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Principles of Corporate Finance

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Financial Management

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

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

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

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

Brooks FinGame Online 5.0

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

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

Cornett, Adair, and Nofsinger M: Finance Fourth 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 Twelfth Edition

Ross, Westerfield, Jaffe, and Jordan Corporate Finance Twelfth Edition

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

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

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

Shefrin Behavioral Corporate Finance: Decisions that Create Value Second Edition

Investments

Bodie, Kane, and Marcus Essentials of Investments Eleventh Edition

Bodie, Kane, and Marcus Investments Eleventh Edition

Hirt and Block Fundamentals of Investment Management Tenth Edition

Jordan and Miller Fundamentals of Investments: Valuation and Management Eighth Edition

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

Sundaram and Das Derivatives: Principles and Practice Second Edition

Financial Institutions and Markets

Rose and Hudgins Bank Management and Financial Services Tenth Edition

Rose and Marquis Financial Institutions and Markets Eleventh Edition

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

Saunders and Cornett Financial Markets and Institutions Seventh Edition

International Finance

Eun and Resnick International Financial Management Eighth Edition

Real Estate

Brueggeman and Fisher Real Estate Finance and Investments Sixteenth Edition

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

Financial Planning and Insurance

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

Altfest Personal Financial Planning Second Edition

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

Kapoor, Dlabay, and Hughes Personal Finance Twelfth Edition

Walker and Walker Personal Finance: Building Your Future Second Edition

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

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Richard A. Brealey Professor of Finance

London Business School

Stewart C. Myers Professor of Financial Economics

Sloan School of Management Massachusetts

Institute of Technology

Franklin Allen Professor of Finance and Economics

Imperial College London

THIRTEENTH EDITION

Principles of Corporate Finance

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PRINCIPLES OF CORPORATE FINANCE, THIRTEENTH EDITION

Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2020 by McGraw-Hill Education. All rights reserved. Printed in the United States of America. Previous editions © 2017, 2014, and 2011. 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.

1 2 3 4 5 6 7 8 9 0 LWI/LWI 22 21 20 19

ISBN 978-1-260-01390-0 MHID 1-260-01390-1

Portfolio Manager: Charles Synovec Product Developer: Noelle Bathurst Marketing Manager: Allison McCabe-Carroll Content Project Managers: Fran Simon and Jamie Koch Buyer: Laura Fuller Design: Matt Diamond Content Licensing Specialist: Ann Marie Jannette Cover Image: Emily Tolan/Shutterstock Compositor: SPi Global All credits appearing on page or at the end of the book are considered to be an extension of the copyright page.

Library of Congress Cataloging-in-Publication Data

Names: Brealey, Richard A., author. | Myers, Stewart C., author. | Allen, Franklin, 1956- author. Title: Principles of corporate finance / Richard A. Brealey, Professor of Finance, London Business School, Stewart C. Myers, Robert C. Merton (1970) Professor of Finance, Sloan School of Management, Massachusetts Institute of Technology, Franklin Allen, Professor of Finance and Economics, Imperial College London. Description: Thirteenth edition. | New York, NY : McGraw-Hill Education, [2020] Identifiers: LCCN 2018040697 | ISBN 9781260013900 (alk. paper) Subjects: LCSH: Corporations—Finance. Classification: LCC HG4026 .B667 2020 | DDC 658.15—dc23 LC record available at https://lccn.loc.gov/2018040697

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.

mheducation.com/highered

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To our parents.

Dedication

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⟩ 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 Associa- tion. He is a fellow of the British Academy and has served as a spe- cial adviser to the Governor of the Bank of England and director of a number of financial institutions. Books written by Professor Brealey include Introduction to Risk and Return from Common Stocks.

⟩ Stewart C. Myers

Professor of Financial Economics at MIT’s Sloan School of Manage- ment. He is past president of the American Finance Association, a research associate at the National Bureau of Economic Research, a principal of the Brattle Group Inc., and a retired director of Entergy Corporation. His research is pri- marily concerned with the valuation of real and financial assets, corpo- rate financial policy, and financial aspects of government regulation of business. He is the author of influential research papers on many topics, including adjusted present value, rate of return regulation, pricing and capital allocation in insurance, real options, and moral hazard and information issues in capital structure decisions.

⟩ Franklin Allen

Professor of Finance and Econom- ics, Imperial College London, and Emeritus Nippon Life Professor of Finance at the Wharton School of the University of Pennsylvania. He is past president of the American Finance Association, Western Finance Association, Society for Financial Studies, Financial Intermediation Research Society, Financial Management Association, and a fellow of the Econometric Society and the British Academy. His research has focused on finan- cial innovation, asset price bubbles, comparing financial systems, and financial crises. He is Director of the Brevan Howard Centre for Financial Analysis at Imperial College Business School.

About the Authors

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Preface

⟩ This book describes the theory and practice of corpo- rate finance. We hardly need to explain why financial

managers have to master the practical aspects of their job, but we should spell out why down-to-earth manag- ers need to bother with theory.

Managers learn from experience how to cope with routine problems. But the best managers are also able to respond to change. To do so you need more than time- honored rules of thumb; you must understand why com- panies and financial markets behave the way they do. In other words, you need a theory of finance.

Does that sound intimidating? It shouldn’t. Good theory helps you to grasp what is going on in the world around you. It helps you to ask the right questions when times change and new problems need to be analyzed. It also tells you which things you do not need to worry about. Throughout this book, we show how managers use financial theory to solve practical problems.

Of course, the theory presented in this book is not per- fect and complete—no theory is. There are some famous controversies where financial economists cannot agree. We have not glossed over these disagreements. We set out the arguments for each side and tell you where we stand.

Much of this book is concerned with understanding what financial managers do and why. But we also say what financial managers should do to increase company value. Where theory suggests that financial managers are making mistakes, we say so, while admitting that there may be hidden reasons for their actions. In brief, we have tried to be fair but to pull no punches.

This book may be your first view of the world of modern finance. If so, you will read first for new ideas, for an understanding of how finance theory translates into practice, and occasionally, we hope, for entertain- ment. But eventually you will be in a position to make financial decisions, not just study them. At that point, you can turn to this book as a reference and guide.

⟩ Changes in the Thirteenth Edition We are proud of the success of previous editions of Principles, and we have done our best to make the thir- teenth edition even better.

Some of the biggest changes in this edition were prompted by the tax changes enacted in the U.S. Tax

Cuts and Jobs Act passed in December 2017. One of the chapters most affected was Chapter 6, which is con- cerned with calculating the present value of capital proj- ects. We describe the major tax changes in that chapter, and we work through an example of a capital budget- ing problem with 100% bonus depreciation and a 21% corporate tax rate. But the U.S. system of immediate expensing of capital expenditures is almost unique. So we also set out examples of the more common systems of straight-line depreciation and double- declining-balance, which is essentially identical to the former U.S. MACRS depreciation.

Another 2017 tax change was the limit imposed on interest tax shields. For companies that are caught by this change, it may no longer make sense to discount cash flows by the weighted average cost of capital. We discuss the implications for company debt policy in Chapter 18. In Chapter 19, we show how adjusted present value can be used in these cases to value companies and projects. Similarly, the cap on interest tax shields complicates the valuation of leases. In Chapter 25, we show that when the cap is operative, leases need to be valued by constructing an equivalent loan. Finally, in Chapter 32, we consider the possible effect on the private-equity market.

The third important change was the switch by the United States to a territorial tax system. This has major implications for tax strategies, which we largely dis- cuss in the chapters on working capital management ( Chapter 30) and mergers (Chapter 31).

U.S. financial managers work in a global environment and need to understand the financial systems of other countries. Also, many of the text’s readers come from countries other than the United States. Therefore, in recent editions we have progressively introduced more interna- tional material, including information about the major developing economies, such as China and India. In the current edition, we have continued to augment the interna- tional content. We hope that an understanding of practices in other countries will also lead to a better understanding of the characteristics of one’s own financial system.

Users of previous editions of this book will not find dramatic changes in coverage or in the ordering of top- ics. However, there are a number of chapters that have been thoroughly rewritten. For example, the material on agency issues in Chapter 12 has been substantially revised. Chapter 13 on market efficiency and behavioral

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finance is now fresher and more up to date. Chapter 23 on credit risk focuses more on the practical issues of forecasting default probabilities.

Throughout, we have tried to make the book more up-to-date and easier to read. In many cases, the changes consist of some updated data here and a new example there. Often, these additions reflect some recent devel- opment in the financial markets or company practice.

In the 11th edition, we added digital extensions through our Beyond the Page features, or “apps” as we call them. This extra material can allow us to escape from some of the constraints of the printed page by providing more explanation for readers who need it and additional mate- rial for those who would like to dig deeper. The Beyond the Page features include extra examples and spreadsheet programs, as well as some interesting anecdotes.

There are now more than 150 of these apps. They are all seamlessly available with a click on the e-versions of the book, but they are also readily accessible from the traditional hard copy of the text through the shortcut URLs. Check out mhhe.com/brealey13e to learn more.

Examples of these applications include:

∙ Chapter 1 In Chapter 1, we refer to Bernard Madoff’s ponzi scheme. But this scam pales into insignificance compared with the great Albanian ponzi scheme, which is described in an app.

∙ Chapter 2 Do you need to learn how to use a finan- cial calculator? The Beyond the Page financial cal- culator application shows how to do so.

∙ Chapter 3 Would you like to calculate a bond’s dura- tion, see how it predicts the effect of small interest rate changes on bond price, calculate the duration of a com- mon stock, or learn how to measure convexity? The duration application for Figure 3.2 allows you to do so.

∙ Chapter 5 Want more practice in valuing annuities? There is an application that provides worked exam- ples and hands-on practice.

∙ Chapter 9 How about measuring the betas of the Fama–French three-factor model for U.S. stocks? The Beyond the Page beta estimation application does this.

∙ Chapter 14 Ever wonder why Google split its stock into A and C shares? An app provides the answer.

∙ Chapter 15 Want to now how companies can raise capital by an initial coin offering? There is an app on the topic.

∙ Chapter 19 The text briefly describes the flow-to- equity method for valuing businesses, but using the method can be tricky. We provide an application that guides you step by step.

∙ Chapter 20 The Black–Scholes Beyond the Page application provides an option calculator. It also shows

how to estimate the option’s sensitivity to changes in the inputs and how to measure an option’s risk.

∙ Chapter 28 Would you like to view the most recent financial statements for different U.S. companies and calculate their financial ratios? There is an appli- cation that will do this for you.

We believe that the apps offer an opportunity to widen the types of material that can be made available and help the reader to decide how deeply he or she wishes to explore a topic.

We have added end-of-chapter questions, merged what was becoming a false distinction between basic and intermediate questions, and reordered the questions to follow better the same sequence as the chapter.

⟩ Making Learning Easier Each chapter of the book includes an introductory pre- view, a summary, and an annotated list of suggested further reading. The list of possible candidates for fur- ther reading is now voluminous. Rather than trying to include every important article, we largely list survey articles or general books. We give more specific refer- ences in footnotes.

Each chapter is followed by a set of problems on both numerical and conceptual topics and a few challenge problems. Answers to the starred problems appear in the Appendix at the end of the book.

We included a Finance on the Web section in chap- ters where it makes sense to do so. This section now houses a number of Web Projects, along with new Data Analysis problems. These exercises seek to familiar- ize the reader with some useful websites and to explain how to download and process data from the web.

The book also contains 13 end-of-chapter Mini- Cases. These include specific questions to guide the case analyses. Answers to the mini-cases are available to instructors on the book’s website.

Spreadsheet programs such as Excel are tailor- made for many financial calculations. Several chapters include boxes that introduce the most useful financial functions and provide some short practice questions. We show how to use the Excel function key to locate the function and then enter the data. We think that this approach is much simpler than trying to remember the formula for each function.

We conclude the book with a glossary of financial terms.

The 34 chapters in this book are divided into 11 parts. Parts 1, 2, and 3 cover valuation and capital invest- ment decisions, including portfolio theory, asset pricing

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models, and the cost of capital. Parts 4 through 8 cover payout policy, capital structure, options (including real options), corporate debt, and risk management. Part 9 covers financial analysis, planning, and working-capital management. Part 10 covers mergers and acquisitions, corporate restructuring, and corporate governance around the world. Part 11 concludes.

We realize that instructors will wish to select topics and may prefer a different sequence. We have therefore written chapters so that topics can be introduced in several logical orders. For example, there should be no difficulty in reading the chapters on financial analysis and planning before the chapters on valuation and capital investment.

⟩ Acknowledgments We have a long list of people to thank for their helpful criticism of earlier editions and for assistance in prepar- ing this one. They include Faiza Arshad, Aleijda de Caze- nove Balsan, Kedran Garrison, Robert Pindyck, Donna Cheung, and Gretchen Slemmons at MIT; Elroy Dim- son, Paul Marsh, Mike Staunton, and Stefania Uccheddu at London Business School; Lynda Borucki, Marjorie Fischer, Larry Kolbe, Michael Vilbert, Bente Villadsen, and Fiona Wang at The Brattle Group Inc.; Alex Triantis at the University of Maryland; Adam Kolasinski at Texas A&M University; Simon Gervais at Duke University; Michael Chui at Bank for International Settlements; Pedro Matos at the University of Southern California; Yupana Wiwattanakantang at National University of Singapore; Nickolay Gantchev at the Southern Methodist University; Tina Horowitz, and Lin Shen, at the University of Penn- sylvania; Darien Huang at Tudor Investment; Julie Wulf at Harvard University; Jinghua Yan at SAC Capital; Ben- nett Stewart at EVA Dimensions; and Mobeen Iqbal and Antoine Uettwiller at Imperial College London. We are grateful to Cyrus Brealey for his suggestions.

We would also like to thank the dedicated experts who have helped with updates to the instructor mate- rials and online content in Connect and LearnSmart, including Kay Johnson, Blaise Roncagli, Deb Bauer, Mishal Rawaf, Marc-Anthony Isaacs, Frank Ryan, Peter Crabb, Victoria Mahan, Nicholas Racculia, Angela Treinen, and Kent Ragan.

We want to express our appreciation to those instruc- tors whose insightful comments and suggestions were invaluable to us during the revision process:

Ibrahim Affaneh Indiana University of Pennsylvania Neyaz Ahmed University of Maryland Alexander Amati Rutgers University, New Brunswick Anne Anderson Lehigh University Noyan Arsen Koc University

Anders Axvarn Gothenburg University John Banko University of Florida, Gainesville Michael Barry Boston College Jan Bartholdy ASB, Denmark Penny Belk Loughborough University Omar Benkato Ball State University Eric Benrud University of Baltimore Ronald Benson University of Maryland, University College Peter Berman University of New Haven Tom Boulton Miami University of Ohio Edward Boyer Temple University Alon Brav Duke University Jean Canil University of Adelaide Robert Carlson Bethany College Chuck Chahyadi Eastern Illinois University Fan Chen University of Mississippi Celtin Ciner University of North Carolina, Wilmington John Cooney Texas Tech University Charles Cuny Washington University, St. Louis John Davenport Regent University Ray DeGennaro University of Tennessee, Knoxville Adri DeRidder Gotland University William Dimovski Deakin University, Melbourne David Ding Nanyang Technological University Robert Duvic University of Texas at Austin Alex Edmans London Business School Susan Edwards Grand Valley State University Riza Emekter Robert Morris University Robert Everett Johns Hopkins University Dave Fehr Southern New Hampshire University Donald Flagg University of Tampa Frank Flanegin Robert Morris University Zsuzanna Fluck Michigan State University Connel Fullenkamp Duke University Mark Garmaise University of California, Los Angeles Sharon Garrison University of Arizona Christopher Geczy University of Pennsylvania George Geis University of Virginia Stuart Gillan University of Delaware Felix Goltz Edhec Business School Ning Gong Melbourne Business School Levon Goukasian Pepperdine University Gary Gray Pennsylvania State University C. J. Green Loughborough University Mark Griffiths Thunderbird, American School of International Management Re-Jin Guo University of Illinois, Chicago Ann Hackert Idaho State University Winfried Hallerbach Erasmus University, Rotterdam Milton Harris University of Chicago Mary Hartman Bentley College Glenn Henderson University of Cincinnati Donna Hitscherich Columbia University Ronald Hoffmeister Arizona State University James Howard University of Maryland, College Park George Jabbour George Washington University

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Ravi Jagannathan Northwestern University Abu Jalal Suffolk University Nancy Jay Mercer University Thadavillil (Nathan) Jithendranathan University of Saint Thomas Kathleen Kahle University of Arizona Jarl Kallberg NYU, Stern School of Business Ron Kaniel University of Rochester Steve Kaplan University of Chicago Eric Kelley University of Arizona Arif Khurshed Manchester Business School Ken Kim University of Wisconsin, Milwaukee Jiro Eduoard Kondo Northwestern University Kellogg School of Management C. R. Krishnaswamy Western Michigan University George Kutner Marquette University Dirk Laschanzky University of Iowa Scott Lee Texas A&M University Bob Lightner San Diego Christian College David Lins University of Illinois, Urbana Brandon Lockhart University of Nebraska, Lincoln David Lovatt University of East Anglia Greg Lucado University of the Sciences in Philadelphia Debbie Lucas Northwestern University Brian Lucey Trinity College, Dublin Suren Mansinghka University of California, Irvine Ernst Maug Mannheim University George McCabe University of Nebraska Eric McLaughlin California State University, Pomona Joe Messina San Francisco State University Tim Michael University of Houston, Clear Lake Dag Michalsen Bl, Oslo Franklin Michello Middle Tennessee State University Peter Moles University of Edinburgh Katherine Morgan Columbia University James Nelson East Carolina University James Owens West Texas A&M University Darshana Palkar Minnesota State University, Mankato Claus Parum Copenhagen Business School Dilip Patro Rutgers University John Percival University of Pennsylvania Birsel Pirim University of Illinois, Urbana Latha Ramchand University of Houston Narendar V. Rao Northeastern University Rathin Rathinasamy Ball State University Raghavendra Rau Purdue University Joshua Raugh University of Chicago Charu Reheja Wake Forest University Thomas Rhee California State University, Long Beach Tom Rietz University of Iowa Robert Ritchey Texas Tech University Michael Roberts University of Pennsylvania Mo Rodriguez Texas Christian University John Rozycki Drake University Frank Ryan San Diego State University Marc Schauten Eramus University

Brad Scott Webster University Nejat Seyhun University of Michigan Jay Shanken Emory University Chander Shekhar University of Melbourne Hamid Shomali Golden Gate University Richard Simonds Michigan State University Bernell Stone Brigham Young University John Strong College of William & Mary Avanidhar Subrahmanyam University of California, Los Angeles Tim Sullivan Bentley College Shrinivasan Sundaram Ball State University Chu-Sheng Tai Texas Southern University Tom Tallerico Dowling College Stephen Todd Loyola University, Chicago Walter Torous University of California, Los Angeles Emery Trahan Northeastern University Gary Tripp Southern New Hampshire University Ilias Tsiakas University of Warwick David Vang St. Thomas University Steve Venti Dartmouth College Joseph Vu DePaul University John Wald Rutgers University Chong Wang Naval Postgraduate School Faye Wang University of Illinois, Chicago Kelly Welch University of Kansas Jill Wetmore Saginaw Valley State University Patrick Wilkie University of Virginia Matt Will University of Indianapolis David Williams Texas A&M University, Commerce Art Wilson George Washington University Shee Wong University of Minnesota, Duluth Bob Wood Tennessee Tech University Fei Xie George Mason University Minhua Yang University of Central Florida David Zalewski Providence College Chenying Zhang University of Pennsylvania

This list is surely incomplete. We know how much we owe to our colleagues at the London Business School, MIT’s Sloan School of Management, Imperial College London, and the University of Pennsylvania’s Whar- ton School. In many cases, the ideas that appear in this book are as much their ideas as ours.

We would also like to thank all those at McGraw-Hill Education who worked on the book, including Chuck Syn- ovec, Executive Brand Manager; Allison McCabe-Carroll, Senior Product Developer; Trina Mauer, Executive Mar- keting Manager; Dave O’Donnell, Marketing Specialist; Fran Simon, Project Manager; Matt Diamond, Designer; and Angela Norris, Digital Product Analyst.

Richard A. Brealey Stewart C. Myers

Franklin Allen

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Guided Tour

Pedagogical Features ⟩ Chapter Overview Each chapter begins with a brief narrative and out- line to explain the concepts that will be covered in more depth. Useful websites related to material for each Part are provided in the Connect library.

⟩ Finance in Practice Boxes Relevant news articles, often from financial pub- lications, appear in various chapters throughout the text. Aimed at bringing real-world flavor into the classroom, these boxes provide insight into the business world today.

⟩ Numbered Examples Numbered and titled examples are called out within chapters to further illustrate concepts. Students can learn how to solve specific problems step-by-step and apply key principles to answer concrete questions and scenarios.

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Part 1 Value

This book is about how corporations make financial decisions. We start by explaining what these decisions are and what they are intended to accomplish.

