Week1

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corporate finance CORE PRINCIPLES & APPLICATIONS

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

FINANCIAL MANAGEMENT Block, Hirt, and Danielsen Foundations of Financial Management Sixteenth Edition

Brealey, Myers, and Allen Principles of Corporate Finance Twelfth 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 Seventh Edition

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

Cornett, Adair, and Nofsinger M: Finance Third Edition

DeMello Cases in Finance Third 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 Eleventh Edition

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

Shefrin Behavioral Corporate Finance: Decisions that Create Value Second Edition

INVESTMENTS Bodie, Kane, and Marcus Essentials of Investments Tenth Edition

Bodie, Kane, and Marcus Investments Tenth Edition

Hirt and Block Fundamentals of Investment Management Tenth Edition

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

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

Sundaram and Das Derivatives: Principles and Practice Second Edition

FINANCIAL INSTITUTIONS AND MARKETS Rose and Hudgins Bank Management and Financial Services Ninth Edition

Rose and Marquis Financial Institutions and Markets Eleventh Edition

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

Saunders and Cornett Financial Markets and Institutions Sixth Edition

INTERNATIONAL FINANCE Eun and Resnick International Financial Management Eighth Edition

REAL ESTATE Brueggeman and Fisher Real Estate Finance and Investments Fifteenth 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 Eleventh Edition

Altfest Personal Financial Planning Second Edition

Harrington and Niehaus Risk Management and Insurance Second Edition

Kapoor, Dlabay, Hughes, and Hart Focus on Personal Finance: An Active Approach to Achieve Financial Literacy Fifth Edition

Kapoor, Dlabay, Hughes, and Hart Personal Finance Twelfth Edition

Walker and Walker Personal Finance: Building Your Future Second Edition

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

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F I F T H E D I T I O N

corporate finance CORE PRINCIPLES & APPLICATIONS

Stephen A. Ross Sloan School of Management Massachusetts Institute of Technology

Randolph W. Westerfield Marshall School of Business University of Southern California

Jeffrey F. Jaffe Wharton School of Business University of Pennsylvania

Bradford D. Jordan Gatton College of Business and Economics University of Kentucky

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CORPORATE FINANCE: CORE PRINCIPLES & APPLICATIONS, FIFTH EDITION

Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2018 by McGraw-Hill Education. All rights reserved. Printed in the United States of America. Previous editions © 2014, 2011, 2009, and 2007. 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 LWI 21 20 19 18 17 ISBN 978-1-259-28990-3 MHID 1-259-28990-7

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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

Name: Ross, Stephen A., author. Title: Corporate finance : core principles & applications / Stephen A. Ross, Sloan School of Management, Massachusetts Institute of Technology, Randolph W. Westerfield, Marshall School of Business, University of Southern California, Jeffrey F. Jaffe, Wharton School of Business, University of Pennsylvania, Bradford D. Jordan, Gatton College of Business and Economics, University of Kentucky. Description: Fifth edition. | New York, NY : McGraw-Hill Education, [2016] | Series: The McGraw-Hill education series in finance, insurance, and real estate Identifiers: LCCN 2016035324 | ISBN 9781259289903 (alk. paper) Subjects: LCSH: Corporations—Finance. Classification: LCC HG4026 .R6755 2016 | DDC 658.15—dc23 LC record available at https://lccn.loc.gov/2016035324

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 family and friends with love and gratitude.

—S.A.R. R.W.W. J.F.J. B.D.J.

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Stephen A. Ross SLOAN SCHOOL OF MANAGEMENT, MASSACHUSETTS INSTITUTE OF TECHNOLOGY

Stephen A. Ross is the Franco Modigliani Professor of Financial Economics at the Sloan School of Management, Massachusetts Institute of Technology. One of the most widely published authors in finance and economics, Professor Ross is recognized for his work in developing the arbitrage pricing theory, as well as for having made substantial contributions to the discipline through his research in signaling, agency theory, option pricing, and the theory of the term structure of interest rates, among other topics. A past president of the American Finance Association, he currently serves as an associate editor of several academic and practitioner journals and is a trustee of CalTech.

Randolph W. Westerfield MARSHALL SCHOOL OF BUSINESS, UNIVERSITY OF SOUTHERN CALIFORNIA

Randolph W. Westerfield is Dean Emeritus of the University of Southern California’s Marshall School of Business and is the Charles B. Thornton Professor of Finance Emeritus. Professor Westerfield came to USC from the Wharton School, University of Pennsylvania, where he was the chairman of the finance department and member of the finance faculty for 20 years. He is a member of the Board of Trustees of Oak Tree Capital Mutual Funds. His areas of expertise include corporate finan- cial policy, investment management, and stock market price behavior.

ABOUT THE AUTHORS

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Bradford D. Jordan GATTON COLLEGE OF BUSINESS AND ECONOMICS, UNIVERSITY OF KENTUCKY

Bradford D. Jordan is professor of finance and holder of the Richard W. and Janis H. Furst Endowed Chair in Finance at the University of Kentucky. He has a long-standing interest in both applied and theoretical issues in corporate finance and has extensive experience teaching all levels of corporate finance and financial management policy. Professor Jordan has published numerous articles on issues such as cost of capital, capital structure, and the behavior of security prices. He is a past president of the Southern Finance Association, and he is coauthor of Fundamentals of Investments: Valuation and Management, 8th edition, a leading investments text, also published by McGraw-Hill Education.

Jeffrey F. Jaffe WHARTON SCHOOL OF BUSINESS, UNIVERSITY OF PENNSYLVANIA

Jeffrey F. Jaffe has been a frequent contributor to finance and economic literatures in such jour- nals as the Quarterly Economic Journal, The Journal of Finance, The Journal of Financial and Quantitative Analysis, The Journal of Financial Economics, and The Financial Analysts Journal. His best-known work concerns insider trading, where he showed both that corporate insiders earn abnormal profits from their trades and that regulation has little effect on these profits. He has also made contributions concerning initial public offerings, the regulation of utilities, the behavior of market makers, the fluctuation of gold prices, the theoretical effect of inflation on interest rates, the empirical effect of inflation on capital asset prices, the relationship between small-capitalization stocks and the January effect, and the capital structure decision.

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IN THE BEGINNING. . . It was probably inevitable that the four of us would collaborate on this project. Over the last 20 or so years, we have been working as two separate “RWJ” teams. In that time, we managed (much to our own amazement) to coauthor two widely adopted undergraduate texts and an equally successful graduate text, all in the corporate finance area. These three books have collectively totaled more than 31 editions (and counting), plus a variety of country-specific editions and international editions, and they have been translated into at least a dozen foreign languages.

Even so, we knew that there was a hole in our lineup at the graduate (MBA) level. We’ve continued to see a need for a concise, up-to-date, and to-the-point product, the majority of which can be realistically covered in a typical single term or course. As we began to develop this book, we realized (with wry chuckles all around) that, between the four of us, we have been teaching and research- ing finance principles for well over a century. From our own very extensive experience with this material, we recognized that corpo- rate finance introductory classes often have students with extremely diverse educational and professional backgrounds. We also recog- nized that this course is increasingly being delivered in alternative formats ranging from traditional semester-long classes to highly compressed modules, to purely online courses, taught both syn- chronously and asynchronously.

OUR APPROACH To achieve our objective of reaching out to the many different types of students and the varying course environments, we worked to distill the subject of corporate finance down to its core, while main- taining a decidedly modern approach. We have always maintained that corporate finance can be viewed as the working of a few very powerful intuitions. We also know that understanding the “why” is just as important, if not more so, than understanding the “how.” Throughout the development of this book, we continued to take a hard look at what is truly relevant and useful. In doing so, we have worked to downplay purely theoretical issues and minimize the use of extensive and elaborate calculations to illustrate points that are either intuitively obvious or of limited practical use.

Perhaps more than anything, this book gave us the chance to pool all that we have learned about what really works in a corporate finance text. We have received an enormous amount of feedback over the years. Based on that feedback, the two key ingredients that we worked to blend together here are the careful attention to peda- gogy and readability that we have developed in our undergraduate

books and the strong emphasis on current thinking and research that we have always stressed in our graduate book.

From the start, we knew we didn’t want this text to be encyclo- pedic. Our goal instead was to focus on what students really need to carry away from a principles course. After much debate and consul- tation with colleagues who regularly teach this material, we settled on a total of 21 chapters. Chapter length is typically 30 pages, so most of the book (and, thus, most of the key concepts and applica- tions) can be realistically covered in a single term or module. Writing a book that strictly focuses on core concepts and applications nec- essarily involves some picking and choosing with regard to both topics and depth of coverage. Throughout, we strike a balance by introducing and covering the essentials, while leaving more special- ized topics to follow-up courses.

As in our other books, we treat net present value (NPV) as the underlying and unifying concept in corporate finance. Many texts stop well short of consistently integrating this basic principle. The simple, intuitive, and very powerful notion that NPV represents the excess of market value over cost often is lost in an overly mechani- cal approach that emphasizes computation at the expense of com- prehension. In contrast, every subject we cover is firmly rooted in valuation, and care is taken throughout to explain how particular decisions have valuation effects.

Also, students shouldn’t lose sight of the fact that financial management is about management. We emphasize the role of the financial manager as decision maker, and we stress the need for managerial input and judgment. We consciously avoid “black box” approaches to decisions, and where appropriate, the approximate, pragmatic nature of financial analysis is made explicit, possible pit- falls are described, and limitations are discussed.

NEW AND NOTEWORTHY TO THE FIFTH EDITION All chapter openers and examples have been updated to reflect the financial trends and turbulence of the last several years. In addition, we have updated the end-of-chapter problems in every chapter. We have tried to incorporate the many exciting new research find- ings in corporate finance. Several chapters have been extensively rewritten.

• In the eight years since the “financial crisis” or “great recession,” we see that the world’s financial markets are more integrated than ever before. The theory and practice of corporate finance has been moving forward at a fast pace and we endeavor to bring the theory and practice to life with completely updated chapter

FROM THE AUTHORS

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openers, many new modern examples, completely updated end of chapter problems and questions. 

• In recent years we have seen unprecedented high stock and bond values and returns as well as histori- cally low interest rates and inflation. Chapter 10 Risk and Return:  Lessons from Market History updates and internationalizes our discussion of historical risk and return. With updated historical data, our estimates of the equity risk premium are on stronger footing And our understanding of the capital market environment is heightened.

• Given the importance of debt in most firms capital structure, it is a mystery that many firms use no debt. There is new and exciting research of this “no debt” behavior that sheds new light on how firms make actual capital structure decisions. Chapter 15 Capital Structure: Limits to the Use of Debt explores this new research and incorporates it into our discussion of Capital Structure.

• Chapter 16 Dividends and Other Payouts updates the record of earnings, dividends, and repurchases for large U.S. firms. The recent trends show repurchases far outpacing dividends in firm payout policy. Since firms may use dividends or repurchases to pay out cash

to equity investors, the recent importance of repur- chases suggests a changing financial landscape. 

• There are several twists and turns to the calculation of the firms weighted average of capital. Since the weighted average cost of capital is the most important benchmark we use for capital budgeting and repre- sents a firm’s “opportunity cost,” its calculation is criti- cal. We update our estimates of Eastman Chemical cost of capital using readily available data from the Internet to distinguish the nuances of this calculation. 

Our attention to updating and improving also extended to the extensive collection of support and enrichment materials that accompany the text. Working with many dedicated and talented colleagues and professionals, we continue to provide supplements that are unrivaled at the graduate level (a complete description appears in the following pages). Whether you use just the textbook, or the book in conjunction with other products, we believe you will be able to find a combination that meets your current as well as your changing needs.

—Stephen A. Ross —Randolph W. Westerfield

—Jeffrey F. Jaffe —Bradford D. Jordan

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Corporate Finance: Core

Principles & Applications is rich in valuable learning tools and support to help students succeed in learning the fundamentals of financial management.

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CHAPTER 5 Interest Rates and Bond Valuation 147

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A convertible bond can be swapped for a fixed number of shares of stock anytime before maturity at the holder’s option. Convertibles are relatively common, but the number has been decreasing in recent years.

A put bond allows the holder to force the issuer to buy the bond back at a stated price. For example, International Paper Co. has bonds outstanding that allow the holder to force International Paper to buy the bonds back at 100 percent of the face value given that cer- tain “risk” events happen. One such event is a change in credit rating from investment grade to lower than investment grade by Moody’s or S&P. The put feature is therefore just the reverse of the call provision.

BEAUTY IS IN THE EYE OF THE BONDHOLDER Many bonds have unusual or exotic features. One of the most common types is an asset-backed, or securitized, bond. Mortgage-backed securities were big news in 2007. For several years, there had been rapid growth in so-called sub- prime mortgage loans, which are mortgages made to individuals with less than top-quality credit. However, a combina- tion of cooling (and in some places dropping) housing prices and rising interest rates caused mortgage delinquencies and foreclosures to rise. This increase in problem mortgages caused a significant number of mortgage-backed securities to drop sharply in value and created huge losses for investors. Bondholders of a securitized bond receive interest and principal payments from a specific asset (or pool of assets) rather than a specific company. For example, at one point rock legend David Bowie sold $55 million in bonds backed by future royalties from his albums and songs (that’s some serious ch-ch-ch-change!). Owners of these “Bowie” bonds received the royalty payments, so if Bowie’s record sales fell, there was a possibility the bonds could have defaulted. Other artists have sold bonds backed by future royalties, includ- ing James Brown, Iron Maiden, and the estate of the legendary Marvin Gaye.

Mortgage-backs are the best known type of asset-backed security. With a mortgage-backed bond, a trustee pur- chases mortgages from banks and merges them into a pool. Bonds are then issued, and the bondholders receive pay- ments derived from payments on the underlying mortgages. One unusual twist with mortgage bonds is that if interest rates decline, the bonds can actually decrease in value. This can occur because homeowners are likely to refinance at the lower rates, paying off their mortgages in the process. Securitized bonds are usually backed by assets with long-term payments, such as mortgages. However, there are bonds securitized by car loans and credit card payments, among other assets, and a growing market exists for bonds backed by automobile leases.

The reverse convertible is a relatively new type of structured note. This type generally offers a high coupon rate, but the redemption at maturity can be paid in cash at par value or paid in shares of stock. For example, one recent General Motors (GM) reverse convertible had a coupon rate of 16 percent, which is a very high coupon rate in today’s interest rate environment. However, at maturity, if GM’s stock declined sufficiently, bondholders would receive a fixed number of GM shares that were worth less than par value. So, while the income portion of the bond return would be high, the potential loss in par value could easily erode the extra return.

CAT bonds are issued to cover insurance companies against natural catastrophes. The type of natural catastrophe is outlined in the bond’s indenture. For example, about 30 percent of all CAT bonds protect against a North Atlantic hurricane. The way these issues are structured is that the borrowers can suspend payment temporarily (or even perma- nently) if they have significant hurricane-related losses. These CAT bonds may seem like pretty risky investments, but to date, only three such bonds have not made their scheduled payments, courtesy of the massive destruction caused by Hurricane Katrina, the 2011 Japanese tsunami, and an unusually active 2011 tornado season.

Perhaps the most unusual bond (and certainly the most ghoulish) is the “death bond.” Companies such as Stone Street Financial purchase life insurance policies from individuals who are expected to die within the next 10 years. They then sell bonds that are paid off from the life insurance proceeds received when the policyholders pass away. The return on the bonds to investors depends on how long the policyholders live. A major risk is that if medical treat- ment advances quickly, it will raise the life expectancy of the policyholders, thereby decreasing the return to the bondholder.

FINANCE MATTERS Finance Matters By exploring information found in recent publica- tions and building upon concepts learned in each chapter, these boxes work through real-world issues relevant to the surrounding text.

PEDAGOGY Confirming Pages

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230 PART 2 Valuation and Capital Budgeting

8 OPENING CASE

Making Capital Investment Decisions Everyone knows that computer chips evolve quickly, getting smaller, faster, and cheaper.

In fact, the famous Moore’s Law (named after Intel cofounder Gordon Moore) predicts that the

number of transistors placed on a chip will double every two years (and this prediction has

held up very well since it was published in 1965). This growth often means that companies

need to build new fabrication facilities. For example, in 2015, GlobalFoundries announced

that it was going to spend about $646 million to further expand its manufacturing plant in

Saratoga, New York. The expansion at the plant would allow the company to produce more

of its new 14 nanometer (nm) chips. Not to be outdone, IBM announced that it was investing

$3 billion in a public-private partnership with New York State, GlobalFoundries, and Samsung

in an effort to manufacture 7 nm chips, which would be smaller, faster, and consume less

energy than current chips.

This chapter follows up on our previous one by delving more deeply into capital budget-

ing and the evaluation of projects such as these chip manufacturing facilities. We identify the

relevant cash flows of a project, including initial investment outlays, requirements for net

working capital, and operating cash flows. Further, we look at the effects of depreciation and

taxes. We also examine the impact of inflation and show how to evaluate consistently the NPV

analysis of a project.

Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.

8.1 INCREMENTAL CASH FLOWS Cash Flows—Not Accounting Income You may not have thought about it, but there is a big difference between corporate finance courses and financial accounting courses. Techniques in corporate finance generally use cash flows, whereas financial accounting generally stresses income or earnings numbers. Certainly, our text follows this tradition, as our net present value techniques discount cash flows, not earnings. When considering a single project, we discount the cash flows that the firm receives from the project. When valuing the firm as a whole, we discount the cash flows—not earnings—that an investor receives.

Chapter Opening Case Each chapter begins with a recent real- world event to introduce students to chap- ter concepts.

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CHAPTER 2 Financial Statements and Cash Flow 19

2 OPENING CASE

Financial Statements and Cash Flow When a company announces a “write-off,” that frequently means that the value of the compa-

ny’s assets has declined. For example, in July 2015, Microsoft announced that it would write

off $7.6 billion related to its purchase of Nokia’s phone business the previous year. What made

the write-off interesting was that Microsoft had only paid $7.2 billion for the phone business.

The oil business was also hit hard in 2015 as the five largest publicly traded oil companies

working in Wyoming wrote off a combined $41 billion for the first nine months of the year.

These write-offs were due to the declining value of oil production facilities in that state.  

While Microsoft’s write-off is large, the record holder is media giant Time Warner, which

took a charge of $45.5 billion in the fourth quarter of 2002. This enormous write-off followed

an earlier, even larger, charge of $54 billion.

So, did the stockholders in these companies lose billions of dollars when these assets

were written off? Fortunately for them, the answer is probably not. Understanding why ulti-

mately leads us to the main subject of this chapter, that all-important substance known as

cash flow.

Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.

2.1 THE BALANCE SHEET The balance sheet is an accountant’s snapshot of the firm’s accounting value on a par- ticular date, as though the firm stood momentarily still. The balance sheet has two sides: On the left are the assets and on the right are the liabilities and stockholders’ equity. The balance sheet states what the firm owns and how it is financed. The accounting definition that underlies the balance sheet and describes the balance is

Assets ≡ Liabilities + Stockholders’ equity [2.1]

We have put a three-line equality in the balance equation to indicate that it must always hold, by definition. In fact, the stockholders’ equity is defined to be the difference between the assets and the liabilities of the firm. In principle, equity is what the stockholders would have remaining after the firm discharged its obligations.

Table 2.1 gives the 2016 and 2017 balance sheets for the fictitious U.S. Composite Corporation. The assets in the balance sheet are listed in order by the length of time it normally would take an ongoing firm to convert them to cash. The asset side depends on the nature of the business and how management chooses to conduct it. Management must make decisions about cash versus marketable securities, credit versus cash sales, whether

ExcelMaster coverage online

www.mhhe.com/RossCore5e

Two excellent sources for company financial information are finance. yahoo.com and money. cnn.com.

Core Calculator Skills This icon, located in the margins of the text near key con- cepts and equations, indicates that additional coverage is available describing how to use a financial calculator when studying the topic. This additional coverage can be found in a special calculator section, Appendix C.

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Spreadsheet Techniques This feature helps students to improve their Excel spreadsheet skills, particularly as they relate to corporate finance. This feature appears in self-contained sections and shows students how to set up spreadsheets to analyze common financial problems—a vital part of every business student’s education. For even more help using Excel, students have access to Excel Master, an in-depth online tutorial.

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PART 2 Valuation and Capital Budgeting

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138

How to Calculate Bond Pr ices and Yie lds Us ing a Spreadsheet SPREADSHEET TECHNIQUES

Most spreadsheets have fairly elaborate routines available for calculating bond values and yields; many of these routines involve details that we have not discussed. However, setting up a simple spreadsheet to cal- culate prices or yields is straightforward, as our next two spreadsheets show:

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1 0

1 1

1 2

1 3

1 4

1 5

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A B C D E F G H

Suppose we have a bond with 22 years to maturity, a coupon rate of 8 percent, and a yield to maturity of 9 percent. If the bond makes semiannual payments, what is its price today?

Settlement date: 1/1/00 Maturity date: 1/1/22

Annual coupon rate: .08 Yield to maturity: .09

Face value (% of par): 100 Coupons per year: 2

Bond price (% of par): 90.49

The formula entered in cell B13 is =PRICE(B7,B8,B9,B10,B11,B12); notice that face value and bond price are given as a percentage of face value.

Using a spreadsheet to calculate bond values

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1 0

1 1

1 2

1 3

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A B C D E F G H

Suppose we have a bond with 22 years to maturity, a coupon rate of 8 percent, and a price of $960.17. If the bond makes semiannual payments, what is its yield to maturity?

Settlement date: 1/1/00 Maturity date: 1/1/22

Annual coupon rate: .08 Bond price (% of par): 96.017 Face value (% of par): 100

Coupons per year: 2 Yield to maturity: .084

The formula entered in cell B13 is =YIELD(B7,B8,B9,B10,B11,B12); notice that face value and bond price are entered as a percentage of face value.

