen. New management had been brought in to cut costs, and there were some indications that the worst was over for the company. Investors appeared to agree with this assess- ment, for the stock price had risen to $5.80 from its low of $4.25 the previous year. Mr. Stamper had in front of him MS’s latest financial statements, which are summarized in Table 20.4 . He rapidly calcu- lated a few key financial ratios and the company’s Z score.

Mr. Stamper also made a number of other checks on MS. The company had a small issue of bonds outstanding, which were rated B by Moody’s. Inquiries through MEC’s bank indicated that MS had unused lines of credit totaling $5 million but had entered into discussions with its bank for a renewal of a $15 million bank loan that was due to be repaid at the end of the year. Telephone calls to MS’s other suppliers suggested that the company had recently been 30 days late in paying its bills.

Mr. Stamper also needed to take into account the profit that the company could make on MS’s order. Encapsulators were sold on standard terms of 2/30, net 60. So if MS paid promptly, MEC would receive additional revenues of 50  ×  $9,800  =  $490,000. However, given MS’s cash position, it was more than likely that it would forgo the cash discount and would not pay until some- time after the 60 days. Since interest rates were about 8%, any such delays in payment could reduce the present value to MEC of the revenues. Mr. Stamper also recognized that there were production and transportation costs in filling MS’s order. These worked out at $475,000, or $9,500 a unit. Corporate profits were taxed at 35%.

QUESTIONS

1. What can you say about Miami Spice’s creditworthiness? 2. What is the break-even probability of default? How is it affected

by the delay before MS pays its bills? 3. How should George Stamper’s decision be affected by the

possibility of repeat orders?

2015 2014

Assets Current assets Cash and marketable securities 5.0 12.2 Accounts receivable 16.2 15.7 Inventories 27.5 32.5 Total current assets 48.7 60.4 Fixed assets Property, plant, and equipment 228.5 228.1 Less accumulated depreciation 129.5 127.6 Net fi xed assets 99.0 100.5 Total assets 147.7 160.9 Liabilities and Shareholders’ Equity Current liabilities Debt due for repayment 22.8 28.0 Accounts payable 19.0 16.2 Total current liabilities 41.8 44.2 Long-term debt 40.8 42.3 Shareholders’ equity Common stock * 10.0 10.0 Retained earnings 55.1 64.4 Total shareholders’ equity 65.1 74.4 Total liabilities and shareholders’ equity 147.7 160.9 Income Statement Revenue 149.8 134.4 Cost of goods sold 131.0 124.2 Other expenses 1.7 8.7 Depreciation 8.1 8.6 Earnings before interest and taxes 9.0 −7.1 Interest expense 5.1 5.6 Income taxes 1.4 − 4.4 Net income 2.5 −8.3 Allocation of net income Addition to retained earnings 1.5 −9.3 Dividends 1.0 1.0

TABLE 20.4 Miami Spice: Summary financial statements (figures in $ millions)

* 10 million shares, $1 par value.

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606

Mergers, Acquisitions, and Corporate Control

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

21-1 Explain why it may make sense for companies to merge.

21-2 Estimate the gains and costs of mergers to the acquiring firm.

21-3 Describe ways that companies change their ownership or management.

21-4 Describe takeover defenses.

21-5 Explain some of the motivations for leveraged and management buyouts.

21-6 Summarize the evidence on whether mergers increase efficiency and on how any gains from mergers are distributed between shareholders of the acquired and acquiring firms.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

21 CHAPTE R

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607

P A

R T

S E

V E

N

T he scale and pace of merger activity have often been remarkable. For example, Table 21.1 lists just a few recent mergers. Notice that many of the largest mergers have involved firms in differ-

ent countries. Look also at Figure 21.1 , which shows

the number of mergers involving U.S. companies for

each year from 1962 to 2013. In 2006, a record year

for mergers, there were nearly 12,000 deals, with a

total value of $1.5 trillion. During periods of intense

merger activity financial managers spend consider-

able time either searching for firms to acquire or wor-

rying whether some other firm is about to take over

their company.

When one company buys another, it is making

an investment, and the basic principles of capital

investment decisions apply. You should go ahead

with the purchase if it makes a net contribution to

shareholders’ wealth. But mergers are often awkward

transactions to evaluate, and you have to be careful

to define benefits and costs properly.

Many marriages between companies are

amicable, but sometimes one party is dragged

kicking and screaming to the altar. We review these

hostile takeovers and the principal methods of attack

and defense.

When a firm is taken over, its management is usu-

ally replaced. That is why we describe takeovers as

part of a broader market for corporate control. Activ-

ity in this market goes far beyond ordinary acquisi-

tions. Ownership or management also changes

if there is a proxy contest, a leveraged buyout, or a

divestiture. We therefore look at these ways to change

control of the firm.

We close the chapter with a discussion of who

gains and loses from mergers, and we discuss

whether mergers are beneficial on balance.

Sp e

c ia

l T o

p ic

s

Most mergers are arranged amicably, but when a firm underperforms, it is likely to be gobbled up by a stronger rival.

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608 Part Seven Special Topics

21.1 Sensible Motives for Mergers Mergers are often categorized as horizontal, vertical, or conglomerate. A horizontal merger is one that takes place between two firms in the same line of business; the merged firms are former competitors. Most recent mergers have been of this type. For example, the financial crisis led to a number of mammoth bank mergers, such as those between Bank of America and Merrill Lynch and between Wells Fargo and Wachovia. Other headline-grabbing horizontal mergers have involved telecom and cable companies, such as Liberty Global’s acquisition of Virgin Media, Verizon’s purchase of Vodafone’s holding in Verizon Wireless, and Comcast’s proposed acquisition of Time Warner.

A vertical merger involves companies at different stages of production. The buyer expands back toward the source of raw materials or forward in the direction of the ulti- mate consumer. Thus, a soft-drink manufacturer might buy a sugar producer (expand- ing backward) or a fast-food chain as an outlet for its product (expanding forward). The acquisition of the Nokia Handset and Services Business by Microsoft was an example of a vertical merger. Nokia mobile phones will be installed with Microsoft’s Windows Phone operating system.

Industry Acquiring Company Selling Company Payment, $ billions

Telecom Verizon Vodafone’s holding of Verizon Wireless (UK) 130 Mining Glencore (Switzerland/UK) Xstrata (Switzerland/UK) 49 Pharmacies Express Scripts Medco Health Solutions 29 Utilities Duke Energy Progress Energy 32 Telecom Liberty Global Virgin Media (UK) 24 Food Berkshire Hathaway and 3G Partners HJ Heinz 23 Pharmaceuticals Johnson & Johnson Synthes (Switzerland) 20 Internet information provider Facebook WhatsApp 19 Advertising Publicis (France) Omnicom 17 Aviation United Technologies Goodrich 16 Health care Thermo Fisher Scientifi c Life Technologies 14 Electricals Eaton Cooper Industries 12 Airlines US Airways AMR 11 Software Microsoft Skype 9 Securities exchanges Intercontinental Exchange NYSE Euronext 8

TABLE 21.1 Some important recent mergers

FIGURE 21.1 The number of mergers in the United States, 1962–2013

Source: www.mergerstat.com .

0

2,000

4,000

6,000

8,000

10,000

12,000

N u

m b

er o

f d

ea ls

Year 19

62

19 65

19 68

19 71

19 74

19 77

19 80

19 83

19 86

19 89

19 92

19 95

19 98

20 01

20 04

20 07

20 10

20 13

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Chapter 21 Mergers, Acquisitions, and Corporate Control 609

A conglomerate merger involves companies in unrelated lines of business. For example, the Indian company Tata Group is a huge, widely diversified company. In recent years its acquisitions have been as diverse as Eight O’Clock Coffee, Corus Steel, Jaguar Land Rover, British Salt, and the Ritz Carlton, Boston. No U.S. com- pany is as diversified as Tata, but in the 1960s and 1970s it was common in the United States for unrelated businesses to merge. The number of U.S. conglomerate mergers declined in the 1980s. In fact much of the action in the 1980s came from breaking up the conglomerates that had been formed 10 to 20 years earlier.

Are the following hypothetical mergers horizontal, vertical, or conglomerate?

a. IBM acquires the computer manufacturer Lenovo. b. Lenovo acquires Safeway (a supermarket chain). c. Safeway acquires Campbell Soup. d. Campbell Soup acquires IBM.

Self-Test 21.1

Many mergers and acquisitions are motivated by possible gains in efficiency from combining operations. These mergers create synergies. By this we mean that the two firms are worth more together than apart.

With these distinctions in mind, we are about to consider why firms may sometimes be worth more together than apart. We proceed with some trepidation. Though mergers often lead to real benefits, the apparent gains are frequently mirages that tempt unwary or overconfident managers into takeover disasters. This was the case for AOL, which spent a record-breaking $156 billion in 2000 to acquire Time Warner. The aim was to create a company that could offer consumers a comprehensive package of media and information products. It didn’t work, and in less than 10 years the two companies threw in the towel and split up. By that point, over $200 billion of value had evaporated.

Many mergers that appear to make sense fail because managers cannot handle the complex task of integrating two firms with different production processes, pay struc- tures, and accounting methods. Moreover, the value of most businesses depends on human assets—managers, skilled workers, scientists, and engineers. If these people are not happy in their new roles in the merged firm, the best of them will leave. Beware of paying too much for assets that go down in the elevator and out to the parking lot at the close of each business day.

Consider the $38 billion merger between Daimler-Benz and Chrysler. Although it was hailed as a model for consolidation in the auto industry, the early years were bedeviled by conflicts between two very different cultures:

German management-board members had executive assistants who prepared detailed position papers on any number of issues. The Americans didn’t have assigned aides and formulated their decisions by talking directly to engineers or other specialists. A German decision worked its way through the bureaucracy for final approval at the top. Then it was set in stone. The Americans allowed midlevel employees to proceed on their own initiative, sometimes without waiting for executive-level approval.

. . . Cultural integration also was proving to be a slippery commodity. The yawning gap in pay scales fueled an undercurrent of tension. The Americans earned two, three, and, in some cases, four times as much as their German counterparts. But the expenses of U.S. workers were tightly controlled compared with the German system. Daimler-side employees thought nothing of flying to Paris or New York for a half-day meeting, then capping the visit with a fancy dinner and a night in an expensive hotel. The Americans blanched at the extravagance. 1

1 From Bill Vlasic and Bradley A. Stertz, Taken for a Ride: How Daimler-Benz Drove Off with Chrysler, pp. 302, 319 © 2000 HarperCollins Publishers.

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610

Nine years after acquiring Chrysler, Daimler announced that it was offloading an 80% stake in Chrysler to a leveraged-buyout firm, Cerberus Capital Management. Daimler actually paid Cerberus $677 million to take Chrysler off its hands. Cerberus in return assumed about $18 billion in pension and employee health care liabilities and agreed to invest $6 billion in Chrysler and its finance subsidiary.

These observations illustrate the difficulties in realizing the benefits of merger. There are also occasions when the merger does achieve the intended synergies, but the buyer nevertheless loses because it pays too much. The buyer may overestimate the value of stale inventory or underestimate the costs of renovating old plant and equip- ment, or it may overlook the warranties on a defective product. For example, when Bank of America took over Countrywide Financial in 2007, it was blindsided by the extent of Countrywide’s mortgage-related losses as well as the legal liabilities it inher- ited from Countrywide’s lending practices. Bank of America’s losses on the merger are now estimated at over $40 billion.

With these caveats in mind, we will now consider some possible sources of synergy.

Economies of Scale Just as most of us believe that we would be happier if only we were a little richer, so managers always seem to believe their firm would be more competitive if only it were just a little bigger. They hope for economies of scale, that is, the opportunity to spread fixed costs across a larger volume of output. For example, when Duke Energy and Progress Energy announced plans to merge in 2011, the savings were estimated to be as high as $1.6 billion over 5 years. Management anticipated that the merger would allow the two companies to reduce fuel costs and improve dispatch of electricity. Sav- ings would also come from a reduction in staff of nearly 2,000. (Some of these sav- ings involved senior management. For example, there were two chief financial officers before the merger and only one afterward.) Beware of overly optimistic predictions of cost savings, however. The nearby box tells the story of one bank merger that resulted in a spectacular debacle rather than the predicted synergies.

These economies of scale are the natural goal of horizontal mergers. But they have been claimed in conglomerate mergers, too. The architects of these mergers have pointed to the economies that come from sharing central services such as accounting, financial control, and top-level management.

Finance in Practice Those Elusive Synergies the banks decided to connect the three different systems together by using “relay” computers.

Three years after the initial announcement the new com- pany opened for business on April 1, 2002. Five days later, computer glitches resulted in a spectacular foul-up. Some 7,000 of the bank’s cash machines did not work; 60,000 accounts were debited twice for the same transaction; and millions of bills went unpaid. The Economist reported that 2 weeks later Tokyo Gas, the biggest gas company, was still missing ¥2.2 billion in payments and the top telephone com- pany, NTT, which was looking for ¥12.7 billion, was forced to send its customers receipts marked with asterisks in place of fi gures, since it did not know which of about 760,000 bills had been paid.

One of the objects behind the formation of Mizuho was to exploit economies in its IT systems. The launch fi asco illus- trated dramatically that it is easier to predict such merger synergies than to realize them.

Source: The creation of Mizuho Bank and its launch problems are described in “Undispensable: A Fine Merger Yields One Fine Mess,” The Economist, April 25, 2002 © The Economist Newspaper Limited, London (April 25, 2002).

When three of Japan’s largest banks combined to form Mizuho Bank, it brought together assets of $1.5 trillion, more than twice those of the world leader Deutsche Bank. The name “Mizuho” means “rich rice harvest,” and the bank’s management forecast that the merger would create a rich harvest of synergies. In a message to shareholders, the bank president claimed that the merger would create “a compre- hensive fi nancial services group that will surge forward in the 21st century.” He predicted that the bank would “lead the new era through cutting-edge comprehensive fi nancial services . . . by exploiting to the fullest extent the Group’s enormous strengths, which are backed by a powerful customer base and state-of-the-art fi nancial and information technologies.” The cost of putting the banks together was forecast at ¥130 billion, but management predicted future benefi ts of ¥466 bil- lion a year.

Within a few months of the announcement reports began to emerge of squabbles between the three partners. One problem area was IT. Each of the three merging banks had a different supplier for its computer system. At fi rst it was proposed to use just one of these three systems, but then

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Chapter 21 Mergers, Acquisitions, and Corporate Control 611

Economies of Vertical Integration Large companies commonly like to gain as much control and coordination as possible over the production process by expanding back toward the output of the raw material and forward to the ultimate consumer. One way to achieve this is to merge with a sup- plier or a customer.

Vertical integration facilitates coordination and administration. We illustrate with an extreme example: Think of an airline that does not own any planes. If it sells tickets for a flight from Boston to San Francisco, it then rents a plane from a separate company. Perhaps this arrangement might work on a small scale, but it would be an administrative nightmare for a major carrier that would have to coordinate hundreds of rental agree- ments each day. It is not surprising that all major airlines have integrated backward by buying and flying their own airplanes rather than patronizing rent-a-plane companies.

As this example suggests, vertical mergers often make sense when two businesses are inextricably linked. For example, a smelter may need to be located next to a mine to reduce the costs of transporting the ore. While it may be possible in such cases to organize the activities as separate firms operating under a long-term contract, such a contract can never allow for every conceivable change in circumstance. Therefore, when two parts of an operation are highly dependent on each other, it can make sense to combine them within the same firm, which then controls how the assets should be used.

Vertical integration has fallen out of fashion recently. Many companies are finding it more efficient to outsource many of their activities. For example, back in the 1950s and 1960s, General Motors was thought to have a cost advantage over its competitors because it produced a greater fraction of its components in-house. By the 1990s Ford and Chrysler had the advantage. They could buy the parts more cheaply from outside suppliers. This was partly because the outside suppliers tended to use nonunion labor. But it also appears that manufacturers have more bargaining power when they are dealing with independent suppliers rather than with another part of the corporate fam- ily. In 1998 GM decided to spin off Delphi, its automotive parts division, as a separate company. After the spin-off, GM continued to buy parts from Delphi in large volumes, but it negotiated the purchases at arm’s length.

Combining Complementary Resources Many small firms are acquired by large firms that can provide the missing ingredients necessary for the firm’s success. The small firm may have a unique product but lack the engineering and sales organization necessary to produce and market it on a large scale. The firm could develop engineering and sales talent from scratch, but it may be quicker and cheaper to merge with a firm that already has ample talent. The two firms have complementary resources —each has what the other needs—so it may make sense for them to merge. Also the merger may open up opportunities that neither firm would pursue otherwise.

In recent years many of the major pharmaceutical firms have faced the loss of pat- ent protection on their more profitable products and have not had an offsetting pipeline of promising new compounds. This has prompted an increasing number of acquisi- tions of biotech firms. For example, in 2012, Amgen acquired KAI Pharmaceuticals for $315 million. Amgen calculated that KAI’s experimental treatment for patients undergoing dialysis would broaden its range of therapies for kidney diseases. At the same time, KAI obtained the resources that it needed to bring its products to market.

Mergers as a Use for Surplus Funds Suppose that your firm is in a mature industry. It is generating a substantial amount of cash, but it has few profitable investment opportunities. Ideally such a firm should distribute the surplus cash to shareholders by increasing its dividend payment or by repurchasing its shares. Unfortunately, energetic managers are often reluctant to shrink their firm in this way.

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612 Part Seven Special Topics

If the firm is not willing to purchase its own shares, it can instead purchase some- one else’s. Thus firms with a surplus of cash and a shortage of good investment oppor- tunities often turn to mergers financed by cash as a way of deploying their capital.

Firms that have excess cash and do not pay it out or redeploy it by acquisition often find themselves targets for takeover by other firms that propose to redeploy the cash for them. During the oil price slump of the early 1980s, many cash-rich oil compa- nies found themselves threatened by takeover. This was not because their cash was a unique asset. The acquirers wanted to capture the companies’ cash flow to make sure it was not frittered away on negative-NPV oil exploration projects. We return to this free-cash-flow motive for takeovers later in the chapter.

Eliminating Inefficiencies Cash is not the only asset that can be wasted by poor management. There are always firms with unexploited opportunities to cut costs and increase sales and earnings. Such firms are natural candidates for acquisition by other firms with better manage- ment. In some instances “better management” may simply mean the determination to force painful cuts or realign the company’s operations. Notice that the motive for such acquisitions has nothing to do with benefits from combining two firms. Acquisition is simply the mechanism by which a new management team replaces the old one.

A merger may not be the only way to improve management, but sometimes there is no simple and practical alternative. Managers are naturally reluctant to fire or demote themselves, and stockholders of large public firms do not usually have much direct influence on how the firm is run or who runs it.

If this motive for merger is important, one would expect to observe that acquisitions often precede a change in the management of the target firm. This seems to be the case. For example, Martin and McConnell found that the chief executive is four times more likely to be replaced in the year after a takeover than during earlier years. 2 The firms that they studied had generally been poor performers. Apparently many of these firms fell on bad times and were rescued by merger.

Industry Consolidation The biggest opportunities to improve efficiency seem to come in industries with too many firms and too much capacity. These conditions often trigger a wave of mergers and acquisitions, which then force companies to cut capacity and employment and release capital for reinvestment elsewhere in the economy. For example, when U.S. defense budgets fell after the end of the Cold War, a round of consolidating takeovers followed in the defense industry.

The banking industry is another example. The United States entered the 1980s with far too many banks, largely as a result of restrictions on interstate banking. When those restrictions were loosened and technology improved, hundreds of small banks were swept up into regional or “super-regional” banks. Europe also experienced a wave of bank mergers as companies sought to gain the financial muscle to compete in a Europe-wide banking market. These included the mergers of UBS and Swiss Bank Corp. (1997), BNP and Banque Paribas (1998), Banco Santander and Banco Central Hispanico (1999), and Commerzbank and Dresdner Bank (2009).

21.2 Dubious Reasons for Mergers The benefits that we have described so far all make economic sense. Other arguments sometimes given for mergers are more dubious. Here are two.

2 K. J. Martin and J. J. McConnell, “Corporate Performance, Corporate Takeovers, and Management Turnover,” Journal of Finance 46 (June 1991), pp. 671–687.

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Chapter 21 Mergers, Acquisitions, and Corporate Control 613

Diversification We have suggested that the managers of a cash-rich company may prefer to see that cash used for acquisitions. That is why we often see cash-rich firms in stagnant indus- tries merging their way into fresh woods and pastures new. But what about diversifica- tion as an end in itself? It is obvious that diversification reduces risk. Isn’t that a gain from merging?

The trouble with this argument is that diversification is easier and cheaper for the stockholder than for the corporation. Why should firm A buy firm B to diversify when the shareholders of firm A can buy shares in firm B to diversify their own portfolios? It is far easier and cheaper for individual investors to diversify than it is for firms to combine operations. There is little evidence that investors pay a premium for diversi- fied firms; in fact, discounts are more common.

The Bootstrap Game During the 1960s some conglomerate companies made acquisitions that offered no evident economic gains. Nevertheless, the conglomerates’ aggressive strategy pro- duced several years of rising earnings per share. To see how this can happen, let us look at the acquisition of Muck and Slurry by the well-known conglomerate World Enterprises.

Example 21.1 The Bootstrap Game The position before the merger is set out in the first two columns of Table  21.2 . Notice that because Muck and Slurry has relatively poor growth prospects, its stock sells at a lower price-earnings ratio than World Enterprises (line 3). The merger, we assume, produces no economic benefits, so the firms should be worth exactly the same together as apart. The value of World Enterprises after the merger is therefore equal to the sum of the separate values of the two firms (line 6).

Since World Enterprises stock is selling for double the price of Muck and Slurry stock (line 2), World Enterprises can acquire the 100,000 Muck and Slurry shares for 50,000 of its own shares. Thus World will have 150,000 shares outstanding after the merger.

World’s total earnings double as a result of the acquisition (line 5), but the number of shares increases by only 50%. Its earnings per share rise from $2.00 to $2.67. We call this a bootstrap effect because there is no real gain created by the merger and no increase in the two firms’ combined value. Since World’s stock price is unchanged by the acquisition of Muck and Slurry, the price-earnings ratio falls (line 3).

World Enterprises (before merger)

Muck and Slurry

World Enterprises (after acquiring

Muck and Slurry)

1. Earnings per share $2 $2 $2.67 2. Price per share $40 $20 $40 3. Price-earnings ratio 20 10 15 4. Number of shares 100,000 100,000 150,000 5. Total earnings $200,000 $200,000 $400,000 6. Total market value $4,000,000 $2,000,000 $6,000,000 7. Current earnings per

dollar invested in stock (line 1 divided by line 2) $.05 $.10 $.067

TABLE 21.2 Impact of merger on market value and earnings per share of World Enterprises

Note: When World Enterprises purchases Muck and Slurry, there are no gains. Therefore, total earnings and total market value should be unaffected by the merger. But earnings per share increase. World Enterprises issues only 50,000 of its shares (priced at $40) to acquire the 100,000 Muck and Slurry shares (priced at $20).

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614 Part Seven Special Topics

You should now see how to play the bootstrap game. Suppose that you manage a company enjoying a high price-earnings ratio. The reason it is high is that inves- tors anticipate rapid growth in future earnings. You achieve this growth not by capital investment, product improvement, or increased operating efficiency but by purchasing slow-growing firms with low price-earnings ratios. The long-run result will be slower growth and a depressed price-earnings ratio, but in the short run earnings per share can increase dramatically. If this fools investors, you may be able to achieve the higher earnings per share without suffering a decline in your price-earnings ratio. But in order to keep fooling investors, you must continue to expand by merger at the same com- pound rate. Obviously you cannot do this forever; one day expansion must slow down or stop. Then earnings growth will cease, and your house of cards will fall. Buying a firm with a lower P/E ratio can increase earnings per share. But the increase should not result in a higher share price. The short-term increase in earnings should be offset by lower future earnings growth.

Before the merger, $1 invested in World Enterprises bought 5 cents of current earnings and rapid growth prospects. On the other hand, $1 invested in Muck and Slurry bought 10 cents of current earnings but slower growth prospects. If the total market value is not altered by the merger, then $1 invested in the merged firm gives World shareholders 6.7 cents of immediate earnings but slower growth than before the merger. Muck and Slurry shareholders get lower immediate earnings but faster growth. Neither side gains or loses provided that everybody understands the deal.

Financial manipulators sometimes try to ensure that the market does not under- stand the deal. Suppose that investors are fooled by the exuberance of the presi- dent of World Enterprises and mistake the 33% postmerger increase in earnings per share for sustainable growth. If they do, the price of World Enterprises stock rises and the shareholders of both companies receive something for nothing.

Suppose that Muck and Slurry has even worse growth prospects than in our example and its share price is only $10. Recalculate the effects of the merger in this case. You should find that earnings per share increase by a greater amount, since World Enterprises can now buy the same current earnings for fewer shares.

Self-Test 21.2

21.3 The Mechanics of a Merger Buying a company is a much more complicated affair than buying a piece of machin- ery. We are not going to get into the tax or accounting complexities here, but we will describe the different forms that an acquisition can take and the way that an acquisi- tion can be stymied by an antitrust ruling.

The Form of Acquisition There are three ways for one firm to acquire another. One possibility is to merge the two companies into one, in which case the acquiring company assumes all the assets and all the liabilities of the other. The acquired firm ceases to exist, and its former shareholders receive cash and/or securities in the acquiring firm. A merger must have the approval of at least 50% of the shareholders of each firm. 3

3 Corporate charters and state laws sometimes specify a higher percentage.

merger Combination of two firms into one, with the acquirer assuming assets and liabilities of the target firm.

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Chapter 21 Mergers, Acquisitions, and Corporate Control 615

An alternative procedure is for the acquiring firm to buy the target firm’s stock in exchange for cash, shares, or other securities. The acquired firm may continue to exist as a separate entity, but it is now owned by the acquirer. The approval and cooperation of the target firm’s managers are generally sought, but even if they resist, the acquirer can attempt to purchase a majority of the outstanding shares. By offering to buy shares directly from shareholders, the acquiring firm can bypass the target firm’s management altogether. The offer to purchase stock is called a tender offer. If the tender offer is suc- cessful, the buyer obtains control and can, if it chooses, toss out incumbent management.

The third approach is to buy the target firm’s assets. In this case ownership of the assets needs to be transferred, and payment is made to the selling firm rather than directly to its stockholders.

The terminology of mergers and acquisitions (M&A) can be confusing. These phrases are used loosely to refer to any kind of corporate combination or takeover. But strictly speaking, merger means the combination of all the assets and liabilities of two firms. The purchase of the stock or assets of another firm is an acquisition.

Mergers, Antitrust Law, and Popular Opposition Mergers may be blocked by the federal government if they are thought to be anticom- petitive or to create too much market power. For example, in 2013 the U.S. Depart- ment of Justice announced that it would challenge the proposed merger of American Airlines and US Airways on antitrust grounds, arguing that the merger would leave 80% of the American air travel market in the control of only four airlines. 4

Companies that do business outside the United States also have to worry about foreign antitrust laws. For example, when Deutsche Börse and the New York Stock Exchange announced plans to merge, the European Commission ruled that the move would create an unduly dominant position in the market for European derivatives.

Mergers may also be stymied by political pressures and popular resentment even when no formal antitrust issues arise. For example, in the wake of concern over cyber espionage, a U.S. House of Representatives committee recommended in 2012 that the federal government should block mergers of U.S. firms with Chinese telecommunica- tions companies.

21.4 Evaluating Mergers If you are given the responsibility for evaluating a proposed merger, you must think hard about the following two questions:

1. Is there an overall economic gain to the merger? In other words, is the merger value-enhancing? Are the two firms worth more together than apart?

2. Do the terms of the merger make my company and its shareholders better off? There is no point in merging if the cost is too high and all the economic gain goes to the other company.

Answering these deceptively simple questions is rarely easy. Some economic gains can be nearly impossible to quantify, and complex merger financing can obscure the true terms of the deal. But the basic principles for evaluating mergers are not too difficult.

Mergers Financed by Cash We will concentrate on a simple numerical example. Your company, Cislunar Foods, is considering acquisition of a smaller food company, Targetco. Cislunar is proposing to finance the deal by purchasing all of Targetco’s outstanding stock for $19 per share. Some financial information on the two companies is given in Table 21.3 .

tender offer Takeover attempt in which outsiders directly offer to buy the stock of the firm’s shareholders.

acquisition Takeover of a firm by purchase of that firm’s common stock or assets.

4 In the end, the merger was allowed to proceed, but this outcome was far from clear at the time. American’s stock price fell by 13% on the day of the Department of Justice’s announcement.

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616 Part Seven Special Topics

Question 1 Why would Cislunar and Targetco be worth more together than apart? Suppose that operating costs can be reduced by combining the companies’ mar- keting, distribution, and administration. Revenues can also be increased in Targetco’s region. The rightmost column of Table 21.3 contains projected revenues, costs, and earnings for the two firms operating together: annual operating costs postmerger will be $2 million less than the sum of the separate companies’ costs, and revenues will be $2 million more. Therefore, projected earnings increase by $4 million. 5 We will assume that the increased earnings are the only synergy to be generated by the merger.

The economic gain to the merger is the present value of the extra earnings. If the earnings increase is permanent (a level perpetuity) and the cost of capital is 20%,

Economic gain = PV(increased earnings) = 4

.20 = $20 million

This additional value is the basic motivation for the merger.

Question 2 What are the terms of the merger? What is the cost to Cislunar and its shareholders?

Targetco’s management and shareholders will not consent to the merger unless they receive at least the stand-alone value of their shares. They can be paid in cash or by new shares issued by Cislunar. In this case we are considering a cash offer of $19 per Targetco share, $3 per share over the prior share price. Targetco has 2.5 million shares outstanding, so Cislunar will have to pay out $47.5 million, a premium of $7.5 million over Targetco’s prior market value. On these terms, Targetco stockholders will cap- ture $7.5 million out of the $20 million gain from the merger. That ought to leave $12.5 million for Cislunar.

This is shown in the Cash Purchase column of Table 21.4 . The total value of the merged firm, $492.5 million, is the sum of the original values of the two firms plus the economic gain from the merger minus the cash paid by Cislunar to Targetco’s share- holders. That cash leaves the merged firm. Shares outstanding of Cislunar remain at 10 million, so price per share rises by $1.25 to $49.25, giving Cislunar shareholders a gain of $1.25 per share × 10 million shares = $12.5 million.

Therefore, the merger makes sense for Cislunar for two reasons. First, it adds $20 million of overall value. Second, the terms of the merger give only $7.5 million of that $20 million overall gain to Targetco’s stockholders, leaving $12.5 million for Cislunar. You could say that the cost of acquiring Targetco is $7.5 million, the differ- ence between the cash payment and the value of Targetco as a separate company:

Cost = cash paid out - Targetco value = $47.5 - 40 = $7.5 million

5 To keep things simple, the example ignores taxes and assumes that both companies are all-equity-financed. We also ignore the interest income that could have been earned by investing the cash used to finance the merger.

Note: Figures in millions except price per share.

TABLE 21.3 Cislunar Foods is considering an acquisition of Targetco. The merger would increase the companies’ combined earnings by $4 million.

Cislunar Foods Targetco Combined Companies

Revenues $150 $20 $172 (+2) Operating costs $118 $16 $132 (-2) Earnings $ 32 $ 4 $ 40 (+4) Cash $ 55 $ 2.5 Other assets’ book value $185 $17.0 Total assets $240 $19.5 Price per share $ 48 $16 Number of shares 10.0 2.5 Market value $480 $40

Merger calculator

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Chapter 21 Mergers, Acquisitions, and Corporate Control 617

Of course, the Targetco stockholders are ahead by $7.5 million. Their gain is your cost. As we’ve already seen, Cislunar stockholders come out $12.5 million ahead. This is the merger’s NPV for Cislunar:

NPV = economic gain - cost = $20 - 7.5 = $12.5 million

Writing down the economic gain and cost of a merger in this way separates the motive for the merger (the economic gain, or value added) from the terms of the merger (the division of the gain between the two merging companies).

Cash Purchase Exchange of Shares

A. Value of fi rms

Original value of Cislunar $480 $480 + Original value of Targetco 40 40 + Economic gain from merger 20 20 − Cash paid to Targetco shareholders 47.5 0 = Value of Cislunar after merger $492.5 $540 Cislunar shares outstanding postmerger 10 10.833 Cislunar price per share postmerger $ 49.25 $ 49.85

B. Gains from merger

Value of original Cislunar shareholders: postmerger $492.5 $498.5 (= 10 × $49.85) − Value of Cislunar shares: premerger 480 480 = Cislunar shareholders’ gain from merger $ 12.5 $ 18.5 Value received by Targetco shareholders $ 47.5

(cash payment) $ 41.5 (= .833 × $49.85)

(value of shares in merged fi rm) − Value of Targetco shares premerger 40 40 = Targetco shareholders’ gain from merger $ 7.5 $ 1.5 Sum of gains to Cislunar and Targetco shareholders 12.5 + 7.5 = $20 18.5 + 1.5 = $20

Note: Figures in millions except price per share.

TABLE 21.4 Financial forecasts after the Cislunar-Targetco merger. The middle column assumes a cash purchase at $19 per Targetco share. The right column assumes Targetco stockholders receive one new Cislunar share for every three Targetco shares.

Killer Shark Inc. makes a surprise cash offer of $22 a share for Goldfish Industries. Before the offer, Goldfish was selling for $18 a share. Goldfish has 1 million shares outstanding. What must Killer Shark believe about the pres- ent value of the improvement it can bring to Goldfish’s operations?

Self-Test 21.3

Mergers Financed by Stock What if Cislunar wants to conserve its cash for other investments and therefore decides to pay for the Targetco acquisition with new Cislunar shares? The deal calls for Targetco shareholders to receive one Cislunar share in exchange for every three Targetco shares.

It’s the same merger, but the financing is different. The right column of Table 21.4 works out the consequences. The value of the merged firm is $540 million in this case because no cash is paid out to the original Targetco shareholders. Instead, they are given shares in the merged firm, specifically one share of Cislunar for every three of their 2.5 million original shares in Targetco, a total of .833 million shares. This means that there will be 10.833 million shares in the merged firm, resulting in a share price of $540/10.833 = $49.85.

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618 Part Seven Special Topics

The value of the shares given to Targetco’s original shareholders is .833 million  × $49.85 = $41.5 million, representing an increase of $1.5 million over the value of their original holdings. Following the merger, Cislunar’s original shareholders hold stock with total market value of 10 million × $49.85 = $498.5 million, an increase of $18.5 million over their original value.

In both cases, the total gains to Cislunar’s original shareholders and Targetco’s shareholders sum to $20 million, the economic gain of the merger. But in the share exchange, less of the gain is captured by Targetco’s shareholders. They get 833,333 shares at $49.85, or $41.5 million, a premium of only $1.5 million over Targetco’s prior market value:

Cost = value of shares issued - Targetco value = $41.5 - 40 = $1.5 million

The merger’s NPV to Cislunar’s original shareholders is

NPV = economic gain - cost = 20 - 1.5 = $18.5 million

Note that Cislunar stock rises by $1.85 from its prior value. The total increase in value for Cislunar’s original shareholders, who retain 10 million shares, is $18.5 million.

Evaluating the terms of a merger can be tricky when there is an exchange of shares. The target company’s shareholders will retain a stake in the merged firms, so you have to figure out what the firm’s shares will be worth after the merger is announced and its benefits appreciated by investors. Notice that we started with the total market value of Cislunar and Targetco postmerger, took account of the merger terms (833,333 new shares issued), and worked back to the postmerger share price. Only then could we work out the division of the merger gains between the two companies.

There is a key distinction between cash and stock for financing mergers. If cash is offered, the cost of the merger is not affected by the size of the merger gains. If stock is offered, the cost depends on the gains because the gains show up in the postmerger share price, and these shares are used to pay for the acquired firm.

Stock financing also mitigates the effects of over- or undervaluation of either firm. Suppose, for example, that A overestimates B’s value as a separate entity, perhaps because it has overlooked some hidden liability. Thus A makes too generous an offer. Other things equal, A’s stockholders are better off if it is a stock rather than a cash offer. With a stock offer, the inevitable bad news about B’s value will fall partly on B’s former stockholders.

Suppose Targetco shareholders demand 1 Cislunar share for every 2.5 Tar- getco shares. Otherwise, they will not accept the merger. Under these revised terms, is the merger still a good deal for Cislunar?

Self-Test 21.4

A Warning The cost of a merger is the premium the acquirer pays for the target firm over its value as a separate company. If the target is a public company, you can measure its separate value by multiplying its stock price by the number of outstanding shares. Watch out, though: If investors expect the target to be acquired, its stock price may overstate the company’s separate value. The target company’s stock price may already have risen in anticipation of a premium to be paid by an acquiring firm.

Another Warning Some companies begin their merger analyses with a forecast of the target firm’s future cash flows. Any revenue increases or cost reductions attributable to the merger are

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Chapter 21 Mergers, Acquisitions, and Corporate Control 619

included in the forecasts, which are then discounted back to the present and compared with the purchase price:

Estimated net gain = DCF valuation of target including merger benefits - cash required for acquisition

This is a dangerous procedure. Even the brightest and best-trained analyst can make large errors in valuing a business. The estimated net gain may come up positive not because the merger makes sense, but simply because the analyst’s cash-flow forecasts are too optimistic. On the other hand, a good merger may not be pursued if the analyst fails to recognize the target’s potential as a stand-alone business.

A better procedure starts with the target’s current and stand-alone market value and concentrates instead on the changes in cash flow that would result from the merger. Always ask why the two firms should be worth more together than apart. Remem- ber, you add value only if you can generate additional economic benefits — some competitive edge that other firms can’t match and that the target firm’s managers can’t achieve on their own.

It makes sense to keep an eye on the value that investors place on the gains from merging. If A’s stock price falls when the deal is announced, investors are sending a message that the merger benefits are doubtful or that A is paying too much for these benefits.

21.5 The Market for Corporate Control The shareholders are the owners of the firm. But most shareholders do not feel like the boss, and with good reason. Try buying a share of IBM stock and marching into the boardroom for a chat with your employee, the chief executive officer.

The ownership and management of large corporations are almost always separated. Shareholders do not directly appoint or supervise the firm’s managers. They elect the board of directors, who act as their agents in choosing and monitoring the managers of the firm. Shareholders have a direct say in very few matters. Control of the firm is in the hands of the managers, subject to the general oversight of the board of directors.

This system of governance creates potential agency costs. Agency costs occur when managers or directors take actions adverse to shareholders’ interests.

The temptation to take such actions may be ever-present, but there are many forces and constraints working to keep managers’ and shareholders’ interests in line. As we pointed out in Chapter 1, managers’ paychecks in large corporations are almost always tied to the profitability of the firm and the performance of its shares. Boards of direc- tors take their responsibilities seriously—they may face lawsuits if they don’t—and therefore are reluctant to rubber-stamp obviously bad financial decisions.

But what ensures that the board has engaged the most talented managers? What happens if managers are inadequate? What if the board of directors is derelict in mon- itoring the performance of managers? Or what if the firm’s managers are fine but resources of the firm could be used more efficiently by merging with another firm? Can we count on managers to pursue arrangements that would put them out of jobs?

These are all questions about the market for corporate control, the mechanisms by which firms are matched up with management teams and owners who can make the most of the firm’s resources. You should not take a firm’s current ownership and management for granted. If it is possible for the value of the firm to be enhanced by changing management or by reorganizing under new owners, there will be incentives for someone to make a change.

There are four ways to change the management of a firm. These are (1) a suc- cessful proxy contest in which a group of stockholders votes in a new group of directors, who then pick a new management team; (2) the purchase of one firm by another in a merger or acquisition; (3) a leveraged buyout of the firm by a

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private group of investors; and (4) a divestiture, in which a firm either sells part of its operations to another company or spins it off as an independent firm.

We will review briefly each of these methods.

21.6 Method 1: Proxy Contests Shareholders elect the board of directors to keep watch on management and replace unsatisfactory managers. If the board is lax, shareholders are free to elect a differ- ent board. In theory this ensures that the corporation is run in the best interests of shareholders.

In practice things are not so clear-cut. Ownership in large corporations is widely dispersed. Usually even the largest single shareholder holds only a small fraction of the shares. Most shareholders have little notion who is on the board or what the mem- bers stand for. Management, on the other hand, deals directly with the board and has a personal relationship with its members. In many corporations, management sits on the committee that nominates candidates for the board. It is not surprising that some boards seem less than aggressive in forcing managers to run a lean, efficient operation and to act primarily in the interests of shareholders.

When a group of investors believe that the board and its management team should be replaced, they can launch a proxy contest. A proxy is the right to vote another shareholder’s shares. In a proxy contest, the dissident shareholders attempt to obtain enough proxies to elect their own slate to the board of directors. Once the new board is in control, management can be replaced and company policy changed. A proxy fight is therefore a direct contest for control of the corporation.

The problem with proxy fights is that they can cost millions of dollars. Dissidents who engage in them must use their own money, but management can draw on the corporation’s funds and lines of communication with shareholders to defend itself. To level the playing field somewhat, the SEC has proposed new rules to make it easier to mount a proxy fight. In the meantime, shareholders have found that a policy of “just say no” to the reelection of existing directors can send a powerful signal. When Disney shareholders voted 43% of the shares against the reelection of Michael Eisner, the company’s autocratic chairman, he heard the message and resigned the next day.

Institutional shareholders, such as large hedge funds, have become more aggressive in pressing for managerial accountability and have been able to gain concessions by threatening proxy fights. For example, in 2008 shareholder activist Carl Icahn indi- cated his intention to put himself forward for nomination to the board of Motorola. Icahn controlled less than 7% of the votes and failed to prevent the reelection of the existing board. Nevertheless, the pressure from Icahn had an effect: Motorola agreed to nominate two new board members and to consult with Icahn about a possible spin- off of the company’s handset division.

21.7 Method 2: Takeovers If the management of one firm believes that another company’s management is not acting in the best interests of investors, it can go over the heads of that firm’s man- agement and make a tender offer directly to its stockholders. The management of the target firm may advise its shareholders to accept the offer and sell their shares, or it may fight the bid in the hope that the acquirer will either raise its offer or walk away from the deal. If the tender offer is successful, the new owner can then install its own management team. Thus, corporate takeovers are the arenas where contests for corpo- rate control are often fought.

In the United States, the rules for tender offers are set largely by the Williams Act of 1968 and by state laws. The courts act as a referee to see that the contests are

proxy contest Takeover attempt in which outsiders compete with management for shareholders’ votes. Also called proxy fight.

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conducted fairly. The problem in setting these rules is that it is unclear who requires protection. Should the management of the target firm be given more weapons to defend itself against unwelcome predators? Or should it simply be encouraged to sit the game out? Or should it be obliged to conduct an auction to obtain the highest price for its shareholders? And what about would-be acquirers? Should they be forced to reveal their intentions at an early stage, or would that allow other firms to piggyback on their good ideas by entering bids of their own? Keep these questions in mind as you read Example 21.2.

Example 21.2 Oracle Bids for PeopleSoft Hostile takeover bids are relatively uncommon in high-tech industries where an acrimonious takeover battle may cause many of the target’s most valued staff to leave. Investors were therefore startled in June 2003 when the software giant Oracle Corp. announced a $5.1 billion cash tender offer for its rival PeopleSoft. The offer price of $16 a share was only a very modest 6% above the recent price of Peo- pleSoft stock. PeopleSoft’s CEO angrily rejected the bid as dramatically undervalu- ing the business and accused Oracle of trying to disrupt PeopleSoft’s business and to thwart its recently announced plan to merge with its smaller rival J.D. Edwards & Co. PeopleSoft immediately filed a suit claiming that Oracle’s management had engaged in “acts of unfair trade practices” and had “disrupted PeopleSoft’s cus- tomer relationships.” In another suit J.D. Edwards claimed that Oracle had wrongly “interfered with its proposed merger with PeopleSoft” and demanded $1.7 billion in compensatory damages.

Oracle’s bid was the opening salvo in a battle that was to last 18 months. Some of the key dates in this battle are set out in Table  21.5 . PeopleSoft had several defenses at its disposal. First, it had in place a poison pill, which would allow it to flood the market with additional shares if a predator acquired 20% of the stock. Sec- ond, the company instituted a customer-assurance program that offered custom- ers money-back guarantees if an acquirer were to reduce customer support. At one point in the takeover battle the potential liability under this program reached nearly $1.6 billion. Third, elections to the PeopleSoft board were staggered, so different directors came up for reelection in different years. This meant that it would take two annual meetings to replace a majority of PeopleSoft’s board.

Oracle not only had to overcome PeopleSoft’s defenses but also had to clear possible antitrust roadblocks. Connecticut’s attorney general instituted an antitrust

poison pill Measure taken by a target firm to avoid acquisition; for example, the right of existing shareholders to buy additional shares at an attractive price if a bidder acquires a large holding.

TABLE 21.5 Some key dates in the Oracle/PeopleSoft takeover battle

Date Event

June 6, 2003 Oracle offers cash of $16 a share for PeopleSoft stock, a premium of 6%.

June 18, 2003 Oracle increases offer to $19.50 a share. February 4, 2004 Oracle raises offer to $26 a share. February 26, 2004 Justice Department fi les suit to block deal. Oracle announces

plans to appeal. May 16, 2004 Oracle reduces offer to $21 a share. September 9, 2004 Oracle wins appeal in a federal court against Department of

Justice antitrust ruling. September 27, 2004 Hearing begins in Delaware court on Oracle’s request to

overturn PeopleSoft’s poison pill. November 1, 2004 Oracle raises offer to $24 a share. Accepted by holders of

61% of PeopleSoft shares. November 23, 2004 Oracle announces plans to mount a proxy fi ght by naming

four nominees for PeopleSoft’s board. December 13, 2004 Oracle raises offer to $26.50 a share. Accepted by

PeopleSoft’s board.

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action to block Oracle’s bid, in part to protect his state’s considerable investment in PeopleSoft software, and announced that he was seeking to assemble a coali- tion of other states and customers as well. Then an investigation of the deal by the U.S. Department of Justice ruled that the deal was anticompetitive. Normally such an objection is enough to kill a deal, but Oracle was persistent and successfully appealed the ruling in a federal court.

While these battles were being fought out, Oracle revised its offer four times. It upped its offer first to $19.50 and then to $26 a share. Then, in an effort to put pres- sure on PeopleSoft shareholders, Oracle reduced its offer to $21 a share, citing a drop of 28% in the price of PeopleSoft’s shares. Six months later it raised the offer again to $24 a share, warning investors that it would walk away if the offer was not accepted by PeopleSoft’s board or a majority of the PeopleSoft shareholders.

Holders of sixty-one percent of PeopleSoft’s shares indicated that they wished to accept this last offer, but before Oracle could gain control of PeopleSoft, it still needed the company to get rid of the poison pill and customer-assurance scheme. That meant putting pressure on PeopleSoft’s management, which had continued to reject every approach. Oracle tried two tactics. First, it initiated a proxy fight to change the composition of PeopleSoft’s board. Second, it filed a suit in a Delaware court alleging that PeopleSoft’s management had breached its fiduciary duty by trying to thwart Oracle’s offer and not giving it “due consideration.” The lawsuit asked the court to require that PeopleSoft dismantle its takeover defenses, includ- ing the poison-pill plan and the customer-assurance program.

PeopleSoft’s CEO had at one point said that he “could imagine no price nor combination of price and other conditions to recommend accepting the offer.” But with so many of PeopleSoft’s shareholders wishing to take up Oracle’s latest offer, it was becoming less easy for the company to keep saying no, and many observers were starting to question whether PeopleSoft’s management was acting in the shareholders’ interest. If management showed itself deaf to shareholders’ interests, the court could well rule in favor of Oracle or disgruntled shareholders might vote to change the composition of the PeopleSoft board. PeopleSoft’s direc- tors therefore decided to be less intransigent and testified at the Delaware trial that they would consider negotiating with Oracle if it were to offer $26.50 or $27 a share. This was the breakthrough that Oracle was looking for. It upped its offer immediately to $26.50 a share, PeopleSoft lifted its defenses, and within a month 97% of PeopleSoft’s shareholders had agreed to the bid. After 18 months of punch and counterpunch the battle for PeopleSoft was over.

What are the lessons? First, the example illustrates some of the stratagems of merger warfare. Firms like PeopleSoft that are worried about being taken over usu- ally prepare their defenses in advance. Often they will persuade shareholders to agree to shark-repellent changes to the corporate charter. For example, the charter may be amended to require that any merger must be approved by a supermajority of 80% of the shares rather than the normal 50%.

Firms frequently deter potential bidders by devising poison pills, which make the company unappetizing. For example, the poison pill may give existing shareholders the right to buy the company’s shares at half-price as soon as a bidder acquires more than 15% of the shares. The bidder is not entitled to the discount. Thus the bidder resembles Tantalus—as soon as it has acquired 15% of the shares, control is lifted away from its reach.

The battle for PeopleSoft illustrates the strength of poison pills and other takeover defenses. Oracle’s offensive still gained ground, but with great expense and at a very slow pace. But eventually the pressure on PeopleSoft’s management became over- whelming. Unless it could demonstrate that it was acting in the shareholders’ interests,

shark repellent Amendment to a company charter made to forestall takeover attempts.

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Chapter 21 Mergers, Acquisitions, and Corporate Control 623

it risked having the poison pill removed by the court. The second reason that the com- pany caved in was the increasing pressure from its shareholders, including some large institutions, who wished to accept Oracle’s offer.

21.8 Method 3: Leveraged Buyouts Leveraged buyouts, or LBOs, differ from ordinary acquisitions in two ways. First, a large fraction of the purchase price is debt-financed. Some, perhaps all, of this debt is junk, that is, below investment grade. Second, the shares of the LBO no longer trade on the open market. The remaining equity in the LBO is privately held by a small group of (usually institutional) investors and is known as private equity. When this group is led by the company’s management, the acquisition is called a management buyout (MBO). Many LBOs are in fact MBOs.

In the 1970s and 1980s many management buyouts were arranged for unwanted divisions of large, diversified companies. Smaller divisions outside the companies’ main lines of business often lacked top management’s interest and commitment, and divisional management chafed under corporate bureaucracy. Many such divisions flowered when spun off as MBOs. Their managers, pushed by the need to generate cash for debt service and encouraged by a substantial personal stake in the business, found ways to cut costs and compete more effectively.

During the 1980s private-equity activity shifted to buyouts of entire businesses, including large, mature public corporations. The largest, most dramatic, and best- documented LBO of them all was the $25 billion takeover of RJR Nabisco in 1988 by Kohlberg Kravis Roberts (KKR). The players, tactics, and controversies of LBOs are writ large in this case.

leveraged buyout (LBO) Acquisition of the firm by a private group using substantial borrowed funds.

management buyout (MBO) Acquisition of the firm by its own management in a leveraged buyout.

Example 21.3 RJR Nabisco 6 On October 28, 1988, the board of directors of RJR Nabisco revealed that Ross Johnson, the company’s chief executive officer, had formed a group of investors prepared to buy all the firm’s stock for $75 per share in cash and take the com- pany private. Johnson’s group was backed up and advised by Shearson Lehman Hutton, the investment bank subsidiary of American Express.

RJR’s share price immediately moved to about $75, handing shareholders a 36% gain over the previous day’s price of $56. At the same time RJR’s bonds fell, since it was clear that existing bondholders would soon have a lot more company.

Johnson’s offer lifted RJR onto the auction block. Once the company was in play, its board of directors was obliged to consider other offers, which were not long coming. Four days later, a group of investors led by LBO specialist Kohlberg Kravis Roberts bid $90 per share, $79 in cash plus preferred stock valued at $11.

The bidding finally closed on November 30, some 32 days after the initial offer was revealed. In the end it was Johnson’s group against KKR. KKR offered $109 per share, after adding $1 per share (roughly $230 million) at the last hour. The KKR bid was $81 in cash, convertible subordinated debentures valued at about $10, and pre- ferred shares valued at about $18. Johnson’s group bid $112 in cash and securities.

But the RJR board chose KKR. True, Johnson’s group had offered $3 per share more, but its security valuations were viewed as “softer” and perhaps overstated. Also, KKR’s planned asset sales were less drastic; perhaps its plans for managing the business inspired more confidence. Finally, the Johnson group’s proposal con- tained a management compensation package that seemed extremely generous and had generated an avalanche of bad press.

6 The story of the RJR Nabisco buyout is reconstructed by B. Burrough and J. Helyar in Barbarians at the Gate: The Fall of RJR Nabisco (New York: Harper & Row, 1990) and is the subject of a movie with the same title.

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Barbarians at the Gate? The buyout of RJR crystallized views on LBOs, the junk bond market, and the take- over business. For many it exemplified all that was wrong with finance in the 1980s, especially the willingness of “raiders” to carve up established companies, leaving them with enormous debt burdens, basically in order to get rich quick.

There was plenty of confusion, stupidity, and greed in the LBO business. Not all the people involved were nice. On the other hand, LBOs generated enormous increases in market value, and most of the gains went to selling stockholders, not raiders. For exam- ple, the biggest winners in the RJR Nabisco LBO were the company’s stockholders.

The most important sources of added value in the buyout of RJR came from making the firm leaner and meaner. The company’s new management was obliged to pay out massive amounts of cash to service the LBO debt. It also had an equity stake in the business and therefore strong incentives to sell off nonessential assets, cut costs, and improve operating profits.

LBOs are usually diet deals. But there may be other motives. Here are some of them.

The Junk Bond Markets LBOs and debt-financed takeovers may have been driven by artificially cheap funding from the junk bond markets. With hindsight it seems that investors in junk bonds underestimated the risks of default. Default rates climbed painfully between 1989 and 1991, yields rose dramatically, and new issues dried up. For a while junk-financed LBOs disappeared from the scene.

Leverage and Taxes As we explained in Chapter 16, borrowing money saves taxes. But taxes were not the main driving force behind LBOs. The value of interest tax shields was just not big enough to explain the observed gains in market value.

Of course, if interest tax shields were the main motive for LBOs’ high debt, then LBO managers would not be so concerned to pay off debt. We saw that this was one of the first tasks facing RJR Nabisco’s new management.

Other Stakeholders It is possible that the gain to the selling stockholders is just someone else’s loss and that no value is generated overall. Therefore, we should look at the total gain to all investors in an LBO, not just the selling stockholders.

Bondholders are the obvious losers. The debt they thought was well-secured may turn into junk when a debt-financed LBO dramatically increases leverage. We noted

But where did the merger benefits come from? What could justify offering $109 per share, about $25 billion in all, for a company that only 33 days previously had been selling for $56 per share?

KKR and other bidders were betting on two things. First, they expected to gener- ate billions of additional dollars from interest tax shields, reduced capital expen- ditures, and sales of assets not strictly necessary to RJR’s core businesses. Asset sales alone were projected to generate $5 billion. Second, they expected to make those core businesses significantly more profitable, mainly by cutting back on expenses and bureaucracy. Apparently there was plenty to cut, including the RJR “Air Force,” which at one point operated 10 corporate jets.

But while KKR’s new management team was cutting costs and selling assets, prices in the junk bond market were rapidly declining, implying much higher future interest charges for RJR and stricter terms on any refinancing. In mid-1990 KKR made an additional equity investment, and later that year the company announced an offer of cash and new shares in exchange for $753 million of junk bonds. By 1993 the burden of debt had been reduced from $26 billion to $14 billion. For RJR, the world’s largest LBO, it seemed that high debt was a temporary, not permanent, virtue.

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how market prices of RJR Nabisco debt fell sharply when Ross Johnson’s first LBO offer was announced. But again, the value losses suffered by bondholders in LBOs are not nearly large enough to explain stockholder gains.

Leverage and Incentives Managers and employees of LBOs work harder and often smarter. They have to generate cash to service the extra debt. Moreover, managers’ personal fortunes are riding on the LBO’s success. They become owners rather than organization men or women.

It is hard to measure the payoff from better incentives, but there is some evidence of improved operating efficiency in LBOs. Kaplan, who studied 48 management buyouts between 1980 and 1986, found average increases in operating income of 24% over the following 3 years. Ratios of operating income and net cash flow to assets and sales increased dramatically. He observed cutbacks in capital expenditures but not in employment. Kaplan suggests that these operating changes “are due to improved incentives rather than layoffs or managerial exploitation of shareholders through inside information.” 7

Free Cash Flow The free-cash-flow theory of takeovers is basically that mature firms with a surplus of cash will tend to waste it. This contrasts with standard finance theory, which says that firms with more cash than positive-NPV investment oppor- tunities should give the cash back to investors through higher dividends or share repurchases. But we see firms like RJR Nabisco spending on corporate luxuries and questionable capital investments. One benefit of LBOs is to put such companies on a diet and force them to pay out cash to service debt.

The free-cash-flow theory predicts that mature, “cash cow” companies will be the most likely targets of LBOs. We can find many examples that fit the theory, including RJR Nabisco. The theory says that the gains in market value generated by LBOs are just the present values of the future cash flows that would otherwise have been frit- tered away. 8

We have reviewed several motives for LBOs. We do not say that all LBOs are good. On the contrary, there have been many mistakes, and even soundly motivated LBOs are risky, as the bankruptcies of a number of highly leveraged transactions have dem- onstrated. Yet we do take issue with those who portray LBOs solely as undertaken by Wall Street barbarians breaking up the traditional strength of corporate America.

21.9 Method 4: Divestitures, Spin-Offs, and Carve-Outs In the market for corporate control, fusion—mergers and acquisitions—gets the most publicity. But fission—the divestiture of assets or entire businesses—can be just as important. Often one firm may sell part of its business to another firm. For example, in 2012 Pfizer announced that it was selling its infant nutrition business to Nestlé for $11.9 billion. The sale represented part of a strategy by Pfizer to focus on its core pharmaceutical activities.

Instead of selling part of their operations, companies sometimes spin off a business by separating it from the parent firm and distributing to their shareholders the stock in the newly independent company. For example, after Carl Icahn pressured Motorola to

7 S. Kaplan, “The Effects of Management Buyouts on Operating Performance and Value,” Journal of Financial Economics 24 (October 1989), pp. 217–254. 8 The free-cash-flow theory’s chief proponent is Michael Jensen. See M. C. Jensen, “The Eclipse of the Public Corporation,” Harvard Business Review 67 (September–October 1989), pp. 61–74, and “The Agency Costs of Free Cash Flow, Corporate Finance and Takeovers,” American Economic Review 76 (May 1986), pp. 323–329.

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spin off its mobile devices division, the division was launched as an independent com- pany, Motorola Mobility, in 2011. Motorola’s shareholders received shares in the spun-off firm, and thus could trade their Motorola Mobility shares as well as those of the slimmed-down original company, now renamed Motorola Solutions. 9

Carve-outs are similar to spin-offs except that shares in the new company are not given to existing stockholders but, instead, are sold in a public offering. Sometimes companies carve out a small proportion of the company to establish a market in the subsidiary and subsequently spin off the remainder of the shares. The nearby box describes how the computer company Palm was first carved and then spun.

The most frequent motive for spin-offs is improved efficiency. Companies some- times refer to a business as being a “poor fit.” By spinning off a poor fit, the manage- ment of the parent company can concentrate on its main activity. If each business must stand on its own feet, there is no risk that funds will be siphoned off from one in order to support unprofitable investments in the other. Moreover, if the two parts of the business are independent, it is easy to see the value of each and to reward managers accordingly.

21.10 The Benefits and Costs of Mergers

Merger Waves Look back at Figure 21.1 , which shows the number of mergers in the United States for each year since 1962. Notice that mergers come in waves. There was an upsurge in merger activity from 1967 to 1969 and then again in the late 1980s and 1990s. Another merger boom began in 2003 but petered out with the onset of the financial crisis.

We don’t really understand why merger activity is so volatile and why it seems to be associated with the level of stock prices. None of the motives that we review in this chapter is related to the general level of stock prices. None burst on the scene in the 1960s, departed in 1970, and reappeared for most of the 1980s and again in the mid- 1990s and early 2000s.

Some mergers may result from mistakes in valuation on the part of the stock mar- ket. In other words, the buyer may believe that investors have underestimated the value of the seller or may hope that they will overestimate the value of the combined firm. But we see (with hindsight) that mistakes are made in bear markets as well as bull markets. Why don’t we see just as many firms hunting for bargain acquisitions when the stock market is low? It is possible that “suckers are born every minute,” but why do they seem more prone to be harvested in bull markets?

There are undoubtedly good acquisitions and bad acquisitions, but economists find it hard to agree on whether acquisitions are beneficial on balance. In general, share- holders of the target firm make a healthy gain. For example, one study found that fol- lowing the announcement of the bid, the stock price of the target company jumped by 16% on average. 10 On the other hand, it appears that investors expected the acquiring companies to just about break even, for the price of their shares fell by .7%. The value of the total package—buyer plus seller—increased by 1.8%. Of course, these are aver- ages; selling shareholders, for example, have sometimes obtained much higher returns. When Hewlett-Packard won its takeover battle to buy data-storage company 3Par, it paid a premium of 230%, or about $1.5 billion, for 3Par’s stock.

9 Seven months after the spin-off, Google acquired Motorola Mobility for $12.5 billion but less than 2 years later sold it to Lenovo for just below $3 billion. The investment may have been disappointing for Google, but not as disappointing as the final sales price suggests, since Google retained the majority of Motorola’s patent portfolio, which was probably the key motivation behind its original purchase.