Corporations invest in real assets, which generate income. Some of these assets, such as plant and machinery, are tan- gible; others, such as brand names and patents, are intangible. Corporations finance their investments by borrowing, by retain- ing and reinvesting cash flow, and by selling additional shares of stock to the corporation’s shareholders. Thus, the financial manager faces two broad financial questions: First, what invest- ments should the corporation make? Second, how should it pay for those investments? The investment decision involves spending money; the financing decision involves raising it.

A large corporation may have hundreds of thousands of shareholders. These shareholders differ in many ways, including their wealth, risk tolerance, and investment horizon. Yet we shall see that they usually share the same financial objective. They want the financial manager to increase the value of the corporation and its current stock price.

Thus, the secret of success in financial management is to increase value. That is easy to say but not very helpful. Instructing the financial manager to increase value is like advising an investor in the stock market to “buy low, sell high.” The problem is how to do it.

There may be a few activities in which one can read a textbook and then just “do it,” but financial management is not one of them. That is why finance is worth studying. Who wants to work in a field where there is no room for judgment, experience, creativity, and a pinch of luck? Although this book cannot guarantee any of these things, it does cover the concepts that govern good financial decisions, and it shows you how to use the tools of the trade of modern finance.

This chapter begins with specific examples of recent investment and financing decisions made by well-known cor- porations. The middle of the chapter covers what a corpora- tion is and what its financial managers do. We conclude by explaining why increasing the market value of the corpora- tion is a sensible financial goal.

Financial managers increase value whenever the corpo- ration earns a higher return than shareholders can earn for themselves. The shareholders’ investment opportunities out- side the corporation set the standard for investments inside the corporation. Financial managers, therefore, refer to the opportunity cost of the capital contributed by shareholders.

Managers are, of course, human beings with their own interests and circumstances; they are not always the perfect servants of shareholders. Therefore, corporations must com- bine governance rules and procedures with appropriate incen- tives to make sure that all managers and employees—not just the financial managers—pull together to increase value.

Good governance and appropriate incentives also help block out temptations to increase stock price by illegal or unethi- cal means. Thoughtful shareholders do not want the maximum possible stock price. They want the maximum honest stock price.

This chapter introduces five themes that occur again and again throughout the book:

1. Corporate finance is all about maximizing value.

2. The opportunity cost of capital sets the standard for investment decisions.

3. A safe dollar is worth more than a risky dollar.

4. Smart investment decisions create more value than smart financing decisions.

5. Good governance matters.

Introduction to Corporate Finance

1C H A P T E R

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● ● ● ● ● FINANCE IN PRACTICE

⟩ Figure 16.6 shows how Apple’s holdings of cash and marketable securities have grown over the past decade. By the start of 2012, Apple Inc. had accumulated cash and long-term securities 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 fiscal conservatism 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 investors for payout steadily increased. “They have a ridiculous 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.”

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’ opinions varied. “A pretty vanilla return-of-cash program” (A. M. Sacconaghi, Bernstein Research). “It’s not too pid- dling, and on the other hand not so large to signal that growth prospects are not what they thought” (David A. Rolfe, Wedgewood Partners). The payout was not so large that it stopped Apple from accumulating cash because, over the following five years, the company more than dou- bled its holdings of cash and marketable securities.

Postcript: Apple more than kept its payout promise. In the 5 years to 2017, it distributed $224 billion through dividends and repurchases. Nevertheless, by the end of the period, its cash mountain was even higher than at the time of the 2012 announcement. At that point Apple announced a plan to buy back a further $100 billion of stock.

Source: N. Wingfield, “Flush with Cash, Apple Declares a Dividend and Buy- back,” The New York Times, March 20, 2012, pp. B1, B9.

Apple Commits to Dividend and Buyback

◗ FIGURE 16.6 The growth in Apple’s holdings of cash and marketable securities, 2002–2017

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Year ending September

Some critics had argued that Apple should pay out the cash because it was earning interest at less than 1% per year. That was a spurious argument because shareholders had no better opportunities. Safe interest rates were extremely low, and neither Apple nor investors could do anything about it.

Note also two further points. First, Apple did not just initiate a cash dividend. It announced a combination of dividends and repurchases. This two-part payout strategy is now standard for large, mature corporations. Second, Apple did not initiate repurchases because its stock

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Since the 14.3% return on the office building exceeds the 12% opportunity cost, you should go ahead with the project.

Building the office block is a smart thing to do, even if the payoff is just as risky as the stock market. We can justify the investment by either one of the following two rules:3

∙ Net present value rule. Accept investments that have positive net present values. ∙ Rate of return rule. Accept investments that offer rates of return in excess of their

opportunity costs of capital.

Properly applied, both rules give the same answer, although we will encounter some cases in Chapter 5 where the rate of return rule is easily misused. In those cases, it is safest to use the net present value rule.

Calculating Present Values When There Are Multiple Cash Flows One of the nice things about present values is that they are all expressed in current dollars—so you can add them up. In other words, the present value of cash flow (A + B) is equal to the present value of cash flow A plus the present value of cash flow B.

Suppose that you wish to value a stream of cash flows extending over a number of years. Our rule for adding present values tells us that the total present value is:

PV = C 1 ______

(1 + r) +

C 2 ______ (1 + r) 2

+ C 3 ______

(1 + r) 3 + ⋅ ⋅ ⋅ +

C T ______ (1 + r) T

This is called the discounted cash flow (or DCF) formula. A shorthand way to write it is

PV = ∑ t=1

C t ______

(1 + r) t

where Σ refers to the sum of the series of discounted cash flows. To find the net present value (NPV) we add the (usually negative) initial cash flow:

NPV = C 0 + PV = C 0 + ∑ t=1

C t ______

(1 + r) t

3You might check for yourself that these are equivalent rules. In other words, if the return of $100,000/$700,000 is greater than r, then the net present value –$700,000 + [$800,000/(1 + r)] must be greater than 0.

Your real estate adviser has come back with some revised forecasts. He suggests that you rent out the building for two years at $30,000 a year, and predicts that at the end of that time you will be able to sell the building for $840,000. Thus there are now two future cash flows—a cash flow of C1 = $30,000 at the end of one year and a further cash flow of C2 = (30,000 + 840,000) = $870,000 at the end of the second year.

The present value of your property development is equal to the present value of C1 plus the present value of C2. Figure 2.5 shows that the value of the first year’s cash flow is C1/(1 + r) = 30,000/1.12 = $26,786 and the value of the second year’s flow is C2/(1 + r)

2 = 870,000/1.122 = $693,559. Therefore our rule for adding present values tells us that the total present value of your investment is:

PV = C 1 _____

1 + r +

C 2 ______ (1 + r) 2

= 30,000 ______

1.12 +

870,000 _______ 1. 12 2

= 26,786 + 69,559 = $720,344

EXAMPLE 2.1 ● Present Values with Multiple Cash Flows

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78 Part One Value

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Boeing has 596 million shares outstanding. Shareholders include large pension funds and insurance companies that each own millions of shares, as well as individuals who own a handful. If you owned one Boeing share, you would own .0000002% of the company and have a claim on the same tiny fraction of its profits. Of course, the more shares you own, the larger your “share” of the company.

If Boeing wishes to raise new capital, it can do so either by borrowing or by selling new shares to investors. Sales of shares to raise new capital are said to occur in the primary market. But most trades in Boeing take place on the stock exchange, where investors buy and sell existing Boeing shares. Stock exchanges are really markets for secondhand shares, but they prefer to describe themselves as secondary markets, which sounds more important.

The two principal U.S. stock exchanges are the New York Stock Exchange and Nasdaq. Both compete vigorously for business and just as vigorously tout the advantages of their trading systems. In addition to the NYSE and Nasdaq, there are electronic communication networks (ECNs) that connect traders with each other. Large U.S. companies may also arrange for their shares to be traded on foreign exchanges, such as the London exchange or the Euronext exchange in Paris. At the same time, many foreign companies are listed on the U.S. exchanges. For example, the NYSE trades shares in Sony, Royal Dutch Shell, Canadian Pacific, Tata Motors, Deutsche Bank, Telefonica Brasil, China Eastern Airlines, and more than 500 other companies.

Suppose that Ms. Jones, a long-time Boeing shareholder, no longer wishes to hold her shares. She can sell them via the stock exchange to Mr. Brown, who wants to increase his stake in the firm. The transaction merely transfers partial ownership of the firm from one investor to another. No new shares are created, and Boeing will neither care nor know that the trade has taken place.

Ms. Jones and Mr. Brown do not trade the Boeing shares themselves. Instead, their orders must go through a brokerage firm. Ms. Jones, who is anxious to sell, might give her broker a market order to sell stock at the best available price. On the other hand, Mr. Brown might state a price limit at which he is willing to buy Boeing stock. If his limit order cannot be executed immediately, it is recorded in the exchange’s limit order book until it can be executed.

Table 4.1 shows a portion of the limit order book for Boeing from the BATS Exchange, one of the largest electronic markets. The bid prices on the left are the prices (and number of shares) at which investors are currently willing to buy. The ask prices on the right are those at which investors are prepared 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 BATS Exchange, where it would be

4-1 How Common Stocks Are Traded

Bid Ask

Price Shares Price Shares

263.76 1,100 264.07 200

263.73 100 264.12 1

263.67 100 264.13 100

263.61 100 264.18 200

⟩ TABLE 4.1 A portion of the limit order book for Boeing on the BATS BZX Exchange, November 20, 2017, at 09:51:03

BEYOND THE PAGE

m h h e.co m / b r e a l e y 13 e

Major world stock exchanges

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Table 4.3 continues the Fledgling Electronics example for various time horizons, assuming that the dividends are expected to increase at a steady 10% compound rate. The expected price Pt increases at the same rate each year. Each line in the table represents an application of our general formula for a different value of H. Figure 4.1 is a graph of the table. Each column shows the present value of the dividends up to the time 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 $100.

How far out could we look? In principle, the horizon period H could be infinitely distant. Common stocks do not expire of old age. Barring such corporate hazards as bankruptcy or acquisition, they are immortal. As H approaches infinity, the present value of the terminal price ought to approach zero, as it does in the final column of Figure 4.1. We can, therefore, forget about the terminal price entirely and express today’s price as the present value of a perpetual stream of cash dividends. This is usually written as

P 0 = ∑ t=1

∞

DIV t ______

(1 + r) t

where ∞ indicates infinity. This formula is the DCF or dividend discount model of stock prices. It’s another present value formula.9 We discount the cash flows—in this case, the dividend stream—by the return that can be earned in the capital market on securities of equivalent risk. Some find the DCF formula implausible because it seems to ignore capital gains. But we know that the formula was derived from the assumption that price in any period is determined by expected dividends and capital gains over the next period.

Notice that it is not correct to say that the value of a share is equal to the sum of the discounted stream of earnings per share. Earnings are generally larger than dividends because part of those earnings is reinvested in new plant, equipment, and working capital. Discounting

9Notice that this DCF formula uses a single discount rate for all future cash flows. This implicitly assumes that the company is all- equity-financed or that the fractions of debt and equity will stay constant. Chapters 17 through 19 discuss how the cost of equity changes when debt ratios change.

Expected Future Values Present Values

Horizon Period (H) Dividend (DIVt) Price (Pt) Cumulative Dividends Future Price Total

0 — 100 — — 100

1 5.00 110 4.35 95.65 100

2 5.50 121 8.51 91.49 100

3 6.05 133.10 12.48 87.52 100

4 6.66 146.41 16.29 83.71 100

10 11.79 259.37 35.89 64.11 100

20 30.58 672.75 58.89 41.11 100

50 533.59 11,739.09 89.17 10.83 100

100 62,639.15 1,378,061.23 98.83 1.17 100

⟩ TABLE 4.3 Applying the stock valuation formula to Fledgling Electronics Assumptions: 1. Dividends increase at 10% per year, compounded. 2. Discount rate (cost of equity or market capitalization rate) is 15%.

BEYOND THE PAGE

m h h e.co m / b r e a l e y 13 e

Try It! Figure 4.1: Value and the investor’s horizon

⟩ Beyond the Page Interactive Content and Applications Additional resources and hands-on applications are just a click away. Students can use the web address or click on the icon in the eBook to learn more about key concepts and try out calculations, tables, and figures when they go Beyond the Page.

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Excel ⟩ Spreadsheet Functions

Boxes These boxes provide detailed examples of how to use Excel spreadsheets when applying financial concepts. Questions that apply to the spreadsheet follow for additional practice.

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● ● ● ● ● USEFUL SPREADSHEET FUNCTIONS

⟩ Spreadsheet programs such as Excel provide built-in functions to solve discounted cash flow (DCF) prob- lems. You can find these functions by pressing fx on the Excel toolbar. If you then click on the function that you wish to use, Excel asks you for the inputs that it needs. At the bottom left of the function box there is a Help facility with an example of how the function is used.

Here is a list of useful functions for DCF problems and some points to remember when entering data: ∙ FV: Future value of single investment or annuity. ∙ PV: Present value of single future cash flow or annuity. ∙ RATE: Interest rate (or rate of return) needed to

produce given future value or annuity. ∙ NPER: Number of periods (e.g., years) that it takes

an investment to reach a given future value or series of future cash flows.

∙ PMT: Amount of annuity payment with a given present or future value.

∙ NPV: Calculates the value of a stream of negative and positive cash flows. (When using this function, note the warning below.)

∙ EFFECT: The effective annual interest rate, given the quoted rate (APR) and number of interest payments in a year.

∙ NOMINAL: The quoted interest rate (APR) given the effective annual interest rate.

be entered as a negative number. Entering both PV and FV with the same sign when solving for RATE results in an error message.

2. Always enter the interest or discount rate as a decimal value (for example, .05 rather than 5%).

3. Use the NPV function with care. Better still, don’t use it at all. It gives the value of the cash flows one period before the first cash flow and not the value at the date of the first cash flow.

Spreadsheet Questions

The following questions provide opportunities to prac- tice each of the Excel functions. 1. (FV) In 1880, five aboriginal trackers were each

promised the equivalent of 100 Australian dollars for helping to capture the notorious outlaw Ned Kelly. One hundred and thirteen years later, the granddaughters of two of the trackers claimed that this reward had not been paid. If the interest rate over this period averaged about 4.5%, how much would the A$100 have accumulated to?

2. (PV) Your adviser has produced revised figures for your office building. It is forecasted to produce a cash flow of $40,000 in year 1, but only $850,000 in year 2, when you come to sell it. If the cost of capital is 12%, what is the value of the building?

3. (PV) Your company can lease a truck for $10,000 a year (paid at the end of the year) for six years, or it can buy the truck today for $50,000. At the end of the six years the truck will be worthless. If the inter- est rate is 6%, what is the present value of the lease payments? Is the lease worthwhile?

4. (RATE) Ford Motor stock was one of the victims of the 2008 credit crisis. In June 2007, Ford stock price stood at $9.42. Eighteen months later it was $2.72. What was the annual rate of return over this period to an investor in Ford stock?

5. (NPER) An investment adviser has promised to double your money. If the interest rate is 7% a year, how many years will she take to do so?

6. (PMT) You need to take out a home mortgage for $200,000. If payments are made annually over 30 years and the interest rate is 8%, what is the amount of the annual payment?

Discounting Cash Flows

All the inputs in these functions can be entered directly as numbers or as the addresses of cells that contain the numbers.

Three warnings: 1. PV is the amount that needs to be invested today

to produce a given future value. It should therefore

⟩ Excel Exhibits Select tables are set as spreadsheets, and the corresponding Excel files are also available in Connect and through the Beyond the Page features.

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Chapter 7 Introduction to Risk and Return 189

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1 (1) (2) (3) (4) (5) (6) (7)

2 Product of

3 Deviation Deviation Squared Deviations

4 from from Average Deviation from Average

5 Market Anchovy Q Average Anchovy Q from Average Returns

6 Month Return Return Market Return Return Market Return (cols 4 × 5) 7 1 −8% −11% −10 −13 100 130

8 2 4 8 2 6 4 12

9 3 12 19 10 17 100 170

10 4 −6 −13 −8 −15 64 120

11 5 2 3 0 1 0 0

12 6 8 6 6 4 36 24

13 Average 2 2 Total 304 456

14 Variance = σ m 2 = 304 / 6 = 50.67

15 Covariance = σim = 456/6 = 76 16 Beta (β) = σ im / σ m 2 = 76/50.67 = 1.5

⟩ TABLE 7.7 Calculating the variance of the market returns and the covariance between the returns on the market and those of Anchovy Queen. Beta is the ratio of the covariance to the variance (i. e., β = σ im / σ m 2 )

We have seen that diversification reduces risk and, therefore, makes sense for investors. But does it also make sense for the firm? Is a diversified firm more attractive to investors than an undiversified one? If it is, we have an extremely disturbing result. If diversification is an appropriate corporate objective, each project has to be analyzed as a potential addition to the firm’s portfolio of assets. The value of the diversified package would be greater than the sum of the parts. So present values would no longer add.

Diversification is undoubtedly a good thing, but that does not mean that firms should prac- tice it. If investors were not able to hold a large number of securities, then they might want firms to diversify for them. But investors can diversify. In many ways they can do so more easily than firms. Individuals can invest in the steel industry this week and pull out next week. A firm cannot do that. To be sure, the individual would have to pay brokerage fees on the pur- chase and sale of steel company shares, but think of the time and expense for a firm to acquire a steel company or to start up a new steel-making operation.

You can probably see where we are heading. If investors can diversify on their own account, they will not pay any extra for firms that diversify. And if they have a sufficiently wide choice of securities, they will not pay any less because they are unable to invest separately in each factory. Therefore, in countries like the United States, which have large and competitive capi- tal markets, diversification does not add to a firm’s value or subtract from it. The total value is the sum of its parts.

This conclusion is important for corporate finance, because it justifies adding present val- ues. The concept of value additivity is so important that we will give a formal definition of it. If the capital market establishes a value PV(A) for asset A and PV(B) for B, the market value of a firm that holds only these two assets is

PV (AB) = PV (A) + PV (B)

7-5 Diversification and Value Additivity

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End-of-Chapter Features

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Chapter 3 Valuing Bonds 71

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there is a direct relationship between the duration of a bond and the exposure of its price to changes in interest rates. A change in interest rates has a greater effect on the price of long-duration bonds.

The term structure of interest rates is upward-sloping more often than not. This means that long-term spot rates are higher than short-term spot rates. But it does not mean that investing long is more profitable than investing short. The expectations theory

worried about risk. Long bonds may be a safe haven for investors with long-term fixed liabilities, but other investors may not like the extra volatility of long-term bonds or may be concerned that a sudden burst of inflation may largely wipe out the real value of these bonds. These investors will be prepared to hold long-term bonds only if they offer the compensation of a higher rate of interest.

Bonds promise fixed nominal cash payments, but the real interest rate that they provide depends on inflation. The best-known theory about the effect of inflation on interest rates was suggested by Irving Fisher. He argued that the nominal, or money, rate of interest is equal to the required real rate plus the expected rate of inflation. If the expected inflation rate increases by 1%, so too will the money rate of interest. During the past 50 years, Fisher’s simple theory has not done a bad job of explaining changes in short-term interest rates.

When you buy a U.S. Treasury bond, you can be fairly confident that you will get your money back. When you lend to a company, you face the risk that it will go belly-up and will not be able to repay its bonds. Defaults are rare for companies with investment-grade bond ratings, but investors worry nevertheless. Companies need to compensate investors for default risk by promising to pay higher rates of interest.

Some good general texts on fixed income markets are:

F. J. Fabozzi and S. V. Mann, Handbook of Fixed Income Securities, 8th ed. (New York: McGraw-Hill, 2012).

S. Sundaresan, Fixed Income Markets and Their Derivatives, 4th ed. (San Diego, CA: Academic Press, 2014).

B. Tuckman, Fixed Income Securities: Tools for Today’s Markets(New York: Wiley, 2002). P. Veronesi, Fixed Income Securities: Valuation, Risk, and Risk Management (New York: Wiley, 2010).

● ● ● ● ●

FURTHER READING

Select problems are available in McGraw-Hill’s Connect. Answers to questions with an “*” are found in the Appendix.

1. Bond prices and yields* A 10-year bond is issued with a face value of $1,000, paying interest of $60 a year. If interest rates increase shortly after the bond is issued, what happens to the bond’s

a. Coupon rate? b. Price? c. Yield to maturity? 2. Bond prices and yields The following statements are true. Explain why. a. If a bond’s coupon rate is higher than its yield to maturity, then the bond will sell for more

than face value. b. If a bond’s coupon rate is lower than its yield to maturity, then the bond’s price will

increase over its remaining maturity.