Using a spreadsheet to calculate bond yields

1 7

In our spreadsheets, notice that we had to enter two dates, a settlement date and a maturity date. The settlement date is just the date you actually pay for the bond, and the maturity date is the day the bond actually matures. In most of our problems, we don’t explicitly have these dates, so we have to make them up. For example, since our bond has 22 years to maturity, we just picked 1/1/2000 (January 1, 2000) as the settlement date and 1/1/2022 (January 1, 2022) as the maturity date. Any two dates would do as long as they are exactly 22 years apart, but these are particularly easy to work with. Finally, notice that we had to enter the coupon rate and yield to maturity in annual terms and then explicitly provide the number of coupon payments per year.

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530 PART 5 Special Topics

As indicated, this ratio is called the delta of the call. In words, a $1 swing in the price of the stock gives rise to a $1/2 swing in the price of the call. Because we are trying to dupli- cate the call with the stock, it seems sensible to buy one-half a share of stock instead of buying one call. In other words, the risk of buying one-half a share of stock should be the same as the risk of buying one call.

DETERMINING THE AMOUNT OF BORROWING How did we know how much to borrow? Buying one-half a share of stock brings us either $30 or $20 at expiration, which is exactly $20 more than the payoffs of $10 and $0, respectively, from the call. To duplicate the call through a purchase of stock, we should also borrow enough money so that we have to pay back exactly $20 of interest and principal. This amount of borrowing is merely the present value of $20, which is $18.18 (= $20/1.10).

Now that we know how to determine both the delta and the amount of borrowing, we can write the value of the call as:

Value of call = Stock price × Delta − Amount borrowed [17.2]

$ 6.82  =  $50  × 1 __ 2

  −  $18.18

We will find this intuition very useful in explaining the Black−Scholes model.

RISK-NEUTRAL VALUATION Before leaving this simple example, we should comment on a remarkable feature. We found the exact value of the option without even knowing the probability that the stock would go up or down! If an optimist thought the probability of an up move was very high and a pessimist thought it was very low, they would still agree on the option value. How could that be? The answer is that the current $50 stock price already balances the views of the optimist and the pessimist. The option reflects that balance because its value depends on the stock price.

This insight provides us with another approach to valuing the call. If we don’t need the probabilities of the two states to value the call, perhaps we can select any probabilities we want and still come up with the right answer. Suppose we selected probabilities such that the return on the stock is equal to the risk-free rate of 10 percent. We know that the stock return given a rise is 20 percent (= $60/$50 − 1) and the stock return given a fall is −20 percent (= $40/$50 − 1). Thus, we can solve for the probability of a rise necessary to achieve an expected return of 10 percent as:

10% = Probability of a rise × 20% + 1 − Probability of a rise × − 20%

Solving this formula, we find that the probability of a rise is 3/4 and the probability of a fall is 1/4. If we apply these probabilities to the call, we can value it as:

Value of call =  3 __ 4

 × $10 +  1 __ 4

 × $0 _______________

1.10  = $6.82

the same value that we got from the duplicating approach. Why did we select probabilities such that the expected return on the stock is 10 percent?

We wanted to work with the special case where investors are risk-neutral. This case occurs when the expected return on any asset (including both the stock and the call) is equal to the risk-free rate. In other words, this case occurs when investors demand no additional com- pensation beyond the risk-free rate, regardless of the risk of the asset in question.

What would have happened if we had assumed that the expected return on the stock was greater than the risk-free rate? The value of the call would still be $6.82. However, the cal- culations would be more difficult. For example, if we assumed that the expected return on

Numbered Equations Key equations are numbered within the text and listed on the back end sheets for easy reference.

END-OF-CHAPTER MATERIAL

The end-of-chapter material reflects and builds on the concepts learned from the chapter and study features.

Questions and Problems Because solving problems is so critical to students’ learning, we provide extensive end-of-chapter questions and prob- lems. The questions and problems are segregated into three learning levels: Basic, Intermediate, and Challenge. All prob- lems are fully annotated so that students and instructors can readily identify particular types. Also, most of the problems are available in McGraw-Hill’s Connect—see the next section of this preface for more details.

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PART 1 Overview34

5. Book Values versus Market Values Under standard accounting rules, it is possible for a company’s liabilities to exceed its assets. When this occurs, the owners’ equity is negative. Can this happen with market values? Why or why not?

6. Cash Flow from Assets Suppose a company’s cash flow from assets was negative for a particular period. Is this necessarily a good sign or a bad sign?

7. Operating Cash Flow Suppose a company’s operating cash flow was negative for several years running. Is this necessarily a good sign or a bad sign?

8. Net Working Capital and Capital Spending Could a company’s change in net working capital be negative in a given year? (Hint: Yes.) Explain how this might come about. What about net capital spending?

9. Cash Flow to Stockholders and Creditors Could a company’s cash flow to stockholders be negative in a given year? (Hint: Yes.) Explain how this might come about. What about cash flow to creditors?

10. Firm Values Referring back to the Microsoft example used at the beginning of the chapter, note that we suggested that Microsoft’s stockholders probably didn’t suffer as a result of the reported loss. What do you think was the basis for our conclusion?

QUESTIONS AND PROBLEMS

1. Building a Balance Sheet Burnett, Inc., has current assets of $6,800, net fixed assets of $29,400, current liabilities of $5,400, and long-term debt of $13,100. What is the value of the shareholders’ equity account for this firm? How much is net working capital?

2. Building an Income Statement    Bradds, Inc., has sales of $528,600, costs of $264,400, depreciation expense of $41,700, interest expense of $20,700, and a tax rate of 35 percent. What is the net income for the firm? Suppose the company paid out $27,000 in cash dividends. What is the addition to retained earnings?

3. Market Values and Book Values Klingon Cruisers, Inc., purchased new cloaking machinery three years ago for $7 million. The machinery can be sold to the Romulans today for $5.3 million. Klingon’s current balance sheet shows net fixed assets of $3.9 million, current liabilities of $1.075 million, and net working capital of $320,000. If all the current accounts were liquidated today, the company would receive $410,000 cash. What is the book value of Klingon’s total assets today? What is the sum of the market value of NWC and market value of assets?

4. Calculating Taxes The Alexander Co. had $328,500 in taxable income. Using the rates from Table 2.3 in the chapter, calculate the company’s income taxes. What is the average tax rate? What is the marginal tax rate?

5. Calculating OCF Timsung, Inc., has sales of $30,700, costs of $11,100, depreciation expense of $2,100, and interest expense of $1,140. If the tax rate is 40 percent, what is the operating cash flow, or OCF?

6. Calculating Net Capital Spending Busch Driving School’s 2016 balance sheet showed net fixed assets of $3.75 million, and the 2017 balance sheet showed net fixed assets of $4.45 million. The company’s 2017 income statement showed a depreciation expense of $395,000. What was the company’s net capital spending for 2017?

7. Building a Balance Sheet The following table presents the long-term liabilities and stockholders’ equity of Information Control Corp. one year ago:

Basic (Questions 1–10)

Long-term debt

Preferred stock

Common stock ($1 par value)

Capital surplus

Accumulated retained earnings

$37,000,000

2,100,000

8,900,000

41,000,000

75,300,000

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Excel Problems Indicated by the Excel icon in the margin, these problems are integrated in the Questions and Problems section of almost all chapters. Located on the book’s website, Excel templates have been created for each of these problems. Students can use the data in the problem to work out the solution using Excel skills.

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CHAPTER 11 Return and Risk: The Capital Asset Pricing Model (CAPM) 349

QUESTIONS AND PROBLEMS

1. Determining Portfolio Weights What are the portfolio weights for a portfolio that has 125 shares of Stock A that sell for $38 per share and 175 shares of Stock B that sell for $26 per share?

2. Portfolio Expected Return You own a portfolio that has $3,850 invested in Stock A and $6,100 invested in Stock B. If the expected returns on these stocks are 7.2 percent and 13.1 percent, respectively, what is the expected return on the portfolio?

3. Portfolio Expected Return You own a portfolio that is 20 percent invested in Stock X, 35 percent invested in Stock Y, and 45 percent invested in Stock Z. The expected returns on these three stocks are 9.2 percent, 11.8 percent, and 14.3 percent, respectively. What is the expected return on the portfolio?

4. Portfolio Expected Return You have $10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 12.4 percent and Stock Y with an expected return of 10.2 percent. If your goal is to create a portfolio with an expected return of 10.9 percent, how much money will you invest in Stock X? In Stock Y?

5. Calculating Expected Return Based on the following information, calculate the expected return.

STATE OF ECONOMY

PROBABILITY OF

STATE OF ECONOMY

RATE OF RETURN

IF STATE OCCURS

Recession .35  –.09 Normal .50    .15

Boom .15    .34

6. Calculating Returns and Standard Deviations Based on the following information, calculate the expected return and standard deviation for the two stocks.

STATE OF ECONOMY

PROBABILITY OF STATE OF ECONOMY

RATE OF RETURN IF STATE OCCURS

STOCK A STOCK B

Recession .15 .01 –.19  

Normal .50 .09 .11

Boom .35 .13 .37

7. Calculating Returns and Standard Deviations Based on the following information, calculate the expected return and standard deviation of the following stock.

STATE OF ECONOMY

PROBABILITY OF STATE OF ECONOMY

RATE OF RETURN IF STATE OCCURS

Depression .10 –.279

Recession .20 –.128

Normal .45   .141

Boom .25   .365

8. Calculating Expected Returns A portfolio is invested 25 percent in Stock G, 60 percent in Stock J, and 15 percent in Stock K. The expected returns on these stocks are 8.6 percent, 10.8 percent, and 13.4 percent, respectively. What is the portfolio’s expected return? How do you interpret your answer?

9. Returns and Standard Deviations Consider the following information:

STATE OF ECONOMY

PROBABILITY OF STATE OF ECONOMY

RATE OF RETURN IF STATE OCCURS

STOCK A STOCK B STOCK C

Boom .15 .26   .40 .38

Good .45 .10   .18 .15

Poor .35 .02 –.19 –.03  

Bust .05 –.08   –.32 –.06  

Basic (Questions 1–19)

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PART 3 Risk and Return354

b. What are the expected return and standard deviation of a portfolio consisting of 70 percent of Stock A and 30 percent of Stock B?

c. What is the beta of the portfolio in part (b)?

38. Minimum Variance Portfolio Assume Stocks A and B have the following characteristics:

STOCK EXPECTED RETURN (%) STANDARD DEVIATION (%)

A 13 34

B 11 58

The covariance between the returns on the two stocks is .01.

a. Suppose an investor holds a portfolio consisting of only Stock A and Stock B. Find the portfolio weights, XA and XB , such that the variance of his portfolio is minimized. (Hint: Remember that the sum of the two weights must equal 1.)

b. What is the expected return on the minimum variance portfolio? c. If the covariance between the returns on the two stocks is –.15, what are the minimum variance

weights? d. What are the variance and standard deviation of the portfolio in part (c)?

WHAT’S ON THE WEB? 1. Expected Return You want to find the expected return for Honeywell using the CAPM. First you need

the market risk premium. Go to money.cnn.com and find the current interest rate for three-month Treasury bills. Use the historic market risk premium from Chapter 10 as the market risk premium. Next, go to finance.yahoo.com, enter the ticker symbol HON for Honeywell, and find the beta for Honeywell. What is the expected return for Honeywell using CAPM? What assumptions have you made to arrive at this number?

2. Portfolio Beta You have decided to invest in an equally weighted portfolio consisting of American Express, Procter & Gamble, Home Depot, and DuPont and need to find the beta of your portfolio. Go to finance.yahoo.com and find the beta for each of the companies. What is the beta for your portfolio?

3. Beta Which companies currently have the highest and lowest betas? Go to finance.yahoo.com and find the “Stock Screener” link. Enter 0 as the maximum beta and search. How many stocks currently have a beta less than or equal to 0? What is the lowest beta? Go back to the stock screener and enter 3 as the minimum. How many stocks have a beta above 3? What stock has the highest beta?

4. Security Market Line Go to finance.yahoo.com and enter the ticker symbol IP for International Paper. Follow the “Key Statistics” link to get the beta for the company. Next, find the estimated (or “target”) price in 12 months according to market analysts. Using the current share price and the mean target price, compute the expected return for this stock. Don’t forget to include the expected dividend payments over the next year. Now go to money.cnn.com and find the current interest rate for three- month Treasury bills. Using this information, calculate the expected return on the market using the reward-to-risk ratio. Does this number make sense? Why or why not?

The CAPM is one of the most thoroughly researched models in financial economics. When beta is estimated in practice, a variation of CAPM called the market model is often used. To derive the market model, we start with the CAPM:

E( R i ) = R F × β[E( R M ) − R F ]

Since CAPM is an equation, we can subtract the risk-free rate from both sides, which gives us

E( R i ) − R F = β[E( R M ) − R F ]

EXCEL MASTER IT ! PROBLEM

What’s On the Web? These end-of-chapter activities show students how to use and learn from the vast amount of financial resources available on the Internet.

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Excel Master-It! Problems These more in-depth mini-case studies highlight higher- level Excel skills. Students are encouraged to use Excel to solve real-life financial problems using the concepts they have learned in the chapter and the Excel skills they have acquired thus far.

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CHAPTER 5 Interest Rates and Bond Valuation 163

EXCEL MASTER IT ! PROBLEM Companies often buy bonds to meet a future liability or cash outlay. Such an investment is called a dedicated portfolio because the proceeds of the portfolio are dedicated to the future liability. In such a case, the port- folio is subject to reinvestment risk. Reinvestment risk occurs because the company will be reinvesting the coupon payments it receives. If the YTM on similar bonds falls, these coupon payments will be reinvested at a lower interest rate, which will result in a portfolio value that is lower than desired at maturity. Of course, if interest rates increase, the portfolio value at maturity will be higher than needed.

Suppose Ice Cubes, Inc., has the following liability due in five years. The company is going to buy five-year bonds today to meet the future obligation. The liability and current YTM are below:

Amount of liability:

Current YTM:

$100,000,000

8%

a. At the current YTM, what is the face value of the bonds the company has to purchase today to meet its future obligation? Assume that the bonds in the relevant range will have the same coupon rate as the current YTM and these bonds make semiannual coupon payments.

b. Assume the interest rates remain constant for the next five years. Thus, when the company reinvests the coupon payments, it will reinvest at the current YTM. What is the value of the portfolio in five years?

c. Assume that immediately after the company purchases the bonds, interest rates either rise or fall by 1 percent. What is the value of the portfolio in five years under these circumstances?

One way to eliminate reinvestment risk is called immunization. Rather than buying bonds with the same maturity as the liability, the company instead buys bonds with the same duration as the liability. If you think about the ded- icated portfolio, if the interest rate falls, the future value of the reinvested coupon payments decreases. However, as interest rates fall, the price of bonds increases. These effects offset each other in an immunized portfolio.

Another advantage of using duration to immunize a portfolio is that the duration of a portfolio is the weighted average of the duration of the assets in the portfolio. In other words, to find the duration of a portfo- lio, you simply take the weight of each asset multiplied by its duration and then sum the results.

d. What is the duration of the liability for Ice Cubes, Inc.?

e. Suppose the two bonds shown below are the only bonds available to immunize the liability. What face amount of each bond will the company need to purchase to immunize the portfolio?

FINANCING EAST COAST YACHTS’ EXPANSION PLANS WITH A BOND ISSUE After Dan’s EFN analysis for East Coast Yachts (see the Closing Case in Chapter 3), Larissa has decided to expand the company’s operations. She has asked Dan to enlist an underwriter to help sell $45 million in new 30-year bonds to finance new construction. Dan has entered into discussions with Renata Harper, an underwriter from the firm of Crowe & Mallard, about which bond features East Coast Yachts should consider and also what coupon

CLOSING CASE

BOND A BOND B

Settlement

Maturity

Coupon rate

YTM

Coupons per year

1/1/2000

1/1/2003

    7.00%

    7.50%

           2

1/1/2000

1/1/2008

    8.00%

    9.00%

           2

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CHAPTER 12 Risk, Cost of Capital, and Valuation 389

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THE COST OF CAPITAL FOR SWAN MOTORS You have recently been hired by Swan Motors, Inc. (SMI), in its relatively new treasury management depart- ment. SMI was founded eight years ago by Joe Swan. Joe found a method to manufacture a cheaper battery with much greater energy density than was previously possible, giving a car powered by the battery a range of 700 miles before requiring a charge. The cars manufactured by SMI are midsized and carry a price that allows the company to compete with other mainstream auto manufacturers. The company is privately owned by Joe and his family, and it had sales of $97 million last year.

SMI primarily sells to customers who buy the cars online, although it does have a limited number of company-owned dealerships. The customer selects any customization and makes a deposit of 20 percent of the purchase price. After the order is taken, the car is made to order, typically within 45 days. SMI’s growth to date has come from its profits. When the company had sufficient capital, it would expand production. Relatively little formal analysis has been used in its capital budgeting process. Joe has just read about capital budget- ing techniques and has come to you for help. For starters, the company has never attempted to determine its cost of capital, and Joe would like you to perform the analysis. Because the company is privately owned, it is difficult to determine the cost of equity for the company. Joe wants you to use the pure play approach to estimate the cost of capital for SMI, and he has chosen Tesla Motors as a representative company. The follow- ing questions will lead you through the steps to calculate this estimate.

1. Most publicly traded corporations are required to submit 10Q (quarterly) and 10K (annual) reports to the SEC detailing their financial operations over the previous quarter or year, respectively. These corporate filings are available on the SEC website at www.sec.gov. Go to the SEC website and enter “TSLA” for Tesla in the “Search for Company Filings” link and search for SEC filings made by Tesla. Find the most recent 10Q or 10K and download the form. Look on the balance sheet to find the book value of debt and the book value of equity. If you look further down the report, you should find a section titled either “Long-Term Debt” or “Long-Term Debt and Interest Rate Risk Management” that will list a breakdown of Tesla’s long-term debt.

2. To estimate the cost of equity for Tesla, go to finance.yahoo.com and enter the ticker symbol “TSLA.” Follow the various links to find answers to the following questions: What is the most recent stock price listed for Tesla? What is the market value of equity, or market capitalization? How many shares of stock does Tesla have outstanding? What is the beta for Tesla? Now go back to finance.yahoo.com and follow the “Bonds” link. What is the yield on three-month Treasury bills? Using a 7 percent market risk premium, what is the cost of equity for Tesla using the CAPM?

3. Go to www.reuters.com and find the list of competitors in the industry. Find the beta for each of these competitors, and then calculate the industry average beta. Using the industry average beta, what is the cost of equity? Does it matter if you use the beta for Tesla or the beta for the industry in this case?

4. You now need to calculate the cost of debt for Tesla. Go to http://finra-markets.morningstar.com/ BondCenter/Default.jsp, enter Tesla as the company, and find the yield to maturity for each of Tesla’s bonds. What is the weighted average cost of debt for Tesla using the book value weights and the market value weights? Does it make a difference in this case if you use book value weights or market value weights?

5. You now have all the necessary information to calculate the weighted average cost of capital for Tesla. Calculate the weighted average cost of capital for Tesla using book value weights and market value weights, assuming Tesla has a 35 percent marginal tax rate. Which cost of capital number is more relevant?

6. You used Tesla as a representative company to estimate the cost of capital for SMI. What are some of the potential problems with this approach in this situation? What improvements might you suggest?

CLOSING CASE

End-of-Chapter Cases Located at the end of each chapter, these mini-cases focus on common company situations that embody important corporate finance topics. Each case presents a new sce- nario, data, and a dilemma. Several questions at the end of each case require students to analyze and focus on all of the material they learned in that chapter.

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COMPREHENSIVE TEACHING

INSTRUCTOR SUPPORT ∙ Instructor’s Manual

prepared by Melissa Frye, University of Central Florida, Ann Marie Whyte, University of Central Florida, and Joseph Smolira, Belmont University A great place to find new lecture ideas. The IM has three main sections. The first section contains a chapter outline and other lecture materials. The annotated outline for each chapter includes lecture tips, real-world tips, ethics notes, suggested PowerPoint slides, and, when appropriate, a video synopsis. Detailed solutions for all end-of-chapter problems appear in Section three.

∙ Test Bank prepared by Kay Johnson Great format for a better testing process. The Test Bank has 75–100 questions per chapter that closely link with the text material and provide a variety of question formats (multiple-choice questions/problems and essay questions) and levels of difficulty (basic, intermediate, and challenge) to meet every instructor’s testing needs. Problems are detailed enough to make them intuitive for students, and solutions are provided for the instructor.

∙ Computerized Test Bank TestGen is a complete, state-of-the-art test generator and editing application software that allows instructors to quickly and easily select test items from McGraw-Hill’s testbank content. The instructors can then organize, edit, and customize questions and answers to rapidly generate tests for paper or online administration. Questions can include stylized text, symbols, graphics, and equations that are inserted directly into questions using built-in mathematical templates. TestGen’s random generator provides the option to display different text or calculated number values each time questions are used. With both quick-and- simple test creation and flexible and robust editing tools, TestGen is a complete test generator system for today’s educators.

∙ PowerPoint Presentation System prepared by Melissa Frye, University of Central Florida, and Ann Marie Whyte, University of Central Florida Customize our content for your course. This presentation has been thoroughly revised to include more lecture-oriented slides, as well as exhibits and examples both from the book and from outside sources. Applicable slides have web links that take you directly to specific Internet sites, or a spreadsheet link to show an example in Excel. You can also go to the Notes Page function for more tips on presenting the slides. This customizable format gives you the ability to edit, print, or rearrange the complete presentation to meet your specific needs.

Online Videos Available in DVD format and online. Current set of videos on hot topics! McGraw-Hill Education has produced a series of finance videos that are 10-minute case studies on

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topics such as financial markets, careers, rightsizing, capital budgeting, EVA (economic value added), mergers and acquisitions, and foreign exchange. Discussion questions for these videos, as well as video clips, are available in the Instructor’s Center in Connect.

STUDENT SUPPORT ∙ Excel Master

Created by Brad Jordan and Joseph Smolira, this extensive Excel tutorial is fully integrated with the text. Learn Excel and corporate finance at the same time.