10 See G. Andrade, M. Mitchell, and E. Stafford, “New Evidence and Perspectives on Mergers,” Journal of Economic Perspectives 15 (Spring 2001), pp. 103–120.

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Since buyers roughly break even and sellers make substantial gains, it seems that there are positive overall benefits from mergers. But not everybody is convinced. Some believe that investors analyzing mergers pay too much attention to short-term earnings gains and don’t notice that these gains are at the expense of long-term prospects.

Since we can’t observe how companies would have fared in the absence of a merger, it is difficult to measure the effects on profitability. However, several studies of merger activity suggest that mergers do seem to improve real productivity. For example, Healy, Palepu, and Ruback examined 50 large mergers and found an average increase in the companies’ pretax returns of 2.4 percentage points. 11 They argue that this gain came from generating a higher level of sales from the same assets. There was no evi- dence that the companies were mortgaging their long-term futures by cutting back on long-term investments; expenditures on capital equipment and research and develop- ment tracked the industry average.

If you are concerned with public policy toward mergers, you do not want to look only at their impact on the shareholders of the companies concerned. For instance, we have already seen that in the case of RJR Nabisco some part of the shareholders’ gain was at the expense of the bondholders and the Internal Revenue Service (through the enlarged interest tax shield). The acquirer’s shareholders may also gain at the expense of the target firm’s employees, who in some cases are laid off or are forced to take pay cuts after takeovers.

Perhaps the most important effect of acquisition is felt by the managers of compa- nies that are not taken over. For example, one effect of LBOs was that the managers of even the largest corporations could not feel safe from challenge. Perhaps the threat of takeover spurs the whole of corporate America to try harder. Unfortunately, we don’t know whether on balance the threat of merger makes for more active days or more sleepless nights.

11 See P. Healy, K. Palepu, and R. Ruback, “Does Corporate Performance Improve after Mergers?” Journal of Financial Economics 31 (April 1992), pp. 135–175. The study examined the pretax returns of the merged com- panies relative to industry averages.

Finance in Practice How Palm Was Carved and Spun $82, or more than $60 a share less than the market value of the shares in Palm that they were due to receive. *

Three years after 3Com spun off its holding in Palm, Palm itself entered the spin-off business by giving shareholders stock in PalmSource, a subsidiary that was responsible for developing and licensing the Palm operating system. The remaining business, renamed palmOne, would focus on mak- ing mobile gadgets. The company gave three reasons for its decision to split into two. First, like 3Com’s management, Palm’s management believed that the company would ben- efi t from clarity of focus and mission. Second, it argued that shareholder value could “be enhanced if investors could evalu- ate and choose between both businesses separately, thereby attracting new and different investors.” Finally, it seemed that Palm’s rivals were reluctant to buy software from a company that competed with them in making handheld hardware.

*This difference would seem to present an arbitrage opportunity. An investor who bought 1 share of 3Com and sold short 1.5 shares of Palm would receive an immediate cash fl ow of $60 and own 3Com’s other assets for free. The dif- fi culty in executing this arbitrage is explored in O. A. Lamont and R. H. Thaler, “Can the Market Add and Subtract? Mispricing in Tech Stock Carve-Outs,” Journal of Political Economy 111 (April 2003), pp. 227–268.

When 3Com acquired U.S. Robotics in 1997, it also became the owner of Palm, a small start-up business developing handheld computers. It was a lucky purchase, for over the next 3 years the Palm Pilot came to dominate the market for handheld computers. But as Palm began to take up an increasing amount of management time, 3Com concluded that it needed to return to its knitting and focus on its basic business of selling computer network systems. It therefore announced that it would carve out 5% of its holding of Palm through an initial public offering. At the same time it published plans to spin off the remaining 95% of Palm shares later in 2000 by giving 3Com shareholders about 1.5 Palm shares for each 3Com share that they owed.

The Palm carve-out occurred at close to the peak of the high-tech boom and got off to a dazzling start. The shares were issued in the IPO at $38 each. On the fi rst day of trading the stock price touched $165 before closing at $95. There- fore, anyone owning a share of 3Com stock could look for- ward later in the year to receiving about 1.5 shares of Palm worth 1.5 × 95 = $142.50. But apparently 3Com’s sharehold- ers were not fully convinced that their newfound wealth was for real, for on the same day 3Com’s stock price closed at

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628 Part Seven Special Topics

The threat of takeover may be a spur to inefficient management, but it is also costly. The companies need to pay for the services provided by the investment bankers, law- yers, and accountants. In addition, mergers can soak up large amounts of management time and effort. When a company is planning a takeover, it can be difficult to give as much attention as one should to the firm’s existing business.

Even if the gains to the community exceed these costs, one wonders whether the same benefits could not be achieved more cheaply another way. For example, are lev- eraged buyouts necessary to make managers work harder? Perhaps the problem lies in the way that many corporations reward and penalize their managers. Perhaps many of the gains from takeover could be captured by linking management compensation more closely to performance.

SUMMARY A merger may be undertaken in order to replace an inefficient management. But some- times two businesses may be more valuable together than apart. Gains may stem from economies of scale, economies of vertical integration, the combination of complemen- tary resources, or redeployment of surplus funds. We don’t know how frequently these benefits occur, but they do make economic sense. Sometimes mergers are undertaken to diversify risks or artificially increase growth of earnings per share. These motives are dubious.

A merger generates an economic gain if the two firms are worth more together than apart. The gain is the difference between the value of the merged firm and the value of the two firms run independently. The cost is the premium that the buyer pays for the selling firm over its value as a separate entity. When payment is in the form of shares, the value of this payment naturally depends on what those shares are worth after the merger is complete. You should go ahead with the merger if the gain exceeds the cost.

If the board of directors fails to replace an inefficient management, there are four ways to effect a change: (1) Shareholders may engage in a proxy contest to replace the board; (2) the firm may be taken over by another; (3) the firm may be purchased by a private group of investors in a leveraged buyout; or (4) it may sell off part of its operations to another company.

Mergers are often amicably negotiated between the management and directors of the two companies; but if the seller is reluctant, the would-be buyer can decide to make a tender offer for the stock. We sketched some of the offensive and defensive tactics used in take- over battles. These defenses include shark repellents (changes in the company charter meant to make a takeover more difficult to achieve) and poison pills (measures that make takeover of the firm more costly).

In a leveraged buyout (LBO) or management buyout (MBO), all public shares are repurchased and the company “goes private.” LBOs tend to involve mature businesses with ample cash flow and modest growth opportunities. LBOs and other debt-financed take- overs are driven by a mixture of motives, including (1) the value of interest tax shields; (2) transfers of value from bondholders, who may see the value of their bonds fall as the firm piles up more debt; and (3) the opportunity to create better incentives for managers and employees, who have a personal stake in the company. In addition, many LBOs have been designed to force firms with surplus cash to distribute it to shareholders rather than plowing it back. Investors feared such companies would otherwise channel free cash flow into negative-NPV investments.

Why may it make sense for companies to merge? (LO21-1)

How should the gains and costs of mergers to the acquiring firm be measured? (LO21-2)

In what ways do companies change the composition of their ownership or management? (LO21-3)

What are some takeover defenses? (LO21-4)

What are some of the motivations for leveraged and management buyouts of the firm? (LO21-5)

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Chapter 21 Mergers, Acquisitions, and Corporate Control 629

We observed that when the target firm is acquired, its shareholders typically win: Target firms’ shareholders earn abnormally large returns. The bidding firm’s shareholders roughly break even. This suggests that the typical merger generates positive net benefits, but com- petition among bidders and active defense by management of the target firm pushes most of the gains toward selling shareholders.

QUESTIONS AND PROBLEMS 1. Merger Motives. Do each of the following motives for mergers make economic sense? Answer

yes or no. (LO21-1)

a. Merging to achieve economies of scale b. Merging to reduce risk by diversification c. Merging to redeploy cash generated by a firm with ample profits but limited growth

opportunities d. Merging to increase earnings per share

2. Merger Motives. Explain why it might or might not make good sense for Northeast Heating and Northeast Air Conditioning to merge into one company. (LO21-1)

3. Mergers and P/E Ratios. Castles in the Sand currently sells at a price-earnings multiple of 10. The firm has 2 million shares outstanding and sells at a price per share of $40. Firm Foundation has a P/E multiple of 8, has 1 million shares outstanding, and sells at a price per share of $20. (LO21-1)

a. If Castles acquires the other firm by exchanging one of its shares for every two of Firm Foundation, what will be the earnings per share of the merged firm?

b. What will happen to Castles’ price per share? c. Show that shareholders of neither Castles nor Firm Foundation realize any change in wealth. d. What should be the P/E of the new firm if the merger has no economic gains? e. What will happen to Castles’ price per share if the market does not realize that the P/E ratio

of the merged firm ought to differ from Castles’ premerger ratio? f. How are the gains from the merger split between shareholders of the two firms if the market

is fooled as in part (c)?

4. Stock versus Cash Offers. Sweet Cola Corp. (SCC) is bidding to take over Salty Dog Pret- zels (SDP). SCC has 3,000 shares outstanding, selling at $50 per share. SDP has 2,000 shares outstanding, selling at $17.50 a share. SCC estimates the economic gain from the merger to be $15,000. (LO21-2)

a. If SDP can be acquired for $20 a share, what is the NPV of the merger to SCC? b. What will SCC sell for when the market learns that it plans to acquire SDP for $20 a share? c. What will SDP sell for? d. What are the percentage gains to the shareholders of each firm? e. Now suppose that the merger takes place through an exchange of stock. On the basis of the

premerger prices of the firms, SCC sells for $50, so instead of paying $20 cash, SCC issues .40 of its shares for every SDP share acquired. What will be the price of the merged firm?

f. What is the NPV of the merger to SCC when it uses an exchange of stock? Why does your answer differ from part (a)?

5. Merger Gains. Acquiring Corp. is considering a takeover of Takeover Target Inc. Acquiring has 10 million shares outstanding, which sell for $40 each. Takeover Target has 5 million shares outstanding, which sell for $20 each. If the merger gains are estimated at $25 million, what is the highest price per share that Acquiring should be willing to pay to Takeover Target sharehold- ers? (LO21-2)

Do mergers increase efficiency, and how are the gains from mergers distributed between shareholders of the acquired and acquiring firms? (LO21-6)

finance

®

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630 Part Seven Special Topics

12. LBO Facts. True or false? (LO21-5)

a. One of the first tasks of an LBO’s financial manager is to pay down debt. b. Leveraged buyouts reduce the free cash flow available to the firm. c. Targets for LBOs in the 1980s tended to be profitable companies in mature industries with

limited investment opportunities.

13. Merger Facts. True or false? (LO21-6)

a. Sellers almost always gain in mergers. b. Buyers almost always gain in mergers. c. Firms that do unusually well tend to be acquisition targets. d. Merger activity in the United States varies dramatically from year to year. e. On average, mergers produce substantial economic gains. f. Tender offers require the approval of the selling firm’s management. g. The cost of a merger is always independent of the economic gain produced by the merger.

6. Mergers Gains. If Acquiring Corp., from Problem 5, has a price-earnings ratio of 12 and Takeover Target has a P/E ratio of 8, what should be the P/E ratio of the merged firm? Assume in this case that the merger is financed by an issue of new Acquiring Corp. shares. Takeover Target will get one Acquiring share for every two Takeover Target shares held. (LO21-2)

7. Merger Gains and Costs. Velcro Saddles is contemplating the acquisition of Pogo Ski Sticks Inc. The values of the two companies as separate entities are $20 million and $10 million, respectively. Velcro Saddles estimates that by combining the two companies, it will reduce mar- keting and administrative costs by $500,000 per year in perpetuity. Velcro Saddles is willing to pay $14 million cash for Pogo. The opportunity cost of capital is 8%. (LO21-2)

a. What is the gain from the merger? b. What is the cost of the cash offer? c. What is the NPV of the acquisition under the cash offer?

8. Stock versus Cash Offers. Suppose that instead of making a cash offer as in Problem 7, Velcro Saddles considers offering Pogo shareholders a 50% holding in Velcro Saddles. (LO21-2)

a. What is the value of the stock in the merged company held by the original Pogo shareholders? b. What is the cost of the stock alternative? c. What is the merger’s NPV under the stock offer?

9. Merger Gains. Immense Appetite Inc. believes that it can acquire Sleepy Industries and improve efficiency to the extent that the market value of Sleepy will increase by $5 million. Sleepy currently sells for $20 a share, and there are 1 million shares outstanding. (LO21-2)

a. Sleepy’s management is willing to accept a cash offer of $25 a share. Can the merger be accomplished on a friendly basis?

b. What will happen if Sleepy’s management holds out for an offer of $28 a share?

10. Market for Corporate Control. Why are both tender offers and proxy contests threatening to the current management of a firm? What are less contentious mechanisms that may lead to a change in management? (LO21-3)

11. Merger Tactics. Connect each term to its correct definition or description. (LO21-4)

a. LBO b. poison pill c. tender offer d. shark repellent e. proxy contest

A. Attempt to gain control of a firm by winning the votes of its stockholders

B. Changes in the corporate charter that are designed to deter an unwelcome takeover

C. Measure in which shareholders are issued rights to buy shares if the bidder acquires a large stake in the firm

D. Offer to buy shares directly from stockholders E. Buyout of a company or business by private investors, largely

debt-financed

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Chapter 21 Mergers, Acquisitions, and Corporate Control 631

CHALLENGE PROBLEMS 14. Bootstrap Game. The Muck and Slurry merger has fallen through (see Section 21.2). But

World Enterprises is determined to report earnings per share of $2.67. It therefore acquires the Wheelrim and Axle Company. You are given the following facts:

World Enterprises

Wheelrim and Axle Merged Firm

Earnings per share $2 $2.50 $2.67 Price per share $40 $25 _____ Price-earnings ratio 20 10 _____ Number of shares 100,000 200,000 _____ Total earnings $200,000 $500,000 _____ Total market value $4,000,000 $5,000,000 _____

Once again there are no gains from merging. In exchange for Wheelrim and Axle shares, World Enterprises issues just enough of its own shares to ensure its $2.67 earnings per share objective. (LO21-1)

a. Complete the above table for the merged firm. b. How many shares of World Enterprises are exchanged for each share of Wheelrim and Axle? c. What is the cost of the merger to World Enterprises? d. What is the change in the total market value of the World Enterprises shares that were out-

standing before the merger?

15. Merger Gains and Costs. As treasurer of Leisure Products Inc. you are investigating the possible acquisition of Plastitoys. You have the following basic data:

Leisure Products Plastitoys

Forecast earnings per share $5 $1.50 Forecast dividend per share $3 $.80 Number of shares 1,000,000 600,000 Stock price $90 $20

You estimate that investors currently expect a steady growth of about 6% in Plastitoys’ earnings and dividends. You believe that Leisure Products could increase Plastitoys’ growth rate to 8% per year, without any additional capital investment required. (LO21-2)

a. What is the gain from the acquisition? b. What is the cost of the acquisition if Leisure Products pays $25 in cash for each share of

Plastitoys? c. What is the cost of the acquisition if Leisure Products offers one share of Leisure Products

for every three shares of Plastitoys? d. How would the cost of the cash offer and the share offer alter if the expected growth rate of

Plastitoys were not increased by the merger?

WEB EXERCISE 1. Look at a recent example of a merger announcement, and log on to the website of the acquir-

ing company. What reasons does the acquirer give for buying the target? How does it intend to pay for the target—with cash, shares, or a mixture of the two? Can you work out how much the target’s shareholders will gain from the offer? Is it more or less than would be the case for an average merger? Now log on to finance.yahoo.com and find out what happened to the stock price of the acquiring company when the merger was announced. Were shareholders pleased with the announcement?

Templates can be found in Connect.

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632 Part Seven Special Topics

MINICASE McPhee Food Halls operated a chain of supermarkets in the west of Scotland. The company had had a lackluster record, and since the death of its founder in late 2004, it had been regarded as a prime target for a takeover bid. In anticipation of a bid, McPhee’s share price moved up from £4.90 in March to a 12-month high of £5.80 on June 10, despite the fact that the London stock market index as a whole was largely unchanged.

Almost nobody anticipated a bid coming from Fenton, a diversi- fied retail business with a chain of clothing and department stores. Though Fenton operated food halls in several of its department stores, it had relatively little experience in food retailing. Fenton’s management had, however, been contemplating a merger with McPhee for some time. The managers not only felt that they could make use of McPhee’s food retailing skills within their department stores, but they also believed that better management and inventory control in McPhee’s business could result in cost savings worth £10 million.

Fenton’s offer of 8 Fenton shares for every 10 McPhee shares was announced after the market close on June 10. Since McPhee had 5 million shares outstanding, the acquisition would add an additional 5 × (8/10) = 4 million shares to the 10 million Fenton shares that were already outstanding. While Fenton’s management believed that it would be difficult for McPhee to mount a successful

takeover defense, the company and its investment bankers privately agreed that the company could afford to raise the offer if it proved necessary.

Investors were not persuaded of the benefits of combining a supermarket with a department store company, and on June 11 Fenton’s shares opened lower and drifted down £.10 to close the day at £7.90. McPhee’s shares, however, jumped to £6.32 a share.

Fenton’s financial manager was due to attend a meeting with the company’s investment bankers that evening, but before doing so, he decided to run the numbers once again. First he reestimated the gain and cost of the merger. Then he analyzed that day’s fall in Fenton’s stock price to see whether investors believed there were any gains to be had from merging. Finally, he decided to revisit the issue of whether Fenton could afford to raise its bid at a later stage. If the effect was simply a further fall in the price of Fenton stock, the move could be self-defeating.

QUESTIONS

1. Does the market believe that the merger will create net gains? 2. What are the costs and benefits of the proposed merger for

Fenton’s shareholders? 3. Would Fenton be wise to raise its bid?

SOLUTIONS TO SELF-TEST QUESTIONS 21.1 a. Horizontal merger. IBM is in the same industry as Lenovo.

b. Conglomerate merger. Lenovo and Safeway are in different industries. c. Vertical merger. Safeway is expanding backward to acquire one of its suppliers, Campbell

Soup. d. Conglomerate merger. Campbell Soup and IBM are in different industries.

21.2 Given current earnings of $2 a share and a share price of $10, Muck and Slurry would have a market value of $1,000,000 and a price-earnings ratio of only 5. It can be acquired for only half as many shares of World Enterprises, 25,000 shares. Therefore, the merged firm will have 125,000 shares outstanding and earnings of $400,000, resulting in earnings per share of $3.20, higher than the $2.67 value in the third column of Table 21.2 .

21.3 The cost of the merger is $4 million: the $4 per share premium offered to Goldfish sharehold- ers times 1 million shares. If the merger has positive NPV to Killer Shark, the gain must be greater than $4 million.

21.4 Yes. Look again at Table 21.4 . Total market value is still $540 million, but Cislunar will have to issue 1 million shares to complete the merger. Total shares in the merged firm will be 11 million. The postmerger share price is $49.09, so Cislunar and its shareholders still come out ahead.

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634

International Financial Management

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

22-1 Understand the difference between spot and forward exchange rates.

22-2 Understand the basic relationships between spot exchange rates, forward exchange rates, interest rates, and inflation rates.

22-3 Formulate simple strategies to protect the firm against exchange rate risk.

22-4 Perform an NPV analysis for projects with cash flows in foreign currencies.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

22 CHAPTE R

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635

P A

R T

S E

V E

N

T hus far we have talked mostly about doing business at home. But many companies have substantial overseas interests. Of course, the objectives of international financial management

are still the same. You want to buy assets that are

worth more than they cost, and you want to pay for

them by issuing liabilities that are, if possible, worth

less than the money raised. But when you try to apply

these criteria to an international business, you come

up against some new wrinkles.

You must, for example, know how to deal with more

than one currency. Therefore we open this chapter

with a look at foreign exchange markets.

The financial manager must also remember

that interest rates differ from country to country. For

Sp e

c ia

l T o

p ic

s

Coca-Cola does business around the world. What new issues does international business raise for the financial manager?

example, in February 2014, the 10-year interest rate

was about .6% in Japan, 2.7% in the United States,

and 13.1% in Brazil. We will discuss the reasons for

these differences in interest rates, along with some of

the implications for financing overseas operations.

Exchange rate fluctuations can knock companies

off course and transform black ink into red. We will

therefore discuss how firms can protect themselves

against exchange risks.

We will also discuss how international companies

decide on capital investments. How do they choose

the discount rate? You’ll find that the basic prin-

ciples of capital budgeting are the same as those

for domestic projects, but there are a few pitfalls to

watch for.

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636 Part Seven Special Topics

22.1 Foreign Exchange Markets An American company that imports goods from France will probably need to exchange its dollars for euros in order to pay for its purchases. Another company exporting to France will probably receive euros, which it then sells in exchange for dollars. Both firms must make use of the foreign exchange market, where currencies are traded.

The foreign exchange market has no central marketplace. All business is conducted via computer terminals and telephone. The principal dealers are the large commercial banks, and a corporation that wants to buy or sell currency usually does so through a commercial bank.

Turnover in the foreign exchange markets is huge. In London alone nearly $1.9 tril- lion of currency changes hands each day. That is equivalent to an annual turnover of around $500 trillion ($500,000,000,000,000). New York accounts for a further $800 bil- lion of turnover per day. Compare this with the trading volume of the New York Stock Exchange, where about $80 billion of stock typically changes hands on any given day.

Spot Exchange Rates Suppose you ask someone the price of bread. He may tell you that you can buy two loaves for a dollar, or he may say that one loaf costs 50 cents. If you ask a foreign exchange dealer to quote you a price for Ruritanian pesos, she may tell you that you can buy 100 pesos for a dollar or that 1 peso costs $.01. The first quote (the number of pesos that you can buy for a dollar) is known as an indirect quote of the exchange rate. The second quote (the number of dollars that it costs to buy 1 peso) is known as a direct quote. Of course, both quotes provide the same information. If you can buy 100 pesos for a dollar, then you can easily calculate that the cost of buying 1 peso is 1/100 = $.01.

(Ruritania is a fictional country, which for arithmetic convenience has a currency that trades for exactly 100 pesos per U.S. dollar. We will use Ruritania in several examples below.)

Table 22.1 shows the exchange rate for several actual countries on February 18, 2014. The second column of the table shows the name of the currency and its common abbreviation. For example, the Mexican peso is usually abbreviated as MXN and the U.S. dollar as USD. By custom, the prices of most currencies are expressed as indirect

exchange rate Amount of one currency needed to purchase one unit of another.

Country Currency Exchange Rate

Europe Eurozone countries Euro (EUR or €) 1.376 * Sweden Krona (SEK) 6.485 Switzerland Franc (CHF) 0.888 United Kingdom Pound (GBP or £) 1.668 * Americas Brazil Real (BRL) 2.396 Canada Dollar (CAD) 1.095 Mexico New peso (MXN) 13.231 Asia/Africa Australia Dollar (AUD) 1.107 China Yuan (CNY) 6.067 China (Hong Kong) Dollar (HKD) 7.755 India Rupee (INR) 62.180 Japan Yen (JPY or ¥) 102.340 South Africa Rand (ZAR) 10.872 South Korea Won (KRW) 1,065.500

* Direct quotes (number of U.S. dollars per unit of foreign currency). Other quotes are indirect (units of foreign currency per U.S. dollar). Source: Financial Times, February 18, 2014, available at www.ft.com .

TABLE 22.1 Exchange rates in February 2014

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Chapter 22 International Financial Management 637

quotes. Thus the third column of Table 22.1 shows that you could buy 13.231 Mexican pesos for 1 dollar. This is sometimes written as MXN13.231 = USD1.

To complicate matters, there are two currencies whose prices are generally expressed as direct quotes. These are the euro and the British pound. For example, you can see that it cost $1.376 to buy 1 euro. We therefore write the euro exchange rate as USD1.376 = EUR1.

Use the exchange rates in Table 22.1 . How many euros can you buy for 1 dollar (an indirect quote)? How many dollars can you buy for 1 yen (a direct quote)?

Self-Test 22.1

Example 22.1 A Yen for Trade How many yen will it cost a Japanese importer to purchase $10,000 worth of oranges from a California farmer? How many dollars will that farmer need in order to buy and import a Japanese tractor priced in Japan at 4.5 million yen?

The exchange rate is JPY102.34 = USD1. The $10,000 of oranges will require the Japanese importer to come up with 10,000 × 102.34 = 1,023.40 yen. The tractor will require the American importer to come up with 4,500,000/102.34 = $43,971.

The exchange rates in the last column of Table 22.1 are the prices of currency for immediate delivery. These are known as spot rates of exchange. For example, the spot rate of exchange for Brazilian reals is BRL2.396 = USD1. In other words, it costs 2.396 Brazilian reals to buy 1 dollar for immediate delivery.

Exchange rates are generally quoted against the dollar. For example, Table  22.1 shows that $1 can buy either 102.34 Japanese yen or 1,065.50 Korean won. This implies that 102.34 yen are equivalent to 1,065.50 won and, therefore, that 1 yen is equivalent to 1,065.5/102.34 = 10.411 won. An exchange rate between two currencies other than the U.S. dollar is known as a cross-rate. In our example, the cross-rate of exchange between the Japanese yen and the South Korean won is KRW10.411 = JPY1.

Cross-rates between any two currencies are locked down by the exchange rate for each currency versus the U.S. dollar. Otherwise, investors could make an easy, risk- free arbitrage profit. For example, suppose that a (really stupid) bank quotes a rate of KRW9 = JPY1. Here’s what you do: You take $1 and exchange it for 1,065.5 Korean won, which you then use to buy 1,065.5/9 = 118.39 Japanese yen. These in turn can be exchanged back to U.S. dollars for 118.39/102.34 = $1.157. You have just taken advantage of a misalignment of prices to make a surefire 15.7% profit. 1 Of course, in real life you and other investors would transact with millions of dollars, not with one dollar at a time. The bank would be forced to revise its quote in short order.

spot rate of exchange Exchange rate for an immediate transaction.

1 In practice foreign exchange dealers quote a spread between the prices at which they are prepared to buy and sell foreign currency, and this spread would reduce your profit. The spread is very small on large trades, but it is a major cost for small transactions by individuals.

Use the exchange rates in Table  22.1 . What is the cross-rate between the Mexican peso and the Hong Kong dollar? How could you make money if a bank quoted you a rate of 2 pesos per Hong Kong dollar?

Self-Test 22.2

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638 Part Seven Special Topics

Most countries allow their currencies to float, so the exchange rate fluctuates from minute to minute and day to day. When the currency increases in value, which means that you need less of the foreign currency to buy 1 dollar, the currency is said to appreciate. When you need more of the currency to buy 1 dollar, the currency is said to depreciate.

Table 22.1 shows that the exchange rate for the Canadian dollar in February 2014 was CAD1.095 = USD1. A year earlier, the spot rate of exchange for the Canadian dollar was CAD1.014 = USD1. Thus, in 2014 you could buy more Canadian dollars for a U.S. dollar than a year earlier. Did the Canadian dollar appreciate or depreciate?

Self-Test 22.3

Some countries try to avoid fluctuations in the value of their currency and seek instead to maintain a fixed exchange rate. But fixed rates seldom last forever. If every- body tries to sell the currency, eventually the country will be forced to allow the cur- rency to depreciate. When this happens, exchange rates can change dramatically. In December 2001, when Argentina gave up defending its fixed exchange rate versus the U.S. dollar, the value of the Argentinian peso fell by over 70% in a few months.

Forward Exchange Rates Fluctuations in exchange rates can get companies into hot water. For example, suppose you have agreed to buy a consignment of machinery from Ruritania. The machinery will be delivered at the end of 12 months at a cost of 100 million Ruritanian pesos (RUPs). Currently, 1 dollar buys 100 pesos (RUP100 = USD1). So, if the exchange rate does not change, the machinery will cost you $1 million. But what if the peso appreciates? For example, suppose that when you come to buy the pesos at the end of the year, one dollar buys only 80 pesos (RUP80 = USD1). Then the dollar cost of your machinery has risen to $1.25 million (100 million/80 = $1.25 million).

You can avoid this exchange rate risk and fix your dollar cost by buying forward, that is, by arranging now to buy pesos at a prespecified price on a future date. This arrangement is called a foreign exchange forward contract. Suppose you enter into a forward contract with a bank to buy 100 million pesos 12 months from now at a price of RUP105 = USD1. You don’t pay anything now; you simply fix today the price that you will pay in the future. After 12 months, the bank pays you 100 million pesos and you hand over in exchange $.952 million (100/105 = $.952 million). 2

The spot exchange rate is the rate that you pay to obtain foreign currency today. The exchange rates in Table 22.1 are all spot exchange rates. The price of currency for delivery at a future date is called the forward exchange rate. The forward exchange rate is not usually the same as the spot rate. In our example 1 dollar bought 100 Ruri- tanian pesos in the spot market but 105 pesos in the forward market. In this case, the peso is said to trade at a forward discount relative to the dollar. It’s a discount because pesos are cheaper—each dollar can buy more pesos—if purchased forward rather than spot. If each dollar bought fewer pesos in the forward market, the peso would trade at a forward premium relative to the dollar.

A forward purchase or sale is a made-to-order transaction between you and the bank. It can be for any currency, any amount, and any delivery day. You could buy, say, 99,999 Vietnamese dong or 101,000 Haitian gourdes for a year and a day forward as

2 If the forward exchange rate is RUP105 = USD1, then 1 peso will cost you 1/105 = $.00952, and 100 million pesos will cost 100 million × $.00952 = $.952 million.

forward exchange rate Exchange rate for a future transaction.

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Chapter 22 International Financial Management 639

long as you can find a bank ready to deal. There is also an organized market for cur- rency for future delivery known as the currency futures market. Futures contracts are highly standardized versions of forward contracts—they exist only for the main cur- rencies, they are for specified amounts, and the choice of delivery dates is limited. But trading is easy on futures exchanges—you don’t have to negotiate a one-off contract with a bank. Almost everything we will say about the pricing of forward contracts applies also to futures. We will describe futures markets in greater detail in Chapter 24.

A skiing vacation in Switzerland costs 1,500 Swiss francs.

a. How many dollars does that represent? Use the exchange rates in Table 22.1 .

b. Suppose that the dollar depreciates by 10% relative to the Swiss franc, so each dollar buys 10% fewer Swiss francs than before. What is the new indirect exchange rate?

c. If the Swiss vacation continues to cost the same number of Swiss francs, what will happen to the cost in dollars?

Self-Test 22.4

22.2 Some Basic Relationships The financial manager of an international business must cope with fluctuations in exchange rates and must be aware of the distinction between spot and forward exchange rates. She must also recognize that two countries may have different inter- est rates. To develop a consistent international financial policy, the financial manager needs to understand how exchange rates are determined and why one country may have a lower interest rate than another.

To keep life as simple as possible, we will stick with our fictitious company doing business in Ruritania. Here are four basic questions that its financial manager needs to consider:

1. Why is the interest rate in Ruritania not the same as the rate in the United States? 2. What is the relationship between the spot exchange rate for the peso today and the

expected exchange rate at some future date? 3. How do different rates of inflation in Ruritania and the United States affect each

country’s interest rate and the exchange rate? 4. What explains the difference between the forward exchange rate for the peso and

the spot rate?

These are complex issues, but as a first cut we suggest that you think of spot and forward exchange rates, interest rates, and inflation rates as being linked as shown in Figure 22.1 .

Exchange Rates and Inflation Consider first the relationship between changes in the exchange rate and inflation rates (the two boxes on the right of Figure 22.1 ). The idea here is simple: If one country suffers a higher rate of inflation than another, then the value of that country’s currency will decline.

But let’s slow down and consider why changes in inflation and spot interest rates are linked. Suppose you notice that gold can be bought in New York for $1,200 an ounce and sold in Ruritania for 130,000 pesos an ounce. If there are no restrictions on the transport of gold, you could be onto a good thing. You buy gold for $1,200 and take it on the first plane to Ruritania, where you sell it for 130,000 pesos. The current

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640 Part Seven Special Topics

exchange rate for the Ruritanian peso is RUP100 = USD1. So you can exchange your 130,000 pesos for 130,000/100 = $1,300. You have made a gross profit of $100 an ounce. Of course, you have to pay transportation and insurance costs, but there should still be something left over for you.

You returned from your trip with a surefire profit. But surefire profits rarely exist, and when they do exist, they don’t last long. As others notice the disparity between the price of gold in Ruritania and the price in New York, the price will be forced down in Ruritania (or up in New York) until the profit opportunity disappears. This ensures that the dollar price of gold is the same in the two countries.

Our conclusion that gold is worth the same regardless of currency is an example of the law of one price. Just as the price of goods in Walmart must be roughly the same as the price of goods in Target, so the prices of goods in Ruritania when converted into dollars should be roughly the same as the prices in the United States:

Dollar price of goods in U.S. = Peso price of goods in Ruritania

Number of pesos per dollar

Gold is a standard and easily transportable commodity, but the same forces push the domestic and foreign prices of other goods toward equality. Those goods that can be bought more cheaply abroad will be imported, which will force down the price of the domestic product. Those goods that can be produced more cheaply at home will be exported, and that will force down the price of the foreign product.

No one who has compared prices in foreign stores with prices at home really believes that the law of one price holds exactly. Look at Table 22.2 , which shows the local price of a Big Mac in different countries converted into dollars. You can see that the price varies considerably across countries. For example, in Norway Big Macs cost 70% more than in the United States, but in South Africa they are less than half the U.S. price. 3

This suggests a possible way to make a quick buck. Why don’t you buy a hamburger-to-go in South Africa for $2.16 and take it for resale in Norway, where the price in dollars is $7.80? The answer, of course, is that the gain would not cover the costs. The law of one price works very well for commodities like gold, where transportation costs are small. It works far less well for Big Macs and worse still for haircuts and appendectomies, which cannot be transported at all.

We need a weaker version of the law of one price, a diluted law that captures the main idea but allows for exceptions. The weaker version is purchasing power parity,

law of one price Theory that prices of goods in all countries should be equal when translated to a common currency.

3 Of course, it could also be that Big Macs come with a bigger smile in Norway. If the quality of the hamburgers or the service differs, we are not comparing like with like.

purchasing power parity (PPP) Theory that the cost of living in different countries is equal and that exchange rates adjust to offset inflation differentials across countries.

FIGURE 22.1 Some simple theories linking spot and forward exchange rates, interest rates, and inflation rates

Difference in interest rates

equals

equals

equals

1 + Ruritanian interest rate 1 + U.S. interest rate

Difference between forward and spot exchange rates

Forward peso exchange rate

Current spot rate

Expected difference in inflation rates

equals

1 + expected Ruritanian inflation rate

1 + U.S. inflation rate

Expected change in spot exchange rates

Expected peso exchange rate

Current spot rate

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Chapter 22 International Financial Management 641

or PPP. PPP states that although some goods, such as Big Macs and haircuts, may cost different amounts in different countries, the overall cost of living should be similar. PPP implies that the relative costs of living in two countries will not be affected by differences in their inflation rates. Instead, different inflation rates in local currencies will be offset by changes in exchange rates.

If purchasing power parity holds, then your forecast of the difference in inflation rates is also your best forecast of the change in the spot rate of exchange. For example, suppose you need a forecast of the exchange rate for the Ruritanian peso. Purchasing power parity says that you should focus on the difference between the inflation rates in Ruritania and the United States.

The current exchange rate for the peso is RUP100 = USD1. If the cost of living is the same in Ruritania and the United States, then 100 pesos buys the same bundle of goods and services as $1. Suppose that economists are forecasting an inflation rate of 6% in Ruritania and 1% in the United States. Then at the end of 1 year 106 pesos will buy the same quantity of goods as $1.01, and $1 will have the same purchasing power as RUP100 × (1.06/1.01) = RUP105. Purchasing power parity implies that the expected exchange rate at the end of the year is RUP105 = USD1. Since inflation is expected to be higher in Ruritania, the peso is forecast to depreciate.

Look back at the two right-hand boxes in Figure 22.1 . We can now fill in those boxes for the Ruritanian peso: 4

4 A warning: Notice that the relationships in Figure 22.1 all apply to indirect exchange rates, i.e., foreign cur- rency per dollar. Remember that the pound/U.S. dollar and euro/U.S. dollar exchange rates are conventionally expressed as direct rates. To use our formulas for euros and pounds, you must first convert the quoted rates to indirect rates.

Country

Local Price Converted to U.S. Dollars Country

Local Price Converted to U.S. Dollars

Australia 4.47 Norway 7.80 Brazil 5.25 Russia 2.62 China 2.74 South Africa 2.16 Euro area 4.96 Switzerland 7.14 Japan 2.97 United Kingdom 4.63 Mexico 2.78 United States 4.62

Source: “The Big Mac Index: Grease-Proof Taper,” The Economist, January 25, 2014.

TABLE 22.2 Price of Big Mac hamburgers in different countries

equals

Expected difference in inflation rates

1 + expected Ruritanian inflation rate

1 + U.S. inflation rate =

1.06

1.01 = 1.05

Expected change in spot exchange rates

Expected peso exchange rate

Current exchange rate =

105

100 = 1.05

Now we have some helpful advice for the U.S. company doing business in Rurita- nia. If the financial manager needs to forecast the future spot exchange rate for Ruri- tanian pesos, he or she can use the difference in expected inflation rates in Ruritania versus in the United States.

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642 Part Seven Special Topics

Suppose that gold currently costs $1,000 an ounce in New York and £600 an ounce in London.

a. What must be the pound/dollar exchange rate? b. Suppose that gold prices rise by 2% in the United States and by 5% in

Great Britain. What will be the price of gold in the two currencies at the end of the year? What must be the exchange rate at the end of the year?

c. Show that at the end of the year each dollar buys about 3% more pounds, as predicted by PPP.

Self-Test 22.5

Real and Nominal Exchange Rates Financial managers distinguish nominal exchange rates from real exchange rates. Nominal exchange rates tell you how many euros or yen or pounds you can buy for your dollar. Real exchange rates measure the quantity of goods you can buy for that dollar in Europe or Japan or the United Kingdom. For example, if the value of the Ruritanian peso declines, you will be able to purchase more pesos for your dollar, but if Ruritania experiences higher inflation, those pesos may buy you only the same amount of goods. In this case the nominal exchange rate has declined but the real exchange rate is unchanged. Purchasing power parity theory implies that any change in the nominal exchange rate will be offset by a change in the relative price of goods in the two countries, leaving the real exchange rate unaffected.

Figure 22.2 plots the nominal and real exchange rates since 1900 in three countries. For example, the first plot shows that in 2010 one pound (£1) bought only 33% of the dollars that it did a century earlier. But this decline in the nominal value of the pound was offset by the higher inflation rate in the United Kingdom. The plot shows that just over a century later the inflation-adjusted, or real, exchange rate was little changed. The plots for France and Italy tell a similar story.

Of course, purchasing power parity theory is not the whole truth, and in the short term real exchange rates do change, sometimes quite sharply. For example, the real value of the yen fell by over a quarter in the 24 months to February 2014. Japanese goods became much cheaper in the United States than they had been. Such changes in real exchange rates can be a major headache for anyone making short-term currency forecasts. But if you are a financial manager called on to make a long-term forecast of an exchange rate, you probably can’t do much better than to assume that changes in the nominal value of the currency will offset the difference in inflation rates. That is the message of purchasing power parity theory.

Inflation and Interest Rates Suppose that a bank deposit earns interest of 3% in the United States and 8.1% in Ruritania. What might explain such a difference?

We can start by looking back to Chapter 5, where we distinguished nominal and real rates of interest. Bank deposits promise you a fixed nominal rate of interest, but they don’t promise what that money will buy. If you invest $100 for a year at an inter- est rate of 3%, you will have 3% more dollars at the end of the year than you did at the start. But you may not be 3% better off. Some of the gain would be needed to compensate for inflation.

In our example, the nominal rate of interest is higher in Ruritania than in the United States, but if the inflation rate is also higher, then the real rates of interest may be much closer than the nominal rates. For example, suppose that the expected inflation rate is 1% in the United States and 6% in Ruritania. Then

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Chapter 22 International Financial Management 643

18 99

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$/ £

ex ch

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= 1

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(a)

U.K. nominal

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1,000

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0.1

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(b)

$/ fr

an c

ex ch

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18 99

= 1

0 0)

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FIGURE 22.2 Nominal versus real exchange rates in (a) the United Kingdom, (b) France, and (c) Italy; December 1899 = 100 (Values are shown on log scale.)

Source: E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns (Princeton, NJ: Princeton University Press, 2002). Updates courtesy of Triumph ’s authors. Note: Since 1999, both the lira and the French franc have been replaced by the euro.

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644 Part Seven Special Topics

Real U.S. interest rate = 1 + nominal interest rate

1 + inflation rate - 1

= 1.03

1.01 - 1 = .0198, or 1.98%

and

Real Ruritanian interest rate = 1 + nominal interest rate

1 + inflation rate - 1

= 1.081

1.06 - 1 = .0198, or 1.98%

The nominal interest rates in the two countries are significantly different, but the real interest rates are the same.

Now you can see why we drew the top two boxes in Figure 22.1 :

American investors can invest $1,000 for 1 year at an interest rate of .3%. Or they can convert the $1,000 to 1,065,500 South Korean won at the current exchange rate and invest at 2.6% in South Korea. If the real interest rates are the same in the two countries and the expected inflation rate in the United States is 1.7%, what must be investors’ forecast of the inflation rate in South Korea?

Self-Test 22.6

equals

Difference in interest rates

1 + Ruritanian interest rate

= 1.081

= 1.05 1 + U.S.

interest rate 1.03

Expected difference in inflation rates

1 + expected Ruritanian inflation rate

= 1.06

= 1.05 1 + U.S. 1.01 inflation rate

If expected real interest rates are the same everywhere, then differences in the nom- inal interest rate must reflect differences in expected inflation rates. This conclusion is often called the international Fisher effect, after the economist Irving Fisher. As long as capital can flow unimpeded across national borders, capital market equilib- rium requires that real interest rates be the same in any two countries. Just as water always flows downhill, so capital always flows where returns are greatest. Capital stops flowing only when expected returns are the same. 5 But it is the real returns that concern investors, not the nominal returns. Two countries may have different nominal interest rates but the same expected real interest rate.

How similar are real interest rates around the world? It is hard to say, because we cannot directly observe expected inflation. However, in Figure  22.3 we have plot- ted the average interest rate in each of 59 countries against the inflation that in fact occurred. You can see that the countries with the highest interest rates generally had the highest inflation rates.

international Fisher effect Theory that real interest rates in all countries should be equal, with differences in nominal rates reflecting differences in expected inflation.

5 Here we assume away any chance of default on loans made in a foreign currency. This assumption is fine for the most important currencies, including the U.S. dollar, pound, euro, Swiss franc, and yen. The assumption is not acceptable for some developing countries where local politics are unstable. We have assumed that loans in Ruritanian pesos are default-risk-free. But if investors worry about default or expropriation by the Ruritanian government, they may demand a higher real interest rate on peso loans.

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Chapter 22 International Financial Management 645

The Forward Exchange Rate and the Expected Spot Rate If you buy Ruritanian pesos forward, you get more pesos for your U.S. dollar than if you buy them spot. So the peso is selling at a forward discount. Now let us think how this discount may be related to expected changes in spot rates of exchange.

The spot rate for the peso is RUP100  =  USD1, and the 1-year forward rate is RUP105 = USD1. Would you sell pesos forward if you were confident that they would rise in value? Probably not. You would be tempted to wait until the end of the year and get a better price (more pesos) in the spot market. If other traders felt the same way, nobody would sell pesos forward. Everybody would want to buy, so the number of pesos that you could get for your dollar in the forward market would fall. On the other hand, if traders expected the peso to fall sharply in value, they might be reluctant to buy forward and, in order to attract buyers, the number of pesos that you could buy for a U.S. dollar in the forward market would need to rise. 6 Trading would stabilize when the forward rate adjusts to equal the expected future spot rate.

This is the reasoning behind the expectations theory of exchange rates, which pre- dicts that the forward rate equals the expected future spot exchange rate. Put another way, we can say that the percentage difference between the forward rate and today’s spot rate is equal to the expected percentage change in the spot rate:

This is the third leg of our quadrilateral in Figure 22.1 .

6 This reasoning ignores risk. If a forward purchase reduces your risk sufficiently, you might be prepared to buy forward even if you expected to pay more as a result. Similarly, if a forward sale reduces risk, you might be prepared to sell forward even if you expected to receive less as a result.

expectations theory of exchange rates Theory that the expected spot exchange rate equals the forward rate.

FIGURE 22.3 Countries with the highest interest rates generally have the highest inflation. In this diagram each of the 59 points represents the experience of a different country.

A ve

ra ge

m on

ey m

ar ke

t r at

e (%

), 20

07 –2

01 1

Average inflation rate (%), 2007–2011

0-5 5 10 15

Ukraine

Japan

8

6

4

0

2

10

12

14

16

18

equals

Difference between forward and spot exchange rates

Forward peso exchange rate

=

105

=

1.05

Current spot rate

100

Expected change in spot exchange rate

Expected peso exchange rate

=

105 = 1.05

Current spot 100 rate

The expectations theory of forward rates does not imply that managers are perfect forecasters. Sometimes the actual future spot rate will turn out to be above the previ- ous forward rate. Sometimes it will fall below. But if the theory is correct, we should

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646 Part Seven Special Topics

find that on average the forward rate is equal to the future spot rate. This predic- tion is roughly true, if we take a long enough average, 7 but there are exceptions and anomalies. 8

Because of the exceptions and anomalies, the expectations hypothesis is not much help to foreign exchange traders. On the other hand, financial managers are not usu- ally in the trading business. For a financial manager who consistently hedges foreign exchange exposure, the expectations theory offers some reassurance. A company that always covers its foreign exchange commitments by buying or selling currency in the forward market does not have to pay a premium to avoid exchange rate risk: On aver- age, the forward price at which it agrees to exchange currency will equal the eventual spot exchange rate, no better but no worse.

Interest Rates and Exchange Rates Now let’s move on to a result that does not require qualification or appeals to long-run averages: The relationship between interest rates and exchange rates, known as cov- ered interest rate parity, almost always works, even in the short run.

You are an investor with $1 million to invest for 1 year. The interest rate in Ruri- tania is 8.1%, and in the United States it is 3%. Is it better to invest your money in Ruritania or in the United States?

The answer seems obvious: Isn’t it better to earn an interest rate of 8.1% than 3%? But appearances may be deceptive. If you lend in Ruritania, you first need to convert your $1 million into pesos. When the loan is repaid at the end of the year, you need to convert your pesos back into U.S. dollars. Of course, you don’t know what the exchange rate will be at the end of the year, but you can fix the future value of your pesos by selling them forward. If the forward rate of exchange is sufficiently low, you may do just as well keeping your money in the United States.

Let’s check which loan is the better deal:

• U.S. dollar loan. The rate of interest on a U.S. dollar loan is 3%. Therefore, at the end of the year, you get $1 million × 1.03 = $1.03 million.

• Ruritanian peso loan. The current (spot) rate of exchange is RUP100  =  USD1. Therefore, you can convert your million dollars into RUP100 million. The interest rate on a peso loan is 8.1%, so at the end of the year you will have RUP100  million × 1.081 = RUP108.1 million. You don’t know what the exchange rate will be at the end of the year, but that doesn’t matter. You can nail down the rate at which you convert your pesos back into U.S. dollars. The 1-year forward exchange rate is RUP105 = USD1. Therefore, by selling the pesos forward, you make sure that you will get RUP108.1/105 = $1.03 million.

Thus the two investments offer exactly the same rate of return. They have to, because they are both risk-free. If the domestic interest rate were different from the “covered” foreign rate, you would have a money machine: You could borrow in the market with the lower rate and lend in the market with the higher rate.

7 It seems that companies are sometimes prepared to give up return in order to buy forward currency and other times they are prepared to give up return in order to sell forward currency. The forward rate overstates the likely future spot rate about half the time, and about half the time it understates the likely spot rate. The over- and underpredictions average out in the long run. 8 Scholars who have studied exchange rates have found that forward rates typically exaggerate the likely change in the spot rate. When the forward rate appears to predict a sharp rise in the spot rate, the forward rate tends to overestimate the rise in the spot rate. When the forward rate appears to predict a fall, it tends to overestimate this fall. There is even evidence that when the forward rate predicts a rise, the spot rate is more likely to fall than rise. For a readable discussion of this puzzling finding, see K. A. Froot and R. H. Thaler, “Anomalies: Foreign Exchange,” Journal of Political Economy 4 (1990), pp. 179–192.

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Chapter 22 International Financial Management 647

We now have the final leg of our quadrilateral in Figure 22.1 :

By 2015 Ruritanian exchange rates had moved to RUP120 = USD1 (spot) and RUP126.92 = USD1 (1-year forward). One-year interest rates were 4% in the United States and 10% in Ruritania. Confirm covered interest rate parity.

Self-Test 22.7

equals

Difference in interest rates

1 + Ruritanian interest rate

=

1.081

=

1.05

1 + U.S. interest rate

1.03

Difference between forward and spot exchange rates

Forward peso exchange rate

=

105 = 1.05

Current spot 100 rate

This link between the forward exchange rate and the difference in interest rates is called interest rate parity. Whereas the other relationships shown in Figure 22.1 tend to hold approximately, interest rate parity almost always holds with great precision. This should not be surprising, since there would be easy opportunities for riskless arbitrage whenever parity is violated. In fact, foreign currency dealers set the forward exchange rate by looking at the difference between the interest rates on deposits in different currencies.

Interest rate parity also holds an important lesson for managers. International capi- tal markets and currency markets function well and offer no free lunches. You can’t assume that it is cheaper to borrow in a currency with a low nominal rate of interest. If you hedge or “cover” your exchange rate exposure, interest rate parity implies that the all-in cost of borrowing will be the same in any currency. 9 If you don’t cover, exchange rate movements can easily erase the apparent advantage of a low interest rate.

Interest rate parity means that covered interest rates are the same in all major currencies. A financial manager who attempts to borrow in currencies with low interest rates can profit only by taking a bet on future exchange rates.

interest rate parity Theory that forward premium equals interest rate differential.

9 A covered foreign interest rate means that you borrow or lend in a foreign currency and hedge the exchange rate risk by entering a forward currency contract. In our example, you could lend RUP100 million, which grows with 8.1% interest to RUP108.1 million. You therefore would sell RUP108.1 million forward to lock in the dollar value of your year-end proceeds.

22.3 Hedging Exchange Rate Risk

Transaction Risk Firms with international operations are subject to exchange rate risk. As exchange rates fluctuate, the dollar value of their revenues or expenses also fluctuates. It is use- ful to distinguish two types of exchange rate risk: transaction risk and economic risk.

Transaction risk arises when the firm agrees to pay or receive a known amount of foreign currency. For example, our importer of machinery was committed to pay RUP100 million at the end of 12 months. If the value of the peso appreciates rapidly over this period, that machinery will cost more dollars than the importer expected.

Transaction risk is easily identified and hedged. For every peso our importer is committed to pay, she can buy 1 peso forward. If she buys RUP100 million forward, the importer fixes the entire dollar cost of the machinery and avoids the risk of an appreciation of the peso.

Of course, it is possible that the peso will depreciate sharply over the year, 10 in which case the importer would regret that she did not wait to buy the peso more

10 By this we mean that the peso falls by more than predicted by the forward rate.

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648 Part Seven Special Topics

cheaply in the spot market. Unfortunately, you cannot have your cake and eat it. By fixing the dollar cost of the machinery, the importer forfeits the chance of pleasant, as well as unpleasant, surprises.

Is there any other way the importer could hedge against exchange rate loss? Think again how covered interest rate parity works. The financial manager could borrow dol- lars, convert them into pesos today, put the proceeds in a Ruritanian bank deposit, and withdraw them at the end of the year to pay her bill. Interest rate parity tells us that the cost of borrowing dollars, buying pesos in the spot market, and leaving them on deposit is exactly the same as the cost of buying pesos forward.

What is the cost of protection against currency risk? You sometimes hear managers say that it is equal to the difference between the forward rate and today’s spot rate. This is wrong. If our importer did not hedge, she would pay the spot price for pesos when the payment is due at the end of the year. Therefore, the cost of hedging is the difference between the forward rate and the expected spot rate when payment is due.

Should companies hedge, or should they just sit back and absorb currency fluc- tuations? We generally vote for hedging. First, it makes life simpler for the firm and allows it to concentrate on its own business. Second, it does not cost much. (In fact, the cost is zero if the forward rate equals the expected spot rate, as our simple theories imply.) Third, the foreign exchange market seems reasonably efficient, at least for the major currencies. Speculation should be a zero-sum game, barring the unlikely case where the financial manager knows more than the pros who make the foreign exchange market.

Economic Risk Even if a firm neither owes nor is owed foreign currency, it still may be affected by currency fluctuations. Consider, for example, the competitive position of foreign auto producers such as Volkswagen and Toyota when the value of the U.S. dollar fell dra- matically in 2006 and 2007. These firms faced a difficult choice between maintaining the dollar price of their product, thus accepting a reduced price in their home currency, or raising the dollar price and becoming less competitive against U.S. producers such as Ford and GM. Economic exposure to the exchange rate arises because exchange rate fluctuations affect competitive positions.

One solution is for the company to undertake operational hedging by balancing production closely with sales. For example, 37% of Ford’s sales are outside North America, but so are 40% of its production costs. It gains protection from currency risks because its costs and revenues in different currencies are more or less balanced.

Japanese auto manufacturers have less operational hedging. For example, Toyota produces 43% of its output in Japan but only 28% is sold there. Exchange rate fluctua- tions are potentially a more serious risk for Toyota than for Ford. On the other hand, the Japanese auto companies operate in a wider range of markets than U.S. firms. They have therefore diversified away some of their currency risks.

Operational hedging rarely eliminates all currency risk. Think again of Toyota. It is a net exporter of autos to North America and is therefore exposed to a decline in the value of the dollar. So, in addition to its operational hedging, Toyota also mitigates exchange rate risk by using financial hedges. For example, it borrows large amounts in dollars rather than yen. So, if the dollar falls, the pressure on Toyota’s profits is offset in part by a reduction in the number of yen needed to service the dollar debt.

A Ford dealer in the United States never needs to buy or sell foreign currency. Does that mean it has no currency risk? Explain.

Self-Test 22.8

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Chapter 22 International Financial Management 649

22.4 International Capital Budgeting

Net Present Values for Foreign Investments Exports by the soft-drink manufacturer Ecsy-Cola Corporation have risen to the point that it is considering establishing a small manufacturing and sales operation overseas in Ruritania. Ecsy-Cola’s decision to invest overseas should be based on the same criteria as a decision to invest in the United States. The company needs to forecast the incremental cash flows from the project, discount the cash flows at the opportunity cost of capital, and accept those projects with a positive NPV.

Suppose Ecsy-Cola’s Ruritanian facility is expected to generate the following cash flows in Ruritanian pesos:

0 1 2 3 4 5

Cash fl ow (millions of pesos) −380 100 125 150 175 200

Year Forward Exchange Rate (RUP per USD)

1 100 × (1.081/1.03)  = RUP104.95/USD1 2 100 × (1.081/1.03) 2  = RUP110.15/USD1 3 100 × (1.081/1.03) 3  = RUP115.60/USD1 4 100 × (1.081/1.03) 4  = RUP121.33/USD1 5 100 × (1.081/1.03) 5  = RUP127.33/USD1

The interest rate in the United States is 3%. Ecsy’s financial manager estimates that the company requires an additional expected return of 10% to compensate for the risk of the project, so the opportunity cost of capital for the project is 3 + 10 = 13%.

Notice that Ecsy’s opportunity cost of capital is stated in terms of the return on a dollar-denominated investment but the cash flows are given in pesos. A project that offers a 13% expected return in pesos could fall far short of offering the required return in dollars if the value of the peso is expected to decline. Conversely, a project that offers an expected return of less than 13% in pesos may be worthwhile if the peso is likely to appreciate.

You cannot compare the project’s return measured in one currency with the return that you require from investing in another currency. If the opportunity cost of capital is measured as a dollar-denominated return, cash flows should also be forecast in dollars.

To translate the peso cash flows into dollars, Ecsy needs a forward exchange rate. Where does this come from? Forward exchange rates for longer than a year are not usually quoted in the financial press, but they can be estimated using interest rate par- ity. For example, suppose that the financial manager looks in the newspaper and finds that the current exchange rate is RUP100 = USD1 and that the interest rate is 3% in the United States and 8.1% in Ruritania. Thus, the manager sees right away that the peso is likely to sell at a forward discount of 5% a year. For example, the 1-year for- ward rate is

Forward rate for year 1 = spot rate in year 0 × 1 + peso interest rate

1 + dollar interest rate

= RUP100/USD1 × 1.081

1.03 = RUP104.95/USD1

The implied forward exchange rates for each year of the project are calculated simi- larly, as follows: 11

11 We assume that the 3% and 8.1% interest rates are the same for longer maturities.

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650 Part Seven Special Topics

The financial manager can use these forward exchange rates to convert the peso cash flows into dollars:

Suppose that the nominal interest rate in Ruritania is 6% rather than 8.1%. The spot exchange rate is still RUP100 = USD1, and the expected peso cash flows on Ecsy’s project are also the same as before.

a. What do you deduce about the likely difference in the inflation rates in Ruritania and the United States?

b. Would you now be able to buy more or fewer pesos in the forward market than when the peso interest rate was 8.1%?

c. Do you think that the NPV of Ecsy’s project will now be higher or lower than the figure we calculated above? Check your answer by calculating NPV under this new assumption.

Self-Test 22.9

Year: 0 1 2 3 4 5

Cash fl ow (millions of pesos) −380 100 125 150 175 200 Forward exchange rate (pesos to the dollar)

100 104.95 110.15 115.60 121.33 127.33

Cash fl ow (millions of dollars) −3.8 0.9528 1.1348 1.2976 1.4424 1.5707

Now the manager discounts these dollar cash flows at the 13% dollar cost of capital:

NPV = -3.8 + .9528

1.13 +

1.1348

1.132 +

1.2976

1.133 +

1.4424

1.134 +

1.5707

1.135

= $.568 million, or $568,000

Notice that the manager discounted cash flows at 13%, not at the U.S. risk-free inter- est rate of 3%. The cash flows are risky, so a risk-adjusted interest rate is appropriate. The positive NPV tells the manager that the project is worth undertaking; it increases shareholder wealth by $568,000.

Notice also that the firm does not have to forecast the future peso/dollar exchange rate to translate its peso cash flows into dollar equivalents. It instead uses the forward exchange rates implied by the interest rate differential in the two countries. No currency forecast is needed, because the company can hedge its foreign exchange exposure.

If it does hedge, for example, by selling pesos forward, then its peso cash flows will be brought back into dollars at the forward exchange rates implied by the interest rate differential. In other words, the firm can, if it chooses, nail down the dollar cash flows that we have just calculated. The decision to accept or reject the project therefore is separate from the firm’s particular view about the future exchange rate.

What if the management actually expects the peso to appreciate rather than depreci- ate? Should it use its own forecasts of the future exchange rate instead of the forward exchange rates implied by interest rate parity? No! For a project to be attractive, it must be able to stand on its own, based on hedged cash flows. It would be foolish for a firm to accept a poor project just because it forecasts exchange rate appreciation. If management is confident in its predictions of future exchange rates, it would be better to speculate on the currency directly rather than use a negative-NPV project to gain exposure to the currency. (Of course, before it speculates, management ought to think very carefully about why it believes its exchange rate forecast is superior to the mar- ket’s. After all, Ecsy’s comparative advantage is presumably in manufacturing fizzy drinks, not in exchange rate speculation.)

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Chapter 22 International Financial Management 651

Political Risk So far we have focused on the management of exchange rate risk, but managers also worry about political risk. They worry that a government will change the rules of the game, breaking a promise or an understanding, after the investment is made. Of course, political risks are not confined to overseas investments. Businesses in every country are exposed to the risk of unanticipated actions by governments, and when political risk increases, share prices become more volatile. The danger for foreign companies is that they may be a particular target for government actions.

Consultancy services offer analyses of political and economic risks and draw up country rankings. 12 For example, Table 22.3 is an extract from the June 2013 political risk rankings provided by the PRS Group. Each country is scored on 12 dimensions and a total score is calculated. Finland comes top of the class overall, while Somalia languishes at the bottom.

Some managers dismiss political risk as an act of God, like a hurricane or earth- quake. But the most successful multinational companies structure their business to reduce political risk. Foreign governments are not likely to expropriate a local busi- ness if it cannot operate without the support of its parent. For example, the foreign subsidiaries of American computer software or pharmaceutical companies would have relatively little value if they were cut off from the know-how of their parents. Such operations are much less likely to be expropriated than, say, a mining operation that can be operated as a stand-alone venture.

We are not recommending that you turn your silver mine into a pharmaceutical company, but you may be able to plan your overseas manufacturing operations to improve your bargaining position with foreign governments. For example, Ford has integrated its overseas operations so that the manufacture of components, subassem- blies, and complete automobiles is spread across plants in a number of countries. None of these plants would have much value on its own, and Ford can switch production between plants if the political climate in one country deteriorates.