● ● ● ● ●

PROBLEM SETSRev.confirming pages

Chapter 3 Valuing Bonds 75

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Bond Maturity (years) Coupon ($) Price ($)

A 3 0 751.30

B 4 50 842.30

C 4 120 1,065.28

D 4 100 980.57

E 3 140 1,120.12

F 3 70 1,001.62

G 2 0 834.00

30. Nominal and real returns* Suppose that you buy a two-year 8% bond at its face value. a. What will be your total nominal return over the two years if inflation is 3% in the first

year and 5% in the second? What will be your total real return? b. Now suppose that the bond is a TIPS. What will be your total two-year real and nominal

returns? 31. Bond ratings A bond’s credit rating provides a guide to its price. In the fall of 2017 Aaa

bonds yielded 3.6% and Baa bonds yielded 4.3%. If some bad news causes a 10% five-year bond to be unexpectedly downrated from Aaa to Baa, what would be the effect on the bond price? (Assume annual coupons.)

CHALLENGE 32. Bond prices and yields Write a spreadsheet program to construct a series of bond tables

that show the present value of a bond given the coupon rate, maturity, and yield to maturity. Assume that coupon payments are semiannual and yields are compounded semiannually.

33. Price and spot interest rates Find the arbitrage opportunity(ies). Assume for simplicity that coupons are paid annually. In each case, the face value of the bond is $1,000.

Maturity (years) Coupon Price (%)

5 2 92.89

5 3 97.43

3 5 105.42

34. Duration The duration of a bond that makes an equal payment each year in perpetuity is (1 + yield)/yield. Prove it.

35. Prices and spot interest rates What spot interest rates are implied by the following Treasury bonds? Assume for simplicity that the bonds pay annual coupons. The price of a one-year strip is 97.56%, and the price of a four-year strip is 87.48%.

36. Prices and spot interest rates Look one more time at Table 3.6. a. Suppose you knew the bond prices but not the spot interest rates. Explain how you would

calculate the spot rates. (Hint: You have four unknown spot rates, so you need four equations.)

b. Suppose that you could buy bond C in large quantities at $1,040 rather than at its equilibrium price of $1,076.20. Show how you could make a zillion dollars without taking on any risk.

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680 Part Seven Debt Financing

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7. Operating leases* Acme has branched out to rentals of office furniture to start-up compa- nies. Consider a $3,000 desk. Desks last for six years and can be depreciated immediately. What is the break-even operating lease rate for a new desk? Assume that lease rates for old and new desks are the same and that Acme’s pretax administrative costs are $400 per desk in each of years 1 to 6. The cost of capital is 9% and the tax rate is 21%. Lease payments are made in advance, that is, at the start of each year. The inflation rate is zero.

8. Inflation and operating leases In Problem 7, we assumed identical lease rates for old and new desks.

a. How does the initial break-even lease rate change if the expected inflation rate is 5% per year? Assume that the real cost of capital does not change. (Hint: Look at the discussion of equivalent annual costs in Chapter 6.)

b. How does your answer to part (a) change if wear and tear force Acme to cut lease rates by 10% in real terms for every year of a desk’s age?

9. Technological change and operating leases Look at Table 25.1. How would the initial break-even operating lease rate change if rapid technological change in limo manufacturing reduces the costs of new limos by 5% per year? (Hint: We discussed technological change and equivalent annual costs in Chapter 6.)

10. Valuing financial leases Look again at Problem 7. Suppose a blue-chip company requests a six-year financial lease for a $3,000 desk. The company has just issued five-year notes at an interest rate of 6% per year. What is the break-even rate in this case? Assume administrative costs drop to $200 per year. Explain why your answers to Problem 7 and this question differ.

11. Valuing financial leases* Suppose that National Waferonics has before it a proposal for a four-year financial lease of a Waferooney machine. The firm constructs a table like Table 25.2. The bottom line of its table shows the lease cash flows:

Year 0 Year 1 Year 2 Year 3

Lease cash flow +62,000 –26,800 –22,200 –17,600

These flows reflect the cost of the machine, depreciation tax shields, and the after-tax lease payments. Ignore salvage value. Assume the firm could borrow at 10% and faces a 21% mar- ginal tax rate.

a. What is the value of the equivalent loan? b. What is the value of the lease? c. Suppose the machine’s NPV under normal financing is –$5,000. Should National Wafer-

onics invest? Should it sign the lease? 12. Valuing Financial Leases Look again at the National Waferonics lease in Problem 11.

Suppose that National Waferonics is highly levered and is unable to deduct further interest payments for tax.

a. Does this make a lease more or less attractive? b. Recalculate the NPV of the lease by constructing an equivalent loan. (Hint: Start with the

final year. The final repayment of the loan with interest should be set equal to the cash flow on the lease.)

Questions 14 to 17 all refer to Greymare’s bus lease. To answer them you may find it helpful to use the Beyond the Page live Excel spreadsheets in Connect.

13. Valuing financial leases Look again at the bus lease described in Table 25.2. a. What is the value of the lease if Greymare’s marginal tax rate is Tc = .30? b. What would the lease value be if the tax rate is 21%, but for tax purposes, the initial

investment had to be written off in equal amounts over years 1 through 5?

BEYOND THE PAGE

m h h e.co m / b r e a l e y 13 e

Try It! Leasing spreadsheets

⟩ Problem Sets For the 13th edition, we continue to use topic labels for each end-of-chapter problem to help instructors create assignments and to provide reinforcement for students. These end-of-chapter problems give students hands-on practice with key concepts and applications. Answers to select problems marked with * are included at the back of the book.

⟩ Excel Problems Most chapters contain problems, denoted by an icon, specifically linked to Excel spreadsheets that are available in Connect and through the Beyond the Page features.

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⟩ Mini-Cases Mini-cases are included in select chapters so students can apply their knowledge to real- world scenarios.

MINI-CASE ● ● ● ● ●

254 Part Two Risk

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The two wells are intended to develop a previously discovered oil field. Unfortunately there is still a 20% chance of a dry hole in each case. A dry hole means zero cash flows and a complete loss of the $10 million investment.

Ignore taxes and make further assumptions as necessary.

a. What is the correct real discount rate for cash flows from developed wells? b. The oil company executive proposes to add 20 percentage points to the real discount

rate to offset the risk of a dry hole. Calculate the NPV of each well with this adjusted discount rate.

c. What do you say the NPVs of the two wells are? d. Is there any single fudge factor that could be added to the discount rate for developed wells

that would yield the correct NPV for both wells? Explain.

● ● ● ● ●

FINANCE ON THE WEB

You can download data for the following questions from finance.yahoo.com.

1. Look at the companies listed in Table 8.2. Calculate monthly rates of return for two succes- sive five-year periods. Calculate betas for each subperiod using the Excel SLOPE function. How stable was each company’s beta? Suppose that you had used these betas to estimate expected rates of return from the CAPM. Would your estimates have changed significantly from period to period?

2. Identify a sample of food companies. For example, you could try Campbell Soup (CPB), General Mills (GIS), Kellogg (K), Mondelez International (MDLZ), and Tyson Foods (TSN).

a. Estimate beta and R2 for each company, using five years of monthly returns and Excel functions SLOPE and RSQ.

b. Average the returns for each month to give the return on an equally weighted portfolio of the stocks. Then calculate the industry beta using these portfolio returns. How does the R2 of this portfolio compare with the average R2 of the individual stocks?

c. Use the CAPM to calculate an average cost of equity (requity) for the food industry. Use current interest rates—take a look at the end of Section 9-2—and a reasonable estimate of the market risk premium.

The Jones Family Incorporated The Scene: It is early evening in the summer of 2018, in an ordinary family room in Manhat- tan. Modern furniture, with old copies of The Wall Street Journal and the Financial Times scat- tered around. Autographed photos of Jerome Powell and George Soros are prominently displayed. A picture window reveals a distant view of lights on the Hudson River. John Jones sits at a com- puter terminal, glumly sipping a glass of chardonnay and putting on a carry trade in Japanese yen over the Internet. His wife Marsha enters.

Marsha: Hi, honey. Glad to be home. Lousy day on the trading floor, though. Dullsville. No vol- ume. But I did manage to hedge next year’s production from our copper mine. I couldn’t get a good quote on the right package of futures contracts, so I arranged a commodity swap.

John doesn’t reply.

⟩ Finance on the Web These web exercises give students the opportunity to explore financial websites on their own. The web exercises make it easy to include cur- rent, real-world data in the classroom.

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MINI-CASE ● ● ● ● ●

254 Part Two Risk

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Ignore taxes and make further assumptions as necessary.

a. What is the correct real discount rate for cash flows from developed wells? b. The oil company executive proposes to add 20 percentage points to the real discount

rate to offset the risk of a dry hole. Calculate the NPV of each well with this adjusted discount rate.

c. What do you say the NPVs of the two wells are? d. Is there any single fudge factor that could be added to the discount rate for developed wells

that would yield the correct NPV for both wells? Explain.

● ● ● ● ●

FINANCE ON THE WEB

You can download data for the following questions from finance.yahoo.com.

2. Identify a sample of food companies. For example, you could try Campbell Soup (CPB), General Mills (GIS), Kellogg (K), Mondelez International (MDLZ), and Tyson Foods (TSN).

a. Estimate beta and R2 for each company, using five years of monthly returns and Excel functions SLOPE and RSQ.

John doesn’t reply.

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Supplements

time is also precious. The grading function enables the instructor to:

∙ Score assignments automatically, giving students immediate feedback on their work and side-by-side comparisons with correct answers.

∙ Access and review each response, manually change grades, or leave comments for students to review.

∙ Reinforce classroom concepts with practice tests and instant quizzes.

Instructor Library

The Connect Instructor Library provides additional resources to improve student engagement in and out of class. This library contains information about the book and the authors, as well as all of the instructor supple- ments, including:

∙ Instructor’s Manual The Instructor’s Manual was extensively revised and updated by Leslie Rush of the University of Hawaii, West Oahu. It contains an over- view of each chapter, teaching tips, learning objectives, challenge areas, key terms, and an annotated outline that provides references to the PowerPoint slides.

∙ Solutions Manual The Solutions Manual, carefully revised by Mishal Rawaf, contains solutions to all basic, intermediate, and challenge problems found at the end of each chapter.

∙ Test Bank The Test Bank, revised by Deb Bauer of the University of Oregon, contains hundreds of multiple-choice and short answer/discussion ques- tions, updated based on the revisions of the authors. The level of difficulty varies, as indicated by the easy, medium, or difficult labels.

∙ PowerPoint Presentations Leslie Rush also pre- pared the PowerPoint presentations, which contain exhibits, outlines, key points, and summaries in a visually stimulating collection of slides. The instruc- tor can edit, print, or rearrange the slides to fit the needs of his or her course.

∙ Beyond the Page The authors have created a wealth of additional examples, explanations, and applica- tions, available for quick access by instructors and stu- dents. Each Beyond the Page feature is called out in the text with an icon that links directly to the content.

⟩ In this edition, we have gone to great lengths to ensure that our supplements are equal in quality and author-

ity to the text itself.

MCGRAW-HILL’S CONNECT

Less Managing. More Teaching. Greater Learning.

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Preface vii

I Part One: Value

1 Introduction to Corporate Finance 1 2 How to Calculate Present Values 20 3 Valuing Bonds 46 4 The Value of Common Stocks 77 5 Net Present Value and Other Investment

Criteria 108 6 Making Investment Decisions with the Net Present

Value Rule 135

I Part Two: Risk

7 Introduction to Risk and Return 167 8 Portfolio Theory and the Capital Asset Pricing

Model 198 9 Risk and the Cost of Capital 228

I Part Three: Best Practices in Capital Budgeting

10 Project Analysis 257 11 How to Ensure that Projects Truly Have Positive

NPVs 284 12 Agency Problems and Investment 311

I Part Four: Financing Decisions and Market Efficiency

13 Efficient Markets and Behavioral Finance 337 14 An Overview of Corporate Financing 365 15 How Corporations Issue Securities 391

I Part Five: Payout Policy and Capital Structure

16 Payout Policy 425 17 Does Debt Policy Matter? 451

18 How Much Should a Corporation Borrow? 475 19 Financing and Valuation 507

I Part Six: Options

20 Understanding Options 542 21 Valuing Options 563 22 Real Options 590

I Part Seven: Debt Financing

23 Credit Risk and the Value of Corporate Debt 614 24 The Many Different Kinds of Debt 631 25 Leasing 663

I Part Eight: Risk Management

26 Managing Risk 683 27 Managing International Risks 717

I Part Nine: Financial Planning and Working Capital Management

28 Financial Analysis 743 29 Financial Planning 770 30 Working Capital Management 801

I Part Ten: Mergers, Corporate Control, and Governance

31 Mergers 830 32 Corporate Restructuring 863 33 Governance and Corporate Control around the

World 888

I Part Eleven: Conclusion

34 Conclusion: What We Do and Do Not Know about Finance 909

Brief Contents

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Preface vii

I Part One: Value

1 Introduction to Corporate Finance 1

1-1 Corporate Investment and Financing Decisions 2 Investment Decisions/Financing Decisions/What Is

a Corporation?/The Role of the Financial Manager

1-2 The Financial Goal of the Corporation 7 Shareholders Want Managers to Maximize Market

Value/A Fundamental Result/The Investment Trade-

Off/Should Managers Look After the Interests

of Their Shareholders?/Agency Problems and

Corporate Governance

1-3 Preview of Coming Attractions 13

Summary 15 • Problem Sets 15 • Appendix: Why Maximizing Shareholder Value Makes Sense 18

2 How to Calculate Present Values 20

2-1 Future Values and Present Values 20 Calculating Future Values/Calculating Present

Values/Valuing an Investment Opportunity/Net

Present Value/Risk and Present Value/Present

Values and Rates of Return/Calculating Present

Values When There Are Multiple Cash Flows/The

Opportunity Cost of Capital

2-2 Looking for Shortcuts—Perpetuities and Annuities 28 How to Value Perpetuities/How to Value Annuities/

Valuing Annuities Due/Calculating Annual

Payments/Future Value of an Annuity

2-3 More Shortcuts—Growing Perpetuities and Annuities 34 Growing Perpetuities/Growing Annuities

2-4 How Interest Is Paid and Quoted 36 Continuous Compounding

Summary 39 • Problem Sets 40 • Finance on the Web 45

3 Valuing Bonds 46 3-1 Using the Present Value Formula to Value

Bonds 47 A Short Trip to Paris to Value a Government Bond/

Back to the United States: Semiannual Coupons

and Bond Prices

3-2 How Bond Prices Vary with Interest Rates 50 Duration and Volatility

3-3 The Term Structure of Interest Rates 56 Spot Rates, Bond Prices, and the Law of One

Price/Measuring the Term Structure/Why the

Discount Factor Declines as Futurity Increases—

and a Digression on Money Machines

3-4 Explaining the Term Structure 60 Expectations Theory of the Term Structure/

Introducing Risk/Inflation and Term Structure

3-5 Real and Nominal Rates of Interest 62 Indexed Bonds and the Real Rate of Interest/What

Determines the Real Rate of Interest?/Inflation and

Nominal Interest Rates

3-6 The Risk of Default 67 Corporate Bonds and Default Risk/Sovereign

Bonds and Default Risk

Summary 70 • Further Reading 71 • Problem Sets 71 Finance on the Web 76

4 The Value of Common Stocks 77 4-1 How Common Stocks Are Traded 78

Trading Results for Boeing

4-2 How Common Stocks Are Valued 80 Valuation by Comparables/Stock Prices and

Dividends

Contents

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Inflation Consistently/Rule 4: Separate Investment

and Financing Decisions/Rule 5: Remember to

Deduct Taxes

6-2 Corporate Income Taxes 142 U.S. Corporate Income Tax Reform

6-3 Example—IM&C’s Fertilizer Project 144 The Three Elements of Project Cash Flows/

Forecasting the Fertilizer Project’s Cash Flows/

Accelerated Depreciation and First-Year

Expensing/Final Comments on Taxes/Project

Analysis/Calculating NPV in Other Countries and

Currencies

6-4 Using the NPV Rule to Choose among Projects 151 Problem 1: The Investment Timing Decision/

Problem 2: The Choice between Long- and Short-

Lived Equipment/Problem 3: When to Replace an

Old Machine/Problem 4: Cost of Excess Capacity

Summary 156 • Further Reading 157 • Problem Sets 157 • Mini-Case: New Economy Transport (A) 165 • New Economy Transport (B) 166

I Part Two: Risk

7 Introduction to Risk and Return 167

7-1 Over a Century of Capital Market History in One Easy Lesson 167 Arithmetic Averages and Compound Annual

Returns/Using Historical Evidence to Evaluate

Today’s Cost of Capital

7-2 Diversification and Portfolio Risk 174 Variance and Standard Deviation/Measuring

Variability/How Diversification Reduces Risk

7-3 Calculating Portfolio Risk 181 General Formula for Computing Portfolio Risk/Do

I Really Have to Add up 36 Million Boxes?

7-4 How Individual Securities Affect Portfolio Risk 185 Market Risk Is Measured by Beta/Why Security

Betas Determine Portfolio Risk

4-3 Estimating the Cost of Equity Capital 87 Using the DCF Model to Set Water, Gas, and

Electricity Prices/Dangers Lurk in Constant-

Growth Formulas

4-4 The Link between Stock Price and Earnings per Share 92 Calculating the Present Value of Growth

Opportunities for Fledgling Electronics

4-5 Valuing a Business by Discounted Cash Flow 95 Valuing the Concatenator Business/Valuation

Format/Estimating Horizon Value/Free Cash Flow,

Dividends, and Repurchases

Summary 100 • Problem Sets 101 • Finance on the Web 106 • Mini-Case: Reeby Sports 106

5 Net Present Value and Other Investment Criteria 108

5-1 A Review of the Basics 108 Net Present Value’s Competitors/Three Points to

Remember about NPV

5-2 Book Rate of Return and Payback 111 Book Rate of Return /Payback/Discounted Payback

5-3 Internal (or Discounted Cash Flow) Rate of Return 114 Calculating the IRR/The IRR Rule/Pitfall 1—

Lending or Borrowing?/Pitfall 2—Multiple Rates of

Return/Pitfall 3—Mutually Exclusive Projects/Pitfall

4—What Happens When There Is More Than One

Opportunity Cost of Capital/The Verdict on IRR

5-4 Choosing Capital Investments When Resources Are Limited 122 An Easy Problem in Capital Rationing/Uses of

Capital Rationing Models

Summary 126 • Further Reading 127 • Problem Sets 127 • Mini-Case: Vegetron’s CFO Calls Again 132

6 Making Investment Decisions with the Net Present Value Rule 135

6-1 Applying the Net Present Value Rule 135 Rule 1: Discount Cash Flows, Not Profits/Rule 2:

Discount Incremental Cash Flows /Rule 3: Treat

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9-4 Certainty Equivalents—Another Way to Adjust for Risk 242 Valuation by Certainty Equivalents/When to Use a

Single Risk-Adjusted Discount Rate for Long-Lived

Assets/A Common Mistake/When You Cannot Use

a Single Risk-Adjusted Discount Rate for Long-

Lived Assets

Summary 248 • Further Reading 249 • Problem Sets 249 • Finance on the Web 254 • Mini-Case: The Jones Family Incorporated 254

I Part Three: Best Practices in Capital Budgeting

10 Project Analysis 257 10-1 Sensitivity and Scenario Analysis 258

Value of Information/Limits to Sensitivity Analysis/

Scenario Analysis

10-2 Break-Even Analysis and Operating Leverage 262 Break-Even Analysis/Operating Leverage and the

Break-Even Point

10-3 Monte Carlo Simulation 264 Simulating the Electric Scooter Project

10-4 Real Options and Decision Trees 266 The Option to Expand/The Option to Abandon/

Production Options/Timing Options/More on

Decision Trees/Pro and Con Decision Trees

Summary 274 • Further Reading 275 • Problem Sets 275 • Mini-Case: Waldo County 282

11 How to Ensure That Projects Truly Have Positive NPVs 284

11-1 How Firms Organize the Investment Process 284 The Capital Budget/Project Authorizations—and

the Problem of Biased Forecasts/Postaudits

11-2 Look First to Market Values 287 The BMW and Your Sporting Idol

11-3 Economic Rents and Competitive Advantage 292

7-5 Diversification and Value Additivity 189

Summary 190 • Further Reading 191 • Problem Sets 191 • Finance on the Web 197

8 Portfolio Theory and the Capital Asset Pricing Model 198

8-1 Harry Markowitz and the Birth of Portfolio Theory 198 Combining Stocks into Portfolios/We Introduce

Borrowing and Lending

8-2 The Relationship between Risk and Return 205 Some Estimates of Expected Returns/Review of the

Capital Asset Pricing Model/What If a Stock Did

Not Lie on the Security Market Line?