PACKAGE OPTIONS AVAILABLE FOR PURCHASE & PACKAGING You may also package either version of the text with a variety of additional learning tools that are available for your students.

FinGame Online 5.0 by LeRoy Brooks, John Carroll University (ISBN 10: 0077219880/ISBN 13: 9780077219888) Just $15.00 when packaged with this text. In this comprehensive simulation game, students control a hypothetical company over numerous periods of operation. As students make major financial and operating decisions for their company, they will develop and enhance their skills in financial management and financial accounting statement analysis.

Financial Analysis with an Electronic Calculator, Sixth Edition by Mark A. White, University of Virginia, McIntire School of Commerce (ISBN 10: 0073217093/ISBN 13: 9780073217093) The information and procedures in this supplementary text enable students to master the use of financial calculators and develop a working knowledge of financial mathematics and problem solving. Complete instructions are included for solving all major problem types on three popular models: HP 10B and 12C, TI BA II Plus, and TI-84. Hands-on problems with detailed solutions allow students to practice the skills outlined in the text and obtain instant reinforcement. Financial Analysis with an Electronic Calculator is a self-contained supplement to the introductory financial management course.

MCGRAW-HILL CUSTOMER CARE CONTACT INFORMATION At McGraw-Hill, we understand that getting the most from new technology can be challenging. That’s why our services don’t stop after you purchase our products. You can e-mail our Product Specialists 24 hours a day to get product training online. Or you can search our knowledge bank of Frequently Asked Questions on our support website. For Customer Support, call 800-331-5094, or visit www.mhhe.com/support. One of our Technical Support Analysts will be able to assist you in a timely fashion.

AND LEARNING PACKAGE

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Required=Results

McGraw-Hill Connect® Learn Without Limits Connect is a teaching and learning platform that is proven to deliver better results for students and instructors.

Connect empowers students by continually adapting to deliver precisely what they need, when they need it, and how they need it, so your class time is more engaging and effective.

Connect Insight® Connect Insight is Connect’s new one- of-a-kind visual analytics dashboard that provides at-a-glance information regarding student performance, which is immediately actionable. By presenting assignment, assessment, and topical performance results together with a time metric that is easily visible for aggregate or individual results, Connect Insight gives the user the ability to take a just-in-time approach to teaching and learning, which was never before available. Connect Insight presents data that helps instructors improve class performance in a way that is efficient and effective.

73% of instructors who use Connect require it; instructor

satisfaction increases by 28% when Connect is required.

Analytics

©Getty Images/iStockphoto

Using Connect improves retention rates by 19.8%, passing rates by 12.7%, and exam scores by 9.1%.

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SmartBook® Proven to help students improve grades and study more efficiently, SmartBook contains the same content within the print book, but actively tailors that content to the needs of the individual. SmartBook’s adaptive technology provides precise, personalized instruction on what the student should do next, guiding the student to master and remember key concepts, targeting gaps in knowledge and offering customized feedback, and driving the student toward comprehension and retention of the subject matter. Available on tablets, SmartBook puts learning at the student’s fingertips—anywhere, anytime.

Adaptive

Over 8 billion questions have been answered, making McGraw-Hill

Education products more intelligent, reliable, and precise.

THE ADAPTIVE READING EXPERIENCE DESIGNED TO TRANSFORM THE WAY STUDENTS READ

More students earn A’s and B’s when they use McGraw-Hill Education Adaptive products.

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ACKNOWLEDGMENTS xix

A C

K N

O W

L E

D G

M E

N T

S To borrow a phrase, writing a finance textbook is easy—all you do is sit down at a word processor and open a vein. We never would have completed this book without the incredible amount of help and sup- port we received from our colleagues, students, edi- tors, family members, and friends. We would like to thank, without implicating, all of you.

Clearly, our greatest debt is to our many col- leagues (and their students). Needless to say, without this support and feedback we would not be publish- ing this text.

We owe a special thanks to Joseph Smolira of Belmont University for his work on this book. Joe worked closely with us to develop portions of the Instructor’s Manual, along with the many vignettes and real-world examples. In addition, we would like to thank Melissa Frye, University of Central Florida, and Ann Marie Whyte, University of Central Florida, for their work on the PowerPoint and Instructor’s Manual. We would also like to thank Kay Johnson for her terrific work and attention to detail in updating our test bank.

Steve Hailey did outstanding work on this edition. To him fell the unenviable task of technical proofread- ing, and in particular, careful checking of each calcu- lation throughout the text and Instructor’s Manual.

Finally, in every phase of this project, we have been privileged to have had the complete and unwavering support of a great organization, McGraw- Hill Education. We especially thank the McGraw-Hill Education sales organization. The suggestions they provide, their professionalism in assisting potential

adopters, and the service they provide have been a major factor in our success.

We are deeply grateful to the select group of pro- fessionals who served as our development team on this edition: Chuck Synovec, director; Jennifer Upton, senior product developer; Trina Maurer, senior mar- keting manager; Kathryn Wright, core content proj- ect manager; Bruce Gin, senior assessment project manager; and Matt Diamond, senior designer. Others at McGraw-Hill Education, too numerous to list here, have improved the book in countless ways.

Finally, we wish to thank our families, Carol, Kate, Jon, Suh-Pyng, Mark, Lynne, and Susan, for their for- bearance and help.

Throughout the development of this edition, we have taken great care to discover and eliminate errors. Our goal is to provide the best textbook avail- able on the subject. To ensure that future editions are error-free, we gladly offer $10 per arithmetic error to the first individual reporting it as a modest token of our appreciation. More than this, we would like to hear from instructors and students alike. Please write and tell us how to make this a better text. Forward your comments to: Dr. Brad Jordan, c/o Editorial- Finance, McGraw-Hill Education, 1333 Burr Ridge Parkway, Burr Ridge, IL 60527.

—Stephen A. Ross —Randolph W. Westerfield

—Jeffrey F. Jaffe —Bradford D. Jordan

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BRIEF CONTENTS xxi

PART ONE OVERVIEW

CHAPTER ONE Introduction to Corporate Finance 1 CHAPTER TWO Financial Statements and Cash Flow 19 CHAPTER THREE Financial Statements Analysis and Financial

Models 43

PART TWO VALUATION AND CAPITAL BUDGETING

CHAPTER FOUR Discounted Cash Flow Valuation 83 CHAPTER FIVE Interest Rates and Bond Valuation 130 CHAPTER SIX Stock Valuation 165 CHAPTER SEVEN Net Present Value and Other Investment

Rules 195 CHAPTER EIGHT Making Capital Investment Decisions 230 CHAPTER NINE Risk Analysis, Real Options, and Capital

Budgeting 262

PART THREE RISK AND RETURN

CHAPTER TEN Risk and Return: Lessons from Market History 287

CHAPTER ELEVEN Return and Risk: The Capital Asset Pricing Model (CAPM) 316

CHAPTER TWELVE Risk, Cost of Capital, and Valuation 357

PART FOUR CAPITAL STRUCTURE AND DIVIDEND POLICY

CHAPTER THIRTEEN Efficient Capital Markets and Behavioral Challenges 390

CHAPTER FOURTEEN Capital Structure: Basic Concepts 423 CHAPTER FIFTEEN Capital Structure: Limits to the Use of Debt 451 CHAPTER SIXTEEN Dividends and Other Payouts 480

PART FIVE SPECIAL TOPICS

CHAPTER SEVENTEEN Options and Corporate Finance 515 CHAPTER EIGHTEEN Short-Term Finance and Planning 550 CHAPTER NINETEEN Raising Capital 582 CHAPTER TWENTY International Corporate Finance 618 CHAPTER TWENTY ONE Mergers and Acquisitions (web only)

APPENDIX A Mathematical Tables 644 APPENDIX B Solutions to Selected End-of-Chapter

Problems 653 APPENDIX C Using the HP 10B and TI BA II Plus Financial

Calculators 658 Indexes 662

B R

IE F

C O

N T

E N

T S

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CONTENTSxxii

PART ONE OVERVIEW CHAPTER ONE Introduction to Corporate Finance 1 1.1 What Is Corporate Finance? 1

The Balance Sheet Model of the Firm 1

The Financial Manager 3

1.2 The Corporate Firm 3

The Sole Proprietorship 4

The Partnership 4

The Corporation 5

A Corporation by Another Name . . . 6

1.3 The Importance of Cash Flows 7

1.4 The Goal of Financial Management 9

Possible Goals 10

The Goal of Financial Management 10

A More General Goal 11

1.5 The Agency Problem and Control of the Corporation 11

Agency Relationships 12

Management Goals 12

Do Managers Act in the Stockholders’ Interests? 13

Stakeholders 14

1.6 Regulation 14

The Securities Act of 1933 and the Securities Exchange Act of 1934 16

Summary and Conclusions 16

Closing Case: East Coast Yachts 18

CHAPTER TWO Financial Statements and Cash Flow 19 2.1 The Balance Sheet 19

Accounting Liquidity 20

Debt versus Equity 21

Value versus Cost 21

2.2 The Income Statement 22

Generally Accepted Accounting Principles 22

Noncash Items 23

Time and Costs 24

2.3 Taxes 24

Corporate Tax Rates 24

Average versus Marginal Tax Rates 25

2.4 Net Working Capital 27

2.5 Cash Flow of the Firm 28

2.6 The Accounting Statement of Cash Flows 31

Cash Flow from Operating Activities 31

Cash Flow from Investing Activities 32

Cash Flow from Financing Activities 32

Summary and Conclusions 33

Closing Case: Cash Flows at East Coast Yachts 41

CHAPTER THREE Financial Statements Analysis and Financial Models 43 3.1 Financial Statements Analysis 43

Standardizing Statements 43

Common-Size Balance Sheets 44

Common-Size Income Statements 45

3.2 Ratio Analysis 46

Short-Term Solvency or Liquidity Measures 47

Long-Term Solvency Measures 49

Asset Management or Turnover Measures 50

Profitability Measures 52

Market Value Measures 54

3.3 The DuPont Identity 57

A Closer Look at ROE 57

Problems with Financial Statement Analysis 59

C O

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3.4 Financial Models 60

A Simple Financial Planning Model 60

The Percentage of Sales Approach 62

3.5 External Financing and Growth 66

EFN and Growth 67

Financial Policy and Growth 69

A Note about Sustainable Growth Rate Calculations 73

3.6 Some Caveats Regarding Financial Planning Models 73

Summary and Conclusions 74

Closing Case: Ratios and Financial Planning at East Coast Yachts 80

PART TWO VALUATION AND CAPITAL BUDGETING

CHAPTER FOUR

Discounted Cash Flow Valuation 83 4.1 Valuation: The One-Period Case 83

4.2 The Multiperiod Case 86

Future Value and Compounding 86

The Power of Compounding: A Digression 89

Present Value and Discounting 90

The Algebraic Formula 94

4.3 Compounding Periods 96

Distinction between Annual Percentage Rate and Effective Annual Rate 98

Compounding over Many Years 99

Continuous Compounding 99

4.4 Simplifications 101

Perpetuity 101

Growing Perpetuity 102

Annuity 104

Trick 1: A Delayed Annuity 106

Trick 2: Annuity Due 107

Trick 3: The Infrequent Annuity 108

Trick 4: Equating Present Value of Two Annuities 108

Growing Annuity 109

4.5 Loan Types and Loan Amortization 111

Pure Discount Loans 111

Interest-Only Loans 111

Amortized Loans 112

4.6 What Is a Firm Worth? 115

Summary and Conclusions 117

Closing Case: The MBA Decision 128

CHAPTER FIVE Interest Rates and Bond Valuation 130 5.1 Bonds and Bond Valuation 130

Bond Features and Prices 131

Bond Values and Yields 131

Interest Rate Risk 134

Finding the Yield to Maturity: More Trial and Error 136

5.2 More on Bond Features 137

Long-Term Debt: The Basics 139

The Indenture 140

Terms of a Bond 140

Security 141

Seniority 141

Repayment 141

The Call Provision 142

Protective Covenants 142

5.3 Bond Ratings 143

5.4 Some Different Types of Bonds 144

Government Bonds 144

Zero Coupon Bonds 145

Floating-Rate Bonds 146

Other Types of Bonds 146

5.5 Bond Markets 148

How Bonds Are Bought and Sold 148

Bond Price Reporting 148

A Note on Bond Price Quotes 151

5.6 Inflation and Interest Rates 152

Real versus Nominal Rates 152

The Fisher Effect 153

5.7 Determinants of Bond Yields 154

The Term Structure of Interest Rates 154

Bond Yields and the Yield Curve: Putting It All Together 155

Conclusion 157

Summary and Conclusions 158

Closing Case: Financing East Coast Yachts’ Expansion Plans with a Bond Issue 163

CHAPTER SIX

Stock Valuation 165 6.1 The Present Value of Common Stocks 165

Dividends versus Capital Gains 165

Valuation of Different Types of Stocks 166

Case 1 (Zero Growth) 167

Case 2 (Constant Growth) 167

Case 3 (Differential Growth) 168

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6.2 Estimates of Parameters in the Dividend Discount Model 170

Where Does g Come From? 170

Where Does R Come From? 171

A Healthy Sense of Skepticism 172

The No-Payout Firm 174

6.3 Comparables 174

Price-to-Earnings Ratio 174

Enterprise Value Ratios 176

6.4 Valuing Stocks Using Free Cash Flows 177

6.5 Some Features of Common and Preferred Stocks 179

Common Stock Features 179

Shareholder Rights 179

Proxy Voting 180

Classes of Stock 180

Other Rights 181

Dividends 181

Preferred Stock Features 182

Stated Value 182

Cumulative and Noncumulative Dividends 182

Is Preferred Stock Really Debt? 182

6.6 The Stock Markets 182

Dealers and Brokers 183

Organization of the NYSE 183

Members 183

Operations 184

Floor Activity 184

NASDAQ Operations 185

ECNs 187

Stock Market Reporting 188

Summary and Conclusions 188

Closing Case: Stock Valuation at Ragan Engines 194

CHAPTER SEVEN Net Present Value and Other Investment Rules 195 7.1 Why Use Net Present Value? 195

7.2 The Payback Period Method 197

Defining the Rule 197

Problems with the Payback Method 198

Problem 1: Timing of Cash Flows within the Payback Period 199

Problem 2: Payments after the Payback Period 199

Problem 3: Arbitrary Standard for Payback Period 199

Managerial Perspective 199

Summary of Payback 200

7.3 The Discounted Payback Period Method 200

7.4 The Average Accounting Return Method 201

Defining the Rule 201

Step 1: Determining Average Net Income 202

Step 2: Determining Average Investment 202

Step 3: Determining AAR 202

Analyzing the Average Accounting Return Method 202

7.5 The Internal Rate of Return 203

7.6 Problems with the IRR Approach 206

Definition of Independent and Mutually Exclusive Projects 206

Two General Problems Affecting Both Independent and Mutually Exclusive Projects 206

Problem 1: Investing or Financing? 206

Problem 2: Multiple Rates of Return 208

NPV Rule 208

Modified IRR 209

The Guarantee against Multiple IRRs 209

General Rules 210

Problems Specific to Mutually Exclusive Projects 210

The Scale Problem 210

The Timing Problem 212

Redeeming Qualities of IRR 214

A Test 214

7.7 The Profitability Index 215

Calculation of Profitability Index 215

Application of the Profitability Index 215

7.8 The Practice of Capital Budgeting 217

Summary and Conclusions 219

Closing Case: Bullock Gold Mining 229

CHAPTER EIGHT Making Capital Investment Decisions 230 8.1 Incremental Cash Flows 230

Cash Flows—Not Accounting Income 230

Sunk Costs 231

Opportunity Costs 231

Side Effects 232

Allocated Costs 232

8.2 The Baldwin Company: An Example 233

An Analysis of the Project 234

Investments 234

Income and Taxes 235

Salvage Value 236

Cash Flow 237

Net Present Value 237

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Which Set of Books? 237

A Note on Net Working Capital 237

A Note on Depreciation 238

Interest Expense 239

8.3 Inflation and Capital Budgeting 239

Discounting: Nominal or Real? 240

8.4 Alternative Definitions of Operating Cash Flow 242

The Bottom-Up Approach 243

The Top-Down Approach 243

The Tax Shield Approach 244

Conclusion 244

8.5 Some Special Cases of Discounted Cash Flow Analysis 244

Setting the Bid Price 244

Evaluating Equipment Options with Different Lives 246

The General Decision to Replace 248

Summary and Conclusions 250

Closing Case: Expansion at East Coast Yachts 260

Closing Case: Bethesda Mining Company 261

CHAPTER NINE Risk Analysis, Real Options, and Capital Budgeting 262 9.1 Decision Trees 262

Warning 264

9.2 Sensitivity Analysis, Scenario Analysis, and Break-Even Analysis 264

Sensitivity Analysis and Scenario Analysis 264

Revenues 265

Costs 266

Break-Even Analysis 268

Accounting Profit 268

Financial Breakeven 270

9.3 Monte Carlo Simulation 271

Step 1: Specify the Basic Model 271

Step 2: Specify a Distribution for Each Variable in the Model 271

Step 3: The Computer Draws One Outcome 273

Step 4: Repeat the Procedure 273

Step 5: Calculate NPV 273

9.4 Real Options 274

The Option to Expand 274

The Option to Abandon 275

Timing Options 277

Summary and Conclusions 278

Closing Case: Bunyan Lumber, LLC 285

PART THREE RISK AND RETURN

CHAPTER TEN Risk and Return: Lessons from Market History 287 10.1 Returns 287

Dollar Returns 287

Percentage Returns 289

10.2 Holding Period Returns 291

10.3 Return Statistics 297

10.4 Average Stock Returns and Risk-Free Returns 298

10.5 Risk Statistics 300

Variance 300

Normal Distribution and Its Implications for Standard Deviation 301

10.6 The U.S. Equity Risk Premium: Historical and International Perspectives 302

10.7 2008: A Year of Financial Crisis 305

10.8 More on Average Returns 306

Arithmetic versus Geometric Averages 306

Calculating Geometric Average Returns 307

Arithmetic Average Return or Geometric Average Return? 308

Summary and Conclusions 309

Closing Case: A Job at East Coast Yachts, Part 1 313

CHAPTER ELEVEN Return and Risk: The Capital Asset Pricing Model (CAPM) 316 11.1 Individual Securities 316

11.2 Expected Return, Variance, and Covariance 317

Expected Return and Variance 317

Covariance and Correlation 318

11.3 The Return and Risk for Portfolios 321

The Expected Return on a Portfolio 321

Variance and Standard Deviation of a Portfolio 322

The Variance 322

Standard Deviation of a Portfolio 322

The Diversification Effect 323

An Extension to Many Assets 324

11.4 The Efficient Set 324

The Two-Asset Case 324

The Efficient Set for Many Securities 328

11.5 Riskless Borrowing and Lending 329

The Optimal Portfolio 331

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11.6 Announcements, Surprises, and Expected Returns 333

Expected and Unexpected Returns 333

Announcements and News 334

11.7 Risk: Systematic and Unsystematic 335

Systematic and Unsystematic Risk 335

Systematic and Unsystematic Components of Return 335

11.8 Diversification and Portfolio Risk 336

The Effect of Diversification: Another Lesson from Market History 336

The Principle of Diversification 336

Diversification and Unsystematic Risk 338

Diversification and Systematic Risk 338

11.9 Market Equilibrium 339

Definition of the Market Equilibrium Portfolio 339

Definition of Risk When Investors Hold the Market Portfolio 339

The Formula for Beta 342

A Test 343

11.10 Relationship between Risk and Expected Return (CAPM) 344

Expected Return on Individual Security 344

Summary and Conclusions 347

Closing Case: A Job at East Coast Yachts, Part 2 355

CHAPTER TWELVE Risk, Cost of Capital, and Valuation 357 12.1 The Cost of Equity Capital 357

12.2 Estimating the Cost of Equity Capital with the CAPM 358

The Risk-Free Rate 360

Market Risk Premium 361

Method 1: Using Historical Data 361

Method 2: Using the Dividend Discount Model (DDM) 361

12.3 Estimation of Beta 362

Real-World Betas 362

Stability of Beta 363

Using an Industry Beta 364

12.4 Determinants of Beta 365

Cyclicality of Revenues 365

Operating Leverage 366

Financial Leverage and Beta 366

12.5 Dividend Discount Model 367

Comparison of DDM and CAPM 368

12.6 Cost of Capital for Divisions and Projects 369

12.7 Cost of Fixed Income Securities 370

Cost of Debt 370

Cost of Preferred Stock 371

12.8 The Weighted Average Cost of Capital 372

12.9 Valuation With RWACC 374

Project Evaluation and the RWACC 374

Firm Valuation with the RWACC 374

12.10 Estimating Eastman Chemical’s Cost of Capital 377

Eastman’s Cost of Equity 377

Eastman’s Cost of Debt 379

Eastman’s WACC 380

12.11 Flotation Costs and the Weighted Average Cost of Capital 380

The Basic Approach 380

Flotation Costs and NPV 381

Internal Equity and Flotation Costs 382

Summary and Conclusions 382

Closing Case: The Cost of Capital for Swan Motors 389

PART FOUR CAPITAL STRUCTURE AND DIVIDEND POLICY

CHAPTER THIRTEEN Efficient Capital Markets and Behavioral Challenges 390 13.1 A Description of Efficient Capital Markets 390

Foundations of Market Efficiency 392

Rationality 392

Independent Deviations from Rationality 392

Arbitrage 393

13.2 The Different Types of Efficiency 393

The Weak Form 393

The Semistrong and Strong Forms 393

Some Common Misconceptions about the Efficient Market Hypothesis 395

The Efficacy of Dart Throwing 395

Price Fluctuations 396

Stockholder Disinterest 396

13.3 The Evidence 396

The Weak Form 396

The Semistrong Form 398

Event Studies 398

The Record of Mutual Funds 400

The Strong Form 401

13.4 The Behavioral Challenge to Market Efficiency 401

Rationality 401

Independent Deviations from Rationality 402

Arbitrage 402

13.5 Empirical Challenges to Market Efficiency 403

13.6 Reviewing the Differences 408

Representativeness 409

Conservatism 409

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13.7 Implications for Corporate Finance 409