12 For a discussion of these services, see C. Erb, C. R. Harvey, and T. Viskanta, “Political Risk, Financial Risk, and Economic Risk,” Financial Analysts Journal 52 (1996), pp. 28–46. Campbell Harvey’s web page ( www. duke.edu/ charvey ) is also a useful source of information on political risk.

Total

Maximum score 100 COUNTRY Finland 89.0 Switzerland 88.0 Canada 87.5 Germany 84.0 United States 84.0 Australia 81.0 Japan 78.5 United Kingdom 77.0 Korea, Republic 76.5 France 73.5 Brazil 68.0 China, People’s Rep. 61.0 Russia 59.5 India 57.0 Pakistan 44.5 Somalia 23.0

Source: PRS Group, International Country Risk Guide, a publication of The PRS Group, Inc., www.prsgroup.com, 2013. Used with permission.

TABLE 22.3 Political risk scores for a sample of countries, June 2013

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652 Part Seven Special Topics

Multinational corporations have also devised financing arrangements to help keep foreign governments honest. For example, suppose your firm is contemplating an investment of $500 million to reopen the San Tomé silver mine in Costaguana with modern machinery, smelting equipment, and shipping facilities. 13 The Costaguanan government agrees to invest in roads and other infrastructure and to take 20% of the silver produced by the mine in lieu of taxes. The agreement is to run for 25 years.

The project’s NPV on these assumptions is quite attractive. But what happens if a new government comes into power 5 years from now and imposes a 50% tax on “any precious metals exported from the Republic of Costaguana”? Or changes the govern- ment’s share of output from 20% to 50%? Or simply takes over the mine “with fair compensation to be determined in due course by the Minister of Natural Resources of the Republic of Costaguana”?

No contract can absolutely restrain sovereign power. But you can arrange project financing to make these acts as painful as possible for the foreign government. For example, you might set up the mine as a subsidiary corporation, which then borrows a large fraction of the required investment from a consortium of major international banks. If your firm guarantees the loan, make sure the guarantee stands only if the Costaguanan government honors its contract. The government will be reluctant to break the contract if doing so causes a default on the loans and undercuts the country’s credit standing with the international banking system.

The Cost of Capital for Foreign Investment We did not say how Ecsy-Cola arrived at a 13% dollar discount rate for its Ruritanian project. That depends on the risk of overseas investment and the reward that investors require for taking this risk. Unfortunately, there is no tidy theory of risk and return in an international context. 14

Remember that the risk of an investment cannot be considered in isolation; it depends on the securities that the investor holds in his or her portfolio. For example, suppose Ecsy-Cola’s shareholders invest mainly in companies that do business in the United States. They could view the Ruritanian market, though volatile, as driven by different forces and therefore a diversifiable risk. If the correlation between the Ruri- tanian and U.S. markets is relatively low, an investment in the Ruritanian soft-drink business would appear to be a relatively low-risk project to Ecsy-Cola’s sharehold- ers. That would not be true of a Ruritanian company, whose shareholders are already exposed to the fortunes of the Ruritanian market. 15

Avoiding Fudge Factors We don’t pretend that we can put an absolutely precise figure on the cost of capital for foreign investment. But we disagree with the practice of automatically increasing the domestic cost of capital when foreign investment is considered.

Some financial managers automatically mark up the required return for foreign investment because it is more costly to manage an operation in a foreign country and

13 The early history of the San Tomé mine is described in Joseph Conrad’s Nostromo. 14 Why is there no tidy theory? One fundamental reason is that economists have never been able to agree on what makes one country different from another. Is it just that they have different currencies? Or is it that their citizens have different tastes and consume different things? Or is it that they are subject to different regulations and taxes? The answers to these questions affect the relationship among security prices in different countries. 15 One can imagine an integrated world in which all investors diversify worldwide, regardless of their domiciles. In this ideal case, U.S. and Ruritanian investors would view the risks of Ecsy-Cola’s investment identically. But in reality investors’ portfolios are strongly weighted toward their home countries. This weighting is called a “home bias.” We do not yet have an integrated world capital market.

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Chapter 22 International Financial Management 653

because they worry about the risks of expropriation, foreign exchange restrictions, or unfavorable tax changes. In other words, they add a fudge factor to the discount rate to offset these costs and risks.

Those managers should leave the discount rate alone and reduce expected cash flows instead. For example, let’s go back to Ecsy-Cola’s cash-flow forecast of 100  million Ruritanian pesos in year 1 . Now the company gets word of a proposed 100 million peso “incorporation fee” to be imposed in “the first year of operations for all new for- eign investments.” The odds that the fee will be imposed are judged at 5%.

Now the expected cash flow for year 1 is not 100 million pesos but .95 × 100  million = 95 million pesos. Ecsy should recalculate NPV using this forecast. It should make similar cash-flow adjustments for possible political risks in later years.

Adjusting cash flows brings management’s assumptions about political risks out in the open for scrutiny and sensitivity analysis. There may be some discount rate fudge factor that gives the correct NPV, but financial managers have no practical way of knowing what the fudge factor is until the cash flows are adjusted and NPV is recalcu- lated. Once the adjusted NPV is in hand, the fudge factor is not needed.

SUMMARY The exchange rate is the amount of one currency needed to purchase one unit of another currency. The spot rate of exchange is the exchange rate for an immediate transaction. The forward rate is the exchange rate for a forward transaction, that is, a transaction at a specified future date.

To produce order out of chaos, the international financial manager needs some model of the relationships between exchange rates, interest rates, and inflation rates. Four very sim- ple theories prove useful:

• In its strict form, purchasing power parity states that $1 must have the same pur- chasing power in every country. You only need to take a vacation abroad to know that this doesn’t square well with all the facts. Nevertheless, on average, changes in exchange rates tend to match differences in inflation rates and, if you need a long- term forecast of the exchange rate, it is difficult to do much better than to assume that the exchange rate will offset the effect of any differences in the inflation rates.

• In an open world capital market real rates of interest would have to be the same. Thus differences in nominal interest rates result from differences in expected infla- tion rates. This international Fisher effect suggests that firms should not simply borrow where interest rates are lowest. Those countries are also likely to have the lowest inflation rates and the strongest currencies.

• The expectations theory of exchange rates tells us that the forward rate equals the expected spot rate (though it is very far from being a perfect forecaster of the spot rate).

• Interest rate parity theory states that the interest differential between two countries must be equal to the difference between the forward and spot exchange rates. In the international markets, arbitrage ensures that parity almost always holds.

Our simple theories about forward rates have two practical implications for the problem of hedging overseas operations. First, the expectations theory suggests that hedging exchange risk is on average costless. Second, there are two ways to hedge against exchange risk: One is to buy or sell currency forward; the other is to lend or borrow abroad. Interest rate parity tells us that the cost of the two methods should be the same.

What is the difference between spot and forward exchange rates? (LO22-1)

What are the basic relationships between spot exchange rates, forward exchange rates, interest rates, and inflation rates? (LO22-2)

What are some simple strategies to protect the firm against exchange rate risk? (LO22-3)

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654 Part Seven Special Topics

Overseas investment decisions are no different in principle from domestic decisions. You need to forecast the project’s cash flows and then discount them at the opportunity cost of capital. But it is important to remember that if the opportunity cost of capital is stated in dollars, the cash flows must also be converted to dollars. This requires a forecast of foreign exchange rates. We suggest that you rely on the simple parity relationships and use the interest rate differential to produce these forecasts.

How do we perform an NPV analysis for projects with cash flows in foreign currencies? (LO22-4)

QUESTIONS AND PROBLEMS 1. Exchange Rates. Use Table 22.1 to answer the following questions: (LO22-1)

a. How many euros can you buy for $100? How many dollars can you buy for 100 euros? b. How many Swiss francs can you buy for $100? How many dollars can you buy for 100

Swiss francs? c. If the British pound depreciates with respect to the dollar, will the exchange rate quoted in

Table 22.1 increase or decrease? d. Someone offers you the choice between a U.S. and a Canadian dollar. Which do you choose?

2. Exchange Rates. Look at Table 22.1. How many Mexican pesos can you buy for $1? How many yen can you buy? How many yen would it cost to buy 1 Mexican peso? (LO22-1)

3. Exchange Rates. Suppose that 2-year interest rates are 5.2% in the United States and 1.0% in Japan. The spot exchange rate is JPY83.63 = USD1. Suppose that 1 year later interest rates are 3% in both countries, while the value of the yen has appreciated to JPY80.00 = USD1. (LO22-1)

a. Benjamin Pinkerton from New York invested in a U.S. 2-year zero-coupon bond at the start of the period and sold it after 1 year. What was his return?

b. Madame Butterfly from Osaka bought some dollars. She also invested in the 2-year U.S. zero-coupon bond and sold it after 1 year. What was her return in yen?

c. Suppose that Madame Butterfly had correctly forecast the price at which she sold her bond and that she hedged her investment against currency risk. What would have been her return in yen?

4. Exchange Rate Relationships. Look at Table 22.1. (LO22-2)

a. How many Brazilian reals do you get for your dollar? b. If the 1-year forward rate on the real is BRL2.579 = USD1, is the real at a forward discount

or premium? c. If the 1-year interest rate on dollars is 1%, what do you think is the interest rate on the real? d. According to the expectations theory, what is the expected spot rate for the real in 1 year’s

time? e. According to purchasing power parity, what is the difference in the expected rate of price

inflation in the United States and the rate in Brazil?

5. Exchange Rate Relationships. The spot and 1-year forward rates on the New Zealand dollar are currently NZD1.2927 = USD1 and NZD1.3285 = USD1, respectively. If the expectations theory of forward rates is correct, would you expect the New Zealand dollar to appreciate or depreciate over the coming year? (LO22-2)

6. Exchange Rate Relationships Choose the correct phrase to complete the sentence: The difference in interest rates between Ruritania and the United States equals: (LO22-2)

a. The forward peso rate divided by the current spot rate. b. The forward peso rate divided by the expected spot rate. c. The current peso rate divided by the Ruritanian inflation rate.

7. Exchange Rate Relationships. Assume that the simple exchange rate relationships described in Section 22.2 hold exactly. (LO22-2)

a. Dollar interest rate  =  5%; Laputian interest rate = 10%; 1-year forward exchange rate = LAP100 = USD1. What is the current spot exchange rate?

b. Current Lilliputian exchange rate  =  LIL40  =  USD1; expected exchange rate at end of year  =  LIL45  =  USD1; Lilliputian 1-year interest rate  =  15%. What is the U.S. dollar interest rate?

finance

®

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Chapter 22 International Financial Management 655

c. The U.S. inflation rate is 6%; the inflation rate in Blefuscu is twice that of the United States; the 1-year forward exchange rate = BLE25 = USD1. What is the current exchange rate between Blefuscu and the United States?

8. Exchange Rate Relationships. The following table shows the local prices of a Grande Latte coffee in Starbucks in 2012: (LO22-2)

Price of Coffee Exchange Rate

China CNY27.00 CNY6.33 = USD1 Germany EUR3.00 USD1.24 = EUR1 India INR95.00 INR55.55 = USD1 Japan JPY425 JPY78.69 = USD1 Sweden SEK37.46 SEK6.69 = USD1 U.K. GBP2.50 USD1.567 = GBP1 U.S. USD3.65

Source: www.humuch.com.

a. Calculate the dollar price of a latte in each country. b. Does purchasing power parity hold? c. What would the local price of a latte need to be in each country to ensure that the cost was

the same as in the United States? In each case state whether the currency would need to appreciate or depreciate to equalize the prices.

9. Exchange Rate Relationships. Look at Table 22.1. If the 1-year forward exchange rate for the Brazilian real is USD1 = BRL2.579 and the 1-year interest rate on dollars is 3%, what do you think is the 1-year interest rate in Brazil? (LO22-2)

10. Exchange Rate Relationships. The following table shows interest rates and exchange rates for the U.S. dollar and the Narnian leo. The spot exchange rate is 15 leos = $1. Complete the missing entries. (Hint: Remember to convert the interest rate to a 1- or 3-month rate when appropriate.) (LO22-2)

1 Month 3 Months 1 Year

Dollar interest rate (annually compounded) 4.0 4.5 (a) Narnian interest rate (annually compounded) 9.2 (b) 9.8 Forward leos per dollar (c) 14.822 15.600

11. Exchange Rate Relationships. In 2010 many investors borrowed money in countries such as the United States, where interest rates were low, and invested the money in countries such as Australia, where rates were high. This is called a “carry trade.” The risk of such a trade is that the Australian dollar may depreciate sharply. Could you eliminate this risk by entering into a forward exchange contract and still make money? (LO22-2)

12. Exchange Rate Relationships. Suppose the interest rate on 1-year loans in the United States is 3% while in Mexico the interest rate is 8%. The spot exchange rate is MXN15 = USD1 and the 1-year forward rate is MXN20 = USD1. (LO22-2)

a. In what country would you choose to borrow? b. In which would you choose to lend?

13. Exchange Rate Relationships. Suppose that the inflation rate in the United States is 4% and in Canada it is 5%. Would you expect the Canadian dollar to appreciate or depreciate against the U.S. dollar? (LO22-2)

14. Exchange Rate Risk. Rick Johnson, the treasurer of Sonora Mining, has noticed that the inter- est rate in Japan is below the rates in most other countries. He is therefore suggesting that the company should make an issue of Japanese yen bonds. What considerations ought he first to take into account? (LO22-3)

15. Exchange Rate Risk. An importer in the United States is due to take delivery of silk scarves from Europe in 6 months. The price is fixed in euros. Which of the following transactions could eliminate the importer’s exchange risk? (LO22-3)

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a. Buy euros forward. b. Sell euros forward. c. Borrow euros; buy dollars at the spot exchange rate. d. Sell euros at the spot exchange rate; lend dollars.

16. Exchange Rate Risk. An American investor buys 100 shares of London Enterprises at a price of £50 when the exchange rate is USD2 = GBP1. A year later the shares are selling at £52. No dividends have been paid. (LO22-3)

a. What is the rate of return to an American investor if the exchange rate is still USD2 = GBP1? b. What if the exchange rate is USD2.20 = GBP1? c. What if the exchange rate is USD1.80 = GBP1?

17. Exchange Rate Risk. Sanyo produces audio and video consumer goods and exports a large fraction of its output to the United States under its own name and the Fisher brand name. It prices its products in yen, meaning that it seeks to maintain a fixed price in terms of yen. Sup- pose the yen moves from JPY102.34 = USD1 to JPY98.18 = USD1. What currency risk does Sanyo face? How can it reduce its exposure? (LO22-3)

18. Exchange Rate Risk. A firm in the United States is due to receive payment of €1 million in 8 years’ time. It would like to protect itself against a decline in the value of the euro, but finds it difficult to get forward cover for such a long period. Is there any other way in which it can protect itself? (LO22-3)

19. International Investment Decisions. It is the year 2018 and Pork Barrels Inc. is considering construction of a new barrel plant in Spain. The forecast cash flows in millions of euros are as follows: (LO22-4)

C0 C1 C2 C3 C4 C5 −80 +10 +20 +23 +27 +25

The spot exchange rate is USD1.2 = EUR1. The interest rate in the United States is 8%, and the euro interest rate is 6%. You can assume that pork barrel production is effectively risk-free.

a. Calculate the NPV of the euro cash flows from the project. What is the NPV in dollars? b. What are the dollar cash flows from the project if the company hedges against exchange rate

changes? c. Suppose that the company expects the euro to depreciate by 5% a year. Does this make the

project less attractive? d. Suppose that Pork Barrels decides to go ahead with the project despite its concerns about

the euro. Would the company do better to finance it by borrowing the present value of the project in euros or in dollars?

20. International Investment Decisions. Carpet Baggers Inc. is proposing to construct a new bag- ging plant in a country in Europe. The two prime candidates are Germany and Switzerland. The forecast cash flows from the proposed plants are as follows:

C0 C1 C2 C3 C4 C5 C6 IRR, %

Germany (millions of euros) -60 +10 +15 +15 +20 +20 +20 18.8 Switzerland (millions of Swiss francs) -120 +20 +30 +30 +35 +35 +35 12.8

The spot exchange rate for euros is USD1.3  =  EUR1, while the rate for Swiss francs is CHF1.5 = USD1. The interest rate is 5% in the United States, 4% in Switzerland, and 6% in the euro countries. The financial manager has suggested that if the cash flows were stated in dollars, a return in excess of 10% would be acceptable. (LO22-4)

a. What is the dollar NPV of the German project? b. What is the dollar NPV of the Swiss project? c. Should the company go ahead with the German project, the Swiss project, or neither?

21. International Investment Decisions. Suppose that you (foolishly) use your own views about exchange rates when valuing an overseas investment proposal. Specifically, suppose that you believe that the peso will depreciate by 2% per year. Recalculate the NPV of Ecsy-Cola’s proj- ect from Section 22.4. (LO22-4)

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24. Exchange Rate Risk. General Gadget Corp. (GGC) is a U.S.-based multinational firm that makes electrical coconut scrapers. These gadgets are made only in the United States using local inputs. The scrapers are sold mainly to Asian and West Indian countries where coconuts are grown. (LO22-3)

a. If GGC sells scrapers in Trinidad, what is the currency risk faced by the firm? b. In what currency should GGC borrow funds to pay for its investment in order to mitigate its

foreign exchange exposure? c. Suppose that GGC begins manufacturing its products in Trinidad using local (Trinidadian)

inputs and labor. How does this affect its exchange rate risk?

25. Exchange Rate Risk. The following table shows a breakdown of sales and costs for four Swiss companies. Swatch produces watches; Lindt & Sprüngli, chocolate; Nestlé, food; and Roche, pharmaceuticals. Discuss the currency exposure that comes from each of their operations. Which company do you think would benefit most by an increase in the value of the dollar? What about an increase in the value of the euro? (LO22-3)

CHALLENGE PROBLEMS 22. Exchange Rate Risk. The current exchange rate is USD2 = GBP1. ClickEasy is a large British

firm that exports computer games to the United States. If the dollar depreciates relative to the pound, ClickEasy will increase the dollar price it charges its U.S. customers. But it cannot raise its U.S. price enough to fully offset any dollar depreciation because if it does so, it will lose cus- tomers to its U.S. competitors. Its rule of thumb is that for every 10-cent increase in the exchange rate (e.g., from USD2 = GBP1 to USD2.10 = GBP1) it will increase prices by $5 (e.g., from $200 to $205 per game). Given this rule, it will lose only some of its U.S. sales.

Suppose its forecast of annual sales in the United States as a function of the dollar price is

Quantity sold = 1,000,000 - 100 × price in dollars

Answer the following questions: (LO22-3)

a. Plot the British pound value of ClickEasy’s revenue from its U.S. sales as a function of the exchange rate for exchange rates ranging from USD1.50 = GBP1 to USD3.00 = GBP1. What is its exchange rate exposure?

b. Suppose each exchange rate scenario in part (a) is equally likely. What would ClickEasy’s expected dollar revenue be? What would be its pound revenue in each scenario if it sold forward that number of U.S. dollars at a forward exchange rate of USD2 = GBP1? Does this seem like an effective hedge?

23. Exchange Rate Risk. You have bid for a possible export order that would provide a cash inflow of €1 million in 6 months. The spot exchange rate is USD1.30 = EUR1, and the 1-year forward rate is USD1.28 = EUR1. There are two sources of uncertainty: (1) The euro could appreciate or depreciate, and (2) you may or may not receive the export order. Fill in the following table to illustrate in each case the profits or losses that you would make if you sell €1  million forward. Assume that the exchange rate in 1 year will be either USD1.20 = EUR1 or USD1.40 = EUR1. (LO22-3)

Percentage of Total Sales or Costs

U.S Sales U.S. Costs Euro-Area Sales Euro-Area Costs

Swatch Group 40 20 40 30 Lindt & Sprüngli 20 15 60 50 Nestlé 45 40 35 35 Roche 35 39 25 19

Source: Hottinger Capital Corporation.

Total Profi t/Loss

Spot Rate Receive Order Lose Order

USD1.20 = EUR1 (a) (c) USD1.40 = EUR1 (b) (d)

Templates can be found in Connect.

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26. International Investment Decisions. An American firm is evaluating an investment in Mexico. The project costs 500 million pesos, and it is expected to produce an income of 250 million pesos a year in real terms for each of the next 3 years. The expected inflation rate in Mexico is 4% a year, and the firm estimates that an appropriate discount rate for the project would be about 8% above the risk-free rate of interest. Calculate the net present value of the project in U.S. dollars. Exchange rates are given in Table 22.1. The interest rate is about 4.3% in Mexico and 1.5% in the United States. (LO22-4)

WEB EXERCISES 1. There are plenty of good sites that show current and past spot rates of exchange. Forward rates

are less easy to come by, but the Bank of England website gives spot and forward rates for the pound (we suggest that you download the forward rate itself rather than the forward premium). Can you deduce from these whether the interest rate is higher in the United States than in the United Kingdom? Warning: Look out for the difference between direct and indirect quotes.

2. Log on to www.prsgroup.com, and get a free sample of the International Country Risk Guide. For which characteristics does the United States score well? For which does it score badly? Is Finland still close to top of the class?

Templates can be found in Connect.

SOLUTIONS TO SELF-TEST QUESTIONS 22.1 Direct quote: USD1.376 = EUR1 Indirect quote: 1/1.376, or EUR.7267 = USD1 Indirect quote: JPY102.34 = USD1 Direct quote: 1/102.34, or USD.0098 = JPY1

22.2 One Hong Kong dollar is worth 13.231/7.755 = 1.706 Mexican pesos (and one peso is worth 7.755/13.231 =  .586 Hong Kong dollars). If a bank quotes 2 pesos per Hong Kong dollar, you could take one U.S. dollar, buy 7.755 Hong Kong dollars, and then exchange the Hong Kong dollars for 7.755  ×  2  =  15.510 pesos. Then you could change the pesos back into 15.510/13.231 = 1.172 U.S. dollars. The profit is $.172.

22.3 The U.S. dollar buys more Canadian dollars, so the Canadian dollar has depreciated with respect to the U.S. dollar.

22.4 a. 1,500/.888 = $1,689. b. Indirect exchange rate: $1 = .9 × .888 = .799 francs. c. 1,500/.799 = $1,877. The dollar price increases.

22.5 a. Since the gold price must be the same in the two countries, GBP600 = USD1,000. There- fore GBP.6 = USD1. The direct quote would be 1/.6 = USD1.667 = GBP1.0.

b. In the United States, price  =  $1,000  ×  1.02  =  $1,020. In Great Britain, price = £600  ×  1.05  =  £630. The new exchange rate is, therefore, USD1,020  =  GBP630, or USD1.619 = GBP1.

c. Initially $1 buys 1/1.667 = £.6. At the end of the year, $1 buys 1/1.619 = £.6177, which is 3% higher than the original value of £.6.

22.6 The real interest rate in the United States is 1.003/1.017 − 1 = − .0138, or −1.38%. If the real rate is the same in South Korea, then expected inflation must be (1 + nominal rate)/(1 + real rate) − 1 = 1.026/.9862 − 1 = .0403, or 4.03%.

22.7 Suppose you want Ruritanian pesos next year. You can put $1 aside, earn interest at 4%, and buy pesos at the forward price of 126.92. You end up with 1 × 1.04 × 126.92 = 132 pesos. As the alternative, you can buy 120 pesos at spot and earn 10% in Ruritania. You end up in exactly the same place, with 120 × 1.1 = 132 pesos.

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Chapter 22 International Financial Management 659

22.8 If the euro or the yen depreciates against the dollar, then foreign cars are likely to become cheaper. The Ford dealer therefore has economic risk even though it never needs to buy or sell foreign currency.

22.9 a. If real interest rates are the same in the two countries, the difference in the inflation rates is now 1.06/1.03 − 1 = .0291, or 2.91%.

b. Less. For example, the 1-year forward rate should now be (1.06/1.03)  ×  100, or RUP102.91 = USD1. A dollar now buys fewer pesos in the forward market than before (or, equivalently, each peso is now worth more dollars in the forward market).

c. The peso cash inflows from Ecsy’s project can now be exchanged for more dollars. So net present value increases:

MINICASE “Jumping jackasses! Not another one!” groaned George Luger. It was a memo from the CEO of DVR Importers dated December 31,

2014. It was the third memo from the CEO that he had received that day. It read as follows:

Year: 0 1 2 3 4 5

Cash fl ow (millions of pesos) −380 100 125 150 175 200 Forward exchange rate (pesos to the dollar) 100 102.91 105.91 108.99 112.17 115.44 Cash fl ow (millions of dollars) −3.8 0.9717 1.1802 1.3762 1.5601 1.7326 PV at 13% −3.8 0.8599 0.9243 0.9538 0.9569 0.9404

NPV = $.835 million

From: CEO’s Office

To: Company Treasurer

George,

I have been looking at some of our foreign exchange deals and they don’t seem to make sense.

First, we have been buying yen forward to cover the cost of our imports. You have explained that this insures us against the risk that the dollar may depreciate over the next year, but it is incredibly expensive insurance. Each dollar buys only 108.173 yen when we buy forward, com- pared with the current spot rate of 111.715 yen to the dollar. We could save a fortune by buying yen as and when we need them rather than buying them forward.

Another possibility has occurred to me. If we are worried that the dollar may depreciate (or do I mean “appreciate”?), why don’t we buy yen at the low spot rate of ¥111.715 to the dollar and then put them on deposit until we have to pay for the DVRs? That way we can make sure that we get a good rate for our yen.

I am also worried that we are missing out on some cheap financing. We are paying about 6% to borrow dollars for one year, but Ben Hur was telling me at lunch that we could get a one-year yen loan for about 2%. I find that a bit surprising, but if that’s the case, why don’t we repay our dollar loans and borrow yen instead?

Perhaps we could discuss these ideas at next Wednesday’s meeting. I would be interested in your views on the matter.

Jill Edison

How should George respond to Jill’s memo? For example:

1. Is the forward purchase of the yen “incredibly expensive insurance”?

2. Would the company be better if it purchased yen and “then put them on deposit”?

3. Should the company “repay its dollar loans and borrow yen instead”?

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660

Options

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

23-1 Calculate the payoff to buyers and sellers of call and put options.

23-2 Understand the determinants of option values.

23-3 Recognize options in capital investment proposals.

23-4 Identify options that are provided in financial securities.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

23 CHAPTE R

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661

P A

R T

S E

V E

N

W hen the Chicago Board Options Exchange (CBOE) was established in 1973, few observers guessed what a suc- cess it would be. Today the CBOE and its younger

rival, the International Securities Exchange (ISE),

each trade options to buy or sell over 60 billion

shares of stock a year. In addition to trading options

on individual stocks, you can now trade options

on stock indexes, bonds, commodities, and foreign

exchange.

You will see that options can be valuable tools

for managing the risk characteristics of an invest-

ment portfolio. But why should the financial man-

ager of an industrial company read further? There

are several reasons. First, most capital budgeting

projects have options embedded in them that allow

the company to expand at a future date or to bail

out. These options enable the company to profit if

things go well but give downside protection when

they don’t.

Second, many of the securities that firms issue

include an option. For example, companies often

issue convertible bonds. The holder has the option

to exchange the bond for common stock. Some cor-

porate bonds also contain a call provision, meaning

that the issuer has the option to buy back the bond

from the investor.

Finally, managers routinely use currency, commod-

ity, and interest rate options to protect the firm against

a variety of risks.

In one chapter we can provide you with only a

brief introduction to options. Our first goal is to explain

how options work and how option value is deter-

mined. Then we will tell you how to recognize some

of the options that crop up in capital investment pro-

posals and in company financing.

Sp e

c ia

l T o

p ic

s

Just another day on the options exchange. But why does the financial manager of an industrial company need to understand options?

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662 Part Seven Special Topics

23.1 Calls and Puts A call option gives its holder the right to buy stock for a fixed exercise price (also called the strike price ) on or before a specified expiration date. 1 For example, if you buy a call option on Apple stock with an expiration date in October and an exercise price of $420, you have the right to buy the stock at a price of $420 any time until October.

You need not exercise a call option; it will be profitable to do so only if the share price exceeds the exercise price. If it does not, the option will be left unexercised and will be valueless. But suppose that when the option expires, Apple shares are sell- ing above the exercise price, say, at $480. In this case you will choose to exercise your option to pay $420 for shares worth $480. Your payoff will equal the difference between the $480 for which you can sell the shares and the $420 that you pay when you exercise the option. More generally, when the stock price is greater than the exer- cise price, the payoff from your call option is equal to the difference between the stock price and the exercise price.

In summary, the value of the call option at expiration is as follows:

1 In some cases, the option can be exercised only on one particular day, and it is then conventionally known as a European call; in other cases, it can be exercised on or before that day, and it is known as an American call.

call option Right to buy an asset at a specified exercise price on or before the expiration date.

Example 23.1 Call Options on Apple In April 2013 a call option on Apple stock with an October 2013 expiration and an exercise price of $420 sold for $35.25. If you bought this call, you gained the right to purchase Apple shares for $420 at any time until the option expired the following October. The price of Apple stock in April was $420. If the stock price did not rise by October, the call would not be worth exercising and you would lose your invest- ment of $35.25. On the other hand, even a relatively modest rise in the stock price could give you a rich profit on your option. For example, if Apple sold for $520 in October, the proceeds from exercising the call would be

Proceeds = stock price - exercise price = $520 - $420 = $100

and the net profit on the call would be

Profit = proceeds - original investment = $100 - $35.25 = $64.75

In 6 months, you would have earned a return of $64.75/$35.25  =  1.84, or 184%.

Stock Price at Expiration Value of Call at Expiration

Greater than exercise price Stock price - exercise price Less than exercise price Zero

Of course, that payoff is not all profit: You have to pay for the option. The price of the call is known as the option premium. Option buyers pay the premium for the right to exercise later. Your profit equals the ultimate payoff to the call option (which may be zero) minus the initial premium.

Whereas a call option gives you the right to buy a share of stock, a put option gives you the right to sell it for the exercise price. If you own a put on a share of stock and the stock price turns out to be greater than the exercise price, you will not want to exercise your option to sell the shares for the exercise price. The put will be left unexercised and will expire valueless. But if the stock price turns out to be less than the exercise price, it will pay to buy the share in the market at the low price and then exercise your option to sell it for the exercise price. The put would then be worth the difference between the exercise price and the stock price.

put option Right to sell an asset at a specified exercise price on or before the expiration date.

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Chapter 23 Options 663

In general, the value of the put option at expiration is as follows:

Stock Price at Expiration Value of Put at Expiration

Greater than exercise price Zero Less than exercise price Exercise price - stock price

Example 23.2 Put Options on Apple In April 2013 it cost $39.20 to buy a put option on Apple stock with an October 2013 expiration and an exercise price of $420. Suppose that Apple is selling for $360 when the put option expires. Then if you hold the put, you can buy a share of stock in the market for $360 and exercise your right to sell it for $420. The put will be worth $420  −  $360  =  $60. Because you paid $39.20 for the put originally, your net profit is $60  −  $39.20 = $20.80. As a put buyer, your worry is that the stock price will rise above the $420 exercise price. If that happens, you will let the put option expire worthless and you will lose the $39.20 that you originally paid for it.

Stock Price: $360 $390 $420 $450 $480

Call value 0 0 0 $30 $60 Put value $60 $30 0 0 0

TABLE 23.1 How the value of an Apple option on its expiration date varies with the price of the stock on that date (exercise price  =  $420)

Table 23.1 shows how the values of Apple calls and puts are affected by the level of the stock price on the expiration date. You can see that once the stock price is above the exercise price, the call value rises dollar for dollar with the stock price, and once the stock price is below the exercise price, the put value rises a dollar for each dollar decrease in the stock price. Figure 23.1 plots the values of each option on the expira- tion date.

Table 23.2 shows the prices of nine options on Apple stock in April 2013. Notice that for any particular expiration date, call options are worth more when the exercise price is lower, while puts are worth more when the exercise price is higher. This makes sense: You would rather have the right to buy at a low price and the right to sell at a high price. Notice also that for any particular exercise price the longer-dated options are the most valuable. This also makes sense. An option that expires in January 2014 gives you everything that a shorter-dated option offers and more. Naturally, you would be prepared to pay for the chance to keep your options open for as long as possible.

FIGURE 23.1 Values of call options and put options on Apple stock on option expiration date (exercise price  =  $420)

C al

l o p

ti o

n v

al u

e

Share price

$60

$420 $480

P u

t o

p ti

o n

v al

u e

Share price

$420

$60

$420$36000

(a) (b)

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664 Part Seven Special Topics

Selling Calls and Puts The traded options that you see quoted in the financial pages are not sold by the com- panies themselves but by other investors. If one investor buys an option on Apple stock, some other investor must be on the other side of the bargain. We will look now at the position of the investor who sells an option. 2

We have already seen that the Apple calls that expire in October 2013 with an exer- cise price of $420 are trading at $35.25. Thus if you sell the October call option on Apple stock, the buyer pays you $35.25. However, in return you promise to sell Apple shares at a price of $420 to the call buyer if he decides to exercise his option. The option seller’s obligation to sell Apple is just the other side of the coin to the option holder’s right to buy the stock. The buyer pays the option premium for the right to exercise; the seller receives the premium but may be required at a later date to deliver the stock for an exercise price that is less than the market price of the stock. If the share price is below the exercise price of $420 when the option expires in October, holders of the call will not exercise their option and you, the seller, will have no fur- ther liability. However, if the price of Apple is greater than $420, it will pay the buyer to exercise and you must give up your shares for $420 each. You lose the difference between the share price and the $420 that you receive from the buyer.

Suppose that Apple’s stock price turns out to be $480. In this case the buyer will exercise the call option and will pay $420 for stock that can be resold for $480. The buyer therefore has a payoff of $60. Of course, that positive payoff for the buyer means a negative payoff for you, the seller, because you are obliged to deliver Apple stock worth $480 for only $420. This $60 loss more than wipes out the $35.25 that you were originally paid for selling the option.

In general, the seller’s loss is the buyer’s gain, and vice versa. Figure 23.2 a shows the payoffs to the call option seller. Note that this figure is just Figure 23.1 a drawn upside down.

The position of an investor who sells the Apple put option can be shown in just the same way by standing Figure 23.1 b on its head. The put buyer has the right to sell a

2 The option seller is known as the writer.

Expiration Date Exercise Price Call Price Put Price

July 2013 $390 $43.16 $14.60 420 25.75 27.85 450 14.20 45.90 October 2013 390 57.77 25.00 420 35.25 39.20 450 23.10 57.00 January 2014 390 63.50 34.60 420 42.85 49.70 450 31.05 67.90

TABLE 23.2 Examples of options on Apple shares in April 2013 when Apple stock was selling for $420

a. What will be the proceeds and net profits (i.e., net of the option premium) to an investor who purchases the January 2014-expiration Apple call option with exercise price of $450 if the stock price at expiration is $360? What if the stock price at expiration is $510? Use the data in Table 23.2 .

b. Now answer part (a) for an investor who purchases a January-expiration Apple put option with exercise price $450.

Self-Test 23.1

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Chapter 23 Options 665

share for $420; so the seller of the put has agreed to pay $420 for the share if the put buyer should demand it. Clearly the seller will be safe as long as the share price remains above $420 but his payoff will be negative if the share price falls below this figure. The worst thing that can happen to the put seller is for the stock to be worthless. The seller would then be obliged to pay $420 for a worthless stock. The payoff to the seller would be − $420. Note that the advantage always lies with the option buyer, and the obligation lies with the seller. Therefore, the buyer must pay the seller to acquire the option.

Table  23.3 summarizes the rights and obligation of buyers and sellers of calls and puts.

Buyer Seller

Call option Right to buy asset Obligation to sell asset Put option Right to sell asset Obligation to buy asset

TABLE 23.3 Rights and obligations of various option positions

a. What will be the proceeds and net profits to an investor who sells the July- expiration Apple call option with exercise price of $450 if the stock price at expiration is $420? What if the stock price at expiration is $480? Use the data in Table 23.2 .

b. Now answer part (a) for an investor who sells a July-expiration Apple put option with exercise price $450.

Self-Test 23.2

FIGURE 23.2 Payoffs to sellers of call and put options on Apple stock (exercise price  =  $420)

P ay

o ff

to c

al l s

el le

r Share price

Share price

P ay

o ff

to p

u t

se lle

r

$420$360

-$60 -$60

-$420

(a) (b)

$420 $480

Payoff Diagrams Are Not Profit Diagrams Figures 23.1 and 23.2 show only the possible payoffs when the option expires; they do not account for the initial cost of buying the option or the initial proceeds from selling it.

This is a common point of confusion. For example, the payoff diagram in Figure 23.1 a makes purchase of a call look like a sure thing—the payoff is at worst zero, with plenty of upside if Apple’s stock price goes above $420 by the expiration date. But compare this with the profit diagram in Figure 23.3 , which subtracts the $35.25 cost of the call in April 2013 from the payoff at expiration. The call buyer loses money at all share prices less than $420  +  $35.25  =  $450.25.

Take another example: The payoff diagram in Figure 23.2 b makes selling a put look like a sure loser—the best payoff is zero. But the profit diagram in Figure 23.4 , which recognizes the $39.20 received by the seller, shows that the seller gains at all prices above $420  −  $39.20  =  $380.80.

Profit diagrams like those in Figures 23.3 and 23.4 may be helpful to the options beginner, but options experts rarely draw them. Now that you’ve graduated from

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666 Part Seven Special Topics

the first options class, we won’t draw them either. We will stick to payoff diagrams, because you have to focus on payoffs at expiration to understand options and to value them properly.

Financial Alchemy with Options Options can be used to modify the risk characteristics of a stock. Suppose, for exam- ple, that you are generally optimistic about Apple’s prospects but you perceive enough risk that a large investment in the stock would cause you sleepless nights. Here is a strategy that might appeal to you: Buy the stock, but also buy a put option on the stock with exercise price $420. If the stock price rises from its current level of $420, your put turns out to be worthless but you win on your investment in the stock. If the stock price falls, your losses are limited, since the put gives you the right to sell your stock for the $420 exercise price. Thus the value of your stock-plus-put position cannot be less than $420.

Here is another way to view your overall position. You hold the stock and the put option. The ultimate value of each component of the portfolio is as follows:

 Stock Price < $420  Stock Price ≥ $420

Value of stock Stock price Stock price Value of put option $420 - stock price 0

Total value $420 Stock price

No matter how far the stock price falls, the total value of your portfolio cannot fall below the $420 exercise price.

The value of your position when the option expires is graphed in Figure 23.5 . You have downside protection at $420, but still share in any increase in the stock price. This strategy is called a protective put, because the put option gives protection against losses. Of course, such protection is not free. Look again at Table 23.2 and you will find the cost of such protection. “Stock price insurance” at a level of $420 between April and October 2013 cost $39.20 per share; this was the price of a put option with exercise price $420 and October expiration.

FIGURE 23.3 Payoff and profit for a purchaser of a call option on Apple stock with exercise price of $420

-$35.25 $420

Profit Share price at expiration

Payoff

FIGURE 23.4 Payoff and profit for a seller of a put option on Apple with exercise price of $420

$39.20

-$420

$420

Profit

Share price

Payoff

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Chapter 23 Options 667

Some More Option Magic Look again at Figure 23.5 , which shows the possible payoffs at expiration from hold- ing both a share of Apple stock and a put option to sell it for $420. Does this picture look somewhat familiar? It should. Turn back to panel a of Figure 23.2 , which shows the payoffs from holding a call option on Apple stock with an exercise price of $420. The only difference between the two sets of payoffs is that the combination of the stock and put option always provides exactly $420 more than the call option. In other words, regardless of the final stock price, holding the stock plus a put option gives the same payoff as an alternative strategy of buying a call option plus investing the present value of $420 in a bank deposit.

Think what happens if you follow this second strategy. If the stock price is below $420 when the option expires, your call option will be valueless but you will still have $420 in the bank. On the other hand, if the stock price rises above $420, you will take your money out of the bank, use it to exercise the call, and own the stock. The follow- ing table confirms that this second investment package gives you exactly the same payoffs as you get from holding the stock and a put option:

Payoffs at Expiration

Stock price ≤ $420 Stock price > $420

Call option 0 Stock price - $420 Bank deposit paying $420 $420 $420

Total value $420 Stock price

If you plan to hold each of these packages until the options expire, the packages must sell for the same price today. This gives us a fundamental relationship between the price of a call and the price of a put: 3

Price of stock + price of put = price of call + present value of exercise price

This basic relationship between share price, call and put prices, and the present value of the exercise price is called put-call parity.

3 This relationship assumes that the two options have the same exercise price and expiration date. It also assumes that the stock does not pay dividends before expiration. Since the buyer of Apple call options misses out on the dividend, we should subtract the dividend payment from the value of the stock. The expanded for- mula becomes

Stock price - PV(dividends before expiration) + put price = call price + PV(exercise price)

Note that the present value of the exercise price is simply the amount that you would need to set aside in a bank deposit in order to receive the exercise price at expiration.

FIGURE 23.5 Payoff to protective put strategy. If the ultimate stock price exceeds $420, the put is valueless but you own the stock. If it is less than $420, you can sell the stock for the exercise price.

V al

u e

o f

st o

ck p

lu s

p u

t

Stock price

$420

$420

Stock price

Option payoffs

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23.2 What Determines Option Values? In Table 23.2 we set out the prices of different Apple options. But we said nothing about how the market values of options are determined. It is time that we do so.

Upper and Lower Limits on Option Values We know what an option is worth when it expires. Consider, for example, the option to buy Apple stock at $420. If the stock price is below $420 at the expiration date, the call will be worthless; if the stock price is above $420, the call will be worth the value of the stock minus the $420 exercise price. The relationship is depicted by the heavy orange line in Figure 23.6 .

Even before expiration, the price of the option can never remain below the heavy orange line in Figure 23.6 . For example, if our option were priced at $20 and the stock at $480, it would pay any investor to buy the option, exercise it for an additional $420, and then sell the stock for $480. That would give a “money machine” with a profit of $480  −  ($20  +  $420)  =  $40. Money machines can’t last. The demand for options from investors using this strategy would quickly force the option price up at least to the heavy orange line in the figure. The heavy orange line is therefore a lower limit on the market price of the option. Thus

Lower limit on value

of call option =

the greater of zero or (stock price - exercise price)

FIGURE 23.6 Value of a call before its expiration date (dashed line). The value depends on the stock price. The call is always worth more than its value if exercised now (heavy orange line). It is never worth more than the stock price itself (blue line).

Share price

V al

u e

o f

ca ll

Exercise price

C

Upper bound: value of call

equals share price

Lower bound: value of call equals payoff if exercised immediately

A

B

A 1-year call option on Witterman stock with an exercise price of $60 costs $8.05. The stock price is $55, and the interest rate on a bank deposit is 4%. What is the value of a 1-year put option on Witterman with an exercise price of $60?

Self-Test 23.3

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Chapter 23 Options 669

The diagonal blue line in Figure 23.6 , which is the plot of the stock price, is the upper limit to the option price. Why? Because the stock itself gives a higher final payoff whatever happens. If when the option expires the stock price ends up above the exer- cise price, the option is worth the stock price less the exercise price. If the stock price ends up below the exercise price, the option is worthless but the stock’s owner still has a valuable security. Thus the extra payoff to holding the stock rather than the option is as follows:

Stock Price at Expiration Stock Payoff Option Payoff

Extra Payoff from Holding Stock rather than Option

Greater than $420 Stock price Stock price - $420 $420 Less than or equal to $420 Stock price $0 Stock price

The Determinants of Option Value The option price must lie between the upper and lower limits in Figure 23.6 . In fact, the price will lie on a curved, upward-sloping line like the dashed curve shown in the figure. This line begins its travels where the upper and lower bounds meet (at zero). Then it rises, gradually becoming parallel to the lower bound. This line tells us an important fact about option values: Given the exercise price, the value of a call option increases as the stock price increases.

That should be no surprise. Owners of call options are clearly happy when the stock price is much higher than the exercise price and are willing to pay more for options that are “in the money.” If you look back at the prices of the Apple options, you will see that the price of the call is higher when the stock price is above the exercise price. But let us look more carefully at the shape and location of the dashed line. Three points, A, B, and C, are marked on the dashed line. As we explain each point, you will see why the option price has to behave as the dashed line predicts.

Point A When the stock is worthless, the option is worthless. A stock price of zero means that there is no possibility the stock will ever have any future value. 4 If so, the option is sure to expire unexercised and worthless, and it is worthless today.

Point B When the stock price becomes very high, the option price approaches the stock price less the present value of the exercise price. Notice that the dashed line rep- resenting the option price in Figure 23.6 eventually becomes parallel to the ascending heavy orange line representing the lower bound on the option price. The reason is as follows: The higher the stock price, the greater the odds that the option will eventually be exercised. If the stock price is high enough, exercise becomes a virtual certainty; the probability that the stock price will fall below the exercise price before the option expires becomes trivial.

If you own an option that you know will be exchanged for a share of stock, you effectively own the stock now. The only difference is that you don’t have to pay for the stock (by handing over the exercise price) until later, when formal exercise occurs. In these circumstances, buying the call is equivalent to buying the stock now with deferred payment and delivery. The value of the call is therefore equal to the stock price less the present value of the exercise price. 5

This brings us to another important point about options. Investors who acquire stock by way of a call option are buying on “installment credit.” They pay the purchase price

4 If a stock can be worth something in the future, then investors will pay something for it today, although pos- sibly a very small amount. 5 We assume here that the stock pays no dividends until after the option expires. If dividends were paid, you would care about when you get to own the stock because the option holder misses out on any dividends.

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670 Part Seven Special Topics

of the option today, but they do not pay the exercise price until they actually exercise the option. The delay in payment is particularly valuable if interest rates are high and the option has a long maturity. Thus the value of a call option increases with both the rate of interest and the time to expiration.

How would the value of a put option be affected by an increase in the exer- cise price? Explain.

Self-Test 23.4

Point C The option price always exceeds its minimum value (except at expiration or when the stock price is zero). We have seen that the dashed and heavy lines in Fig- ure 23.6 coincide when stock price is zero (point A ), but elsewhere the lines diverge; that is, the option price must exceed the minimum value given by the heavy orange line. You can see why by examining point C.

At point C, the stock price exactly equals the exercise price. The option therefore would be worthless if it expired today. However, suppose that the option will not expire until 3 months hence. Of course, we do not know what the stock price will be at the expi- ration date. There is roughly a 50% chance that it will be higher than the exercise price, and a 50% chance that it will be lower. The possible payoffs to the option are therefore:

Outcome Payoff

Stock price rises (50% probability)

Stock price - exercise price (option is exercised)

Stock price falls (50% probability)

Zero (option expires worthless)

If there is some chance of a positive payoff, and if the worst payoff is zero, then the option must be valuable. That means the option price at point C exceeds its lower bound, which at point C is zero. In general, the option price will exceed the lower bound as long as there is time left before expiration.

One of the most important determinants of the height of the dashed curve (that is, of the difference between actual and lower-bound value) is the likelihood of substantial movements in the stock price. An option on a stock whose price is unlikely to change by more than 1% or 2% is not worth much; an option on a stock whose price may halve or double is very valuable.

For example, suppose that a call option has an exercise price of $420 and the stock price will be either $360 or $480 when the option expires. The possible payoffs to the option are as follows:

Stock price at expiration $360 $480

Call value at expiration 0 $ 60

Now suppose that the value of the stock when the option expires can be $300 or $540. The average of the possible stock prices is the same as before, but the volatility is greater. In this case the payoffs to the call are:

Stock price at expiration $300 $540

Call value at expiration 0 $120

A comparison of the two cases highlights the valuable asymmetry that options offer. If the stock price turns out to be below the exercise price when the option expires, the option is valueless regardless of whether the shortfall is a cent or a dollar. However,

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Chapter 23 Options 671

the option holder reaps all the benefits of stock price advances. Thus in our example the option is worth only $60 if the stock price reaches $480, but it is worth $120 if the stock price rises to $540. Therefore, volatility helps the option holder.

The probability of large stock price changes during the remaining life of an option depends on two things: (1) the variability of the stock price per unit of time and (2) the length of time until the option expires. Other things equal, you would like to hold an option on a volatile stock. Given volatility, you would like to hold an option with a long life ahead of it, since that longer life means that there is more opportunity for the stock price to change. The value of an option increases with both the variability of the share price and the time to expiration.

It’s a rare person who can keep all these properties straight at first reading. There- fore, we have summed them up in Table 23.4 .

Rework our numerical example for a put option with an exercise price of $420. Show that put options also are more valuable when the stock price is more volatile.

Self-Test 23.5

TABLE 23.4 What the price of a call option depends on If the following variables increase, . . . . . . the value of a call option will

Stock price Increase Exercise price Decrease Interest rate Increase Time to expiration Increase Volatility of stock price Increase

Option-Valuation Models If you want to value an option, you need to go beyond the qualitative statements of Table 23.4 ; you need an exact option-valuation model—a formula that you can plug numbers into and come up with a figure for option value.

Valuing complex options is a high-tech business and well beyond the scope of this book. Our aim here is not to make you into instant option whizzes, but we can illus- trate the basics of option valuation by walking you through an example. The trick to option valuation is to find a combination of borrowing and an investment in the stock that exactly replicates the option. The nearby box illustrates a simple version of one of these option-valuation models.

This model achieves simplicity by assuming that the share price can take on only two values at the expiration date of the option. This assumption is clearly unrealistic, but it turns out that the same approach can be generalized to allow for a large number of possible future share prices rather than just the two values in our example.

In 1973 Fischer Black, Myron Scholes, and Robert Merton came up with a formula which showed that even when share prices are changing continuously, you can still replicate an option by a series of levered investments in the stock. The Black-Scholes formula is regularly used by option traders, investment bankers, and financial manag- ers to value a wide variety of options. Scholes and Merton shared the 1997 Nobel Prize in economics for their work on the development of this formula. 6 The box on page 673 shows you how to set up a Black-Scholes calculator in Excel.

6 Fischer Black passed away in 1995.

A simple option valuation model

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Today, there are many ever-more-sophisticated variants on the Black-Scholes for- mula that can better capture some aspect of real-life markets. As computer power con- tinues to increase, these models can be made more complex and increasingly accurate. Rather than using an estimate of volatility to calculate the value of an option, investors sometimes use option prices to back out an estimate of future volatility. A nearby box describes how these estimates of volatility are used to create a “fear index.”

Finance in Practice A Simple Option-Valuation Model $100 bank loan is $101 no matter what happens to the price of Apple stock.

Now consider two investment strategies. The fi rst (strat- egy A) is to buy 100 call options. The second (strategy B) is to buy 54 Apple shares and borrow the present value of $19,300. Table 23.5 shows the possible payoffs from the two strategies. Notice that when you borrow from the bank you receive a positive cash fl ow now but have a negative cash fl ow when the loan is repaid in October.

You can see that, regardless of whether the stock price falls to $357.45 or rises to $493.50, the payoffs from the two strategies are identical. To put it another way, you can exactly replicate an investment in call options by a combination of a bank loan and an investment in the stock. * If two invest- ments give the same payoffs in all circumstances, then their value must be the same today. In other words, the cost of buying 100 call options must be exactly the same as borrow- ing PV($19,300) from the bank and buying 54 Apple shares:

Price of 100 calls = $22,680 - $19,110 = $3,570

Price of 1 call = $3,570/100 = $35.70

Presto! You have just valued a call option.

It is April 2013, and you are contemplating the purchase of a call option on Apple stock. The call has an October 2013 expiration date and an exercise price of $420. Apple’s stock price is also currently $420, so the option will be valueless unless the stock price appreciates over the next 6 months. The outlook for Apple is uncertain, and all you know is that at the end of the 6 months the price will either rise by 17.5% to 1.175  ×  $420  =  $493.50 or fall by the same proportion to $420/1.175  =  $357.45. Finally, the rate of interest on a bank loan at this time is about 1% for 6 months. For simplicity, we ignore the fact that Apple pays a small dividend which the call buyer is not entitled to.

The following table depicts the outlook for three alterna- tive investments:

Payoff in October If Stock Price Equals

Cash Flow in April 2013 $357.45 $493.50

Strategy A Buy 100 calls ? $ 0 + $ 7,350 Strategy B Buy 54 shares − $22,680 + $19,300 + $26,650 Borrow PV($19,300) + $ 19,110 − $19,300 − $19,300 − $ 3,570 $ 0 + $ 7,350

Note: PV($19,300) paid 6 months from now is $19,300/1.01  =  $19,110.

TABLE 23.5 It is possible to replicate the payoffs from Apple call options by borrowing to invest in Apple stock

Apple Stock Call Option Bank Loan

April October April October April October

$493.50 $73.50 $101 $420 ? $100

357.45 $0 $101

The fi rst investment is Apple stock. Its current price is $420, but the price could rise to $493.50 or fall to $357.45. The sec- ond investment is the call option. When the call expires in October, the option will be valueless if the stock price falls, and it will be worth $493.50  −  $420  =  $73.50 if the stock price rises to $493.50. We don’t know (yet) what the call is worth today, so for the time being we put a question mark against the April value. Our third investment is a $100 bank loan at an interest rate of 1% for 6 months. The payoff on the

* The only tricky part in valuing the Apple option was to work out the number of shares that were needed to replicate the call option. Fortunately, there is a simple formula which says that the number of shares needed is equal to

Spread of possible option prices

Spread of possible stock prices =

$73.50 - 0

$493.50 - 357.45 = .54

To replicate 1 call option, you need to buy .54 of a share. To replicate 100 calls, you need to buy 54 shares of stock.

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Use the Simple Option Valuation Model Finance in Practice box on page 672 as a model to help you answer this question. Suppose that the price of Fly- by-Night stock is $30 and could either double to $60 or halve to $15 over the next 3 months. Show that the following two strategies have exactly the same payoffs regardless of whether the stock price rises or falls:

Strategy A. Buy three call options with an exercise price of $30. Strategy B. Buy two shares and borrow the present value of $30. What is your cash outflow today if you follow strategy B? What does this

tell you about the value of three call options? Assume that the interest rate is 1% per 3 months.

Self-Test 23.6

calculate Black-Scholes values. The following spreadsheet shows how you do it. First, type in the formulas shown on the right side of the spreadsheet in cells E2 to E8. Now enter the data for the Apple October 2013 call in cells B2 to B6. Notice that the values for the standard deviation and interest rate are entered as decimals. * On past evidence, the standard deviation of Apple’s annual returns has been about 30%, so we enter the standard deviation in cell B2 as .30, not 30. We ignore here the fact that Apple pays a small dividend which the call buyer is not entitled to. The correct procedure is to deduct the present value of such dividends before inputting the stock price. The last two lines of the output column show that the Black-Scholes formula gives a value of $37.41 for the Apple call option, pretty close to its market price in April 2013. (Don’t worry about the other lines of output.)

Spreadsheet Questions 1. Use the option-pricing spreadsheet to calculate the value

of the call option at stock prices ranging from $300 to $600 at intervals of $25.

2. Plot the values as a function of the stock price. How does your graph compare to the plot in Figure 23.4 ?

You may like to try your hand at using the Black-Scholes option-pricing formula to value the Apple option. You can use the spreadsheet provided in Connect, but it takes only a few moments to construct your own Excel program to

Solutions Spreadsheet Using the Black-Scholes Formula

You can find this spreadsheet in Connect.

1

2

3

4

5

6

7

8

INPUTS Standard deviation (annual)

Maturity (in years)

Risk-free rate (effective annual rate)

Stock price

Exercise price

PV(Ex. Price)

d1

d2

N(d1)

N(d2)

B/S call value

B/S put value

B6/(1+B4)∧B3

(LN(B5/E2)+(0.5*B2∧2)*B3)/(B2*SQRT(B3))

E3-B2*SQRT(B3)

NORMSDIST(E3)

NORMSDIST(E4)

B5*E5 - E2*E6

E7+E2 - B5

0.300

0.500

0.02

420

420

415.8620

0.1527

-0.0594

0.5607

0.4763

37.41

33.27

BA D EC F G H I J

OUTPUTS FORMULA FOR OUTPUT IN COLUMN E

*Chapter 11 described how to calculate standard deviations. Notice also that in cell E2, we compute the present value of the exercise price by treating the interest rate as an effective annual yield. You should be aware, however, that many Black-Scholes calculators require that the interest rate be expressed as a continuously compounded rate. See Chapter 5, Table 5.7, if you need a review of continuous compounding.

The Black-Scholes model

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23.3 Spotting the Option In our discussion so far we may have given you the impression that financial manag- ers are concerned only with traded options to buy or sell shares. But once you have learned to recognize the different kinds of options, you will find that they are every- where. Unfortunately, they rarely come with a large label attached. Often the trickiest part of the problem is to identify the option.

We will start by looking briefly at options on real assets and then turn to options on financial assets. You should find that you have already encountered many of these options in earlier chapters.

Options on Real Assets In Chapter 10 we pointed out that the capital investment projects that you accept today may affect the opportunities you have tomorrow. Today’s capital budgeting decisions need to recognize these future opportunities.

Other things equal, a capital investment project that generates new opportunities is more valuable than one that doesn’t. A flexible project—one that doesn’t commit manage- ment to a fixed operating strategy—is more valuable than an inflexible one. When a proj- ect is flexible or generates new opportunities for the firm, it is said to contain real options.

If you look out for real options, you’ll find them almost everywhere. A nearby Finance in Practice box provides an illustration of a firm that took real options into account in an important capital budgeting decision. In Chapter 10 we looked at sev- eral ways that companies may build future flexibility into a project. Here is a brief reminder of two types of real options that we introduced in that chapter.

The Option to Expand Many capital investment proposals include an option to expand in the future. For instance, some of the world’s largest oil reserves are found in the tar sands of Athabasca, Canada. Unfortunately, in many cases the cost of extract- ing oil was higher than the current market price. Yet oil companies were prepared to pay considerable sums for these tracts of barren land. The reason? Ownership of the tar sands gave the companies an option. If prices remained below the cost of extrac- tion, the Athabasca sands would remain undeveloped. But if prices rose above the cost

real options Options to invest in, modify, or dispose of a capital investment project.

Finance in Practice The Fear Index Between January 1986 and January 2014 the VIX has

averaged 21.4%, almost identical to the long-term level of market volatility that we cited in Chapter 11. The high point for the index was on October 19, 1987, when the VIX closed at 151%. Fortunately, market volatility returned fairly rapidly to less heady levels.

Although the VIX is the most widely quoted measure of volatility, volatility measures are also available for several other U.S. and overseas stock market indexes (such as the FTSE 100 Index in the United Kingdom and the CAC 40 in France), as well as for gold, oil, and the euro.

The Market Volatility Index, or VIX, measures the volatility implied by near-term options on the Standard & Poor’s 500 Index and is therefore an estimate of expected future market volatility over the next 30 calendar days. Implied market vola- tilities have been calculated by the Chicago Board Options Exchange (CBOE) since January 1986, though in its current form the VIX dates back only to 2003.

Investors regularly trade volatility. They do so by buying or selling VIX futures and options contracts. Since these were introduced by the Chicago Board Options Exchange (CBOE), they have become two of the most successful innovations ever introduced by the exchange.

Because VIX measures investor uncertainty, it has been dubbed the “fear index.” The market for index options tends to be dominated by equity investors who buy put options on the index when they are concerned about a potential drop in the stock market. Any subsequent decline in the value of their portfolio is then offset by the increase in the value of the put option. The more that investors value such insurance, the higher the price of index put options. Thus VIX is an indicator that refl ects the price of portfolio insurance.

Implied volatilities in the U.S., Europe, and Japan

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A real estate developer buys 70 acres of land in a rural area, planning to build a subdivision on the land if and when the population from the city begins to expand into the area. If population growth is less than anticipated, the devel- oper believes that the land can be sold to a country club that would build a golf course on the property.

a. In what way does the possibility of sale to the country club provide a put option to the developer?

b. What is the exercise price of the option? The asset value? c. How does the golf course option increase the NPV of the land project to

the developer?

Self-Test 23.7

of extraction, those land purchases could prove very valuable. Thus, ownership gives the companies a real option—a call option to extract the oil.

The Option to Abandon Suppose that you need a new plant ready to produce turboencabulators in 3 years. You have a choice of designs. If design A is chosen, con- struction must start immediately. Design B is more expensive, but you can wait a year before breaking ground.

If you know with certainty that the plant will be needed, you should opt for design A. But suppose that there is some possibility that demand for turboencabulators will fall off and that in a year’s time you will decide the plant is not required. Then design B may be preferable because it gives you the option to bail out at low cost any time during the next 12 months.

You can think of the option to abandon as a put option. The exercise price of the put is the amount that you could recover if you abandon the project. The abandonment option makes design B more attractive by limiting the downside exposure. The more uncertain is the need for the new plant, the more valuable is the downside protection offered by the option to abandon.

Finance in Practice Allegheny Acquires a Real Option Allegheny concluded that it would pay to acquire some

cheap power plants, even if they were relatively high-cost electricity producers. Most of the time, the plants will sit idle, with market prices for electricity below the marginal cost of production. But every so often, when electricity prices spike, the plants can be fi red up to produce electricity–at a great profi t. Even if they operate only a few weeks a year, they can be positive-NPV investments.

These plants are in effect call options on electrical power. The options are currently out of the money, but the possibility that power prices will increase makes these calls worth more than their price. The decision to build them therefore makes the fi rm more valuable.