8-3 Validity and Role of the Capital Asset Pricing Model 208 Tests of the Capital Asset Pricing Model/

Assumptions behind the Capital Asset Pricing

Model

8-4 Some Alternative Theories 213 Arbitrage Pricing Theory/A Comparison of the

Capital Asset Pricing Model and Arbitrage Pricing

Theory/The Three-Factor Model

Summary 217 • Further Reading 218 • Problem Sets 219 • Finance on the Web 225 • Mini-Case: John and Marsha on Portfolio Selection 225

9 Risk and the Cost of Capital 228 9-1 Company and Project Costs of Capital 229

Perfect Pitch and the Cost of Capital/Debt and the

Company Cost of Capital

9-2 Measuring the Cost of Equity 232 Estimating Beta/The Expected Return on CSX’s

Common Stock/CSX’s After-Tax Weighted-Average

Cost of Capital/CSX’s Asset Beta

9-3 Analyzing Project Risk 236 What Determines Asset Betas?/Don’t Be Fooled

by Diversifiable Risk/Avoid Fudge Factors in

Discount Rates/Discount Rates for International

Projects

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11-4 Marvin Enterprises Decides to Exploit a New Technology—an Example 295 Forecasting Prices of Gargle Blasters/The Value

of Marvin’s New Expansion/Alternative Expansion

Plans/The Value of Marvin Stock/The Lessons of

Marvin Enterprises

Summary 303 • Further Reading 303 • Problem Sets 303 • Mini-Case: Ecsy-Cola 309

12 Agency Problems and Investment 311

12-1 What Agency Problems Should You Watch Out For? 311 Agency Problems Don’t Stop at the Top/Risk Taking

12-2 Monitoring 314 Boards of Directors /Auditors/Lenders/

Shareholders/Takeovers

12-3 Management Compensation 316 Compensation Facts and Controversies/The

Economics of Incentive Compensation/The Specter

of Short-Termism

12-4 Measuring and Rewarding Performance: Residual Income and EVA 323 Residual Income or Economic Value Added

(EVA®)/Pros and Cons of EVA

12-5 Biases in Accounting Measures of Performance 326 Example: Measuring the Profitability of the Nodhead

Supermarket/Measuring Economic Profitability/Do the

Biases Wash Out in the Long Run?/What Can We Do

about Biases in Accounting Profitability Measures?

Summary 331 • Further Reading 332 • Problem Sets 332

I Part Four: Financing Decisions and Market Efficiency

13 Efficient Markets and Behavioral Finance 337

13-1 Differences between Investment and Financing Decisions 338 We Always Come Back to NPV

13-2 The Efficient Market Hypothesis 340 A Startling Discovery: Price Changes Are

Random/Random Walks: The Evidence/Semistrong

Market Efficiency: The Evidence/Strong Market

Efficiency: The Evidence

13-3 Bubbles and Market Efficiency 348 13-4 Behavioral Finance 349

Sentiment/Limits to Arbitrage/Incentive Problems

and the Financial Crisis of 2008–2009

13-5 The Five Lessons of Market Efficiency 354 Lesson 1: Markets Have No Memory/Lesson 2:

Trust Market Prices/Lesson 3: Read the Entrails/

Lesson 4: The Do-It-Yourself Alternative/Lesson 5:

Seen One Stock, Seen Them All/What If Markets

Are Not Efficient? Implications for the Financial

Manager

Summary 359 • Further Reading 360 • Problem Sets 361 • Finance on the Web 364

14 An Overview of Corporate Financing 365

14-1 Patterns of Corporate Financing 365 Do Firms Rely Too Much on Internal Funds?/How

Much Do Firms Borrow?

14-2 Common Stock 369 Ownership of the Corporation/Voting Procedures/

Dual-Class Shares and Private Benefits/Equity in

Disguise/Preferred Stock

14-3 Debt 374 Debt Comes in Many Forms/A Debt by Any Other

Name/Variety’s the Very Spice of Life

14-4 Financial Markets and Intermediaries 377 Financial Markets/Financial Intermediaries/

Investment Funds/Financial Institutions

14-5 The Role of Financial Markets and Intermediaries 382 The Payment Mechanism/Borrowing and Lending/

Pooling Risk/Information Provided by Financial

Markets/The Financial Crisis of 2007–2009

Summary 386 • Further Reading 387 • Problem Sets 388 • Finance on the Web 390

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15 How Corporations Issue Securities 391

15-1 Venture Capital 391 The Venture Capital Market

15-2 The Initial Public Offering 396 The Public-Private Choice/Arranging an Initial

Public Offering/The Sale of Marvin Stock/The

Underwriters/Costs of a New Issue/Underpricing

of IPOs/Hot New-Issue Periods/The Long-Run

Performance of IPO Stocks

15-3 Alternative Issue Procedures for IPOs 406 Types of Auction: A Digression

15-4 Security Sales by Public Companies 408 General Cash Offers/International Security

Issues/The Costs of a General Cash Offer/Market

Reaction to Stock Issues/Rights Issues

15-5 Private Placements and Public Issues 413

Summary 413 • Further Reading 414 Problem Sets 415 • Finance on the Web 420 Appendix: Marvin’s New-Issue Prospectus 421

I Part Five: Payout Policy and Capital Structure

16 Payout Policy 425 16-1 Facts about Payout 426

How Firms Pay Dividends/How Firms Repurchase

Stock

16-2 The Information Content of Dividends and Repurchases 428 The Information Content of Share

Repurchases

16-3 Dividends or Repurchases? The Payout Controversy 431 Payout Policy Is Irrelevant in Perfect Capital

Markets/Dividends or Repurchases? An Example/

Stock Repurchases and DCF Models of Share

Price/Dividends and Share Issues

16-4 The Rightists 436 Payout Policy, Investment Policy, and Management

Incentives

16-5 Taxes and the Radical Left 437 Empirical Evidence on Dividends and Taxes/

Alternative Tax Systems

16-6 Payout Policy and the Life Cycle of the Firm 441 Payout and Corporate Governance

Summary 443 • Further Reading 444 • Problem Sets 445

17 Does Debt Policy Matter? 451 17-1 The Effect of Financial Leverage in a

Competitive Tax-Free Economy 452 Enter Modigliani and Miller/The Law of

Conservation of Value/An Example of Proposition 1

17-2 Financial Risk and Expected Returns 457 Proposition 2/Leverage and the Cost of Equity/

How Changing Capital Structure Affects Beta/

Watch Out for Hidden Leverage

17-3 No Magic in Financial Leverage 464 Today’s Unsatisfied Clienteles Are Probably

Interested in Exotic Securities/Imperfections and

Opportunities

17-4 A Final Word on the After-Tax Weighted- Average Cost of Capital 467

Summary 468 • Further Reading 469 • Problem Sets 470 • Mini-Case: Claxton Drywall Comes to the Rescue 474

18 How Much Should a Corporation Borrow? 475

18-1 Corporate Taxes 476 How Do Interest Tax Shields Contribute to the

Value of Stockholders’ Equity?/Recasting Johnson

& Johnson’s Capital Structure/MM and Taxes

18-2 Corporate and Personal Taxes 480 18-3 Costs of Financial Distress 482

Bankruptcy Costs/Evidence on Bankruptcy Costs/

Direct versus Indirect Costs of Bankruptcy/

Financial Distress without Bankruptcy/Debt and

Incentives/Risk Shifting: The First Game/Refusing

to Contribute Equity Capital: The Second Game/

And Three More Games, Briefly/What the Games

Cost/Costs of Distress Vary with Type of Asset/The

Trade-Off Theory of Capital Structure

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18-4 The Pecking Order of Financing Choices 495 Debt and Equity Issues with Asymmetric

Information/Implications of the Pecking Order/The

Trade-Off Theory vs. the Pecking-Order Theory—

Some Evidence/The Bright Side and the Dark Side

of Financial Slack/Is There a Theory of Optimal

Capital Structure?

Summary 501 • Further Reading 502 • Problem Sets 503 • Finance on the Web 506

19 Financing and Valuation 507 19-1 The After-Tax Weighted-Average Cost of

Capital 508 Review of Assumptions/Mistakes People Make in

Using the Weighted-Average Formula

19-2 Valuing Businesses 512 Valuing Rio Corporation/Estimating Horizon

Value/WACC vs. the Flow-to-Equity Method

19-3 Using WACC in Practice 517 Some Tricks of the Trade/Adjusting WACC When

Debt Ratios and Business Risks Differ/Unlevering

and Relevering Betas/The Importance of

Rebalancing/The Modigliani–Miller Formula, Plus

Some Final Advice

19-4 Adjusted Present Value 524 APV for the Perpetual Crusher/Other Financing

Side Effects/APV for Entire Businesses/APV

and Limits on Interest Deductions/APV for

International Investments

19-5 Your Questions Answered 529

Summary 531 • Further Reading 532 • Problem Sets 532 • Finance on the Web 537 • Appendix: Discounting Safe, Nominal Cash Flows 538

I Part Six: Options

20 Understanding Options 542 20-1 Calls, Puts, and Shares 543

Call Options and Position Diagrams/Put Options/

Selling Calls and Puts/Position Diagrams Are Not

Profit Diagrams

20-2 Financial Alchemy with Options 547 Spotting the Option

20-3 What Determines Option Values? 552 Risk and Option Values

Summary 557 • Further Reading 558 Problem Sets 558 • Finance on the Web 562

21 Valuing Options 563 21-1 A Simple Option-Valuation Model 564

Why Discounted Cash Flow Won’t Work for

Options/Constructing Option Equivalents from

Common Stocks and Borrowing/Valuing the

Amazon Put Option

21-2 The Binomial Method for Valuing Options 568 Example: The Two-Step Binomial Method/The

General Binomial Method/The Binomial Method

and Decision Trees

21-3 The Black–Scholes Formula 573 Using the Black–Scholes Formula/The Risk of

an Option/The Black–Scholes Formula and the

Binomial Method

21-4 Black–Scholes in Action 577 Executive Stock Options/Warrants/Portfolio

Insurance/Calculating Implied Volatilities

21-5 Option Values at a Glance 580 21-6 The Option Menagerie 582

Summary 582 • Further Reading 583 • Problem Sets 583 • Finance on the Web 588 • Mini-Case: Bruce Honiball’s Invention 588

22 Real Options 590 22-1 The Value of Follow-On Investment

Opportunities 590 Questions and Answers about Blitzen’s Mark II/

Other Expansion Options

22-2 The Timing Option 594 Valuing the Malted Herring Option/Optimal

Timing for Real Estate Development

22-3 The Abandonment Option 597 Bad News for the Perpetual Crusher/Abandonment

Value and Project Life/Temporary Abandonment

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22-4 Flexible Production and Procurement 600 Aircraft Purchase Options

22-5 Investment in Pharmaceutical R&D 604 22-6 Valuing Real Options 606

A Conceptual Problem?/What about Taxes?/

Practical Challenges

Summary 608 • Further Reading 609 Problem Sets 609

I Part Seven: Debt Financing

23 Credit Risk and the Value of Corporate Debt 614

23-1 Yields on Corporate Debt 614 What Determines the Yield Spread?

23-2 Valuing the Option to Default 618 The Value of Corporate Equity/A Digression:

Valuing Government Financial Guarantees

23-3 Bond Ratings and the Probability of Default 622

23-4 Predicting the Probability of Default 624 Statistical Models of Default/Structural Models

of Default

Summary 628 • Further Reading 628 • Problem Sets 629 • Finance on the Web 630

24 The Many Different Kinds of Debt 631

24-1 Long-Term Bonds 632 Bond Terms/Security and Seniority/Asset-Backed

Securities/Call Provisions/Sinking Funds/Bond

Covenants/Privately Placed Bonds/Foreign Bonds

and Eurobonds

24-2 Convertible Securities and Some Unusual Bonds 641 The Value of a Convertible at Maturity/

Forcing Conversion/Why Do Companies Issue

Convertibles?/Valuing Convertible Bonds/A

Variation on Convertible Bonds: The Bond–

Warrant Package/Innovation in the Bond Market

24-3 Bank Loans 647 Commitment/Maturity/Rate of Interest/Syndicated

Loans/Security/Loan Covenants

24-4 Commercial Paper and Medium-Term Notes 650 Commercial Paper/Medium-Term Notes

Summary 652 • Further Reading 653 • Problem Sets 653 • Mini-Case: The Shocking Demise of Mr. Thorndike 658 • Appendix: Project Finance 660 Appendix Further Reading 662

25 Leasing 663 25-1 What Is a Lease? 663 25-2 Why Lease? 664

Sensible Reasons for Leasing/Some Dubious

Reasons for Leasing

25-3 Operating Leases 667 Example of an Operating Lease/Lease or Buy?

25-4 Valuing Financial Leases 669 Example of a Financial Lease/Who Really Owns

the Leased Asset?/Leasing and the Internal

Revenue Service/A First Pass at Valuing a Lease

Contract/The Story So Far/Financial Leases When

There Is No Interest Tax Shield

25-5 When Do Financial Leases Pay? 675 Leasing around the World

25-6 Leveraged Leases 676

Summary 677 • Further Reading 678 • Problem Sets 678

I Part Eight: Risk Management

26 Managing Risk 683 26-1 Why Manage Risk? 684

Reducing the Risk of Cash Shortfalls or Financial

Distress/Agency Costs May Be Mitigated by Risk

Management/The Evidence on Risk Management

26-2 Insurance 687 26-3 Reducing Risk with Options 689 26-4 Forward and Futures Contracts 690

A Simple Forward Contract/Futures Exchanges/

The Mechanics of Futures Trading/Trading and

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Pricing Financial Futures Contracts/Spot and

Futures Prices—Commodities/More about Forward

Contracts/Homemade Forward Rate Contracts

26-5 Swaps 697 Interest Rate Swaps/Currency Swaps/Some Other

Swaps

26-6 How to Set Up a Hedge 702 Hedging Interest Rate Risk/Hedge Ratios and

Basis Risk

26-7 Is “Derivative” a Four-Letter Word? 705

Summary 707 • Further Reading 708 • Problem Sets 708 • Finance on the Web 714 • Mini-Case: Rensselaer Advisers 714

27 Managing International Risks 717 27-1 The Foreign Exchange Market 717 27-2 Some Basic Relationships 719

Interest Rates and Exchange Rates/The Forward

Premium and Changes in Spot Rates/Changes in the

Exchange Rate and Inflation Rates/Interest Rates

and Inflation Rates/Is Life Really That Simple?

27-3 Hedging Currency Risk 728 Transaction Exposure and Economic Exposure

27-4 Exchange Risk and International Investment Decisions 731 The Cost of Capital for International Investments

27-5 Political Risk 734

Summary 736 • Further Reading 737 • Problem Sets 738 • Finance on the Web 741 • Mini-Case: Exacta, S.a. 742

I Part Nine: Financial Planning and Working Capital Management

28 Financial Analysis 743 28-1 Financial Ratios 743 28-2 Financial Statements 744 28-3 Home Depot’s Financial Statements 745

The Balance Sheet/The Income Statement

28-4 Measuring Home Depot’s Performance 748 Economic Value Added/Accounting Rates of

Return/Problems with EVA and Accounting

Rates of Return

28-5 Measuring Efficiency 752 28-6 Analyzing the Return on Assets: The Du Pont

System 754 The Du Pont System

28-7 Measuring Leverage 756 Leverage and the Return on Equity

28-8 Measuring Liquidity 758 28-9 Interpreting Financial Ratios 760

Summary 763 • Further Reading 763 • Problem Sets 763 • Finance on the Web 769

29 Financial Planning 770 29-1 Links between Short-Term and Long-Term

Financing Decisions 770 29-2 Tracing Changes in Cash 773

The Cash Cycle

29-3 Cash Budgeting 778 29-4 Dynamic’s Short-Term Financial Plan 780

Dynamic Mattress’s Financing Plan/Evaluating

the Plan/A Note on Short-Term Financial Planning

Models

29-5 Long-Term Financial Planning 784 Why Build Financial Plans?/A Long-Term

Financial Planning Model for Dynamic

Mattress/Pitfalls in Model Design/Choosing a

Plan

29-6 Growth and External Financing 789

Summary 791 • Further Reading 791 • Problem Sets 792 • Finance on the Web 800

30 Working Capital Management 801

30-1 The Composition of Working Capital 802 30-2 Inventories 804 30-3 Credit Management 806

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Terms of Sale/The Promise to Pay/Credit Analysis/

The Credit Decision/Collection Policy

30-4 Cash 812 How Purchases Are Paid For/Speeding Up Check

Collections/International Cash Management/

Paying for Bank Services

30-5 Marketable Securities 816 Tax Strategies/Investment Choices/Calculating

the Yield on Money Market Investments/Returns

on Money Market Investments/The International

Money Market/Money Market Instruments

Summary 822 • Further Reading 823 • Problem Sets 824 • Finance on the Web 829

I Part Ten: Mergers, Corporate Control, and Governance

31 Mergers 830 31-1 Sensible Motives for Mergers 831

Economies of Scale/Economies of Vertical

Integration/Complementary Resources/Surplus Funds/

Eliminating Inefficiencies/Industry Consolidation

31-2 Some Dubious Reasons for Mergers 836 Diversification/Increasing Earnings per Share:

The Bootstrap Game/Lower Financing Costs

31-3 Estimating Merger Gains and Costs 839 Right and Wrong Ways to Estimate the Benefits

of Mergers/More on Estimating Costs—What If

the Target’s Stock Price Anticipates the Merger?/

Estimating Cost When the Merger Is Financed by

Stock/Asymmetric Information

31-4 The Mechanics of a Merger 844 Mergers, Antitrust Law, and Popular Opposition/

The Form of Acquisition/Merger Accounting/Some

Tax Considerations/Cross-Border Mergers and Tax

Inversion

31-5 Proxy Fights, Takeovers, and the Market for Corporate Control 847 Proxy Contests/Takeovers/Valeant Bids for Allergan/

Takeover Defenses/Who Gains Most in Mergers?

31-6 Merger Waves and Merger Profitability 853 Merger Waves/Merger Announcements and the

Stock Price/Merger Profitability/Do Mergers

Generate Net Benefits?

Summary 855 • Further Reading 856 • Problem Sets 856 • Appendix: Conglomerate Mergers and Value Additivity 861

32 Corporate Restructuring 863 32-1 Leveraged Buyouts 863

The RJR Nabisco LBO/Barbarians at the Gate?/

Leveraged Restructurings/LBOs and Leveraged

Restructurings

32-2 The Private-Equity Market 868 Private-Equity Partnerships/Are Private-Equity

Funds Today’s Conglomerates?

32-3 Fusion and Fission in Corporate Finance 873 Spin-Offs/Carve-Outs/Asset Sales/Privatization

and Nationalization

32-4 Bankruptcy 878 Is Chapter 11 Efficient?/Workouts/Alternative

Bankruptcy Procedures

Summary 883 • Further Reading 884 • Problem Sets 885

33 Governance and Corporate Control around the World 888

33-1 Financial Markets and Institutions 888 Investor Protection and the Development of

Financial Markets

33-2 Ownership, Control, and Governance 892 Ownership and Control in Japan/Ownership and

Control in Germany/European Boards of Directors/

Shareholders versus Stakeholders/Ownership and

Control in Other Countries/Conglomerates Revisited

33-3 Do These Differences Matter? 902 Risk and Short-Termism/Growth Industries and

Declining Industries/Transparency and Governance

Summary 905 • Further Reading 906 Problem Sets 907

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I Part Eleven: Conclusion

34 Conclusion: What We Do and Do Not Know about Finance 909

34-1 What We Do Know: The Seven Most Important Ideas in Finance 909 1. Net Present Value/2. The Capital Asset Pricing

Model/3. Efficient Capital Markets/4. Value

Additivity and the Law of Conservation of Value/

5. Capital Structure Theory/6. Option Theory/

7. Agency Theory

34-2 What We Do Not Know: 10 Unsolved Problems in Finance 912 1. What Determines Project Risk and Present

Value?/2. Risk and Return—What Have We

Missed?/3. How Important Are the Exceptions to

the Efficient-Market Theory?/4. Is Management

an Off-Balance-Sheet Liability?/5. How Can We

Explain the Success of New Securities and New

Markets?/6. How Can We Resolve the Payout

Controversy?/7. What Risks Should a Firm

Take?/8. What Is the Value of Liquidity?/9. How

Can We Explain Merger Waves?/10. Why Are

Financial Systems So Prone to Crisis?

34-3 A Final Word 918

APPENDIX A-1

GLOSSARY G-1

INDEX I-1

Note: Present value tables are available in Connect.

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Part 1 Value

This book is about how corporations make financial decisions. We start by explaining what these decisions are and what they are intended to accomplish.

This chapter introduces five themes that occur again and again throughout the book:

1. Corporate finance is all about maximizing value.

2. The opportunity cost of capital sets the standard for investment decisions.

3. A safe dollar is worth more than a risky dollar.

4. Smart investment decisions create more value than smart financing decisions.

5. Good governance matters.

Introduction to Corporate Finance

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To carry on business, a corporation needs an almost endless variety of real assets. These do not drop free from a blue sky; they need to be paid for. The corporation pays for its real assets by selling claims on them and on the cash flow that they will generate. These claims are called financial assets or securities. Take a bank loan as an example. The bank provides the corpo- ration with cash in exchange for a financial asset, which is the corporation’s promise to repay the loan with interest. An ordinary bank loan is not a security, however, because it is held by the bank and is not traded in financial markets.