1. Accounting Choices, Financial Choices, and Market Efficiency 410

2. The Timing Decision 410

3. Speculation and Efficient Markets 412

4. Information in Market Prices 413

Summary and Conclusions 415

Closing Case: Your 401(K) Account at East Coast Yachts 421

CHAPTER FOURTEEN Capital Structure: Basic Concepts 423 14.1 The Capital Structure Question and the Pie Theory 423

14.2 Maximizing Firm Value versus Maximizing Stockholder Interests 424

14.3 Financial Leverage and Firm Value: An Example 426

Leverage and Returns to Shareholders 426

The Choice between Debt and Equity 428

A Key Assumption 430

14.4 Modigliani and Miller: Proposition II (No Taxes) 430

Risk to Equityholders Rises with Leverage 430

Proposition II: Required Return to Equityholders Rises with Leverage 431

MM: An Interpretation 436

14.5 Taxes 437

The Basic Insight 437

Present Value of the Tax Shield 439

Value of the Levered Firm 439

Expected Return and Leverage under Corporate Taxes 441

The Weighted Average Cost of Capital (RWACC) and Corpo- rate Taxes 442

Stock Price and Leverage under Corporate Taxes 442

Summary and Conclusions 444

Closing Case: Stephenson Real Estate Recapitalization 450

CHAPTER FIFTEEN Capital Structure: Limits to the Use of Debt 451 15.1 Costs of Financial Distress 451

Direct Bankruptcy Costs 452

Indirect Bankruptcy Costs 452

Agency Costs 453

Selfish Investment Strategy 1: Incentive to Take Large Risks 453

Selfish Investment Strategy 2: Incentive Toward Underinvestment 454

Selfish Investment Strategy 3: Milking the Property 455

Summary of Selfish Strategies 455

15.2 Can Costs of Debt be Reduced? 456

Protective Covenants 456

Consolidation of Debt 457

15.3 Integration of Tax Effects and Financial Distress Costs 457

Pie Again 457

15.4 Signaling 460

15.5 Shirking, Perquisites, and Bad Investments: A Note on Agency Cost of Equity 461

Effect of Agency Costs of Equity on Debt–Equity Financing 463

Free Cash Flow 463

15.6 The Pecking-Order Theory 464

Rules of the Pecking Order 465

Rule #1 Use Internal Financing 465

Rule #2 Issue Safe Securities First 466

Implications 466

15.7 How Firms Establish Capital Structure 467

15.8 A Quick Look at the Bankruptcy Process 472

Liquidation and Reorganization 472

Bankruptcy Liquidation 472

Bankruptcy Reorganization 473

Financial Management and the Bankruptcy Process 474

Agreements to Avoid Bankruptcy 475

Summary and Conclusions 475

Closing Case: Dugan Corporation’s Capital Budgeting 479

CHAPTER SIXTEEN Dividends and Other Payouts 480 16.1 Different Types of Dividends 480

16.2 Standard Method of Cash Dividend Payment 481

16.3 The Benchmark Case: An Illustration of the Irrelevance of Dividend Policy 483

Current Policy: Dividends Set Equal to Cash Flow 483

Alternative Policy: Initial Dividend Is Greater than Cash Flow 483

The Indifference Proposition 484

Homemade Dividends 485

A Test 486

Dividends and Investment Policy 486

16.4 Repurchase of Stock 487

Dividend versus Repurchase: Conceptual Example 488

Dividends versus Repurchases: Real-World Considerations 489

1. Flexibility 489

2. Executive Compensation 489

3. Offset to Dilution 489

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4. Undervaluation 489

5. Taxes 490

16.5 Personal Taxes, Issuance Costs, and Dividends 490

Firms without Sufficient Cash to Pay a Dividend 490

Firms with Sufficient Cash to Pay a Dividend 491

Summary on Personal Taxes 493

16.6 Real-World Factors Favoring A High-Dividend Policy 493

Desire for Current Income 493

Behavioral Finance 494

Agency Costs 495

Information Content of Dividends and Dividend Signaling 495

16.7 The Clientele Effect: A Resolution of Real-World Factors? 496

16.8 What We Know and Do Not Know about Dividend Policy 498

Corporate Dividends Are Substantial 498

Fewer Companies Pay Dividends 498

Corporations Smooth Dividends 499

Some Survey Evidence about Dividends 500

16.9 Putting It All Together 501

16.10 Stock Dividends and Stock Splits 503

Example of a Small Stock Dividend 504

Example of a Stock Split 504

Example of a Large Stock Dividend 505

Value of Stock Splits and Stock Dividends 505

The Benchmark Case 505

Popular Trading Range 505

Reverse Splits 506

Summary and Conclusions 507

Closing Case: Electronic Timing, Inc. 513

PART FIVE SPECIAL TOPICS

CHAPTER SEVENTEEN Options and Corporate Finance 515 17.1 Options 515

17.2 Call Options 516

The Value of a Call Option at Expiration 516

17.3 Put Options 517

The Value of a Put Option at Expiration 517

17.4 Selling Options 519

17.5 Option Quotes 520

17.6 Combinations of Options 521

17.7 Valuing Options 524

Bounding the Value of a Call 524

Lower Bound 524

Upper Bound 524

The Factors Determining Call Option Values 524

Exercise Price 524

Expiration Date 525

Stock Price 525

The Key Factor: The Variability of the Underlying Asset 526

The Interest Rate 527

A Quick Discussion of Factors Determining Put Option Values 527

17.8 An Option Pricing Formula 528

A Two-State Option Model 529

Determining the Delta 529

Determining the Amount of Borrowing 530

Risk-Neutral Valuation 530

The Black–Scholes Model 531

17.9 Stocks and Bonds as Options 535

The Firm Expressed in Terms of Call Options 536

The Stockholders 536

The Bondholders 537

The Firm Expressed in Terms of Put Options 537

The Stockholders 537

Cash Flow Is Less Than $800 538

Cash Flow Is Greater Than $800 538

The Bondholders 538

Cash Flow Is Less Than $800 538

Cash Flow Is Greater Than $800 538

A Resolution of the Two Views 538

A Note on Loan Guarantees 539

Summary and Conclusions 540

Closing Case: Exotic Cuisines Employee Stock Options 548

CHAPTER EIGHTEEN Short-Term Finance and Planning 550 18.1 Tracing Cash and Net Working Capital 551

18.2 The Operating Cycle and the Cash Cycle 552

Defining the Operating and Cash Cycles 552

The Operating Cycle 553

The Cash Cycle 553

The Operating Cycle and the Firm’s Organization Chart 554

Calculating the Operating and Cash Cycles 554

The Operating Cycle 556

The Cash Cycle 557

Interpreting the Cash Cycle 558

18.3 Some Aspects of Short-Term Financial Policy 558

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The Size of the Firm’s Investment in Current Assets 559

Alternative Financing Policies for Current Assets 560

An Ideal Case 560

Different Policies for Financing Current Assets 562

Which Financing Policy Is Best? 563

Current Assets and Liabilities in Practice 564

18.4 The Cash Budget 564

Sales and Cash Collections 565

Cash Outflows 566

The Cash Balance 566

18.5 Short-Term Borrowing 567

Unsecured Loans 567

Compensating Balances 568

Cost of a Compensating Balance 568

Letters of Credit 568

Secured Loans 569

Accounts Receivable Financing 569

Inventory Loans 570

Commercial Paper 570

Trade Credit 570

Understanding Trade Credit Terms 570

Cash Discounts 570

18.6 A Short-Term Financial Plan 571

Summary and Conclusions 572

Closing Case: Keafer Manufacturing Working Capital Management 581

CHAPTER NINETEEN Raising Capital 582 19.1 Early-Stage Financing and Venture Capital 582

Venture Capital 583

Stages of Financing 584

Some Venture Capital Realities 585

Crowdfunding 586

19.2 Selling Securities to the Public: The Basic Procedure 586

19.3 Alternative Issue Methods 587

19.4 Underwriters 589

Choosing an Underwriter 589

Types of Underwriting 590

Firm Commitment Underwriting 590

Best Efforts Underwriting 590

Dutch Auction Underwriting 590

The Green Shoe Provision 591

The Aftermarket 591

Lockup Agreements 591

The Quiet Period 592

19.5 IPOs and Underpricing 592

Evidence on Underpricing 593

IPO Underpricing: The 1999–2000 Experience 594

Why Does Underpricing Exist? 594

The Partial Adjustment Phenomenon 598

19.6 What CFOs Say About the IPO Process 599

19.7 SEOs and the Value of the Firm 599

19.8 The Cost of Issuing Securities 600

19.9 Rights 603

The Mechanics of a Rights Offering 605

Subscription Price 605

Number of Rights Needed to Purchase a Share 606

Effect of Rights Offering on Price of Stock 606

Effects on Shareholders 608

The Underwriting Arrangements 608

The Rights Puzzle 608

19.10 Dilution 609

Dilution of Proportionate Ownership 609

Dilution of Value: Book versus Market Values 609

A Misconception 610

The Correct Arguments 610

19.11 Issuing Long-Term Debt 611

19.12 Shelf Registration 611

Summary and Conclusions 612

Closing Case: East Coast Yachts Goes Public 617

CHAPTER TWENTY International Corporate Finance 618 20.1 Terminology 619

20.2 Foreign Exchange Markets and Exchange Rates 620

Exchange Rates 621

Exchange Rate Quotations 621

Cross-Rates and Triangle Arbitrage 622

Types of Transactions 623

20.3 Purchasing Power Parity 624

Absolute Purchasing Power Parity 624

Relative Purchasing Power Parity 626

The Basic Idea 626

The Result 627

Currency Appreciation and Depreciation 628

20.4 Interest Rate Parity, Unbiased Forward Rates, and the International Fisher Effect 628

Covered Interest Arbitrage 628

Interest Rate Parity 629

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Forward Rates and Future Spot Rates 630

Putting It All Together 631

Uncovered Interest Parity 631

The International Fisher Effect 631

20.5 International Capital Budgeting 632

Method 1: The Home Currency Approach 633

Method 2: The Foreign Currency Approach 633

Unremitted Cash Flows 634

20.6 Exchange Rate Risk 634

Short-Run Exposure 634

Long-Run Exposure 635

Translation Exposure 636

Managing Exchange Rate Risk 637

20.7 Political Risk 637

Summary and Conclusions 638

Closing Case: East Coast Yachts Goes International 643

CHAPTER TWENTY ONE Mergers and Acquisitions (web only)

APPENDIX A Mathematical Tables 644

APPENDIX B Solutions to Selected End-of-Chapter Problems 653

APPENDIX C Using the HP 10B and TI BA II Plus Financial Calculators 658 NAME INDEX 662

COMPANY INDEX 664

SUBJECT INDEX 666

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LIST OF BOXES xxxi

L IS

T O

F B

O X

E S FINANCE MATTERS

CHAPTER 1 Sarbanes-Oxley 15

CHAPTER 2 What is Warren Buffett’s Tax Rate? 27

CHAPTER 3 What’s in a Ratio? 60

CHAPTER 4 Jackpot! 96

CHAPTER 5 Beauty Is in the Eye of the Bondholder 147

CHAPTER 6 How Fast Is Too Fast? 173

The Wild, Wild West of Stock Trading 186

CHAPTER 9 When Things Go Wrong . . . 265

CHAPTER 11 Beta, Beta, Who’s Got the Beta? 343

CHAPTER 12 The Cost of Capital, Texas Style 378

CHAPTER 13 Can Stock Market Investors Add and Subtract? 405

CHAPTER 16 Stock Buybacks: No End in Sight 492

CHAPTER 18 A Look at Operating and Cash Cycles 555

CHAPTER 19 IPO Underpricing around the World 596

Anatomy of an IPO 603

CHAPTER 20 McPricing 626

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CHAPTER 1 Introduction to Corporate Finance 1

1 OPENING CASE

Introduction to Corporate Finance George Zimmer, founder of The Men’s Wearhouse, for years ap peared in television ads prom-

ising “You’re going to like the way you look. I guarantee it.” But, in mid-2013, Zimmer evi-

dently didn’t look so good to the company’s board of directors, which abruptly fired him. It

was reported that Zimmer had a series of dis agreements with the board, including a desire to

take the company private. Evidently, Zimmer’s ideas did not “suit” the board. Of course, you

can’t keep a good entrepreneur down: After Zimmer was fired, he started zTailors, a market-

place for customers to contact tailors and have them visit the customer’s home, as well as

Generation Tux, an online tuxedo rental company with home delivery. 

Understanding Zimmer’s journey from the founder of a clothing store that used a cigar

box as a cash register, to corporate execu tive, and finally to ex-employee takes us into issues

involving the corporate form of organization, corporate goals, and corporate con trol, all of

which we discuss in this chapter. You’re going to learn a lot if you read it. We guarantee it.

Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.

1.1 WHAT IS CORPORATE FINANCE? Suppose you decide to start a firm to make tennis balls. To do this you hire managers to buy raw materials, and you assemble a workforce that will produce and sell finished ten- nis balls. In the language of finance, you make an investment in assets such as inventory, machinery, land, and labor. The amount of cash you invest in assets must be matched by an equal amount of cash raised by financing. When you begin to sell tennis balls, your firm will generate cash. This is the basis of value creation. The purpose of the firm is to create value for you, the owner. The value is reflected in the framework of the simple balance sheet model of the firm.

The Balance Sheet Model of the Firm Suppose we take a financial snapshot of the firm and its activities at a single point in time. Figure 1.1 shows a graphic conceptualization of the balance sheet, and it will help intro- duce you to corporate finance.

The assets of the firm are on the left side of the balance sheet. These assets can be thought of as current and fixed. Fixed assets are those that will last a long time, such as buildings. Some fixed assets are tangible, such as machinery and equipment. Other fixed assets are intangible, such as patents and trademarks. The other category of assets, current assets, comprises those that have short lives, such as inventory. The tennis balls that your firm has made, but has not yet sold, are part of its inventory. Unless you have overpro- duced, they will leave the firm shortly.

Before a company can invest in an asset, it must obtain financing, which means that it must raise the money to pay for the investment. The forms of financing are represented on

PART ONE: OVERVIEW

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the right side of the balance sheet. A firm will issue (sell) pieces of paper called debt (loan agreements) or equity shares (stock certificates). Just as assets are classified as long-lived or short-lived, so too are liabilities. A short-term debt is called a current liability. Short- term debt represents loans and other obligations that must be repaid within one year. Long- term debt is debt that does not have to be repaid within one year. Shareholders’ equity represents the difference between the value of the assets and the debt of the firm. In this sense, it is a residual claim on the firm’s assets.

From the balance sheet model of the firm, it is easy to see why finance can be thought of as the study of the following three questions:

1. In what long-lived assets should the firm invest? This question concerns the left side of the balance sheet. Of course the types and proportions of assets the firm needs tend to be set by the nature of the business. We use the term capital budgeting to describe the process of making and managing expenditures on long-lived assets.

2. How can the firm raise cash for required capital expenditures? This question concerns the right side of the balance sheet. The answer to this question involves the firm’s capital structure, which represents the proportions of the firm’s financing from current liabilities, long-term debt, and equity.

3. How should short-term operating cash flows be managed? This question con- cerns the upper portion of the balance sheet. There is often a mismatch between the timing of cash inflows and cash outflows during operating activities.

Furthermore, the amount and timing of operating cash flows are not known with cer- tainty. Financial managers must attempt to manage the gaps in cash flow.

From a balance sheet perspective, short-term management of cash flow is associated with a firm’s net working capital. Net working capital is defined as current assets minus current liabilities. From a financial perspective, short-term cash flow problems come from the mismatching of cash inflows and outflows. This is the subject of short-term finance.

FIGURE 1.1 The Balance Sheet Model of the Firm

Long-term debt

Current assets

Fixed assets

1. Tangible fixed assets 2. Intangible fixed assets

Net working capital

Current liabilities

Shareholders’ equity

Total Value of Assets Total Value of the Firm to Investors=

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The Financial Manager In large firms, the finance activity is usually associated with a top officer of the firm, such as the vice president and chief financial officer, and some lesser officers. Figure 1.2 depicts a general organizational structure emphasizing the finance activity within the firm. Reporting to the chief financial officer are the treasurer and the controller. The treasurer is responsible for handling cash flows, managing capital expenditure decisions, and making financial plans. The controller handles the accounting function, which includes taxes, cost and financial accounting, and information systems.

1.2 THE CORPORATE FIRM The firm is a way of organizing the economic activity of many individuals. A basic prob- lem of the firm is how to raise cash. The corporate form of business—that is, organizing the firm as a corporation—is the standard method for solving problems encountered in raising large amounts of cash. However, businesses can take other forms. In this section we

For current issues facing CFOs, see www.cfo.com.

FIGURE 1.2 Hypothetical Organization ChartBoard of Directors

Chairman of the Board and Chief Executive O�cer (CEO)

President and Chief Operations O�cer (COO)

Vice President and Chief Financial O�cer (CFO)

Treasurer Controller

Cash Manager Credit Manager Tax Manager Cost Accounting

Manager

Information Systems Manager

Financial Accounting

Manager

Financial Planning

Capital Expenditures

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consider the three basic legal forms of organizing firms, and we see how firms go about the task of raising large amounts of money under each form.

The Sole Proprietorship A sole proprietorship is a business owned by one person. Suppose you decide to start a business to produce mousetraps. Going into business is simple: You announce to all who will listen, “Today, I am going to build a better mousetrap.”

Most large cities require that you obtain a business license. Afterward, you can begin to hire as many people as you need and borrow whatever money you need. At year-end all the profits or the losses will be yours.

Here are some factors that are important in considering a sole proprietorship:

1. The sole proprietorship is the cheapest business to form. No formal charter is required, and few government regulations must be satisfied for most industries.

2. A sole proprietorship pays no corporate income taxes. All profits of the business are taxed as individual income.

3. The sole proprietorship has unlimited liability for business debts and obligations. No distinction is made between personal and business assets.

4. The life of the sole proprietorship is limited by the life of the sole proprietor. 5. Because the only money invested in the firm is the proprietor’s, the equity

money that can be raised by the sole proprietor is limited to the proprietor’s per- sonal wealth.

The Partnership Any two or more people can get together and form a partnership. Partnerships fall into two categories: (1) general partnerships and (2) limited partnerships.

In a general partnership all partners agree to provide some fraction of the work and cash and to share the profits and losses. Each partner is liable for all of the debts of the partner- ship. A partnership agreement specifies the nature of the arrangement. The partnership agreement may be an oral agreement or a formal document setting forth the understanding.

Limited partnerships permit the liability of some of the partners to be limited to the amount of cash each has contributed to the partnership. Limited partnerships usually require that (1) at least one partner be a general partner and (2) the limited partners do not participate in managing the business. Here are some things that are important when considering a partnership:

1. Partnerships are usually inexpensive and easy to form. Written documents are required in complicated arrangements. Business licenses and filing fees may be necessary.

2. General partners have unlimited liability for all debts. The liability of limited partners is usually limited to the contribution each has made to the partnership. If one general partner is unable to meet his or her commitment, the shortfall must be made up by the other general partners.

3. The general partnership is terminated when a general partner dies or withdraws (but this is not so for a limited partner). It is difficult for a partnership to transfer ownership without dissolving. Usually all general partners must agree. However, limited partners may sell their interest in a business.

4. It is difficult for a partnership to raise large amounts of cash. Equity contribu- tions are usually limited to a partner’s ability and desire to contribute to the part- nership. Many companies, such as Apple Computer, start life as a proprietorship or partnership, but at some point they choose to convert to corporate form.

5. Income from a partnership is taxed as personal income to the partners.

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6. Management control resides with the general partners. Usually a majority vote is required on important matters, such as the amount of profit to be retained in the business.

It is difficult for large business organizations to exist as sole proprietorships or partner- ships. The main advantage to a sole proprietorship or partnership is the cost of getting started. Afterward, the disadvantages, which may become severe, are (1) unlimited liabil- ity, (2) limited life of the enterprise, and (3) difficulty of transferring ownership. These three disadvantages lead to (4) difficulty in raising cash.

The Corporation Of the forms of business enterprises, the corporation is by far the most important. It is a distinct legal entity. As such, a corporation can have a name and enjoy many of the legal powers of natural persons. For example, corporations can acquire and exchange property. Corporations can enter contracts and may sue and be sued. For jurisdictional purposes the corporation is a citizen of its state of incorporation (it cannot vote, however).

Starting a corporation is more complicated than starting a proprietorship or partnership. The incorporators must prepare articles of incorporation and a set of bylaws. The articles of incorporation must include the following:

1. Name of the corporation. 2. Intended life of the corporation (it may be forever). 3. Business purpose. 4. Number of shares of stock that the corporation is authorized to issue, with a

statement of limitations and rights of different classes of shares. 5. Nature of the rights granted to shareholders. 6. Number of members of the initial board of directors.

The bylaws are the rules to be used by the corporation to regulate its own existence, and they concern its shareholders, directors, and officers. Bylaws range from the briefest possible statement of rules for the corporation’s management to hundreds of pages of text.

In its simplest form, the corporation comprises three sets of distinct interests: the share- holders (the owners), the directors, and the corporation officers (the top management). Traditionally, the shareholders control the corporation’s direction, policies, and activities. The shareholders elect a board of directors, who in turn select top management. Members of top management serve as corporate officers and manage the operations of the corpora- tion in the best interest of the shareholders. In closely held corporations with few share- holders, there may be a large overlap among the shareholders, the directors, and the top management. However, in larger corporations, the shareholders, directors, and the top management are likely to be distinct groups.

The potential separation of ownership from management gives the corporation several advantages over proprietorships and partnerships:

1. Because ownership in a corporation is represented by shares of stock, ownership can be readily transferred to new owners. Because the corporation exists inde- pendently of those who own its shares, there is no limit to the transferability of shares as there is in partnerships.