Allegheny Corporation acquired open gas-fi red power plants in Mississippi and Tennessee. These plants were expected to sit idle most of the year and, when operating, to produce electricity at a cost at least 50% higher than the most effi- cient state-of-the-art facilities. Allegheny’s decision to acquire these power plants resulted from a sophisticated application of real options analysis.

The fi rm observed that electricity prices in an increasingly free energy market can be wildly volatile. For example, during some power shortages in the Midwest during the hot sum- mer months the cost of 1 megawatt-hour of electricity has increased briefl y from a typical level of $40 to several thou- sand dollars. The option to obtain additional energy in these situations obviously would be quite valuable.

Options on Financial Assets The Apple options that we considered earlier were sold by one group of investors to another. They had no effect on the company’s cash flows. However, firms may also issue options to their managers or investors, and these do have a potential impact on the companies’ cash flows. Here are a few examples.

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676 Part Seven Special Topics

Executive Stock Options In fiscal 2012 Larry Ellison, the CEO of Oracle, was paid a salary of just $1, but before you send him a food parcel, note that he also received options worth $90.7 million. The amount of Larry Ellison’s compensation is unusual, but these days the chief executives of most major U.S. corporations are com- pensated largely with stock options.

These stock options are valuable and therefore are an expense just like salaries and wages. The Financial Accounting Standards Board (FASB) now requires companies to use an option-valuation model, such as the Black-Scholes model, to estimate the fair value of option grants and to recognize this value when calculating expenses. For exam- ple, in fiscal 2012 Oracle granted options to its directors, management, and employ- ees to buy 112 million shares of the company’s stock. Oracle’s accounts showed that according to the Black-Scholes model the total value of these options was $659 million.

Stock options, such as those provided by Oracle, are an important part of managers’ compensation. There is nothing wrong with that if the options encourage managers to work hard to increase the value of their companies’ stock. However, in recent years some companies illegally boosted the value of the stock options that they had given to managers by backdating the grant of their executive stock options.

Warrants A warrant is a long-term call option on the company’s stock. For exam- ple, in return for helping to bail out the Bank of America in 2008, the U.S. Treasury received 150 million Bank of America warrants. Each warrant entitled the Treasury to buy one share in the bank for $13.30 at any time before January 2019.

In March 2010 the Treasury sold the warrants to investors for $8.35 each. At that time the price of Bank of America stock was $16.40 a share. So investors who bought the warrants would realize a profit if the stock price rose above $13.30  +  $8.35  =  $21.65.

Warrants are sometimes issued when a firm becomes bankrupt; the bankruptcy court offers the firm’s bondholders warrants in the reorganized company as part of the settlement. At other times warrants are given to underwriters as part of their com- pensation for managing an issue of securities. When a company issues a bond, it will occasionally add some warrants as a “sweetener.” Since these warrants are valuable to investors, they are prepared to pay a higher price for a package of bonds and warrants than for the bond on its own. Managers sometimes look with delight at this higher price, forgetting that in return the company has incurred a liability to sell its shares to the warrant holders at what, with hindsight, may turn out to be a low price.

Convertible Bonds The convertible bond is a close relative of the bond- warrant package. It allows the bondholder to exchange the bond for a given number of shares of common stock. Therefore, it is a package of a straight bond and a call option. The exercise price of the call option is the value of the “straight bond” (that is, a bond that is not convertible). It will be profitable to convert if the value of the stock to which the investor is entitled exceeds the value of the straight bond.

The owner of a convertible bond owns a bond and a call option on the firm’s stock. So does the owner of a package of a bond and a warrant. However, there are differ- ences, the most important being that a convertible bond’s owner must give up the bond to exercise the option. The owner of a package of bonds and warrants exercises the warrants for cash and keeps the bond.

warrant Right to buy shares from a company at a stipulated price before a set date.

convertible bond Bond that the holder may exchange for a specified amount of another security.

Example 23.3 Convertible Bonds In March 2013, U.S. Steel issued $275 million of 2.75% convertible bonds maturing in 2019. Each of these bonds can be converted before maturity into 39.5491 shares of common stock. In other words, the owner of the convertible has the option to return the bond to the company and receive 39.5491 shares in exchange. The number of shares that are received for each bond is called the bond’s conversion ratio. The conversion ratio of the U.S. Steel bond is 39.5491.

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Chapter 23 Options 677

a. What would be the conversion value of the U.S. Steel convertible bond if the stock price rose to $40? What would happen to its conversion price?

b. At the same time as making the convertible bond issue, U.S. Steel also sold some straight bonds to yield 6.875%. What does this suggest the bond value of the convertible issue was? (Assume annual coupon payments.)

Self-Test 23.8

Since the owner of the convertible always has the option not to convert, bond value establishes a lower bound, or floor, to the price of a convertible. Of course, this floor is not completely flat. If the firm falls on hard times, the bond may not be worth much. In the extreme case where the firm becomes worthless, the bond is also worthless.

When the firm does well, conversion value exceeds bond value. In this case the investor would choose to convert if forced to make an immediate choice. Bond value exceeds conversion value when the firm does poorly. In these circumstances the inves- tor would hold on to the bonds if forced to choose. Convertible holders do not have to make a now-or-never choice for or against conversion. They can wait and then, with the benefit of hindsight, take whatever course turns out to give them the highest pay- off. Thus a convertible is always worth more than both its bond value and its conver- sion value (except when time runs out at the bond’s maturity).

We stated earlier that it is useful to think of a convertible bond as a package of a straight bond and an option to buy the common stock in exchange for the straight bond. The value of this call option is equal to the difference between the convertible’s market price and its bond value.

In order to receive 39.5491 shares of U.S. Steel stock, you must surrender bonds with a face value of $1,000. Therefore, to receive one share, you have to surrender a face amount of $1,000/39.5491  =   $25.29. This figure is called the conversion price. Anybody who originally bought the bond at $1,000 in order to convert it into 39.5491 shares paid the equivalent of $25.29 a share.

When the convertible was issued, U.S. Steel’s stock price was $19.45. So, if inves- tors were obliged to convert their bond immediately, their investment would have been worth 39.5491  ×   $19.45  =   $769. This was the bond’s conversion value. Of course, investors did not need to convert in 2013. They obviously hoped that U.S. Steel’s stock price would zoom up, making conversion profitable. But they had the comfort of knowing that if the stock price did not zoom, they could choose not to convert and simply hold on to the bond. The value of the bond if it could not be converted is known as its bond value.

Callable Bonds Unlike warrants and convertibles, which give the investor an option, a callable bond gives an option to the issuer. A company that issues a callable bond has an option to buy the bond back at the stated exercise or “call” price. There- fore, you can think of a callable bond as a package of a straight bond (a bond that is not callable) and a call option held by the issuer.

The option to call the bond is obviously attractive to the issuer. If interest rates decline and bond prices rise, the company has the opportunity to repurchase the bond at a fixed call price. Therefore, the option to call the bond puts a ceiling on the bond price.

Of course, when the company issues a callable bond, investors are aware of this ceiling on the bond price and will pay less for a callable bond than for a straight bond.

callable bond Bond that may be repurchased by the issuer before maturity at a specified call price.

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The difference between the value of a straight bond and a callable bond with the same coupon rate and maturity is the value of the call option that investors have given to the company:

Value of callable bond = value of straight bond - value of the issuer’s call option

SUMMARY There are two basic types of options. A call option is the right to buy an asset at a specific exercise price on or before the exercise date. A put is the right to sell an asset at a specific exercise price on or before the exercise date. The payoff to a call is the value of the asset minus the exercise price if the difference is positive, and zero otherwise. The payoff to a put is the exercise price minus the value of the asset if the difference is positive, and zero otherwise. The payoff to the seller of an option is the negative of the payoff to the option buyer.

The value of a call option depends on the following considerations: • To exercise the call option you must pay the exercise price. Other things equal, the

less you are obliged to pay, the better. Therefore, the value of the option is higher when the exercise price is low relative to the stock price.

• Investors who buy the stock by way of a call option are buying on installment credit. They pay the purchase price of the option today, but they do not pay the exercise price until they exercise the option. The higher the rate of interest and the longer the time to expiration, the more this “free credit” is worth.

• No matter how far the stock price falls, the owner of the call cannot lose more than the price of the call. On the other hand, the more the stock price rises above the exercise price, the greater the profit on the call. Therefore, the option holder does not lose from increased variability if things go wrong, but gains if they go right. The value of the option increases with the variability of stock returns. Of course, the longer the time to the final exercise date, the more opportunity there is for the stock price to vary.

The importance of building flexibility into investment projects (discussed in Chapter 10) can be reformulated in the language of options. For example, many capital investments provide the flexibility to expand capacity in the future if demand turns out to be unusu- ally buoyant. They are in effect providing the firm with a call option on the extra capacity. Firms also think about alternative uses for their assets if things go wrong. The option to abandon a project is a put option; the put’s exercise price is the value of the project’s assets if shifted to an alternative use. The ability to expand or to abandon are both examples of real options.

What is the payoff to buyers and sellers of call and put options? (LO23-1)

What are the determinants of option values? (LO23-2)

What options may be present in capital investment proposals? (LO23-3)

“Puttable bonds” allow the investor to redeem the bond at face value or let the bond remain outstanding until maturity. Suppose a 20-year puttable bond is issued with the investor allowed after 5 years to redeem the bond at face value.

a. On what asset is the option written? (What asset do the option holders have the right to sell?)

b. What is the exercise price of the option? c. In what circumstances will the option be exercised? d. Does the put option make the bond more or less valuable?

Self-Test 23.9

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Chapter 23 Options 679

Many of the securities that firms issue contain an option. For example, a warrant is noth- ing but a long-term call option issued by the firm. Convertible bonds give the investor the option to buy the firm’s stock in exchange for the value of the underlying bond. Unlike warrants and convertibles, which give an option to the investor, callable bonds give the option to the issuing firm. If interest rates decline and the value of the underlying bond rises, the firm can buy the bonds back at a specified exercise price.

What options may be provided in financial securities? (LO23-4)

QUESTIONS AND PROBLEMS 1. Option Payoffs. Fill in the blanks by choosing the appropriate terms from the following list:

call, exercise, put. (LO23-1) A(n) ______ option gives its owner the opportunity to buy a stock at a specific price, which is generally called the ______ price. A(n) ______ option gives its owner the opportunity to sell stock at a specified ______ price.

2. Option Payoffs. Turn back to Table 23.2 , which lists prices of various Apple options. Use the data in the table to calculate the payoff and the profits for investments in each of the following July maturity options, assuming that the stock price on the expiration date is $420. (LO23-1)

a. Call option with exercise price of $390 b. Put option with exercise price of $390 c. Call option with exercise price of $420 d. Put option with exercise price of $420 e. Call option with exercise price of $450 f. Put option with exercise price of $450

3. Option Payoffs. (LO23-1)

a. Turn back again to Table 23.2 , which lists prices of various Apple options. Use the data in the table to calculate the payoff and the profits for investments in each of the following July maturity options, assuming that the stock price on the expiration date is $440. i. Call option with exercise price of $390 ii. Put option with exercise price of $390 iii. Call option with exercise price of $420 iv. Put option with exercise price of $420 v. Call option with exercise price of $450 vi. Put option with exercise price of $450

b. Now repeat part (a), assuming that the stock price is $400.

4. Option Payoffs. (LO23-1)

a. Note Figure 23.7 a. Match the graph with one of the following positions: i. Call buyer ii. Call seller iii. Put buyer iv. Put seller

b. Now do the same with Figure 23.7 b.

5. Option Payoffs. “The buyer of a call and the seller of a put both hope that the stock price will rise. Therefore the two positions are identical.” Is the speaker correct? (LO23-1)

finance

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FIGURE 23.7 See Problem 4.

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(a) (b)

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680 Part Seven Special Topics

6. Option Payoffs. Suppose that you hold a share of stock and a put option on that share with an exercise price of $100. What is the value of your portfolio when the option expires if: (LO23-1)

a. The stock price is below $100? b. The stock price is above $100?

7. Option Payoffs. Mixing options and securities can often create interesting payoffs. For each of the following combinations, show what the payoff would be when the option expires if (i) the stock price is below the exercise price and (ii) the stock price is above the exercise price. Assume that each option has the same exercise price and expiration date. (LO23-1)

a. Buy a call and invest the present value of the exercise price in a bank deposit. b. Buy a share and a put option on the share. c. Buy a share, buy a put option on the share, and sell a call option on the share. d. Buy a call option and a put option on the share.

8. Option Payoffs. Look at Figure 23.8 , which shows the possible future payoffs in October 2013 from a particular package of investments. Incidentally, this package of investments is called a “straddle” by option buffs. (LO23-1)

a. What package of investments would provide you with this set of payoffs? b. How much would the package have cost you in April 2013? (See Table 23.2 .) c. Would it have made sense to hold this package if you thought that the price of Apple stock

was unlikely to change much?

9. Option Values. Look at the data in Table 23.2 . (LO23-2)

a. What is the price of a call option with an exercise price of $420 and expiration in July 2013? What if expiration is in January 2014?

b. Why do you think the January 2014 calls cost more than the July 2013 calls? c. Is the same true of put options? Why?

10. Option Values. Answer the questions below by choosing from the following terms: stock price; stock price – exercise price; the greater of zero or stock price – exercise price; the lesser of zero or stock price – exercise price; exercise price (LO23-2)

a. Which is the lower bound to the price of a call option? b. Which is the upper bound?

11. Option Values. What is a call option worth if: (LO23-2)

a. The stock price is zero? b. The stock price is extremely high relative to the exercise price?

12. Option Values. Table 23.2 shows call options on Apple stock with the same exercise date in October 2013 and with exercise prices $390, $420, and $450. Notice that the price of the middle call option (with exercise price $420) is less than halfway between the prices of the other two calls (with exercise prices $390 and $450). Suppose that this were not the case. For example, suppose that the price of the middle call were the average of the prices of the other two calls. Show that if you sell two of the middle calls and use the proceeds to buy one each of the other calls, your proceeds in October may be positive but cannot be negative despite the fact that your net outlay today is zero. What can you deduce from this example about option pricing? (LO23-2)

13. Option Values. How does the price of a put option respond to the following changes, other things equal? Does the put price go up or down? (LO23-2)

FIGURE 23.8 This strategy provides a payoff of $0 if the Apple stock price remains at $420 and a payoff of $420 if Apple’s stock price either falls to zero or rises to $840. See Problem 8.

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Apple’s stock price in October

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$420 $840

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a. Stock price increases. b. Exercise price is increased. c. Risk-free interest rate increases. d. Expiration date of the option is extended. e. Volatility of the stock price falls. f. Time passes, so the option’s expiration date comes closer.

14. Option Values. (LO23-2)

a. Circular File stock is selling for $25 a share. You see that call options on the stock with exer- cise price $20 are selling at $3. What should you do? What will happen to the option price as investors identify this opportunity?

b. Now you observe that put options on Circular File with exercise price $30 are selling for $4. What should you do?

15 Option Values. As manager of United Bedstead you own substantial executive stock options. These options entitle you to buy the firm’s shares during the next 5 years at a price of $100 a share. The plant manager has just outlined two alternative proposals to reequip the plant. Both proposals have the same net present value, but project A is substantially riskier than B. At first you are undecided which to choose, but then you selfishly remember your stock options. Which project is better for your wealth? (LO23-2)

16. Real and Financial Options. Fill in the blanks. (LO23-3)

a. An oil company acquires mining rights to a silver deposit. It is not obliged to mine the silver, however. The company has effectively acquired a ______ option, where the exercise price is the cost of opening the mine and extracting the silver.

b. Some preferred shareholders have the right to redeem their shares at par value after a speci- fied date. (If they hand over their shares, the firm sends them a check equal to the shares’ par value.) These shareholders have a ______ option.

c. A firm buys a standard machine with a ready secondhand market. The secondhand market gives the firm a ______ option.

17. Real Options. Describe each of the following situations in the language of options. State in each case whether the situation involves a call or a put and the option’s exercise price. (LO23-3)

a. A company has drilling rights to undeveloped heavy crude oil in southern California. Devel- opment and production of the oil now is a negative-NPV endeavor. The break-even price is $180 per barrel, versus a spot price of $140. However, the decision to develop can be put off for up to 5 years.

b. A restaurant produces net cash flows, after all out-of-pocket expenses, of $700,000 per year. There is no upward or downward trend in the cash flows, but they fluctuate. The real estate occupied by the restaurant is owned, and it could be sold for $5 million.

18. Real Options. Price support systems for various agricultural products have allowed farmers to sell their crops to the government for a specified “support price.” What kind of option has the government given to the farmers? What is the exercise price? (LO23-3)

19. Real Options. After dramatic increases in oil prices in the 1970s, the U.S. government funded several projects to create synthetic oil or natural gas from abundant U.S. supplies of coal and oil shale. Although the cost of producing such synthetic fuels at the time was greater than the price of oil, it was argued that the projects still could be justified for their insurance value since the cost of synthetic fuel would be essentially fixed while the price of oil was risky. Evaluate the synthetic fuel program as an option on fuel sources. Is it a call or a put option? What is the exercise price? How would uncertainty in the future price of oil affect the amount the United States should have been willing to spend on such projects? (LO23-3)

20. Financial Options. A 10-year maturity convertible bond with a 6% coupon on a company with a bond rating of Aaa is selling for $1,050. Each bond can be exchanged for 20 shares, and the stock price currently is $50 per share. Other Aaa-rated bonds with the same maturity would sell at a yield to maturity of 8%. (LO23-4)

a. What is the value of the bondholders’ call option? b. What is the difference between the value of the convertible and the value of the shares it can

be converted into?

21. Financial Options. Some investment management contracts give the portfolio manager a bonus proportional to the amount by which a portfolio return exceeds a specified threshold. (LO23-4)

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682 Part Seven Special Topics

a. In what way is this an implicit call option on the portfolio? b. Can you think of a way in which such contracts can lead to incentive problems? For exam-

ple, what happens to the value of the prospective bonus if the manager invests in very vola- tile stocks?

22. Financial Options. The Rank and File Company is considering a stock issue to raise $50 mil- lion. An underwriter offers to guarantee the success of the issue by buying any unwanted stock at the $25 issue price. The underwriter’s fee is $2 million. (LO23-4)

a. What kind of option does Rank and File acquire if it accepts the underwriter’s offer? b. What determines the value of the option?

23. Financial Options. (LO23-4)

a. Some banks have offered their customers an unusual type of time deposit. The deposit does not pay any interest if the market falls, but instead the depositor receives a proportion of any rise in the Standard & Poor’s Index. What implicit option do the investors hold? How should the bank invest the money in order to protect itself against the risk of offering this deposit?

b. You can also make a deposit with a bank that does not pay interest if the market index rises but makes an increasingly large payment as the market index falls. How should the bank protect itself against the risk of offering this deposit?

24. Financial Options. The FDIC insures bank deposits. If a bank’s assets are insufficient to pay off all depositors, the FDIC will contribute enough money to ensure that all depositors can be paid off in full. (We ignore the $250,000 maximum coverage on each account.) In what way is this guarantee of deposits the provision of a put option by the FDIC? ( Hint: Write out the funds the FDIC will have to contribute when bank assets are less than deposits owed to depositors.) What is the exercise price of the put option? (LO23-4)

CHALLENGE PROBLEMS 25. Option Payoffs. Look at Figure 23.9 , which shows the possible future payoffs in October 2013

from a particular package of investments. This package of investments is called a “butterfly” by option buffs. (LO23-1)

a. What package of investments would provide you with this set of payoffs? b. How much would the package have cost you in April 2013? (See Table 23.2 .) c. Would it have made sense to hold this package if you thought that the price of Apple stock

was unlikely to change much?

26. Option Values. Look again at the Apple call option that we valued in Section 23.2. Suppose that by the end of October 2013 the price of Apple stock could double to $840 or halve to $210. Everything else is unchanged from our example. (LO23-2)

a. What would be the value of the Apple call in October 2013 if the stock price is $840? b. What would be the value of the call if the stock price in October is $210? c. A strategy of buying three calls provides exactly the same payoffs as borrowing the present

value of $ X from the bank and buying two shares. What is X? d. What is the net cash flow in April 2013 from the policy of borrowing PV($ X ) and buying

two shares?

FIGURE 23.9 This strategy provides a total payoff of $30 if the stock price is $420 and a payoff of zero if Apple’s stock price is either (a) $390 or less or (b) $450 or more. See Problem 25.

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Chapter 23 Options 683

WEB EXERCISES 1. You can find option prices on finance.yahoo.com . Enter the company symbol and then click on

Options. Try looking up option prices for Intel (INTC) and Pfizer (PFE). Does the price of calls increase or decrease with (a) the exercise price and (b) time to expiration? Would your answer be the same for puts? Why or why not?

2. Try using the Black-Scholes model to value a call option on Google or Amazon . The inputs are the same as those in our simple valuation example, except that instead of putting in the spread of possible stock prices, you must put in the standard deviation of stock returns. You can find estimates of the standard deviation of Google and Amazon in Table 11.5. (At the time of writing neither firm pays a dividend.) How different are the values you obtain from the prices shown on finance.yahoo.com? What happens to the option value if you change the standard deviation? Can you explain?

3. Find IBM’s most recent income statement. What was the value that IBM assigned to the stock options it granted its employees in the most recent year? How did IBM estimate the value?

e. What is the value of the call option? f. We have now assumed greater stock volatility than in our example in Section 23.2. Has this

increased or decreased the value of the option?

27. Option Values. Look once more at the Apple call option that we valued in Section 23.2. Sup- pose (just suppose) that the interest rate on bank loans is 20%. Recalculate the value of the Apple call option. What does this tell you about the relationship between interest rates and the value of a call? (LO23-2)

28. Option Values. (LO23-2)

a. Use the Black-Scholes formula to find the value of a call option on the following stock. (You can find the spreadsheet in this chapter as well as in Connect.)

i. Time to expiration 1 year ii. Standard deviation 40% per year iii. Exercise price $50 iv. Stock price $50 v. Interest rate 4% (effective annual yield)

b. Now recalculate the value of this call option, but use the following parameter values. Each change should be considered independently. Confirm that the value of the option changes in agreement with the prediction of Table 23.4 .

i. Time to expiration 2 years ii. Standard deviation 50% per year iii. Exercise price $60 iv. Stock price $60 v. Interest rate 6%

c. In which case did increasing the value of the input not increase your calculation of option value?

29. Option Values. Option prices are determined in part by volatility, and traders sometimes use the volatility estimates built into option prices to assess market conditions. The volatility estimate built into S&P 500 options may be found at Yahoo! Finance (get quotes for ticker symbol VIX). If you look at the historical plot of the VIX, you’ll see that it spikes during periods of turbulence (e.g., the recent subprime crisis or the lead-up to the invasion of Iraq), and for this reason it is often called a “fear gauge.” Let’s see how traders back out these estimates of volatility from option prices. To do so, consider the option in the previous problem. Assume that option traders see the option selling at a price of $9.50 and wonder what volatility level this price implies. (LO23-2)

a. Go to the Black-Scholes spreadsheet in this chapter (available in Connect) and go to the sheet Implied Volatility. In the box on the right enter the value that you have just calculated for the call option. Press Find Std Dev and you will see the option’s implied volatility, that is, the volatility level implied by its market price. This sort of inference is the basis for the VIX.

b. What happens to implied volatility if you enter a lower call value? Why has it decreased?

Templates can be found in Connect.

Templates can be found in Connect.

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684 Part Seven Special Topics

Note: PV($30) at an interest rate of 1% for 3 months is 30/1.01 = $29.70.

Payoff in 3 Months If Stock Price Equals:

Cash Flow Today $15 $60

Strategy A Buy three calls ? $ 0 1$ 90 Strategy B Buy two shares 2$60 1$30 1$120 Borrow PV($30) 1 29.70 2 30 2 30

2$30.30 $ 0 1$ 90

SOLUTIONS TO SELF-TEST QUESTIONS 23.1 a. The call with exercise price $450 costs $31.05. If the stock price at the expiration date is

$360, the call expires valueless and the investor loses the entire $31.05. If the stock price is $510, the value of the call at expiration is $510  −  $450  =  $60 and the investor’s profit is $60  −  $31.05  =  $28.95.

b. The put with exercise price $450 costs $67.90. If the stock price at the expiration date is $360, the value of the put is $450  −   $360  =   $90 and the investor’s profit is $90  −  $67.90  =  $22.10. If the stock price is $510, the put expires valueless and the inves- tor loses the entire $67.90.

23.2 a. The call seller receives $14.20 for writing the call. If the stock price at expiration is $420, the call expires valueless and the investor keeps the entire $14.20 as a profit. If the stock price is $480, the value of the call at expiration is $480  −  $450  =  $30. In other words, the call seller must deliver a stock worth $480 for an exercise price of only $450. The inves- tor’s net profit is negative at $14.20  −  $30  =   − $15.80. The call seller makes a loss when- ever the value of the call at expiration is more than the initial premium received for writing the option. In other words, he loses if the stock price is above $450  +  $14.20  =  $464.20.

b. The put seller receives $45.90 for writing the put. If the stock price at expiration is $420, the final value of the put is $450  −   $420  =   $30. In other words, the put seller must pay an exercise price of $450 for a stock worth only $420. The investor’s net profit is $45.90  −  $30  =  $15.90. If the stock price is $480, the put expires valueless and the put seller keeps the entire $45.90 as a profit. The put seller makes a loss when the value of the put at expiration is greater than the initial premium received for writing the option. In other words, he loses if the stock price is below $450  −  $45.90  =  $404.10.

23.3 Put-call parity states that price of stock  +  price of put  =  price of call  +  present value of exer- cise price. Therefore, in the case of Witterman,

$55 + price of put = $8.05 + $60

1.04

and price of put  =  $8.05  +  $57.69  −  $55  =  $10.74.

23.4 The value of a put option is higher when the exercise price is higher. You would be willing to pay more for the right to sell a stock at a high price than the right to sell it at a low price.

23.5 First consider the payoff to the put holder in the lower-volatility scenario:

Stock price $360 $480 Put value $ 60 0

In the higher-volatility scenario, the value of the stock can be $300 or $540. Now the payoff to the put is

Stock price $300 $540 Put value $120 0

The expected value of the payoff of the put is higher in the high-volatility scenario.

23.6 The payoffs are as follows:

The initial net cash outflow from strategy B is $30.30. Since the three calls offer the same payoffs in the future, they must also cost $30.30. One call is worth 30.30/3  =  $10.10.

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Chapter 23 Options 685

23.7 a. The developer has the option to sell the potential housing development to the country club. This abandonment option is like a put that guarantees a minimum payoff from the investment.

b. The exercise price of the option is the price at which it can be sold to the country club. The asset value is the present value of the project if maintained as a housing development. If this value is less than the value as a golf course, the project will be sold.

c. The abandonment option increases NPV by placing a lower bound on the possible payoffs from the project.

23.8 a. Conversion value  =  39.5491  ×  $40  =  $1,582. Conversion price  =  $1,000/39.5491  =  $25.29 (unchanged).

b. Bond value  =  $27.50/1.06875  +  $27.50/1.06875 2   +  $27.50/1.06875 3   +  $27.50/1.06875 4

+  27.50/1.06875 5   + 1,027.50/1.068756 = $802.62.

23.9 a. In 5 years, the bond will be a 15-year maturity bond. The bondholder can sell the bond back to the firm at face value. The bondholder therefore has a put option to sell a 15-year bond for face value even if interest rates have risen and the bond would otherwise sell below face value.

b. The exercise price is the face value of the bond. c. The bondholder will sell the bond back to the company if interest rates increase or the

company’s credit deteriorates. d. More valuable. The bondholder now has the right, but not the obligation, to sell the bond at

face value in 5 years.

SOLUTIONS TO SPREADSHEET QUESTIONS 1.

0

20

40

60

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300 350 400 450 500 550 600

Stock price

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300 2.00 325 4.71 350 9.48 375 16.85 400 27.10 425 40.27 450 56.13 475 74.31 500 94.39 525 115.93 550 138.57 575 161.98 600 185.94

2.

The initial slope between 300 and 325 is (4.71 - 2.00)/25 = .108. As the stock price increases, the slope approaches 1.

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686

Risk Management

LEARNING OBJECTIVES

After reading this chapter, you should be able to:

24-1 Understand why companies hedge to reduce risk.

24-2 Use options, futures, and forward contracts to devise simple hedging strategies.

24-3 Explain how companies can use swaps to change the risk of securities that they have issued.

R E L A T E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T F I N A N C E .

24 CHAPTE R

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687

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W e often assume that risk is beyond our con-trol. A business is exposed to unpredictable changes in raw material costs, tax rates, technology, and a long list of other variables. There’s

nothing the manager can do about it.

This is not wholly true. To some extent a manager

can select which risks to accept. For example, in the

previous chapter we saw that companies can con-

sciously affect the risk of an investment by building in

flexibility. A company that reduces the cost of bailing

out of a project by using standardized equipment is

taking less risk than a similar firm that uses special-

ized equipment with no alternative uses. In this case

the option to resell the equipment serves as an insur-

ance policy.

Sometimes, rather than building flexibility into the

project, companies accept the risk but then use

financial instruments to offset it. This practice of taking

offsetting risks is known as hedging. In this chapter we

will explain how hedging works and we will describe

some of the specialized financial instruments that

have been devised to help manage risk. These instru-

ments include options, futures, forwards, and swaps.

Each of these instruments provides a payoff that

depends on the price of some underlying commod-

ity or financial asset. Because their payoffs derive

from the prices of other assets, they are often known

collectively as derivative instruments (or derivatives

for short). 1

This is just about the shortest chapter in the book,

little more than a chef’s taster. It provides only a quick

overview of a huge topic. For example, it doesn’t

explain how to value derivatives or how to set up

a hedge. But most companies employ derivatives

extensively to adjust their risk, and it is important that

you have some basic understanding of what they

are and how they can be used (and misused).

1 Derivatives often conjure up an image of wicked specula- tors. Derivative instruments attract their share of specula- tors, some of whom may be wicked, but they are also used by sober and prudent businesspeople who simply want to reduce risk.

Sp e

c ia

l T o

p ic

s

Risk management does not mean avoiding risk. It means deciding what risks to take.

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688 Part Seven Special Topics

24.1 Why Hedge? In this chapter we will explain how companies hedge the risks of their business. But first we should give some of the reasons why they do it.

Surely, the answer to this question is obvious. Isn’t less risk always better than more? Well, not necessarily. Even if hedging is costless, transactions undertaken solely to reduce risk are unlikely to add value. There are two basic reasons for this:

• Reason 1: Hedging is a zero-sum game. A company that hedges a risk does not eliminate it. It simply passes the risk on to someone else. For example, suppose that a heating-oil distributor agrees with a refiner to buy all of next winter’s heating-oil deliveries at a fixed price. This contract is a zero-sum game, because the refiner loses what the distributor gains and vice versa. If next winter’s price of heating oil turns out to be unusually high, the distributor wins from having locked in a below- market price but the refiner is forced to sell below market. Conversely, if the price of heating oil is unusually low, the refiner wins because the distributor is forced to buy at the high fixed price. Of course, neither party knows next winter’s price at the time that the deal is struck, but they consider the range of possible prices and negotiate terms that are fair (zero NPV) on both sides of the bargain.

• Reason 2: Investors’ do-it-yourself alternative. Companies cannot increase the value of their shares by undertaking transactions that investors can easily do on their own. We came across this idea when we discussed whether leverage increases company value, and we met it again when we came to dividend policy. It also applies to hedg- ing. For example, when the shareholders in our heating-oil distributor invested in the company, they were presumably aware of the risks of the business. If they did not want to be exposed to the ups and downs of energy prices, they could have pro- tected themselves in several ways. Perhaps they own shares in both the distributor and the refiner and do not care whether one wins at the other’s expense.

Of course, shareholders can adjust their exposure only when companies keep investors fully informed of the transactions that they have made. For example, when a group of European central banks announced in 1999 that they would limit their sales of gold, the gold price immediately shot up. Investors in gold-mining shares rubbed their hands at the prospect of rising profits. But when they discovered that some mining companies had protected themselves against price fluctuations and would not benefit from the price rise, the hand-rubbing turned to hand-wringing.

Some stockholders of these gold-mining companies wanted to make a bet on rising gold prices; others didn’t. But all of them gave the same message to manage- ment. The first group said, “Don’t hedge! I’m happy to bear the risk of fluctuat- ing gold prices, because I think gold prices will increase.” The second group said, “Don’t hedge! I’d rather do it myself.”

We have seen that although hedging reduces risk, this doesn’t in itself increase firm value. So when does it make sense to hedge? Sometimes hedging is worthwhile because it makes financial planning easier and reduces the odds of an embarrassing cash shortfall. A shortfall might mean only an unexpected trip to the bank, but on other occasions the firm might have to forgo worthwhile investments, and in extreme cases the shortfall could trigger bankruptcy. Why not reduce the odds of these awkward outcomes with a hedge?

We saw in our discussion of debt policy in Chapter 16 that financial distress can result in indirect as well as direct costs to a firm. Costs of financial distress arise from disruption to normal business operations as well as from the effect that financial dis- tress has on the firm’s investment decisions. The better the risk management policies, the less chance that the firm will incur these costs of distress. As a side benefit, better risk management increases the firm’s debt capacity.

In some cases hedging also makes it easier to decide whether an operating manager deserves a stern lecture or a pat on the back. Suppose that your export division shows

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Chapter 24 Risk Management 689

a 50% decline in profits when the dollar unexpectedly strengthens against other cur- rencies. How much of that decrease is due to the exchange rate shift and how much to poor management? If the company had protected itself against the effect of exchange rate changes, it’s probably bad management. If it wasn’t protected, you have to make a judgment with hindsight, probably by asking, “What would profits have been if the firm had hedged against exchange rate movements?”

Finally, hedging extraneous events can help focus the operating manager’s atten- tion. We know we shouldn’t worry about events outside our control, but most of us do anyway. It’s naive to expect the manager of the export division not to worry about exchange rate movements if his bottom line and bonus depend on them. The time spent worrying could be better spent if the company hedged itself against such movements.

A sensible risk strategy needs answers to the following questions:

• What are the major risks that the company faces, and what are the possible conse- quences? Some risks are scarcely worth a thought, but there are others that might bankrupt the company.

• Is the company being paid for taking these risks? Managers are not paid to avoid all risks, but if they can reduce their exposure to risks for which there are no com- pensating rewards, they can afford to place larger bets when the odds are stacked in their favor.

• Can the company take any measures to reduce the probability of a bad outcome or to limit its impact? For example, most businesses install alarm and sprinkler systems to prevent damage from fire and invest in backup facilities in case damage does occur.

• Can the company purchase fairly priced insurance to offset any losses? Insurance companies have some advantages in bearing risk. In particular, they may be able to spread the risk across a portfolio of different insurers.

• Can the company use derivatives, such as options or futures, to hedge the risk? In the remainder of this chapter we explain when and how derivatives may be used.

The Evidence on Risk Management There are three principal ways to manage risk. First, the firm can reduce risk by build- ing flexibility into its operations. For example, a petrochemical plant that is designed to use either oil or natural gas as a feedstock reduces the threat of an unfavorable shift in the price of raw materials. Or think of a company that reduces the risk of a disaster by test marketing a new product before launching it nationally. Both firms are using real options to limit their risk. A second way to reduce risk is to buy an insurance pol- icy against such hazards as fire, accidents, and theft. Finally, the firm may enter into specialized financial contracts that fix its costs or prices. These contracts are known collectively as derivatives, and they include options, futures, and swaps.

A survey of the world’s 500 largest companies found that almost all the companies use derivatives in some way to manage their risk. 2 Ninety-four percent employ them to manage currency risk. Eighty-eight percent use them to control interest rate risk and 51% to manage the risk of fluctuations in commodity prices.

Risk policies differ. For example, some natural resource companies work hard to hedge their exposure to price fluctuations; others shrug their corporate shoulders and let prices wander as they may. Explaining why some hedge and others don’t is not easy. One study of oil and gas companies found that the firms hedged most if they had high debt ratios, no debt ratings, and low dividend payouts. 3 It seems that for these firms, hedging programs were designed to reduce the likelihood of financial distress and to improve the firms’ access to debt finance.

derivatives Securities whose payoffs are determined by the values of other financial variables such as prices, exchange rates, or interest rates.

2 International Swap Dealers Association (ISDA), “2009 Derivatives Usage Survey,” www.isda.org . 3 G. D. Haushalter, “Financing Policy, Basis Risk and Corporate Hedging,” Journal of Finance 55 (February 2000), pp. 107–152.

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690 Part Seven Special Topics

24.2 Reducing Risk with Options In the previous chapter we introduced you to put and call options. Managers regularly buy options on currencies, interest rates, and commodities to limit their downside risk. Many of these options are traded on options exchanges, but often they are simply pri- vate deals between the corporation and a bank.

Consider, for example, the problem faced by the Mexican government. Thirty per- cent of its revenue comes from Pemex, the state-owned oil company. So, if oil prices fall, the government may be compelled to reduce its planned spending.

The government’s solution was to establish a floor on the price at which it could sell 211 million barrels of oil, equivalent to the country’s total expected net oil exports in 2012. To do this, it bought put options that gave it the right to sell oil at an exercise price of $85 per barrel. If oil prices rose above this figure, Mexico would reap the benefit. But if oil prices fell below $85 a barrel, the payoff to the put options would exactly offset the revenue shortfall. In effect, the options put a floor of $85 a barrel on the value of its oil.

Figure 24.1 illustrates the nature of Mexico’s insurance strategy. Panel a shows the revenue derived from selling 211 million barrels of oil. As the price of oil rises or falls, so do the government’s revenues. Panel b shows the payoffs to the government’s options to sell 211 million barrels at $85 a barrel. The payoff on these options rises as oil prices fall below $85 a barrel. This payoff exactly offsets any decline in oil reve- nues. Panel c shows the government’s total revenues after buying the put options. For prices below $85 per barrel, revenues are fixed at 211 × $85 = $17,935 million. But for every dollar that oil prices rise above $85, revenues increase by $211 million. The profile in panel c should be familiar to you. It represents the payoffs to the protective put strategy that we first encountered in Section 23.1. 4

24.3 Futures Contracts Suppose you are a wheat farmer. You are optimistic about next year’s wheat crop, but still you can’t sleep. You are worried that when the time comes to sell the wheat, prices may have fallen through the floor. The cure for insomnia is to sell wheat futures. In this case, you agree to deliver so many bushels of wheat in (say) September at a price that is set today. Do not confuse this futures contract with an option, where the holder has a choice whether to make delivery; your futures contract is a firm promise to deliver wheat at a fixed selling price.

A miller is in the opposite position. She needs to buy wheat after the harvest. If she would like to fix the price of this wheat ahead of time, she can do so by buying wheat futures. In other words, she agrees to take delivery of wheat in the future at a price that is fixed today. The miller also does not have an option; if she still holds the futures contract when it matures, she is obliged to take delivery.

Let’s suppose the farmer and the miller strike a deal. They enter a futures contract. What happens? First, no money changes hands when the contract is initiated. 5 The miller agrees to buy wheat at the futures price on a stated future date (the contract maturity date). The farmer agrees to sell at the same price and date. Second, the futures contract is a binding obligation, not an option. Options give the right to buy or sell if buying or selling turns out to be profitable. The futures contract requires the farmer to

4 The Mexican government option position was slightly more complicated than our description. On some of the production, it agreed to take a hit if prices fell below $60 a barrel. On this portion of production, government revenues were protected only against prices between $60 and $80.

futures contract Exchange-traded promise to buy or sell an asset in the future at a prespecified price.

5 Actually, each party will be required to set up a margin account to guarantee performance on the contract. Despite this, the futures contract still may be considered as essentially requiring no money down. First, the amount of margin is small. Second, it may be posted in interest-bearing securities, so that the parties to the trade need not suffer an opportunity cost from placing assets in the margin account.

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Chapter 24 Risk Management 691

sell and the miller to buy regardless of who profits and who loses. Just remember, no money changes hands when a futures contract is entered into. The contract is a binding obligation to buy or sell at a fixed price at contract maturity.

The profit on the futures contract is the difference between the initial futures price and the ultimate price of the asset when the contract matures. For example, if the futures price is originally $7 and the market price of wheat turns out to be $7.50, the farmer delivers and the miller receives the wheat for a price $.50 below market value. The farmer loses $.50 per bushel and the miller gains $.50 per bushel as a result of the futures transaction. In general, the seller of the contract benefits if the price initially locked in turns out to exceed the price that could have been obtained at contract matu- rity. Conversely, the buyer of the contract benefits if the ultimate market price of the

FIGURE 24.1 How options protected Mexico against a sharp fall in oil prices

$17.9

$85

Price per barrel

$85

Price per barrel

$85

Price per barrel

$17.9

Sell 211 million barrels of oil at the market price

+ buy put options with $85 exercise price

= lock in minimum price of $85 per barrel

$17.9

R ev

en u

e ($

b ill

io n

s) R

ev en

u e

($ b

ill io

n s)

R ev

en u

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b ill

io n

s)

(a)

(b)

(c)

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692 Part Seven Special Topics

asset turns out to exceed the initial futures price. Therefore, the profits on the futures contract to each party are

Profit to seller = initial futures price - ultimate market price Profit to buyer = ultimate market price - initial futures price

Now it is easy to see how the farmer and the miller can both use the contract to hedge. Consider the farmer’s overall cash flows:

The profits on the futures contract offset the risk surrounding the sales price of wheat and lock in total revenue equal to the futures price. Similarly, the miller’s all-in cost for the wheat also is fixed at the futures price. Any increase in the cost of wheat will be offset by a commensurate increase in the profit realized on the futures contract.

Both the farmer and the miller have less risk than before. The farmer has hedged (that is, offset) risk by selling wheat futures; the miller has hedged risk by buying wheat futures. 6

Cash Flow

Sale of wheat Ultimate price of wheat Futures profi ts Futures price − ultimate price of wheat Total Futures price

6 Neither has eliminated all risk. For example, the farmer still has quantity risk. He does not know for sure how many bushels of wheat he will produce.

Example 24.1 Hedging with Futures Suppose that the farmer originally sold 5,000 bushels of September wheat futures at a price of $7 a bushel. In September, when the futures contract matures, the price of wheat is only $6 a bushel. The farmer buys back the wheat futures at $6 just before maturity, giving him a profit of $1 a bushel on the sale and subsequent repurchase. At the same time he sells his wheat at the spot price of $6 a bushel. His total receipts are therefore $7 a bushel:

You can see that the futures contract has allowed the farmer to lock in total proceeds of $7 a bushel.

Profi t on sale and repurchase of futures $1 Sale of wheat at the September spot price 6 Total receipts $7

Figure 24.2 illustrates how the futures contract enabled the farmer in Example 24.1 to hedge his position. Panel a shows how the value of 5,000 bushels of wheat varies with the spot price of wheat. The value rises by $5,000 for every dollar increase in wheat prices. Panel b is the profit on a futures contract to deliver 5,000 bushels of wheat at a futures price of $7 per bushel. The profit will be zero if the ultimate price of wheat equals the original futures price, $7. The profit on the contract to deliver at $7 rises by $5,000 for every dollar the price of wheat falls below $7. The exposures to the price of wheat depicted in panels a and b obviously cancel out. Panel c shows that the total value of the 5,000 bushels plus the futures position is unaffected by the ultimate price of wheat, and equals $7 × 5,000 = $35,000. In other words, the farmer has locked in proceeds of $7 per bushel, equal to the original futures price.

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Chapter 24 Risk Management 693

The Mechanics of Futures Trading In practice the farmer and miller would not sign the futures contract face-to-face. Instead, each would go to an organized futures exchange such as the Chicago Board of Trade. 7

Table 24.1 shows the price of wheat futures at the Chicago Board of Trade in April 2013, when the price for immediate delivery was about $7 a bushel. Notice that there is a choice of possible delivery dates. If, for example, you were to sell wheat for deliv- ery in May 2013, you would get a lower price than by selling December 2013 futures.

The miller would not be prepared to buy futures contracts if the farmer were free to deliver half-rotten wheat to a leaky barn at the end of a cart track. Futures trading is

7 The Chicago Board of Trade is part of the CME Group.

FIGURE 24.2 The farmer can use wheat futures to hedge the value of the crop. See Example 24.1.

$35,000

$7

Price per bushel

Price per bushel

Price per bushel

$35,000

$7

$35,000

V al

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o f

w h

ea t

P ro

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u tu

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To ta

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Sell 5,000 bushels of wheat at market price

+ sell 5,000 bushels of wheat futures at $7 a bushel

= certain income of $35,000 (i.e., $7 per bushel)

(c)

(b)

(a)

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694 Part Seven Special Topics

Suppose that 2 days after taking out the futures contract the price of Septem- ber wheat increases from $7.05 to $7.20 a bushel. What additional payments will be made by or to the farmer and the miller? What will be their remaining obligation at the end of this second day?

Self-Test 24.1

TABLE 24.1 The price of wheat futures at the Chicago Board of Trade on April 19, 2013

Delivery Date Price per Bushel

May 2013 $7.09 July 2013 7.12 September 2013 7.18 December 2013 7.32 March 2014 7.45 May 2014 7.44

Source: The Chicago Board of Trade website, www.cmegroup.com .

possible only because the contracts are highly standardized. For example, in the case of wheat futures, each contract calls for the delivery of 5,000 bushels of wheat of a specified quality at a warehouse in Chicago, Toledo, or Burns Harbor.

When you buy or sell a futures contract, the price is fixed today, but payment is not made until later. However, you will be asked to put up some cash or securities as margin to demonstrate that you are able to honor your side of the bargain.

In addition, futures contracts are marked to market. This means that each day any profits or losses on the contract are calculated; you pay the exchange any losses and receive any profits. For example, our farmer agreed to deliver 5,000 bushels of wheat at $7 a bushel. Suppose that the next day the price of wheat futures increases to $7.05 a bushel. The farmer, who has agreed to deliver corn at only $7.00 a bushel, has a loss of 5,000 × $.05 = $250 and must pay this sum to the exchange. You can think of the farmer as buying back his futures position each day and then opening up a new position. Thus after the first day the farmer has realized a loss on his trade of $.05 a bushel and now has an obligation to deliver wheat for $7.05 a bushel.

Of course our miller is in the opposite position. The rise in the futures price leaves her with a profit of 5 cents a bushel. The exchange will therefore pay her this profit. In effect the miller sells her futures position at a profit and opens a new contract to take delivery at $7.05 a bushel.

The price of wheat for immediate delivery is known as the spot price. When the farmer sells wheat futures, the price that he agrees to take for his wheat may be very different from the spot price. But the future eventually becomes the present. As the date for delivery approaches, the futures contract becomes more and more like a spot contract and the price of the futures contract snuggles up to the spot price.

The farmer may decide to wait until the futures contract matures and then deliver wheat to the buyer. But in practice such delivery is rare, for it is more convenient for the farmer to buy back the wheat futures just before maturity. 8

spot price Price that is paid for immediate delivery.

8 In the case of some of the financial futures described later, you cannot deliver the asset. At maturity the buyer simply receives (or pays) the difference between the spot price and the price at which he or she has agreed to purchase the asset.

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The strange case of WTI

Commodity and Financial Futures We have shown how the farmer and the miller can both use wheat futures to hedge their risk. It is also possible to trade futures in a wide variety of other commodities, such as sugar, soybean oil, pork bellies, orange juice, crude oil, and copper.

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Chapter 24 Risk Management 695

Commodity prices can bounce up and down like a bungee jumper. For example, at the start of 2009 copper prices were about $3,000 a ton. Just 2 years later they were over $10,000. For a large user of copper, such as General Cable, these price fluctua- tions could knock the company badly off course. General Cable therefore reduces its exposure to movements in the price of copper and other metals by hedging with com- modity futures. A number of copper producers have also found that hedging increases their debt capacity. So, when the Canadian company Equinox needed to borrow $584 million to finance its new Zambian mine, the lenders first insisted that Equinox reduce its exposure to fluctuations in the copper price by hedging 30% of its planned output.

For many firms, the wide fluctuations in interest rates and exchange rates have become at least as important a source of risk as changes in commodity prices. You can use financial futures to hedge against these risks.

Financial futures are similar to commodity futures, but instead of placing an order to buy or sell a commodity at a future date, you place an order to buy or sell a financial asset at a future date. You can use financial futures to pro- tect yourself against fluctuations in short- and long-term interest rates, exchange rates, and the level of share prices.

Figure 24.3 shows the explosive growth of worldwide futures trading. Table 24.2 lists some of the more popular financial futures contracts.

You plan to issue long-term bonds in 9 months but are worried that inter- est rates may have increased in the meantime. How could you use financial futures to protect yourself against a general rise in interest rates?

Self-Test 24.2

TABLE 24.2 Some financial futures contracts Contract Principal Exchange

U.S. Treasury notes and bonds CBT Eurodollar deposits CME Standard & Poor’s Index CME Euro CME Yen CME German government bonds (Bunds) Eurex

Key to abbreviations: CBT Chicago Board of Trade CME Chicago Mercantile Exchange

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Worldwide futures volume

FIGURE 24.3 Worldwide turnover in futures contracts has expanded sharply.

Source: Bank for International Settlements, Quarterly Review, www.bis.org .

0

Commodity futures

Financial futures

2,000

4,000

6,000

8,000

10,000

12,000

C o

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ac ts

( m

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Year

20 11

20 10

20 09

20 08

20 07

20 06

20 05

20 04

20 03

20 02

20 01

20 00

19 99

19 98

19 97

19 96

19 95

19 94

19 93

19 92

19 91

19 90

19 89

19 88

19 87

19 86

20 12

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24.4 Forward Contracts Each day billions of dollars of futures contracts are bought and sold. We have seen that this liquidity is possible only because futures contracts are standardized. Futures con- tracts mature on a limited number of dates each year (take another look at the wheat contract in Table 24.1 ), and the contract size is standardized. For example, a contract may call for delivery of 5,000 bushels of wheat, 100 ounces of gold, or 62,500 British pounds. If the terms of a futures contract do not suit your particular needs, you may be able to buy or sell a forward contract.

Forward contracts are custom-tailored futures contracts. 9 You can write a for- ward contract with any maturity date for delivery of any quantity of goods. For example, suppose that you know that you will need to pay out yen in 3 months’ time. You can fix today the price that you will pay for the yen by arranging with your bank to buy yen forward. At the end of the 3 months, you pay the agreed sum and take deliv- ery of the yen.

forward contract Agreement to buy or sell an asset in the future at an agreed price.

9 One difference between forward and futures contracts is that forward contracts are not marked to market. Thus with a forward contract you settle up any profits or losses when the contract matures.

Example 24.2 Forward Contracts Computer Parts Inc. has ordered memory chips from its supplier in Japan. The bill for ¥53 million must be paid on July 27. The company can arrange with its bank today to buy this number of yen forward for delivery on July 27 at a forward price of ¥99 per dollar. Therefore, on July 27, Computer Parts pays the bank $53 mil- lion/99 = $535,353 and receives ¥53 million, which it can use to pay its Japanese supplier. By committing forward to exchange $535,353 for ¥53 million, its dollar costs are locked in. Notice that if the firm had not used the forward contract to hedge and the dollar had depreciated over this period, the firm would have had to pay a greater amount of dollars. For example, if the dollar had depreciated to JPR90 = USD1, the firm would have had to exchange $588,589 for the ¥53 million necessary to pay its bill. The firm could have used a futures contract to hedge its foreign exchange exposure, but standardization of futures would not allow for delivery of precisely ¥53 million on precisely July 27.

The most active trading in forwards is in foreign currencies, but companies also enter into forward rate agreements (FRAs) that allow them to fix in advance the inter- est rate at which they borrow or lend.

24.5 Swaps Suppose Computer Parts from Example 24.2 decides to produce memory chips instead of purchasing them from outside suppliers. It has issued $100 million in floating-rate bonds to help finance the construction of a new plant. (Recall from Chapter 14 that floating-rate loans make interest payments that go up and down with the general level of interest rates. The coupon payments on the bonds are tied to a specific short-term interest rate.) But the financial manager is concerned that interest rates are becoming more volatile, and she would like to lock in the firm’s interest expenses. One approach would be to buy back the floating-rate bonds and replace them with a new issue of fixed-rate debt. But it is costly to issue new debt to the public; in addition, buying back the outstanding bonds in the market will result in considerable trading costs.

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Chapter 24 Risk Management 697

A better approach to hedge out its interest rate exposure is for the firm to enter an interest rate swap. The firm will pay or “swap” a fixed payment for another payment that is tied to the level of interest rates. Thus if rates do rise, increasing the firm’s inter- est expense on its floating-rate debt, its cash flow from the swap agreement will rise as well, offsetting its exposure.

Suppose the firm pays the LIBOR rate on its floating-rate bonds. (Recall that LIBOR, or London Interbank Offer Rate, is the interest rate at which banks borrow from each other in the eurodollar market. It is the most frequently used short-term interest rate in the swap market.) The firm’s interest expense each year therefore equals the LIBOR rate times $100 million. It would like to transform this obligation into one that will not fluctuate with interest rates.

Suppose that current rates in the swaps market are “LIBOR for 5% fixed.” This means that Computer Parts can enter into a swap agreement to pay 5% on “notional principal” of $100 million to a swap dealer and receive payment of the LIBOR rate on the same amount of notional principal. The dealer and the firm are called coun- terparties in the swap. The firm pays the dealer .05  ×  $100 million and receives LIBOR × $100 million in return. The firm’s net cash payment to the dealer is there- fore (.05 − LIBOR) × $100 million. (If LIBOR exceeds 5%, the firm receives money from the dealer; if it is less than 5%, the firm pays money to the dealer.) Figure 24.4 illustrates the cash flows paid by Computer Parts and the swap dealer.

Table 24.3 shows Computer Parts’s net payments for three possible interest rates. The total payment on the bond-with-swap agreement equals $5 million regardless of the interest rate. The swap has transformed the floating-rate bond into synthetic fixed- rate debt with an effective coupon rate of 5%. The firm has thus hedged away its inter- est rate exposure without actually having to replace its floating-rate bonds with fixed-rate bonds. Swaps offer a much cheaper way to “rearrange the balance sheet.” 10

There are many other applications of interest rate swaps. A portfolio manager who is holding a portfolio of long-term bonds but is worried that interest rates might increase, causing a capital loss on the portfolio, can enter a swap to pay a fixed rate and receive

swap Arrangement by two counterparties to exchange one stream of cash flows for another.

10 You might wonder what’s in this arrangement for the swap dealer. The dealer will profit by charging a bid- ask spread. Since the dealer pays LIBOR in return for 5% in this swap, it might search for another trader who wishes to receive a fixed rate and pay LIBOR. The dealer will pay a 4.9% rate to that trader in return for the LIBOR rate. So the dealer pays a fixed rate and receives floating with one trader but pays floating and receives fixed with the other. Its net cash flow is thus fixed and equal to .1% of notional principal.

FIGURE 24.4 Interest rate swap. Computer Parts currently pays the LIBOR rate on its outstanding bonds (the arrow on the left). If the firm enters a swap to pay a fixed rate of 5% and receive a floating rate of LIBOR, its exposure to LIBOR will cancel out and its net cash outflow will be a fixed rate of 5%.

Computer Parts Swap dealer LIBOR

to bondholders

5%

LIBOR

LIBOR Rate

4.5% 5.0% 5.5%

Interest paid on fl oating-rate bonds (= LIBOR × $100 million)

$4,500,000 $5,000,000 $5,500,000

+  Cash payment on swap [= (.05 − LIBOR)  × notional principal of $100 million]

500,000 0 −500,000

Total payment $5,000,000 $5,000,000 $5,000,000

TABLE 24.3 An interest rate swap can transform floating- rate bonds into synthetic fixed-rate bonds.

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698 Part Seven Special Topics

Consider the portfolio manager who is holding a $100 million portfolio of long-term 5% coupon bonds and wishes to reduce price risk by transforming the holdings into a synthetic floating-rate portfolio. Assume that the portfolio currently pays a 5% fixed rate and that swap dealers currently offer terms of 5% fixed for LIBOR. What swap would the manager establish? Show the total income on the fund in a table like Table 24.3 , and illustrate the cash flows in a diagram like Figure 24.4 .

Self-Test 24.3

Example 24.3 Currency Swaps Suppose that the Possum Company wishes to borrow Swiss francs (SFr) to help finance its European operations. Since Possum is better known in the United States, the financial manager believes that the company can obtain more attractive terms on a dollar loan than on a Swiss franc loan. Therefore, the company borrows $10 million for 5 years at 5% in the United States. At the same time Possum arranges with a swap dealer to trade its future dollar liability for Swiss francs. Under this arrangement the dealer agrees to pay Possum sufficient dollars to service its dollar loan, and in exchange Possum agrees to make a series of annual payments in Swiss francs to the dealer.

Possum’s cash flows are set out in Table 24.4 . Line 1 shows that when Possum takes out its dollar loan, it promises to pay annual interest of $.5 million and to repay the $10 million that it has borrowed. Lines 2a and 2b show the cash flows from the swap, assuming that the spot exchange rate for Swiss francs is $1 = SFr2. Possum hands over to the dealer the $10 million that it borrowed and receives in exchange 2 × $10 million = SFr20 million. In each of the next 4 years the dealer pays Possum $.5 million, which it uses to pay the annual interest on its loan. In year 5 the dealer pays Possum $10.5 million to cover both the final year’s interest and the repayment of the loan. In return for these future dollar receipts, Possum agrees to pay the dealer SFr1.2 million in each of the next 4 years and SFr21.2 million in year 5.

Notice that Possum’s payments equal those it would have made if it had bor- rowed SFr20 million at an interest rate of 6%. Therefore, the combined effect of Pos- sum’s two steps (line 3) is the conversion of its 5% dollar loan into a 6% Swiss franc loan. The device that makes this possible is the currency swap.

a floating rate, thereby converting the holdings into a synthetic floating-rate portfolio (see Self-Test 24.3). Or a pension fund manager might identify some money market securities that are paying excellent yields compared with other comparable-risk short- term securities. However, the manager might believe that short-term assets are inap- propriate for the portfolio. The fund can receive the interest rate on these high-yielding securities and enter a swap in which it receives a fixed rate and pays a floating rate based on a lower-yielding money market security. It thus captures the benefit of the advantageous relative yields on its securities but still establishes a portfolio with the fixed interest rate risk characteristic of long-term bonds.

There are many variations on the interest rate swap. For example, currency swaps allow firms to exchange a series of payments in dollars (which may be tied to a fixed or floating rate) for a series of payments in another currency (which also may be tied to a fixed or floating rate). These swaps can therefore be used to manage exposure to exchange rate fluctuations.

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Chapter 24 Risk Management 699

24.6 Innovation in the Derivatives Market Almost every day some new derivative contract seems to be invented. At first there may be just a few private deals between a bank and its customers, but if the contract proves popular, one of the futures exchanges may try to muscle in on the business.

Derivatives dealers try to identify the major risks that face businesses and then design a contract that will allow them to lay off these risks. For example, a major haz- ard for many financial institutions is the possibility that a large customer will get into difficulties and default on its debts. Credit default swaps offer a way for the lender to insure against such a default. The provider of the insurance promises to pay out if the borrower defaults on its debts and in return charges a premium for taking on the risk. We described credit default swaps in Chapter 6.

Iron ore prices are volatile. With fluctuating demand from China, iron ore prices nearly tripled between early 2009 and 2011 before slumping over the next year and a half. The futures exchanges reasoned that both producers and users might welcome a contract that allowed them to hedge these price movements. Therefore, in July 2010 the New York Mercantile Exchange (part of the CME Group) introduced a futures contract based on the price of iron ore landed in China.

Real estate businesses and builders worry about fluctuations in house prices. So wouldn’t it be nice if they could stop worrying and hedge themselves against these fluctuations? Well, now they can do so by dealing in real estate futures or options on the Chicago Mercantile Exchange. Real estate futures were launched in 2006 and enable participants to protect themselves against changes in house prices in 10 U.S. cities.

It seems to be very difficult to predict which new contracts will succeed and which will bomb. By the time you read this, iron ore contracts may have been forgotten, and everyone will be talking about the new growth market in _____ derivatives. Perhaps you can help fill in the missing word.

Year 0 Years 1–4 Year 5

$ SFr $ SFr $ SFr

1. Issue dollar loan +10 −.5 −10.5 2. Arrange currency swap a. Possum receives $ −10 +.5 +10.5 b. Possum pays SFr +20 ___ −1.2 −21.2 3. Net cash fl ow 0 +20 0 −1.2 0 −21.2

TABLE 24.4 Cash flows from Possum’s dollar loan and currency swap (figures in millions)

Suppose that the spot exchange rate had been $1  = SFr3 and that Swiss interest rates were 8%. Recalculate the Swiss franc cash flows that the dealer would agree to (line 2b of Table 24.4 ) and Possum’s net cash flows (line 3).

Self-Test 24.4

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700

Finance in Practice The World’s Poorest Man For a while fortune smiled on Kerviel, and by 2007 he had

made a profi t of €1.4 billion. But in January 2008 everything started to unravel. As stock prices collapsed, Kerviel took larger and larger bets that the markets would recover. Every time he lost, Kerviel doubled up on his bets. By mid-January, he had about €50 billion—more than the bank’s total mar- ket capitalization—riding on a market turnaround. By late January the bank had learned the full extent of Kerviel’s posi- tions and frantically moved to close them out. The resulting loss of €4.9 billion amounted to more than 10% of the value of the bank’s equity.