Take a corporate bond as a second example. The corporation sells the bond to investors in exchange for the promise to pay interest on the bond and to pay off the bond at its maturity. The bond is a financial asset, and also a security, because it can be held and traded by many investors in financial markets. Securities include bonds, shares of stock, and a dizzying vari- ety of specialized instruments. We describe bonds in Chapter 3, stocks in Chapter 4, and other securities in later chapters.

This suggests the following definitions:

Investment decision

purchase of real assets

Financing decision

sale of securities and other financial assets

But these equations are too simple. The investment decision also involves managing assets already in place and deciding when to shut down and dispose of assets when they are no lon- ger profitable. The corporation also has to manage and control the risks of its investments. The financing decision includes not just raising cash today but also meeting its obligations to banks, bondholders, and stockholders that have contributed financing in the past. For exam- ple, the corporation has to repay its debts when they become due. If it cannot do so, it ends up insolvent and bankrupt. Sooner or later the corporation will also want to pay out cash to its shareholders.1

Let’s go to more specific examples. Table 1.1 lists 10 corporations from all over the world. We have chosen very large public corporations that you are probably already familiar with. You may have used Facebook to chat with your friends, eaten at McDonald’s, or used Crest toothpaste.

Investment Decisions The second column of Table 1.1 shows an important recent investment decision for each corporation. These investment decisions are often referred to as capital budgeting or capital expenditure (CAPEX) decisions because most large corporations prepare an annual capital budget listing the major projects approved for investment. Some of the investments in Table 1.1, such as ExxonMobil’s new oil field or Lenovo’s factory, involve the purchase of tangible assets—assets that you can touch and kick. However, corporations also need to invest in intan- gible assets, such as research and development (R&D), advertising, and computer software. For example, GlaxoSmithKline and other major pharmaceutical companies invest billions every year on R&D for new drugs. Similarly, consumer goods companies such as Procter & Gamble invest huge sums in advertising and marketing their products. These outlays are investments because they build know-how, brand recognition, and reputation for the long run.

Today’s capital investments generate future cash returns. Sometimes the cash inflows last for decades. For example, many U.S. nuclear power plants, which were initially licensed by

1We have referred to the corporation’s owners as “shareholders” and “stockholders.” The two terms mean exactly the same thing and are used interchangeably. Corporations are also referred to casually as “companies,” “firms,” or “businesses.” We also use these terms interchangeably.

1-1 Corporate Investment and Financing Decisions

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the Nuclear Regulatory Commission to operate for 40 years, are now being re-licensed for 20 more years and may be able to operate efficiently for 80 years overall.

Of course, not all investments have such distant payoffs. For example, Walmart spends about $50 billion each year to stock up its stores and warehouses before the holiday season. The company’s return on this investment comes within months as the inventory is drawn down and the goods are sold.

In addition, financial managers know (or quickly learn) that cash returns are not guaran- teed. An investment could be a smashing success or a dismal failure. For example, the Iridium communications satellite system, which offered instant telephone connections worldwide, soaked up $5 billion of investment before it started operations in 1998. It needed 400,000 subscribers to break even, but attracted only a small fraction of that number. Iridium defaulted on its debt and filed for bankruptcy in 1999. The Iridium system was sold a year later for just $25 million. (Iridium has recovered and is now profitable, however.)2

Among the contenders for the all-time worst investment was Hewlett-Packard’s (HP) pur- chase of the British software company Autonomy. HP paid $11.1 billion for Autonomy. Just 13 months later, it wrote down the value of this investment by $8.8 billion. HP claimed that it was misled by improper accounting at Autonomy. Nevertheless, the acquisition was a disas- trous investment, and HP’s CEO was fired in short order.

In some cases, the costs and risks of an investment can be huge. For example, the cost of developing the Gorgon natural gas field in Australia has been estimated at more than

2The private investors who bought the bankrupt system concentrated on aviation, maritime, and defense markets rather than retail customers. In 2010 the company arranged $1.8 billion in new financing to replace and upgrade its satellite system. The first launches of a fleet of 66 new satellites took place in 2017.

Company Recent Investment Decisions Recent Financing Decisions

Ahold Delhaize (Netherlands)

Invests €1.4 billion in supermarkets in the U.S. and Europe.

Announces a €1 billion share repurchase program.

ExxonMobil (U.S.) Announces decision to proceed with development of a huge offshore oil discovery in Guyana.

Reinvests $8.5 billion of the cash that it generates from operations.

Facebook (U.S.) Acquires Two Big Ears, a British virtual reality audio company.

Leases large new office building in San Francisco.

Fiat Chrysler (Italy) Spins off its Ferrari luxury car unit. Repays $1.8 billion of bank debt.

GlaxoSmithKline (U.K.) Spends $3.6 billion on research and development for new drugs.

Issues additional short-term euro debt.

Lenovo (China) Announces plans to build a new manufacturing facility in India to produce PCs and smartphones.

Issues $850 million of 5-year dollar bonds.

McDonald’s (U.S.) Announces plans to sell 2,000 restaurants in China. Issues C$1 billion of Canadian dollar bonds.

Procter & Gamble (U.S.) Spends over $7 billion on advertising. Buys back $4.6 billion of stock and pays a $7.2 billion dividend.

Tesla Motors (U.S.) Starts battery cell production at its new Gigafactory in Nevada.

Raises about $250 million by the sale of new shares.

Vale (Brazil) Loads first shipment from its new $14.3 billion iron-ore mine in the Amazon rainforest.

Lines up a 5-year revolving credit facility, allowing it to borrow up to $2 billion from a group of international banks.

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

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$40 billion. But do not think of the financial manager as making such large investments on a daily basis. Most investment decisions are smaller and simpler, such as the purchase of a truck, machine tool, or computer system. Corporations make thousands of these smaller investment decisions every year. The cumulative amount of small investments can be just as large as that of the occasional big investments.

Also, financial managers do not make major investment decisions in solitary confinement. They may work as part of a team of engineers and managers from manufacturing, marketing, and other business functions.

Financing Decisions The third column of Table 1.1 lists a recent financing decision by each corporation. A corpo- ration can raise money from lenders or from shareholders. If it borrows, the lenders contrib- ute the cash, and the corporation promises to pay back the debt plus a fixed rate of interest. If the shareholders put up the cash, they do not get a fixed return, but they hold shares of stock and therefore get a fraction of future profits and cash flow. The shareholders are equity investors, who contribute equity financing. The choice between debt and equity financing is called the capital structure decision. Capital refers to the firm’s sources of long-term financing.

The financing choices available to large corporations seem almost endless. Suppose the firm decides to borrow. Should it borrow from a bank or borrow by issuing bonds that can be traded by investors? Should it borrow for 1 year or 20 years? If it borrows for 20 years, should it reserve the right to pay off the debt early? Should it borrow in Paris, receiving and promis- ing to repay euros, or should it borrow dollars in New York?

Corporations raise equity financing in two ways. First, they can issue new shares of stock. The investors who buy the new shares put up cash in exchange for a fraction of the corpora- tion’s future cash flow and profits. Second, the corporation can take the cash flow generated by its existing assets and reinvest that cash in new assets. In this case the corporation is rein- vesting on behalf of existing stockholders. No new shares are issued.

What happens when a corporation does not reinvest all of the cash flow generated by its existing assets? It may hold the cash in reserve for future investment, or it may pay the cash back to its shareholders. Table 1.1 shows that Procter & Gamble paid back $4.6 billion to its stockholders by repurchasing shares. This was in addition to $7.2 billion paid out as cash divi- dends. The decision to pay dividends or repurchase shares is called the payout decision. We cover payout decisions in Chapter 16.

In some ways, financing decisions are less important than investment decisions. Finan- cial managers say that “value comes mainly from the asset side of the balance sheet.” In fact, the most successful corporations sometimes have the simplest financing strategies. Take Microsoft as an example. It is one of the world’s most valuable corporations. In December 2017, Microsoft shares traded for about $88 each. There were 7.7 billion shares outstanding. Therefore Microsoft’s overall market value—its market capitalization or market cap—was $88 × 7.7 = $680 billion. Where did this market value come from? It came from Microsoft’s product development, from its brand name and worldwide customer base, from its research and development, and from its ability to make profitable future investments. The value 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 retaining and reinvesting cash flow.

Financing decisions may not add much value, compared with good investment deci- sions, but they can destroy value if they are stupid or if they are ambushed by bad news. For example, after a consortium of investment companies bought the energy giant TXU in 2007, the company took on an additional $50 billion of debt. This may not have been a stupid

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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. In 2014, the company (renamed Energy Future Holdings) was no longer able to service its debts and filed for bankruptcy.

Business is inherently risky. The financial manager needs to identify the risks and make sure they are managed properly. For example, debt has its advantages, but too much debt can land the company in bankruptcy, as the buyers of TXU discovered. Companies can also be knocked off course by recessions, by changes in commodity prices, interest rates and exchange rates, or by adverse political developments. Some of these risks can be hedged or insured, however, as we explain in Chapters 26 and 27.

What Is a Corporation? We have been referring to “corporations.” Before going too far or too fast, we need to offer some basic definitions. Details follow in later chapters.

A corporation is a legal entity. In the view of the law, it is a legal person that is owned by its shareholders. As a legal person, the corporation can make contracts, carry on a busi- ness, borrow or lend money, and sue or be sued. One corporation can make a takeover bid for another and then merge the two businesses. Corporations pay taxes—but cannot vote!

In the United States, corporations are formed under state law, based on articles of incorpo- ration that set out the purpose of the business and how it is to be governed and operated.3 For example, the articles of incorporation specify the composition and role of the board of direc- tors.4 A corporation’s directors are elected by the shareholders. They choose and advise top management and must sign off on important corporate actions, such as mergers and the pay- ment of dividends to shareholders.

A corporation is owned by its shareholders but is legally distinct from them. Therefore the shareholders have limited liability, which means that they cannot be held personally responsible for the corporation’s debts. When the U.S. financial corporation Lehman Broth- ers 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.

When a corporation is first established, its shares may be privately held by a small group of investors, such as 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. These corporations are known as public companies. Most well-known corporations in the U.S. are public companies with widely dispersed sharehold- ings. 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. The latter cate- gory includes such well-known names as Volkswagen (Germany), Alibaba (China), Softbank (Japan), and the Swatch Group (Switzerland).

A large public corporation may have hundreds of thousands of shareholders, who own the business but cannot possibly manage or control it directly. This separation of owner- ship and control gives corporations permanence. Even if managers quit or are dismissed and

3In the U.S., corporations are identified by the label “Corporation,” “Incorporated,” or “Inc.,” as in Iridium Communications Inc. The U.K. 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”) or “AG” (“Aktiengesellschaft”). 4The corporation’s bylaws set out in more detail the duties of the board of directors and how the firm should conduct its business.

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Zipcar’s articles

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Zipcar’s bylaws

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replaced, the corporation survives. Today’s stockholders can sell all their shares to new inves- tors 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 corpora- tions is the Hudson’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 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’ inter- est. 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 particularly burdensome for small businesses. There is also an important tax drawback to corpora- tions in the United States. Because the corporation is a separate legal entity, it is taxed separately. So corporations pay tax on their profits, and shareholders are taxed again when they receive dividends from the company or sell their shares at a profit. By con- trast, income generated by businesses that are not incorporated is taxed just once as personal income.

Almost all large and medium-sized businesses are corporations, but the nearby box describes how smaller businesses may be organized.

● ● ● ● ● FINANCE IN PRACTICE

⟩ Corporations do not have to be prominent, multina- tional 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 or businesses that aspire to grow. Small “mom-and-pop” businesses are usually organized as sole proprietorships.

What about the middle ground? What about busi- nesses 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. The solution is to form a partnership and enter into a partnership agree- ment that sets out how decisions are to be made and how profits are to be split up. Partners, like sole propri- etors, 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 unlimited per- sonal 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) or professional limited liability com- pany (PLCC), 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 Stan- ley 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 corporations. The partnership form of organization does not work well when ownership is widespread and separation of own- ership and management is essential.

Other Forms of Business Organization

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S-corporations

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The financial managers

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The Role of the Financial Manager What is the essential role of the financial manager? Figure 1.1 gives one answer. The figure traces how money flows from investors to the corporation and back to investors again. The flow starts when cash is raised from investors (arrow 1 in the figure). The cash could come from banks or from securities sold to investors in financial markets. The cash is then used to pay for the real assets (capital investment projects) needed for the corporation’s business (arrow 2). Later, as the business operates, the assets produce cash inflows (arrow 3). That cash is either reinvested (arrow 4a) or returned to the investors who furnished the money in the first place (arrow 4b). Of course, the choice between arrows 4a and 4b 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 4b.

You can see examples of arrows 4a and 4b in Table 1.1. ExxonMobil financed its new proj- ects by reinvesting earnings (arrow 4a). Procter & Gamble decided to return cash to share- holders by paying cash dividends and by buying back its stock (arrow 4b).

Notice how the financial manager stands between the firm and outside investors. On the one hand, the financial manager helps manage the firm’s operations, particularly by help- ing to make good investment decisions. On the other hand, the financial manager deals with investors—not just with shareholders but also with financial institutions such as banks and with financial markets such as the New York Stock Exchange.

1-2 The Financial Goal of the Corporation

◗ FIGURE 1.1 Flow of cash between financial markets and the firm’s operations. Key: (1) Cash raised by selling financial assets to investors; (2) cash invested in the firm’s operations and used to purchase real assets; (3) cash generated by the firm’s opera- tions; (4a) cash reinvested; (4b) cash returned to investors.

(1)(2)

(4b)

(4a)

(3)

Financial manager

Financial markets (investors holding financial assets)

Firm’s operations (a bundle of real assets)

Shareholders Want Managers to Maximize Market Value Major corporations may have hundreds of thousands of 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 to professional managers. But how can the company’s managers make decisions that satisfy all the shareholders? No two shareholders are exactly the same. Some may plan to cash in their investments next year; others may be investing for a distant old age. Some may be wary of taking much risk; others may be more venturesome. Delegating the operation of the firm to professional managers can work only if these shareholders have a common objective. Fortunately, there is a natural financial objective on which almost all shareholders agree: Maximize the current market value of shareholders’ investment in the firm.

A smart and effective manager makes decisions that increase the current value of the com- pany’s shares and the wealth of its stockholders. This increased wealth can then be put to whatever purposes the shareholders want. They can give their money to charity or spend it in glitzy nightclubs; they can save it or spend it now. Whatever their personal tastes or objec- tives, they can all do more when their shares are worth more.

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B-corporations

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Maximizing shareholder wealth is a sensible goal when the shareholders have access to well-functioning financial markets.5 Financial markets allow them to adjust risks and trans- port savings across time. Financial markets give them the flexibility to manage their own savings and investment plans, leaving the corporation’s financial managers with only one task: to increase market value.

A corporation’s roster of shareholders usually includes both risk-averse and risk-tolerant inves- tors. 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 OK, 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 invest- ment portfolio to make it safer.” For example, the risk-averse shareholders can shift more of their investment to safer assets, such as U.S. government bonds. They can also just say good-bye, selling 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 if the risky investments were turned down.

A Fundamental Result The goal of maximizing shareholder value is widely accepted in both theory and practice. It’s important to understand why. Let’s walk through the argument step by step, assuming that the financial manager should act in the interests of the firm’s owners, its stockholders.

1. Each stockholder wants three things: a. To be as rich as possible, that is, to maximize his or her current wealth. b. To transform that wealth into the most desirable time pattern of consumption either

by borrowing to spend now or investing to spend later. c. To manage the risk characteristics of that consumption plan. 2. But stockholders do not need the financial manager’s help to achieve the best time pat-

tern of consumption. They can do that on their own, provided they have free access to competitive financial markets. They can also choose the risk characteristics of their consumption plan by investing in more- or less-risky securities.

3. How then can the financial manager help the firm’s stockholders? There is only one way: by increasing their wealth. That means increasing the market value of the firm and the current price of its shares.

Economists have proved this value-maximization principle with great rigor and generality. After you have absorbed this chapter, take a look at the Appendix, which contains a further example. The example, though simple, illustrates how the principle of value maximization follows from formal economic reasoning.

We have suggested that shareholders want to be richer rather than poorer. But sometimes you hear managers speak as if shareholders have different goals. For example, managers may say that their job is to “maximize profits.” That sounds reasonable. After all, don’t sharehold- ers want their company to be profitable? But taken literally, profit maximization is not a well- defined financial objective for at least 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 may result in lower profits in the future. Shareholders will not welcome higher short-term profits if long-term profits are damaged.

5Here we use “financial markets” as shorthand for the financial sector of the economy. Strictly speaking, we should say “access to well-functioning financial markets and institutions.” Many investors deal mostly with financial institutions, for example, banks, insur- ance companies, or mutual funds. The financial institutions in turn engage in financial markets, including the stock and bond markets. The institutions act as financial intermediaries on behalf of individual investors.

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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 modest return on the money.

The Investment Trade-Off OK, let’s take the objective as maximizing market value. But why do some investments increase market value, while others reduce it? The answer is given by Figure 1.2, which sets out the fun- damental trade-off for corporate investment decisions. Suppose the corporation has a proposed investment in a real asset and enough cash on hand to finance the investment. If the corporation does not invest, it can instead pay out the cash to shareholders—say, as an extra dividend. How does the financial manager decide whether to go ahead with the project or to pay out the cash? (The investment and dividend arrows in Figure 1.2 are arrows 2 and 4b in Figure 1.1.)

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 project’s rate of return and on the rate of return that the stockholders can earn by investing in financial markets. If the return offered by the investment project is higher than 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, they would vote to cancel the project and take the cash instead.

Perhaps the investment project in Figure 1.2 is a proposal for Tesla to launch a new elec- tric car. Suppose Tesla has set aside cash to launch the new model in 2020. It could go ahead with the launch, or it could choose to cancel the investment and instead pay the cash out to its stockholders. If it pays out the cash, the stockholders can then invest for themselves.

Suppose that Tesla’s new project 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 project offers a superior rate of return—say, 20%—then Tesla’s stockholders would be happy for the company to keep the cash and invest it in the new model. If the project offers only a 5% return, then the stockholders are better off with the cash and without the new model; in that case, the financial manager should turn down the project.

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

◗ FIGURE 1.2 The firm can either keep and reinvest cash or return it to inves- tors. (Arrows represent possible cash flows or transfers.) If cash is rein- vested, the opportunity cost is the expected rate of return that sharehold- ers could have obtained by investing in financial assets.

Financial manager

Invest

Shareholders

Cash

Investment project

(real asset)

Investment opportunity

(financial asset)

Alternative: pay dividend

to shareholders

Shareholders invest for themselves

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

Notice that the opportunity cost of capital depends on the risk of the proposed investment proj- ect. 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 was down 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.

Also notice that the opportunity cost of capital is generally not the interest rate that the com- pany pays on a loan from a bank. If the company is making a risky investment, the opportunity cost is the expected return that investors can achieve in financial markets at the same level of risk. The expected return on risky securities is well above the interest rate on a bank loan.

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 invest- ments 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 7.

Should Managers Look After the Interests of Their Shareholders? So far we have assumed that financial managers should act on behalf of shareholders by trying to maximize their wealth. But perhaps this begs the questions: Is it desirable for managers to act in the selfish interests of their shareholders? Does a focus on enriching the shareholders mean that managers must act as greedy mercenaries riding roughshod over the weak and helpless?

Most of this book is devoted to financial policies that increase value. None of these policies requires gallops over the weak and helpless. In most instances, little conflict arises between doing well (maximizing value) and doing good. Profitable firms are those with satisfied cus- tomers and loyal employees; firms with dissatisfied customers and a disgruntled workforce will probably end up with declining profits and a low stock price.

Most established corporations can add value by building long-term relationships with their customers and establishing a reputation for fair dealing and financial integrity. When some- thing happens to undermine that reputation, the costs can be enormous.

So, when we say that the objective of the firm is to maximize shareholder wealth, we do not mean that anything goes. The law deters managers from making blatantly dishonest decisions, but most managers should not be simply concerned with observing the letter of the law or with keeping to written contracts. In business and finance, as in other day-to-day affairs, there are unwritten rules of behavior. These rules make routine financial transactions feasible because each party to the transaction has to trust the other to keep to his or her side of the bargain.6

When something happens to damage that trust, the costs can be enormous. Volkswagen (VW) is a case in point. VW had installed secret software that cut back pollution from its diesel cars, but only when the cars were tested. Discovery of the software in 2015 caused a tidal wave of opprobrium. VW’s stock price dropped by 35%. Its CEO was fired. VW diesel vehicles piled up unsold in car dealers’ lots. In the United States alone, the scandal is likely to cost the company more than $20 billion in fines and compensation payments.

6See L. Guiso, P. Sapienza, and L. Zingales, “Trusting the Stock Market,” Journal of Finance 63 (December 2008), pp. 2557–2600. The authors show that an individual’s lack of trust is a significant impediment to participation in the stock market. “Lack of trust” means a subjective fear of being cheated.