2. The corporation has unlimited life. Because the corporation is separate from its owners, the death or withdrawal of an owner does not affect the corporation’s legal existence. The corporation can continue on after the original owners have withdrawn.

3. The shareholders’ liability is limited to the amount invested in the owner- ship shares. For example, if a shareholder purchased $1,000 in shares of a

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corporation, the potential loss would be $1,000. In a partnership, a general part- ner with a $1,000 contribution could lose the $1,000 plus any other indebtedness of the partnership.

Limited liability, ease of ownership transfer, and perpetual succession are the major advantages of the corporate form of business organization. These give the corporation an enhanced ability to raise cash.

There is, however, one great disadvantage to incorporation. The federal government taxes corporate income (the states do as well). This tax is in addition to the personal income tax that shareholders pay on dividend income they receive. This is double taxation for shareholders when compared to taxation on proprietorships and partnerships. Table 1.1 summarizes our discussion of partnerships and corporations.

Today all 50 states have enacted laws allowing for the creation of a relatively new form of business organization, the limited liability company (LLC). The goal of this entity is to operate and be taxed like a partnership but retain limited liability for owners, so an LLC is essentially a hybrid of partnership and corporation. Although states have differing definitions for LLCs, the more important scorekeeper is the Internal Revenue Service (IRS). The IRS will consider an LLC a corporation, thereby subjecting it to double taxation, unless it meets certain specific criteria. In essence, an LLC cannot be too corporation-like, or it will be treated as one by the IRS. LLCs have become common. For example, Goldman, Sachs and Co., one of Wall Street’s last remaining partnerships, decided to convert from a private partnership to an LLC (it later “went public,” becom- ing a publicly held corporation). Large accounting firms and law firms by the score have converted to LLCs.

A Corporation by Another Name . . . The corporate form of organization has many variations around the world. The exact laws and regulations differ from country to country, of course, but the essential features of pub- lic ownership and limited liability remain. These firms are often called joint stock compa- nies, public limited companies, or limited liability companies, depending on the specific nature of the firm and the country of origin.

Table 1.2 gives the names of a few well-known international corporations, their coun- tries of origin, and a translation of the abbreviation that follows each company name.

To find out more about LLCs, visit www.incorporate.com.

CORPORATION PARTNERSHIP

Liquidity and marketability

Shares can be exchanged without termination of the corporation. Common stock can be listed on a stock exchange.

Units are subject to substantial restrictions on transferability. There is usually no established trading market for partnership units.

Voting rights Usually each share of common stock entitles the holder to one vote per share on matters requiring a vote and on the election of the directors. Directors determine top management.

Some voting rights by limited partners. However, general partners have exclusive control and management of operations.

Taxation Corporations have double taxation: Corporate income is taxable, and dividends to shareholders are also taxable.

Partnerships are not taxable. Partners pay personal taxes on partnership profits.

Reinvestment and dividend payout

Corporations have broad latitude on dividend payout decisions.

Partnerships are generally prohibited from reinvesting partnership profits. All profits are distributed to partners.

Liability Shareholders are not personally liable for obligations of the corporation.

Limited partners are not liable for obligations of partner- ships. General partners may have unlimited liability.

Continuity of existence

Corporations may have a perpetual life. Partnerships have limited life.

TABLE 1.1 A Comparison of Partnerships and Corporations

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1.3 THE IMPORTANCE OF CASH FLOWS The most important job of a financial manager is to create value from the firm’s capital budgeting, financing, and net working capital activities. How do financial managers create value? The answer is that the firm should create more cash flow than it uses.

The cash flows paid to bondholders and stockholders of the firm should be greater than the cash flows put into the firm by the bondholders and stockholders. To see how this is done, we can trace the cash flows from the firm to the financial markets and back again.

The interplay of the firm’s activities with the financial markets is illustrated in Figure 1.3. The arrows in Figure 1.3 trace cash flow from the firm to the financial markets and back again. Suppose we begin with the firm’s financing activities. To raise money, the firm sells debt and equity shares to investors in the financial markets. This results in cash flows from the financial markets to the firm (A). This cash is invested in the investment

TYPE OF COMPANY

COMPANY COUNTRY OF ORIGIN IN ORIGINAL LANGUAGE INTERPRETATION

Bayerische Motoren Werke (BMW) AG Germany Aktiengesellschaft Corporation

Rolls-Royce PLC United Kingdom Public limited company Public limited company

Shell UK Ltd. United Kingdom Limited Corporation

Unilever NV Netherlands Naamloze Vennootschap Joint stock company

Fiat SpA Italy Società per Azioni Joint stock company

Volvo AB Sweden Aktiebolag Joint stock company

Peugeot SA France Société Anonyme Joint stock company

TABLE 1.2 International Corporations

FIGURE 1.3 Cash Flows between the Firm and the Financial Markets

Total Value of Assets

Firm invests in assets

(B)

Current assets Fixed assets

Cash for securities issued by the firm (A)

Retained cash flows (E )

Government (D)

Cash flow from firm (C)

Dividends and debt payments (F )

Financial markets

Short-term debt Long-term debt Equity shares

Total Value of the Firm to Investors in

the Financial Markets

Taxes

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activities (assets) of the firm (B) by the firm’s management. The cash generated by the firm (C) is paid to shareholders and bondholders (F). The shareholders receive cash in the form of dividends; the bondholders who lent funds to the firm receive interest and, when the initial loan is repaid, principal. Not all of the firm’s cash is paid out. Some is retained (E), and some is paid to the government as taxes (D).

Over time, if the cash paid to shareholders and bondholders (F) is greater than the cash raised in the financial markets (A), value will be created.

IDENTIFICATION OF CASH FLOWS Unfortunately, it is sometimes not easy to observe cash flows directly. Much of the information we obtain is in the form of accounting state- ments, and much of the work of financial analysis is to extract cash flow information from accounting statements. The following example illustrates how this is done.

E X

A M

P L

E  

1. 1

The Midland Company refines and trades gold. At the end of the year, it sold 2,500 ounces of gold for $1 million. The company had acquired the gold for $900,000 at the beginning of the year. The company paid cash for the gold when it was purchased. Unfortunately it has yet to collect from the customer to whom the gold was sold. The following is a standard accounting of Midland’s financial circumstances at year-end:

By generally accepted accounting principles (GAAP), the sale is recorded even though the customer has yet to pay. It is assumed that the customer will pay soon. From the accounting perspective, Midland seems to be profitable. However, the perspective of corporate finance is different. It focuses on cash flows:

The perspective of corporate finance is interested in whether cash flows are being created by the gold trading operations of Midland. Value creation depends on cash flows. For Midland, value creation depends on whether and when it actually receives $1 million.

Accounting Profit versus Cash Flows

THE MIDLAND COMPANY Account ing View

Income Statement Year Ended December 31

Sales $1,000,000

−Costs    −900,000 Profit $   100,000

THE MIDLAND COMPANY F inancia l V iew

Income Statement Year Ended December 31

Cash inflow $                0

Cash outflow   −900,000 $−900,000

TIMING OF CASH FLOWS The value of an investment made by a firm depends on the tim- ing of cash flows. One of the most important principles of finance is that individuals prefer to receive cash flows earlier rather than later. One dollar received today is worth more than one dollar received next year.

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RISK OF CASH FLOWS The firm must consider risk. The amount and timing of cash flows are not usually known with certainty. Most investors have an aversion to risk.

E X

A M

P L

E  

1. 2

The Midland Company is attempting to choose between two proposals for new products. Both proposals will provide additional cash flows over a four-year period and will initially cost $10,000. The cash flows from the proposals are as follows:

At first it appears that new Product A would be best. However, the cash flows from Product B come ear- lier than those of A. Without more information, we cannot decide which set of cash flows would create the most value for the bondholders and shareholders. It depends on whether the value of getting cash from B up front outweighs the extra total cash from A. Bond and stock prices reflect this preference for earlier cash, and we will see how to use them to decide between A and B.

Cash Flow Timing

YEAR NEW PRODUCT A NEW PRODUCT B

1 $          0 $ 4,000

2             0    4,000

3             0    4,000

4   20,000    4,000

Total $20,000 $16,000 

E X

A M

P L

E  

1. 3

The Midland Company is considering expanding operations overseas. It is evaluating Europe and Japan as possible sites. Europe is considered to be relatively safe, whereas operating in Japan is seen as very risky. In both cases the company would close down operations after one year.

After doing a complete financial analysis, Midland has come up with the following cash flows of the alternative plans for expansion under three scenarios—pessimistic, most likely, and optimistic:

If we ignore the pessimistic scenario, perhaps Japan is the best alternative. When we take the pessimis- tic scenario into account, the choice is unclear. Japan appears to be riskier, but it also offers a higher expected level of cash flow. What is risk and how can it be defined? We must try to answer this impor- tant question. Corporate finance cannot avoid coping with risky alternatives, and much of our book is devoted to developing methods for evaluating risky opportunities.

Risk

PESSIMISTIC MOST L IKELY OPTIMISTIC

Europe $75,000   $100,000  $125,000  

Japan              0     150,000    200,000  

1.4 THE GOAL OF FINANCIAL MANAGEMENT Assuming that we restrict our discussion to for-profit businesses, the goal of financial management is to make money or add value for the owners. This goal is a little vague, of course, so we examine some different ways of formulating it to come up with a more precise definition. Such a definition is important because it leads to an objective basis for making and evaluating financial decisions.

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Possible Goals If we were to consider possible financial goals, we might come up with some ideas like the following: ∙ Survive. ∙ Avoid financial distress and bankruptcy. ∙ Beat the competition. ∙ Maximize sales or market share. ∙ Minimize costs. ∙ Maximize profits. ∙ Maintain steady earnings growth.

These are only a few of the goals we could list. Furthermore, each of these possibilities presents problems as a goal for the financial manager.

For example, it’s easy to increase market share or unit sales: All we have to do is lower our prices or relax our credit terms. Similarly, we can always cut costs by doing away with things such as research and development. We can avoid bankruptcy by never borrowing any money or never taking any risks, and so on. It’s not clear that any of these actions are in the stockholders’ best interests.

Profit maximization would probably be the most commonly cited goal, but even this is not a precise objective. Do we mean profits this year? If so, then we should note that actions such as deferring maintenance, letting inventories run down, and taking other short-run cost-cutting measures will tend to increase profits now, but these activities aren’t necessarily desirable.

The goal of maximizing profits may refer to some sort of “long-run” or “average” prof- its, but it’s still unclear exactly what this means. First, do we mean something like account- ing net income or earnings per share? As we will see in more detail in the next chapter, these accounting numbers may have little to do with what is good or bad for the firm. We are actually more interested in cash flows. Second, what do we mean by the long run? As a famous economist once remarked, in the long run, we’re all dead! More to the point, this goal doesn’t tell us what the appropriate trade-off is between current and future profits.

The goals we’ve listed here are all different, but they tend to fall into two classes. The first of these relates to profitability. The goals involving sales, market share, and cost control all relate, at least potentially, to different ways of earning or increasing profits. The goals in the second group, involving bankruptcy avoidance, stability, and safety, relate in some way to controlling risk. Unfortunately, these two types of goals are somewhat contradictory. The pursuit of profit normally involves some element of risk, so it isn’t really possible to maxi- mize both safety and profit. What we need, therefore, is a goal that encompasses both factors.

The Goal of Financial Management The financial manager in a corporation makes decisions for the stockholders of the firm. So, instead of listing possible goals for the financial manager, we really need to answer a more fundamental question: From the stockholders’ point of view, what is a good financial management decision?

If we assume that stockholders buy stock because they seek to gain financially, then the answer is obvious: Good decisions increase the value of the stock, and poor decisions decrease the value of the stock.

From our observations, it follows that the financial manager acts in the shareholders’ best interests by making decisions that increase the value of the stock. The appropriate goal for the financial manager can thus be stated quite easily:

The goal of financial management is to maximize the current value per share of the existing stock.

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The goal of maximizing the value of the stock avoids the problems associated with the different goals we listed earlier. There is no ambiguity in the criterion, and there is no short-run versus long-run issue. We explicitly mean that our goal is to maximize the cur- rent stock value.

If this goal seems a little strong or one-dimensional to you, keep in mind that the stockhold- ers in a firm are residual owners. By this we mean that they are entitled only to what is left after employees, suppliers, and creditors (and everyone else with legitimate claims) are paid their due. If any of these groups go unpaid, the stockholders get nothing. So if the stockholders are winning in the sense that the leftover, residual portion is growing, it must be true that everyone else is winning also. In other words, managers should make decisions that they believe will achieve the highest firm value because by doing so shareholders will benefit the most.

Because the goal of financial management is to maximize the value of the stock, we need to learn how to identify investments and financing arrangements that favorably impact the value of the stock. This is precisely what we will be studying. In the previous section we emphasized the importance of cash flows in value creation. In fact, we could have defined corporate finance as the study of the relationship between business decisions, cash flows, and the value of the stock in the business.

A More General Goal If our goal is to maximize the value of the stock, as stated in the preceding section, an obvi- ous question comes up: What is the appropriate goal when the firm has no traded stock? Corporations are certainly not the only type of business; and the stock in many corporations rarely changes hands, so it’s difficult to say what the value per share is at any particular time.

As long as we are considering for-profit businesses, only a slight modification is needed. The total value of the stock in a corporation is equal to the value of the owners’ equity. Therefore, a more general way of stating our goal is

Maximize the value of the existing owners’ equity.

With this in mind, we don’t care whether the business is a proprietorship, a partnership, or a corporation. For each of these, good financial decisions increase the value of the own- ers’ equity, and poor financial decisions decrease it. In fact, although we choose to focus on corporations in the chapters ahead, the principles we develop apply to all forms of busi- ness. Many of them even apply to the not-for-profit sector.

Finally, our goal does not imply that the financial manager should take illegal or unethi- cal actions in the hope of increasing the value of the equity in the firm. What we mean is that the financial manager best serves the owners of the business by identifying goods and ser- vices that add value to the firm because they are desired and valued in the free marketplace.

1.5 THE AGENCY PROBLEM AND CONTROL OF THE CORPORATION

The processes, policies, laws, and institutions that direct a company’s actions are all included under the broad category of corporate governance. Corporate governance can also include the relationships among various stakeholders including shareholders, manage- ment, employees, the board of directors, suppliers, and the community at large, among others. As such, corporate governance is a wide-ranging topic.

We’ve seen that the financial manager acts in the best interests of the stockholders by taking actions that increase the value of the firm and thus the stock. However, in large cor- porations, ownership can be spread over a huge number of stockholders. This dispersion of ownership arguably means that stockholders cannot directly control the firm and that management effectively controls the firm. In this case, will management necessarily act in

Business ethics are considered at business- ethics.com.

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the best interests of the stockholders? Put another way, might not management pursue its own goals at the stockholders’ expense?

Corporate governance varies quite a bit around the world. For example, in most coun- tries other than the U.S. and the U.K., publicly traded companies are usually controlled by one or more large shareholders. Moreover, in countries with limited shareholder pro- tection, when compared to countries with strong shareholder protection like the U.S. and the U.K., large shareholders may have a greater opportunity to take advantage of minor- ity shareholders. Research shows that a country’s investor protection framework is important to understanding a firm’s cash holdings and dividend payouts. For example, studies find that shareholders do not highly value cash holdings in firms in countries with low investor protection when compared to firms in the U.S. where investor protec- tion is high.1

In the basic corporate governance setup, the shareholders elect the board of directors who in turn appoint the top corporate managers, such as the CEO. The CEO is usually a member of the board of directors. One aspect of corporate governance that has received attention recently concerns the chair of a firm’s board of directors. In a large number of U.S. corporations, the CEO and the board chair are the same person. An argument can be made that combining the CEO and board chair positions can contribute to poor corporate governance. When comparing corporate governance in the U.S. and the U.K., an edge is often given to the U.K., partly because over 90 percent of U.K. companies are chaired by outside directors rather than the CEO.2 This is a contentious issue confronting many U.S. corporations. For example, in 2015, 29 percent of the S&P 500 companies had named an independent outsider as board chair, up from only 10 percent eight years earlier.

Agency Relationships The relationship between stockholders and management is called an agency relationship. Such a relationship exists whenever someone (the principal) hires another (the agent) to represent his or her interests. For example, you might hire someone (an agent) to sell a car that you own while you are away at school. In all such relationships there is a possibility of a conflict of interest between the principal and the agent. Such a conflict is called an agency problem.

Suppose you hire someone to sell your car and you agree to pay that person a flat fee when he or she sells the car. The agent’s incentive in this case is to make the sale, not nec- essarily to get you the best price. If you offer a commission of, say, 10 percent of the sales price instead of a flat fee, then this problem might not exist. This example illustrates that the way in which an agent is compensated is one factor that affects agency problems.

Management Goals To see how management and stockholder interests might differ, imagine that a firm is con- sidering a new investment. The new investment is expected to favorably impact the share value, but it is also a relatively risky venture. The owners of the firm will wish to take the investment (because the stock value will rise), but management may not because there is the possibility that things will turn out badly and management jobs will be lost. If manage- ment does not take the investment, then the stockholders may lose a valuable opportunity. This is one example of an agency cost.

1 See, for example, “Investor Protection and Corporate Valuation,” by Rafael La Porta, Florencio Lopez-de-Silanes, Andrei Shleifer, and Robert Vishny, Journal of Finance 57 (2002), pp. 1147–1170; and “Cash Holdings, Dividend Policy, and Corporate Governance: A Cross-Country Analysis,” by Lee Pinkowitz, René M. Stulz, and Rohan Williamson, Journal of Applied Corporate Finance, Vol. 19, No. 1 (2007), pp. 81–87. 2 “U.S. Corporate Governance: Accomplishments and Failings, a Discussion with Michael Jensen and Robert Monks” (moderated by Ralph Walkling), Journal of Applied Corporate Finance, Vol. 20, No. 1 (Winter 2008), pp. 28–46.

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More generally, the term agency costs refers to the costs of the conflict of interest between stockholders and management. These costs can be indirect or direct. An indirect agency cost is a lost opportunity, such as the one we have just described.

Direct agency costs come in two forms. The first type is a corporate expenditure that benefits management but costs the stockholders. Perhaps the purchase of a luxurious and unneeded corporate jet would fall under this heading. The second type of direct agency cost is an expense that arises from the need to monitor management actions. Paying outside auditors to assess the accuracy of financial statement information could be one example.

It is sometimes argued that, left to themselves, managers would tend to maximize the amount of resources over which they have control or, more generally, corporate power or wealth. This goal could lead to an overemphasis on corporate size or growth. For example, cases in which management is accused of overpaying to buy up another company just to increase the size of the business or to demonstrate corporate power are not uncommon. Obviously, if overpayment does take place, such a purchase does not benefit the stockhold- ers of the purchasing company.

Our discussion indicates that management may tend to overemphasize organizational survival to protect job security. Also, management may dislike outside interference, so independence and corporate self-sufficiency may be important goals.

Do Managers Act in the Stockholders’ Interests? Whether managers will, in fact, act in the best interests of stockholders depends on two factors. First, how closely are management goals aligned with stockholder goals? This question relates, at least in part, to the way managers are compensated. Second, can man- agers be replaced if they do not pursue stockholder goals? This issue relates to control of the firm. As we will discuss, there are a number of reasons to think that, even in the largest firms, management has a significant incentive to act in the interests of stockholders.

MANAGERIAL COMPENSATION Management will frequently have a significant economic incentive to increase share value for two reasons. First, managerial compensation, par- ticularly at the top, is usually tied to financial performance in general and often to share value in particular. For example, managers are frequently given the option to buy stock at a bargain price. The more the stock is worth, the more valuable is this option. In fact, options are often used to motivate employees of all types, not just top management. Many firms also give managers an ownership stake in the company by granting stock or stock options. In 2015, the total compensation of David Zaslav, CEO of Discovery Communications, was $156.1 million. His base salary and cash bonus was $11 million with stock and options of $145.1 million. Although there are many critics of the high level of CEO compensation, from the stockholders’ point of view, sensitivity of compensation to firm performance is usually more important.

The second incentive managers have relates to job prospects. Better performers within the firm will tend to get promoted. More generally, managers who are successful in pursu- ing stockholder goals will be in greater demand in the labor market and thus command higher salaries.

In fact, managers who are successful in pursuing stockholder goals can reap enormous rewards. For example, also in 2015, Michael Fries, the CEO of Liberty Global made about $111.9 million. By way of comparison, Floyd Mayweather made $300 million and Robert Downey, Jr., made about $80 million.3

3 This raises the issue of the level of top management pay and its relationship to other employees. According to recent research by the Economic Policy Institute, the average CEO compensation was 20 times greater than that of the average employee in 1965, 383 times greater in 2000, and 231 times greater in 2011 (http://www.epi.org/publication/ib331-ceo-pay-top-1-percent/). However, there is no precise formula that governs the gap between top management compensation and that of other employees.

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CONTROL OF THE FIRM Control of the firm ultimately rests with stockholders. They elect the board of directors, who, in turn, hire and fire management.

An important mechanism by which unhappy stockholders can replace existing man- agement is called a proxy fight. A proxy is the authority to vote someone else’s stock. A proxy fight develops when a group solicits proxies in order to replace the existing board and thereby replace existing management. In 2002, the proposed merger between HP and Compaq triggered one of the most widely followed, bitterly contested, and expensive proxy fights in history, with an estimated price tag of well over $100 million.

Another way that management can be replaced is by takeover. Firms that are poorly man- aged are more attractive as acquisitions than well-managed firms because a greater profit potential exists. Thus, avoiding a takeover by another firm gives management another incen- tive to act in the stockholders’ interests. Unhappy prominent shareholders can suggest differ- ent business strategies to a firm’s top management. This was the case in 2015, when digital imaging company Shutterfly lost a proxy fight with Marathon Partners, which won two seats on the board of directors in June 2015. However, another activist investor, Ancora Advisors, threatened Shutterfly with another proxy fight in late 2015. Ancora felt that Shutterfly hadn’t adequately addressed corporate strategy, capital allocation, and compensation.