Société Générale’s failure to spot the unauthorized trad- ing was the subject of much criticism. Some commented that a trader who had worked in the back office would be particularly well informed about ways to hide his activities. Banks took comfort in the fact that such a breakdown in con- trols could never happen again—that is, until 2011, when the Swiss Bank UBS revealed that a trader who had been pro- moted from the back office to the Delta One desk had lost over $2 billion in unauthorized trading.

In October 2010 Jérôme Kerviel became the world’s poorest man when a French court sentenced him to 5 years in prison and fi ned him €4.9 billion. Until his arrest 2 years earlier, he had been a trader in the French bank Société Générale. But then it was discovered that he had engaged in unauthorized trading, resulting in record losses for the bank of €4.9 billion, or $7.2 billion.

Kerviel joined the back office of SocGen in 2000. Five years later he realized his dream when he was promoted to be a trader on the Delta One desk, which mainly trades equi- ties, futures, and exchange-traded funds. In most banks the Delta One desk focuses on arbitrage opportunities, and Ker- viel’s job was to exploit small price differences between equity futures contracts, rather than to bet on the market’s direction.

Soon after taking up his new position, Kerviel took an unauthorized bet on a downturn for the market. The trade proved successful and resulted in a profi t of €500,000. Although it was not hedged and exceeded Kerviel’s credit limit, the bank took no action. Spurred on by this success, Kerviel continued to take unhedged bets on the outlook for the market. To hide the fact that his trades were unhedged, he created a series of fi ctitious offsetting trades.

24.7 Is “Derivative” a Four-Letter Word? Our earlier examples of the farmer and the miller showed how derivatives—futures, options, or swaps, for example—can be used to reduce business risk. However, if you were to copy the farmer and sell wheat futures without an offsetting holding of wheat, you would not be reducing risk; you would be speculating.

A successful futures market needs speculators who are prepared to take on risk and provide the farmer and the miller with the protection they need. For example, if an excess of farmers wished to sell wheat futures, the price of futures would be forced down until enough speculators were tempted to buy in the hope of a profit. If there is a surplus of millers wishing to buy wheat futures, the reverse will happen. The price will be forced up until speculators are drawn in to sell.

Speculation may be necessary to a thriving derivatives market, but it can get companies into serious trouble. In 1995 Baring Brothers, a blue-chip British mer- chant bank with a 200-year history, became insolvent. The reason: Nick Leeson, a trader in its Singapore office, had lost $1.4 billion speculating in futures on the Japanese stock market index. Barings has plenty of company. For example, the nearby Finance in Practice box describes how the French bank Société Générale took a $7.2 billion bath from unauthorized trading by one of its staff, and in 2011 the Swiss bank UBS joined the billion-dollar club when a rogue trader notched up losses of $2.3 billion.

Do these horror stories mean that firms should ban the use of derivatives? Of course not. But they do illustrate that derivatives need to be used with care. Speculation is foolish unless you have reason to believe that the odds are stacked in your favor. If you are not better informed than the highly paid professionals in banks and other institutions, you should use derivatives for hedging, not for speculation.

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Metallgesellschaft

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Major derivatives losses

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Chapter 24 Risk Management 701

SUMMARY Fluctuations in commodity prices, interest rates, or exchange rates can make planning difficult and can throw companies badly off course. Financial managers therefore look for opportunities to manage these risks, and a number of specialized instruments have been invented to help them. These are collectively known as derivative instruments. They include options, futures, forwards, and swaps.

Futures contracts are agreements made today to buy or sell an asset in the future. The price is fixed today, but the final payment does not occur until the delivery date. Futures contracts are highly standardized and are traded on organized exchanges. Commodity futures allow firms to fix the future price that they pay for a wide range of agricultural commodities, metals, and oil. Financial futures help firms to protect themselves against unforeseen movements in interest rates, exchange rates, and stock prices.

Forward contracts are equivalent to tailor-made futures contracts. For example, firms often enter into forward agreements with a bank to buy or sell foreign exchange or to fix the interest rate on a loan to be made in the future.

Swaps allow firms to exchange one series of future payments for another. For example, the firm might agree to make a series of regular payments in one currency in return for receiv- ing a series of payments in another currency.

Why do companies hedge to reduce risk? (LO24-1)

How can futures and forward contracts be used to devise simple hedging strategies? (LO24-2)

How can companies use swaps to change the risk of securities that they have issued? (LO24-3)

QUESTIONS AND PROBLEMS 1. Risk Management. True or false? (LO24-1)

a. Hedging is a zero-sum game. b. Reducing risk always increases company value. c. Hedging can reduce the likelihood of financial distress. d. Investors may prefer to hedge themselves. e. Risk may be reduced by real options. f. Derivatives include futures, forwards, preferred stock, and swaps.

2. Risk Management. Large businesses spend millions of dollars annually on insurance. Why? Should they insure against all risks, or does insurance make more sense for some risks than others? (LO24-1)

3. Commodity Futures. Match each of the following terms with one of the definitions below: spot price, futures price, forward contract, marked to market. ( Note: Not all of the definitions will be used.) (LO24-2)

a. Price for immediate delivery b. A tailor-made futures contract c. The expected price in the future d. System in which profits and losses are settled with the futures exchange on a daily basis e. The price fixed today for delivery in the future

4. Commodity Futures. True or false? (LO24-2)

a. Buyers of futures contracts generally wait until the contract matures and then take delivery of the commodity.

b. The great advantage of a futures contract is that the buyer is not obliged to deliver the con- tract at maturity. He will do so only if the price at maturity is above the contract price.

c. Because the buyer of the futures can sell his contract before maturity rather than take deliv- ery, the futures contract is equivalent to a call option.

d. In contrast to a futures contract, a forward contract requires payment up front.

5. Commodity Futures. What do you think are the advantages of holding futures rather than the underlying commodity? What do you think are the disadvantages? (LO24-2)

finance

®

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702 Part Seven Special Topics

6. Hedging Strategies. “The farmer does not avoid risk by selling wheat futures. If wheat prices rise above $9.40 a bushel, then he will suffer losses if he sells wheat futures at $9.40.” Is this a fair comment? (LO24-2)

7. Hedging Strategies. (LO24-2)

a. An investor currently holding $1 million in long-term Treasury bonds becomes concerned about increasing volatility in interest rates. She decides to hedge her risk by using Treasury bond futures contracts. Should she buy or sell such contracts?

b. The treasurer of a corporation that will be issuing bonds in 3 months also is concerned about interest rate volatility and wants to lock in the price at which he can sell 8% coupon bonds. Should he buy or sell Treasury bond futures contracts to hedge his firm’s position?

8. Marking to Market. Suppose that in the 5 days following a farmer’s sale of September wheat futures at a futures price of $9.83 the futures price is:

At the end of day 5 the farmer decides to quit wheat farming and buys back his futures contract. What payments are made between the farmer and the exchange on:

a. Day 1? b. Day 2? c. Day 3? d. Day 4? e. Day 5? What is the total payment over the 5 days? Would the total payment be any different if the con- tract was not marked to market? (LO24-3)

9. Hedging. When the euro strengthened in 2007, German luxury-car manufacturers found it increasingly difficult to compete in the U.S. market. How could they have hedged themselves against this risk? Would a company that was hedged have been in a better position to compete? Explain why or why not. (LO24-2)

10. Hedging. Assume that the 1-year interest rate is 4% and the 2-year interest rate is 5%. You approach a bank and ask at what rate the bank will promise to make a 1-year loan in 12 months’ time. The bank offers to make a forward commitment to lend to you at 10%. (LO24-2)

a. Would you accept the offer? b. Can you think of a simple, cheaper alternative?

11. Hedging. Phoenix Motors wants to lock in the cost of 10,000 ounces of platinum to be used in next quarter’s production of catalytic converters. It buys 3-month futures contracts for 10,000 ounces at a price of $1,650 per ounce. (LO24-2)

a. Suppose the spot price of platinum falls to $1,500 in 3 months’ time. Does Phoenix have a profit or loss on the futures contract?

b. Has it locked in the cost of purchasing the platinum it needs? c. How does your answer to (a) change if the spot price of platinum increases to $1,800 after

3 months? d. How does your answer to (b) change?

12. Hedging. Your firm has just tendered for a contract in Japan. You won’t know for 3 months whether you get the contract, but if you do, you will receive a payment of ¥10 million 1 year from now. You are worried that if the yen declines in value, the dollar value of this payment will be less than you expect and the project could even show a loss. Discuss the possible ways that you could protect the firm against a decline in the value of the yen. Illustrate the possible outcomes if you do get the contract and if you don’t. (LO24-2)

13. Commodity Futures. Listed below are some commodity futures contracts and some possible users of these contracts. State which contract each user would be most likely to use to hedge its risk and whether it would be likely to buy or sell the contract. (LO24-2)

Day 1 2 3 4 5

Price $9.83 $9.89 $9.70 $9.50 $9.60

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Chapter 24 Risk Management 703

14. Commodity Futures. Log on to the online Wall Street Journal, www.wsj.com , and find the prices of gold futures in the Markets Data Center. (LO24-2)

a. What is the date of the most distant contract? b. Is the futures price higher or lower than the current spot price? c. Suppose that you buy 100 ounces of gold futures for this date. When do you receive the gold? d. When do you pay for it?

15. Swaps. (LO24-3)

a. Look back at our example of the interest rate swap in Section 24.5. Since Computer Parts entered into the swap, interest rates have risen. Is the company showing a profit or a loss on the contract?

b. Now look at our example of Possum’s currency swap. Since arranging the swap, the Swiss franc has depreciated against the dollar. Is Possum showing a profit or a loss?

16. Swaps. What is a currency swap? An interest rate swap? Give one example of how each might be used. (LO24-3)

CHALLENGE PROBLEM 17. Swaps. Firms A and B face the following borrowing rates for a 5-year fixed-rate debt issue in

U.S. dollars or euros: (LO24-3)

Suppose that A wishes to borrow U.S. dollars and B wishes to borrow euros. Show how a swap could be used to reduce the borrowing costs of each company. Assume a spot exchange rate of 1 euro to the dollar.

U.S. Dollars Euros

Firm A 8% 6% Firm B 6 5

Templates can be found in Connect.

WEB EXERCISES 1. Log on to www.cmegroup.com and find the recent quotes for soybean futures. What is the

longest maturity for this contract? Is there more trading in the nearer or more distant contracts? Does it cost more to buy soybeans for delivery in the next few months or for later delivery?

2. Every 3 years the Bank for International Settlements undertakes a survey of derivatives trading which is available on its website, www.bis.org . Which are the most important types of deriva- tive contract? Which have been growing most rapidly? Why? Who do you think would find them useful?

a. oil futures A. An airline b. wheat futures B. A Kansas wheat farmer c. lumber futures C. A Texas cattle ranch d. copper futures D. A meatpacker e. live cattle futures E. A home builder

F. An oil producer G. A milling company H. A mining company I. A timber company J. A cable manufacturer

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704 Part Seven Special Topics

The total payment equals LIBOR × $100 million, so this position is in effect a synthetic float- ing rate bond tied to LIBOR. The diagram describing the cash flows of each party to the swap is as follows:

LIBOR Rate

4.5% 5.0% 5.5%

Interest received on fi xed-rate bonds (= .05 × $100 million)

$5,000,000 $5,000,000 $5,000,000

+ Cash fl ow on swap [= (LIBOR − .05)  × notional principal of $100 million]

−500,000 0 +500,000

Total payment $4,500,000 $5,000,000 $5,500,000

Year 0 Years 1–4 Year 5

$ SFr $ SFr $ SFr

1. Issue dollar loan +10 −.5 −10.5 2. Arrange currency swap a. Possum receives $ −10 +.5 +10.5 b. Possum pays SFr +30 −2.4 −32.4 3. Net cash fl ow 0 +30 0 −2.4 0 −32.4

Portfolio manager Swap dealer 5% income on

bond portfolio

5%

LIBOR

SOLUTIONS TO SELF-TEST QUESTIONS 24.1 The farmer has a further loss of 15 cents a bushel ($7.20 - $7.05) and will be required to pay

this amount to the exchange. The miller has a further profit of 15 cents per bushel and will receive this from the exchange. The farmer is now committed to delivering wheat in Septem- ber for $7.20 per bushel, and the miller is committed to paying $7.20 per bushel.

24.2 You sell long-term bond futures with a delivery date of 9 months. Suppose, for example, that you agree to deliver long-term bonds in 9 months at a price of $100. If interest rates rise, the price of the bond futures will fall to (say) $95. (Remember that when interest rates rise, bond prices fall.) In this case the profit that you make on your bond futures offsets the lower price that the firm is likely to receive on the sale of its own bonds. Conversely, if interest rates fall, the company will make a loss on its futures position but will receive a higher price for its own bonds.

24.3 The manager wants to convert the fixed rate portfolio, whose value will fall if interest rates rise, into a “synthetic” floating rate portfolio. Floating rate bonds always pay close to current- market interest rates, and therefore their prices have little exposure to interest rate fluctua- tions. The manager should enter a swap to pay a 5% fixed rate and receive LIBOR on notional principal of $100 million. The cash flows will then rise in tandem with the LIBOR rate:

24.4 The following table shows revised cash flows from Possum’s dollar loan and currency swap (figures in millions). The Swiss franc cash flows correspond to the payments on a SFr30 mil- lion bond with a coupon rate of 8%.

Notice that in exchange for $10 million today the dealer is now prepared to pay SFr30 million. Since the Swiss interest rate is now 8%, the dealer will expect to earn .08 × 30 = SFr2.4  million interest on its Swiss franc outlay.

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706

What We Do and Do Not Know about Finance 25 CHAPTE

R

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707

P A

R T

E IG

H T

I t is time to sum up. We begin this chapter with a very brief recap of the six most important ideas in finance. By now, these should be second nature to you.

Of course, there are still many puzzles that remain

to be worked out. We will give you our list of the nine

most important unsolved problems in finance.

We have tried to provide you with the essentials of

finance, but it would be a dull subject if you could

learn all that there is to know in one book. Therefore,

we provide a short road map of the important topics

that you may encounter in more advanced finance

classes.

C o

n c

lu si

o n

Too bad Einstein didn’t tackle the unsolved problems of finance.

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708 Part Eight Conclusion

25.1 What We Do Know: The Six Most Important Ideas in Finance What would you say if you were asked to name the six most important ideas in finance? Here is our list.

Net Present Value (Chapter 5) When you wish to know the value of a used car, you look at prices in the secondhand car market. Similarly, when you wish to know the value of a future cash flow, you look at prices quoted in the capital markets, where claims to future cash flows are traded (remember, those highly paid investment bankers are just secondhand cash-flow dealers). If you can buy cash flows for your shareholders at a cheaper price than they would have to pay in the capital market, you have increased the value of their investment.

This is the simple idea behind net present value (NPV). When we calculate a proj- ect’s NPV, we are asking whether the project is worth more than it costs. We are esti- mating its value by calculating what its cash flows would be worth if a claim on them were offered separately to investors and traded in the capital markets.

This is why we calculate NPV by discounting future cash flows at the opportunity cost of capital—that is, at the expected rate of return offered by securities having the same degree of risk as the project. In well-functioning capital markets, all equivalent- risk assets are priced to offer the same expected return. By discounting at the oppor- tunity cost of capital, we calculate the price at which investors in the project could expect to earn that rate of return.

Like most good ideas, the net present value rule is obvious when you think about it. But notice what an important idea it is. The NPV rule allows thousands of sharehold- ers, who may have vastly different levels of wealth and attitudes toward risk, to par- ticipate in the same enterprise and to delegate its operation to a professional manager. They give the manager one simple instruction: “Maximize net present value.”

Risk and Return (Chapters 11 and 12) Some people say that modern finance is all about the capital asset pricing model. That’s nonsense. If the capital asset pricing model had never been invented, our advice to financial managers would be essentially the same. The attraction of the model is that it gives us a manageable way of thinking about the required return on a risky investment.

Again, it is an attractively simple idea. There are two kinds of risks—those that you can diversify away and those that you can’t. The only risks people care about are the ones that they can’t get rid of—the nondiversifiable ones.

You can measure the nondiversifiable, or market, risk of an investment by the extent to which the value of the investment is affected by a change in the aggregate value of all the assets in the economy. This is called the beta of the investment. The required return on an asset increases in line with its beta.

Many people are worried by some of the rather strong assumptions behind the capi- tal asset pricing model, or they are concerned about the difficulties of estimating a project’s beta. They are right to be worried about these things. One day, we will have much better theories than we do now, but we are prepared to bet that these more sophis- ticated theories will retain the two crucial ideas behind the capital asset pricing model:

• Investors don’t like risk and require a higher return to compensate. • The risk that matters is the risk that investors cannot get rid of.

Efficient Capital Markets (Chapter 7) The third fundamental idea is that security prices accurately reflect available informa- tion and respond rapidly to new information as soon as it becomes available. This

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Chapter 25 What We Do and Do Not Know about Finance 709

efficient-market theory comes in three flavors, corresponding to different definitions of “available information.” The weak form (or random-walk theory) says that prices reflect all the information in past prices; the semistrong form says that prices reflect all publicly available information; and the strong form holds that prices reflect all acquir- able information.

Don’t misunderstand the efficient-market idea. It doesn’t say that there are no taxes or costs; it doesn’t say that there aren’t some clever people and some stupid ones. It merely implies that competition in capital markets is very tough—there are no money machines, and security prices reflect the true underlying values of assets on the basis of the best information available to investors.

The efficient-market hypothesis has been extensively tested, and the tests have revealed several pricing “anomalies,” or seeming profit opportunities with simple investment strategies. We showed you just a few examples of these anomalies in Chapter 7. But the academic journals are now filled with dozens and dozens more of these puzzles. Does this mean that investors are leaving easy money on the table?

Unfortunately for all of us, this body of evidence has not translated into easy money. Superior returns are elusive, and only a few mutual fund managers have been able to generate such returns with any consistency. Implementing the anomalies in real mar- kets is apparently far more difficult than finding them on data tapes of past returns.

MM’s Irrelevance Propositions (Chapters 16 and 17) The irrelevance propositions of Modigliani and Miller (MM) imply that you can’t increase value through financing policies unless these policies also increase the total cash flow available to investors. Financing decisions that simply repackage the same cash flows don’t add value.

Financial managers often ask how much their company should borrow. MM’s response is that as long as borrowing does not alter the total cash flow generated by the firm’s assets, it does not affect firm value.

Miller and Modigliani used a similar argument to show that payout policy does not affect value unless it affects the total cash flow available to present and future share- holders. If investment and borrowing are fixed, the only way that the company can pay an increased dividend is by cutting back on share repurchases or by issuing more shares. In either case the firm is simply putting cash in one of your pockets and taking it out of another.

The same ideas can be run in reverse. Just as splitting up the cash flows doesn’t add value, neither does combining different cash-flow streams. This implies that you can’t increase value by putting two whole companies together unless you thereby increase total cash flow. Thus there are no benefits to mergers solely for diversification.

You can think of these irrelevance propositions as a form of “conservation of value.” You can’t increase value simply by putting two companies together, nor can you cre- ate value by splitting up total cash flow into several pieces, for example, into debt and equity claims. The whole is just the sum of the parts.

Option Theory (Chapter 23) In everyday conversation we often use the word “option” as synonymous with “choice” or “alternative”; thus we speak of someone as having a number of options. In finance an option refers specifically to the opportunity to trade in the future on terms that are fixed today. Smart managers know that it is often worth paying today for the option to buy or sell an asset tomorrow.

We saw in Chapters 10 and 23 that companies are willing to pay extra for capital projects that give them future flexibility. Also, many securities provide the company or the investor with options. For example, a convertible bond gives the owner an option to exchange the bond for shares.

Managers spend much more time thinking about options than they used to. This is partly because they increasingly use options to help limit risk. Also, managers and

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710 Part Eight Conclusion

economists are more aware that many assets contain disguised real options. For exam- ple, the opportunity to abandon a project and recover its salvage value is a put option.

If options are so prevalent, it is important to know how to value them. One of the great finance developments of recent years was the discovery by Black, Scholes, and Merton of a formula to value options. We reviewed briefly the determinants of option value in Chapter 23.

Agency Theory A modern corporation is a team effort involving many players, including management, employees, shareholders, and bondholders. The members of this corporate team are bound together by a series of formal and informal contracts to ensure that they pull together.

For a long time economists assumed that all players acted instinctively for the com- mon good. But in the last 20 years we have learned a lot about the possible conflicts of interest and how companies try to overcome such conflicts. These ideas are collec- tively known as agency theory.

Consider, for example, the relationship between the firm’s shareholders and manag- ers. The shareholders (the principals ) want managers (their agents ) to maximize firm value. To encourage managers to do so, firms seek to tie the managers’ compensation to the value they have added. Moreover, managers who persistently neglect shareholders’ interests face the threat that their firm will be taken over and they will be turfed out.

Although we didn’t allocate a separate chapter to agency theory, the theory has helped us to think about such questions as these:

• How can an entrepreneur persuade venture capital investors to join in his or her enterprise? (Chapter 15)

• What are the reasons for all the fine print in bond agreements? (Chapter 16) • Are mergers, acquisitions, and LBOs simply attempts to “rip off” other players, or

do they change management’s incentives to maximize company value? (Chapter 21)

Are these six ideas exciting theories or plain common sense? Call them what you will, they are basic to the financial manager’s job. If after reading this book you really understand these ideas and know how to apply them, you have learned a great deal.

25.2 What We Do Not Know: Nine Unsolved Problems in Finance Since the unknown is never exhausted, the list of what we do not know about finance could go on forever. Here are nine unsolved problems that seem ripe for productive research.

What Determines Project Risk and Present Value? A good capital investment is one that has a positive NPV. We have talked at some length about how to calculate NPV, but we have given you very little guidance about how to find positive-NPV projects, except to say in Chapter 10 that projects have posi- tive NPVs when the firm has some competitive advantage. But why do some compa- nies earn superior returns while others in the same industry do not?

When are superior returns merely windfall gains, and when can they be anticipated, created, and planned for? What is their source, and how long do they persist before competition wears them away? Very little is known about any of these important questions.

Here is a related question: Why are some real assets risky and others relatively safe? In Chapter 12 we suggested a few reasons for differences in project betas—differences

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Chapter 25 What We Do and Do Not Know about Finance 711

in operating leverage, for example, or in the extent to which a project’s cash flows respond to the performance of the national economy. These are useful clues, but we have as yet no general procedure for estimating project betas. Assessing project risk is therefore still largely a seat-of-the-pants matter.

Risk and Return—Have We Missed Something? In 1848 John Stuart Mill wrote, “Happily there is nothing in the laws of value which remains for the present or any future writer to clear up; the theory is complete.” Econ- omists today are not so sure about that. For example, the capital asset pricing model is an enormous step toward understanding the effect of risk on the value of an asset, but there are many puzzles left, some statistical and some theoretical.

The statistical problems arise because the capital asset pricing model is hard to prove or disprove conclusively. It appears that average returns from low-beta stocks are too high (that is, higher than the capital asset pricing model predicts), and those from high-beta stocks are too low. But this could be a problem with the way the tests are conducted and not with the model itself.

We also described the puzzling discovery that expected returns appear to be related to firm size and to the ratio of the book value of the stock to its market value. Of course, these findings could be just a coincidence—an accidental result that is unlikely to be repeated. But if they are not a coincidence, the capital asset pricing model cannot be the whole truth. Perhaps firm size and the book-to-market ratio are related to some other variable x that, along with beta, truly determines the expected returns demanded by investors. But we cannot yet identify variable x and prove that it matters.

Meanwhile, work is proceeding on the theoretical front to relax the simple assump- tions underlying the capital asset pricing model. Here is one example: Suppose that you love fine wine. It may make sense for you to buy shares in a grand cru chateau, even if that soaks up a large fraction of your personal wealth and leaves you with a relatively undiversified portfolio. However, you are hedged against a rise in the price of fine wine: Your hobby will cost you more in a bull market for wine, but your stake in the chateau will make you correspondingly richer. Thus you are holding a relatively undiversified portfolio for a good reason. We would not expect you to demand a pre- mium for bearing that portfolio’s undiversifiable risk.

In general, if two people have different tastes, it may make sense for them to hold different portfolios. You may hedge your consumption needs with an investment in winemaking, whereas somebody else may do better to invest in Baskin-Robbins. The capital asset pricing model isn’t rich enough to deal with such a world. It assumes that all investors have similar tastes; the “hedging motive” does not enter, and therefore they hold the same portfolio of risky assets.

Merton has extended the capital asset pricing model to accommodate the hedging motive. 1 If enough investors are attempting to hedge against the same thing, this model implies a more complicated risk–return relationship. However, it is not yet clear who is hedging against what, so the model remains difficult to test. Given the rich possibili- ties for these extra hedging motives, there are many plausible alternative risk measures beyond beta and many potential competitors to the simple capital asset pricing model.

In the meantime, we must recognize the CAPM for what it is: an incomplete but extremely useful way of linking risk and return. Recognize too that its most basic mes- sage, that diversifiable risk doesn’t matter, is accepted by nearly everyone.

Are There Important Exceptions to the Efficient-Market Theory? The efficient-market theory is persuasive, but no theory is perfect—there must be exceptions.

1 See R. Merton, “An Intertemporal Capital Asset Pricing Model,” Econometrica 41 (1973), pp. 867–887.

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712 Part Eight Conclusion

Some of the apparent exceptions could simply be coincidences, for the more that researchers study stock performance, the more strange coincidences they are likely to find. For example, there is evidence that daily returns around new moons have been roughly double those around full moons. 2 It seems difficult to believe that this is any- thing other than a chance relationship—fun to read about but not a concern for serious investors or financial managers. But not all exceptions can be dismissed so easily. We saw that the stocks of firms that announce unexpectedly good earnings continue to perform well for a couple of months after the announcement date. Some scholars believe that this may mean that the stock market is inefficient and investors have con- sistently been slow to react to earnings announcements. Of course, we can’t expect investors never to make mistakes. If they have been slow to react in the past, it will be interesting to see whether they learn from their mistake and price the stocks more efficiently in the future.

Some researchers believe that the efficient-market theory ignores important aspects of human behavior. For example, psychologists find that people place too much emphasis on recent events when they are predicting the future. We don’t yet know how far such behavioral observations can help us to understand apparent anomalies.

During the dot-com boom of the late 1990s stock prices rose to astronomical levels. The NASDAQ Composite Index rose 580% from the beginning of 1995 to its peak in March 2000 and then fell by nearly 80%. Maybe such extreme price movements can be explained by standard valuation techniques. However, others argue that stock prices are liable to speculative bubbles, where investors are caught up in a whirl of irrational exu- berance. Now it may well be true that some of us are liable to become overexcited, but why don’t professional investors bail out of the overpriced stocks? Perhaps they would do so if it were their own money at stake, but maybe there is something in the way that their performance is measured and rewarded that encourages them to run with the herd.

These are important questions. Much more research is needed before we have a full understanding of why asset prices sometimes seem to get so out of line with what appears to be their discounted future payoffs.

Is Management an Off-Balance-Sheet Liability? In Chapter 7, we argued that the market value of the firm should equal intrinsic value, the value of the firm as a going concern. But sometimes it appears that price does not equal intrinsic value. For example, closed-end funds are firms whose only asset is a portfolio of common stocks; intrinsic value should be easy to observe here, yet the stock of closed-end funds often sells for less than the value of the fund’s portfolio. Other examples abound. For instance, real estate stocks often appear to sell for less than the market value of the firm’s net assets. In the early 1980s, the market values of many large oil companies were less than the market values of their oil reserves. Ana- lysts joked that you could buy oil cheaper on Wall Street than in west Texas.

These are cases where it is relatively easy to compare the market value of the firm with the value of its underlying assets. The discrepancies that sometimes arise here suggest that similar discrepancies might be widespread in other firms where value is harder to measure.

One possibility is that gaps between market value and asset value reflect the value added of management. Of course, if market value is less than the value of assets, then the market seems to view managers’ value added as negative. Perhaps investors are worried that managers extract too much of the firm’s cash flow for their own interests or pet projects. Of course, managers commit their human capital to the firm and right- fully expect a reasonable return on their personal investment. In most firms, manag- ers and employees coinvest with stockholders and creditors—human capital from the

2 K. Yuan, L. Zheng, and Q. Zhu, “Are Investors Moonstruck? Lunar Phases and Stock Returns,” Journal of Empirical Financ e, 13 (2006), pp. 1–23.

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Chapter 25 What We Do and Do Not Know about Finance 713

insiders and financial capital from outside investors. So far, we know very little about how this coinvestment works.

How Can We Explain Capital Structure? Modigliani and Miller’s article about capital structure emphasized that the value of a firm depends on real variables—the goods it produces, the prices it charges, and the costs that it incurs. Financing decisions merely affect the way that the cash flows are packaged for distribution to investors. What goes into the package is more important than the package itself.

Does it really not matter how much your firm borrows? We have come across sev- eral reasons why it may matter. Tax is one possibility. Debt provides a corporate tax shield, and this tax shield may more than compensate for any extra personal tax that the investor has to pay on debt interest. Perhaps managers are concerned with poten- tial bankruptcy costs. Perhaps differences in capital structure reflect differences in the relative importance of growth opportunities. So far, none of these possibilities has been either proved relevant or definitely excluded.

The upshot of the matter is that we still don’t have an accepted, coherent theory of capital structure. It is not for want of argument on the subject.

How Can We Resolve the Payout Controversy? We spent all of Chapter 17 on payout policy without being able to resolve the divi- dend controversy. Many people believe dividends are good; others believe they are bad and repurchases are good; and still others believe that as long as the firm’s invest- ment decisions are unaffected, the payout decision is largely irrelevant. If pressed, we largely take the middle view, but we can’t be dogmatic about it.

Perhaps the problem is that we are asking the wrong question. Instead of inquiring whether dividends are good or bad, perhaps we should be asking when it makes sense to pay out high or low dividends. Investors in mature firms with few investment oppor- tunities may welcome the financial discipline imposed by a high dividend payout, while for younger firms or firms with a large cash surplus, the tax advantage of stock repurchase may be more influential.

The way that companies distribute cash has changed over the last few decades. An increasing number of companies do not pay any dividends, while the volume of stock repurchase has mushroomed. This may partly reflect an increase in the proportion of small high-growth firms with lots of investment opportunities, but this does not appear to be the complete explanation. Understanding these shifts in payout policy may help us to understand how that policy affects firm value.

How Can We Explain Merger Waves? There are many plausible reasons why two firms might wish to merge. If you single out a particular merger, it is usually possible to think up a reason why that merger could make sense. But that leaves us with a special hypothesis for each merger. What we need is a general hypothesis to explain merger waves. For example, nobody seemed to be merging in 2002, yet only 4 years later, mergers were back in fashion. Why?

We can think of other instances of financial fashions. For example, from time to time there are hot new-issue periods when there seems to be an endless supply of speculative new issues and an insatiable demand for them. In recent years economists have been developing new theories of speculative bubbles. Perhaps such theories will help to explain these mystifying financial fashions.

What Is the Value of Liquidity? Unlike Treasury bills, cash pays no interest. On the other hand, cash provides more liquidity than Treasury bills. The value of this liquidity declines as you hold increasing amounts of cash. When you have only a small proportion of your assets in cash, a little

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714 Part Eight Conclusion

extra can be extremely useful; when you have a substantial holding, any additional liquidity is not worth much. Unfortunately, we don’t really understand how to value the liquidity service of cash, and therefore we can’t say how much cash is enough or how readily the firm should be able to raise it. In our chapters on working capital man- agement we largely finessed these questions by speaking vaguely of the need to ensure an “adequate” liquidity reserve.

A better knowledge of liquidity would also help us to understand how corporate bonds are priced. We already know part of the reason that corporate bonds sell for lower prices than Treasury bonds—corporate bonds are risky. However, the differences between the prices of corporate bonds and Treasury bonds are too large to be explained just by the possibility that the company will default. It seems likely that the price difference is partly due to the fact that corporate bonds are less liquid than Treasury bonds. But until we know how to price differences in liquidity, we can’t really say much more than this.

Investors seem to value liquidity much more highly at some times than at others. When liquidity suddenly dries up, firms can find it very difficult to borrow. This hap- pened in the financial crisis of 2007–2009 when investors became concerned about the rising default levels in the subprime mortgage market. Many banks that had sold these mortgages had subsequently repackaged them and traded the packages to finan- cial institutions both in the United States and abroad. As the music began to stop, no one was quite sure who would be left holding the parcel. Dealers became increasingly reluctant to quote a price for buying or selling bonds, and banks became wary about lending to each other. Those banks that earlier in the year had been able to borrow at .1% above the Federal Reserve’s target interest rate found that they now needed to pay a spread of over 4%—if they could borrow at all.

Why Are Financial Systems Prone to Crisis? Financial markets work well most of the time, but we don’t understand why they sometimes shut down or clog up, and we can offer relatively little advice to managers as to how to respond.

The crisis that started in 2007 was an unwelcome reminder of the fragility of finan- cial systems. One moment everything seems to be going fine; the next moment mar- kets crash and banks fail, and before long the economy is in recession. We know that systemic banking crises are often preceded by credit booms and asset price bubbles. When the bubbles burst, housing prices and stock prices fall, often precipitously, and deep recession follows.

Our understanding of these financial crises is limited. We need to know what causes them, how they can be prevented, and how they can be managed when they do occur. Crisis prevention will have to incorporate good governance systems, well-constructed compensation schemes, and efficient risk management. Understanding financial crises will occupy economists and financial regulators for many years to come. Let’s hope that they figure out the last one before the next one knocks on the door.

That concludes our list of unsolved problems. We have given you the nine upper- most in our minds. If there are others that you find more interesting and challenging, by all means construct your own list and start thinking about it.

25.3 A Final Word We titled this chapter “What We Do and Do Not Know about Finance.” We should perhaps have added a third section, “What We Know about Finance but Haven’t Told You.” After all, this book is an introduction to finance and there are plenty of topics that we have only skimmed over. Here are some examples:

• Investment decisions always have side effects on financing—every dollar has to be raised somehow. Sometimes these side effects may be important. For instance, if

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Chapter 25 What We Do and Do Not Know about Finance 715

the project allows the company to issue more debt, it may bring with it valuable tax shields. How can companies allow for these financing side effects when evaluating new investment projects? We touched on this issue in Chapter 13 when we showed you how to calculate the weighted-average cost of capital, but there is a huge body of knowledge about how best to allow for financing side effects in project valuation.

• We stressed in Chapter 14 the wide variety of claims that companies can sell to raise money. We described the principal ones, but there are others that we largely ignored. Leasing is an example. Companies lease assets rather than buy them because it is convenient and because in some circumstances there can be tax advan- tages. A lot is now known about how to value leases.

• Treasurers of large corporations worry about fluctuations in exchange rates, interest rates, and commodity prices. Various tools—including options, futures, forwards, and swaps—have been invented to help managers hedge against these risks. Many of the best brains in finance have been applied to devising and valuing these new instruments. We only touched on the problem of option valuation and said nothing at all about valuing futures. It’s an exciting area and there is no shortage of books and articles to help you learn more.

QUESTIONS AND PROBLEMS If you have reached this far, you deserve a break. So we haven’t provided any heavyweight problems at the end of this chapter. Instead we have included a quiz of the “Trivial Pursuit” variety. You don’t need to know the answers to be a financial wizard, and for the most part they are not to be found in earlier chapters. However, they may help you to impress your friends at smart dinner parties. 3

1. What do these countries’ currencies have in common?

• Australia • Canada • Hong Kong • New Zealand • Singapore • Taiwan • United States [Score 10]

2. What do the following countries’ currencies have in common?

• Estonia • Finland • Ireland • Greece • Portugal [Score 10]

3. Government bonds are known by a variety of names. In which countries are the following government bonds issued?

• Bunds • JGBs • Gilts • OATs • Tesobonos [Score 2 for each correct answer]

3 The answers are given on pages 718–720.

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716 Part Eight Conclusion

4. Each of these indexes measures stock market performance in a different country. What are the countries?

• CAC Index • DAX Index • FTSE Index • Hang Seng Index • Nikkei Index [Score 2 for each correct answer]

5. In which city is each of these futures markets located?

• CME • Intercontinental Exchange • LME • NYMEX • TFX [Score 2 for each correct answer]

6. Name the company:

a. Among the world’s largest insurance companies, this firm required emergency loans of over $80 billion from the U.S. government to cover its losses on credit default swaps.

b. In 2007, depositors in this U.K. bank formed long queues as they rushed to withdraw their money.

c. This former investment banking giant filed for bankruptcy in September 2008, at the time the largest-ever U.S. bankruptcy.

d. This bank failed after a 10-day bank run in September 2008, the largest bank failure in U.S. history.

[Score 2.5 for each correct answer]

7. Match the two merging firms.

Acquiring Firms Acquired Firms

Berkshire Hathaway NBC Universal Microsoft Skype Comcast Goodrich United Technologies Xstrata Glencore Heinz

[Score 2 for each correct answer]

8. To which country does each of the following banks belong?

• ING • Banesto • Barclays Bank • Commerzbank • Mizuho Bank [Score 2 for each correct answer]

9. In which state are the major U.S. corporations commonly incorporated?

• Alabama • California • Delaware • Illinois • Maryland [Score 10]

10. Spot the “odd one out.”

• Butterfly • Odd lot • Straddle • Vertical spread [Score 10]

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Chapter 25 What We Do and Do Not Know about Finance 717

11. What do the following abbreviations stand for?

• CFTC • FDIC • PCAOB • FSOC • SEC

[Score 2 for each correct answer]

12. Spot the “odd one out.”

• Delta Airlines • United Airlines • Southwest Airlines • Eastern Airlines • Pan Am

[Score 10]

13. Match up the following events and dates: • 1963 The first financial futures contract was traded in Chicago. • 1972 The first swap was arranged (between the World Bank and IBM). • 1973 The first eurobond was issued (by the Italian company Autostrade). • 1981 The first traded options market was formed in the United States. • 1997 The U.S. Treasury first issued indexed bonds.

[Score 2 for each correct answer]

14. Match each of the following Asian countries with its currency: • China Baht • South Korea Dong • Myanmar (Burma) Kyat • Thailand Won • Vietnam Yuan

[Score 2 for each correct answer]

15. In which year did the U.S. stock market decline by 43%?

• 1931 • 1939 • 1987

[Score 10]

16. Stocks are often referred to by their ticker symbols. To which companies do the following symbols refer?

• LUV • RIG • HOG • BID • ZEUS

[Score 2 for each correct answer]

17. Each of the following organizations made large losses from trading. Match each firm with a major cause of the loss. • Barings Copper futures • Metallgesellschaft Nikkei Index futures • Allied Irish Bank Oil futures • Procter & Gamble Currencies • Sumitomo Corporation Swaps

[Score 2 for each correct answer]

18. What do the following professors of finance have in common?

• Harry Markowitz • Merton Miller • William Sharpe

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718 Part Eight Conclusion

• Eugene Fama • Robert Shiller • Robert Merton • Myron Scholes [Score 10]

19. Match each of the following individuals with one of the quotations. • Gordon Gekko a. “When the music stops . . . things will be complicated. But as • Charles Prince long as the music is playing, you’ve got to get up and dance. • John Maynard Keynes We’re still dancing.” • John D. Rockefeller b. “Where are the customers’ yachts?” • Fred Schwed c. “Believing that fundamental conditions of the country are

sound . . . my son and I have for some days been purchasing sound common stocks.”

d. The stock market “is, so to speak, a game of Snap, of Old Maid, of Musical Chairs—a pastime in which he is a vic- tor who says Snap neither too soon nor too late, who passes the Old Maid to his neighbor before the game is over, who secures a chair for himself when the music stops.”

e. “Greed is good.”

[Score 2 for each correct answer]

20. International bond issues are often known by nicknames. For example, an international bond issued in Southeast Asia is known as a “dragon bond.” What is the common term for a bond issued by a foreign company in the bond market of each of the following countries?

• Japan • Netherlands • Spain • United Kingdom • United States

[Score 2 for each correct answer]

ANSWERS TO QUIZ 1. Each of their currencies is called the dollar.

2. They are all members of the European Monetary Union (EMU) and therefore all use the euro.

3. Bunds = Germany JGBs (Japanese Government Bonds) = Japan Gilts = United Kingdom OATs (Obligations Assimilables du Trésor) = France Tesobonos = Mexico

4. CAC Index = France DAX Index = Germany FTSE Index = United Kingdom Hang Seng Index = Hong Kong Nikkei Index = Japan

5. CME (Chicago Mercantile Exchange) = Chicago Intercontinental Exchange (ICE) = Atlanta LME (London Metal Exchange) = London NYMEX (New York Mercantile Exchange) = New York TFX (Tokyo Financial Exchange) = Tokyo

6. a. AIG b. Northern Rock c. Lehman Brothers d. Washington Mutual

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Chapter 25 What We Do and Do Not Know about Finance 719

8. ING = Netherlands Banesto = Spain Barclays Bank = United Kingdom Commerzbank = Germany Mizuho Bank = Japan

9. Delaware

10. “Odd lot” refers to an order to buy or sell fewer than 100 shares. The other terms all refer to combinations of options.

11. CFTC = Commodity Futures Trading Commission FDIC = Federal Deposit Insurance Corporation PCAOB = Public Company Accounting Oversight Board FSOC = Financial Stability Oversight Council

12. Southwest is the only one of these airlines that has not been through Chapter 11 bankruptcy proceedings.

13. 1963 The first eurobond was issued (by the Italian company Autostrade). 1972 The first financial futures contract was traded in Chicago. 1973 The first traded options market was formed in the United States. 1981 The first swap was arranged (between the World Bank and IBM). 1997 The U.S. Treasury first issued indexed bonds.

14. China = Yuan South Korea = Won Myanmar = Kyat Thailand = Baht Vietnam = Dong

15. 1931

16. LUV = Southwest Airlines RIG = Transocean HOG = Harley-Davidson BID = Sotheby’s ZEUS = Olympic Steel

17. Barings Nikkei Index futures Metallgesellschaft Oil futures Allied Irish Bank Currencies Procter & Gamble Swaps Sumitomo Corporation Copper futures

18. Each received the Nobel Prize for his contribution to financial economics.

19. Gordon Gekko (in the movie Wall Street ) = e Charles Prince (CEO of Citigroup commenting in 2007 on why the bank’s

leveraged lending was expanding so rapidly) = a John Maynard Keynes (writing in The General Theory of Employment, Interest and

Money, 1936) = d John D. Rockefeller (at the start of the 1929 Great Crash) = c Fred Schwed (in a 1940 book of that title) = b

20. Japan = Samurai bond Netherlands = Rembrandt bond Spain = Matador bond

7. Acquiring Firms Acquired Firms

Berkshire Hathaway Heinz Microsoft Skype Comcast NBC Universal United Technologies Goodrich Glencore Xstrata

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720 Part Eight Conclusion

United Kingdom = Bulldog bond

United States = Yankee bond

If you scored:

0–50 You weren’t trying.

51–80 Not bad.

81–120 You are probably going to be an investment banker.

121–160 You are probably an investment banker already.

161–200 You probably cheated.

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A-1

APPENDIX A Present Value and Future Value Tables

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A-2 Appendix A

A P P E N D I X T A B L E A . 1 Future value of $1 after t years = (1 + r )t

Interest Rate per Year

Number of Years 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%

1 1.0100 1.0200 1.0300 1.0400 1.0500 1.0600 1.0700 1.0800 1.0900 1.1000 1.1100 1.1200 1.1300 1.1400 1.1500

2 1.0201 1.0404 1.0609 1.0816 1.1025 1.1236 1.1449 1.1664 1.1881 1.2100 1.2321 1.2544 1.2769 1.2996 1.3225

3 1.0303 1.0612 1.0927 1.1249 1.1576 1.1910 1.2250 1.2597 1.2950 1.3310 1.3676 1.4049 1.4429 1.4815 1.5209

4 1.0406 1.0824 1.1255 1.1699 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641 1.5181 1.5735 1.6305 1.6890 1.7490

5 1.0510 1.1041 1.1593 1.2167 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105 1.6851 1.7623 1.8424 1.9254 2.0114

6 1.0615 1.1262 1.1941 1.2653 1.3401 1.4185 1.5007 1.5869 1.6771 1.7716 1.8704 1.9738 2.0820 2.1950 2.3131

7 1.0721 1.1487 1.2299 1.3159 1.4071 1.5036 1.6058 1.7138 1.8280 1.9487 2.0762 2.2107 2.3526 2.5023 2.6600

8 1.0829 1.1717 1.2668 1.3686 1.4775 1.5938 1.7182 1.8509 1.9926 2.1436 2.3045 2.4760 2.6584 2.8526 3.0590

9 1.0937 1.1951 1.3048 1.4233 1.5513 1.6895 1.8385 1.9990 2.1719 2.3579 2.5580 2.7731 3.0040 3.2519 3.5179

10 1.1046 1.2190 1.3439 1.4802 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937 2.8394 3.1058 3.3946 3.7072 4.0456

11 1.1157 1.2434 1.3842 1.5395 1.7103 1.8983 2.1049 2.3316 2.5804 2.8531 3.1518 3.4785 3.8359 4.2262 4.6524

12 1.1268 1.2682 1.4258 1.6010 1.7959 2.0122 2.2522 2.5182 2.8127 3.1384 3.4985 3.8960 4.3345 4.8179 5.3503

13 1.1381 1.2936 1.4685 1.6651 1.8856 2.1329 2.4098 2.7196 3.0658 3.4523 3.8833 4.3635 4.8980 5.4924 6.1528

14 1.1495 1.3195 1.5126 1.7317 1.9799 2.2609 2.5785 2.9372 3.3417 3.7975 4.3104 4.8871 5.5348 6.2613 7.0757

15 1.1610 1.3459 1.5580 1.8009 2.0789 2.3966 2.7590 3.1722 3.6425 4.1772 4.7846 5.4736 6.2543 7.1379 8.1371

16 1.1726 1.3728 1.6047 1.8730 2.1829 2.5404 2.9522 3.4259 3.9703 4.5950 5.3109 6.1304 7.0673 8.1372 9.3576

17 1.1843 1.4002 1.6528 1.9479 2.2920 2.6928 3.1588 3.7000 4.3276 5.0545 5.8951 6.8660 7.9861 9.2765 10.7613

18 1.1961 1.4282 1.7024 2.0258 2.4066 2.8543 3.3799 3.9960 4.7171 5.5599 6.5436 7.6900 9.0243 10.5752 12.3755

19 1.2081 1.4568 1.7535 2.1068 2.5270 3.0256 3.6165 4.3157 5.1417 6.1159 7.2633 8.6128 10.1974 12.0557 14.2318

20 1.2202 1.4859 1.8061 2.1911 2.6533 3.2071 3.8697 4.6610 5.6044 6.7275 8.0623 9.6463 11.5231 13.7435 16.3665

Interest Rate per Year

Number of Years 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 30%

1 1.1600 1.1700 1.1800 1.1900 1.2000 1.2100 1.2200 1.2300 1.2400 1.2500 1.2600 1.2700 1.2800 1.2900 1.3000

2 1.3456 1.3689 1.3924 1.4161 1.4400 1.4641 1.4884 1.5129 1.5376 1.5625 1.5876 1.6129 1.6384 1.6641 1.6900

3 1.5609 1.6016 1.6430 1.6852 1.7280 1.7716 1.8158 1.8609 1.9066 1.9531 2.0004 2.0484 2.0972 2.1467 2.1970

4 1.8106 1.8739 1.9388 2.0053 2.0736 2.1436 2.2153 2.2889 2.3642 2.4414 2.5205 2.6014 2.6844 2.7692 2.8561

5 2.1003 2.1924 2.2878 2.3864 2.4883 2.5937 2.7027 2.8153 2.9316 3.0518 3.1758 3.3038 3.4360 3.5723 3.7129

6 2.4364 2.5652 2.6996 2.8398 2.9860 3.1384 3.2973 3.4628 3.6352 3.8147 4.0015 4.1959 4.3980 4.6083 4.8268

7 2.8262 3.0012 3.1855 3.3793 3.5832 3.7975 4.0227 4.2593 4.5077 4.7684 5.0419 5.3288 5.6295 5.9447 6.2749

8 3.2784 3.5115 3.7589 4.0214 4.2998 4.5950 4.9077 5.2389 5.5895 5.9605 6.3528 6.7675 7.2058 7.6686 8.1573

9 3.8030 4.1084 4.4355 4.7854 5.1598 5.5599 5.9874 6.4439 6.9310 7.4506 8.0045 8.5948 9.2234 9.8925 10.6045

10 4.4114 4.8068 5.2338 5.6947 6.1917 6.7275 7.3046 7.9259 8.5944 9.3132 10.0857 10.9153 11.8059 12.7614 13.7858

11 5.1173 5.6240 6.1759 6.7767 7.4301 8.1403 8.9117 9.7489 10.6571 11.6415 12.7080 13.8625 15.1116 16.4622 17.9216

12 5.9360 6.5801 7.2876 8.0642 8.9161 9.8497 10.8722 11.9912 13.2148 14.5519 16.0120 17.6053 19.3428 21.2362 23.2981

13 6.8858 7.6987 8.5994 9.5964 10.6993 11.9182 13.2641 14.7491 16.3863 18.1899 20.1752 22.3588 24.7588 27.3947 30.2875

14 7.9875 9.0075 10.1472 11.4198 12.8392 14.4210 16.1822 18.1414 20.3191 22.7374 25.4207 28.3957 31.6913 35.3391 39.3738

15 9.2655 10.5387 11.9737 13.5895 15.4070 17.4494 19.7423 22.3140 25.1956 28.4217 32.0301 36.0625 40.5648 45.5875 51.1859

16 10.7480 12.3303 14.1290 16.1715 18.4884 21.1138 24.0856 27.4462 31.2426 5.5271 40.3579 45.7994 51.9230 58.8079 66.5417

17 12.4677 14.4265 16.6722 19.2441 22.1861 25.5477 29.3844 33.7588 38.7408 44.4089 50.8510 58.1652 66.4614 75.8621 86.5042

18 14.4625 16.8790 19.6733 22.9005 26.6233 30.9127 35.8490 41.5233 48.0386 55.5112 64.0722 73.8698 85.0706 97.8622 112.4554

19 16.7765 19.7484 23.2144 27.2516 31.9480 37.4043 43.7358 51.0737 59.5679 69.3889 80.7310 93.8147 108.8904 126.2422 146.1920

20 19.4608 23.1056 27.3930 32.4294 38.3376 45.2593 53.3576 62.8206 73.8641 86.7362 101.7211 119.1446 139.3797 162.8524 190.0496

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Appendix A A-3

Interest Rate per Year

Number of Years 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%

1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 0.9009 0.8929 0.8850 0.8772 0.8696

2 0.9803 0.9612 0.9426 0.9246 0.9070 0.8900 0.8734 0.8573 0.8417 0.8264 0.8116 0.7972 0.7831 0.7695 0.7561

3 0.9706 0.9423 0.9151 0.8890 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 0.7312 0.7118 0.6931 0.6750 0.6575

4 0.9610 0.9238 0.8885 0.8548 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830 0.6587 0.6355 0.6133 0.5921 0.5718

5 0.9515 0.9057 0.8626 0.8219 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209 0.5935 0.5674 0.5428 0.5194 0.4972

6 0.9420 0.8880 0.8375 0.7903 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645 0.5346 0.5066 0.4803 0.4556 0.4323

7 0.9327 0.8706 0.8131 0.7599 0.7107 0.6651 0.6227 0.5835 0.5470 0.5132 0.4817 0.4523 0.4251 0.3996 0.3759

8 0.9235 0.8535 0.7894 0.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 0.4339 0.4039 0.3762 0.3506 0.3269

9 0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3909 0.3606 0.3329 0.3075 0.2843

10 0.9053 0.8203 0.7441 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 0.3522 0.3220 0.2946 0.2697 0.2472

11 0.8963 0.8043 0.7224 0.6496 0.5847 0.5268 0.4751 0.4289 0.3875 0.3505 0.3173 0.2875 0.2607 0.2366 0.2149

12 0.8874 0.7885 0.7014 0.6246 0.5568 0.4970 0.4440 0.3971 0.3555 0.3186 0.2858 0.2567 0.2307 0.2076 0.1869

13 0.8787 0.7730 0.6810 0.6006 0.5303 0.4688 0.4150 0.3677 0.3262 0.2897 0.2575 0.2292 0.2042 0.1821 0.1625

14 0.8700 0.7579 0.6611 0.5775 0.5051 0.4423 0.3878 0.3405 0.2992 0.2633 0.2320 0.2046 0.1807 0.1597 0.1413

15 0.8613 0.7430 0.6419 0.5553 0.4810 0.4173 0.3624 0.3152 0.2745 0.2394 0.2090 0.1827 0.1599 0.1401 0.1229

16 0.8528 0.7284 0.6232 0.5339 0.4581 0.3936 0.3387 0.2919 0.2519 0.2176 0.1883 0.1631 0.1415 0.1229 0.1069

17 0.8444 0.7142 0.6050 0.5134 0.4363 0.3714 0.3166 0.2703 0.2311 0.1978 0.1696 0.1456 0.1252 0.1078 0.0929

18 0.8360 0.7002 0.5874 0.4936 0.4155 0.3503 0.2959 0.2502 0.2120 0.1799 0.1528 0.1300 0.1108 0.0946 0.0808

19 0.8277 0.6864 0.5703 0.4746 0.3957 0.3305 0.2765 0.2317 0.1945 0.1635 0.1377 0.1161 0.0981 0.0829 0.0703

20 0.8195 0.6730 0.5537 0.4564 0.3769 0.3118 0.2584 0.2145 0.1784 0.1486 0.1240 0.1037 0.0868 0.0728 0.0611

A P P E N D I X T A B L E A . 2 Discount factors: Present value of $1 to be received after t years = 1/(1 + r )t

Interest Rate per Year

Number of Years 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 30%

1 0.8621 0.8547 0.8475 0.8403 0.8333 0.8264 0.8197 0.8130 0.8065 0.8000 0.7937 0.7874 0.7813 0.7752 0.7692

2 0.7432 0.7305 0.7182 0.7062 0.6944 0.6830 0.6719 0.6610 0.6504 0.6400 0.6299 0.6200 0.6104 0.6009 0.5917

3 0.6407 0.6244 0.6086 0.5934 0.5787 0.5645 0.5507 0.5374 0.5245 0.5120 0.4999 0.4882 0.4768 0.4658 0.4552

4 0.5523 0.5337 0.5158 0.4987 0.4823 0.4665 0.4514 0.4369 0.4230 0.4096 0.3968 0.3844 0.3725 0.3611 0.3501

5 0.4761 0.4561 0.4371 0.4190 0.4019 0.3855 0.3700 0.3552 0.3411 0.3277 0.3149 0.3027 0.2910 0.2799 0.2693

6 0.4104 0.3898 0.3704 0.3521 0.3349 0.3186 0.3033 0.2888 0.2751 0.2621 0.2499 0.2383 0.2274 0.2170 0.2072

7 0.3538 0.3332 0.3139 0.2959 0.2791 0.2633 0.2486 0.2348 0.2218 0.2097 0.1983 0.1877 0.1776 0.1682 0.1594

8 0.3050 0.2848 0.2660 0.2487 0.2326 0.2176 0.2038 0.1909 0.1789 0.1678 0.1574 0.1478 0.1388 0.1304 0.1226

9 0.2630 0.2434 0.2255 0.2090 0.1938 0.1799 0.1670 0.1552 0.1443 0.1342 0.1249 0.1164 0.1084 0.1011 0.0943

10 0.2267 0.2080 0.1911 0.1756 0.1615 0.1486 0.1369 0.1262 0.1164 0.1074 0.0992 0.0916 0.0847 0.0784 0.0725

11 0.1954 0.1778 0.1619 0.1476 0.1346 0.1228 0.1122 0.1026 0.0938 0.0859 0.0787 0.0721 0.0662 0.0607 0.0558

12 0.1685 0.1520 0.1372 0.1240 0.1122 0.1015 0.0920 0.0834 0.0757 0.0687 0.0625 0.0568 0.0517 0.0471 0.0429

13 0.1452 0.1299 0.1163 0.1042 0.0935 0.0839 0.0754 0.0678 0.0610 0.0550 0.0496 0.0447 0.0404 0.0365 0.0330

14 0.1252 0.1110 0.0985 0.0876 0.0779 0.0693 0.0618 0.0551 0.0492 0.0440 0.0393 0.0352 0.0316 0.0283 0.0254

15 0.1079 0.0949 0.0835 0.0736 0.0649 0.0573 0.0507 0.0448 0.0397 0.0352 0.0312 0.0277 0.0247 0.0219 0.0195

16 0.0930 0.0811 0.0708 0.0618 0.0541 0.0474 0.0415 0.0364 0.0320 0.0281 0.0248 0.0218 0.0193 0.0170 0.0150

17 0.0802 0.0693 0.0600 0.0520 0.0451 0.0391 0.0340 0.0296 0.0258 0.0225 0.0197 0.0172 0.0150 0.0132 0.0116

18 0.0691 0.0592 0.0508 0.0437 0.0376 0.0323 0.0279 0.0241 0.0208 0.0180 0.0156 0.0135 0.0118 0.0102 0.0089

19 0.0596 0.0506 0.0431 0.0367 0.0313 0.0267 0.0229 0.0196 0.0168 0.0144 0.0124 0.0107 0.0092 0.0079 0.0068

20 0.0514 0.0433 0.0365 0.0308 0.0261 0.0221 0.0187 0.0159 0.0135 0.0115 0.0098 0.0084 0.0072 0.0061 0.0053

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A-4 Appendix A

A P P E N D I X T A B L E A . 3 Annuity table: Present value of $1 per year for each of t years = 1/ r - 1/[ r (1 + r ) t ]

Interest Rate per Year

Number of Years 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%

1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 0.9009 0.8929 0.8850 0.8772 0.8696

2 1.9704 1.9416 1.9135 1.8861 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355 1.7125 1.6901 1.6681 1.6467 1.6257

3 2.9410 2.8839 2.8286 2.7751 2.7232 2.6730 2.6243 2. 5771 2.5313 2.4869 2.4437 2.4018 2.3612 2.3216 2.2832

4 3.9020 3.8077 3.7171 3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.1024 3.0373 2.9745 2.9137 2.8550

5 4.8534 4.7135 4.5797 4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6959 3.6048 3.5172 3.4331 3.3522

6 5.7955 5.6014 5.4172 5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.2305 4.1114 3.9975 3.8887 3.7845

7 6.7282 6.4720 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.7122 4.5638 4.4226 4.2883 4.1604

8 7.6517 7.3255 7.0197 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 5.1461 4.9676 4.7988 4.6389 4.4873

9 8.5660 8.1622 7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7590 5.5370 5.3282 5.1317 4.9464 4.7716

10 9.4713 8.9826 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.8892 5.6502 5.4262 5.2161 5.0188

11 10.3676 9.7868 9.2526 8.7605 8.3064 7.8869 7.4987 7.1390 6.8052 6.4951 6.2065 5.9377 5.6869 5.4527 5.2337

12 11.2551 10.5753 9.9540 9.3851 8.8633 8.3838 7.9427 7.5361 7.1607 6.8137 6.4924 6.1944 5.9176 5.6603 5.4206

13 12.1337 11.3484 10.6350 9.9856 9.3936 8.8527 8.3577 7.9038 7.4869 7.1034 6.7499 6.4235 6.1218 5.8424 5.5831

14 13.0037 12.1062 11.2961 10.5631 9.8986 9.2950 8.7455 8.2442 7.7862 7.3667 6.9819 6.6282 6.3025 6.0021 5.7245

15 13.8651 12.8493 11.9379 11.1184 10.3797 9.7122 9.1079 8.5595 8.0607 7.6061 7.1909 6.8109 6.4624 6.1422 5.8474

16 14.7179 13.5777 12.5611 11.6523 10.8378 10.1059 9.4466 8.8514 8.3126 7.8237 7.3792 6.9740 6.6039 6.2651 5.9542

17 15.5623 14.2919 13.1661 12.1657 11.2741 10.4773 9.7632 9.1216 8.5436 8.0216 7.5488 7.1196 6.7291 6.3729 6.0472

18 16.3983 14.9920 13.7535 12.6593 11.6896 10.8276 10.0591 9.3719 8.7556 8.2014 7.7016 7.2497 6.8399 6.4674 6.1280

19 17.2260 15.6785 14.3238 13.1339 12.0853 11.1581 10.3356 9.6036 8.9501 8.3649 7.8393 7.3658 6.9380 6.5504 6.1982

20 18.0456 16.3514 14.8775 13.5903 12.4622 11.4699 10.5940 9.8181 9.1285 8.5136 7.9633 7.4694 7.0248 6.6231 6.2593

Interest Rate per Year

Number of Years 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 30%

1 0.8621 0.8547 0.8475 0.8403 0.8333 0.8264 0.8197 0.8130 0.8065 0.8000 0.7937 0.7874 0.7813 0.7752 0.7692

2 1.6052 1.5852 1.5656 1.5465 1.5278 1.5095 1.4915 1.4740 1.4568 1.4400 1.4235 1.4074 1.3916 1.3761 1.3609