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Ethical dilemmas

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FINANCE IN PRACTICE

Short-Selling

Investors who take short positions are betting that secu- rities will fall in price. Usually they do this by borrow- ing 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 profit of $1 billion for his fund.†

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

Investors who sell their shares are often described as doing the Wall Street Walk. Short-selling is the Wall Street Walk on steroids. Not only do short-sellers sell all the shares they may have previously owned, 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 managers natu- rally complain, often bitterly. Governments sometimes listen to such complaints. For example, in 2008 the U.S. government temporarily banned short sales of financial stocks in an attempt to halt their decline.

But defendants of short-selling argue that to sell 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 com- panies, 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 profitably split up and redeployed.

This has led many 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.”

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 combina- tion of unrelated businesses was unfocused and ineffi- cient. Timken management responded that the breakup would “deprive our shareholders of long-run value—all in an attempt to create illusory short-term gains through financial engineering.” But Timken’s stock price rose at the prospect of a breakup, and a nonbinding shareholder 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 portfo- lio of businesses can create difficult adjustments and job losses. Some stakeholders, such as the company’s employ- ees, may 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 Starbucks had operated in the U.K., 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

Ethical Disputes in Finance ● ● ● ● ●

*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. See the nearby Beyond the Page feature “Goldman Sachs causes a ruckus.”

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avoidance by U.S. technology firms reported that Apple had used a “highly questionable” web of offshore enti- ties to avoid billions of dollars of U.S. taxes.

Multinational companies, such as Starbucks and Apple, have reduced their tax bills using legal tech- niques with exotic names such as the “Dutch Sandwich,”

“Double Irish,” and “Check-the-Box.” But the pub- lic outcry over these revelations suggested that many believed that their use, though legal, was unethical. If they were unethical, that leaves an awkward question: How do companies decide which tax schemes are ethi- cal and which are not?

Charlatans and swindlers are often able to hide behind booming markets. It is only “when the tide goes out that you learn who’s been swimming naked.”7 The tide went out in 2008, and a number of frauds were exposed. One notorious example was the Ponzi scheme run by the New York financier Bernard Madoff.8 Individuals and institutions put about $65 billion in the scheme before it collapsed in 2008. (It’s not clear what Madoff did with all this money, but much of it was apparently paid out to early investors 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 Madoff.

Madoff’s Ponzi scheme was (we hope) a once-in-a-lifetime event.9 It was astonishingly unethical, illegal, and bound to end in tears. That much is obvious. The difficult ethical prob- lems for financial managers lurk in the grey areas. Look, for example, at the nearby Finance in Practice box that presents three ethical problems. Think about where you stand on these issues and where you would draw the ethical red line.

What is the underlying source of unethical business behavior? Sometimes it is simply because an employee is dishonest. But frequently the behavior stems from a culture in the firm that encourages high-pressure selling or unscrupulous dealing. In this case, the root of the problem lies with top management that promotes such values. (Click on the nearby Beyond the Page feature for an interesting demonstration of this in the banking industry.)

Agency Problems and Corporate Governance We have emphasized the separation of ownership and control in public corporations. The owners (shareholders) cannot control what the managers do, except indirectly through the board of direc- tors. This separation is necessary but also dangerous. You can see the risks. Managers may be tempted to buy sumptuous corporate jets or to schedule business meetings at tony resorts. They may shy away from attractive but risky projects because they are worried more about the safety of their jobs than about maximizing shareholder value. They may work just to maximize their own bonuses, and therefore redouble their efforts to make and resell flawed subprime mortgages.

Conflicts between shareholders’ and managers’ objectives create agency problems. Agency problems arise when agents work for principals. The shareholders are the principals; the manag- ers are their agents. Agency costs are incurred when (1) managers do not attempt to maximize firm value and (2) shareholders incur costs to monitor the managers and constrain their actions.

Agency problems can sometimes lead to outrageous behavior. For example, when Dennis Kozlowski, the CEO of Tyco, threw a $2 million 40th birthday bash for his wife, he charged half of the cost to the company. This of course was an extreme conflict of interest, as well as illegal. But more subtle and moderate agency problems arise whenever managers think just a little less hard about spending money when it is not their own.

7The quotation is from Warren Buffett’s annual letter to the shareholders of Berkshire Hathaway, March 2008. 8Ponzi 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 three-hour period. Ponzi invested only about $30 of the money that he raised, but used part of the cash provided by later investors to pay generous divi- dends to the original investors. Within months, the scheme collapsed, and Ponzi started a five-year prison sentence. 9Ponzi schemes pop up frequently, but few have approached the scope and duration of Madoff’s.

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The great Albanian Ponzi scheme

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Goldman Sachs causes a ruckus

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Business culture and unethical behavior

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Later in the book we will look at how good systems of governance ensure that share- holders’ pockets are close to the managers’ hearts. This means well-designed incentives for managers, standards for accounting and disclosure to investors, requirements for boards of directors, and legal sanctions for self-dealing by management. When scandals happen, we say that corporate governance has broken down. When corporations compete effectively and ethi- cally to deliver value to shareholders, we are comforted that governance is working properly.

Figure 1.2 illustrates how the financial manager can add value for the firm and its sharehold- ers. He or she searches for investments that offer rates of return higher than the opportunity cost of capital. But that search opens up a treasure chest of follow-up questions.

∙ How do I calculate the rate of return? The rate of return is calculated from the cash inflows and outflows generated by the investment project. See Chapters 2 and 5.

∙ Is a higher rate of return on investment always better? Not always, for two reasons. First, a lower-but-safer return can be better than a higher-but-riskier return. Second, an invest- ment with a higher percentage return can generate less value than a lower-return invest- ment that is larger or lasts longer. In Chapter 2, we show how to calculate the present value (PV) of the stream of cash flows from an investment. Present value is a workhorse concept of corporate finance that shows up in almost every chapter.

∙ What determines value in financial markets? We cover valuation of bonds and common stocks in Chapters 3 and 4. We will return to valuation principles again and again in later chapters. Sometimes the financial manager may be lucky, and may find an almost identi- cal asset whose value is already known.10 But there is no identical asset to ExxonMobil’s offshore oil field in Guyana or Facebook’s new investment in virtual reality. For most major financial decisions, the manager needs some fundamental principles to help him to determine value.

∙ What are the cash flows? The future cash flows from an investment project should be the sum of all cash inflows and outflows caused by the decision to invest. Cash flows are cal- culated after corporate taxes are paid. They are the free cash flows that can be paid out to shareholders or reinvested on their behalf. Chapter 6 explains free cash flows in detail.

∙ How does the financial manager judge whether cash-flow forecasts are realistic? As Niels Bohr, the 1922 Nobel Laureate in Physics, observed, “Prediction is difficult, espe- cially if it’s about the future.” But good financial managers take care to assemble relevant information and to purge forecasts of bias and thoughtless optimism. See Chapters 6 and 9 through 11.

∙ How do we measure risk? We look to the risks borne by shareholders, recognizing that investors can dilute or eliminate some risks by holding diversified portfolios (Chapters 7 and 8).

∙ How does risk affect the opportunity cost of capital? Here we need a theory of risk and return in financial markets. The most widely used theory is the Capital Asset Pricing Model (Chapters 8 and 9).

∙ Where does financing come from? Broadly speaking, from borrowing or from cash invested or reinvested by stockholders. But financing can get complicated when you get down to specifics. Chapter 14 gives an overview of financing. Chapters 23 through 25 cover sources of debt financing, including financial leases, which are debt in disguise.

10The idea that identical assets must have the same value is sometimes called the law of one price or the no-arbitrage condition.

1-3 Preview of Coming Attractions

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∙ Debt or equity? Does it matter? Not in a world of perfect financial markets. But in the real world, the choice between debt and equity does matter for many possible reasons, including taxes, the risks of bankruptcy, information differences, and incentives. See Chapters 17 and 18.

That’s enough questions to start, but you can see certain themes emerging. For example, corporate finance is “all about valuation,” not only for the reasons just listed, but because value maximization is the natural financial goal of the corporation. Another theme is the importance of the opportunity cost of capital, which is established in financial markets. The financial manager is an intermediary, who has to understand financial markets as well as the operations and investments of the corporation.

● ● ● ● ● FINANCE IN PRACTICE

⟩ The financial world is continually changing. A num- ber of markets that barely existed a few decades ago are now trillion-dollar businesses. In some cases, the innovation may be nothing more than someone spot- ting an untapped demand; in others, it may stem from new economic ideas. But change may also be a result of technological advances. The application of technology to financial markets is commonly known as fintech. Here are four ways that fintech is changing financial practice.

Payment Systems Not that many years ago, cash or checks were the principal way to pay for purchases, but in many countries, cash is fast disappearing. For example, in Sweden cash transactions make up barely 2% of the value of all payments. You can’t use cash to buy a bus ticket or a ticket on the Stockholm metro, and retailers are not legally obliged to accept coins and notes. The majority of Sweden’s bank branches no longer keep cash on hand or take cash deposits— and many branches no longer have ATMs. Instead of cash, Swedes use either a card or a mobile phone app to transfer money from one bank account to another in real time.

Peer-to-Peer (P2P) Lending Peer-to-peer lending platforms directly link individuals willing to lend money with people seeking to borrow. For example, in the United States would-be borrowers can apply to Lending Club for a personal loan of up to $40,000 or a business loan of up to $300,000. The company then assigns a credit score to that customer, and on the basis of this score, potential investors can choose whether to

participate in the loan. Thus, Lending Club cuts banks out of the lending equation entirely. It does not lend itself; instead, it verifies the identity of borrowers and lenders, uses the credit score to set the interest rate for the loan, and services the loan.

Robo Advice Providing investment advice to individu- als and tailoring portfolios to their particular needs can be a costly business. Robo advisers seek to reduce these costs by automating the process. You will first need to complete an online questionnaire describing your personal situation and your risk tolerance. The robo adviser will then recommend a portfolio, usually a bas- ket of low-cost funds. Then, once you deposit money in the account, the robo adviser will buy the investments and rebalance your portfolio to maintain your ideal mix of assets.

Blockchains A blockchain consists of a network of computers that simultaneously update a ledger of trans- actions or other data. This ledger doesn’t exist in one place but is distributed across many participants in the network. Many believe that the technology offers a major advance in the speed and security of financial record-keeping. Stock exchanges around the world have begun to experiment with blockchains as a method for companies to list and trade their shares, and to ballot their shareholders. The effect should be lower costs of trading, faster transfers of ownership, and more accu- rate records.

Fintech and the Changing World of Finance*

*The Winter 2015 issue of the Journal of Financial Perspectives contains a collection of articles on fintech.

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Corporations face two principal financial decisions. First, what investments should the corporation make? Second, how should it pay for the investments? The first decision is the investment deci- sion; the second is the financing decision.

The stockholders who own the corporation want its managers to maximize its overall value and the current price of its shares. The stockholders can all agree on the goal of value maximization, so long as financial markets give them the flexibility to manage their own savings and investment plans. Of course, the objective of wealth maximization does not justify unethical behavior. Share- holders do not want the maximum possible stock price. They want the maximum honest share price.

How can financial managers increase the value of the firm? Mostly by making good investment decisions. Financing decisions can also add value, and they can surely destroy value if you screw them up. But it’s usually the profitability of corporate investments that separates value winners from the rest of the pack.

Investment decisions involve a trade-off. The firm can either invest cash or return it to share- holders, for example, as an extra dividend. When the firm invests cash rather than paying it out, shareholders forgo the opportunity to invest it for themselves in financial markets. The return that they are giving up is therefore called the opportunity cost of capital. If the firm’s investments can earn a higher return than the opportunity cost of capital, stock price increases. If the firm invests at a return lower than the opportunity cost of capital, stock price falls.

Managers are not endowed with a special value-maximizing gene. They will be tempted to consider their own personal interests, which may create a conflict of interest with outside share- holders. This conflict is called a principal-agent problem. Any loss of value that results is called an agency cost.

Investors will not entrust the firm with their savings unless they are confident that management will act ethically on their behalf. Successful firms have governance systems that help to align man- agers’ and shareholders’ interests.

Remember the following five themes, for you will see them again and again throughout this book: 1. Corporate finance is all about maximizing value. 2. The opportunity cost of capital sets the standard for investment decisions. 3. A safe dollar is worth more than a risky dollar. 4. Smart investment decisions create more value than smart financing decisions. 5. Good governance matters.

● ● ● ● ●

SUMMARY

Select problems are available in McGraw-Hill’s Connect. Answers to questions with an “*” are found in the Appendix.

1. Investment and financing decisions Read the following passage: “Companies usually buy (a) assets. These include both tangible assets such as (b) and intangible assets such as (c). To pay for these assets, they sell (d) assets such as (e). The decision about which assets to buy is usually termed the (f) or (g) decision. The decision about how to raise the money is usually termed the (h) decision.”

Now fit each of the following terms into the most appropriate space: financing, real, bonds, investment, executive airplanes, financial, capital budgeting, brand names.

2. Investment and financing decisions* Which of the following are real assets, and which are financial?

a. A share of stock. b. A personal IOU.

● ● ● ● ●

PROBLEM SETS

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c. A trademark. d. A factory. e. Undeveloped land. f. The balance in the firm’s checking account. g. An experienced and hardworking sales force. h. A corporate bond. 3. Investment and financing decisions Vocabulary test. Explain the differences between: a. Real and financial assets. b. Capital budgeting and financing decisions. c. Closely held and public corporations. d. Limited and unlimited liability. 4. Corporations* Which of the following statements always apply to corporations? a. Unlimited liability. b. Limited life. c. Ownership can be transferred without affecting operations. d. Managers can be fired with no effect on ownership. 5. Separation of ownership In most large corporations, ownership and management are sepa-

rated. What are the main implications of this separation? 6. Corporate goals* We can imagine the financial manager doing several things on behalf of

the firm’s stockholders. For example, the manager might: 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.

But in well-functioning capital markets, shareholders will vote for only one of these goals. Which one? Why?

7. Maximizing shareholder value Ms. Espinoza is retired and depends on her investments for her income. Mr. Liu is a young executive who wants to save for the future. Both are stock- holders in Scaled Composites LLC, which is building SpaceShipOne to take commercial passengers into space. This investment’s payoff is many years away. Assume it has a positive NPV for Mr. Liu. Explain why this investment also makes sense for Ms. Espinoza.

8. Opportunity cost of capital F&H Corp. continues to invest heavily in a declining industry. Here is an excerpt from a recent speech by F&H’s CFO:

We at F&H have of course noted the complaints of a few spineless investors and uninformed security analysts about the slow growth of profits and dividends. Unlike those confirmed doubters, we have confidence in the long-run demand for mechani- cal encabulators, despite competing digital products. We are therefore determined to invest to maintain our share of the overall encabulator market. F&H has a rigorous CAPEX approval process, and we are confident of returns around 8% on investment. That’s a far better return than F&H earns on its cash holdings. The CFO went on

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to explain that F&H invested excess cash in short-term U.S. government securities, which are almost entirely risk-free but offered only a 4% rate of return.

a. Is a forecasted 8% return in the encabulator business necessarily better than a 4% safe return on short-term U.S. government securities? Why or why not?

b. Is F&H’s opportunity cost of capital 4%? How in principle should the CFO determine the cost of capital?

9. Ethical issues The Beyond the Page feature, “Goldman Sachs causes a ruckus,” describes the controversial involvement of Goldman Sachs in a mortgage-backed securities deal in 2006. When this involvement was revealed, the market value of Goldman Sachs’ common stock fell overnight by $10 billion. This was far more than any fine that might have been imposed. Explain.

10. Ethical issues Most managers have no difficulty avoiding blatantly dishonest actions. But sometimes there are gray areas, where it is debatable whether an action is unethical and unac- ceptable. Suggest an important ethical dilemma that companies may face. What principles should guide their decision?

11. Ethical issues The Finance in Practice box in Section 1-2 describes three corporate practices that have been criticized as unethical. Select one of these and discuss at what point (if any) does the practice slide into unethical behavior.

12. Agency issues Why might one expect managers to act in shareholders’ interests? Give some reasons.

13. Agency issues Many firms have devised defenses that make it more difficult or costly for other firms to take them over. How might such defenses affect the firm’s agency problems? Are managers of firms with formidable takeover defenses more or less likely to act in the shareholders’ interests rather than their own? What would you expect to happen to the share price when management proposes to institute such defenses?

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APPENDIX ● ● ●

◗ FIGURE 1A.1 The green line shows the possible spending patterns for the ant and grasshop- per if they invest $100,000 in the capital market. The maroon line shows the possible spending patterns if they invest in their friend’s business. Both are better off by investing in the business as long as the grasshop- per can borrow against the future income.

The ant consumes here

The grasshopper consumes here

Do lla

rs n

ex t y

ea r

121,000

110,000

110,000100,000 Dollars now

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Foundations of NPV

Why Maximizing Shareholder Value Makes Sense We have suggested that well-functioning financial markets allow different investors to agree on the objective of maximizing value. This idea is sufficiently important that we need to pause and examine it more carefully.

How Financial Markets Reconcile Preferences for Current vs. Future Consumption Suppose that there are two possible investors with entirely different preferences. Think of A as an ant, who wishes to save for the future, and of G as a grasshopper, who would prefer to spend all his wealth on some ephemeral frolic, taking no heed of tomorrow. Suppose that each has a nest egg of exactly $100,000 in cash. G chooses to spend all of it today, while A prefers to invest it in the financial market. If the interest rate is 10%, A would then have 1.10 × $100,000 = $110,000 to spend a year from now. Of course, there are many possible intermediate strategies. For example, A or G could choose to split the difference, spending $50,000 now and putting the remaining $50,000 to work at 10% to provide 1.10 × $50,000 = $55,000 next year. The entire range of pos- sibilities is shown by the green line in Figure 1A.1.

In our example, A used the financial market to postpone consumption. But the market can also be used to bring consumption forward in time. Let’s illustrate by assuming that instead of having cash on hand of $100,000, our two friends are due to receive $110,000 each at the end of the year. In this case, A will be happy to wait and spend the income when it arrives. G will prefer to borrow against his future income and party it away today. With an interest rate of 10%, G can borrow and spend $110,000/1.10 = $100,000. Thus the financial market provides a kind of time machine that allows people to separate the timing of their income from that of their spending. Notice that with an interest rate of 10%, A and G are equally happy with cash on hand of $100,000 or an income of $110,000 at the end of the year. They do not care about the timing of the cash flow; they just prefer the cash flow that has the highest value today ($100,000 in our example).

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Investing in Real Assets In practice, individuals are not limited to investing in financial markets; they may also acquire plant, machinery, and other real assets. For example, suppose that A and G are offered the oppor- tunity to invest their $100,000 in a new business that a friend is founding. This will produce a one-off surefire payment of $121,000 next year. A would clearly be happy to invest in the busi- ness. It will provide her with $121,000 to spend at the end of the year, rather than the $110,000 that she gets by investing her $100,000 in the financial market. But what about G, who wants money now, not in one year’s time? He too is happy to invest, as long as he can borrow against the future payoff of the investment project. At an interest rate of 10%, G can borrow $110,000 and so will have an extra $10,000 to spend today. Both A and G are better off investing in their friend’s venture. The investment increases their wealth. It moves them up from the green to the maroon line in Figure 1A.1.

Why can both A and G spend more by investing $100,000 in their friend’s business? Because the business provides a return of $21,000, or 21%, whereas they would earn only $10,000, or 10%, by investing their money in the capital market.

A Crucial Assumption The key condition that allows A and G to agree to invest in the new venture is that both have access to a well-functioning, competitive financial market, in which they can borrow and lend at the same rate. Whenever the corporation’s shareholders have equal access to competitive financial markets, the goal of maximizing market value makes sense.

It is easy to see how this rule would be damaged if we did not have such a well-functioning financial market. For example, suppose that G could not easily borrow against future income. In that case he might well prefer to spend his cash today rather than invest it in the new venture. If A and G were shareholders in the same enterprise, A would be happy for the firm to invest, while G would be clamoring for higher current dividends.

No one believes unreservedly that financial markets function perfectly. Later in this book we discuss several cases in which differences in taxation, transaction costs, and other imperfections must be taken into account in financial decision making. However, we also discuss research indi- cating that, in general, financial markets function fairly well. In this case maximizing shareholder value is a sensible corporate objective. But for now, having glimpsed the problems of imperfect markets, we shall, like an economist in a shipwreck, simply assume our life jacket and swim safely to shore.

QUESTIONS 1. Maximizing shareholder value Look back to the numerical example graphed in Figure 1A.1.

Suppose the interest rate is 20%. What would the ant (A) and grasshopper (G) do if they both start with $100,000? Would they invest in their friend’s business? Would they borrow or lend? How much and when would each consume?

2. Maximizing shareholder value Answer this question by drawing graphs like Figure 1A.1. Casper Milktoast has $200,000 on hand to support consumption in periods 0 (now) and 1 (next year). He wants to consume exactly the same amount in each period. The interest rate is 8%. There is no risk.

a. How much should he invest, and how much can he consume in each period? b. Suppose Casper is given an opportunity to invest up to $200,000 at 10% risk-free. The inter-

est rate stays at 8%. What should he do, and how much can he consume in each period?