Historically, proxy fights have been relatively rare. One reason is that the expenses in a proxy fight can become quite large. Further, outsiders waging a proxy fight must cover their own expenses, while the current directors use company finances to back their bid to retain board seats. In recent years, proxy fights appear to have become more civil. In 2014, about 50 percent of proxy fights went the distance, meaning they ultimately resulted in a shareholder vote. Before that, it was not uncommon for 70 percent or more of proxy fights to result in shareholder votes. Companies today appear to be more willing to work with activist shareholders, perhaps because both parties have become more concerned with the potential high costs of a long, bitter proxy fight.

CONCLUSION The available theory and evidence are consistent with the view that stock- holders control the firm and that stockholder wealth maximization is the relevant goal of the corporation. Even so, there will undoubtedly be times when management goals are pursued at the expense of the stockholders, at least temporarily.

Stakeholders Our discussion thus far implies that management and stockholders are the only parties with an interest in the firm’s decisions. This is an oversimplification, of course. Employees, cus- tomers, suppliers, and even the government all have a financial interest in the firm.

Taken together, these various groups are called stakeholders in the firm. In general, a stakeholder is someone other than a stockholder or creditor who potentially has a claim on the cash flows of the firm. Such groups will also attempt to exert control over the firm, perhaps to the detriment of the owners.

1.6 REGULATION Until now, we have talked mostly about the actions that shareholders and boards of direc- tors can take to reduce the conflicts of interest between themselves and management. We have not talked about regulation.4 Until recently the main thrust of federal regulation has been to require that companies disclose all relevant information to investors and

4 At this stage in our book, we focus on the regulation of disclosure of relevant information and corporate governance. We do not talk about many other regulators in financial markets such as the Federal Reserve Board. In Chapter 5, we discuss the nationally recognized statistical rating organizations (NRSROs) in the U.S., such as Fitch Ratings, Moody’s, and Standard & Poor’s. Their ratings are used by market partici- pants to help value securities such as corporate bonds. Many critics of the rating agencies blame the 2007–2009 subprime credit crisis on weak regulatory oversight of these agencies.

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SARBANES-OXLEY In response to corporate scandals at companies such as Enron, WorldCom, Tyco, and Adelphia, Congress enacted the Sarbanes-Oxley Act in 2002. The act, better known as “Sarbox,” is intended to protect investors from corporate abuses. For example, one section of Sarbox prohibits personal loans from a company to its officers, such as the ones that were received by WorldCom CEO Bernie Ebbers.

One of the key sections of Sarbox took effect on November 15, 2004. Section 404 requires, among other things, that each company’s annual report must have an assessment of the company’s internal control structure and financial report- ing. The auditor must then evaluate and attest to management’s assessment of these issues.

Sarbox contains other key requirements. For example, the officers of the corporation must review and sign the annual reports. They must explicitly declare that the annual report does not contain any false statements or material omissions; that the financial statements fairly represent the financial results; and that they are responsible for all internal controls. Finally, the annual report must list any deficiencies in internal controls. In essence, Sarbox makes company management responsible for the accuracy of the company’s financial statements.

Of course, as with any law, there are costs. Sarbox has increased the expense of corporate audits, sometimes dra- matically. In 2004, the average compliance cost was $4.51 million. By 2007, however, the average compliance cost had fallen to $1.7 million. More recent numbers show that Sarbox costs are becoming more manageable. In 2012, 10 years after Sarbox was passed, it was reported that most small companies spent less than $100,000 on compliance annually, and a third of midsized companies spent $100,000 to $500,000. And there appear to be economies in Sarbox costs. By the fourth year of Sarbox compliance, a company is expected to spend between $100,000 and $500,000, regardless of size.

However, the added expense of Sarbox compliance has led to several unintended results. Over the seven-year period from 1998 to 2004, 484 firms delisted their shares from exchanges, or “went dark.” Within the first two years alone of Sarbox, 370 companies delisted. Many of the companies that delisted stated the reason was to avoid the cost of compli- ance with Sarbox. And small companies are not the only ones to delist because of Sarbox. For example, German insurer Allianz applied to delist its shares from the New York Stock Exchange. The company estimated that canceling its listings outside of its home exchange of Frankfurt could save 5 million euros (about $6 million) per year.

A company that goes dark does not have to file quarterly or annual reports. Annual audits by independent auditors are not required, and executives do not have to certify the accuracy of the financial statements, so the savings can be huge. Of course, there are costs. Stock prices typically fall when a company announces it is going dark. Further, such companies will typically have limited access to capital markets and usually will have a higher interest cost on bank loans.

Sarbox has also probably affected the number of companies choosing to go public in the United States. For exam- ple, when Peach Holdings, based in Boynton Beach, Florida, decided to go public, it shunned the U.S. stock markets, instead choosing the London Stock Exchange’s Alternative Investment Market (AIM). To go public in the United States, the firm would have paid a $100,000 fee, plus about $2 million to comply with Sarbox. Instead, the company spent only $500,000 on its AIM stock offering. 

FINANCE MATTERS

potential investors.5 Disclosure of relevant information by corporations is intended to put all investors on a level information playing field and, thereby to reduce conflicts of interest. More recent regulation has been aimed at corporate governance. Of course, regulation imposes costs on corporations, and any analysis of regulation must include both benefits and costs. Our nearby Finance Matters box discusses some of the costs exchange-listed companies face arising from corporate governance requirements.

5 Here, we are speaking mostly of public companies and not private companies. You will learn more about this distinction in Chapter 19. If you can’t wait, go to investopedia.com and search “public vs. private companies.”

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16

The Securities Act of 1933 and the Securities Exchange Act of 1934 The Securities Act of 1933 (the 1933 Act) and the Securities Exchange Act of 1934 (the 1934 Act) provide the basic regulatory framework in the United States for the public trading of securities.

The 1933 Act focuses on the issuing of new securities. Basically, the 1933 Act requires a corporation to file a registration statement with the Securities and Exchange Commission (SEC) that must be made available to every buyer of a new security. The intent of the reg- istration statement is to provide potential stockholders with all the necessary information to make a reasonable decision. The 1934 Act extends the disclosure requirements of the 1933 Act to securities trading in markets after they have been issued. The 1934 Act establishes the SEC and covers a large number of issues including corporate reporting, tender offers, and insider trading. The 1934 Act requires corporations to file reports to the SEC on an annual basis (Form 10K), on a quarterly basis (Form 10Q), and on a monthly basis (Form 8K).

As mentioned, the 1934 Act deals with the important issue of insider trading. Illegal insider trading occurs when any person who has acquired nonpublic, special information (i.e., inside information) buys or sells securities based upon that information. One section of the 1934 Act deals with insiders such as directors, officers, and large shareholders, while another deals with any person who has acquired inside information. The intent of these sections of the 1934 Act is to prevent insiders or persons with inside information from taking unfair advantage of this information when trading with outsiders.

To illustrate, suppose you learned that ABC firm was about to publicly announce that it had agreed to be acquired by another firm at a price significantly greater than its current price. This is an example of inside information. The 1934 Act prohibits you from buying ABC stock from shareholders who do not have this information. This prohibition would be especially strong if you were the CEO of the ABC firm. Other kinds of inside information could be knowledge of an initial dividend about to be paid, the discovery of a drug to cure cancer, or the default of a debt obligation.

A recent example of insider trading involved Mathew Martoma, a portfolio manager at SAC Capital, who was convicted of insider trading in 2014. SAC Capital had already plead guilty to fraud charges and paid $1.8 billion in fines. Martoma was found guilty of trading on inside information he learned about a new Alzheimer’s drug and received a nine-year prison term. 

SUMMARY AND CONCLUSIONS This chapter introduced you to some of the basic ideas in corporate finance:

1. Corporate finance has three main areas of concern:

a. Capital budgeting: What long-term investments should the firm take?

b. Capital structure: Where will the firm get the short-term and long-term financing to pay for its invest- ments? Also, what mixture of debt and equity should it use to fund operations?

c. Working capital management: How should the firm manage its everyday financial activities?

2. The goal of financial management in a for-profit business is to make decisions that increase the value of the stock, or, more generally, increase the value of the equity.

3. The corporate form of organization is superior to other forms when it comes to raising money and trans- ferring ownership interests, but it has the significant disadvantage of double taxation.

4. There is the possibility of conflicts between stockholders and management in a large corporation. We called these conflicts agency problems and discussed how they might be controlled and reduced.

5. To create value companies must generate more cash than they use.

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CHAPTER 1 Introduction to Corporate Finance 17

6. Until recently the main thrust of federal regulation has been to require companies to disclose all relevant information to investors and potential investors. More recent regulation has been aimed at corporate governance. 

Of the topics we’ve discussed thus far, the most important is the goal of financial management: maxi- mizing the value of the stock. Throughout the text we will be analyzing many different financial decisions, but we will always ask the same question: How does the decision under consideration affect the value of the stock?

1. Forms of Business What are the three basic legal forms of organizing a business? What are the advantages and disadvantages of each? What business form do most start-up companies take? Why?

2. Goal of Financial Management What goal should always motivate the actions of the firm’s financial manager?

3. Agency Problems Who owns a corporation? Describe the process whereby the owners control the firm’s management. What is the main reason that an agency relationship exists in the corporate form of organization? In this context, what kinds of problems can arise?

4. Not-for-Profit Firm Goals Suppose you were the financial manager of a not-for-profit business (a not- for-profit hospital, perhaps). What kinds of goals do you think would be appropriate?

5. Goal of the Firm Evaluate the following statement: Managers should not focus on the current stock value because doing so will lead to an overemphasis on short-term profits at the expense of long-term profits.

6. Ethics and Firm Goals Can our goal of maximizing the value of the stock conflict with other goals, such as avoiding unethical or illegal behavior? In particular, do you think subjects like customer and employee safety, the environment, and the general good of society fit in this framework, or are they essentially ignored? Try to think of some specific scenarios to illustrate your answer.

7. International Firm Goal Would our goal of maximizing the value of the stock be different if we were thinking about financial management in a foreign country? Why or why not?

8. Agency Problems Suppose you own stock in a company. The current price per share is $25. Another company has just announced that it wants to buy your company and will pay $35 per share to acquire all the outstanding stock. Your company’s management immediately begins fighting off this hostile bid. Is management acting in the shareholders’ best interests? Why or why not?

9. Agency Problems and Corporate Ownership Corporate ownership varies around the world. Historically, individuals have owned the majority of shares in public corporations in the United States. In Germany and Japan, however, banks, other large financial institutions, and other companies own most of the stock in public corporations. Do you think agency problems are likely to be more or less severe in Germany and Japan than in the United States? Why? In recent years, large financial institutions such as mutual funds and pension funds have been becoming the dominant owners of stock in the United States, and these institutions are becoming more active in corporate affairs. What are the implications of this trend for agency problems and corporate control?

10. Executive Compensation Critics have charged that compensation to top management in the United States is too high and should be cut back. For example, focusing on large corporations, Mario Gabelli of GAMCO Investors was been one of the best-compensated CEOs in the United States, earning about $88.5 million in 2015. Are such amounts excessive?

In answering, it might be helpful to recognize that superstar athletes such as LeBron James, top people in entertainment such as Oprah Winfrey and Jerry Bruckheimer, and many others at the peak of their respective fields can earn at least as much, if not a great deal more.

CONCEPT QUESTIONS

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EAST COAST YACHTS In 1969, Tom Warren founded East Coast Yachts. The company’s operations are located near Hilton Head Island, South Carolina, and the company is structured as a sole proprietorship. The company has manufactured custom midsize, high-performance yachts for clients, and its products have received high reviews for safety and reliability. The company’s yachts have also recently received the highest award for customer satisfaction. The yachts are primarily purchased by wealthy individuals for pleasure use. Occasionally, a yacht is manufac- tured for purchase by a company for business purposes.

The custom yacht industry is fragmented, with a number of manufacturers. As with any industry, there are market leaders, but the diverse nature of the industry ensures that no manufacturer dominates the market. The competition in the market, as well as the product cost, ensures that attention to detail is a necessity. For instance, East Coast Yachts will spend 80 to 100 hours on hand-buffing the stainless steel stem-iron, which is the metal cap on the yacht’s bow that conceivably could collide with a dock or another boat.

Several years ago, Tom retired from the day-to-day operations of the company and turned the operations of the company over to his daughter, Larissa. Because of the dramatic changes in the company, Larissa has approached you to help manage and direct the company’s growth. Specifically, she has asked you to answer the following questions.

1. What are the advantages and disadvantages of changing the company organization from a sole proprietorship to an LLC?

2. What are the advantages and disadvantages of changing the company organization from a sole proprietorship to a corporation?

3. Ultimately, what action would you recommend the company undertake? Why?

CLOSING CASE

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PART 1 Overview18

WHAT’S ON THE WEB? 1. Listing Requirements This chapter mentioned listing requirements for public companies. Find the

complete listing requirements for NYSE Euronext at www.nyse.com and NASDAQ at www.nasdaq.com. Which exchange has more stringent listing requirements? Why don’t the exchanges have the same listing requirements?

2. Business Formation As you may (or may not) know, many companies incorporate in Delaware for a variety of reasons. Visit BizFilings at www.bizfilings.com to find out why. Which state has the highest fee for incorporation? For an LLC? While at the site, look at the FAQ section regarding corporations and LLCs.

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CHAPTER 2 Financial Statements and Cash Flow 19

2 OPENING CASE

Financial Statements and Cash Flow When a company announces a “write-off,” that frequently means that the value of the compa-

ny’s assets has declined. For example, in July 2015, Microsoft announced that it would write

off $7.6 billion related to its purchase of Nokia’s phone business the previous year. What made

the write-off interesting was that Microsoft had only paid $7.2 billion for the phone business.

The oil business was also hit hard in 2015 as the five largest publicly traded oil companies

working in Wyoming wrote off a combined $41 billion for the first nine months of the year.

These write-offs were due to the declining value of oil production facilities in that state.  

While Microsoft’s write-off is large, the record holder is media giant Time Warner, which

took a charge of $45.5 billion in the fourth quarter of 2002. This enormous write-off followed

an earlier, even larger, charge of $54 billion.

So, did the stockholders in these companies lose billions of dollars when these assets

were written off? Fortunately for them, the answer is probably not. Understanding why ulti-

mately leads us to the main subject of this chapter, that all-important substance known as

cash flow.

Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.

2.1 THE BALANCE SHEET The balance sheet is an accountant’s snapshot of the firm’s accounting value on a par- ticular date, as though the firm stood momentarily still. The balance sheet has two sides: On the left are the assets and on the right are the liabilities and stockholders’ equity. The balance sheet states what the firm owns and how it is financed. The accounting definition that underlies the balance sheet and describes the balance is

Assets ≡ Liabilities + Stockholders’ equity [2.1]

We have put a three-line equality in the balance equation to indicate that it must always hold, by definition. In fact, the stockholders’ equity is defined to be the difference between the assets and the liabilities of the firm. In principle, equity is what the stockholders would have remaining after the firm discharged its obligations.

Table 2.1 gives the 2016 and 2017 balance sheets for the fictitious U.S. Composite Corporation. The assets in the balance sheet are listed in order by the length of time it normally would take an ongoing firm to convert them to cash. The asset side depends on the nature of the business and how management chooses to conduct it. Management must make decisions about cash versus marketable securities, credit versus cash sales, whether

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Two excellent sources for company financial information are finance. yahoo.com and money. cnn.com.

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20

Annual and quarterly financial statements for most public U.S. corpora- tions can be found in the EDGAR database at www. sec.gov.

TABLE  2.1 The Balance Sheet of the U.S. Composite Corporation

U.S. COMPOSITE CORPORATION Balance Sheet

2016 and 2017 ( in $ mi l l ions)

ASSETS 2016 2017 LIABIL IT IES (DEBT) AND 

STOCKHOLDERS’ EQUITY 2016 2017

Current assets:

Cash and equivalents

Accounts receivable

Inventories

Total current assets

$ 157

270

280

$ 707

$ 198

294

269

$ 761

Current liabilities:

Accounts payable

Total current liabilities

$ 455

$ 455

$ 486

$ 486

Long-term liabilities:

Deferred taxes

Long-term debt*

Total long-term liabilities

$ 104

458

$ 562

$ 117

471

$ 588

Fixed assets:

Property, plant, and equipment

Less accumulated depreciation

Net property, plant, and equipment

Intangible assets and others

Total fixed assets

$ 1,274

460

$ 814

221

$ 1,035

$ 1,423

550

$ 873

245

$ 1,118

Stockholders’ equity:

Preferred stock

Common stock ($1 par value)

Capital surplus

Accumulated retained earnings

Less treasury stock†

Total equity

$ 39

32

327

347

20

$ 725

$ 39

55

347

390

26

$ 805

Total assets $ 1,742 $ 1,879 Total liabilities and stockholders’ equity‡ $ 1,742 $ 1,879

* Long-term debt rose by $471 million – 458 million = $13 million. This is the difference between $86 million new debt and $73 million in retirement of old debt.

† Treasury stock rose by $6 million. This reflects the repurchase of $6 million of U.S. Composite’s company stock.

‡ U.S. Composite reports $43 million in new equity. The company issued 23 million shares at a price of $1.87. The par value of common stock increased by $23 million, and capital surplus increased by $20 million.

to make or buy commodities, whether to lease or purchase items, the types of business in which to engage, and so on.

The liabilities and stockholders’ equity side reflects the types and proportions of financ- ing, which depend on management’s choice of capital structure, as between debt and equity and between current debt and long-term debt. The liabilities and the stockholders’ equity are listed in the order in which they would typically be paid over time.

When analyzing a balance sheet, the financial manager should be aware of three con- cerns: accounting liquidity, debt versus equity, and value versus cost.

Accounting Liquidity Accounting liquidity refers to the ease and quickness with which assets can be converted to cash. Current assets are the most liquid and include cash and those assets that will be turned into cash within a year from the date of the balance sheet. Accounts receivable are amounts not yet collected from customers for goods or services sold to them (after adjust- ment for potential bad debts). Inventory is composed of raw materials to be used in produc- tion, work in process, and finished goods. Fixed assets are the least liquid kind of assets. Tangible fixed assets include property, plant, and equipment. These assets do not convert to cash from normal business activity, and they are not usually used to pay expenses such as payroll.

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CHAPTER 2 Financial Statements and Cash Flow 21

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Some fixed assets are not tangible. Intangible assets have no physical existence but can be very valuable. Examples of intangible assets are the value of a trademark or the value of a patent. The more liquid a firm’s assets, the less likely the firm is to experience prob- lems meeting short-term obligations. Thus, the probability that a firm will avoid financial distress can be linked to the firm’s liquidity. Unfortunately, liquid assets frequently have lower rates of return than fixed assets; for example, cash generates no investment income. To the extent a firm invests in liquid assets, it sacrifices an opportunity to invest in more profitable investment vehicles.

Debt versus Equity Liabilities are obligations of the firm that require a payout of cash within a stipulated time period. Many liabilities involve contractual obligations to repay a stated amount at some point, along with interest over a period. Thus, liabilities are debts and are frequently asso- ciated with nominally fixed cash burdens, called debt service, that put the firm in default of a contract if they are not paid. Stockholders’ equity is a claim against the firm’s assets that is residual and not fixed. In general terms, when the firm borrows, it gives the bond- holders first claim on the firm’s cash flow.1 Bondholders can sue the firm if the firm defaults on its bond contracts. This may lead the firm to declare itself bankrupt. Stockholders’ equity is the residual difference between assets and liabilities:

Assets – Liabilities ≡ Stockholders’ equity [2.2]

This is the stockholders’ share in the firm stated in accounting terms. The account- ing value of stockholders’ equity increases when retained earnings are added. This occurs when the firm retains part of its earnings instead of paying them out as dividends.

Value versus Cost The accounting value of a firm’s assets is frequently referred to as the carrying value or the book value of the assets.2 Under generally accepted accounting principles (GAAP), audited financial statements of firms in the United States carry the assets at cost.3 Thus the terms carrying value and book value are unfortunate. They specifically say “value,” when in fact the accounting numbers are based on cost. This misleads many readers of financial statements to think that the firm’s assets are recorded at true market values. Market value is the price at which willing buyers and sellers would trade the assets. It would be only a coincidence if accounting value and market value were the same. In fact, management’s job is to create value for the firm that exceeds its cost.

Many people use the balance sheet, but the information each may wish to extract is not the same. A banker may look at a balance sheet for evidence of accounting liquidity and working capital. A supplier may also note the size of accounts payable and therefore the general promptness of payments. Many users of financial statements, including managers and investors, want to know the value of the firm, not its cost. This information is not found on the balance sheet. In fact, many of the true resources of the firm do not appear on the balance sheet: good management, proprietary assets, favorable economic conditions, and so on. Henceforth, whenever we speak of the value of an asset or the value of the firm, we will normally mean its market value. So, for example, when we say the goal of the finan- cial manager is to increase the value of the stock, we mean the market value of the stock.

1 Bondholders are investors in the firm’s debt. They are creditors of the firm. In this discussion, the term bondholder means the same thing as creditor. 2 Confusion often arises because many financial accounting terms have the same meaning. This presents a problem with jargon for the reader of financial statements. For example, the following terms usually refer to the same thing: assets minus liabilities, net worth, stock- holders’ equity, owners’ equity, book equity, and equity capitalization. 3 Generally, GAAP requires assets to be carried at the lower of cost or market value. In most instances, cost is lower than market value. However, in some cases when a fair market value can be readily determined, the assets have their value adjusted to the fair market value.

The home page for the Financial Accounting Standards Board (FASB) is www.fasb.org.

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2.2 THE INCOME STATEMENT The income statement measures performance over a specific period of time, say, a year. The accounting definition of income is

Revenue – Expenses ≡ Income [2.3]

If the balance sheet is like a snapshot, the income statement is like a video recording of what the firm did between two snapshots. Table 2.2 gives the income statement for the U.S. Composite Corporation for 2017.