3 2.2459 2.2096 2.1743 2.1399 2.1065 2.0739 2.0422 2.0114 1.9813 1.9520 1.9234 1.8956 1.8684 1.8420 1.8161

4 2.7982 2.7432 2.6901 2.6386 2.5887 2.5404 2.4936 2.4483 2.4043 2.3616 2.3202 2.2800 2.2410 2.2031 2.1662

5 3.2743 3.1993 3.1272 3.0576 2.9906 2.9260 2.8636 2.8035 2.7454 2.6893 2.6351 2.5827 2.5320 2.4830 2.4356

6 3.6847 3.5892 3.4976 3.4098 3.3255 3.2446 3.1669 3.0923 3.0205 2.9514 2.8850 2.8210 2.7594 2.7000 2.6427

7 4.0386 3.9224 3.8115 3.7057 3.6046 3.5079 3.4155 3.3270 3.2423 3.1611 3.0833 3.0087 2.9370 2.8682 2.8021

8 4.3436 4.2072 4.0776 3.9544 3.8372 3.7256 3.6193 3.5179 3.4212 3.3289 3.2407 3.1564 3.0758 2.9986 2.9247

9 4.6065 4.4506 4.3030 4.1633 4.0310 3.9054 3.7863 3.6731 3.5655 3.4631 3.3657 3.2728 3.1842 3.0997 3.0190

10 4.8332 4.6586 4.4941 4.3389 4.1925 4.0541 3.9232 3.7993 3.6819 3.5705 3.4648 3.3644 3.2689 3.1781 3.0915

11 5.0286 4.8364 4.6560 4.4865 4.3271 4.1769 4.0354 3.9018 3.7757 3.6564 3.5435 3.4365 3.3351 3.2388 3.1473

12 5.1971 4.9884 4.7932 4.6105 4.4392 4.2784 4.1274 3.9852 3.8514 3.7251 3.6059 3.4933 3.3868 3.2859 3.1903

13 5.3423 5.1183 4.9095 4.7147 4.5327 4.3624 4.2028 4.0530 3.9124 3.7801 3.6555 3.5381 3.4272 3.3224 3.2233

14 5.4675 5.2293 5.0081 4.8023 4.6106 4.4317 4.2646 4.1082 3.9616 3.8241 3.6949 3.5733 3.4587 3.3507 3.2487

15 5.5755 5.3242 5.0916 4.8759 4.6755 4.4890 4.3152 4.1530 4.0013 3.8593 3.7261 3.6010 3.4834 3.3726 3.2682

16 5.6685 5.4053 5.1624 4.9377 4.7296 4.5364 4.3567 4.1894 4.0333 3.8874 3.7509 3.6228 3.5026 3.3896 3.2832

17 5.7487 5.4746 5.2223 4.9897 4.7746 4.5755 4.3908 4.2190 4.0591 3.9099 3.7705 3.6400 3.5177 3.4028 3.2948

18 5.8178 5.5339 5.2732 5.0333 4.8122 4.6079 4.4187 4.2431 4.0799 3.9279 3.7861 3.6536 3.5294 3.4130 3.3037

19 5.8775 5.5845 5.3162 5.0700 4.8435 4.6346 4.4415 4.2627 4.0967 3.9424 3.7985 3.6642 3.5386 3.4210 3.3105

20 5.9288 5.6278 5.3527 5.1009 4.8696 4.6567 4.4603 4.2786 4.1103 3.9539 3.8083 3.6726 3.5458 3.4271 3.3158

bre61620_appA_A1-A6.indd A-4bre61620_appA_A1-A6.indd A-4 7/31/14 9:44 AM7/31/14 9:44 AM

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Appendix A A-5

Interest Rate per Year

Number of Years 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%

1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

2 2.0100 2.0200 2.0300 2.0400 2.0500 2.0600 2.0700 2.0800 2.0900 2.1000 2.1100 2.1200 2.1300 2.1400 2.1500

3 3.0301 3.0604 3.0909 3.1216 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100 3.3421 3.3744 3.4069 3.4396 3.4725

4 4.0604 4.1216 4.1836 4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 4.7097 4.7793 4.8498 4.9211 4.9934

5 5.1010 5.2040 5.3091 5.4163 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051 6.2278 6.3528 6.4803 6.6101 6.7424

6 6.1520 6.3081 6.4684 6.6330 6.8019 6.9753 7.1533 7.3359 7.5233 7.7156 7.9129 8.1152 8.3227 8.5355 8.7537

7 7.2135 7.4343 7.6625 7.8983 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872 9.7833 10.0890 10.4047 10.7305 11.0668

8 8.2857 8.5830 8.8923 9.2142 9.5491 9.8975 10.2598 10.6366 11.0285 11.4359 11.8594 12.2997 12.7573 13.2328 13.7268

9 9.3685 9.7546 10.1591 10.5828 11.0266 11.4913 11.9780 12.4876 13.0210 13.5795 14.1640 14.7757 15.4157 16.0853 16.7858

10 10.4622 10.9497 11.4639 12.0061 12.5779 13.1808 13.8164 14.4866 15.1929 15.9374 16.7220 17.5487 18.4197 19.3373 20.3037

11 11.5668 12.1687 12.8078 13.4864 14.2068 14.9716 15.7836 16.6455 17.5603 18.5312 19.5614 20.6546 21.8143 23.0445 24.3493

12 12.6825 13.4121 14.1920 15.0258 15.9171 16.8699 17.8885 18.9771 20.1407 21.3843 22.7132 24.1331 25.6502 27.2707 29.0017

13 13.8093 14.6803 15.6178 16.6268 17.7130 18.8821 20.1406 21.4953 22.9534 24.5227 26.2116 28.0291 29.9847 32.0887 34.3519

14 14.9474 15.9739 17.0863 18.2919 19.5986 21.0151 22.5505 24.2149 26.0192 27.9750 30.0949 32.3926 34.8827 37.5811 40.5047

15 16.0969 17.2934 18.5989 20.0236 21.5786 23.2760 25.1290 27.1521 29.3609 31.7725 34.4054 37.2797 40.4175 43.8424 47.5804

16 17.2579 18.6393 20.1569 21.8245 23.6575 25.6725 27.8881 30.3243 33.0034 35.9497 39.1899 42.7533 46.6717 50.9804 55.7175

17 18.4304 20.0121 21.7616 23.6975 25.8404 28.2129 30.8402 33.7502 36.9737 40.5447 44.5008 48.8837 53.7391 59.1176 65.0751

18 19.6147 21.4123 23.4144 25.6454 28.1324 30.9057 33.9990 37.4502 41.3013 45.5992 50.3959 55.7497 61.7251 68.3941 75.8364

19 20.8109 22.8406 25.1169 27.6712 30.5390 33.7600 37.3790 41.4463 46.0185 51.1591 56.9395 63.4397 70.7494 78.9692 88.2118

20 22.0190 24.2974 26.8704 29.7781 33.0660 36.7856 40.9955 45.7620 51.1601 57.2750 64.2028 72.0524 80.9468 91.0249 102.4436

A P P E N D I X T A B L E A . 4 Annuity table: Future value of $1 per year for each of t years = [(1 + r ) t - 1]/r

Interest Rate per Year

Number of Years 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 30%

1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

2 2.1600 2.1700 2.1800 2.1900 2.2000 2.2100 2.2200 2.2300 2.2400 2.2500 2.2600 2.2700 2.2800 2.2900 2.3000

3 3.5056 3.5389 3.5724 3.6061 3.6400 3.6741 3.7084 3.7429 3.7776 3.8125 3.8476 3.8829 3.9184 3.9541 3.9900

4 5.0665 5.1405 5.2154 5.2913 5.3680 5.4457 5.5242 5.6038 5.6842 5.7656 5.8480 5.9313 6.0156 6.1008 6.1870

5 6.8771 7.0144 7.1542 7.2966 7.4416 7.5892 7.7396 7.8926 8.0484 8.2070 8.3684 8.5327 8.6999 8.8700 9.0431

6 8.9775 9.2068 9.4420 9.6830 9.9299 10.1830 10.4423 10.7079 10.9801 11.2588 11.5442 11.8366 12.1359 12.4423 12.7560

7 11.4139 11.7720 12.1415 12.5227 12.9159 13.3214 13.7396 14.1708 14.6153 15.0735 15.5458 16.0324 16.5339 17.0506 17.5828

8 14.2401 14.7733 15.3270 15.9020 16.4991 17.1189 17.7623 18.4300 19.1229 19.8419 20.5876 21.3612 22.1634 22.9953 23.8577

9 17.5185 18.2847 19.0859 19.9234 20.7989 21.7139 22.6700 23.6690 24.7125 25.8023 26.9404 28.1287 29.3692 30.6639 32.0150

10 21.3215 22.3931 23.5213 24.7089 25.9587 27.2738 28.6574 30.1128 31.6434 33.2529 34.9449 36.7235 38.5926 40.5564 42.6195

11 25.7329 27.1999 28.7551 30.4035 32.1504 34.0013 35.9620 38.0388 40.2379 42.5661 45.0306 47.6388 50.3985 53.3178 56.4053

12 30.8502 32.8239 34.9311 37.1802 39.5805 42.1416 44.8737 47.7877 50.8950 54.2077 57.7386 61.5013 65.5100 69.7800 74.3270

13 36.7862 39.4040 42.2187 45.2445 48.4966 51.9913 55.7459 59.7788 64.1097 68.7596 73.7506 79.1066 84.8529 91.0161 97.6250

14 43.6720 47.1027 50.8180 54.8409 59.1959 63.9095 69.0100 74.5280 80.4961 86.9495 93.9258 101.4654 109.6117 118.4108 127.9125

15 51.6595 56.1101 60.9653 66.2607 72.0351 78.3305 85.1922 92.6694 100.8151 109.6868 119.3465 129.8611 141.3029 153.7500 167.2863

16 60.9250 66.6488 72.9390 79.8502 87.4421 95.7799 104.9345 114.9834 126.0108 138.1085 151.3766 165.9236 181.8677 199.3374 218.4722

17 71.6730 78.9792 87.0680 96.0218 105.9306 116.8937 129.0201 142.4295 157.2534 173.6357 191.7345 211.7230 233.7907 258.1453 285.0139

18 84.1407 93.4056 103.7403 115.2659 128.1167 142.4413 158.4045 176.1883 195.9942 218.0446 242.5855 269.8882 300.2521 334.0074 371.5180

19 98.6032 110.2846 123.4135 138.1664 154.7400 173.3540 194.2535 217.7116 244.0328 273.5558 306.6577 343.7580 385.3227 431.8696 483.9734

20 115.3797 130.0329 146.6280 165.4180 186.6880 210.7584 237.9893 268.7853 303.6006 342.9447 387.3887 437.5726 494.2131 558.1118 630.1655

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G-1

capital budget List of planned investment projects.

capital budgeting decision Decision to invest in tangible or intangible assets. Also called capital expenditure (CAPEX) decision.

capital expenditure (CAPEX) decision See capital budgeting decision.

capital markets Markets for long-term financing.

capital rationing Limit set on the amount of funds available for investment.

capital structure The mix of long-term debt and equity financing.

CAPM See capital asset pricing model.

carrying costs Costs of maintaining current assets, including opportunity cost of capital.

cash conversion cycle Period between firm’s payment for materials and collection on its sales.

cash dividend Payment of cash by the firm to its shareholders.

CEO Acronym for chief executive officer.

CFO See chief financial officer.

chief financial officer (CFO) Supervises all financial functions and sets overall financial strategy.

collection policy Procedures to collect and monitor receivables.

commercial paper Short-term unsecured notes issued by firms.

common-size balance sheet Balance sheet that presents items as a percentage of total assets.

common-size income statement Income statement that presents items as a percentage of revenues.

common stock Ownership shares in a corporation.

company cost of capital Opportunity cost of capital for investment in the firm as a whole. The company cost of capital is the appropriate discount rate for an average-risk investment project undertaken by the firm.

compound interest Interest earned on interest.

concentration account System whereby customers make payments to a regional collection center which transfers funds to a principal bank.

constant-growth dividend discount model Version of the dividend discount model in which dividends grow at a constant rate.

consumer credit Bills awaiting payment from the final customer to a company.

controller Officer responsible for budgeting, accounting, and taxes.

convertible bond Bond that the holder may exchange for a specified amount of another security.

corporate governance The laws, regulations, institutions, and corporate practices that protect shareholders and other investors.

corporation Business organized as a separate legal entity owned by stockholders.

A ACH See Automated Clearing House.

acquisition Takeover of a firm by purchase of that firm’s common stock or assets.

additional paid-in capital Difference between issue price and par value of stock. Also called capital surplus.

agency cost Value lost from agency problems or from the cost of mitigating agency problems.

agency problem Managers are agents for stockholders, and are tempted to act in their own interests rather than maximizing value.

aging schedule Classification of accounts receivable by time outstanding.

annual percentage rate (APR) Interest rate that is annualized using simple interest.

annuity Level stream of cash flows at regular intervals with a finite maturity.

annuity due Level stream of cash flows starting immediately.

annuity factor Present value of an annuity of $1 per period.

authorized share capital Maximum number of shares that the company is permitted to issue.

Automated Clearing House (ACH) An electronic network for cash transfers in the United States.

average tax rate Total taxes owed divided by total income.

B balance sheet Financial statement that shows the value of the firm’s assets and liabilities at a particular time.

balancing item Variable that adjusts to maintain the consistency of a financial plan. Also called plug.

bankruptcy The reorganization or liquidation of a firm that cannot pay its debts.

beta Sensitivity of a stock’s return to the return on the market portfolio.

bond Security that obligates the issuer to make specified payments to the bondholder.

book value Net worth of the firm according to the balance sheet.

break-even analysis Analysis of the level of sales at which the project breaks even.

business risk See operating risk.

C call option Right to buy an asset at a specified exercise price on or before the expiration date.

callable bond Bond that may be repurchased by the issuing firm before maturity at a specified call price.

capital asset pricing model (CAPM) Theory of the relationship between risk and return which states that the expected risk premium on any security equals its beta times the market risk premium.

Glossary

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G-2 Glossary

cost of capital Minimum acceptable rate of return on capital investment.

costs of financial distress Costs arising from bankruptcy or distorted business decisions before bankruptcy.

coupon The interest payments paid to the bondholder.

coupon rate Annual interest payment as a percentage of face value.

credit analysis Procedure to determine the likelihood a customer will pay its debts.

credit policy Standards set to determine the amount and nature of credit to extend to customers.

credit risk See default risk.

cumulative voting Voting system in which all the votes one shareholder is allowed to cast can be cast for one candidate for the board of directors.

current yield Annual coupon payment divided by bond price.

D debt overhang Firms threatened with default may pass up positive-NPV projects because bondholders capture part of the value added.

decision tree Diagram of sequential decisions and possible outcomes.

default premium The additional yield that bond investors require for bearing credit risk.

default risk The risk that a bond issuer may default on its bonds. Also called credit risk.

degree of operating leverage (DOL) Percentage change in profits given a 1 percent change in sales.

depreciation tax shield Reduction in taxes attributable to depreciation.

derivatives Securities whose payoffs are determined by the values of other financial variables such as prices, exchange rates, or interest rates.

discount factor Present value of a $1 future payment.

discount rate Interest rate used to compute present values of future cash flows.

discounted cash flow (DCF) Method of calculating present value by discounting future cash flows.

diversification Strategy designed to reduce risk by spreading the portfolio across many investments.

dividend Periodic cash distribution to shareholders.

dividend discount model Discounted cash-flow model which states that today’s stock price equals the present value of all expected future dividends.

Dow Jones Industrial Average Index of the investment performance of a portfolio of 30 “blue-chip” stocks.

Du Pont formula A breakdown of ROE and ROA into component ratios.

E economic value added (EVA) Income that is measured after deduction of the cost of capital. Also called residual income.

effective annual interest rate Interest rate that is annualized using compound interest.

efficient market Market in which prices reflect all available information.

equivalent annual annuity The cash flow per period with the same present value as the cost of buying and operating a machine.

ETF See exchange-traded fund.

eurobond Bond denominated in a currency not of the country in which it is issued.

eurodollars Dollars held on deposit in a bank outside the United States.

EVA See economic value added.

exchange rate Amount of one currency needed to purchase one unit of another.

exchange-traded fund (ETF) Portfolio of stocks that can be bought or sold by an investor in a single trade.

ex-dividend Without the dividend. Buyer of a stock after the ex-dividend date does not receive the most recently declared dividend.

expectations theory of exchange rates Theory that the expected spot exchange rate equals the forward rate.

F face value Payment at the maturity of the bond. Also called principal or par value.

financial assets Claims to the income generated by real assets. Also called securities.

financial deficit Difference between the cash companies need and the amount generated internally.

financial institution A bank, insurance company, or similar financial intermediary.

financial intermediary An organization that raises money from many investors and provides financing to individuals, corporations, or other organizations.

financial leverage Debt financing to amplify the effects of changes in operating income on the returns to stockholders.

financial markets Markets in which securities are issued and traded.

financial risk Risk to shareholders resulting from the use of debt.

financial slack Ready access to cash or debt financing.

financing decision Decision on the sources and amounts of financing.

fixed costs Costs that do not depend on the level of output.

fixed-income market Market for debt securities.

floating-rate preferred Preferred stock for which the dividend rate is linked to current market interest rates

flotation costs The costs incurred when a firm issues new securities to the public.

forex Abbreviation for foreign exchange; also abbreviated FX.

forward contract Agreement to buy or sell an asset in the future at an agreed price.

forward exchange rate Exchange rate agreed today for a future transaction.

free cash flow Cash available for distribution to investors after the company has paid for any new capital investments or additions to working capital.

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Glossary G-3

free-cash-flow problem Companies with ample cash flow are tempted to overinvest and to operate inefficiently. Companies facing this problem may benefit from the discipline imposed by more debt and higher debt-service requirements.

fundamental analysts Investors who attempt to find mispriced securities by analyzing fundamental information, such as firm performance and earnings prospects.

funded debt Debt with more than 1 year remaining to maturity.

future value (FV) Amount to which an investment will grow after earning interest.

futures contract Exchange-traded promise to buy or sell an asset in the future at a prespecified price.

FV See future value.

FX Abbreviation for foreign exchange; also abbreviated forex.

G GAAP See generally accepted accounting principles.

general cash offer Sale of securities open to all investors by an already-public company.

generally accepted accounting principles (GAAP) U.S. procedures for preparing financial statements.

H hedge fund Private investment fund that pursues complex, high-risk investment strategies.

I income statement Financial statement that shows the revenues, expenses, and net income of a firm over a period of time.

inflation Rate at which prices as a whole are increasing.

information content of dividends Dividend increases convey managers’ confidence about future cash flow and earnings. Dividend cuts convey lack of confidence and therefore are bad news.

initial public offering (IPO) First offering of stock to the general public.

interest rate parity Theory that forward premium equals interest rate differential.

interest rate risk The risk in bond prices due to fluctuations in interest rates.

interest tax shield Tax savings resulting from deductibility of interest payments.

internal growth rate Maximum rate of growth without external financing.

internal rate of return (IRR) Discount rate at which project NPV = 0.

internally generated funds Cash reinvested in the firm; depreciation plus earnings not paid out as dividends.

international Fisher effect Theory that real interest rates in all countries should be equal, with differences in nominal rates reflecting differences in expected inflation.

intrinsic value The present value of the cash payoffs anticipated by an investor in a security.

investment grade Bonds rated Baa or above by Moody’s or BBB or above by Standard & Poor’s or Fitch.

investment opportunity frontier Plot of the combinations of expected return versus standard deviation for various portfolio weights.

IPO See initial public offering.

IRR See internal rate of return.

issued shares Shares that have been issued by the company.

J junk bond Bond with a rating below Baa or BBB.

just-in-time approach System of inventory management that requires minimum inventories of materials and very frequent deliveries by suppliers.

L law of one price Theory that prices of goods in all countries should be equal when translated to a common currency.

lease Long-term rental agreement.

leveraged buyout (LBO) Acquisition of a firm by a private group using substantial borrowed funds.

limited liability The owners of the corporation are not personally responsible for its obligations.

liquidation Sale of bankrupt firm’s assets.

liquidation value Net proceeds that could be realized by selling the firm’s assets and paying off its creditors.

liquidity Access to cash or to assets that can be turned into cash on short notice.

loan covenant Agreement between firm and lender requiring the firm to fulfill certain conditions to safeguard the loan.

lock-box system System whereby customers send payments to a post-office box and a local bank collects and processes checks.

M MACRS See modified accelerated cost recovery system.

majority voting Voting system in which each director is voted on separately.

management buyout (MBO) Acquisition of the firm by its own management in a leveraged buyout.

M&A Abbreviation for mergers and acquisitions.

marginal tax rate Additional taxes owed per dollar of additional income.

market capitalization Total market value of equity, equal to share price times number of shares outstanding.

market index Measure of the investment performance of the overall market.

market portfolio Portfolio of all assets in the economy. In practice a broad stock market index is used to represent the market.

market risk Economywide (macroeconomic) sources of risk that affect the overall stock market. Also called systematic risk.

market risk premium Risk premium of market portfolio. Difference between market return and return on risk-free Treasury bills.

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G-4 Glossary

P par value Value of security shown in the company’s accounts.

payback period Time until cash flows recover the initial investment in the project.

payout ratio Fraction of earnings paid out as dividends.

P/E ratio See price-earnings multiple.

pecking order theory Firms prefer to issue debt rather than equity if internal finance is insufficient.

pension fund Investment plan set up by an employer to provide for employees’ retirement.

percentage of sales model Planning model in which sales forecasts are the driving variables and most other variables are proportional to sales.

perpetuity Stream of level cash payments that never ends.

planning horizon Time horizon for a financial plan.

plowback ratio Fraction of earnings retained by the firm.

poison pill Measure taken by a target firm to avoid acquisition; for example, the right of existing shareholders to buy additional shares at an attractive price if a bidder acquires a large holding.

preferred stock Stock that takes priority over common stock in regard to dividends.

present value (PV) Value today of a future cash flow.

present value of growth opportunities (PVGO) Net present value of a firm’s future investments.

price-earnings multiple (P/E ratio) Ratio of stock price to earnings per share.

primary market Market for the sale of newly issued securities.

primary offering Sale of new securities by corporations.

prime rate Benchmark interest rate charged by banks.

private placement Sale of securities to a limited number of investors without a public offering.

pro formas Projected or forecast financial statements.

profitability index Ratio of net present value to initial investment.

project cost of capital Minimum acceptable expected rate of return on a project given its risk.

prospectus Formal summary that provides information on an issue of securities.

protective covenant Condition imposed on borrowers to protect lenders from unreasonable risks.

proxy contest Takeover attempt in which outsiders compete with management for shareholders’ votes. Also called proxy fight.

purchasing power parity (PPP) Theory that the cost of living in different countries is equal and exchange rates adjust to offset inflation differentials across countries.

put option Right to sell an asset at a specified exercise price on or before the expiration date.

PV See present value.

R random walk Security prices change randomly, with no predictable trends or patterns.

rate of return Total income (including capital appreciation) per period per dollar invested.

market-to-book ratio Ratio of market value of equity to book value of equity

market value added The difference between the market value of firm’s equity and its book value.

market-value balance sheet Financial statement that shows the market value of all assets and liabilities.

maturity premium Extra average return from investing in long- versus short-term Treasury securities.

merger Combination of two firms into one, with the acquirer assuming assets and liabilities of the target firm.

MM’s dividend-irrelevance proposition Under ideal conditions, the value of the firm is unaffected by dividend policy.

MM’s proposition I (debt-irrelevance proposition) Under ideal conditions, the value of a firm is unaffected by its capital structure.

MM’s proposition II The required rate of return on equity increases as the firm’s debt-equity ratio increases.

modified accelerated cost recovery system (MACRS) Depreciation method that allows higher tax deductions in early years and lower deductions later.

money market Market for short-term financing (less than 1 year).

mutual fund An investment company that pools the savings of many investors and invests in a portfolio of securities.

mutually exclusive projects Two or more projects that cannot be pursued simultaneously.

N net present value (NPV) Present value of cash flows minus investment.

net working capital Current assets minus current liabilities.

net worth Book value of common stockholders’ equity plus preferred stock.

nominal interest rate Rate at which money invested grows.

NPV See net present value.

NPV break-even point Minimum level of sales needed to cover all costs including the cost of capital.

NYSE New York Stock Exchange.

O open account Agreement whereby sales are made with no formal debt contract.

operating leverage Degree to which costs are fixed.

operating profit margin After-tax operating income as a percentage of sales.

operating risk Risk in firm’s operating income. Also called business risk.

opportunity cost Benefit or cash flow forgone as a result of an action.

opportunity cost of capital The minimum acceptable rate of return on capital investment is set by the investment opportunities available to shareholders in financial markets.

outstanding shares Shares that have been issued by the company and are held by investors.

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Glossary G-5

specific risk Risk factors affecting only that firm. Also called diversifiable risk.

spot price Price paid for immediate delivery.

spot rate of exchange Exchange rate for an immediate transaction.

spread Difference between public offer price and price paid by underwriter.

stakeholder Anyone with a financial interest in the corporation.

Standard & Poor’s Composite Index Index of the investment performance of a portfolio of 500 large stocks. Also called the S&P 500.

standard deviation Square root of variance. A measure of volatility.

statement of cash flows Financial statement that shows the firm’s cash receipts and cash payments over a period of time.

stock dividends and splits Distributions of additional shares to a firm’s stockholders.

stock repurchase Firm distributes cash to stockholders by repurchasing shares.

straight-line depreciation Constant depreciation for each year of the asset’s accounting life.

subordinated debt Debt that may be repaid in bankruptcy only after senior debt is paid.

sustainable growth rate Steady rate at which a firm can grow without changing leverage; return on equity × plowback ratio.

swap Arrangement by two counterparties to exchange one stream of cash flows for another.

T technical analysts Investors who attempt to identify undervalued stocks by searching for patterns in past prices.

tender offer Takeover attempt in which outsiders directly offer to buy the stock of the firm’s shareholders.

terms of sale Credit, discount, and payment terms offered on a sale.

trade credit Bills awaiting payment from one company to another.

trade-off theory Debt levels are chosen to balance interest tax shields against the costs of financial distress.

treasurer Manager responsible for financing, cash management, and relationships with banks and other financial institutions.

treasury stock Stock that has been repurchased by the company and is held in its treasury.

U underpricing Issuing securities at an offering price set below the true value of the security.

underwriter Firm that buys an issue of securities from a company and resells it to the public.

real assets Assets used to produce goods and services.

real interest rate Rate at which the purchasing power of an investment increases.

real options Options to invest in, modify, postpone, or dispose of a capital investment project.

reorganization Restructuring of financial claims on failing firm to allow it to keep operating.

residual income See economic value added.

restructuring Process of changing the firm’s capital structure without changing its assets.

retained earnings Earnings not paid out as dividends.

return on assets (ROA) After-tax operating income as a percentage of total assets.

return on capital (ROC) After-tax operating income as a percentage of long-term capital.

return on equity (ROE) Net income as a percentage of shareholders’ equity.

rights issue Issue of securities offered only to current stockholders.

risk premium Expected return in excess of risk-free return as compensation for risk.

risk shifting Firms threatened with default are tempted to shift to riskier investments.

revolving line of credit Agreement by a bank that a company may borrow at any time up to an established limit.

ROA See return on assets.

ROC See return on capital.

ROE See return on equity.

S S&P 500 See Standard & Poor’s Composite Index.

scenario analysis Project analysis given a particular combination of assumptions.

seasoned offering Sale of securities by a firm that is already publicly traded.

secondary market Market in which previously issued securities are traded among investors.

secured debt Debt that, in the event of a default, has first claim on specified assets.

security market line Relationship between expected return and beta.

sensitivity analysis Analysis of the effects on project profitability of changes in sales, costs, and so on.

shark repellent Amendment to a company charter made to forestall takeover attempts.

shelf registration A procedure that allows firms to file one registration statement for several issues of the same security.

shortage costs Costs incurred from shortages in current assets.

simple interest Interest earned only on the original investment; no interest is earned on interest.

simulation analysis Estimation of the probabilities of different possible outcomes, e.g., from an investment project.

sinking fund Fund established to retire debt before maturity.

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G-6 Glossary

weighted-average cost of capital (WACC) Expected rate of return on a portfolio of all the firm’s securities, adjusted for tax savings due to interest payments.

workout Agreement between a company and its creditors establishing the steps the company must take to avoid bankruptcy.

Y yield curve Graph of the relationship between time to maturity and yield to maturity.

yield to maturity Interest rate for which the present value of the bond’s payments equals the price.

V variable costs Costs that change as the level of output changes.

variance Average value of squared deviations from mean. A measure of volatility.

venture capital Money invested to finance a new firm.

W WACC See weighted-average cost of capital.

warrant Right to buy shares from a company at a stipulated price before a set date.

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IND-1

A Accounting standards, 71 Airbus, 314 Apple Inc., tax avoidance, 20 Argentina, debt default, 180 Asia

Federal Express in, 4 financial crisis of 1997, 426

Assets, undervalued, 101 Athabasca oil reserves, Canada, 624–625 Australia

exchange rate in Feb. 2014, 636 financial reporting, 71 Gorgon natural gas field, 6, 24, 235 Macquarie Bank, 42 National Safety Council, 566 political risk score, 651 risk premium, 334

Autonomy, 6, 69

B Banco Central Hispanico, 612 Banco Santander, 612 Bank bailouts in Europe, 50 Bank mergers

Europe, 612 Japan, 610

Banks and Banking crisis in Europe, 50 stock ownership in Germany, 18

Banque Paribas, 612 Barclays Bank, 17, 598

rights issue, 447 as underwriter, 445

Barings Bank collapse, 25, 700 Barrick, 17 Belgium, risk premium, 334 BHP Billiton, 564 Big Mac index, 640–641 Black, Conrad, 15 BNP, 612 BNP Paribas, 427 Board(s) of directors in Germany, 18 BP (British Petroleum) dividend policy,

502 Brazil

exchange rate in Feb. 2014, 636 financial reporting, 71 political risk score, 651 10-year interest rate, 635

Brazilian real, 637 British pound, 637

British Salt, 609 Bulgari, 5 Buying forward, 638

C CAC 40, France, 624–625 Canada

Athabasca oil reserves, 624–625 corporate governance, 18 Equinox Company, 695 exchange rate in Feb. 2014, 636 Federal Express in, 4 financial reporting, 71 Hudson’s Bay Company, 9 nonexecutive chairs, 423 payment systems, 594 political risk score, 651 risk premium, 334

Capital budgeting. see International capital budgeting

Capital investments, 635 Carrefour, 17 Cash flow(s)

hedged, 650 in international capital budgeting,

650, 653 Cash management, international, 595–596 Channel Tunnel, 24 China

exchange rate in Feb. 2014, 636 Federal Express in, 4 financial reporting, 71 iron ore demand, 699 payment systems, 594 political risk score, 651 rare-earth metals in, 316

China Telecom, 37 Coca-Cola Company, overseas sales, 635 Code of Hammurabi, 24 Commerzbank, 612 Conrad, Joseph, 652n Consols, 133 Corporate governance

Canada, 18 Europe, 18 Japan, 18 United Kingdom, 18

Corus Steel, 609 Cost of capital

automatic increases in, 652–653 in international capital budgeting,

649, 652 Covered foreign interest rate, 647n

Covered interest rate parity, 646 Credit Suisse, as underwriter, 445 Cross-rate, 637 Currency appreciation, 638 Currency depreciation, 638, 647–648 Cyber espionage, 615 Cyprus, in financial crisis of

2007–2009, 50

D Default, by Greece, 50 Default rates, on microloans, 36 Denmark, risk premium, 334 Derivatives

Barings Bank collapse, 700 Société Générale losses, 700 and speculation, 700 UBS losses, 700

Deutsche Bank, 7, 37, 46, 427, 610 as underwriter, 445

Deutsche Börse, 37, 615 Dimson, E., 643 Direct quote, 627, 636 Discount rate, fudge factor, 653 Dojima Rice Market, 24 Dresdner Bank, 612

E East India Company, 24 EBIT. see Earnings before interest

and taxes Economic risk, 648 Economist, 610 EDF, 426 Equinox Company, 695 Erb, C., 651n Euro, 25, 428 Eurobonds, 428 Eurobor, 598 Eurodollar deposit, 598 Eurodollar market, 598

origin of, 24 Eurodollars, 427–428 Euronext, 194, 608 Europe

banking crisis, 50 bank mergers, 612 corporate governance, 18 exchange rate in Feb. 2014, 636 factoring in, 588 Federal Express in, 4

Global Index Page numbers followed by n refer to notes.

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IND-2 Global Index

in international capital budgeting, 649–650 simple theories, 640 versus spot rate, 638–639, 645–646 spot rate exaggerated by, 646n

Forward premium, 638 Forward rate agreements, 696 France

CAC 40, 674 EDF, 426 Federal Express in, 4 identifying corporations, 8n nominal vs. real exchange rate

1899–2011, 643 payment systems, 594 political risk score, 651 risk premium, 334 Société Générale losses, 25, 700

Frankfurt stock exchange, 194 Fraud, Australia National Safety

Council, 566 Friedrich, John, 566 Froot, K. A., 646n Fudge factors, 652–653 Futures contracts, 639

Barings Bank collapse, 700 Société Générale losses, 700 UBS losses, 700 worldwide turnover 1986–2012, 695

Futures market, 639 in 17th-century Japan, 24

G Générale des Eaux, 534 Germany

board(s) of directors, 18 credit default swap costs, 182 hyperinflation of 1922–23, 149 identifying corporations, 8n payment systems, 594 political risk score, 651 risk premium, 334

GlaxoSmithKline, 6, 7, 37 investment and financing decisions, 5

Glencore, 608 GlencoreXstrata, 598 Gold, 640 Gorgon natural gas field, 6, 24, 235 Greece

credit default swap costs, 182 debt default, 25 in financial crisis of 2007–2009, 50

H Haitian gourde, 638 Harvey, C. R., 651n HBOS rights issue, 445–446

Fidelity Investments, funds outside United States, 40

Financial crisis of 1997, Asia, 426 Financial hedges, 648 Financial managers

coping with exchange rate fluctuations, 639

and interest rate differences, 635 Financial Times Company, 329 Financial Times Index, 329, 674 Finland

Internet bill payments, 594 political risk score, 651 risk premium, 334

Fisher, Irving, 644 Fixed exchange rate, 638 Floating exchange rates, 638 Ford Motor Company

overseas operations, 651 overseas sales, 648

Forecasting exchange rates, 641 Foreign exchange markets, 37, 38

buying forward, 638 case, 659 conduct of, 636 cross-rates, 637 daily turnover, 636 direct quotes, 636, 637 exchange rate fluctuations, 635 exchange rate quotes Feb.

2014, 636 exchange rates and inflation, 640 expectations theory of exchange rates,

645–646 expected spot rate, 635–636 floating vs. fixed rates, 639 forward contract, 639 forward premium, 639 forward rate, 635–636, 638–639 forward rate agreements, 696 futures market, 639 hedging in

economic risk, 648 financial hedges, 648 operational hedging, 648 transaction risk, 647–648

indirect quotes, 636–637 interest rate parity, 647 and interest rates, 646–647 international Fisher effect, 644 liquidity of, 46 spot rate, 636–637

Forward contract, 638 Forward exchange rate

definition, 638 expectations theory, 645–646 forward premium, 638 and interest rate parity, 647 and interest rates, 646–647

Europe—Cont. in financial crisis of 2007–2009, 50 regional cash management, 596 sovereign debt crisis, 50

European Commission, 615 European Monetary Union, 25, 598 European Union

common currency, 25 principles-based accounting, 70, 71

Euroyen, 427 Euroyen market, 598 Eurozone crisis, 25, 50

credit default swap costs, 182 Exchange rate fluctuations, 635

avoiding, 638–639 coping with, 639 economic risk, 648 problems caused by, 638 transaction risk, 647–648

Exchange rate risk avoiding, 638 case, 659 exposure, 648 hedging

economic risk, 648 financial hedges, 648 operational hedging, 648 transaction risk, 647–648

Exchange rates Big Mac index, 640–641 cross-rate, 637–638 definition, 636 expectations theory, 645–646 expected spot rate, 645–646 fixed rates, 638 floating rates, 638 forecasting, 641 forward rate, 638–639, 645–646 futures market, 639 and inflation, 639–641 inflation and interest rates, 642–645 interest rate parity, 647 and interest rates, 646–647 international Fisher effect, 644 and law of one price, 640 nominal, 642 and purchasing power parity, 640–641 quotations for Feb. 2014, 636 real, 642 spot rate, 636–638

Expectations theory of exchange rates, 645–646

Expected inflation, 644 Expropriation risk, 651, 652, 653

F Factoring, in Europe, 588 Federal Express, overseas expansion, 4

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Global Index IND-3

real estate bubble, 222 risk premium, 334 10-year interest rate, 635

Japanese yen, 637 Joint stock corporations, 24

K Kerviel, Jérôme, 700 Korean won, 637

L Latin Monetary Union, 25 Law of one price, 640 Leeson, Nick, 25, 700 Lenovo, 609, 626n LOKmicro, 36 London

bank branches in, 427 foreign exchange market, 636

London Interbank Offered Rate, 426, 564, 598

London stock exchange, 194 LVMH, investment and financing

decisions, 5

M Macquarie Bank, 42 Maldives, 194 Manchester United, 37 Marsh, P. R., 643 Medici banking empire, 24 Messier, Jean-Marie, 534 Mexican peso, 636 Mexico

exchange rate in Feb. 2014, 636 payment systems, 594 Pemex, 690

Microfinance institutions, 36 Mitsubishi UFJ, 427 Mizuho Bank, 610 Moët Hennessy Louis Vuitton, 5n Money market, international, 598 Morgan Stanley Capital International, 329 Mortality bonds, 429 Multinational corporations, 596

political risks, 652 tax avoidance, 20

N National Safety Council, Australia, 566 Nestlé, 625 Net present value, in international capital

budgeting, 649–650

International capital markets, 427–428, 647 International cash management, 595–596 International Exchange, 608 International financial management

basic relationships exchange rates and inflation,

639–641 expectations theory, 645–646 expected spot rate, 645–646 forward exchange rate, 645–646 interest rate parity, 647 interest rates and exchange rates,

646–647 international Fisher effect, 644 law of one price, 640 nominal exchange rate, 642–645 purchasing power parity, 640–641 questions for financial managers, 639 real exchange rate, 642–645

capital budgeting, 649–653 foreign exchange markets, 636–639 hedging exchange rate risk, 647–648

International Financial Reporting Standards, 70, 71

International Fisher effect, 644 International money market

eurodollar market, 598 euroyen market, 598 London Interbank Offered Rate, 598

International Securities Exchange, 661 Investment decisions

Channel Tunnel, 24 examples, 5 Gorgon natural gas project, 24 Toyota, 271

Investments, considering risks of, 652 Investors, in Greek debt, 50 Ireland

credit default swap costs, 182 risk premium, 334

Israel, inflation-indexed debt, 25 Italy

credit default swap costs, 182 Medici banking empire, 24 nominal vs. real exchange rate

1899–2011, 643 risk premium, 334

J Jaguar Land Rover, 609 Japan

bank mergers, 610 corporate governance, 18 early futures market, 24 exchange rate in Feb. 2014, 636 money market, 598 Nikkei Index, 222, 329 political risk score, 651

Hedged cash flows, 650 Hedging exchange rate risk

economic risk, 648 financial hedges, 648 operational hedging, 648 transaction risk, 647–648

Hollinger International, 15 Hong Kong

exchange rate in Feb. 2014, 636 Octopus card system, 594

HSBC, 24, 427 Hudjur, Vahed, 36 Hudson’s Bay Company, 9 Hungary, inflation in, 25 Hyperinflation

in Germany 1922–23, 149

I India

exchange rate in Feb. 2014, 636 payment systems, 594 political risk score, 651

Indirect quote, 636–637 Inflation

Big Mac index, 640–641 and exchange rates, 639–641 expected, 644 in Hungary, 25 and interest rates, 642–645 International Fisher effect, 644 and law of one price, 640 purchasing power parity, 640–641 in Yugoslavia, 25

Inflation-indexed bonds, United Kingdom, 180

Information technology, problems in Japan, 610

Initial public offering by HBOS, 445–446 Intercontinental Exchange, 37 Interest rate parity, 647 Interest rates

in ancient Babylonia, 24 and exchange rates, 646–647 and inflation, 642–645 international Fisher effect, 644 on microloans, 36 national differences, 635 nominal, 642–643 real, 642–643

International Accounting Standards Board, 71

International capital budgeting, 635 avoiding fudge factors, 652–653 cash flows, 653 cost of capital, 649, 652 and forward exchange rate, 640–650 net present value analysis, 649–650 political risk, 651–652

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IND-4 Global Index

U UBS, 427, 612

losses by, 700 as underwriter, 445

Uhlfelter, Eric, 36 Underwriters

Barclays, 445 Credit Suisse, 445 Deutsche Bank, 445 UBS, 445

Unilever, 37 United Kingdom

Barings Bank collapse, 25, 700 consols, 133 corporate governance, 18 exchange rate in Feb. 2014, 636 Financial Times Index, 329, 674 identifying corporations, 8n inflation-indexed bonds, 180 inflation-indexed debt, 25 International Accounting Standards

Board, 71 and Lehman Brothers, 69–70 nominal vs. real exchange rate

1899–2011, 643 nonexecutive chairs, 423 payment systems, 594 political risk score, 651 prison inmate survey, 224n risk premium, 334 shareholders’ rights, 16 Starbucks in, 20

V Vale, investment and financing decisions, 5 Vietnam dong, 638 Virgin Media, 608 Viskanta, T., 651n Vivendi, 70

failure of financial planning, 534 Vodafone, 608 Volkswagen, 7, 37, 523, 648

investment and financing decisions, 5

W Wagner, Deidre, 36

X Xstrata, 608

Y Yugoslavia, inflation in, 25

S Seagram, 534 Secured bank landing, Australia, 566 Siemens, 17 Singapore Airlines, 314 Smith, Adam, 18 Société Générale losses, 25 Somalia, political risk score, 651 Sony Corporation, 37 South Africa

exchange rate in Feb. 2014, 636 risk premium, 334

South Korea exchange rate in Feb. 2014, 636 payment systems, 594 political risk score, 651

South Sea Bubble, 24 Sovereign debt crisis, in Europe, 50 Sovereign debt defaults, 25 Spain, risk premium, 334 Spot exchange rate

and cross-rates, 637 definition, 637 exaggerated by forward rate, 646n expectations theory, 645–646 for Feb. 2014, 636 forecasting, 641 versus forward rate, 645–646,

648–649 and interest rate differences,

646–648 interest rate parity, 647 simple theories, 640

Starbucks, tax avoidance, 20 Staunton, M., 643 Strategy, failure at Vivendi, 534 Sweden

exchange rate in Feb. 2014, 636 risk premium, 334

Swiss Bank Corporation, 612 Swiss Re, 429 Switzerland

exchange rate in Feb. 2014, 636 payment systems, 594 political risk score, 651 risk premium, 334

Sykes, T., 566 Synthes, 608

T Tata Group, 609 Taxation as political risk, 652 Tokyo Gas, 610 Tokyo stock exchange, 194 Toyota Motor Corporation, 92, 271,

591, 648 Transaction risk, 647–648

New Zealand risk premium, 334

Nikkei Index, 222, 329 Nokia, 608 Nominal exchange rate

definition, 642 in selected countries 1899–2011, 643

Nominal interest rate, 642–643 Nomura, 43 Nonexecutive chairs, 423 Norway, risk premium, 334 Novartis, 37

O Octopus card system, Hong Kong, 594 Operational hedging, 648

P Pakistan, political risk score, 651 Parmalat, 25, 70 Payment systems, international, 594, 596 Pemex, 690 Petrobas, 37 Philippines, Federal Express in, 4 Political risk

expropriation risk, 651, 652, 653 heavy taxes, 652 in international capital budgeting,

651–652 scores for selected countries, 651

Portugal, in financial crisis of 2007–2009, 50

Prison inmate survey, United Kingdom, 224n

PRS Group, 651 Publicis, 608 Purchasing power parity

Big Mac index, 640–641 definition, 640–641 real vs. nominal exchange rates, 642

R Rare-earth metals, 316 Real estate bubble

Japan, 222 Real exchange rate

definition, 642 in selected countries 1899–2011, 643

Real interest rate, 642–643 Regional cash management, 596 Research in Motion, 17 Rights issues, 445–446, 447 Rio Tinto, 17 Risk premium, for selected countries, 334 Russia, political risk score, 651

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IND-5

Subject

A A. M. Saccionaghi, Bernstein

Research, 508 Accelerated depreciation, 286 Accounting

break-even point, 306–308 cash vs. accrual, 63 convergence of standards, 70–71 practice and malpractice

constant scrutiny of companies, 68–69 cookie-jar reserves, 69 and Financial Accounting Standards

Board, 69 Lehman Brothers repo agreements,

69–70 off-balance-sheet assets and

liabilities, 70 revenue recognition, 69

principles-based, 70, 71 and Public Company Accounting

Oversight Board, 70 rules-based, 70 transparency, 70

Accounting income vs. economic value added, 88–89

Accounting profits, adjusted, 280 Accounting rate of return

and economic value added, 89 problem with, 91 return on assets, 90 return on capital, 89–90 return on equity, 91

Accounting standards, 71 Accounts, dangerous, 587 Accounts payable

on balance sheet, 57 as current liability, 550 Home Depot, 66 payment of, 559

Accounts payable period definition, 552 estimating, 553

Accounts receivable on balance sheet, 56 collection policy, 587–589 credit policy, 578–589 credit sales, 577 as current asset, 549

Accounts receivable period definition, 552 estimating, 553

Accrual accounting, 63 for income statement, 65

Acid-test ratio, 100 Acquisitions; see also Mergers

compared to LBOs, 623 to create synergies, 609 definition, 615 form of, 614–615

Activist shareholders, 17–18 Additional paid-in capital, 421 Administrative expenses, 559

general cash offer, 448 After-tax company cost of

capital, 393 After-tax cost of debt interest, 387 After-tax income, 424 After-tax operating income, 88

calculating, 90 After-tax rate of interest, 474 After-tax rate of return, 509 Agency costs, 15, 619 Agency problems

and activist shareholders, 17–18 control of, 16 and crisis of 2007–2009, 50 definition, 15 and executive compensation, 16 losses from, 15 and stakeholders, 16

Agency theory, 710 Aggressive stocks, 358 Aging schedule, 587 Aguirreamalloa, J., 339n AIG, 49, 175 Airline industry, market risk, 349 Alaska Air Group, 47–48 Allegheny Corporation, 675 Allen, F., 403n, 474n Allen, Paul, 437 Allied Crude Vegetable Oil Refining

Corporation fraud, 566 Allocated overhead costs, 276 Altman, Edward I., 583 Amazon, 198–199, 339, 363, 372,

401, 498 inventory value, 577 market-to-book ratio, 200 market vs. book value, 197

American Airlines, 419, 615 American Electric Power

market-to-book ratio, 200 market vs. book value, 197

America Online–Time Warner merger, 609

Amgen, 611 Amhud, Y., 502

Amortization, 98n Amortizing loan, 138 AMR, 608 Andrade, G., 626n Android smartphones, 274 Angel investors, 439 Announcement effect, 482n Annually compounded rate, 144 Annual percentage rate, 144 Annuities

versus annuity due future value, 141 definition, 133 financial calculators for, 143 future value, 138–141 lottery winnings, 136–137 present value, 135 spreadsheets for, 143–144 valuing, 134–138

Annuity due versus annuity future value, 141 definition, 141 future value, 141 present value, 141

Annuity due factor, 142 Annuity factor, 135

for Bill Gates, 137 for lottery winners, 136–137

Annuity formula, to value coupon payments, 168

Anti-takeover tactics poison pill, 621–622 shark-repellent, 622

Antitrust law and mergers, 615 and Oracle-PeopleSoft takeover,

621–622 Apple Inc., 274, 437, 481–482, 548,

672, 673 bond issue of 2013, 166, 428–429 cash holdings 2002–2011, 508 economic value added, 89 financing decisions 1976–3013,

34–35 IPO, 37 IPO banned in Massachusetts, 442n market value added, 86 options and stock, 662–667 revenues, 36 stock trading, 37

Approximation rule, 149 Aramark, 441 Arthur Andersen, 25 Articles of incorporation, 8 Asked price, 166, 167

Index

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IND-6 Subject Index

liquidation, 483 reorganization, 483 workout, 483

Bankruptcy Reform Act of 1978, 493 Banks and Banking

certificates of deposit, 596 check handling and float, 592–593 commercial banks, 42 concentration accounts, 592 credit checks by, 580 dividend restrictions, 500 functions, 21 industry consolidation, 612 investment banks, 42–43 lock-box system, 592–593 sweep programs, 591–592

Barnes and Noble, 17 Base period, 146 Baskin-Robbins, 711 Bear Stearns, 49, 430 Beaver, William H., 581, 582 Bechtel, 441 Before-tax income, 425 Behavioral finance

attitudes toward risk, 223 beliefs about probabilities, 223–224 sentiment about economy, 224

Behavioral psychology, 507 Benchmarks for risk, 334 Benefit-cost ratio, 250 Berkshire Hathaway, 608 Berra, Yogi, 462 Best-case plan, 522 Best efforts, 441 Beta(s), 357, 708

aggressive vs. defensive stocks, 358 of common stock, 358–359 Consolidated Edison, 361–362 definition, 358 Dow Chemical, 361–362 example, 358–359 Intel Corporation, 364–365 “is beta dead” question, 374 measuring, 358–361 of portfolios, 363–366 for predicting total risk, 366 project, 710–711 and risk of diversified portfolios,

366–367 and risk premium, 366n, 367–368 for selected companies, 363 spreadsheet solutions, 360 of Treasury bills, 367 Vanguard Growth and Income Fund,

364–365 Bid-ask spread, 195 Bid price, 166, 167 Bill and Melinda Gates Foundation, 137

net current assets on, 57 other current assets, 56 pro forma, 524–528 shareholders’ equity on, 58 tangible assets on, 56 and value of the firm, 462

Balance sheet identity, 58 Balancing item, 525–526 Bank accounts, effective interest rate, 145 Bank bailouts, 503 Banker’s acceptance, 580 Bank loans, 6, 9n, 36

floating-rate, 426 long-term, 564 revolving line of credit, 564 secured loans, 564–566 self-liquidating, 564 for short-term financing, 564

Bank of America, 36–37, 43, 43n, 46, 49, 88, 609, 676

economic value added, 89 losses from Countrywide Financial,

610 market value added, 86

Bank of America Merrill Lynch, 445 Bank runs, 46n Bankruptcy, 24

Chapter 11, 477 Chrysler Corporation, 415 and credit scoring, 581–583 definition, 494 Enron, 70, 494 examples, 478 financial distress without, 479–481 General Motors, 415 L. A. Gear, 550 of LBOs, 625n Lehman Brothers, 49, 174, 424,

494, 567 prepackaged, 493n and warrants, 676 WorldCom, 181

Bankruptcy costs, 476–479 direct, 478 Eastern Airlines, 478 Enron, 478 indirect, 478 Lehman Brothers, 478 paid out of assets, 477 from value of the firm, 477 varying with type of asset, 479–480

Bankruptcy procedures, 476–477 Chapter 11, 483–494 Chapter 7, 493 choosing between liquidation and

reorganization, 494–495 cram-down, 493 length of time for, 494

Asked yield to maturity, 166 Asquith, P., 448n, 500n Asset risk vs. portfolio risk, 340–345 Assets

abandonment value, 315 on balance sheet, 56–59, 197 and bankruptcy costs, 478–479 book vs. market value, 59 classes of, 58 excluded from balance sheet, 198 illiquid, 99 intangible, 3, 6, 117 leased, 97n liquid, 99 liquidity, 46 long-lived vs. short-lived, 545 on market-value balance

sheet, 215 needed by corporations, 3 negative-risk, 342 of pension funds in 2013, 41 real vs. financial, 6–7, 39 short-term, 275, 577 tangible, 3, 6, 117 total, 90

Asset turnover ratio, 91 Asymmetric information, 482 Auction

initial public offering by, 445 for stock repurchase, 501

Authorized share capital, 421 Automated Clearing House, 595 Automatic dividend reinvestment

plan, 499 Average risk, 387 Average tax rate, 73

B Balance sheet

accounts payable on, 57 assets excluded from, 198 assets on, 56–59, 197 book vs. market values, 58–61 common-size, 58 current assets on, 56 current liabilities on, 57 current market value excluded, 91 definition, 56 depreciation on, 56 fixed assets on, 56 Home Depot, 56–59, 86 intangible assets on, 56 liabilities on, 56–59, 59, 197 liquid assets on, 56 long-term liabilities on, 57 main items, 59 market-value, 60, 215 means of obtaining, 58

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Subject Index IND-7

Business organization corporations, 8–9 direct vs. indirect ownership, 9 ethical issues, 19 exposure to unpredictable

changes, 687 limited liability companies, 10 limited liability partnership, 10 limited partnership, 10 partnerships, 10 professional corporations, 10 sole proprietors, 15 sole proprietorship, 8–9, 10

Business plans best-case, 522 normal growth, 522 retrenchment, 522 and venture capital, 438–439

Business risk, 466

C California State Teachers’ Retirement

System, 20 Callable bonds, 426, 677–678 Callaway Golf, 47–48 Call options

Apple Inc., 662 definition, 662 exercise price, 662 and interest rates, 670 payoff diagram, 665–666 profit diagram, 665–666 versus put options, 662–663 for risk reduction, 690 selling, 664–665 and stock prices, 667 value and stock prices, 669–671 value at expiration, 662, 668–669 warrants, 676

Call premium, 661, 662 Call price, 426, 677 Campbell Soup Company, 339, 609

market-to-book ratio, 200 market vs. book value, 197

Capacity expansion, 301 Cape Wind project, 240–241 Capital, 38

tied up in inventory, 577, 589–590 total requirements, 546–548

Capital asset pricing model, 387 assumptions behind, 708 assumptions on stock market, 369 basis of, 371 to calculate company cost of capital,

390–391 definition, 368 to estimate expected returns, 371 expected returns based on, 398

investment grade, 47 issuers of, 165 junk bonds, 47 long-term, 178 maturities, 166 maturity premium, 330–331 municipal, 180n par value, 166 premium, 173 rate of return, 174–177 short-term, 178 strips, 177 yield curve, 177–180 yield to maturity, 172–174

Bond valuation, 165 spreadsheet calculation, 176–177

Bookbuilding method, 445 Book value

basis of, 60 debt and equity, 91 debt as proportion of, 404n for debt ratio, 97 definition, 58–59, 197 Geothermal equity, 392 Home Depot, 58–59 versus market value, 58–61, 197–199 summary of, 199

Bootstrap game, 613–614 Borden Chemical, price and yield on

bonds, 181 Borrowing

effect on value, 709 debt and cost of equity, 467–471 earnings per share, 464–466 MM proposition I, 462–464 restructuring, 463–464 risk and return, 466–467

loan covenants, 480–481 MM proposition I, 709 short-term, 551 tax disadvantage, 476

Brav, A., 502 Break-even analysis

accounting break-even point, 306–308 in credit decision, 585 definition, 306 and economic value added, 309n example, 309–310 at Lockheed, 310–311 net present value break-even point,

308–309 sales volume, 306–307

Brealey, R. A., 403n, 474n Bridge loans, 42n Brin, Sergey, 437 Bristol Myers, price and yield on

bonds, 181 Brokerage firms, 194 Buffett, Warren, 19n Burrough, B., 623n

Black, F., 373 Black, Fischer, 671 Black-Scholes formula, 671–673, 676 Blockholders, 17 Bloomingdales strategy, 94 Blue sky laws, 442 Board(s) of directors, 9

classified, 423 composition of, 423 in corporate governance, 17 election of, 423

Boeing Company, 5, 14, 339, 363, 366, 372, 401

Boeing 787 Dreamliner, 235 Bondholders, 165

and LBOs, 624–625 risk of call to, 426–427 risk-shifting strategies, 480 RJR Nabisco, 184

Bond market size of, 166 trading in, 167

Bond market indexes, 329–332 Bond prices

asked price, 166, 167 asked yield to maturity, 166, 167 bid price, 166, 167 calculating, 168–169 changes at approach to maturity, 167 in financial press, 166, 167 fluctuating, 178 and interest rates, 167–172 percentage of face value, 168 at premium, 173 and semiannual coupon payments,

169–170 strips, 177 and time value of money, 165 varying with interest rates, 170–172

Bond ratings, 181 Bonds; see also Corporate bonds;

Treasury bonds callable, 677–678 called, 38 capital loss on, 173 compared to stock, 38 convertible, 38, 661 coupon, 166, 178n definition, 166 differences among, 166 discount, 173 effective annual rate, 169n floating interest payments, 38 floating-rate, 696–697 forms of return, 328 historical returns 1900–2013, 335 indexed, 179 inflation-indexed, 179 interest payments, 166 interest rate risk, 172

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IND-8 Subject Index

effect of debt on risk and return, 466–467

effect of restructuring, 463–464 and financial planning, 522 and financing options

financial slack, 483 pecking order theory, 482–483 trade-off theory, 481–482

industry differences, 461, 471–472 L. A. Gear, 550 lack of coherent theory, 713 measuring, 396–397 MM proposition I, 462–463 MM proposition II, 468–471 optimal, 461, 476 and return on assets, 90 and sustainable growth rate, 536 and taxation, 471–476

implications, 475–476 interest tax shield, 472–473 value of shareholders’ equity, 473 weighted average cost of capital,

474–475 trade-off theory, 476 and value of the firm, 462–467, 713 valuing entire businesses, 403–405

Capital structure decisions, 6 CAPM; see Capital asset pricing model Careers in finance, 20–22 Cargill, 441 Carnival, 17 Carrying costs, 555, 589, 590 Carve outs

definition, 626 example, 627

Cash advantages of holding, 548–549, 591 calculating, 63 corporate sources of, 416–417, 419 as current asset, 549 forecasting sources of, 558–559 forecasting uses of, 559 held by Apple Inc., 508 versus installment plan, 128 management of, 591–595 mergers financed by, 612, 615–617 money market investments, 596–598 sales before, 273 versus short-term securities, 591 tracing changes in, 556–557 transported across time, 45 valuing liquidity of, 713–714

Cash accounting, 63 Cash balance

cumulative financing requirements, 560 decisions about, 577 example, 559–560 minimum operating cash balance, 560 versus retained earnings, 58n what-if questions, 560

definition, 235 internal rate of return rule

long-lived projects, 243–245 pitfalls, 245–250

mutually exclusive choosing between long- vs. short-

lived equipment, 254, 255–257 investment timing, 253, 254–255 replacement problem, 254, 257

net present value rule mutually exclusive projects,

241–242 and opportunity cost of capital, 237 and risk, 237 timing decision, 236 valuing long-lived projects,

238–242 payback rule, 251–253

discounted payback, 253 payback period, 252 problems with, 252 reasons for using, 252–253 simplicity of, 252

profitability index capital rationing, 250–251 pitfalls, 251 purpose, 250

and risk, 237 and shareholders, 235–236 valuing long-lived projects

Cape Wind project, 240–241 choosing between projects, 242 net present value rule, 238–239 new computer system, 239–240 office block project, 238–239 rule for selecting, 241 spreadsheet solutions, 242

Capital loss, 173, 328 Capital market history

estimating today’s cost of capital from, 332–333

historical record, 329–332 market indexes, 329

Capital markets, 38 dividends and share issues, 506–507 international, 427–428

Capital rationing definition, 250 hard rationing, 251 soft rationing, 251

Capital structure case, 492 changes in, 461 and corporate taxes, 403 debt and cost of equity, 467–471 definition, 388, 461, 462 effect of changes on rate of return,

402–403 effect of debt on earnings per share,

464–466

Capital asset pricing model—Cont. expected vs. actual returns,

373–374 and growth stocks, 373 hedging motive, 711 “is beta dead” question, 374 making sense of, 369–370 operation of, 372–374 and opportunity cost of capital

company cost of capital, 376 determinants of project risk, 376–37 fudge factors, 377

percent of managers using, 374n security market line, 370–371 and value stocks, 373

Capital budget, 300 and cash flow estimates, 299

Capital budgeting; see also Discounted cash flow analysis

consistent forecasts, 301 examples, 235 importance of what-if analysis, 303 options embedded in, 661 in strategic planning, 522 techniques used in practice, 259 tracing incremental cash flows,

274–276 Capital budgeting decisions, 6

decision rules comparison of, 258 summary of, 266–267

and payout policy, 506 and real options, 675 and value of the firm, 193

Capital expenditure decisions, 6 Capital expenditures, 559

on income statement, 63, 65 on statement of cash flows, 66

Capital gains, 328 from bonds, 173 taxation of, 73, 509–510

Capital gains tax, 510 Capital investment, 279 Capital investment decisions

internal rate of return rule, 243–250 and mutually exclusive projects,

253–257 net present value analysis, 236–242 payback rule, 251–253 profitability index, 250–251

Capital investment projects decision rules, 243, 252

for assets with different lives, 255–257

case, 266–267 comparison of, 258 internal rate of return rule, 243 net present value rule, 237 payback rule, 236, 251–252 profitability index, 254