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C H A P T E R

Companies 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 col- lege education may cost you $40,000 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 education by borrowing money that you plan to pay back in the future out of that fat salary.

All these financial decisions require comparisons of cash payments at different dates. Will your future salary be suf- ficient to justify the current expenditure on college tuition? How much will you have to repay the bank if you borrow to finance your degree?

In this chapter, we take the first steps toward understand- ing the relationship between the values of dollars today and dollars in the future. We start by looking at how money invested at a specific interest rate will grow over time. We next ask how much you would need to invest today to pro- duce a specified future sum of money, and we describe some shortcuts for working out the value of a series of cash payments.

The term interest rate sounds straightforward enough, but rates can be quoted in different ways. We, therefore, con- clude the chapter by explaining the difference between the quoted rate and the true or effective interest rate.

Once you have learned how to value cash flows that occur at different points in time, we can move on in the next two chapters to look at how bonds and stocks are valued. After that, we will tackle capital investment decisions at a practical level of detail.

For simplicity, every problem in this chapter is set out in dollars, but the concepts and calculations are identical in euros, Japanese yen, or Mongolian tugrik.

How to Calculate Present Values

2 Part 1 Value

Calculating Future Values Money can be invested to earn interest. So, if you are offered the choice between $100 today and $100 next year, you naturally take the money now to get a year’s interest. Financial man- agers make the same point when they say that money has a time value or when they quote the most basic principle of finance: A dollar today is worth more than a dollar tomorrow.

2-1 Future Values and Present Values

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Chapter 2 How to Calculate Present Values 21

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Suppose you invest $100 in a bank account that pays interest of r = 7% a year. In the first year, you will earn interest of .07 × $100 = $7 and the value of your investment will grow to $107:

Value of investment after 1 year = $100 × (1 + r) = 100 × 1.07 = $107

By investing, you give up the opportunity to spend $100 today, but you gain the chance to spend $107 next year.

If you leave your money in the bank for a second year, you earn interest of .07 × $107 = $7.49 and your investment will grow to $114.49:

Value of investment after 2 years = $107 × 1.07 = $100 × 1.07 2 = $114.49

Notice that in the second year you earn interest on both your initial investment ($100) and the previous year’s interest ($7). Thus your wealth grows at a compound rate and the interest that you earn is called compound interest.

If you invest your $100 for t years, your investment will continue to grow at a 7% compound rate to $100 × (1.07)t. For any interest rate r, the future value of your $100 investment will be

Future value of $100 = $100 × (1 + r) t

The higher the interest rate, the faster your savings will grow. Figure 2.1 shows that a few per- centage points added to the interest rate can do wonders for your future wealth. For example, by the end of 20 years, $100 invested at 10% will grow to $100 × (1.10)20 = $672.75. If it is invested at 5%, it will grow to only $100 × (1.05)20 = $265.33.

Calculating Present Values We have seen that $100 invested for two years at 7% will grow to a future value of 100 × 1.072 = $114.49. Let’s turn this around and ask how much you need to invest today to

Today Year 2

$100 × 1.072 $114.49

◗ FIGURE 2.1 How an investment of $100 grows with compound interest at different interest rates

20 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 ue

o f $

10 0,

d ol

la rs

1,800

1,600

1,400

1,200

1,000

800

600

400

200

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produce $114.49 at the end of the second year. In other words, what is the present value (PV) of the $114.49 payoff?

You already know that the answer is $100. But, if you didn’t know or you forgot, you can just run the future value calculation in reverse and divide the future payoff by (1.07)2:

Present value = PV = $114.49 _______ (1.07)2

= $100

In general, suppose that you will receive a cash flow of Ct dollars at the end of year t. The present value of this future payment is

Present value = PV = C t ______

(1 + r) t

The rate, r, in the formula is called the discount rate, and the present value is the discounted value of the cash flow, Ct. You sometimes see this present value formula written differently. Instead of dividing the future payment by (1 + r)t, you can equally well multiply the payment by 1/(1 + r)t. The expression 1/(1 + r)t is called the discount factor. It measures the present value of one dollar received in year t. For example, with an interest rate of 7% the two-year discount factor is

DF 2 = 1 / (1.07) 2 = .8734

Investors are willing to pay $.8734 today for delivery of $1 at the end of two years. If each dollar received in year 2 is worth $.8734 today, then the present value of your payment of $114.49 in year 2 must be

Present value = DF 2 × C 2 = .8734 × 114.49 = $100

The longer you have to wait for your money, the lower its present value. This is illustrated in Figure 2.2. Notice how small variations in the interest rate can have a powerful effect on the present 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.

Valuing an Investment Opportunity How do you decide whether an investment opportunity is worth undertaking? Suppose you own a small company that is contemplating construction of a suburban office block. The cost of buying the land and constructing the building is $700,000. Your company has cash in the bank to finance construction. Your real estate adviser forecasts a shortage of office space and predicts that you will be able to sell next year for $800,000. For simplicity, we will assume initially that this $800,000 is a sure thing.

The rate of return on this one-period project is easy to calculate. Divide the expected profit ($800,000 − 700,000 = $100,000) by the required investment ($700,000). The result is 100,000/700,000 = .143, or 14.3%.

Figure 2.3 summarizes your choices. (Note the resemblance to Figure 1.2 in the previous chapter.) You can invest in the project or pay cash out to shareholders, who can invest on their own. We assume that they can earn a 7% profit by investing for one year in safe assets (U.S. Treasury debt securities, for example). Or they can invest in the stock market, which is risky but offers an average return of 12%.

Today Year 2

$100 ÷ 1.072 $114.49

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◗ FIGURE 2.2 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.

20 4 6 8 10 12 14 16 18 20 Number of years

Pr es

en t v

al ue

o f $

10 0,

d ol

la rs

100

110

r = 0% r = 5% r = 10% r = 15%

What is the opportunity cost of capital, 7% or 12%? The answer is 7%: That’s the rate of return that your company’s shareholders could get by investing on their own at the same level of risk as the proposed project. Here the level of risk is zero. (Remember, we are assuming for now that the future value of the office block is known with certainty.) Your shareholders would vote unanimously for the investment project because the project offers a safe return of 14% versus a safe return of only 7% in financial markets.

The office-block project is therefore a “go,” but how much is it worth and how much will the investment add to your wealth? The project produces a cash flow at the end of one year. To find its present value we discount that cash flow by the opportunity cost of capital:

Present value = PV = C 1 ____

1 + r =

800,000 _______ 1.07

= $747,664

Suppose that as soon as you have bought the land and paid for the construction, you decide to sell your project. How much could you sell it for? That is an easy question. If the venture will return a surefire $800,000, then your property ought to be worth its PV of $747,664 today.

◗ FIGURE 2.3 Your company can either invest $700,000 in an office block and sell it after 1 year for $800,000, or it can return the $700,000 to shareholders to invest in the financial marketsFinancial

manager

Invest $700,000

Investment Investment opportunities

in financial markets

Shareholders

Cash

Build o�ce block, sell for $800,000

after 1 year

Opportunity cost of capital:

7% (safe assets) 12% (stock market)

Pay out $700,000

Shareholders invest for

themselves

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That is what investors in the financial markets would need to pay to get the same future pay- off. If you tried to sell it for more than $747,664, there would be no takers because the prop- erty would then offer an expected rate of return lower than the 7% available on government securities. Of course, you could always sell your property for less, but why sell for less than the market will bear? The $747,664 present value is the only feasible price that satisfies both buyer and seller. Therefore, the present value of the property is also its market price.

Net Present Value The office building is worth $747,664 today, but that does not mean you are $747,664 better off. You invested $700,000, so the net present value (NPV) is $47,664. Net present value equals present value minus the required investment:

NPV = PV − investment = 747,664 − 700,000 = $47,664

In other words, your office development is worth more than it costs. It makes a net contribu- tion to value and increases your wealth. The formula for calculating the NPV of your project can be written as:

NPV = C 0 + C 1 / (1 + r)

Remember that C0, the cash flow at time 0 (that is, today) is usually a negative number. In other words, C0 is an investment and therefore a cash outflow. In our example, C0 = −$700,000.

When cash flows occur at different points in time, it is often helpful to draw a timeline showing the date and value of each cash flow. Figure 2.4 shows a timeline for your office devel- opment. It sets out the net present value calculation assuming that the discount rate r is 7%.1

Risk and Present Value We made one unrealistic assumption in our discussion of the office development: Your real estate adviser cannot be certain about the profitability of an office building. Those future cash flows represent the best forecast, but they are not a sure thing.

If the cash flows are uncertain, your calculation of NPV is wrong. Investors could achieve those cash flows with certainty by buying $747,664 worth of U.S. government securities, so

1You sometimes hear lay people refer to “net present value” when they mean “present value,” and vice versa. Just remember, present value is the value of the investment today; net present value is the addition that the investment makes to your wealth.

◗ FIGURE 2.4 Calculation showing the NPV of the office development

Year0 1

Present value (year 0)

+ $800,000/1.07

Total = NPV

– $700,000

= + $747,664

= + $47,664

+ $800,000

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they would not buy your building for that amount. You would have to cut your asking price to attract investors’ interest.

Here we can invoke a second basic financial principle: A safe dollar is worth more than a risky dollar. Most investors dislike risky ventures and won’t invest in them unless they see the prospect of a higher return. However, the concepts of present value and the opportunity cost of capital still make sense for risky investments. It is still proper to discount the payoff by the rate of return offered by a risk-equivalent investment in financial markets. But we have to think of expected payoffs and the expected rates of return on other investments.2

Not all investments are equally risky. The office development is more risky than a govern- ment security but less risky than a start-up biotech venture. Suppose you believe the project is as risky as investment in the stock market and that stocks are expected to provide a 12% return. Then 12% is the opportunity cost of capital for your project. That is what you are giv- ing up by investing in the office building and not investing in equally risky securities.

Now recompute NPV with r = .12:

800,000 _______

1.12 = $741,286

NPV

PV − 700,000 = $14,286

The office building still makes a net contribution to value, but the increase in your wealth is smaller than in our first calculation, which assumed that the cash flows from the project were risk-free.

The value of the office building depends, therefore, on the timing of the cash flows and their risk. The $800,000 payoff would be worth just that if you could get it today. If the office building is as risk-free as government securities, the delay in the cash flow reduces value by $52,336 to $747,664. If the building is as risky as investment in the stock market, then the risk further reduces value by $33,378 to $714,286.

Unfortunately, adjusting asset values for both time and risk is often more complicated than our example suggests. Therefore, we take the two effects separately. For the most part, we dodge the problem of risk in Chapters 2 through 6, either by treating all cash flows as if they were known with certainty or by talking about expected cash flows and expected rates of return without worrying how risk is defined or measured. Then in Chapter 7 we turn to the problem of understanding how financial markets cope with risk.

Present Values and Rates of Return We have decided that constructing the office building is a smart thing to do since it is worth more than it costs. To discover how much it is worth, we asked how much you would need to invest directly in securities to achieve the same payoff. That is why we discounted the proj- ect’s future payoff by the rate of return offered by these equivalent-risk securities—the overall stock market in our example.

We can state our decision rule in another way: Your real estate venture is worth undertak- ing because its rate of return exceeds the opportunity cost of capital. The rate of return is simply the profit as a proportion of the initial outlay:

Return = profit

_________ investment

= 800,000 − 700,000 _______________

700,000 = .143, or 14.3%

The cost of capital is once again the return foregone by not investing in financial markets. If the office building is as risky as investing in the stock market, the return foregone is 12%.

2We define “expected” more carefully in Chapter 9. For now think of expected payoff as a realistic forecast, neither optimistic nor pessimistic. Forecasts of expected payoffs are correct on average.

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Since the 14.3% return on the office building exceeds the 12% opportunity cost, you should go ahead with the project.

Building the office block is a smart thing to do, even if the payoff is just as risky as the stock market. We can justify the investment by either one of the following two rules:3

∙ Net present value rule. Accept investments that have positive net present values. ∙ Rate of return rule. Accept investments that offer rates of return in excess of their

opportunity costs of capital.

Suppose that you wish to value a stream of cash flows extending over a number of years. Our rule for adding present values tells us that the total present value is:

PV = C 1 ______

(1 + r) +

C 2 ______ (1 + r) 2

+ C 3 ______

(1 + r) 3 + ⋅ ⋅ ⋅ +

C T ______ (1 + r) T

This is called the discounted cash flow (or DCF) formula. A shorthand way to write it is

PV = ∑ t=1

C t ______

(1 + r) t

where Σ refers to the sum of the series of discounted cash flows. To find the net present value (NPV) we add the (usually negative) initial cash flow:

NPV = C 0 + PV = C 0 + ∑ t=1

C t ______

(1 + r) t

2 = 870,000/1.122 = $693,559. Therefore our rule for adding present values tells us that the total present value of your investment is:

PV = C 1 _____

1 + r +

C 2 ______ (1 + r) 2

= 30,000 ______ 1.12

+ 870,000 _______

1. 12 2 = 26,786 + 69,559 = $720,344

EXAMPLE 2.1 ● Present Values with Multiple Cash Flows

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Chapter 2 How to Calculate Present Values 27

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Your two-period calculations in Example 2.1 required just a few keystrokes on a calculator. Real problems can be much more complicated, so financial managers usually turn to financial calculators especially programmed for present value calculations or to computer spreadsheet programs. A box near the end of the chapter introduces you to some useful Excel functions that can be used to solve discounting problems.

The Opportunity Cost of Capital By investing in the office building you are giving up the opportunity to earn an expected return of 12% in the stock market. The opportunity cost of capital is therefore 12%. When you discount the expected cash flows by the opportunity cost of capital, you are asking how much investors in the financial markets are prepared to pay for a security that produces a similar stream of future cash flows. Your calculations showed that these investors would need to pay $720,344 for an investment that produces cash flows of $30,000 at year 1 and $870,000 at year 2. Therefore, they won’t pay any more than that for your office building.

Confusion sometimes sneaks into discussions of the cost of capital. Suppose a banker approaches. “Your company is a fine and safe business with few debts,” she says. “My bank will lend you the $700,000 that you need for the office block at 8%.” Does this mean that the cost of capital is 8%? If so, the project would be even more worthwhile. At an 8% cost of capi- tal, PV would be 30,000/1.08 + 870,000/1.082 = $773,663 and NPV = $773,663 − $700,000 = +$73,663.

But that can’t be right. First, the interest rate on the loan has nothing to do with the risk of the project: it reflects the good health of your existing business. Second, whether you take the loan or not, you still face the choice between the office building and an equally risky investment in the stock market. A financial manager who borrows $700,000 at 8% and invests in an office building is not smart, but stupid, if the company or its shareholders can borrow at 8% and make an equally risky investment in the stock market offering an even higher return. That is why the 12% expected return on the stock market is the opportunity cost of capital for your project.

◗ FIGURE 2.5 Calculation showing the NPV of the revised office project

0 1

Present value (year 0)

+$30,000/1.12

+$870,000/1.122

Total = NPV

– $700,000

= + $26,786

= + $693,559

= + $20,344

+ $30,000

+ $870,000

Year2

It looks as if you should take your adviser’s suggestion. NPV is higher than if you sell in year 1:

NPV = $720,344 − $700,000 = $20,344 ● ● ● ● ●

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Introduction to financial calculators

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Introduction to Excel

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How to Value Perpetuities Sometimes there are shortcuts that make it easy to calculate present values. Let us look at some examples.

On occasion, the British and the French have been known to disagree and sometimes even to fight wars. At the end of some of these wars the British consolidated the debt they had issued during the war. The securities issued in such cases were called consols. Consols are perpetuities. They are bonds that the government is under no obligation to repay but that offer a fixed income for each year to perpetuity. The British government is still paying interest on consols issued all those years ago. The annual rate of return on a perpetuity is equal to the promised annual payment divided by the present value:

Return

cash flow ___________ present value

r =

C ___ PV

We can obviously twist this around and find the present value of a perpetuity given the dis- count rate r and the cash payment C:4

PV = C __ r

The year is 2030. You have been fabulously successful and are now a billionaire many times over. It was fortunate indeed that you took that finance course all those years ago. You have decided to follow in the footsteps of two of your philanthropic heroes, Bill Gates and Warren Buffett. Malaria is still a scourge and you want to help eradicate it and other infectious diseases by endowing a foundation to combat these diseases. You aim to provide $1 billion a year in perpetuity, starting next year. So, if the interest rate is 10%, you need to write a check today for

Present value of perpetuity = C __ r =

$1 billion ________ .1

= $10 billion

Two warnings about the perpetuity formula. First, at a quick glance, you can easily confuse the formula with the present value of a single payment. A payment of $1 at the end of one year has a present value of 1/(1 + r). The perpetuity has a value of 1/r. These are quite different.

Second, the perpetuity formula tells us the value of a regular stream of payments starting one period from now. Thus your $10 billion endowment would provide the foundation with its first payment in one year’s time. If you also want to provide an up-front sum, you will need to lay out an extra $1 billion.

4You can check this by writing down the present value formula

PV = C _____ 1 + r

+ C ________ (1 + r) 2

+ C ________ (1 + r) 3

+ · · ·

Now let C/(1 + r) = a and 1/(1 + r) = x. Then we have (1) PV = a(1 + x + x2 + · · · ). Multiplying both sides by x, we have (2) PVx = a(x + x2 + · · ·). Subtracting (2) from (1) gives us PV(1 − x) = a. Therefore, substituting for a and x,

PV ( 1 − 1 _

1 + r ) =

C _ 1 + r

Multiplying both sides by (1 + r) and rearranging gives PV = C __ r

2-2 Looking for Shortcuts—Perpetuities and Annuities

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Chapter 2 How to Calculate Present Values 29

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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 you decide to provide $1 billion a year with the first payment four years from now. Figure 2.6 provides a timeline of these payments. Think first about how much they will be worth in year 3. At that point the endowment will be an ordinary perpetuity with the first payment due at the end of the year. So our perpetuity for- mula tells us that in year 3 the endowment will be worth $1/r = $1/.1 = $10 billion. But it is not worth that much now. To find today’s value we need to multiply by the three-year discount factor 1/(1 + r)3 = 1/(1.1)3 = .751. Thus, the “delayed” perpetuity is worth $10 billion × .751 = $7.51 billion. The full calculation is:

PV = $1 billion × 1 __ r × 1 ______

(1 + r) 3 = $1 billion ×

1 ___ .10

× 1 ______ (1.10) 3

= $7.51 billion

How to Value Annuities An annuity is an asset that pays a fixed sum each year for a specified number of years. The equal-payment house mortgage or installment credit agreement are common examples of annuities. So are interest payments on most bonds, as we shall see in the next chapter.

You can always value an annuity by calculating the value of each cash flow and finding the total. However, it is often quicker to use a simple formula that states that if the interest rate is r, then the present value of an annuity that pays $C a period for each of t periods is:

Present value of t-year annuity = C [ 1 __ r − 1 ______

r (1 + r) t ]

The expression in brackets shows the present value of $1 a year for each of t years. It is gener- ally known as the t-year annuity factor.

If you are wondering where this formula comes from, look at Figure 2.7. It shows the pay- ments and values of three investments.

◗ FIGURE 2.7 An annuity that makes payments in each of years 1 through 3 is equal to the differ- ence between two perpetuities

Present Value

Cash Flow

$1 $1 $1

Year:

$1 $1 . . .

. . .

$1 $1 $1 . . .

1 r

2. Perpetuity B 1

r (1 + r )3

1 r (1 + r )3

1 r

3. Three-year annuity (1 – 2)

1. Perpetuity A

654321

◗ FIGURE 2.6 This perpetuity makes a series of payments of $1 billion a year starting in year 4

Year

0 1 2 3 4 5 6

$1bn $1bn $1bn

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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 2.7. 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 three years. In year 3, the investment will be an ordinary perpetuity with payments starting in one year and will therefore be worth 1/r in year 3. To find the value today, we simply multiply this figure by the three-year discount factor. Thus, as we saw earlier

PV = 1 __ r × 1 ______

(1 + r) 3

Row 3 Finally, look at the investment shown in the third row of Figure 2.7. This provides a level payment of $1 a year for each of three years. In other words, it is a three-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 annuity of $1 a year = 1 __ r − 1 _______

r (1 + r) 3

Remembering formulas is about as difficult as remembering other people’s birthdays. 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.5

5Some people find the following equivalent formula more intuitive: Present value of annuity = 1 __ r × [1 −

1 _____ (1 + r) t

]

Perpetuity formula

$1 Starting next year

Minus $1 starting at

t + 1

Most installment plans call for level streams of payments. Suppose that Tiburon Autos offers an “easy payment” scheme on a new Toyota of $5,000 a year, paid at the end of each of the next five years, with no cash down. What is the car really costing you?