The income statement usually includes several sections. The operations section reports the firm’s revenues and expenses from principal operations. One number of particu- lar importance is earnings before interest and taxes (EBIT), which summarizes earnings before taxes and financing costs. Among other things, the nonoperating section of the income statement includes all financing costs, such as interest expense. Usually a second section reports as a separate item the amount of taxes levied on income. The last item on the income statement is the bottom line, or net income. Net income is frequently expressed per share of common stock, that is, earnings per share.

When analyzing an income statement, the financial manager should keep in mind GAAP, noncash items, time, and costs.

Generally Accepted Accounting Principles Revenue is recognized on an income statement when the earnings process is virtually com- pleted and an exchange of goods or services has occurred. Therefore, the unrealized appre- ciation from owning property will not be recognized as income. This provides a device for smoothing income by selling appreciated property at convenient times. For example, if the firm owns a tree farm that has doubled in value, then, in a year when its earn- ings from other businesses are down, it can raise overall earnings by selling some trees.

E X

A M

P L

E  

2 .1

The Cooney Corporation has fixed assets with a book value of $700 and an appraised market value of about $1,000. Net working capital is $400 on the books, but approximately $600 would be realized if all the current accounts were liquidated. Cooney has $500 in long-term debt, both book value and market value. What is the book value of the equity? What is the market value?

We can construct two simplified balance sheets, one in accounting (book value) terms and one in economic (market value) terms:

COONEY CORPORATION Balance Sheets

Market Value versus Book Value

Assets Liabilities and Shareholders’ Equity

BOOK MARKET BOOK MARKET

Net working capital

Net fixed assets

$ 400

700

$1,100

$ 600

1,000

$1,600

Long-term debt

Shareholders’ equity

$ 500

600

$1,100

$ 500

1,100

$1,600

In this example, shareholders’ equity is actually worth almost twice as much as what is shown on the books. The distinction between book and market values is important precisely because book values can be so different from true economic value.

Market Value versus Book Value

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CHAPTER 2 Financial Statements and Cash Flow 23

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U. S . COMPOSITE CORPORATION Income Statement

2017 ( in $ mi l l ions)

Total operating revenues

Cost of goods sold

Selling, general, and administrative expenses

Depreciation

Operating income

Other income

Earnings before interest and taxes (EBIT)

Interest expense

Pretax income

Taxes

Current: $71

Deferred: $13

Net income

Addition to retained earnings:

Dividends:

$ 2,262

1,655

327

90

$ 190

29

$ 219

49

$ 170

84

$ 86

$ 43

43

TABLE 2.2 The Income Statement of the U.S. Composite Corporation

The matching principle of GAAP dictates that revenues be matched with expenses. Thus, income is reported when it is earned, or accrued, even though no cash flow has necessar- ily occurred (for example, when goods are sold for credit, sales and profits are reported).

Noncash Items The economic value of assets is intimately connected to their future incremental cash flows. However, cash flow does not appear on an income statement. There are several noncash items that are expenses against revenues but do not affect cash flow. The most important of these is depreciation. Depreciation reflects the accountant’s estimate of the cost of equipment used up in the production process. For example, suppose an asset with a five-year life and no resale value is purchased for $1,000. According to accountants, the $1,000 cost must be expensed over the useful life of the asset. If straight-line depreciation is used, there will be five equal installments and $200 of depreciation expense will be incurred each year. From a finance perspective, the cost of the asset is the actual negative cash flow incurred when the asset is acquired (that is, $1,000, not the accountant’s smoothed $200-per-year depreciation expense).

Another noncash expense is deferred taxes. Deferred taxes result from differences between accounting income and true taxable income.4 Notice that the accounting tax shown on the income statement for the U.S. Composite Corporation is $84 million. It can be broken down as current taxes and deferred taxes. The current tax portion is actually sent to the tax authorities (for example, the Internal Revenue Service). The deferred tax portion is not. However, the theory is that if taxable income is less than accounting income in the 4 One situation in which taxable income may be lower than accounting income is when the firm uses accelerated depreciation expense procedures for the IRS but uses straight-line procedures allowed by GAAP for reporting purposes.

Note: There are 29 million shares outstanding. Earnings per share and dividends per share can be calculated as follows:

Earnings per share 

= Net income

____________________ Total shares outstanding

= $86

____ 29

= $2.97 per share

Dividends per share 

= Dividends

____________________ Total shares outstanding

= $43

____ 29

= $1.48 per share

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current year, it will be more than accounting income later on. Consequently, the taxes that are not paid today will have to be paid in the future, and they represent a liability of the firm. This shows up on the balance sheet as deferred tax liability. From the cash flow per- spective, though, deferred tax is not a cash outflow.

In practice, the difference between cash flows and accounting income can be quite dra- matic, so it is important to understand the difference. For example, in January 2016, United States Steel Corporation reported a loss of $1.5 billion for the 2015 year. That sounds bad, but U.S. Steel reported a positive cash flow of $359 million for the year! In large part, the loss was due to charges attributable to restructuring and other strategic actions.

Time and Costs It is often useful to think of all of future time as having two distinct parts, the short run and the long run. The short run is that period of time in which certain equipment, resources, and commitments of the firm are fixed; but the time is long enough for the firm to vary its output by using more labor and raw materials. The short run is not a precise period of time that will be the same for all industries. However, all firms making deci- sions in the short run have some fixed costs, that is, costs that will not change because of fixed commitments. In real business activity, examples of fixed costs are bond interest, overhead, and property taxes. Costs that are not fixed are variable. Variable costs change as the output of the firm changes; some examples are raw materials and wages for laborers on the production line.

In the long run, all costs are variable. Financial accountants do not distinguish between variable costs and fixed costs. Instead, accounting costs usually fit into a classification that distinguishes product costs from period costs. Product costs are the total production costs incurred during a period—raw materials, direct labor, and manufacturing overhead—and are reported on the income statement as cost of goods sold. Both variable and fixed costs are included in product costs. Period costs are costs that are allocated to a time period; they are called selling, general, and administrative expenses. One period cost would be the company president’s salary.

2.3 TAXES Taxes can be one of the largest cash outflows that a firm experiences. For example, for the fiscal year 2015, Walmart’s earnings before taxes were about $24.8 billion. Its tax bill, including all taxes paid worldwide, was a whopping $7.99 billion, or about 30.2 percent of its pretax earnings. The size of the tax bill is determined through the tax code, an often amended set of rules. In this section, we examine corporate tax rates and how taxes are calculated.

If the various rules of taxation seem a little bizarre or convoluted to you, keep in mind that the tax code is the result of political, not economic, forces. As a result, there is no rea- son why it has to make economic sense.

Corporate Tax Rates Corporate tax rates in effect for 2016 are shown in Table 2.3. A peculiar feature of taxa- tion instituted by the Tax Reform Act of 1986 and expanded in the 1993 Omnibus Budget Reconciliation Act is that corporate tax rates are not strictly increasing. As shown, cor- porate tax rates rise from 15 percent to 39 percent, but they drop back to 34 percent on income over $335,000. They then rise to 38 percent and subsequently fall to 35 percent.

According to the originators of the current tax rules, there are only four corporate rates: 15 percent, 25 percent, 34 percent, and 35 percent. The 38 and 39 percent brackets arise because of “surcharges” applied on top of the 34 and 35 percent rates. A tax is a tax is a tax, however, so there are really six corporate tax brackets, as we have shown.

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Average versus Marginal Tax Rates In making financial decisions, it is frequently important to distinguish between average and marginal tax rates. Your average tax rate is your tax bill divided by your taxable income, in other words, the percentage of your income that goes to pay taxes. Your marginal tax rate is the tax you would pay (in percent) if you earned one more dollar. The percentage tax rates shown in Table 2.3 are all marginal rates. Put another way, the tax rates apply to the part of income in the indicated range only, not all income.

The difference between average and marginal tax rates can best be illustrated with a simple example. Suppose our corporation has a taxable income of $200,000. What is the tax bill? Using Table 2.3, we can figure our tax bill as:

TAXABLE INCOME TAX RATE

$ 0–50,000 50,001–75,000 75,001–100,000 

100,001–335,000 335,001–10,000,000

10,000,001–15,000,000 15,000,001–18,333,333 18,333,334+

15%

25   

34   

39   

34   

35   

38   

35   

TABLE 2.3 Corporate Tax Rates

.15($  50,000) = $   7,500 .25($  75,000 – 50,000) = 6,250 .34($100,000 – 75,000) = 8,500 .39($200,000 – 100,000) = 39,000 $ 61,250

Our total tax is thus $61,250. In our example, what is the average tax rate? We had a taxable income of $200,000 and

a tax bill of $61,250, so the average tax rate is $61,250/200,000 = 30.625%. What is the marginal tax rate? If we made one more dollar, the tax on that dollar would be 39 cents, so our marginal rate is 39 percent.

The IRS has a great web- site! (www.irs.gov)

Table 2.4 summarizes some different taxable incomes, marginal tax rates, and average tax rates for corporations. Notice how the average and marginal tax rates come together at 35 percent.

With a flat-rate tax, there is only one tax rate, so the rate is the same for all income levels. With such a tax, the marginal tax rate is always the same as the average tax rate. As

Algernon, Inc., has a taxable income of $85,000. What is its tax bill? What is its average tax rate? Its mar- ginal tax rate?

From Table 2.3, we see that the tax rate applied to the first $50,000 is 15 percent; the rate applied to the next $25,000 is 25 percent, and the rate applied after that up to $100,000 is 34 percent. So Algernon must pay .15 × $50,000 + .25 × 25,000 + .34 × (85,000 – 75,000) = $17,150. The average tax rate is thus $17,150/85,000 = 20.18%. The marginal rate is 34 percent because Algernon’s taxes would rise by 34 cents if it had another dollar in taxable income.

Deep in the Heart of Taxes

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A M

P L

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it stands now, corporate taxation in the United States is based on a modified flat-rate tax, which becomes a true flat rate for the highest incomes.

In looking at Table 2.4, notice that the more a corporation makes, the greater is the per- centage of taxable income paid in taxes. Put another way, under current tax law, the aver- age tax rate never goes down, even though the marginal tax rate does. As illustrated, for corporations, average tax rates begin at 15 percent and rise to a maximum of 35 percent.

It will normally be the marginal tax rate that is relevant for financial decision making. The reason is that any new cash flows will be taxed at that marginal rate. Because financial decisions usually involve new cash flows or changes in existing ones, this rate will tell us the marginal effect of a decision on our tax bill.

There is one last thing to notice about the tax code as it affects corporations. It’s easy to verify that the corporate tax bill is just a flat 35 percent of taxable income if our taxable income is more than $18.33 million. Also, for the many midsize corporations with taxable incomes in the range of $335,000 to $10,000,000, the tax rate is a flat 34 percent. Because we will normally be talking about large corporations, you can assume that the average and marginal tax rates are 35 percent unless we explicitly say otherwise. We should note that the tax rates we have discussed in this section relate to federal taxes only. Overall tax rates can be higher once state, local, and any other taxes are considered.

With the increasing globalization of business, accounting standards need to be more globally similar. In recent years, U.S. accounting standards have increasingly become more closely tied to International Financial Reporting Standards (IFRS). In particular, the Financial Accounting Standards Board (in charge of U.S. GAAP) and the International Accounting Standards Board (IASB, the entity in charge of IFRS), had been working toward a conver- gence of policies, although it appears that the convergence has been tabled, at least for now.

We should note that we have simplified the U.S. tax code in our discussions. In reality, the tax code is much more complex, and it is riddled with various tax deductions and loopholes allowed for certain industries. As a result, the average corporate tax rate can be far from 35 percent for many companies. Table 2.5 displays average tax rates for various industries.

(1) TAXABLE INCOME

(2) MARGINAL TAX RATE

(3) TOTAL TAX

(3) / (1) AVERAGE TAX RATE

$         45,000

           70,000

   95,000

         250,000

      1,000,000

    17,500,000

    50,000,000

  100,000,000

15%

25   

34   

39   

34   

38   

35   

35   

$         6,750 

         12,500 

         20,550

         80,750

       340,000

    6,100,000

  17,500,000

  35,000,000

15.00%

17.86   

21.63   

32.30   

34.00   

34.86   

35.00   

35.00   

TABLE 2.4 Corporate Taxes and Tax Rates

For more information about IFRS, check out the website www.ifrs.org.

INDUSTRY NUMBER OF COMPANIES AVERAGE TAX RATE

Electric utilities (Eastern U.S.)

Trucking

Railroad

Securities brokerage

Banking

Medical supplies

Internet

Pharmaceutical

Biotechnology

  24

  33

  15

  30

481

264

239

337

121

33.8%

32.7

27.4

20.5

17.5

11.2

5.9

5.6

4.5

TABLE 2.5 Average Tax Rates in Various Industries

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As you can see, the average tax rate ranges from 33.8 percent for electric utilities to 4.5 percent for biotechnology firms. For a discussion of one of the complexities of the tax code, see the nearby Finance Matters box.

2.4 NET WORKING CAPITAL Net working capital is current assets minus current liabilities. Net working capital is posi- tive when current assets are greater than current liabilities. This means the cash that will become available over the next 12 months will be greater than the cash that must be paid

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WHAT IS WARREN BUFFETT’S TAX RATE? In 2011, famed investor Warren Buffett, one of the wealthiest individuals in the world, created a stir when he publicly stated that his tax rate was lower than the tax rate paid by his secretary. The previous year, Buffett’s gross income was about $63 million, on which he paid only a 15 percent tax rate. His secretary (with a substantially lower income) had a 31 percent marginal tax rate. Also in 2011, when Republican presidential contender Mitt Romney released his income taxes, it was revealed that he too only paid an income tax rate of 15 percent on his $21 million annual income.

Why do Buffett’s and Romney’s tax rates appear so low? Currently, under the U.S. tax system, wage income is taxed at a much higher rate than dividends and long-term capital gains. In fact, in the highest tax bracket, wage income is taxed at 35 percent, while dividends and long-term capital gains are taxed at 15 percent. Most of Buffett’s and Romney’s annual income comes from their investments, not wages, hence the 15 percent rates.

So do rich guys get all the (tax) breaks? U.S. President Barack Obama seemed to think so. In his 2012 State of the Union address, with Buffett’s secretary Debbie Bosanek joining First Lady Michelle Obama in her box as a special guest, he called for the creation of a “Buffett tax.” As he described it, such a tax would be an extra tax paid by very high-income individuals. Maybe President Obama was angry about the fact that he and the First Lady paid $1.7 million in federal taxes on their joint income of $5.5 million in 2009, implying an average tax rate of 31 percent.

Of course, you know that income received from dividends is already taxed. Dividends are paid from corporate income, which is taxed at 35 percent for larger dividend-paying companies. Effectively, any tax on dividends is double taxation on that money. The tax code realizes this. The lower tax rate on dividends lowers the double tax rate. The same thing is true for capital gains; taxes are paid on the money before the investment is made.

In Buffett’s case, most of his wealth stems from his approximately 30 percent ownership of Berkshire Hathaway Corporation. Based on its 23,000 (no typo!) page tax return, Berkshire’s 2014 corporate tax bill was $7.9 billion on income of $28.1 billion, a 28 percent average rate. Buffett’s share of Berkshire’s tax bill therefore amounts to something on the order of $2.37 billion! If we include Berkshire’s corporate taxes, Buffett’s average tax rate is more like 28 + 15 = 43 percent.

To give another example, consider the situation described by N. Gregory Mankiw, the well-known economist and textbook author. Mankiw considers taking a writing job for $1,000. He figures that if he earns an 8 percent return and there are no taxes, he would be able to leave his children about $10,000 in 30 years when he passes on. However, because of federal, state, and Medicare taxes, he would only receive about $523 after taxes today. And because of corporate taxes and personal income taxes, his return on the same investment would only be about 4 percent, which will result in a balance of $1,700 in 30 years. When he dies, his account will be taxed using the marginal estate tax rate, which is as high as 55 percent. As a result, his children will receive only about $1,000, implying a tax rate of 90 percent!

FINANCE MATTERS

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out. The net working capital of the U.S. Composite Corporation is $275 million in 2017 and $252 million in 2016:

Current assets

($millons) − Current liabilities

($millons) = Net working capital

($millons)

2017        $761 −           $486 =             $275 2016          707 −              455 =                252

In addition to investing in fixed assets (i.e., capital spending), a firm can invest in net work- ing capital. This is called the change in net working capital. The change in net working capital in 2017 is the difference between the net working capital in 2017 and 2016; that is, $275 million – 252 million = $23 million. The change in net working capital is usually positive in a growing firm.5

2.5 CASH FLOW OF THE FIRM Perhaps the most important item that can be extracted from financial statements is the actual cash flow of the firm. There is an official accounting statement called the statement of cash flows. This statement helps to explain the change in accounting cash and equiva- lents, which for U.S. Composite is $33 million in 2017. (See Section 2.6.) Notice in Table 2.1 that cash and equivalents increase from $157 million in 2016 to $198 million in 2017. However, we will look at cash flow from a different perspective, the perspective of finance. In finance, the value of the firm is its ability to generate cash flow. (We will talk more about cash flow in Chapter 8.)

The first point we should mention is that cash flow is not the same as net working capi- tal. For example, increasing inventory requires using cash. Because both inventories and cash are current assets, this does not affect net working capital. In this case, an increase in a particular net working capital account, such as inventory, is associated with decreasing cash flow.

Just as we established that the value of a firm’s assets is always equal to the sum of the value of the liabilities and the value of the equity, the cash flows generated from the firm’s assets (that is, its operating activities), CF(A), must equal the cash flows it can distribute to the firm’s creditors, CF(B), and equity investors, CF(S):

CF(A) = CF(B) + CF(S) [2.4]

The first step in determining the cash flow of the firm is to figure out the operating cash flow. As can be seen in Table 2.6, operating cash flow is the cash flow generated by busi- ness activities, including sales of goods and services. Operating cash flow reflects tax pay- ments, but not financing, capital spending, or changes in net working capital.

5 A firm’s current liabilities sometimes include short-term interest-bearing debt usually referred to as notes payable. However, financial ana- lysts often distinguish between interest-bearing short-term debt and non-interest-bearing short-term debt (such as accounts payable). When this distinction is made, only non-interest-bearing short-term debt is usually included in the calculation of net working capital. This version of net working capital is called “operating” net working capital. The interest-bearing short-term debt is not forgotten but instead is included in cash flow from financing activities, and the interest is considered a return on capital.

IN $ MILLIONS

Earnings before interest and taxes

Depreciation

Current taxes

Operating cash flow

$219

90

  –71 $238

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Another important component of cash flow involves changes in fixed assets. For example, when U.S. Composite sold its power systems subsidiary in 2017, it generated $25 million in cash flow. The net change in fixed assets equals the acquisition of fixed assets minus sales of fixed assets. The result is the cash flow used for capital spending:

U.S. COMPOSITE CORPORATION Cash F low 2017

( in $ mi l l ions)

Distributable Cash Flow of the Firm

Operating cash flow

(Earnings before interest and taxes plus depreciation minus taxes)

Capital spending

(Acquisitions of fixed assets minus sales of fixed assets)

Additions to net working capital

Total

$ 238

−173

−23 $   42

Cash Flow to Investors in the Firm

Debt

(Interest plus retirement of debt minus long-term debt financing)

Equity

(Dividends plus repurchase of equity minus new equity financing)

Total

$  36

6

$  42

TABLE 2.6 Cash Flow of the U.S. Composite Corporation

Acquisition of fixed assets

Sales of fixed assets

Capital spending

$198

–25 $173 ($149 + 24 = Increase in property,

plant, and equipment + Increase in intangible assets)

We can also calculate capital spending as

2.5

Capital spending

=

Ending net fixed assets – Beginning net fixed assets

+ Depreciation

= $1,118 – 1,035 + 90

=

$173

Cash flows are also used for making investments in net working capital. In U.S. Composite Corporation in 2017, additions to net working capital are

Additions to net working capital $23

Note that this $23 is the change in net working capital we previously calculated. Total cash flows generated by the firm’s assets are the sum of

Operating cash flow

Capital spending

Additions to net working capital

Total distributable cash flow of the firm

$ 238

−173 −23 $    42

The total outgoing cash flow of the firm can be separated into cash flow distributed to creditors and cash flow distributed to stockholders. The cash flow distributed to credi- tors represents a regrouping of the data in Table 2.6 and an explicit recording of interest

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expense. Creditors are paid an amount generally referred to as debt service. Debt service is interest payments plus repayments of principal (that is, retirement of debt).

An important source of cash flow is the sale of new debt. U.S. Composite’s long-term debt increased by $13 million (the difference between $86 million in new debt and $73 million in retirement of old debt).6 Thus, an increase in long-term debt is the net effect of new borrowing and repayment of maturing obligations plus interest expense.

6 New debt and the retirement of old debt are usually found in the “notes” to the balance sheet.

CASH FLOW PAID TO CREDITORS ( in $ mi l l ions)

Interest

Retirement of debt

Debt service

Proceeds from long-term debt sales

Total

$ 49

73

122

−86 $  36

Cash flow distributed to creditors can also be calculated as

Cash flow paid to creditors = Interest paid – Net new borrowing [2.6] = Interest paid – (Ending long-term debt – Beginning long-term debt) = $49 – (471 – 458) = $36

CASH FLOW TO STOCKHOLDERS ( in $ mi l l ions)

Dividends

Repurchase of stock

Cash to stockholders

Proceeds from new stock issue

Total

$43

6

49

–43 $ 6

Cash flow of the firm also is distributed to the stockholders. It is the net effect of paying dividends plus repurchasing outstanding shares of stock and issuing new shares of stock.