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Subject Index IND-9

CEOs as board chairs, 423 forced out, 17

Cerberus Capital Management, 610 Certificates of deposit, 596 Chang, Judy, 242n Channel stuffing, 69 Chapter 11 bankruptcy, 477,

493–494 L. A. Gear, 550

Chapter 7 bankruptcy, 493 Charge cards, 594 Check Clearing for the 21st Century

Act, 592 Check conversion, 592 Check handling, 592 Checks, 593–594 Check 21, 592 Chicago Board of Trade, 693, 694 Chicago Board Options Exchange,

661, 674 Chicago Mercantile Exchange, 24,

38, 699 Chief financial officer, 10 Choi, Bill, 508 Chordia, T., 221n Chrysler Corporation, 419, 479n, 611

bankruptcy, 415 failed merger, 609–610

Cisco Systems, 548 Citicorp, 427 Citigroup, 17, 43, 501 Class A or B shares, 424 Classified boards, 423 Clearing House Interbank Payment

System, 595 Closed-end funds, 40n, 224n Closely held corporations, 9 CME Group, 693n, 699 Coca-Cola Company, 88, 339, 363, 366,

371, 372, 401 economic value added, 89 market value added, 86

Collateral, 183 accounts receivable financing, 565 inventory financing, 565–566 secured loans, 564–566

Collateralized debt obligations in crisis of 2007–2009, 429–430

Collection policy aging schedule, 587 costs imposed by slow payers, 587 definition, 587 and factoring, 588 and sales department, 588 statement of account, 588 and trade credit, 588–589

Comcast, 609 Commercial banks, 42 Commercial draft, 580

discount nominal cash flows, 277–278

separating financing from investment decisions, 278

versus income cash vs. accrual accounting, 63–64 depreciation, 62–63

level, 133–143 from long-lived projects, 238–242 multiple, 126–127, 131–133 versus net income, 65 new computer system, 239–240 nominal, 277 from office block project, 238–239 and opportunity cost of capital, 14–15 and payout policy, 506 versus profits, 64–65 real, 277 real vs. nominal, 146–147, 179 from recovering working capital, 276 terminal, 276 on TIPS, 179 and value of the firm, 462 with zero Net present value, 395

Cash flow analysis changes in working capital, 284 investment in fixed asserts, 282–283 multiple cash flows, 127 operating cash flow, 283–284 total project cash flow, 284

Cash flow estimates, 299 Cash-flow forecasts, 377

sources of cash, 558–559 uses of cash, 559

Cash flow from financing activities, 66, 68

Cash flow from investments, 65–66 Cash flow from operations, 65, 68 Cash inflow, 63 Cash management, 21

cash vs. short-term securities, 591 check handling and float, 592–593 concentration account, 592 decentralized, 592 electronic funds transfer, 594–595 lock-box system, 592–593 money market investments, 596–598 payment systems, 593–594 reasons for holding cash, 591 sweep programs, 591–592

Cash on delivery, 578 Cash outflows, 63, 64

from investment in working capital, 276

Cash payment from lottery winnings, 136–137 valuing, 149–150

from annuities, 134–136 from perpetuities, 133–1345

Cash ratio, 100

Cash before delivery, 578 Cash budgeting

cash balances, 559–560 financial manager forecasting, 557 forecasting sources of cash, 558–559 forecasting uses of cash, 559 preparation steps, 557 spreadsheet for, 560–561

Cash conversion cycle accounts payable period, 552 accounts receivable period, 552, 554 calculating, 553–554 cycle of operations, 551 data for selected industries, 552 definition, 552 estimating accounts payable

period, 553 estimating accounts receivable

period, 553 estimating inventory period, 552 inventory period, 552 and net working capital, 551 production cycle data, 552

Cash coverage ratio, 97–98 Cash cow companies, 625n Cash discounts, 578 Cash dividends, 497

definition, 499 ex-dividend date, 499 no-dividend companies, 498 payment date, 499 practices of U. S. firms, 498 record date, 499 Union Pacific policy, 499 in U.S. 1980–2012, 499–500

Cash flow(s) annuity vs. annuity due, 141, 142 basic financial resource, 461 from bonds, 167 calculating

capital investment, 279 changes in working capital,

281–282 operating cash flow, 279–281

from Cape Wind project, 240–241 changes from merger, 619 from changes in working capital,

281–282 in corporations, 11 discounted

by nominal interest rate, 150 by real interest rate, 150

discounted to a common date, 125 effect of inflation, 277–278 free, 67–68, 212 identifying

discount cash flows, not profits, 272–273

discount incremental cash flows, 274–276

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IND-10 Subject Index

Constant-growth dividend discount model, 205–207, 209, 399

definition, 206 example, 206 and forecasting, 205–206 formula, 206 and present value of perpetuities, 206

Consumer credit, 549, 578 Consumer Price Index

definition, 146 and inflation 1950–2013, 147

Continental Airlines, 484 Contingency planning, 523 Continuous compounding, 145 Controller, 10–11 Conversion price, 677 Conversion value, 677 Convertible bonds, 184, 430–431, 661

options on, 676–677 Convertible preferred stock, 431 Convertible securities

convertible bonds, 430–431 convertible preferred stock, 431 warrants, 430

Cookie-jar reserves, 69 Coolidge, Calvin, 331 Cooper Industries, 608 Corning, price and yield on bonds, 181 Corporate bonds, 165

asset-backed bonds, 429–430 callable, 426, 677–678 in capital structure, 396–397 compared to Treasury bonds, 180 convertible, 184, 661, 676–677 and convertible securities, 430–431 credit-default swaps, 182 default premium, 180 default risk, 180–182 defaults on, 181 floating-rate, 184 heavily traded, 181 high-yield, 181 insuring against default, 182 interest payments, 166 interest rates, 47 investment grade, 181 issued by Apple in 2013, 428 liquid, 182 mortality bonds, 429 noncallable, 426 prices vs. Treasury bonds, 714 promised vs. expected yield to

maturity, 182–183 protecting against default risk

protective covenants, 183–184 security, 183 seniority, 183

ratings, 180–181 RJR Nabisco, 184 speculative grade, 181

rights issue, 446–447 riskiest investments, 367 riskiest of securities, 330 risk premium, 331 seasoned offering, 446 shareholder rights, 422–423 shareholders in 2012, 422 treasury stock, 420 undervalued, 448–449 underwriting IPO, 444–445 valuation by comparables, 199–200 value stock, 373 voting procedures, 423

Companies; see Business organizations; Corporate entries; Corporations

Company cost of capital, 411–413 after-tax, 393 based on market value of

securities, 392 calculated as weighted average,

390–391 definition, 376 Geothermal, 388–389 and investors, 392 minimum acceptable rate of return,

389–390 and mixture of financing, 387 as opportunity cost of capital, 390 and taxes, 387, 392–393

Company-specific risk, 45 Company values, 47 Competition in financial markets, 416 Competitive advantage

in product markets, 416 in project analysis, 302

Complementary resources, combined by mergers, 611

Compound growth, 24 Compounding, power of, 121 Compound interest

definition, 118 future value, 118–121 present value calculation using,

123–124 purchase price of Manhattan,

120–121 Concentration accounts, 592 Conflicts of interest

eliminating, 301 sales vs. collection departments, 588 shareholders vs. debt holders, 480

Conglomerate merger, 609 bootstrap game, 613–614 definition, 608

Conservation of value, 709 Consistency in financial planning, 523 Consolidated Edison, 198–199, 215, 339,

361, 363, 371, 372, 376, 401 Constant dollars, 147

Commercial paper, 38, 418 backup line of credit, 566–567 as current asset, 549 defaults, 567 definition, 566 Ford Credit, 567 maturities, 566 in money market, 596 recent problems with, 567

Commodities markets, 38 Commodity futures, 694–695 Commodity options, 661 Commodity prices, 47 Common-size balance sheet, 58

Home Depot, 59 Common-size income statement, 62 Common stock, 193

additional paid-in capital, 421 aggressive, 358 authorized share capital, 421 betas, 358–359 breakdown of returns, 359 case, 232–233 classes of, 424 and company cost of capital, 390–391 and convertible bonds, 184, 661,

676–677 defensive, 358 dividend discount model, 202–205 dividends, 201–202 expected rate of return, 201

based on CAPM, 398 based on dividend discount

model, 399 estimating, 208–209 warning on false precision,

399–400 Facebook initial public offering, 214 forecasting dividends, 205–206 forms of return, 328 growth stocks, 212–215, 373 historical returns 1900–2013, 335 income stocks, 212–213 initial public offering, 194 issued but not outstanding, 420 issued outstanding shares, 420 measuring variation in returns,

337–339 net common equity, 421 no-growth, 205 nonconstant growth stock, 210 overvalued, 449 and ownership of corporations,

422–423 par value, 421 portfolios of, 330 price and intrinsic value, 200–202 rates of return 1900–2013, 331 repurchases, 212 and retained earnings, 421

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Subject Index IND-11

Cost of capital; see also Company cost of capital; Project cost of capital

case, 411–413 economic value added, 89 estimating from historical evidence,

332–333 excluded from income statement, 87 Geothermal, 388–389 information from financial markets, 48 measuring, 332–333 for merchant businesses, 376 nominal, 277–278 and rate of return, 48, 327 for regulated businesses, 376 and restructuring, 468

Cost of equity, false precision, 399–400 Cost valuation, 301 Countercyclical firms, 340 Counterparties, 697 Countrywide Financial, 610 Coupon, 425

definition, 166 Coupon bonds, 178n Coupon payments

semiannual, 169–170 valuing, 168

Coupon rate, 171 Cowgill, B., 39 Cox, Jo Ann, 388–389 Cram-down, 493 Credit

five C’s of, 581 net present value of granting, 585 types of, 578

Credit agencies, 580 and money market, 596

Credit agreements banker’s acceptance, 580 commercial draft, 580 open account, 580 sight draft, 580 time draft, 580 trade acceptance, 580

Credit analysis agencies for, 580 based on financial ratios, 581 definition, 580 hazard analysis, 583 numerical credit scoring, 581–583 Z-score model, 583

Credit cards, 594 Credit decision

basics of dangerous accounts, 587 profit maximization, 586–587

credit policy, 583 looking beyond immediate order, 587 with repeat orders, 585–586 without repeat orders, 583–585

assets needed by, 3 bankruptcies, 24 boards of directors, 7, 423 closely hold, 9 corporate governance, 17–18 cost disadvantages, 7 definition, 8 executive compensation, 16–17 financial manager roles, 11 financial manager tasks, 10–12 flow of savings to, 35–37 goals

market value maximization, 13–15 profit maximization, 13 value maximization, 12–15

going-concern value, 198 importance of financial markets to,

34–35 life cycle and payout policy, 510–511 limited liability, 7 mix of financing, 387 net common equity, 421 no-growth, 205 ownership of, 422–423 professional, 10 public companies, 9 raising cash

with bonds, 165 with stock, 193

raising money, 117 recent mergers, 608 separation of ownership and

management, 7, 619 shareholders, 8 tax drawback, 7 total financing by, 43–44

Corporations stock issues, 33 Correlations across industries, 343 Cost(s)

of debt, 469 disadvantages for corporations, 9 of equity, 376 explicit, 469 of financial distress, 688

bankruptcy costs, 476–479 definition, 476 investor assessment, 476 varying by type of asset, 478–479 without bankruptcy, 479–481

fixed, 303, 311, 312 of general cash offers, 447 implicit, 469 of IPOs, 444–445 of proxy contests, 620 sunk costs, 274–275 variable, 304, 308–309, 311

Cost-benefit analysis of mergers, 626–628 working capital trade-off, 555

Cost-cutting projects, 280

and warrants, 676 yield on, 149 yield spread, 182–183 yield spread vs. Treasury bonds,

182–183 zero-coupon, 184

Corporate debt Apple Inc., 428–429 compared to preferred stock, 424 distinguishing characteristics

callable bonds, 426 country and currency, 427–428 funded debt, 426 interest rates, 425–426 maturity, 425 public vs. private placements, 428 repayment provisions, 426 sinking fund, 426 unfunded debt, 426

interest rates, 425–426 and limited liability, 425

Corporate finance financing vs. investment decisions, 415 patterns of

cash sources, 416, 419 commercial paper, 418 debt issues, 418–419 debt ratios, 418, 419–420 financial deficits, 417 importance of internal funds, 419 internally generated funds, 416–417

Corporate financing common stock, 420–424 convertible securities, 430–431 debt financing, 425–428 preferred stock, 424–425

Corporate governance and activist shareholders, 17–18 board of directors role, 17 definition, 17 information for investors, 18 legal requirements, 17 and takeovers, 18

Corporate raiders, 20 Corporate scandals, 15, 17, 25, 70, 566 Corporate taxes

and capital structure changes, 403 and dividend policy, 510 expense deduction, 71 implications for capital structure,

475–476 interest deduction, 72 loss carryback, 72 state income taxes, 71n tax rates, 71 and WACC, 474

Corporate venturers, 439 Corporations

agency problems, 15–16 agency theory, 710

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IND-12 Subject Index

and financial slack, 483 pecking order theory, 482–483 trade-off theory, 481–482

loan covenants, 480–481 MM proposition II, 468–470 optimal, 475 and taxation, 471–476

capital structure, 476–476 interest tax shield, 472–473 shareholders’ equity, 483

and WACC, 474–475 Debt ratios, 96–97, 403

and financial planning, 522 in financing decisions, 418 industry differences, 462 measuring, 418 nonfinancial sector, 420 RJR Nabisco, 184 size of, 419–420 in trade-off theory, 481–482

Debt secured, 183 debt-to-value ratio, 392 Decentralized cash management, 592 Decision rules

for assets with different lives, 255–257

case, 266–267 comparison of, 258 internal rate of return rule, 237 investment timing, 253, 254 net present value rule, 237 payback rule, 251–252 profitability index, 250

Decision tree, 314 Default

on commercial paper, 567 insuring against, 182 in junk bond market, 624 Lehman Brothers, 597 probability of, 480 subprime mortgage market, 714

Default premium, 180 Default risk, 165

and bond ratings, 181 definition, 180 in money market, 596, 597 protecting against

protective covenants, 183–181 security, 183 seniority, 183

Defensive stocks, 358 Defined contribution plans, 41 Deflation, 147 Degree of operating leverage, 311–313 Dell Inc., 591 Delphi division of General Motors, 611 Delta Air Lines, 349 Demand deposits

as current asset, 549 Department of Justice, 615

D Dangerous accounts, 587 Days’ sales in inventory, 552 DeAngelo, H., 550 Debentures, 166 Debit cards, 594 Debt; see also Corporate debt

book value, 91 in capital structure, 396–397 and cost of equity, 467–471 costs of, 470 and expected return to shareholders,

466–467 explicit cost of, 469 funded, 426 hidden, 470–471 implicit cost of, 469 increase in financial risk, 469 inflation-indexed, 25 MM proposition I, 468 MM proposition II, 468–469 as proportion of book value, 404n subordinated, 183 unfunded, 426

Debt burden, 98 Debt-equity ratio, 96

MM proposition II, 469–470 Debt financing

with commercial paper, 418 by corporations, 425–426 versus equity financing, 6 as financial leverage, 466 financial risk, 467 loan covenants, 480–481 over-reliance on, 419–420 tax advantages, 472, 473

Debt holders; see also Bondholders

effects of LBOs, 96 rate of return for, 390–391

Debt investors, 6 Debt market innovations, 428–430

asset-backed bonds, 429–430 mortality bonds, 429

Debt overhang problem, 480 Debt policy

case, 491 and cost of equity, 467–471 costs of financial distress

bankruptcy costs, 476–479 without bankruptcy,

479–481 effect on value of the firm

earnings per share, 464–466 MM proposition I, 462–464 restructuring, 463–464 risk and return, 466–467

and financial slack, 483 and financing choices

Credit-default swaps, 182, 699 Credit management steps, 578 Creditors

and bankruptcy costs, 477, 478 in bankruptcy procedures, 493 choosing reorganization or liquidation,

494–495 junior, 494 postpetition, 494 prepetition, 494 secured, 493 senior, 494 unsecured, 493

Credit policy aging schedule, 587 collection policy, 587–589 consumer credit, 578 credit agreements, 580 credit analysis, 580–583 credit decision, 583–587 definition, 583 open account, 580 statement of account, 588 terms of sale, 578–579 trade credit, 578

Credit ratings, 47, 181 Credit risk, 180 Credit sales, 93n, 577, 578–579 Credit scoring

models, 581–583 for small business, 584

Credit transfer, 594 Crowdfunding, 439, 440 Cumulative financing

requirements, 560 Cumulative voting, 423 Currency options, 661 Currency swaps, 698–699 Current assets, 58

on balance sheet, 56 in working capital

accounts receivable, 549 demand deposits, 549 inventory, 549 marketable securities, 549 time deposits, 549 trade credit, 549 varying by industries, 550, 551

Current dollar cash flow, 150 Current expenditures, 63 Current liabilities, 58

accounts payable, 550 on balance sheet, 57 in capital structure, 396 short-term borrowing, 551 types of, 549

Current ratio, 100 Cyber espionage, 615 Cyclical businesses, 377 Cyclical firms, 340

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Subject Index IND-13

Dividend income, 73 Dividend payout ratio, 207 Dividend policy

Apple Inc., 508 case, 527–518 cash dividends, 498–499 and corporate tax, 510 effects of shifts in, 509 and financial planning, 522 high payout policy, 507–508 and legal capital, 499–500 low-payout policy, 509–510 managerial views, 501 payout controversy

capital budgeting decisions, 506 dividend discount model, 505–506 investment and financing

decisions, 506 MM dividend irrelevance

proposition, 504–505, 507 value of the firm, 503

in percentage of sales models, 525 resolving controversy about, 713 stock dividends, 500–501 stock splits, 500–501 taxation effects, 509–510 Union Pacific, 499 and value of the firm, 510–511

Dividend reinvestment plan, 499 Dividend restrictions, 499–500 Dividends, 328

and cash budgeting, 559 from common stock, 201–202 determining growth rate, 213–214 forecasting, 205–206 information content, 501–502 limitations on, 499–500 nonconstant growth stock, 210 not deductible, 72 paid by Home Depot, 62 payment of, 497 preferred stock, 424 on preferred stock, 394, 400 and repurchases, 212 and retained earnings, 35 and share issues, 506–507 Standard and Poor’s 500

companies, 223 stock splits, 500–501 taxation of, 509–510 Union Pacific, 497

Dividend yield, 196, 328 Dodd-Frank law, 16–17 Dollars, nominal vs. constant, 147 Dot-com boom/bubble, 222, 224, 712 Double taxation, 73 Dow Chemical, 339, 344, 358, 360, 361,

363, 371, 372, 401, 416–418, 431 book value of equity in 2012, 421 common stock, 420–421

identifying cash flows cash flows vs. profits, 272–273 incremental cash flows, 274–276 nominal cash flows/nominal cost of

capital, 277–278 separating financing from investment

decisions, 278–279 operating cash flow, 279–281

Discounted cash flow calculation, 122 Discounted cash flow methods, 245 Discounted cash flow rate of return, 244 Discounted payback period, 253 Discount factor, 123 Discounting

cash flow, not profits, 272–273 free cash flows, 404 incremental cash flows, 274–276 nominal cash flow, 277–278 real cash flow, 277

Discount rate avoiding fudge factors, 377 on bonds, 174 definition, 122 for different projects, 376 and net present value, 244–245 nominal, 277 for stock’s cash flow, 200 for valuing capital investment, 374 and zero net present value, 244

Disney; see Walt Disney Company Diversification, 327

asset vs. portfolio risk, 340–346 of big risks, 348 definition, 339 by financial markets, 45–46 investment opportunity frontier,

342–343 lack of benefits from, 709 and macro risks, 349 market vs. specific risk, 346–347 in mutual funds, 40 pace of risk reduction, 347 as reason for merger, 613 to reduce volatility, 339 risks eliminated by, 358

Divestitures, 625 Dividend discount model

for common stock valuation, 202–205 constant-growth, 205–206 definition, 202 estimating expected rate of return,

208–209 forecasting dividends, 205–206 investment time horizon, 202–205 with no growth, 205 nonconstant growth, 210–212 and repurchases of stock, 212 returns based on, 399 and stock repurchases, 505–506 sustainable growth rate, 207–208

Depreciation, 66 accelerated, 286 on balance sheet, 56 and cash coverage ratio, 97–98 in financial planning, 530 on income statement, 62–63 modified accelerated cost recovery

system, 286–288 and project cash flows, 280–281,

285–287 purpose of, 59 straight-line, 284, 287

Depreciation allowance, 71n Depreciation charge, 63, 280 Depreciation tax shield, 280, 287, 530 Derivatives

credit default swaps, 182, 699 definition, 689 forward contracts, 696 futures contracts, 690–695 identifying risks, 700 innovation in market, 699 iron ore futures, 699 options, 690 percent of companies using, 689 speculation and, 700 swaps, 696–699 types of, 687

Derivatives markets, 38 Detroit, financial crisis, 180n Deutsche Bank, 37, 46 Diet deals, 624 Dimon, James, 503 Dimson, Elroy, 329–330, 331, 334, 335,

337, 338 Direct costs

of bankruptcy, 478 of initial public offering, 444

Direct debit systems, 594 Direct deposit, 595 Direct negotiation for stock

repurchase, 501 Direct ownership, 9 Direct payment, 594 Direct payment systems, 594 Discount basis interest rate quotes, 597 Discount bonds, 173 Discounted cash flow, 708 Discounted cash flow analysis

calculating cash flows, 279 capital investment, 279 changes in working capital, 281–282 example

calculating net present value, 284–285

cash flow analysis, 282–284 depreciation, 285–287 forecasting working capital, 285 salvage value, 287 spreadsheet solutions, 288

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IND-14 Subject Index

Home Depot, 58 and internal growth rate, 535 meanings of, 393n

Equity financing versus debt financing, 6 high-tech firms, 461

Equity investors, 6 Equity market capitalization, 506 Equity markets, 37 Equivalent annual annuity, 256–257 Estée Lauder, 47–48 Ethical issues, 19 EVA; see Economic value added EVA Dimensions, 86 Excess capacity, 532 Exchange-traded funds, 45–46, 221 Ex-dividend date, 499 Executive compensation, 17 Executive stock options, 676 Exercise price

Apple Inc., 662 call options, 662, 676 put options, 662–663 and stock prices, 669–671

Expected profit, 584 Expected rate of return, 411–413, 708

on bonds, 398 calculating, 367–368 common stock, 201 on common stock

estimates based on CAPM, 368–369, 398

estimates based on dividend discount model, 399

warning on false precision, 399–400 and company cost of capital, 390–391 compared to return to

shareholders, 235 dependent factors, 368 effect of capital structure changes,

402–403 from equally divided portfolios, 367 estimates based on CAPM, 371 estimating, 332–333 estimating, for common stock,

208–209 Geothermal, 388–389 plotted against betas, 368 on preferred stock, 400 on risky securities, 48 for selected companies, 372

Expected risk premium, 333 Expenses

deductible, 71 on income statement, 61–62 from shutting down, 276

Experian, 581n Expiration date, 662, 668–669 Explicit costs, 469 Express Scripts, 608

Economies of scale, 610 Edmans, A., 18n Effective annual interest rate

on bank accounts, 145 on bonds, 169n calculating, 145 definition, 144 quote variations, 144

Efficiency measures, 84 asset turnover ratio, 92 inventory turnover, 92 receivables turnover, 92–93

Efficient capital markets, 416 Efficient market hypothesis

exceptions to, 711–712 coincidences, 712 irrational exuberance, 712

investor performance, 220 and market anomalies, 221–222 money manager performance, 220–221 pricing anomalies, 709 relative merits of, 708–709 semistrong-form efficiency, 220 and stock market bubbles, 222–223 strong-form efficiency, 220 weak-form efficiency, 219–220

Ehrbar, A., 555n Eight O’Clock Coffee, 609 Einstein, Albert, 707 Eisner, Michael, 620 Electric utilities, market risk, 349 Electronic bill presentation and payment,

594 Electronic communication networks, 194 Electronic funds transfer

advantages, 595 Automated Clearing House, 595 Clearing House Interbank Payment

System, 595 direct deposits, 595 direct payment, 594–595 wire transfer, 595

Ellison, Larry, 16, 17n, 676 E-money, 594 End-of-month sales, 579 Energy Future Holdings, 7 Enron Corporation, 25, 441, 478, 494

special-purpose entities, 70, 428 Entrepreneurs

business plan, 438 crowdfunding, 439, 440 and venture capital, 438–440

Equifax, 581n Equipment, long- vs. short-lived, 254,

255–256 Equity, 197n

book value, 91 in capital structure, 396–397 costs of, 376 debt and cost of, 467–471

Dow Chemical—Cont. market-to-book ratio, 200 market vs. book value, 197 preferred stock, 424 WACC, 393

Dow Jones Industrial Average annualized standard deviation

1900–2013, 338 history and functions, 329 low in 1932, 331

Dow Jones Wilshire 5000 Index, 329 DRIP; see Dividend reinvestment plan Duke Energy, 608, 610 Dun & Bradstreet, 580 Du Pont formula

definition, 94 profit margin, 93–95 and return on assets, 93–95 and return on equity, 98

E Earning power, 198

future, 198 Earnings

low-quality, 69 plowback ratio, 207–208 plowing back, 213 project risk and variability of, 377

Earnings announcement puzzle, 221 Earnings before interest, taxes,

depreciation, and amortization, 98n, 581

Earnings before interest and taxes, 62, 72 versus free cash flow, 64–65 and leverage ratio, 89, 97

Earnings per share effect of borrowing on, 464–466 effect of changes in operating

income, 466 Eastern Airlines, 478 Eastman Kodak, 476 Eaton, 608 eBay, 198, 442, 498 EBIT; see Earnings before interest

and taxes Economic indicators, 301 Economic order quantity, 590 Economic scenarios, 340–342 Economics of vertical integration, 611 Economic value added

versus accounting income, 88–89 and accounting rates of return, 89–91 calculating, 88 definition, 87 and excess liquid assets, 99 Home Depot, 88 for selected companies, 89 and working capital, 555

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Subject Index IND-15

lack of liquidity during, 714 money market during, 597 origin of, 49–50 responsibility for, 49–50 structured investment vehicles, 99 subprime mortgages, 49–50

Financial deficit, 417 Financial distress

costs of, 688 bankruptcy costs, 476–479 without bankruptcy, 479–481

effect on managers of threat, 483 Financial futures, 695 Financial institutions; see also Financial

markets commercial banks, 42 compared to financial

intermediaries, 42n in crisis of 2007–2009, 49–50 definition, 42 factors, 565 financing U.S. corporations, 43–44 flow of savings to corporations, 35–37 functions

diversification, 45–46 payment mechanism, 46 providing liquidity, 46 risk transfer, 45–46 transferring cash across time, 44

importance to companies, 34–35 insurance companies, 43 investment banks, 42–43 for microfinance, 36 understanding, 33

Financial intermediaries compared to financial institutions, 42n compared to manufacturing

corporations, 39 definition, 39 functions, 39 hedge funds, 40–41 mutual funds, 40 pension funds, 41

Financial leverage, 466 cash coverage ratio, 97–98 and cost of debt, 470 debt ratio, 96–97 definition, 96 excluding short-term debt, 97 hidden debt, 470–471 Home Depot, 96–98 and return on equity, 98n times interest earned ratio, 97

Financial managers capital budgeting decisions, 6 chief financial officer, 10 conflicts of interest, 3 controller, 10–11 day-to-day activities, 7–8 essential role of, 11

Finance careers in, 20–22 corporate raiders, 20 ethical disputes, 20 history of, 23–24 importance of reputation, 19 most important ideas

agency costs, 710 efficient capital markets, 708–709 MM irrelevance propositions, 709 net present value, 708 option theory, 709–710 risk and return, 708

short selling, 20 tax avoidance, 20 topics skimmed over

financing side-effects, 714–715 leasing, 715 new financial instruments, 715

unresolved problems capital structure, 713 exceptions to efficient market theory,

711–712 financial crises, 714 merger waves, 713 payment policy, 713 present value determination,

710–711 project risk determination, 710–711 risk and return, 711 value of liquidity, 713–714 value of the firm, 712–713

Finance lease, 96n Financial Accounting Standards

Board, 69 on option valuation models, 676

Financial assets, 39 definition, 6 liquidity, 46 options on, 675–678

callable bonds, 677–678 convertible bonds, 676–677 executive stock options, 676 warrants, 676

of pension funds in 2013, 41 variety of, 6–7

Financial calculators for annuity problems, 136, 143 for bond prices, 168–169 to compute bond yield, 175 to find discount factor, 123 to find present value, 123, 129–130 for future value, 120, 129–130 for internal rate of return, 247 for net present value, 247

Financial crises, attempts to understand, 714

Financial crisis of 2007–2009, 430 financial system meltdown, 49–50 fragility of financial system, 714

External finance, 482–483 External financing

and growth rate, 533–536 internal rate, 535 sustainable rate, 536

required, 533–535 at zero, 535

ExxonMobil, 87, 88, 90, 339, 349–350, 363, 366, 372, 401, 503

economic value added, 89 market value added, 86

F Facebook, 437, 498, 608

initial public offering, 214 investment and financing decisions, 5

Face value bond prices versus percentage of, 168 definition, 166 and interest rates, 171 and yield to maturity, 176–177

Factoring, 565 Factors

for collection policy, 588 definition, 565

Fair, Isaac & Company, 581n, 584 Fama, Eugene F., 500n Fannie Mae, 49, 174 FCX mining company, 276 Fear index, 672, 674 Federal Deposit Insurance

Corporation, 46n Federal Express, 197, 416–418,

440, 480 economic value added, 89 financing decisions, 5 initial public offering, 4, 194 investment decisions, 4–5 limit order book, 195 market capitalization, 195 market-to-book ratio, 200 market value added, 86 market vs. book value, 197 as start-up, 4 stock performance, 4 trading information, 196 and venture capitalists, 4, 5 website, 4

Federal Reserve System easy money policies, 49 Fedwire, 595 interest-free reserves, 427n target interest rate, 714 tight money policy, 170

Fedwire, 595 Fernandez, P., 333n FICO score, 581n Field warehousing, 566

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IND-16 Subject Index

Federal Express, 5 financial assets issues, 6–7 and financial slack, 483 investors, 6 kinds of financing, 6 means of, 6–7 Microsoft, 7 more complex than investment

decisions, 415 pecking order theory, 482–483 poor, 7 real vs. financial asset, 6 recent examples, 5 separate from investment decisions,

278–279 and shareholder value, 84 and time value of money, 117 trade-off theory, 476, 481–482 value creation with, 416

Fire insurance, 348 Firm commitment, 441 First Call, 210n First-stage financing, 438 Fisher, L., 500n Fitch, 596 Five C’s of credit, 581 Fixed assets, 58

on balance sheet, 56 book vs. market value, 59 investment in, 282–283

Fixed costs, 303 break-even point, 311 differences in, 312 in economies of scale, 610

Fixed-income market, 38 Fixed-income securities, 596–597 Flexible production facilities, 316 Flight to quality, 597 Float

definition, 592–593 reduction of, 595

Floatation costs, 444–445 Floating interest payments, 38 Floating interest rates, 425 Floating-rate bonds, 184, 696–697 Floating-rate loans, 426 Floating-rate portfolio, 698 Floating-rate preferred stock, 425 Food and Drug Administration, 377 Food companies, market risk, 349 Forbes, 41n, 220 Ford Credit, 567 Ford Motor Company, 363, 371, 372,

401, 415, 424, 428, 498, 500, 567, 611

economic value added, 89 market value added, 86 price and yield on bonds, 181 WACC, 400n

Forecast bias, 301–302

improved model, 536–530 limits on, 533 percentage of sales models, 525–526 pitfalls in design, 530–531 purpose, 524 reasons for

considering options, 523 contingency planning, 523 forcing consistency, 523

role of, 532–533 Financial ratios

benefit-cost ratio, 250 calculation of, 83 case, 113–114 cash ratio, 100 credit analysis based on, 581, 582 days’ sales in inventory, 552 debt-equity ratio, 96 debt-to-value ratio, 392 dividend payout ratio, 207 efficiency measures, 92–93 interpreting, 100–103 leverage ratios, 96–98 liquidity ratios, 99–100 major industry groups, 103 median, for nonfinancial

corporations, 104 organizational chart, 84 payout ratio, 207 plowback ratio, 207–208 profitability ratios, 92–93 role of, 104–105 to understand value added, 84–85

Financial risk, 467 Financial slack

dark side of, 483 and debt policy, 483 definition, 483

Financial statements balance sheet, 56–61 income statement, 61–65 pro forma, 524–528 SEC requirements, 56 statement of cash flows, 65–68

Financial system, fragility of, 714 Financing

first-stage, 438 of mergers by cash, 612, 615–617 of mergers by stock, 617–618 mix of, 387 multiple sources and WACC, 394 second-stage, 439 and value, 83

Financing decisions, 3 by Apple Inc., 34–35 board of directors approval, 17 compared to investment

decisions, 6–7 definition, 6 effect on value, 709

Financial managers—Cont. financing decisions, 6–8 investment decisions and financial

planning, 521 in large corporations, 11 and outside investors, 11 questions faced by, 3 short-term vs. long-term decisions, 545 treasurer, 10–11 understanding financial institutions, 33 use of debt-to-value ratio, 392 value added by, 3

Financial markets capital markets, 38 commodities market, 38 cost of capital, 48 in crisis of 2007–2009, 49–50, 714 definition, 37 derivatives and options markets, 38 financial intermediaries, 39–41 fixed-income markets, 38 foreign exchange market, 38 importance to companies, 34–35 information provided by, 48

commodity prices, 47 company values, 47–48 interest rates, 47

initial public offerings, 37 intense competition in, 416 money markets, 38, 596–597 over-the-counter markets, 37 prediction markets, 39 risk sharing methods, 46 stock market, 37

Financial plan, 557 Financial planning; see also Short-term

financial planning alternative business plans, 522 to avoid surprises, 521 by financial managers, 521 focus on big picture, 522 goals in, 523 and growth rate changes, 530 issues involved in, 522 planning horizon, 522 short- vs. long-term, 522 and strategic planning, 522

Financial planning models assumptions in percentage of sales

models, 531–532 case, 543 components

inputs, 524 outputs, 524 planning model and forecasting, 524

consistency between assumptions and financing plans, 526

danger of complexities, 533 external financing and growth rates,

533–536

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Subject Index IND-17

Global Crossing, 70 Goals

of corporations, 12–15 in financial planning, 523

Going-concern value, 198 Goldman Sachs, 10, 21, 43, 43n, 445 Goodrich, 608 Goodwill, 57 Google Finance, 58 Google Inc., 39, 88, 199, 214, 339,

363, 372, 401, 418, 424, 437, 440, 445, 481–482, 498, 626n

economic value added, 89 market value added, 86

Gordon, Myron, 206 Gordon growth model, 206 Gradley, Richard, 22 Graham, J. R., 68, 339n, 374n, 483n,

502, 548n Grand Union, 484 Greenbacks, 24 Greenmail transactions, 501 Greenspan, Alan, 224n Gresham’s law, 24 Growth companies, 198

investment opportunities, 510 small or no dividends, 498

Growth rate and external financing, 533–536 financial planning and changes in, 530 internal, 535 sustainable, 536

Growth stocks, 199, 373 dividend growth, 213–214 reasons for buying, 212–213 valuing, 215

Guiso, L., 18n

H H. J. Heinz Company, 608 Haircut, 565 Hard rationing, 251 Harvard Industries, 484 Harvey, C. R., 68, 339n, 374n, 483n,

502, 548n Haushalter, G.D., 689n Hazard analysis, 583 HCA, price and yield on

bonds, 181 Healy, P., 500n, 502, 627 Hedge funds

definition and functions, 40–41 investment strategies, 41 large fees, 41n vulture funds, 41

Hedging and capital asset pricing model, 711 extraneous events, 689

standardized, 696 wheat futures, 690–694 worldwide turnover, 695

Futures markets Chicago Board of Trade, 693, 694 Chicago Mercantile Exchange, 699 CME Group, 693n, 699 New York Mercantile Exchange, 699 speculation in, 700

Future value of annuity, 138–140 annuity due, 141–142 annuity vs. annuity due, 141 calculating, 120 case, 163 and compound interest, 118–121 definition, 118 multiple cash flows, 126–127, 132–133 in present value calculations, 122–123 and purchase price of Manhattan,

120–121 retirement savings, 140–141 and simple interest, 118 solutions

with financial calculators, 129–130 with spreadsheets, 130–133

Future value table, 120

G Gantchev, Nickolay, 444 Gasoline prices, 147 Gates, Bill, 137, 150, 151, 437 General Cable, 695 General cash offer

costs of, 448 definition, 447 market reaction to, 448–449 rights issue, 446–447 seasoned offering, 446 shelf registration, 447–448

General Dynamics, 4 General Electric, 47–48, 329, 339,

345–346, 363, 372, 401 market-to-book ratio, 200 market vs. book value, 197

Generally accepted accounting principles, 58, 69

versus international standards, 71 General Mills, 349 General Motors, 235, 419, 503, 567, 611

bankruptcy, 415 stock sold by Treasury Department, 441

Geothermal Corporation, 387, 402–403 company cost of capital, 388–389 cost of capital, 390–391 Weighted average cost of capital,

394–395 Gere, Richard, 20

Forecasting in cash budgeting

sources of cash, 558–559 steps, 557 uses of cash, 559

cash flows, 299, 404 consistent, 301 and constant-growth dividend discount

model, 205–206 dividends, 205–206 earnings and dividends per share, 506 economic indicators, 301 in financial planning, 523 stock prices, 202–205 working capital, 285

Foreign exchange market, 37, 38 Forward contracts

characteristics, 696 definition, 696 and futures contracts, 696 for risk management, 696

Forward rate agreements, 696 Fraud; see also Corporate scandals

Allied Crude Vegetable Oil Refining, 566

Bernard Madoff, 19 Freddie Mac, 49, 174

collapse of, 69 Free cash flow

components, 68 definition, 67 Home Depot, 67–68 Valuing, 212 for valuing entire businesses, 403–405

Free-cash-flow problem, 483 Free-cash-flow theory of takeovers,

612, 625n Free credit, 124–125 Friedman, Milton, 24 Fudge factors, 377 Fundamental analysis, 218–219 Fundamental analysts, 219 Funded debt, 426 Futures contracts, 674

characteristics, 690–693 commodity futures, 694–695 definition, 690 financial futures, 695 and forward contracts, 696 for hedging, 687, 692 iron ore, 699 margin account, 690n mechanics of, 693–694

margin requirement, 694 marked to market, 694 spot price, 694

versus options, 690n profit on, 691–692 real estate, 699 for risk management, 690–695

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IND-18 Subject Index

Inefficiencies, eliminated by merger, 612 Inflation

and Bill Gates, 150 and Consumer Price Index, 146 definition, 146 and gasoline prices, 147 and interest rates, 25 and time value of money

interest rates, 148–149 real vs. nominal cash flows, 146–147 real vs. nominal present value

calculation, 151 valuing real cash payments, 149–150

inflation-adjusted interest rates, 165 Inflation-indexed bonds, 179 inflation-indexed debt, 25 Inflation rate

and cash flows, 277–278 and real interest rate, 179 in United States 1900–2013, 147

Information and efficient market hypothesis,

219–220 for investors, 18 value in sensitivity analysis, 305

Information content of dividends, 501–502

Information content of stock repurchase, 503

Initial public offering Apple Inc., 37 bookbuilding method, 445 case, 455 costs of, 444–445 definition, 194, 440 Facebook, 214 Federal Express, 4, 5, 194 open auction, 445 Palm, 627 versus remaining privately owned, 441 and Sarbanes-Oxley Act, 441 versus secondary offerings, 440 state blue sky laws, 442 total costs, 444 types of firms using, 437 underwriters, 445–446 underwriting arrangement

best-efforts basis, 441 firm commitment, 441 floatation costs, 444–445 issue pricing, 442 prospectus, 442 roadshows, 442 SEC regulations, 441–442 spread, 441 underpricing, 442–443

Inputs in financial planning, 524 Insolvency, 499n installment credit, 669–670 Installment plan, 128

I IBES, 210n IBM, 38, 339, 349–350, 363, 372, 401,

609, 619 Icahn, Carl, 620, 625 Idle cash, 592

in money market, 596–598 Illiquid assets, 99 Immoo, Lee, 444 Implicit annual interest rate, 579 Implicit costs, 469 Improved financial planning model,

526–530 Income

versus cash flow cash vs. accrual accounting, 63 depreciation, 72–63

subject to corporate tax, 71–72 subject to personal tax, 62–73

Income statement accrual accounting, 63, 65 capital expenditures on, 63, 65 common-size, 62 cost of capital excluded, 87 definition, 61 depreciation on, 62–63 earnings before interest and

taxes, 62 effects of transactions, 64–65 expense items, 61–62 Home Depot, 61–63, 85 income vs. cash flow, 62–65 profits vs. cash flow, 64–65 pro forma, 524–528 retained earnings, 62 taxes on, 62

Income stocks, 199 dividend growth, 213 reasons for buying, 212–213

Incremental cash flows allocated overhead costs, 276 discounting, 274–276 forecasting, 274 ignoring sunk costs, 274–275 including all direct effects, 274 including opportunity costs, 275 recognize investments in working

capital, 275–276 terminal cash flow, 276

Incremental risk, 343 Independent outside directors, 423 Index funds, 45

fully diversified, 365 Index mutual funds, 45 Index options, 674 Indirect costs of bankruptcy, 478 Indirect effects, 274 Indirect ownership, 9 Industry consolidation, 612

Hedging—Cont. and financial distress, 688 financial instruments for, 687 with forward contracts, 696 with futures contracts, 690–695 innovation in derivatives, 699 investors’ do-it-yourself

alternative, 688 with options, 690 problems with derivatives, 699–700 reasons for, 688–689 sensible risk strategy, 689 with swaps, 696–698 timing of, 688 types of derivatives, 689 value of tools for, 700 as zero-sum game, 688

Helyar, J., 623n Herman Miller Corporation, 555 Hess, 11

investment and financing decisions, 5 Hewlett-Packard, 6, 16, 626

write down by, 69 Hidden debt, 470–471 High-dividend policy, 507–508, 713 High-yield bonds, 181 Historical cost, 58, 197, 215 Home Depot, 16, 87, 97

after-tax operating income, 88 balance sheet, 56–59, 86 book vs. market value, 59 economic value added, 88 efficiency measures, 92–93 financial leverage, 96–98 free cash flow, 67–68 income statement, 61–63, 85 liquidity ratios, 99–100 net income, 88 profit margin, 93 return on assets, 90 return on capital, 90 return on equity, 91 selected financial measures, 102–103 statement of cash flows, 65–68 summary of

financial ratios over time, 101–103

performance measures, 101 Home mortgage payments, 137–138 Horizontal merger

definition, 608 economies of scale as goal of, 610

Horizon value, 404–405 Hostile takeovers

PeopleSoft by Oracle, 621–622 and poison pills, 621–622 and shark-repellent, 622

Human behavior, and investing, 712 Hurdle rate, 412

for investments, 48

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Subject Index IND-19

economic order quantity, 590 essential features, 590 just-in-time systems, 591 production to order, 591 shortage costs, 589

Inventory period definition, 552 estimating, 552

Inventory turnover versus profit margin, 94–95 for selected industries, 95

Inventory turnover ratio, 92 Investment(s); see also Capital

investment projects; Future value; Present value

adding market value, 14 annuity factor, 135 compound interest, 118 effects of inflation, 146–151 in fixed assets, 282–283 future value, 198 by individuals, 117 in intangible assets, 117 in inventories, 63 least and most risky, 367 in new products, 301 options for investors, 369–370 and risk, 237 risky, 12 in tangible assets, 117

Investment banks, 21, 22 bridge loans, 42n compared to commercial banks, 43n functions, 42–34 investments by, 42 largest, 43 underwriters, 445–446 underwriting, 42

Investment decisions, 3; see also Capital budgeting decisions; Financial investment criteria

examples, 235 Federal Express, 4–5 and financial planning, 521 and investment trade-off, 13–14 less complex than financing

decisions, 415 long-term consequences, 6 recent examples, 5 separate from financing decisions,

278–279 and shareholder value, 84 side effects on financing, 714–715

Investment grade bonds, 47, 181 Investment horizon, 202–205, 210 Investment income, tax policy, 73 Investment opportunity frontier, 342–343 Investment process

analysis of competitive advantage, 302 bottom-up, 300

Interest tax shield, 624, 627 definition, 472 and market value, 474 as perpetuity, 472 and value of shareholders’ equity, 473

Internal finance, 482–483 Internal growth rate, 534, 535 Internally generated funds

definition, 416 reliance on, 417, 419

Internal rate of return financial calculator solutions, 247 and interest rates, 248 with multiple internal rate of

returns, 268 spreadsheet solutions, 246

Internal rate of return rule agreement with NPV rule, 245 for choosing between mutually

exclusive projects, 267–268 definition, 243 discounted cash flow method, 245 long-lived projects, 243–245 opportunity cost of capital, 244–245 percentage of firms using, 259 pitfalls

lending or borrowing, 248 multiple rates of return, 249–250 mutually exclusive projects,

245–247 mutually exclusive projects with

different outlays, 248 summary on, 258

Internal Revenue Service, 71, 72, 282, 287, 627

International Monetary Fund, 50 Internet payment system, 594 Internet stock bubble of 2000, 49 Intrade, 39 Intrinsic value

of common stock, 200–202 definition, 200 and market value, 712

Inventories Amazon, 577 on balance sheet, 56 capital tied up in, 577, 589–590 carrying costs, 555 composition of, 589 as current asset, 549 investment in, 63 just-in-time systems, 92 optimal levels, 590 reduction in, 63 shortage costs, 555 valuation of, 553n

Inventory management carrying costs, 578–590 composition of inventories, 589 costs of capital, 589–590

Institutional shareholders, 17 proxy contests, 620

Insurance companies functions, 43 risk reduction by, 45

Insurance industry, 21 Intangible assets, 3, 6

abandonment value, 314 on balance sheet, 57 and going-concern value, 198 investments in, 117

Intel Corporation, 59, 121, 339, 363, 364–365, 372, 401, 439, 461, 548

Intercontinental Exchange, 37 Interest

and cash budgeting, 559 compound, 118–121 deductible, 72, 389 simple, 118

Interest coverage, 97 Interest-free reserves, 427n Interest payments, 166, 328 Interest rate options, 661 Interest rate risk, 172

in money market, 596 Interest rates

ancient, 24 annual percentage rate, 144 and bond prices, 165, 167–172 call options, 670 and capital structure, 396 and compound interest, 118–121 on corporate debt, 425–426 discount basis of quotes, 597 discount rate, 122 effective annual, 144–145 floating, 425 on government bonds as benchmark,

165 implicit annual, 579 information from financial

markets, 47 and internal rate of return, 248 and long-term bond prices, 178 long-term corporate bonds, 47 on microloans, 36 money market instruments, 597 and net present value, 248 present value calculation, 123–124 prime rate, 425–426 quoted in nominal terms, 277 real vs. nominal, 148–149, 165,

178–180 risk-free, 398 simple interest, 118 TED spread, 564 trade credit, 579 varying bond prices, 170–172

Interest rate swaps, 697–698

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IND-20 Subject Index

Legal capital, 500 Lehman Brothers, 8, 24, 25, 49, 174, 424,

478, 494, 567 default, 597 repurchase agreements, 69–70

Level cash flows annuity due, 141 future value of annuity, 138–141 lottery winnings, 136–137, 142 mortgage payments, 137–138 valuing annuities, 134–135 valuing perpetuities, 133–134

Leverage and incentives, 625 and taxes, 624

Leveraged buyouts, 96 and bondholders, 624–625 case, 632 cash cow targets, 625 compared to other acquisitions, 623 definition, 623 as diet deals, 624 ending in bankruptcy, 625 and incentives, 625 junk bond market, 624 management buyouts, 623 private equity activity, 623 RJR Nabisco, 623–624, 625, 627 and stakeholders, 624–625 and taxes, 624

Leverage ratios, 85 cash coverage ratio, 97 debt ratio, 96–97 and return on equity, 98 times interest earned ratio, 97

Levered firm, 466 Levi Strauss, 441 Li, K., 502 Liabilities

on balance sheet, 56–59, 197 book vs. market value, 60 classes of, 58 long-lived vs. short-lived, 545 long-term, 57–58

Liberty Global, 608 Life cycle of the firm, 510–511 Life insurance companies, 21

mortality bonds, 429 Life Technologies, 608 Limited liability, 7 Limited liability companies, 10 Limited liability partnerships, 10 Limited partnership, 10 Limit order book, 195 Linares, P., 333n Line of credit, 564, 566–567 Liquid assets, 56, 99 Liquidation

definition, 493 versus reorganization, 494–495

Iowa Electronic Markets, 39 IPO; see Initial public offering Iron ore futures, 699 Irrational exuberance, 224, 712 Issued and outstanding shares, 420 Issued but not outstanding shares, 420

J J. D. Edwards & Company, 621 JCPenney, 17 Jensen, Michael C., 483, 500n, 625n Jobs, Steve, 437, 508 John Deere, 11

investment and financing decisions, 5

Johnson, J., 534 Johnson, Ross, 623, 625 Johnson & Johnson, 199, 439, 608

market-to-book ratio, 200 market vs. book value, 197–198 price and yield on bonds, 181

JPMorgan Chase, 42, 49, 445, 447, 502, 598

dividend policy, 503 Junk bond market, 624 Junk bonds, 47, 181 Just-in-time systems, 92, 591

K Kahn, V. M., 584 KAI Pharmaceuticals, 611 Kaplan, S., 625 Kellogg’s, 349 Keown, A., 219n Kickstarter, 440 Kinko’s, 4 Koch Industries, 441 Kohlberg Kravis Roberts RJR

Nabisco LBO, 623–624, 625, 627

Kolasinski, Alan, 373 Korwar, A. N., 448n Kozlowski, Dennis, 15, 17

L L. A. Gear, 548

bankruptcy, 550 Labor expenses, 559 Lamont, O. A., 627 Lazard, 43 LBO; see Leveraged buyouts Lease, 428 Leased assets, 97n Leasing, 715 Lee, C. M., 224n

Investment process—Cont. capital budget, 300 consistent forecasts for, 301 eliminating conflicts of interest, 301 project authorization, 300–301 proposals, 300 reducing forecast bias, 301–302 top-down, 300

Investment proposals, 300 Investment risk, 15 Investment timing decision, 253, 254 Investment trade-off and value

maximization, 13–14 Investors; see also Shareholders

angel, 439 assessment of financial distress, 476 and behavioral finance

attitudes toward risk, 223 beliefs about probabilities, 223–224 sentiment, 224

in callable bonds, 677–678 and corporate governance, 18 diversification by, 45 and efficient market hypothesis, 220 equity vs. debt, 6 and financial managers, 11–12 flight to quality, 597 fundamental analysts, 219 and general cash offerings, 449 and growth companies, 198 in growth stocks, 199 in hedge funds, 40–41 hedging choice, 688 high-dividend policy, 507–508 in income stocks, 199 installment credit purchases, 669–670 investment options, 369–370 irrational exuberance, 224 liquid bond preference, 182 and macro risks, 349 versus managers, 15 in mutual funds, 40, 364–365 number of securities to choose from, 329 overconfidence, 224 and prediction markets, 39 in proxy contests, 620 rate of return from Geothermal,

390–391 required return, 371, 372n risk-averse, 12 risk-tolerant, 12 short sellers, 41n short-sellers, 20 and stock price quotes, 217–218 technical analysts, 216 time horizon, 202–205 trading demand, 38 trading volatility, 674 value assessment by, 416 value of liquidity, 714

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Subject Index IND-21

Market for corporate control agency costs, 619 definition, 619 and poison pills, 621–622 and separation of ownership and

management, 619 and shark-repellent, 622 ways of changing management

divestitures, spin-offs, and carve- outs, 625–626

leveraged buyouts, 623–625 proxy contests, 620 takeovers, 620–623

Market indexes, 329 Market interest rate, 171 Market order, 195 Market portfolio, 332

definition, 358 Market price, 198 Market risk

definition, 347 industry differences, 349 and macroeconomic events, 357 as macro risk, 349 measuring, 708

betas, 357, 358–361 portfolio betas, 363–367 total risk, 361–363

versus specific risk, 346–347 and total risk, 361–363

Market risk premium calculating, 367–367 definition, 367 measuring, 398

Market-to-book ratio definition, 86–87 for selected companies, 86, 199–200

Market value added by investments, 14 company cost of capital, 392 and debt ratio, 97 definition, 197 drawback of performance

measures, 87 excluded from balance sheet, 91 and intrinsic value, 712 and liquidation value, 198 maximizing, 13–14 measure of current assets and

liabilities, 60 measuring, 86–87 summary of, 199 WACC based on, 396

Market value added, 86–87 Home Depot, 85–86 for selected companies, 86

Market-value balance sheet, 60, 215, 397

Market Volatility Index, 674 Marriott, 419

M Machine tool manufacturers, market

risk, 349 Macquarie Bank, 42 Macroeconomic events

creating market risk, 357 and rate of return on market

portfolio, 358 Macro risks, 349 Madoff, Bernard, 19 Maintenance, 301 Majluf, N. C., 449n Majority voting, 423 Makkula, Mike, 34 Malkiel, Burton G., 220n Management

and agency theory, 710 improved by merger, 612 value added by, 712–713 ways of changing

carve-outs, 625–626 divestiture, 625–626 leveraged buyouts, 623–625 proxy contests, 620 spin-offs, 625–626 takeovers, 620–623

Managerial buyout, 623 Managers

agency problems, 15–16 in corporate governance, 17–18 of corporations, 9 effect of no takeover, 627 effect of threat of financial

distress, 483 ethics of value maximization, 18–22 executive compensation, 16–17 versus investors, 15 profit maximization, 13 use of WACC, 387 and vesting, 16n views of dividend policy, 501–502

Manchester United, 37 Manhattan Island purchase, 120–121 Manville Corporation, 494 Margin account, 690n Marginal tax rate, 73

corporate tax, 510 Margin requirement, 694 Marked to market, 694, 696n Marketable securities, 548–549

as current asset, 549 Market anomalies

earnings announcement puzzle, 221 new-issue puzzle, 222

Market capitalization, 7, 506 definition, 85 Federal Express, 195 Home Depot, 85 for selected companies, 86

Liquidation value, 199 Liquid bonds, 182 Liquidity

advantages of, 548–549 corporate vs. Treasury bonds, 714 definition, 46, 99 drawbacks of, 99 in holding cash, 591 lacking during financial crisis, 714 in money market, 596 provided by financial institutions, 46 value for investors, 714 value of, 713

Liquidity ratios cash ratio, 100 current ratio, 100 less desirable characteristics, 99 net working capital to total assets

ratio, 99–100 quick (acid test) ratio, 100

Loan covenants, 480–481 Loans, amortizing, 138 Lochhead, Scott, 444 Lock-box systems, 592–593 Lockheed Corporation, 274–275,

310–311 LOKmicro, 36 Long-lived projects

calculating rate of return for, 243–244

cash flows from, 238–242 net present value, 244–245

Long-term bonds, 178 Long-term debt, 38, 96

in financial planning, 530–531 Long-term debt-equity ratio, 96 Long-term debt ratio, 96

and sustainable growth rate, 208 Long-term financial decisions, 545 Long-term financial planning, 522

focus on big picture, 522 links to short-term financing

advantages of liquidity, 548–549

alternative approaches, 547 time horizon, 546 total capital requirements,

546–548 planning horizon, 522

Long-term liabilities, 57–58, 396–397

Long-term Treasury bonds, 330 Loss carryback, 72 Loss of a degree of freedom, 338n Lotteries, 136–137 Low-dividend policy, 509–510, 713 Lowe’s, 16

selected financial measures, 102–103

Low-quality earnings, 69

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IND-22 Subject Index

Money; see also Time value of money greenbacks, 24 real vs. constant dollars, 147 in 17th-century America, 24

Money management, 21 Money managers, 220–221 Money market, 38

corporate vs. government securities, 597

default risk, 596, 597 definition, 596 during financial crisis, 597 fixed-income securities, 596 instruments

certificates of deposit, 596 commercial paper, 596 repurchase agreements, 596 Treasury bills, 596

interest rate risk, 596 interest rates, 597 liquidity of, 596 market turmoil, 597 maturities, 596 yields, 597

Moody’s Investors Services, 180–181, 580, 596

Moore, Gordon, 121 Moore’s law, 121 Morgan Stanley, 10, 21, 43, 43n, 445 Mortgage amortization, 139 Mortgage-backed securities, 49 Mortgage default rates, 99 Mortgage pass-through

securities, 429 Motorola, 620, 625 Motorola Mobility, 626 Motorola Solutions, 626 Mullins, D. W., 448n Multiple cash flows

future value, 126–127 present value, 128–129 spreadsheet solution, 12–133

Multiple discriminant analysis, 583 Multiple rates of return, 249–250 Municipal bonds, 180n Murphy, T., 591n Mutual funds, 21

advantages, 40 closed-end, 40n compared to exchange-traded

funds, 45n functions, 40 management fees, 40 number of, 40 open end, 40n risks, 364–365

Mutually exclusive projects choosing among, 241–242 choosing between long - vs. short-lived

equipment, 254, 255–256

mechanics of and antitrust law, 615 form of acquisition, 614–615 tender offer, 615

pharmaceutical firms, 611 popular opposition to, 615 recent, 608 RJR Nabisco, 24–25, 623–624,

625, 627 sensible reasons for

combining complementary resources, 611

to create synergies, 609, 610 economies of scale, 610 economies of vertical integration,

611 eliminating inefficiencies, 612 industry consolidation, 612 use for surplus cash, 611–612

types of, 608–609 in U.S. 1962–1013, 607, 608

Merrill Lynch, 25, 43n, 49, 609 Merton, Robert, 671, 711n Mian, L. L., 588n Michaely, R., 502 Microfinance institutions, 36 Microsoft Corporation, 87, 90, 91,

196, 437, 440, 461, 481–482, 608, 609

economic value added, 89 market cap, 7 market value added, 86

Mikkelson, W. H., 448n Mill, John Stuart, 711 Miller, Merton H., 462, 504, 709, 713 Minimum operating cash balance, 560 Minuit, Peter, 120–121 Mitchell, M., 626n MM debt-irrelevance proposition, 466 MM dividend irrelevance

proposition assumptions, 507 example, 504–505 and shareholder value, 510

MM proposition I, 709 and corporate taxes, 473 cost of equity, 468 definition, 466 expected return on stock, 467 shareholder risk, 462–467 simplifying assumptions, 462 value of the firm, 462–464

MM proposition II, 709 debt-equity ratio, 469–470 definition, 468

Modified accelerated cost recovery system, 286–288

Modified Internal rate of return, 268 Modigliani, Franco, 462, 504,

709, 713

Marsh, Paul R., 329–330, 331, 334, 335, 337, 338

Marten, K. J., 612 Massachusetts

ban on Apple initial public offering, 442n

Department of Public Utilities, 242

Masulis, R. W., 448n Matching maturities, 547–548 Maturities, 166

commercial paper, 566 corporate debt, 426 of debt securities, 38 forward contracts, 696 matching, 547–548 in money market, 596

Maturity date, 38, 176 lacking for preferred stock, 394

Maturity premium, 330 Maximizing value; see Value

maximization McConnell, J. J., 612 McDonald’s, 210–211, 339, 363,

372, 401 market-to-book ratio, 200 market vs. book value, 197

McNichols, Maureen, 581, 582 Medco Health Solutions, 608 Median financial ratios, 104 Memorex, 484 Merchant banks, 42n Merchant businesses, 376 Mergers

case, 632 cash flow changes, 619 cost-benefit analysis, 607 costs of, 626–628 Daimler-Chrysler failure, 609–610 definition, 614 distinction between cash and stock

financing, 618 dubious reasons for, 612–614

bootstrap game, 613–614 diversification, 613

evaluation of cash financing, 616–617 stock financing, 617–618 warnings on, 618–619

explaining waves of, 626–628, 713 failures, 609–610 hostile takeovers, 607 integration problems, 609–610 and market for corporate control,

619–626 divestitures, spin-offs, and carve-

outs, 625–626 leveraged buyouts, 623–625 proxy contests, 620 takeovers, 620–623

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Subject Index IND-23

O Obama, Barack, 39 Occidental Petroleum, 595 Off-balance-sheet assets and

liabilities, 70 Omnicom, 608 One-at-a-time sensitivity analysis, 305 Open account, 580 Open auction issue, 445 Open end funds, 40n Open-market repurchase, 501 Operating cash flow

break-even point, 308 of cost-cutting projects, 280 dealing with depreciation, 280, 284 example, 281 forecasting, 283–286 formula, 279

Operating income, 88 effect of earnings per share, 466

Operating leverage, 467n definition, 311 degree of, 311–313 and project risk, 313, 376

Operating profit margin, 94 Operating risk, 466 Opportunity cost

definition, 275 ignored, 310 in incremental cash flows, 275

Opportunity cost of capital, 33, 87, 332, 708

and break-even point, 308 and capital asset pricing model

avoiding fudge factors, 377 company cost of capital, 376 determinants of project risk,