First let us do the calculations the slow way, to show that if the interest rate is 7%, the pres- ent value of these payments is $20,501. The timeline in Figure 2.8 shows the value of each cash flow and the total present value. The annuity formula, however, is generally quicker; you simply need to multiply the $5,000 cash flow by the annuity factor:

PV = 5,000 [ 1 ___ .07

− 1 _________ .07 (1.07) 5

]

= 5,000 × 4.100 = $20,501

EXAMPLE 2.2 ● Costing an Installment Plan

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Chapter 2 How to Calculate Present Values 31

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◗ FIGURE 2.8 Calculations showing the year-by-year present value of the installment payments

Year10 2 3 4 5

$5,000

Present value (year 0)

$5,000/1.075 = $3,565

$5,000 $5,000 $5,000 $5,000

$5,000/1.07 = $4,673 $5,000/1.072 = $4,367

$5,000/1.073 = $4,081

$5,000/1.074 = $3,814

Total = PV = $20,501

● ● ● ● ●

Valuing Annuities Due When we costed the installment plan we assumed that the first payment was made at the end of the year. Suppose instead that the first of the five yearly payments is due immediately. How does this change the cost of the car?

If we discount each cash flow by one less year, the present value is increased by the multiple (1 + r). In the case of the car purchase the present value of the payments becomes 20,501 × (1 + r) = 20,501 × 1.07 = $21,936.

A level stream of payments starting immediately is called an annuity due. An annuity due is worth (1 + r) times the value of an ordinary annuity.

Calculating Annual Payments Annuity problems can be confusing on first acquaintance, but you will find that with practice they are generally straightforward. For example, here is a case where you need to use the annuity formula to find the amount of the payment given the present value.

Bank loans are paid off in equal installments. Suppose that you take out a four-year loan of $1,000. The bank requires you to repay the loan evenly over the four years. It must therefore set the four annual payments so that they have a present value of $1,000. Thus,

PV = annual loan payment × 4-year annuity factor = $1,000

Annual loan payment = $1,000 / 4-year annuity factor

Suppose that the interest rate is 10% a year. Then

4-year annuity factor = [ 1 ___ .10

− 1 _________ .10 (1.10) 4

]

= 3.170

and

Annual loan payment = 1,000 / 3.170 = $315.47

EXAMPLE 2.3 ● Paying Off a Bank Loan

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Try It! More on annuities

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Let’s check that this annual payment is sufficient to repay the loan. Table 2.1 provides the calculations. At the end of the first year, the interest charge is 10% of $1,000, or $100. So $100 of the first payment is absorbed by interest, and the remaining $215.47 is used to reduce 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 paying off the loan. Because the loan is pro- gressively paid off, the fraction of each payment devoted to interest steadily falls over time, while the fraction used to reduce the loan increases. By the end of year 4, the amortization is just enough to reduce the balance of the loan to zero.

Loans that involve a series of level payments are known as amortizing loans. “Amortizing” means that part of the regular payment is used to pay interest on the loan and part is used to pay off or amortize the loan.

Year Beginning-

of-Year Balance Year-End Interest

on Balance Total 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

⟩ TABLE 2.1 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 four years to repay that loan with interest.

● ● ● ● ●

Most mortgages are amortizing loans. For example, suppose that you take out a $250,000 house mortgage from your local savings bank when the interest rate is 12%. The bank requires you to repay the mortgage in equal annual installments over the next 30 years. Thus,

Annual mortgage payment = $250,000 / 30-year annuity factor

30-year annuity factor = [

1 ___ .12

− 1 __________ .12 (1.12) 30

]

= 8.055

and

Annual mortgage payment = 250,000 / 8.055 = $31,036

Figure 2.9 shows that in the early years, almost all of the mortgage payment is eaten up by interest and only a small fraction is used to reduce the amount of the loan. Even after 15 years, the bulk of the annual payment goes to pay the interest on the loan. From then on, the amount of the loan begins to decline rapidly.

EXAMPLE 2.4 ● Calculating Mortgage Payments

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Chapter 2 How to Calculate Present Values 33

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◗ FIGURE 2.9 Mortgage amortization. This figure shows the breakdown of mortgage payments between interest and amortization.

1 5 9 13 17 21 25 29 Year

Do lla

rs 35,000

25,000

30,000

20,000

15,000

10,000

5,000

Amortization Interest paid

● ● ● ● ●

Future Value of an Annuity Sometimes you need to calculate the future value of a level stream of payments.

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Try It! Figure 2.9: The amortzation schedule

Perhaps your ambition is to buy a sailboat; something like a 40-foot Beneteau would fit the bill very well. But that means some serious saving. You estimate that, once you start work, you could save $20,000 a year out of your income and earn a return of 8% on these savings. How much will you be able to spend after five years?

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 annuity. 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 savings are worth today. You will set aside $20,000 in each of the next five years. The present value of this five-year annuity is therefore equal to

$20,000 × 5-year annuity factor

$20,000 ×

[ 1 ___ .08

− 1 _________ .08 (1.08) 5

]

= $79,854

Once you know today’s value of the stream of cash flows, it is easy to work out its value in the future. Just multiply by (1.08)5:

Value at end of year 5 = $79,854 × 1. 08 5 = $117,332

You should be able to buy yourself a nice boat for $117,000.

EXAMPLE 2.5 ● Saving to Buy a Sailboat

● ● ● ● ●

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2-3 More Shortcuts—Growing Perpetuities and Annuities

Growing Perpetuities You now know how to value level streams of cash flows, but you often need to value a stream of cash flows that grows at a constant rate. For example, think back to your plans to donate $10 billion to fight malaria and other infectious diseases. Unfortunately, you made no allowance for the growth in salaries and other costs, which will probably average about 4% a year starting in year 1. Therefore, instead of providing $1 billion a year in perpetuity, you must provide $1 billion in year 1, 1.04 × $1 billion in year 2, and so on. If we call the growth rate in costs g, we can write down the present value of this stream of cash flows as follows:

PV = C 1 _____

1 + r +

C 2 ______ (1 + r) 2

+ C 3 ______

(1 + r) 3 + ⋅ ⋅ ⋅

= C 1 _____

1 + r +

C 1 (1 + g) ________ (1 + r) 2

+ C 1 (1 + g) 2 ________

(1 + r) 3 + ⋅ ⋅ ⋅

Fortunately, there is a simple formula for the sum of this geometric series.6 If we assume that r is greater than g, our clumsy-looking calculation simplifies to

Present value of growing perpetuity = C 1 ____ r − g

Therefore, if you want to provide a perpetual stream of income that keeps pace with the growth rate in costs, the amount that you must set aside today is

PV = C 1 ____ r − g =

$1 billion ________ .10 − .04

= $16.667 billion

You will meet this perpetual-growth formula again in Chapter 4, where we use it to value the stocks of mature, slowly growing companies.

6We need to calculate the sum of an infinite geometric series PV = a(1 + x + x2 + · · ·) where a = C1/(1 + r) and x = (1 + g)/(1 + r). In footnote 4 we showed that the sum of such a series is a/(1 − x). Substituting for a and x in this formula,

PV = C 1 _____

( r − g )

In Example 2.5, we calculate the future value of an annuity by first calculating its present value and then multiplying by (1 + r)t. The general formula for the future value of a level stream of cash flows of $1 a year for t years is, therefore,

Future value of annuity

present value of annuity of $1 a year × (1 + r) t

[

1 __ r − 1 ______

r (1 + r) t ]

× (1 + r) t = (1 + r) t − 1 __________

There is a general point here. If you can find the present value of any series of cash flows, you can always calculate future value by multiplying by (1 + r)t:

Future value at the end of year t = present value × (1 + r) t

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Chapter 2 How to Calculate Present Values 35

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In August 2017, a Massachusetts woman invested in a Powerball lottery ticket and won a record $758.7 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 $758.7 million. That sum was to be paid in 30 annual installments. The payment in the first year was only $11.42 million, but it then increased each year by 5% so that the final payment was $47.00 mil- lion. The total amount paid out was $758.7 million, but the winner had to wait to get it.

If the interest rate was 2.7%, what was that $758.7 prize really worth? Suppose that the first payment occurs at the end of year 1, so that C1 = $11.42 million. If the payments then grow at the rate of g = .05 each year, the payment in year 2 is 11.42 × 1.05, and in year 3 it is 11.42 × 1.052. Of course, you could calculate each of the 30 cash flows and discount them at 2.7%. The alternative is to use the following formula for the present value of a growing annuity:7

PV of growing annuity = C × 1 _____ r − g

[

1 − (1 + g) t

______ (1 + r) t

]

In the case of our lottery, the present value of the growing stream of payments is

PV = 11.42 × [ 1 − (1.05)

30 ________ (1.027) 30

]

1 _________ .027 − .05

= 11.42 × 41.02 = $468 million

Thus, the present value of a growing stream of payments starting at the end of the first year is $468 million. In practice, the news is not quite that bad because the lottery winner receives the first payment immediately (in year 0) and the last one is received in year 29 rather than in year 30. Therefore, we need to increase our estimate of present value by 1 + r. So the present value of the prize is 468 × 1.027 = $481 million.

If the total Powerball prize money was paid out immediately, it would be worth $757.8 million. Paying out this money over the next 29 years reduces the value of the prize to $481 million, much below the well-trumpeted prize but still not a bad day’s haul.

For winners with big spending plans, lottery operators generally make arrangements so that they may take an equivalent lump sum. In our example, the winner could either take the $758.7 million spread over 30 years or receive $481 million up front. Both arrangements had the same present value.

7We can derive the formula for a growing annuity by taking advantage of our earlier trick of finding the difference between the values of two perpetuities. Imagine three investments (A, B, and C) that make the following dollar payments:

Year 1 2 3 4 5 6 . . .

A $1 (1 + g) (1 + g)2 (1 + g)3 (1 + g)4 (1 + g)5 etc.

B (1 + g)3 (1 + g)4 (1 + g)5 etc.

C $1 (1 + g) (1 + g)2

Investments A and B are growing perpetuities; A makes its first payment of $1 in year 1, while B makes its first payment of $(1 + g) 3 in year 4. C is a three-year growing annuity; its cash flows are equal to the difference between the cash flows of A and B. You know how to value growing perpetuities such as A and B. So you should be able to derive the formula for the value of growing annuities such as C:

PV(A) = 1 _____ (r − g)

PV(B) =

(1 + g) 3 _______

(r − g) × 1 ______

(1 + r) 3

PV(C) = PV(A) − PV(B) = 1 ______ (r − g)

− (1 + g) 3

_______ (r − g)

× 1 ______ (1 + r) 3

= 1 _____ r − g

[ 1 − (1 + g) 3

_ (1 + r) 3

]

If r = g, then the formula blows up. In that case, the cash flows grow at the same rate as the amount by which they are discounted. Therefore, each cash flow has a present value of C/(1 + r) and the total present value of the annuity equals t × C/(1 + r). If r < g, then this particular formula remains valid, though still treacherous.

EXAMPLE 2.6 ● Winning Big at the Lottery

● ● ● ● ●

Growing Annuities

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2-4 How Interest Is Paid and Quoted

In our examples we have assumed that cash flows occur only at the end of each year. This is sometimes the case. For example, in France and Germany, the government pays interest on its bonds annually. However, in the United States and Britain, government bonds pay interest semiannually. So if a U.S. government bond promises to pay interest of 10% a year, the inves- tor in practice receives interest of 5% every six months.

If the first interest payment is made at the end of six months, you can earn an additional six months’ interest on this payment. For example, if you invest $100 in a bond that pays interest of 10% compounded semiannually, your wealth will grow to 1.05 × $100 = $105 by the end of six months and to 1.05 × $105 = $110.25 by the end of the year. In other words, an interest rate of 10% compounded semiannually is equivalent to 10.25% compounded annually. The effective annual interest rate on the bond is 10.25%.

Let’s take another example. Suppose a bank offers you an automobile loan at an annual percentage rate, or APR, of 12% with interest to be paid monthly. By this the bank means that each month you need to pay one-twelfth of the annual rate, that is, 12/12 = 1% a month. Thus the bank is quoting a rate of 12%, but the effective annual interest rate on your loan is 1.0112 – 1 = .1268 or 12.68%.8

Our examples illustrate that you need to distinguish between the quoted annual interest rate and the effective annual rate. The quoted annual rate is usually calculated as the total annual payment divided by the number of payments in the year. When interest is paid once a year, the quoted and effective rates are the same. When interest is paid more frequently, the effective interest rate is higher than the quoted rate.

In general, if you invest $1 at a rate of r per year compounded m times a year, your investment at the end of the year will be worth [1 + (r/m)]m and the effective interest rate is

8In the U.S., truth-in-lending laws oblige the company to quote an APR that is calculated by multiplying the payment each period by the number of payments in the year. APRs are calculated differently in other countries. For example, in the European Union, APRs must be expressed as annually compounded rates, so consumers know the effective interest rate that they are paying.

Too many formulas are bad for the digestions. So we will stop at this point and spare you any more of them. The formulas discussed so far appear in Table 2.2.

Year: 0 1 2 . . . . . . t − 1 t t + 1 . . . Present Value

Perpetuity 1 1 . . . 1 1 1 . . . 1 __ r

t-period annuity 1 1 . . . 1 1 1 __ r − 1 ______

r (1 + r) t

t-period annuity due 1 1 1 . . . 1 (1 + r) (

1 __ r − 1 ______

r (1 + r) t )

Growing perpetuity 1 1 × (1 + g) . . . 1 × (1 + g)t – 2 1 × (1 + g)t – 1 1 × (1 + g)t. . 1 ____ r − g

t-period growing annuity 1 1 × (1 + g) . . . 1 × (1 + g)t – 2 1 × (1 + g)t – 1 1 ____ r − g [

1 − (1 + g) t

______ (1 + r) t

]

⟩ TABLE 2.2 Some useful shortcut formulas Note: a. The growing perpetuity formula works only if the discount rate r is greater than the growth rate g. b. The growing annuity formula blows up if r = g . In this case, the value of the growing annuity is C × t/(1 + r ).

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Chapter 2 How to Calculate Present Values 37

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[1 + (r/m)]m – 1. In our automobile loan example r = .12 and m = 12. So the effective annual interest rate was [1 + .12/12]12 – 1 = .1268, or 12.68%.

Continuous Compounding Instead of compounding interest monthly or semiannually, the rate could be compounded weekly (m = 52) or daily (m = 365). In fact, there is no limit to how frequently interest could be paid. One can imagine a situation where the payments are spread evenly and continuously throughout the year, so the interest rate is continuously compounded.9 In this case m is infinite.

It turns out that there are many occasions in finance when continuous compounding is useful. For example, one important application is in option pricing models, such as the Black– Scholes model that we introduce in Chapter 21. These are continuous time models. So you will find that most computer programs for calculating option values ask for the continuously compounded interest rate.

It may seem that a lot of calculations would be needed to find a continuously compounded interest rate. However, think back to your high school algebra. You may recall that as m approaches infinity [1 + (r/m)]m approaches (2.718)r . The figure 2.718—or e, as it is called—is the base for natural logarithms. Therefore, $1 invested at a continuously compounded rate of r will grow to er = (2.718)r by the end of the first year. By the end of t years it will grow to ert = (2.718)rt.

Example 1 Suppose you invest $1 at a continuously compounded rate of 11% (r = .11) for one year (t = 1). The end-year value is e.11, or $1.116. In other words, investing at 11% a year continuously compounded is exactly the same as investing at 11.6% a year annually compounded.

Example 2 Suppose you invest $1 at a continuously compounded rate of 11% (r = .11) for two years (t = 2). The final value of the investment is ert = e.22, or $1.246.

Sometimes it may be more reasonable to assume that the cash flows from a project are spread evenly over the year rather than occurring at the year’s end. It is easy to adapt our previous formulas to handle this. For example, suppose that we wish to compute the present value of a perpetuity of C dollars a year. We already know that if the payment is made at the end of the year, we divide the payment by the annually compounded rate of r:

PV = C __ r

If the same total payment is made in an even stream throughout the year, we use the same formula but substitute the continuously compounded rate.

Suppose the annually compounded rate is 18.5%. The present value of a $100 perpetuity, with each cash flow received at the end of the year, is 100/.185 = $540.54. If the cash flow is received continuously, we must divide $100 by 17%, because 17% continuously compounded is equivalent to 18.5% annually compounded (e.17 = 1.185). The present value of the continu- ous cash flow stream is 100/.17 = $588.24. Investors are prepared to pay more for the contin- uous cash payments because the cash starts to flow in immediately.

Example 3 After you have retired, you plan to spend $200,000 a year for 20 years. The annually compounded interest rate is 10%. How much must you save by the time you retire to support this spending plan?

9When we talk about continuous payments, we are pretending that money can be dispensed in a continuous stream like water out of a faucet. One can never quite do this. For example, instead of paying out $1 billion every year to combat malaria, you could pay out about $1 million every 8 3/4 hours or $10,000 every 5 1/4 minutes or $10 every 3 1/6 seconds but you could not pay it out con tinuously. Financial managers pretend that payments are continuous rather than hourly, daily, or weekly because (1) it simplifies the calculations and (2) it gives a very close approximation to the NPV of frequent payments.

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● ● ● ● ● USEFUL SPREADSHEET FUNCTIONS

produce given future value or annuity. ∙ NPER: Number of periods (e.g., years) that it takes

an investment to reach a given future value. ∙ PMT: Amount of annuity payment with a given

present or future value. ∙ NPV: Calculates the value of a stream of negative

and positive cash flows. (When using this function, note the warning below.)

∙ EFFECT: The effective annual interest rate, given the quoted rate (APR) and number of interest payments in a year.

∙ NOMINAL: The quoted interest rate (APR) given the effective annual interest rate.

be entered as a negative number. Entering both PV and FV with the same sign when solving for RATE results in an error message.

2. Always enter the interest or discount rate as a decimal value (for example, .05 rather than 5%).

Spreadsheet Questions

The following questions provide opportunities to prac- tice each of the Excel functions. 1. (FV) In 1880, five aboriginal trackers were each

5. (NPER) An investment adviser has promised to double your money. If the interest rate is 7% a year, how many years will she take to do so?

6. (PMT) You need to take out a home mortgage for $200,000. If payments are made annually over 30 years and the interest rate is 8%, what is the amount of the annual payment?

Discounting Cash Flows

All the inputs in these functions can be entered directly as numbers or as the addresses of cells that contain the numbers.

Three warnings: 1. PV is the amount that needs to be invested today

to produce a given future value. It should therefore

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Chapter 2 How to Calculate Present Values 39

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Let us first do the calculations assuming that you spend the cash at the end of each year. In this case we can use the simple annuity formula that we derived earlier:

( 1 __ r − 1 ______

r (1 + r) t )

$200,000

( 1 ___ .10

− 1 __________ .10 (1.10) 20

)

= $200,000 × 8.514 = $1,702,800

Thus, you will need to have saved $1.7 million by the time you retire. Instead of waiting until the end of each year before you spend any cash, it is more reason-

able to assume that your expenditure will be spread evenly over the year. In this case, instead of using the annually compounded rate of 10%, we must use the continuously compounded rate of r = 9.53% (e.0953 = 1.10). Therefore, to cover a steady stream of expenditure, you need to set aside the following sum:10

( 1 __ r − 1 __

r × 1 ___

e rt )

$200,000 (

1 _____ .0953

− 1 _____ .0953

× 1 _____ 6.727

) = $200,000 × 8.932 = $1,786,400

To support a steady stream of outgoings, you must save an additional $83,600. Often in finance you need only a ballpark estimate of present value. An error of 5% in a pre-

sent value calculation may be perfectly acceptable. In such cases it doesn’t usually matter whether you assume that cash flows occur at the end of the year or in a continuous stream. At other times precision matters, and you do need to worry about the exact frequency of the cash flows.

10Remember that an annuity is simply the difference between a perpetuity received today and a perpetuity received in year t. A con- tinuous stream of C dollars a year in perpetuity is worth C/r, where r is the continuously compounded rate. Our annuity, then, is worth

PV = C __ r − Present value of C __ r received in year t

Since r is the continuously compounded rate, C/r received in year t is worth (C/r) × (1/e rt) today. Our annuity formula is therefore

PV = C __ r − C __

r × 1 ___

e rt

sometimes written as

C __ r (1 − e −rt )

7. (EFFECT) First National Bank pays 6.2% interest compounded annually. Second National Bank pays 6% interest compounded monthly. Which bank offers the higher effective annual interest rate?

8. (NOMINAL) What monthly compounded interest rate would Second National Bank need to pay on savings deposits to provide an effective rate of 6.2%?

Firms can best help their shareholders by accepting all projects that are worth more than they cost. In other words, they need to seek out projects with positive net present values. To find net present value we first calculate present value. Just discount future cash flows by an appropriate rate r, usu- ally called the discount rate, hurdle rate, or opportunity cost of capital:

Present value (PV) = C 1 ______

(1 + r) +

C 2 ______ (1 + r) 2

+ C 3 ______

(1 + r) 3 + ⋅ ⋅ ⋅

Net present value is present value plus any immediate cash flow:

Net present value (NPV) = C 0 + PV

● ● ● ● ●

SUMMARY

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