376–377 estimating, 375 project cost of capital, 374

definition, 14 expected rate of return, 48 and internal rate of return rule, 245 and investment risk, 15 and net present value, 237 project estimation, 375

Option(s) as choices, 709 in financial planning, 523

Option ARM, 49n Option premium, 662 Options

calls and puts, 662–665 on financial assets

callable bonds, 677–678 convertible bonds, 676–677 executive stock options, 676 warrants, 676

versus futures contracts, 690n

payback rule, 252 replacement problem, 254, 257 timing decision, 253, 254

definition, 237 discounting cash flows, 271–272 merits of, 708 and opportunity cost of capital, 237 percentage of firms using, 259 and risk, 237 steps, 271 summary on, 258

Net working capital, 57, 99; see also Working capital

in capital structure, 396 definition, 275, 551 function of sales, 531 incremental cash flows, 275–276

Net working capital to total assets ratio, 99–100

Net worth, 424 New-issue puzzle, 222 Newmont Mining, 339, 345–346, 362–

363, 372, 401 New product launch, 274 New York Mercantile Exchange, 47, 699 New York Stock Exchange, 9, 37, 194,

347, 423, 615 daily turnover, 636 formation of, 24

New York Stock Exchange Euronext, 608 NINJA loan, 49 No-growth dividend discount model, 205 Nokia Handset and Services Business,

609 Nominal cash flows, 146–147, 179,

277–278 Nominal cost of capital, 277–278 Nominal dollars, 147 Nominal interest rate, 148–149, 165,

178–180 Nominal present value calculation, 157 Nominal rate of return, 328 Noncallable bonds, 426 Noncash expenses, 63 Nonconstant growth stock

estimating McDonald’s value, 210–211 investment horizon, 210 terminal value, 210 valuation errors, 210–211 value of dividends, 210

Nondiversifiable risk, 708 Normal growth plan, 522 NPV; see Net present value Numerical credit scoring

FICO score, 581n financial ratios for, 581–582 five C’s of credit, 581 hazard analysis, 583 for small business, 584 Z-score model, 583

with different outlays, 248 and internal rate of return rule,

245–247 internal rate of return rule for choosing

between, 267–268 investment timing decision, 253, 254 profitability index, 250 replacement problem, 254, 257

Myers, S. C., 403n, 449n, 474n

N Nardelli, Robert, 16 NASDAQ, 37, 194, 423

decline in 2000–2002, 332 in dot-com bubble, 222

NASDAQ Composite Index, 712 NASDAQ market index, 329 National Association of Securities

Dealers Automated Quotation System, 194n; see also NASDAQ

Negative-risk asset, 342 Net asset value, 40n Net common equity, 421 Net current assets, 57 Net income

versus cash flow, 65 and internal growth rate, 535

Net present value, 236–242 and abandonment option, 315 break-even point, 308–309 calculating, 384–385, 708 calculating cost of capital, 237 calculation steps, 240 Cape Wind project, 241–242 and competitive advantage, 302 definition, 235, 237 and discount rate, 244–245 financial calculator solutions, 247 and forecast bias, 301–302 long-lived projects, 244–245 to measure worth of projects, 272–273 new computer system, 239–240 office block project, 238–238,

238–239 and option to expand, 315 positive, 250 and risk, 237 simulation analysis, 305–306 spreadsheet solutions, 242 timing option, 315–316 and wrong forecasts, 304 zero, 395

Net present value rule, 237–242 agreement with internal rate of return

rule, 245 choosing among projects, 241–242

long- vs. short-lived equipment, 253, 254–255

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IND-24 Subject Index

Pension Benefit Guarantee Corporation, 493

Pension funds definition and functions, 41 total assets in 2013, 41

PeopleSoft, takeover by Oracle, 621–622 PepsiCo

market-to-book ratio, 200 market vs. book value, 197

Percentage capital gain, 328 Percentage of sales models

assumptions and complexities, 531–532

balancing item, 525–526 definition, 525

Percentage returns, 328 Perpetuities, 426

definition, 133 no-growth, 205 preferred stock dividends as, 394 present value, 206 valuing, 133–134

Personal tax average rate, 73 on capital gains, 73 on dividend income, 73 marginal rate, 73 on ordinary income, 73 tax rates, 72

Petersen, M. A., 589n Pfizer, Inc., 339, 363, 372, 401, 625 Pharmaceutical firms, 611 Pinkerton, J., 219n Pinkowitz, L., 548–549 Pirates of the Caribbean, 235 Planet Hollywood, 484 Planning horizon, 522 Planning model, 524 Plowback ratio, 207–208, 211n

and sustainable growth rate, 536 Plug; see Balancing item Ponzi, Charles, 19n Ponzi schemes, 19 Portfolio betas, 363–366 Portfolio rate of return, 341 Portfolio risk, 330, 331

versus asset risk, 340–345 calculating, 345 economic scenarios for, 340–342 example, 345–346 investment opportunity frontier,

342–343 market risks as macro risks, 349 market vs. specific risk, 346–347

Portfolios; see also Market portfolio diversification, 339–340 floating-rate, 698 risk of diversification, 366–367

Positive net present value, 250 Positive-NPV projects, 510, 522, 710

Paulson, John, 20 Payback period, 252

percentage of firms using, 259 summary on, 258

Payback rule, 236, 251–253 cutoff period, 252 discounted payback period, 253 length of payback periods, 253 payback period, 252 problems with, 252 reasons for using, 252–253 simplicity of, 252

Payment date, 499 Payment mechanism, 46–47 Payment systems

checks, 593–594 commonly used, 594 electronic bill presentation and

payment, 594 electronic funds transfer, 594–595 stored value cards, 594 in United States, 594, 595

Payoff on derivatives, 687 on options, 665, 667

Payoff diagram, 665–666 Payout policy, 497

and capital budgeting decisions, 506 controversy

dividends and share issues, 506–507

MM dividend irrelevance proposition, 504–505, 507

repurchase vs. dividend discount model, 505–506

views on value of the firm, 503 high-dividend policy, 507–508 implications of taxation, 509–510 information content

of dividends, 501–503 of stock repurchase, 503

and life cycle of firms, 510–511 low-dividend policy, 509–510 managerial views, 501 means used

cash dividends, 498–499 stock dividends, 500–501 stock repurchase, 501 stock splits, 500–501

reasons for value decrease by dividends, 509–510

reasons for value increase by dividends, 507–508

resolving dividend controversy, 713 Payout ratio, 207 Pecking order theory of capital structure

asymmetric information, 482 definition, 482 internal and external equity, 482–483

Penn Central Railroad, 24

Options—Cont. for hedging, 687 Market Volatility Index, 674 modifying risk characteristics of stock,

666–667 payoff and profit diagrams, 665–666 versus payoff from holding stock, 667 protective put, 666 put-call parity, 667 on real assets

option to abandon, 675 option to expand, 674–675

for risk management, 661 for risk reduction, 690 selling calls and puts, 664–665 types traded, 661 value at expiration date, 668–669

Options contracts, 674 Options markets, 38 Options trading, 661 Options writer, 664n Option to abandon, 315, 675 Option to expand, 313–315, 674–675 Option valuation models

Black-Scholes formula, 671–673 Financial Accounting Standards Board

requirements, 676 simple models, 672

Option values, 709–710 Apple Inc., 663 determinants, 669–671 upper and lower limits, 668–669 valuation models, 671–673

Oracle Corporation, 16, 17n, 676 takeover of PeopleSoft, 621–622

Orange, M., 534 Ordinary income, 73 Other current assets, 56 Outputs in financial planning, 524 Outsourcing vs. vertical integration, 611 Overconfidence, 224 Overhead costs, 276 Over-the-counter markets, 37

P Pacific Gas & Electric, 567 Page, Larry, 437 Palepu, K., 500n, 502, 627 Palm, 626, 627 Partch, M. M., 448n Partnership

definition, 10 tax advantages, 10 types of, 10 unlimited liability, 10

Partnership agreement, 10 Par value, 166

common stock, 421

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Subject Index IND-25

receivables turnover, 92–93 return on assets, 90 return on equity, 91

Profit diagram, 665–666 Profit margin, 83, 93–94

for elected industries, 95 high versus low, 94 versus inventory turnover, 94–95

Profit maximization, 13 and credit decision, 586–587

Pro formas, 524–528 Progress Energy, 608, 610 Project analysis

break-even analysis accounting, 306–308 net present value, 308–311 operating leverage, 311–313

case, 324 investment process

analysis of competitive advantage, 302 capital budget, 300 consistent forecasts, 301 eliminating conflicts of interest, 301 project authorization, 300–301 reducing forecast bias, 301–302

real options flexible production facilities, 316 option to abandon, 315 option to expand, 313–315 timing option, 315–316

what-if questions, 299, 302–306 crucial for capital budgeting, 303 scenario analysis, 305–306 sensitivity analysis, 303–305 simulation analysis, 305–306

Project authorization, backup information, 300–301

Project betas, 710–711 Project cash flows, 278

capital investment, 279 cash flow analysis, 282–284 changes in working capital, 282–284 and depreciation, 280–281, 285–287 financing, 271–272 and financing, 278 forecasting mistakes, 276 forecasting working capital, 284 Geothermal, 395 identifying

allocated overhead costs, 276 incremental cash flows, 274–276 terminal cash flows, 276

ignoring sunk costs, 274–275 investment in fixed assets, 282–283 operating cash flow, 279–280, 283–284 opportunity costs, 275 salvage value, 287 separate investment from financing

decisions, 278 spreadsheet solutions, 288

of financial assets, 694 futures contracts, 695 of gasoline, 147 with inflation, 146–147 of oil, 690 spot price, 694 valuation of common stock,

200–202 Price-earnings multiple, 196 Price-earnings ratio, 193, 199–200

in bootstrap game, 614 definition, 196 infinite, 214 and stock prices, 214

Price indexes, 146 Primary issue, 37 Primary market, 37 Primary markets, 194 Primary offerings, 194, 440 Prime rate, 425–426 Principal, 166 Principles-based accounting, 70, 71 Private equity, 623 Private equity investing, 439 Privately owned firms, 441 Private placement, 428

advantages, 449 definition, 449 and Rule 144a, 449

Probabilities, beliefs about, 223–224 Procter & Gamble, 17

investment and financing decisions, 5

Production cycle, 552 Production to order, 591 Productivity gains from mergers, 627 Product markets, competitive advantage

in, 416 Professional corporations, 10 Profit

accounting, 280 calculating, 63 versus cash flow, 272 versus cash flows, 64–65 deliberate inflation of, 69 as earned, 273 expected, 584 on futures contracts, 691–692 on options, 662, 665–666

Profitability and profit margin, 83 Profitability index, 236

with capital rationing, 250–251 definition, 250 percentage of firms using, 259 pitfalls, 251 positive net present value, 250 summary on, 258

Profitability ratios asset turnover ratio, 92 inventory turnover, 92

Postpetition creditors, 494 Potash, 564 Power Ball lottery, 136–137 Power purchase agreement, 240 Prediction markets, 39 Preferred stock

characteristics, 394 convertible, 431 definition, 424 dividends, 424 expected return on, 400 floating-rate, 425 lack of voting privilege, 424 and net worth, 424 tax advantage, 424

Premium bonds, 173 Prepackaged bankruptcy, 493n Prepetition creditors, 494 Present value

of annuities, 134–136 on annuity, 139 calculating, 122–124 Cape Wind project, 241 case, 163 of cash flows, 272, 284 definition, 121–122 determinants, 710–711 discounted cash flow calculation, 122 discount factor, 123 and discount rate, 122 examples, 124–125 finding interest rates, 125–126 formula, 122, 123 of free cash flows, 405 free credit, 124–125 of future cash flow, 123 and interest rates, 168, 169 interest tax shield, 472 lottery winnings, 136–137 mortgage payments, 137–138 of multiple cash flows, 128, 132–133 of perpetuities, 133–134 of real cash payments, 149–150 and risk, 237 solutions

with financial calculators, 129–130 with spreadsheets, 130, 242

of spending stream of wealth, 137 in stock valuation, 203–204 and varying interest rates, 170–171 and yield to maturity, 173

Present value of growth opportunities, 213, 215

Present value table, 124 Presidential futures prices, 39 Pretax return, 509 Pretty Woman (film), 20 Price(s)

of commodities, 695 corporate vs. Treasury bonds, 714

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IND-26 Subject Index

Regression line, 361n Regulated businesses, 376 Reinhardt, U. E., 311n Reinsurance, 45n Relational Investors, 20 Reorganization

definition, 493 versus liquidation, 494–495

Repayment provisions, 426–427 Repeat orders and credit decision,

585–586 Replacement problem, 254, 257 Repo 105, 69 Repurchase agreements

Lehman Brothers, 69–70 in money market, 597

Reputation, in financial transactions, 19 Reserve borrowing power, 100 Residual claimants, 58 Residual income, 87

and working capital, 555 Restricted stock, 16 Restructuring

and cost of capital, 468 effect on capital structure, 463–464 MM proposition I, 466

Retained earnings, 62 Apple Inc., 35 versus cash balances, 58n definition, 421

Retirement savings, 140–141 Retrenchment plan, 522 Return on assets

and credit scoring, 581 definition, 90 Du Pont formula, 93–95 extra earning power, 198 fluctuations, 101–102 Home Depot, 90 profit margin, 93–94

Return on capital calculating, 90 definition, 89–90 Home Depot, 89–90 for selected companies, 89

Return on equity definition, 91 and financial leverage, 98 Home Depot, 91 and internal growth rate, 535 and plowback ratio, 207–208 and sustainable growth rate, 536

Returns; see also Rates of return common stock, 359 historical record 1900–2013, 335 required, 371, 372n small-firm vs. large-firm stocks,

373–374 standard deviation of, 344 value vs. growth stocks, 373

Q Quick ratio, 100 Qwest Communications, 70

R Rajan, P. G., 589n Rajgopal, S., 68 Random walk, 216–217 Random-walk theory, 709 Rare-earth metals, 316 Rate of return rule, 243 Rates of return; see also Accounting rate

of return; Expected rate of return after-tax, 509 on bonds, 173 case, 232–233 common stock 1900–2013, 331 and cost of capital, 48 definition, 175 expected, 708 hurdle rates, 14 and investment trade-off, 14 multiple, 249–250 nominal, 328 and opportunity cost of capital, 14–15 from past investments, 327 percentage return, 328 portfolio, 341 pretax, 509 real, 328 on various portfolios, 330–332 versus yield to maturity, 174–177

Real assets, 39 definition, 6

Real cash flow, 146–147, 179, 277 Real-company WACCs, 400–401 Real dollars, 147 Real estate futures, 699 Real interest rate, 148–149, 165, 178–180

and supply and demand, 179 Real options

Allegheny Corporation, 675 decision tree for, 314 definition, 315, 674 flexible production facilities, 316 option to abandon, 315, 675 option to expand, 313–315, 674–675 timing option, 315–316

Real present value calculation, 157 Real rate of return, 328 Receivables, 56; see also Accounts

receivable aging schedule, 587 valuation, 553n

Receivables turnover ratio, 92 Record date, 499 Registration statement, 441, 444

general cash offer, 447

Project cash flows—Cont. total, 284 working capital investment, 275–276

Project cost of capital definition, 374 estimating, 375 and project risk, 376–377

Project risk contemplating

big risks as diversifiable, 347–350 market risks as macro risks, 349 risks as measurable, 349–350

determinants, 710–711 earnings variability, 377 operating leverage, 376

and diversification asset vs. portfolio risk, 340–346 market vs. specific risk, 346–347

estimating cost of capital, 332–333 measuring

benchmarks, 334 calculating variance, 337 standard deviation, 334–337 variance, 334–337 variation in stock returns, 337–339

and operating leverage, 313 and opportunity cost of capital, 327 and rates of return, 328 wildcat oil drills, 348

Property, plant, and equipment, 56, 66 Prospect Global Resources, 194 Prospectus

definition, 442 example, 456–459 for general cash offer, 447

Protective covenants, 183–184 Protective put, 666 Proxy, 620 Proxy contests, 423

costs of, 620 definition, 620 Motorola, 620

Public companies, 9 under constant scrutiny, 68–69 financial statement requirements, 56

Public Company Accounting Oversight Board, 70

Public placement, 428 Purchasing power, 147 Put-call parity, 667 Put options

Apple Inc., 663 definition, 62 index, 674 payoff diagram, 665–666 profit diagram, 665–666 protective put, 666 and risk characteristics of stock, 666 selling, 664–665 and stock prices, 667

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Subject Index IND-27

pooled in pension funds, 41 for retirement, 140–141

Savings banks, 42n Scenario analysis

definition, 305 example, 306 in financial planning, 523 and simulation analysis, 303–306

Scenarios, economic, 340–342 Scholes, Myron, 671 Schreffler, R., 591n Schwartz, S. L., 222 Seagram, 534 Seasoned offering, 446–447

definition, 446 direct costs, 444

Secondary market, 37, 194 for stock repurchase, 501

Secondary offerings, 440–441 Secondary transactions, 37 Second-stage financing, 439 Second-stage pro formas, 527–528 Secured creditors, 493 Secured debt, 183 Secured loans

accounts receivable financing, 565 definition, 564–565 hazards of, 566 inventory financing, 565–566

Securities, 7; see also Bonds; Common stock; Corporate bonds; Preferred stock

convertible, 430–431 in money market, 596–597 number to choose from, 329 valuation difficulties, 223 varying risks, 387

Securities and Exchange Commission financial statement requirements, 56 on initial public offerings,

441–442 and international accounting

standards, 71 on maturities, 566 on proxy contests, 620 reporting standards, 18 Rule 144a, 449

Security market line, 370–371 definition, 370 and expected risk premium, 373 and project expected rate of

return, 376 Self-liquidating loans, 564 Selling, Thomas I., 95 Semiannual coupon payments,

169–170 Semistrong-form efficiency,

220, 709 Senior creditors, 494 Seniority, 183

reasons for hedging, 688–689 sensible strategy issues, 689 with swaps, 696–699 three ways of, 689 tools for, 715 variation in, 689

Risk premium, 331 average, 333 and betas, 366n, 367–368 and CAPM, 368–370 expected, 333, 369, 373 future, 333 proportional to beta, 357 and security market line, 370 for selected countries, 334 in United States, 333, 334

Risk reduction, 45, 347 Risk-return trade-off, 15 Risk sharing, 46 Risk shifting, 480 Risk tolerant, 12 Risk transfer, 45–46 Ritter, Jay, 222, 444 Ritz Carlton, Boston, 609 RJR Nabisco LBO, 24–25, 184,

623–624, 625, 627 Roadshows, 442 Rodriguez, Albert, 22 Rolfe, David A., 508 Roll, R., 500n Rolls-Royce, 310 Ruback, R., 627 Rule 144a (SEC), 449 Rules-based accounting, 70

S Safeway, 609 Sales

before cash, 273 on credit, 577, 578–579 end-of-month, 579 and excess capacity, 532 net working capital as function

of, 531 Sales volume, 306

break-even, 307 break-even point, 307–308

Salvage value, 287 Sapienza, P., 18n Sarbanes-Oxley Act, 25

on boards of directors, 17 and initial public offerings, 441 provisions of, 70

Savings flow to corporations, 35–37 pooled in hedge funds, 40–41 pooled in mutual funds, 40

Revenue recognition, 69, 273 Revenues

Apple Inc., 36 Facebook, 214 Federal Express, 4 inflated, 69

Reverse splits, 501 Revolving line of credit, 564 Rhee, Jung-Wu, 581, 582 Rieker, M., 503 Rights issue

definition, 446 rarity in United States, 447

Risk(s); see also Portfolio risk; Project risk

acceptable, 687 asset vs. portfolio, 340–345 attitudes toward, 223 average, 387 company-specific, 45 cost of capital estimation, 332–333 credit risk, 180 diversifiable, 348 of fully diversified portfolios, 366 hedging, 687 identifying, 699 incremental, 342, 343 interest rate risk, 172 market risk, 45, 708 market vs. specific, 346–347, 357 in mutual funds, 364–365 and net present value, 237 New York Stock Exchange

stocks, 347 not eliminated by hedging, 688 and operating leverage, 313 in stock ownership, 194

Risk and return, 357 capital asset pricing model, 711 and CAPM, 368–370, 371–374, 708 effect of borrowing, 466–467 firm size and book value of

stock, 711 least and most risky investments, 367 market risk premium, 367–368 for portfolios, 342 security market line, 370–371 statistical problems, 711

Risk averse, 12 Risk-free interest rates, 398 Risk management

with derivatives, 689 evidence on, 689 with forward contracts, 696 with futures contracts, 690–695 identifying risks, 699 innovation in derivatives, 699 with options, 661, 690 problems with derivatives,

699–700

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IND-28 Subject Index

Smith, C. A., Jr., 588n Smith, Fred, 4, 480 Soft rationing, 251 Sole proprietors, 15 Solera, Sherry, 22 Southern California Edison, 567 Southwest Airlines, 6, 14

investment and financing decisions, 5

Specialists, 194 Special-purpose entities, 70, 428 Specific risk, 357

definition, 347 versus market risk, 346–347

Speculation, 700 Speculative bubbles, 712 Speculative grade bonds, 181 Spin-offs, 625–626 Spot price, 694 Spread, 166, 167, 441, 444 Spreadsheets

for annuity factor, 136, 143–144 for betas, 360 Black-Scholes formula, 63 for bond prices, 168–169 for bond valuation, 176–177 for calculating risk, 360 cash budgeting, 558–559, 561 discounted cash flow analysis, 288 in financial planning, 529–530 future value calculation, 130–133 for internal rate of return, 246 multiple cash flows, 132–133 for net present value, 242 for present value, 242 present value calculation, 130–133 single cash flows, 131–132 for volatility, 344

Sprint, 449 Stafford, E., 626n Stakeholders

definition, 16 and LBOs, 624–625

Standard and Poor’s, 180–181, 580, 596 Standard and Poor’s Composite (500)

Index, 216, 217, 329, 339, 344, 347, 358, 360, 365, 674

decline in 2000–2002, 332 Standard and Poor’s Corporate market

index, 45 Standard and Poor’s Depository Receipts,

45, 46 Standard deviation, 334–337

betas for predicting, 366 calculating, 335–336 for common stock, 339 definition, 335 formula, 336 of Newmont Mining returns, 362–363

Shelf registration advantages, 448 definition, 447 financial managers’ use of, 447

Shiller, Robert, 224n Shivakumar, L., 221n Shliefer, A., 224n Shortage costs, 555 Short sellers, 41n Short-selling, 20 Short-term assets, 275

accounts receivable, 577 cash balances, 577 inventories, 577

Short-term bonds, 178 Short-term borrowing, 551 Short-term debt, 97, 396n, 426

commercial paper, 566–567 Short-term financial decisions, 545 Short-term financial planning, 522 Short-term financing

case, 574–575 cash budgeting, 557–561 financing plan execution and

evaluation, 561–563 links to long-term financial planning

advantages of liquidity, 548–549 alternative approaches, 547 time horizon, 546 total capital requirements, 546–548

revolving line of credit, 564 sources of

bank loans, 564 commercial paper, 566–567 secured loans, 564–566

tracing changes in cash and working capital, 556–557

working capital, 549–555 Short-term financing plan, 561–563

evaluation of, 563 execution of, 562–563 trial and error in developing, 563

Short-term securities versus cash, 591 in money market, 596–597

Shutting-down expenses, 276 Sidel, R., 503 Sight draft, 580 Simple options valuation models, 672 Simulation analysis, 305–306 Single cash flow, 136 Sinking fund, 426 Skinner, Douglas, 508 Skype, 608 Small Business Administration, 493 Small business credit scoring, 584 Small Business Scoring Service, 584 Small-firm vs. large-firm stocks,

373–374

Sensitivity analysis definition, 303 fixed costs, 303 limitations, 305 net present value, 304 one-at-a-time, 305 unknown unknowns, 304 value of information, 305 variable costs, 304

Sentiment about economy, 224 Separation of ownership and

management, 619; see also Agency problems

definition, 9 downside, 9

Shareholders, 8; see also Investors activist, 17–18 and agency theory, 710 blockholders, 17 and capital investment projects,

235–236 debt overhang problem, 480 definition, 420 delegation of decision making, 12 effect of borrowing, 466–469 ethics of value maximization,

18–19 and executive compensation, 16–17 hedging choice, 688 institutional, 17 and integrity, 18n investing in market portfolios, 332 ownership of corporations, 422–423 and profit maximization, 13 in proxy contests, 620 and reorganization, 493 risk-return trade-off, 15 taxation of, 9n value maximization goal, 12–15 voting procedures

cumulative voting, 423 majority voting, 423 proxy contests, 423

voting rights, 9 Shareholders’ equity, 56n

on balance sheet, 58 book value in 2013, 421 book vs. market value, 60 in eBay, 198 and interest tax shield, 473

Shareholder value and corporate raiders, 20 and financial distress, 479–481 and financing decisions, 84 and investment decisions, 84 MM dividend irrelevance

proposition, 510 Shark-repellent, 622 Sharpe, William F., 357

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Subject Index IND-29

high, 500n Home Depot, 85 intrinsic value, 200 liquidation value, 197–198 nonconstant growth stock, 210 and plowing back earnings, 213 and price-earnings ratio, 214 and put options, 662–663, 667 random walk, 216–217 rapid changes in, 196 reaction to general cash offer,

448–449 reaction to news, 219 technical analysis, 216–218 value of assets showing up

in, 198 and value of call options, 669–671

Stock repurchase compared to dividends, 498 definition, 501 versus dividends

capital budgeting decisions, 506 dividend discount model, 505–506 MM dividend irrelevance

proposition, 504–505, 507 value of the firm, 503

effect on stock prices, 505 information content, 503 means of

auction, 501 direct negotiation, 501 greenmail transactions, 501 open market repurchase, 501 tender offer, 501

and share valuation, 503 Union Pacific, 497 in U.S. 1980–2012, 498

Stock splits, 500–501 Stored value cards, 594 Straight-line depreciation, 284, 287 Strategic planning, 522 Strategic plans and capital

budget, 300 Strategy and Du Pont formula, 94 Strike price; see Exercise price Strips, 177–178, 184 Strong-form efficiency, 220, 709 Structured investment vehicles, 99 Subordinated debt, 183 Subprime mortgage market, 714 Subprime mortgages, 25, 99, 430

in crisis of 2007–2009, 49 Sunk costs, ignoring, 274–275 Super-regional banks, 612 Supply and demand

for real interest rate, 179 for trade credit, 589n

Surplus funds, mergers as use for, 611–612

Stockbroking firms, 21–22 Stock dividends, 500–501 Stock exchanges

and brokerage firms, 194 daily trading volume, 194 electronic communication

networks, 194 limit order book, 195 market order, 194–195 NASDAQ, 194 New York Stock Exchange, 194 specialists, 194 trading data sources, 195n

Stockholders, 8n; see also Shareholders Stock market

average returns and standard deviation, 337

bubbles and sentiment, 224 CAPM assumptions, 369 crash of 1929, 24, 339 crash of 2008, 24 efficient market hypothesis,

219–221 as equity market, 37 functions, 37 fundamental analysts, 219 market anomalies

earnings announcement puzzle, 221

new-issue puzzle, 222 primary market, 37, 194 secondary market, 37, 194 shirt selling in, 20 technical analysts, 216

Stock market bubbles, 222–223, 712 Stock market indexes, 329–332 Stock market listings, 195–196 Stock options, 16

executive, 676 risk characteristics, 666

Stock prices Amazon, 198–199 announcement effect, 482 and behavioral finance, 223–224 bid-ask spread, 195 book vs. market value, 197–199 and call options, 662, 667 and company value, 48 Consolidated Edison, 198–199 cycles, 217–218 determination of, 193 in dot-com bubble, 712 effect of repurchases, 505 effects of dividends, 501–502 efficient market hypothesis, 219–221 expected rate of return and risk, 201 and Facebook, 214 forecasting, 202–205 fundamental analysis, 218–219

percentage changes in Dow Jones Industrial Average, 338

of returns, 344 of returns 1900–2013, 338 stock market returns, 337

Starbucks, 339, 363, 366, 372, 401 Start-ups

business plan, 438 crowdfunding, 439, 440 Federal Express, 4 and venture capital, 438–440

Statement of account, 588 Statement of cash flows

capital expenditures, 66 cash flow from financing

activities, 66 cash flow from investments, 65–66 cash flow from operations, 65 definition, 65 free cash flow, 67–68 Home Depot, 65–68

States blue sky laws, 442 laws on dividend payments,

499–500 laws on tender offer, 620–621

State Street Global Advisors, 46 Staunton, Mike, 38, 330, 331, 334,

335, 337 Stern Stewart & Company, 87, 555 Stertz, Bradley A., 609n Stewart, G. Bennett, III, 555n Stickney, Clyde B., 95 Stock; see also Common stock;

Preferred stock compared to bonds, 38 dividend yield, 196 Federal Express performance, 4 as financial asset, 6 forms of return, 328 initial public offering, 194 installment credit purchases,

669–670 irrational exuberance, 224 issues of, 33 measuring variation in returns,

337–339 mergers financed by, 617–618 need to know valuation, 193 primary issue, 37 primary offerings, 194 restricted, 16 risk in ownership of, 194 secondary market, 194 secondary transactions in, 37 small-firm vs. large-firm, 373–374 underwriting, 42 underwriting IPOs, 444–445 valuation, 193

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IND-30 Subject Index

real vs. nominal present value calculations, 151

valuing real cash payments, 149–150

level cash flows, 123–142 multiple cash flows, 126–129 present values, 121–126 solutions

using financial calculators, 129–130 using spreadsheets, 120–133

Time Warner, 609 economic value added, 89 market value added, 86

Time Warner–AOL merger, 609 Timing option, 315–316 Timken Company, 20 TIPS; see Treasury Inflation-Protected

Securities Total assets, 90 Total capitalization, 88 Total capital requirements

finding best level of advantages of liquidity, 548–549 matching maturities, 547–548 permanent requirements, 548

in long- vs. short-term financing, 546–548

seasonal variations, 546 Total debt ratio, 97 Total project cash flow, 284 Total return

on bonds, 173 yield to maturity as measure of,

173–174 Total risk

betas for predicting, 366 and market risk, 361–363

Trade acceptance, 580 Trade credit

as current asset, 549 definition, 578 interest rates, 579 source of funds, 588–589 supply and demand determinants, 589n

Trade-off theory of capital structure, 476, 481–482

Transparency, 70 Trans Union, 581n Travel and entertainment cards, 594 Treasurer, 10–11 Treasury bills, 369

betas of, 367 as current asset, 549 historical returns 1900–2013, 335 measure of risk-free interest rate, 398n in money market, 596

Treasury bonds, 166 asked price, 166, 167 asked yield to maturity, 166, 167

of investment income, 73 and leverage, 624 of partnerships, 10 personal tax, 72–73 and preferred stock, 424 and WACC, 392–393

Tax avoidance, 20, 509n Tax rates

average, 73 on capital gains, 510 on corporations, 72 on individuals, 72–73 marginal, 73

Tax shield, 88n; see Depreciation tax shield; Interest tax shield

Technical analysis, 216–218 Technical analysts, 216 TED spread, 564 Tender offer, 501

definition, 615 laws on, 620–621

10 K forms, 56 10 Q forms, 56 Terminal cash flows, 276 Terminal value, 210 Terms of sale

cash before delivery, 578 cash discounts, 578–579 cash on delivery, 578 credit sales, 578–579 definition, 578 end-of-month sales, 579 implicit annual interest rate, 579 trade credit interest rate, 579

Thaler, R. H., 224n, 627 Thermo Fisher Scientific, 608 Thermopolis, Costas, 388 3Com, 627 3G Partners, 608, 626 Tiffany & Company, 104, 554 Time deposits

certificates of deposit, 596 as current asset, 549

Time draft, 580 Time horizon

of investors, 202–205 long-term financing, 522 long- vs. short-term financing, 546

Times interest earned ratio, 97 Time value of money

annuity due, 141–142 and bond prices, 165 case, 163 definition, 117 future values and compound interest,

118–121 and inflation

and interest rates, 148–149 real vs. nominal cash flows, 146–147

Sustainable growth rate, 213, 536 calculating, 207 definition, 207 long-term debt ratio, 208 variability, 208

Swaps counterparties, 697 credit-default, 182, 699 currency swaps, 698–699 definition, 697 for hedging, 687 interest rate swaps, 697–698 reasons for, 696–697 for risk management, 696–699

Sweep programs, 591–592 Synergies

elusive, 610 mergers to create, 609 sources of

combining complementary resources, 611

economies of scale, 610 economies of vertical integration, 611 eliminating inefficiencies, 612 industry consolidation, 612

Systematic risk, 347

T Takeover, 18

anti-takeover tactics, 621–622 case, 632 effect of threat on management, 628 free-cash-flow theory, 612, 625 hostile, 621–622 PeopleSoft by Oracle, 621–622 by proxy contests, 620 RJR Nabisco, 24–25 tender offer, 620–621

Tangible assets, 3, 6 on balance sheet, 56 easy to sell, 315 investments in, 117

Target interest rate, 714 Target Stores, 554, 640 Taxation

of capital gains, 73 and cash budgeting, 559 corporate tax, 71–72 and debt, 472–473 deductible interest, 389 and depreciation, 286–287 disadvantage for borrowing, 476 disadvantages for corporations, 9 and dividend policy, 509–510 double, 73 on income statement, 62 interest tax shield, 472–474

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Subject Index IND-31

of options determinants, 669–671 upper and lower limits, 668–669 valuation models, 671–673

and sound financing, 83 Value added

by financial managers, 3 financial ratios to understand, 84–85 by management, 713–714 need for measures of, 83

Value maximization, 3, 83 ethics of, 18–19 investment trade-off, 13–14 and opportunity cost of capital, 14–15 shareholder goal, 12–15

Value of the firm and capital budgeting decisions, 193 and capital structure, 462–467, 713 determining, 47–48 and dividend policy, 503–505,

507–510 going-concern value, 198 intrinsic value vs. price, 712 and liquidation value, 197–198,

494–495 MM proposition I, 462–464 and payout policy, 510–511 value added by management, 712–713 and value of underlying assets, 712

Value stocks, 373 Vanguard Explorer Fund, 40 Vanguard 500 funds, 45 Vanguard Growth and Income Fund,

364–356 Vanguard index fund, 369 Vanguard Index Trust 500

Portfolio, 365 Variable costs, 304

break-even point, 308–309 definition, 304 and operating leverage, 311 in sales, 307

Variables in scenario analysis, 305 in sensitivity analysis, 304 trade-off between, 311

Variance, 334–337 calculating, 337 definition, 335 formula, 336

Venture capital and business plan, 438 definition, 438 first-stage financing, 438 second-stage financing, 439

Venture capital firms, 437, 439–440 and start-ups, 438–439

Venture capitalists, 4, 5 Verizon, 235

Underwriting, 42 Unethical financial actions, 3 Unfunded debt, 426 Unilever, 37 Union Pacific, 339, 363, 372, 401, 497,

500, 501 dividend policy, 499

United Health, 329 United States, 334

dividends and stock repurchases 1980–2012, 498

inflation rate 1900–2013, 147 number of mergers 1962–2013, 608 payment systems, 595 political risk score, 651 risk premium, 333 tax system, 9n total financing by corporations,

43–44 United Technologies, 608 Universal Studios, 534 Unknown unknowns, 304 Unlimited liability, 10 Unsecured creditors, 493 U.S. Airways Group Inc., 8n,

608, 615 U.S. Robotics, 627 U.S. Steel, 339, 363, 372, 401,

676–677 economic value added, 89 market value added, 86

V VA Linux, 446 Valuation

of common stock by comparables, 199–200 dividend discount model,

202–205 price and intrinsic value,

200–202 growth stocks, 215 of inventories, 553n of long-lived projects, 238–242

Valuation by comparables, 199–200, 212, 214

Valuation errors, 211 Value

assessment by investors, 416 of callable bonds, 678 conservation of, 709 and cost of capital, 87 created by financing decisions, 416 of entire businesses, 403–405 of future investments, 198 from investment, 7 MM proposition I, 709

bid price, 166, 167 compared to corporate bonds, 180 and interest rates, 167–172 issues of 1986, 166 long-term, 330 number of, 166 portfolios of, 330 prices vs. corporate bonds, 714 rate of return vs. yield to maturity,

174–175 real interest rate, 179 semiannual coupon payments,

169–170 spread, 166, 167 strips, 177–178, 184 trading, 167 yield spread vs. corporate bonds,

182–183 yield to maturity, 174

Treasury Department purchase of toxic securities, 49 sale of warrants, 676 selloff of General Motors stock, 441

Treasury Inflation-Protected Securities, 25, 179

Treasury stock, 420 Troubled Asset Relief Program, 503 True value, 416 Truth-in-lending laws, 144n TWA, 484 TXU, 7 Tyco International, 15, 17

U Uhlfelter, Eric, 36 Underpricing

definition, 442 of eBay, 442 reasons for, 442–443 and winner’s curse, 443

Underwriters best-efforts basis, 441 characteristics, 445 definition, 441 firm commitment, 441 floatation costs, 444–445 general cash offer, 447 largest in United States, 445 prospectus, 442 reputation, 446 roadshows, 442 and SEC regulations, 441–442 setting issue price, 442 underpricing, 442–443 VA Linux scandal, 446 and winner’s curse, 443

Underwriters spread, 441

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IND-32 Subject Index

definition, 577 forecasting, 285 forecasting mistakes, 276 major components, 577 permanent requirements, 548 recognizing investments, 275–26 short-term assets needed, 275 total capital requirements, 546–548 tracing changes in, 556–557

Working capital management, 554 accounts receivable and credit policy,

578–589 case, 605 cash management, 591–596 inventory management, 589–591 investing idle cash, 596–598 and money market, 596–598

Working capital trade-off carrying costs, 555 cost-benefit analysis, 555 shortage costs, 555

Workout, 493 WorldCom, 25, 70, 181, 441 Wozniak, Steve, 437 Writer, 664n Wruck, K. H., 550

X Xerox Corporation, 69, 88

economic value added, 89 market value added, 86

Y Yahoo!, 17 Yahoo! Finance, 58 Yield

on corporate bonds, 149 and default premium, 180 financial calculators for, 175 long- vs. short-term bonds, 178 money market instruments

corporate vs. government securities, 597

default risk, 597 recent market turmoil, 597

Yield curve definition, 177 nominal vs. real interest rate,

178–180 upward-sloping, 178

Yield spread, Treasury vs. corporate bonds, 181, 182–183

Yield to maturity asked, 166, 167 calculating, 174

calculating company cost of capital, 390–392, 396–397

case, 411–413 and corporate taxes, 474 and debt policy, 474–475 definition, 393 to discount cash flows, 398n Dow Chemical, 393 Ford Motor Company, 400n formula, 393 Geothermal, 394–395 interpreting

common mistakes, 401–402 corporate taxes, 403 effect of changes in capital

structure on returns, 402–403 when unusable, 401

managerial use of, 387 multiple sources of financing, 394 real-company, 400 for selected companies, 400 and taxes, 392–393 valuing entire businesses, 403–405

Weiss, Jurgen, 242n Weiss, L. A., 478n Wells Fargo, 609 What-if questions, 299, 302–306

on cash balances, 560 crucial for capital budgeting, 303 in financial planning, 523 purpose, 303 scenario analysis, 305–306 sensitivity analysis, 303–305

WhatsApp, 608 Wildcat oil drills, 348 Williams Act of 1968, 620 Williamson, R., 548–549 Wilshire 5000 Market Index, 220 Wingfeld, N., 508 Winner’s curse, 443 Wire transfer, 595 WobbleWorks, 440 Wolfers, J., 39 Working capital, 275–276

additional investment in, 276 and cash conversion cycle,

552–554 cash flow from, 276 cash flow from changes in,

281–282 changes in, 281, 284 components

changing with cycle of operations, 552

current assets, 549–550 current liabilities, 550–51

cost-benefit analysis of investing in, 555

Verizon Communications, 522, 523, 608, 609

Verizon Wireless, 609 Vertical integration

economies of, 611 versus outsourcing, 611

Vertical merger, 608 Vesting, 16n Visa, initial public offering of 2008,

444–445 VIX; see Market Volatility Index Vlasic, Bill, 609n Vodafone, 609 Volatility

of portfolios, 340–344 spreadsheet solutions, 344

Volatility measures, 674 Voting procedures

with common stock, 423 lacking for preferred stock, 424

Vulture funds, 41

W Wachovia, 25, 609 Wagner, Deidre, 36 Wall Street (film), 20 Wall Street Journal, 209, 211

bond listings, 166, 167 stock listings, 193 stock market listings, 195

Walmart, 6, 88, 104, 339, 363, 372, 401, 591, 640

economic value added, 89 investment and financing

decisions, 5 market-to-book ratio, 200 market value added, 86 market vs. book value, 197 price and yield on bonds, 181

Walmart strategy, 94 Walt Disney Company, 339, 363, 366,

372, 401, 620 Warrants, 430, 676 Weak-form efficiency, 219–220, 709 Webb, Susan, 22 Weighted average cost of capital, 88n

accuracy of, 395 based on market values, 396 calculating, 400

expected return on bonds, 398 expected return on common stock,

398–400 expected returns from preferred

stock, 400 summary on, 400 using market value, 392

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Subject Index IND-33

Zheng, L., 712n Zhu, Q, 712n Ziemba, W. T., 222 Zingales, L., 18n Zitewitz, E., 39 Z-score model, 583 Zuckerman, G., 20

Z Zach’s, 210n Zero-coupon bonds, 184 Zero Net present value, 308, 395 Zero-NPV investment, 548 Zero-sum game, hedging as, 688 Zhao Quanshui, 444

and current yield, 173 definition, 173 financial calculators for, 175 measure of total return, 173–174 promised vs. expected, 182–183 versus rate of return, 173, 174–177

Yuan, K., 712n Yum! Brands, 47–48

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  • Cover
  • Fundamentals ofCorporate Finance
  • About the Authors
  • Preface
  • Key Features
  • End-of-Chapter Material
  • Supplements
  • Acknowledgments
  • Contents in Brief
  • Contents
  • Chapter 1 Goals and Governance of the Corporation
    • 1.1 Investment and Financing Decisions
      • The Investment (Capital Budgeting) Decision
      • The Financing Decision
    • 1.2 What Is a Corporation?
      • Other Forms of Business Organization
    • 1.3 Who Is the Financial Manager?
    • 1.4 Goals of the Corporation
      • Shareholders Want Managers to Maximize Market Value
    • 1.5 Agency Problems, Executive Compensation, and Corporate Governance
      • Executive Compensation
      • Corporate Governance
    • 1.6 The Ethics of Maximizing Value
    • 1.7 Careers in Finance
    • 1.8 Preview of Coming Attractions
    • 1.9 Snippets of Financial History
      • Summary
      • Questions and Problems
  • Chapter 2 Financial Markets and Institutions
    • 2.1 The Importance of Financial Markets and Institutions
    • 2.2 The Flow of Savings to Corporations
      • The Stock Market
      • Other Financial Markets
      • Financial Intermediaries
      • Financial Institutions
      • Total Financing of U.S. Corporations
    • 2.3 Functions of Financial Markets and Intermediaries
      • Transporting Cash across Time
      • Risk Transfer and Diversification
      • Liquidity
      • The Payment Mechanism
      • Information Provided by Financial Markets
    • 2.4 The Crisis of 2007_2009
      • Summary
      • Questions and Problems
  • Chapter 3 Accounting and Finance
    • 3.1 The Balance Sheet
      • Book Values and Market Values
    • 3.2 The Income Statement
      • Income versus Cash Flow
    • 3.3 The Statement of Cash Flows
      • Free Cash Flow
    • 3.4 Accounting Practice and Malpractice
    • 3.5 Taxes
      • Corporate Tax
      • Personal Tax
      • Summary
      • Questions and Problems
  • Chapter 4 Measuring Corporate Performance
    • 4.1 Value and Value Added
      • How Financial Ratios Help to Understand Value Added
    • 4.2 Measuring Market Value and Market Value Added
    • 4.3 Economic Value Added and Accounting Rates of Return
      • Accounting Rates of Return
      • Problems with EVA and Accounting Rates of Return
    • 4.4 Measuring Efficiency
    • 4.5 Analyzing the Return on Assets: The Du Pont System
      • The Du Pont System
    • 4.6 Measuring Financial Leverage
      • Leverage and the Return on Equity
    • 4.7 Measuring Liquidity
    • 4.8 Interpreting Financial Ratios
    • 4.9 The Role of Financial Ratios
      • Summary
      • Questions And Problems
      • Minicase
  • Chapter 5 The Time Value of Money
    • 5.1 Future Values and Compound Interest
    • 5.2 Present Values
      • Finding the Interest Rate
    • 5.3 Multiple Cash Flows
      • Future Value of Multiple Cash Flows
      • Present Value of Multiple Cash Flows
    • 5.4 Reducing the Chore of the Calculations: Part 1
      • Using Financial Calculators to Solve Simple Time-Value-of-Money Problems
      • Using Spreadsheets to Solve Simple Time-Value-of-Money Problems
    • 5.5 Level Cash Flows: Perpetuities and Annuities
      • How to Value Perpetuities
      • How to Value Annuities
      • Future Value of an Annuity
      • Annuities Due
    • 5.6 Reducing the Chore of the Calculations: Part 2
      • Using Financial Calculators to Solve Annuity Problems
      • Using Spreadsheets to Solve Annuity Problems
    • 5.7 Effective Annual Interest Rates
    • 5.8 Inflation and the Time Value of Money
      • Real versus Nominal Cash Flows
      • Inflation and Interest Rates
      • Valuing Real Cash Payments
      • Real or Nominal?
      • Summary
      • Questions and Problems
      • Minicase
  • Chapter 6 Valuing Bonds
    • 6.1 The Bond Market
      • Bond Characteristics
    • 6.2 Interest Rates and Bond Prices
      • How Bond Prices Vary with Interest Rates
      • Interest Rate Risk
    • 6.3 Yield to Maturity
      • Calculating the Yield to Maturity
    • 6.4 Bond Rates of Return
    • 6.5 The Yield Curve
      • Nominal and Real Rates of Interest
    • 6.6 Corporate Bonds and the Risk of Default
      • Protecting against Default Risk
      • Not All Corporate Bonds Are Plain Vanilla
      • Summary
      • Questions and Problems
  • Chapter 7 Valuing Stocks
    • 7.1 Stocks and the Stock Market
      • Reading Stock Market Listings
    • 7.2 Market Values, Book Values, and Liquidation Values
    • 7.3 Valuing Common Stocks
      • Valuation by Comparables
      • Price and Intrinsic Value
      • The Dividend Discount Model
    • 7.4 Simplifying the Dividend Discount Model
      • The Dividend Discount Model with No Growth
      • The Constant-Growth Dividend Discount Model
      • Sustainable Growth
      • A Caveat
      • Estimating Expected Rates of Return
      • Nonconstant Growth
      • Repurchases and the Dividend Discount Model
    • 7.5 Growth and Growth Opportunities
      • Valuing Growth Stocks
      • Market-Value Balance Sheets
    • 7.6 There Are No Free Lunches on Wall Street
      • Method 1: Technical Analysis
      • Method 2: Fundamental Analysis
      • A Theory to Fit the Facts
    • 7.7 Market Anomalies and Behavioral Finance
      • Market Anomalies
      • Bubbles and Market Efficiency
      • Behavioral Finance
      • Summary
      • Questions and Problems
      • Minicase
  • Chapter 8 Net Present Value and Other Investment Criteria
    • 8.1 Net Present Value
      • A Comment on Risk and Present Value
      • Valuing Long-Lived Projects
    • 8.2 The Internal Rate of Return Rule
      • A Closer Look at the Rate of Return Rule
      • Calculating the Rate of Return for Long-Lived Projects
      • A Word of Caution
      • Some Pitfalls with the Internal Rate of Return Rule
    • 8.3 The Profitability Index
      • Capital Rationing
      • Pitfalls of the Profitability Index
    • 8.4 The Payback Rule
      • Discounted Payback
    • 8.5 More Mutually Exclusive Projects
      • Problem 1: The Investment Timing Decision
      • Problem 2: The Choice between Long- and Short-Lived Equipment
      • Problem 3: When to Replace an Old Machine
    • 8.6 A Last Look
      • Summary
      • Questions and Problems
      • Minicase
      • Appendix: More on the IRR Rule
      • Using the IRR to Choose between Mutually Exclusive Projects
      • Using the Modified Internal Rate of Return When There Are Multiple IRRs
  • Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions
    • 9.1 Identifying Cash Flows
      • Discount Cash Flows, Not Profits
      • Discount Incremental Cash Flows
      • Discount Nominal Cash Flows by the Nominal Cost of Capital
      • Separate Investment and Financing Decisions
    • 9.2 Calculating Cash Flow
      • Capital Investment
      • Operating Cash Flow
      • Changes in Working Capital
    • 9.3 An Example: Blooper Industries
      • Cash-Flow Analysis
      • Calculating the NPV of BlooperÕs Project
      • Further Notes and Wrinkles Arising from BlooperÕs Project
      • Summary
      • Questions and Problems
      • Minicase
  • Chapter 10 Project Analysis
    • 10.1 How Firms Organize the Investment Process
      • Stage 1: The Capital Budget
      • Stage 2: Project Authorizations
      • Problems and Some Solutions
    • 10.2 Some ÒWhat-IfÓ Questions
      • Sensitivity Analysis
      • Scenario Analysis
    • 10.3 Break-Even Analysis
      • Accounting Break-Even Analysis
      • NPV Break-Even Analysis
      • Operating Leverage
    • 10.4 Real Options and the Value of Flexibility
      • The Option to Expand
      • A Second Real Option: The Option to Abandon
      • A Third Real Option: The Timing Option
      • A Fourth Real Option: Flexible Production Facilities
      • Summary
      • Questions and Problems
      • Minicase
  • Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital
    • 11.1 Rates of Return: A Review
    • 11.2 A Century of Capital Market History
      • Market Indexes
      • The Historical Record
      • Using Historical Evidence to Estimate TodayÕs Cost of Capital
    • 11.3 Measuring Risk
      • Variance and Standard Deviation
      • A Note on Calculating Variance
      • Measuring the Variation in Stock Returns
    • 11.4 Risk and Diversification
      • Diversification
      • Asset versus Portfolio Risk
      • Market Risk versus Specific Risk
    • 11.5 Thinking about Risk
      • Message 1: Some Risks Look Big and Dangerous but Really Are Diversifiable
      • Message 2: Market Risks Are Macro Risks
      • Message 3: Risk Can Be Measured
      • Summary
      • Questions and Problems
  • Chapter 12 Risk, Return, and Capital Budgeting
    • 12.1 Measuring Market Risk
      • Measuring Beta
      • Betas for Dow Chemical and Consolidated Edison
      • Total Risk and Market Risk
    • 12.2 What Can You Learn from Beta?
      • Portfolio Betas
      • The Portfolio Beta Determines the Risk of a Diversified Portfolio
    • 12.3 Risk and Return
      • Why the CAPM Makes Sense
      • The Security Market Line
      • Using the CAPM to Estimate Expected Returns
      • How Well Does the CAPM Work?
    • 12.4 The CAPM and the Opportunity Cost of Capital
      • The Company Cost of Capital
      • What Determines Project Risk?
      • DonÕt Add Fudge Factors to Discount Rates
      • Summary
      • Questions and Problems
  • Chapter 13 The Weighted-Average Cost of Capital and Company Valuation
    • 13.1 GeothermalÕs Cost of Capital
    • 13.2 The Weighted-Average Cost of Capital
      • Calculating Company Cost of Capital as a Weighted Average
      • Use Market Weights, Not Book Weights
      • Taxes and the Weighted-Average Cost of Capital
      • What If There Are Three (or More) Sources of Financing?
      • Wrapping Up Geothermal
      • Checking Our Logic
    • 13.3 Measuring Capital Structure
    • 13.4 Calculating the Weighted-Average Cost of Capital
      • The Expected Return on Bonds
      • The Expected Return on Common Stock
      • The Expected Return on Preferred Stock
      • Adding It All Up
      • Real-Company WACCs
    • 13.5 Interpreting the Weighted-Average Cost of Capital
      • When You Can and CanÕt Use WACC
      • Some Common Mistakes
      • How Changing Capital Structure Affects Expected Returns
      • What Happens When the Corporate Tax Rate Is Not Zero
    • 13.6 Valuing Entire Businesses
      • Calculating the Value of the Concatenator Business
      • Summary
      • Questions and Problems
      • Minicase
  • Chapter 14 Introduction to Corporate Financing
    • 14.1 Creating Value with Financing Decisions
    • 14.2 Patterns of Corporate Financing
      • Are Firms Issuing Too Much Debt?
    • 14.3 Common Stock
      • Ownership of the Corporation
      • Voting Procedures
      • Classes of Stock
    • 14.4 Preferred Stock
    • 14.5 Corporate Debt
      • Debt Comes in Many Forms
      • Innovation in the Debt Market
    • 14.6 Convertible Securities
      • Summary
      • Questions and Problems
  • Chapter 15 How Corporations Raise Venture Capital and Issue Securities
    • 15.1 Venture Capital
      • Venture Capital Companies
    • 15.2 The Initial Public Offering
      • Arranging a Public Issue
      • Other New-Issue Procedures
      • The Underwriters
    • 15.3 General Cash Offers by Public Companies
      • General Cash Offers and Shelf Registration
      • Costs of the General Cash Offer
      • Market Reaction to Stock Issues
    • 15.4 The Private Placement
      • Summary
      • Questions and Problems
      • Minicase
      • Appendix: Hotch PotÕs New-Issue Prospectus
  • Chapter 16 Debt Policy
    • 16.1 How Borrowing Affects Value in a Tax-Free Economy
      • MMÕs ArgumentÑA Simple Example
      • How Borrowing Affects Earnings per Share
      • How Borrowing Affects Risk and Return
    • 16.2 Debt and the Cost of Equity
      • No Magic in Financial Leverage
    • 16.3 Debt, Taxes, and the Weighted-Average Cost of Capital
      • Debt and Taxes at River Cruises
      • How Interest Tax Shields Contribute to the Value of StockholdersÕ Equity
      • Corporate Taxes and the Weighted-Average Cost of Capital
      • The Implications of Corporate Taxes for Capital Structure
    • 16.4 Costs of Financial Distress
      • Bankruptcy Costs
      • Costs of Bankruptcy Vary with Type of Asset
      • Financial Distress without Bankruptcy
    • 16.5 Explaining Financing Choices
      • The Trade-Off Theory
      • A Pecking Order Theory
      • The Two Faces of Financial Slack
      • Summary
      • Questions and Problems
      • Minicase
      • Appendix: Bankruptcy Procedures
  • Chapter 17 Payout Policy
    • 17.1 How Corporations Pay Out Cash to Shareholders
      • How Firms Pay Dividends
      • Limitations on Dividends
      • Stock Dividends and Stock Splits
      • Stock Repurchases
    • 17.2 The Information Content of Dividends and Repurchases
    • 17.3 Dividends or Repurchases? The Payout Controversy
      • Dividends or Repurchases? An Example
      • Repurchases and the Dividend Discount Model
      • Dividends and Share Issues
    • 17.4 Why Dividends May Increase Value
    • 17.5 Why Dividends May Reduce Value
      • Taxation of Dividends and Capital Gains under Current Tax Law
    • 17.6 Payout Policy and the Life Cycle of the Firm
      • Summary
      • Questions and Problems
      • Minicase
  • Chapter 18 Long-Term Financial Planning
    • 18.1 What Is Financial Planning?
      • Financial Planning Focuses on the Big Picture
      • Why Build Financial Plans?
    • 18.2 Financial Planning Models
      • Components of a Financial Planning Model
      • Percentage of Sales Models
      • An Improved Model
    • 18.3 Planners Beware
      • Pitfalls in Model Design
      • The Assumption in Percentage of Sales Models
      • The Role of Financial Planning Models
    • 18.4 External Financing and Growth
      • Summary
      • Questions and Problems
      • Minicase
  • Chapter 19 Short-Term Financial Planning
    • 19.1 Links between Long-Term and Short-Term Financing
    • 19.2 Working Capital
      • The Components of Working Capital
      • Working Capital and the Cash Conversion Cycle
      • The Working Capital Trade-Off
    • 19.3 Tracing Changes in Cash and Working Capital
    • 19.4 Cash Budgeting
      • Forecast Sources of Cash
      • Forecast Uses of Cash
      • The Cash Balance
    • 19.5 A Short-Term Financing Plan
      • Dynamic MattressÕs Financing Plan
      • Evaluating the Plan
    • 19.6 Sources of Short-Term Financing
      • Bank Loans
      • Secured Loans
      • Commercial Paper
      • Summary
      • Questions and Problems
      • Minicase
  • Chapter 20 Working Capital Management
    • 20.1 Accounts Receivable and Credit Policy
      • Terms of Sale
      • Credit Agreements
      • Credit Analysis
      • The Credit Decision
      • Collection Policy
    • 20.2 Inventory Management
    • 20.3 Cash Management
      • Check Handling and Float
      • Other Payment Systems
      • Electronic Funds Transfer
      • International Cash Management
    • 20.4 Investing Idle Cash: The Money Market
      • Yields on Money Market Investments
      • The International Money Market
      • Summary
      • Questions and Problems
      • Minicase
  • Chapter 21 Mergers, Acquisitions, and Corporate Control
    • 21.1 Sensible Motives for Mergers
      • Economies of Scale
      • Economies of Vertical Integration
      • Combining Complementary Resources
      • Mergers as a Use for Surplus Funds
      • Eliminating Inefficiencies
      • Industry Consolidation
    • 21.2 Dubious Reasons for Mergers
      • Diversification
      • The Bootstrap Game
    • 21.3 The Mechanics of a Merger
      • The Form of Acquisition
      • Mergers, Antitrust Law, and Popular Opposition
    • 21.4 Evaluating Mergers
      • Mergers Financed by Cash
      • Mergers Financed by Stock
      • A Warning
      • Another Warning
    • 21.5 The Market for Corporate Control
    • 21.6 Method 1: Proxy Contests
    • 21.7 Method 2: Takeovers
    • 21.8 Method 3: Leveraged Buyouts
      • Barbarians at the Gate?
    • 21.9 Method 4: Divestitures, Spin-Offs, and Carve-Outs
    • 21.10 The Benefits and Costs of Mergers
      • Merger Waves
      • Summary
      • Questions and Problems
      • Minicase
  • Chapter 22 International Financial Management
    • 22.1 Foreign Exchange Markets
      • Spot Exchange Rates
      • Forward Exchange Rates
    • 22.2 Some Basic Relationships
      • Exchange Rates and Inflation
      • Real and Nominal Exchange Rates
      • Inflation and Interest Rates
      • The Forward Exchange Rate and the Expected Spot Rate
      • Interest Rates and Exchange Rates
    • 22.3 Hedging Exchange Rate Risk
      • Transaction Risk
      • Economic Risk
    • 22.4 International Capital Budgeting
      • Net Present Values for Foreign Investments
      • Political Risk
      • The Cost of Capital for Foreign Investment
      • Avoiding Fudge Factors
      • Summary
      • Questions and Problems
      • Minicase
  • Chapter 23 Options
    • 23.1 Calls and Puts
      • Selling Calls and Puts
      • Payoff Diagrams Are Not Profit Diagrams
      • Financial Alchemy with Options
      • Some More Option Magic
    • 23.2 What Determines Option Values?
      • Upper and Lower Limits on Option Values
      • The Determinants of Option Value
      • Option-Valuation Models
    • 23.3 Spotting the Option
      • Options on Real Assets
      • Options on Financial Assets
      • Summary
      • Questions and Problems
  • Chapter 24 Risk Management
    • 24.1 Why Hedge?
      • The Evidence on Risk Management
    • 24.2 Reducing Risk with Options
    • 24.3 Futures Contracts
      • The Mechanics of Futures Trading
      • Commodity and Financial Futures
    • 24.4 Forward Contracts
    • 24.5 Swaps
    • 24.6 Innovation in the Derivatives Market
    • 24.7 Is ÒDerivativeÓ a Four-Letter Word?
      • Summary
      • Questions and Problems
  • Chapter 25 What We Do and Do Not Know about Finance
    • 25.1 What We Do Know: The Six Most Important Ideas in Finance
      • Net Present Value (Chapter 5)
      • Risk and Return (Chapters 11 and 12)
      • Efficient Capital Markets (Chapter 7)
      • MMÕs Irrelevance Propositions (Chapters 16 and 17)
      • Option Theory (Chapter 23)
      • Agency Theory
    • 25.2 What We Do Not Know: Nine Unsolved Problems in Finance
      • What Determines Project Risk and Present Value?
      • Risk and ReturnÑHave We Missed Something?
      • Are There Important Exceptions to the Efficient-Market Theory?
      • Is Management an Off-Balance-Sheet Liability?
      • How Can We Explain Capital Structure?
      • How Can We Resolve the Payout Controversy?
      • How Can We Explain Merger Waves?
      • What Is the Value of Liquidity?
      • Why Are Financial Systems Prone to Crisis?
    • 25.3 A Final Word
      • Questions and Problems
      • Appendix A
      • Glossary
      • Global Index
      • Subject Index
      • Credits
  • APPENDIX A Present Value and Future Value Tables
  • Glossary
  • Global Index
  • Subject Index
  • Credits
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    2. Preflight Ticket Signature