In general, cash flow to stockholders can be determined as

Cash flow to stockholders = Dividends paid – Net new equity raised [2.7] = Dividends paid –  ( Stock sold  – Stock repurchased )

To determine stock sold, notice that the common stock and capital surplus accounts went up by a combined $23 + 20 = $43, which implies that the company sold $43 million worth of stock. Second, treasury stock went up by $6, indicating that the company bought back $6 million worth of stock. Net new equity is thus $43 – 6 = $37. Dividends paid were $43, so the cash flow to stockholders was

Cash flow to stockholders = $43 – 43 – 6 = $6

which is what we previously calculated. Some important observations can be drawn from our discussion of cash flow:

1. Several types of cash flow are relevant to understanding the financial situation of the firm. Operating cash flow, defined as earnings before interest and deprecia- tion minus taxes, measures the cash generated from operations not counting cap- ital spending or working capital requirements. It is usually positive; a firm is in

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trouble if operating cash flow is negative for a long time because the firm is not generating enough cash to pay operating costs. Total distributable cash flow of the firm includes adjustments for capital spending and additions to net working capital. It will frequently be negative. When a firm is growing at a rapid rate, the spending on inventory and fixed assets can be higher than cash flow from sales.

2. Net income is not cash flow. The net income of the U.S. Composite Corporation in 2017 was $86 million, whereas cash flow was $42 million. The two numbers are not usually the same. In determining the economic and financial condition of a firm, cash flow is more revealing.

A firm’s total cash flow sometimes goes by a different name, free cash flow. Of course, there is no such thing as “free” cash (we wish!). Instead, the name refers to cash that the firm is free to distribute to creditors and stockholders because it is not needed for working capital or fixed asset investments. We will stick with “total distributable cash flow of the firm” as our label for this important concept because, in practice, there is some variation in exactly how free cash flow is computed; different users calculate it in different ways. Nonetheless, whenever you hear the phrase “free cash flow,” you should understand that what is being discussed is cash flow from assets after adjusting for capital spending and changes in net working capital or something quite similar.

2.6 THE ACCOUNTING STATEMENT OF CASH FLOWS

As previously mentioned, there is an official accounting statement called the statement of cash flows. This statement helps explain the change in accounting cash, which for U.S. Composite is $33 million in 2017. It is very useful in understanding financial cash flow.

The first step in determining the change in cash is to figure out cash flow from operating activities. This is the cash flow that results from the firm’s normal activities producing and selling goods and services. The second step is to make an adjustment for cash flow from investing activities. The final step is to make an adjustment for cash flow from financing activities. Financing activities are the net payments to creditors and owners (excluding interest expense) made during the year.

The three components of the statement of cash flows are determined below.

Cash Flow from Operating Activities To calculate cash flow from operating activities we start with net income. Net income can be found on the income statement and is equal to $86 million. We now need to add back noncash expenses and adjust for changes in current assets and liabilities (other than cash and notes payable). The result is cash flow from operating activities.

U.S. COMPOSITE CORPORATION Cash F low f rom Operat ing Act iv i t ies

2017 ( in $ mi l l ions)

Net income

Depreciation

Deferred taxes

Change in current assets and liabilities

Accounts receivable

Inventories

Accounts payable

Cash flow from operating activities

$   86

90

13

−  24 11

     31

 $207

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Cash Flow from Investing Activities Cash flow from investing activities involves changes in capital assets: acquisition of fixed assets and sales of fixed assets (i.e., net capital expenditures). The result for U.S. Composite is below:

U.S. COMPOSITE CORPORATION Cash F low f rom Invest ing Act iv i t ies

2017 ( in $ mi l l ions)

Acquisition of fixed assets

Sales of fixed assets

Cash flow from investing activities

–$198        25

–$173

Cash Flow from Financing Activities Cash flows to and from creditors and owners include changes in equity and debt.

U.S. COMPOSITE CORPORATION Statement of Cash F lows

2017 ( in $ mi l l ions)

Operations

Net income

Depreciation

Deferred taxes

Changes in current assets and liabilities

Accounts receivable

Inventories

Accounts payable

Total cash flow from operations

$  86

90

13

−    24 11

        31

  $207

Investing activities

Acquisition of fixed assets

Sales of fixed assets

Total cash flow from investing activities

−$198       25

− $173

Financing activities

Retirement of long-term debt

Proceeds from long-term debt sales

Dividends

Repurchase of stock

Proceeds from new stock issue

Total cash flow from financing activities

Change in cash (on the balance sheet)

−$  73 86

− 43 −   6        43

  $  7

  $   41

TABLE 2.7    Statement of Consolidated Cash Flows of the U.S. Composite Corporation

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U.S. COMPOSITE CORPORATION Cash F low f rom F inancing Act iv i t ies

2017 ( in $ mi l l ions)

Retirement of long-term debt

Proceeds from long-term debt sales

Dividends

Repurchase of stock

Proceeds from new stock issue

Cash flow from financing activities

−$73 86

−  43 − 6     43

  $  7

The statement of cash flows is the addition of cash flows from operations, cash flows from investing activities, and cash flows from financing activities, and is produced in Table 2.7. When we add all the cash flows together, we get the change in cash on the bal- ance sheet of $33 million.

There is a close relationship between the official accounting statement called the statement of cash flows and the total distributable cash flow of the firm used in finance. Going back to the previous section, you should note a slight conceptual problem here. Interest paid should really go under financing activities, but unfortunately that is not how the accounting is handled. The reason is that interest is deducted as an expense when net income is computed. As a consequence, a primary difference between the accounting cash flow and the cash flow of the firm (see Table 2.6) is interest expense.

SUMMARY AND CONCLUSIONS Besides introducing you to corporate accounting, the purpose of this chapter has been to teach you how to determine cash flow from the accounting statements of a typical company.

1. Cash flow is generated by the firm and paid to creditors and shareholders. It can be classified as

a. Cash flow from operations.

b. Cash flow from changes in fixed assets.

c. Cash flow from changes in working capital.

2. Calculations of cash flow are not difficult, but they require care and particular attention to detail in prop- erly accounting for noncash expenses such as depreciation and deferred taxes. It is especially important that you do not confuse cash flow with changes in net working capital and net income.

1. Liquidity What does liquidity measure? Explain the trade-off a firm faces between high liquidity and low liquidity levels.

2. Accounting and Cash Flows Why is it that the revenue and cost figures shown on a standard income statement may not be representative of the actual cash inflows and outflows that occurred during the period?

3. Accounting Statement of Cash Flows Looking at the accounting statement of cash flows, what does the bottom-line number mean? How useful is this number for analyzing a company?

4. Cash Flows How do financial cash flows and the accounting statement of cash flows differ? Which is more useful when analyzing a company?

CONCEPT QUESTIONS

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5. Book Values versus Market Values Under standard accounting rules, it is possible for a company’s liabilities to exceed its assets. When this occurs, the owners’ equity is negative. Can this happen with market values? Why or why not?

6. Cash Flow from Assets Suppose a company’s cash flow from assets was negative for a particular period. Is this necessarily a good sign or a bad sign?

7. Operating Cash Flow Suppose a company’s operating cash flow was negative for several years running. Is this necessarily a good sign or a bad sign?

8. Net Working Capital and Capital Spending Could a company’s change in net working capital be negative in a given year? (Hint: Yes.) Explain how this might come about. What about net capital spending?

9. Cash Flow to Stockholders and Creditors Could a company’s cash flow to stockholders be negative in a given year? (Hint: Yes.) Explain how this might come about. What about cash flow to creditors?

10. Firm Values Referring back to the Microsoft example used at the beginning of the chapter, note that we suggested that Microsoft’s stockholders probably didn’t suffer as a result of the reported loss. What do you think was the basis for our conclusion?

QUESTIONS AND PROBLEMS

1. Building a Balance Sheet Burnett, Inc., has current assets of $6,800, net fixed assets of $29,400, current liabilities of $5,400, and long-term debt of $13,100. What is the value of the shareholders’ equity account for this firm? How much is net working capital?

2. Building an Income Statement    Bradds, Inc., has sales of $528,600, costs of $264,400, depreciation expense of $41,700, interest expense of $20,700, and a tax rate of 35 percent. What is the net income for the firm? Suppose the company paid out $27,000 in cash dividends. What is the addition to retained earnings?

3. Market Values and Book Values Klingon Cruisers, Inc., purchased new cloaking machinery three years ago for $7 million. The machinery can be sold to the Romulans today for $5.3 million. Klingon’s current balance sheet shows net fixed assets of $3.9 million, current liabilities of $1.075 million, and net working capital of $320,000. If all the current accounts were liquidated today, the company would receive $410,000 cash. What is the book value of Klingon’s total assets today? What is the sum of the market value of NWC and market value of assets?

4. Calculating Taxes The Alexander Co. had $328,500 in taxable income. Using the rates from Table 2.3 in the chapter, calculate the company’s income taxes. What is the average tax rate? What is the marginal tax rate?

5. Calculating OCF Timsung, Inc., has sales of $30,700, costs of $11,100, depreciation expense of $2,100, and interest expense of $1,140. If the tax rate is 40 percent, what is the operating cash flow, or OCF?

6. Calculating Net Capital Spending Busch Driving School’s 2016 balance sheet showed net fixed assets of $3.75 million, and the 2017 balance sheet showed net fixed assets of $4.45 million. The company’s 2017 income statement showed a depreciation expense of $395,000. What was the company’s net capital spending for 2017?

7. Building a Balance Sheet The following table presents the long-term liabilities and stockholders’ equity of Information Control Corp. one year ago:

Basic (Questions 1–10)

Long-term debt

Preferred stock

Common stock ($1 par value)

Capital surplus

Accumulated retained earnings

$37,000,000

2,100,000

8,900,000

41,000,000

75,300,000

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CHAPTER 2 Financial Statements and Cash Flow 35

During the past year, the company issued 4 million shares of new stock at a total price of $26 million, and issued $9.5 million in new long-term debt. The company generated $15.3 million in net income and paid $3.1 million in dividends. Construct the current balance sheet reflecting the changes that occurred on the company’s balance sheet during the year.

8. Cash Flow to Creditors The 2016 balance sheet of Maria’s Tennis Shop, Inc., showed long-term debt of $2.4 million, and the 2017 balance sheet showed long-term debt of $2.53 million. The 2017 income statement showed an interest expense of $187,000. What was the firm’s cash flow to creditors during 2017?

9. Cash Flow to Stockholders The 2016 balance sheet of Maria’s Tennis Shop, Inc., showed $540,000 in the common stock account and $5.6 million in the additional paid-in surplus account. The 2017 balance sheet showed $595,000 and $6.18 million in the same two accounts, respectively. If the company paid out $270,000 in cash dividends during 2017, what was the cash flow to stockholders for the year?

10. Calculating Total Cash Flows Given the information for Maria’s Tennis Shop, Inc., in the previous two problems, suppose you also know that the firm’s net capital spending for 2017 was $640,000, and that the firm reduced its net working capital investment by $65,000. What was the firm’s 2017 operating cash flow, or OCF?

11. Cash Flows Ritter Corporation’s accountants prepared the following financial statements for year-ends. Intermediate (Questions 11–25)

RITTER CORPORATION Income Statement

2017

Revenue

Expenses

Depreciation

EBT

Tax

Net income

Dividends

$1,068

745

77

$   246

98

$ 148

$ 40

RITTER CORPORATION Balance Sheets

December 31

2016 2017

Assets

Cash

Other current assets

Net fixed assets

Total assets

Liabilities and Equity

Accounts payable

Long-term debt

Stockholders’ equity

Total liabilities and equity

$ 81

253

690

$1,024

$ 295

0

729

$1,024

$ 93

265

824

$1,182

$ 301

44

837

$1,182

a. Explain the change in cash during the year 2017.

b. Determine the change in net working capital in 2017.

c. Determine the cash flow generated by the firm’s assets during the year 2017.

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PART 1 Overview36

12. Cash Flow Identity Freeman, Inc., reported the following financial statements for the last two years. Construct the cash flow identity for the company. Explain what each number means.

FREEMAN, INC. Balance Sheet as of December 31, 2017

Cash

Accounts receivable

Inventory

Current assets

Net fixed assets

Total assets

$  18,143

19,527

28,614

$  66,284

$498,312

$564,596

Accounts payable

Long-term debt

Owners’ equity

Total liabilities and owners’ equity

$  32,978 

$179,400 

$352,218 

$564,596 

FREEMAN, INC. 2017 Income Statement

Sales

Cost of goods sold

Selling & administrative

Depreciation

EBIT

Interest

EBT

Taxes

Net income

Dividends

Addition to retained earnings

$703,100

329,413

153,405

66,513

$153,769

23,280

$130,489

45,671

$ 84,818

15,200

$ 69,618

FREEMAN, INC. Balance Sheet as of December 31, 2016

Cash

Accounts receivable

Inventory

Current assets

Net fixed assets

Total assets

$ 16,302

16,849

23,875

57,026

415,289

$472,315

Accounts payable

Long-term debt

Owners’ equity

Total liabilities and owners’ equity

$ 29,342

165,300

277,673

$472,315

13. Financial Cash Flows The Stancil Corporation provided the following current information:

Proceeds from long-term borrowing

Proceeds from the sale of common stock

Purchases of fixed assets

Purchases of inventories

Payment of dividends

$16,500 

2,700 

19,200 

2,700 

7,100 

Determine the cash flows from the firm and the cash flows to investors of the firm.

14. Building an Income Statement During the year, the Senbet Discount Tire Company had gross sales of $757,000. The company’s cost of goods sold and selling expenses were $249,800 and $146,000,

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CHAPTER 2 Financial Statements and Cash Flow 37

respectively. The company also had debt of $675,000, which carried an interest rate of 6 percent. Depreciation was $87,000. The tax rate was 35 percent.

a. What was the company’s net income?

b. What was the company’s operating cash flow?

15. Calculating Total Cash Flows Schwert Corp. shows the following information on its 2017 income statement: sales = $225,000; costs = $103,200; other expenses = $6,100; depreciation expense = $15,300; interest expense = $11,200; taxes = $31,227; dividends = $18,100. In addition, you’re told that the firm issued $6,000 in new equity during 2017, and redeemed $8,500 in outstanding long-term debt.

a. What was the 2017 operating cash flow?

b. What was the 2017 cash flow to creditors?

c. What was the 2017 cash flow to stockholders?

d. If net fixed assets increased by $33,000 during the year, what was the addition to net working capital?

16. Using Income Statements Given the following information for O’Hara Marine Co., calculate the depreciation expense: sales = $57,900; costs = $28,600; addition to retained earnings = $8,100; dividends paid = $5,200; interest expense = $2,050; tax rate = 35 percent.

17. Preparing a Balance Sheet Prepare a 2017 balance sheet for Jarrow Corp. based on the following information: cash = $168,000; patents and copyrights = $827,000; accounts payable = $429,000; accounts receivable = $237,000; tangible net fixed assets = $3,410,000; inventory = $385,000; notes payable = $171,000; accumulated retained earnings = $2,084,000; long-term debt = $1,985,000.

18. Residual Claims Huang, Inc., is obligated to pay its creditors $11,600 very soon.

a. What is the market value of the shareholders’ equity if assets have a market value of $15,100?

b. What if assets equal $9,900?

19. Marginal versus Average Tax Rates (Refer to Table 2.3.) Corporation Growth has $79,500 in taxable income, and Corporation Income has $7,950,000 in taxable income.

a. What is the tax bill for each firm?

b. Suppose both firms have identified a new project that will increase taxable income by $10,000. How much in additional taxes will each firm pay? Why is this amount the same?

20. Net Income and OCF During 2017, Raines Umbrella Corp. had sales of $809,000. Cost of goods sold, administrative and selling expenses, and depreciation expenses were $549,000, $136,000, and $85,000, respectively. In addition, the company had an interest expense of $67,000 and a tax rate of 35 percent. (Ignore any tax loss carryback or carryforward provisions.)

a. What was the company’s net income for 2017?

b. What was its operating cash flow?

c. Explain your results in (a) and (b).

21. Accounting Values versus Cash Flows In the previous problem, suppose Raines Umbrella Corp. paid out $75,000 in cash dividends. Is this possible? If net capital spending and the change in net working capital were both zero, and if no new stock was issued during the year, what was the change in the firm’s long-term debt account?

22. Calculating Cash Flows Blue Diamond Industries had the following operating results for 2017; sales = $44,600; cost of goods sold = $27,500; depreciation expense = $4,630; interest expense = $1,050; dividends paid = $2,275. At the beginning of the year, net fixed assets were $27,510,

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current assets were $6,840, and current liabilities were $4,580. At the end of the year, net fixed assets were $35,610, current assets were $7,720, and current liabilities were $4,830. The tax rate was 40 percent.

a. What was net income for 2017?

b. What was the operating cash flow for 2017?

c. What was the cash flow from assets for 2017? Is this possible? Explain.

d. If no new debt was issued during the year, what was the cash flow to creditors? What was the cash flow to stockholders? Explain and interpret the positive and negative signs of your answers in (a) through (d).

23. Calculating Cash Flows Consider the following abbreviated financial statements for Weston Enterprises:

a. What was owners’ equity for 2016 and 2017?

b. What was the change in net working capital for 2017?

c. In 2017, the company purchased $2,740 in new fixed assets. How much in fixed assets did the company sell? What was the cash flow from assets for the year? The tax rate is 35 percent.

d. During 2017, the company raised $634 in new long-term debt. How much long-term debt must the company have paid off during the year? What was the cash flow to creditors?

Use the following information for Ingersoll, Inc., for Problems 24 and 25 (assume the tax rate is 35 percent):

WESTON ENTERPRISES 2017 Income Statement

Sales

Costs

Depreciation

Interest paid

$15,690

3,739

1,339

562 

WESTON ENTERPRISES 2016 and 2017 Part ia l Balance Sheets

Assets L iabi l i t ies and Owners’ Equi ty

Current assets

Net fixed assets

2016

$1,066

5,184

2017

$1,145

5,472

Current liabilities

Long-term debt

2016

$ 475

2,880

2017

$ 518

3,090

2016 2017

Sales

Depreciation

Cost of goods sold

Other expenses

Interest

Cash

Accounts receivable

Long-term debt

Net fixed assets

Accounts payable

Inventory

Dividends

$  40,743  

    5,853

  14,020

    3,322

    2,098

  21,364

  28,283

  71,550

179,166

  27,349

  50,287

    4,966

$  43,277  

    5,858

  15,912

    2,776

    3,142

  21,856

  31,864

  83,476

183,440

  25,639

  51,675

    5,468

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CHAPTER 2 Financial Statements and Cash Flow 39

24. Financial Statements Draw up an income statement and balance sheet for this company for 2016 and 2017.

25. Calculating Cash Flow For 2017, calculate the cash flow from assets, cash flow to creditors, and cash flow to stockholders.

26. Cash Flows You are researching Time Manufacturing and have found the following accounting statement of cash flows for the most recent year. You also know that the company paid $185 million in current taxes and had an interest expense of $96 million. Use the accounting statement of cash flows to construct the financial statement of cash flows.

Challenge (Questions 26–28)

TIME MANUFACTURING Statement of Cash F lows

( in $ mi l l ions)

Operations

Net income

Depreciation

Deferred taxes

Changes in current assets and liabilities

Accounts receivable

Inventories

Accounts payable

Accrued expenses

Other

Total cash flow from operations

Investing activities

Acquisition of fixed assets

Sale of fixed assets

Total cash flow from investing activities

Financing activities

Retirement of long-term debt

Proceeds from long-term debt sales

Dividends

Repurchase of stock

Proceeds from new stock issue

Total cash flow from financing activities

Change in cash (on balance sheet)

$321 

177 

34 

– 52  41 

33 

– 17          4 

  $541

–$332        42 

–$290 

–$195  105 

–  158  – 26    50 

–$224 

  $  27 

27. Net Fixed Assets and Depreciation On the balance sheet, the net fixed assets (NFA) account is equal to the gross fixed assets (FA) account, which records the acquisition cost of fixed assets, minus the accumulated depreciation (AD) account, which records the total depreciation taken by the firm against its fixed assets. Using the fact that NFA = FA – AD, show that the expression given in the chapter for net capital spending, NFAend – NFAbeg + D (where D is the depreciation expense during the year), is equivalent to FAend – FAbeg.

28. Tax Rates Refer to the corporate marginal tax rate information in Table 2.3.

a. Why do you think the marginal tax rate jumps up from 34 percent to 39 percent at a taxable income of $100,001, and then falls back to a 34 percent marginal rate at a taxable income of $335,001?

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b. Compute the average tax rate for a corporation with exactly $335,001 in taxable income. Does this confirm your explanation in part (a)? What is the average tax rate for a corporation with income of exactly $18,333,334? Is the same thing happening here?

c. The 39 percent and 38 percent tax rates both represent what is called a tax “bubble.” Suppose the government wanted to lower the upper threshold of the 39 percent marginal tax bracket from $335,000 to $200,000. What would the new 39 percent bubble rate have to be?

WHAT’S ON THE WEB? 1. Change in Net Working Capital Find the most recent abbreviated balance sheets for General

Dynamics at finance.yahoo.com. Enter the ticker symbol “GD” and follow the “Balance Sheet” link. Using the two most recent balance sheets, calculate the change in net working capital. What does this number mean?

2. Book Values versus Market Values The home page for The Coca-Cola Company can be found at www.coca-cola.com. Locate the most recent annual report, which contains a balance sheet for the company. What is the book value of equity for Coca-Cola? The market value of a company is the number of shares of stock outstanding times the price per share. This information can be found at finance.yahoo. com using the ticker symbol for Coca-Cola (KO). What is the market value of equity? Which number is more relevant for shareholders?

3. Cash Flows to Stockholders and Creditors Cooper Tire and Rubber Company provides financial information for investors on its website at www.coopertire.com. Follow the “Investors” link and find the most recent annual report. Using the consolidated statements of cash flows, calculate the cash flow to stockholders and the cash flow to creditors.

EXCEL MASTER IT ! PROBLEM Using Excel to find the marginal tax rate can be accomplished with the VLOOKUP function. However, calculat- ing the total tax bill is a little more difficult. Below we have shown a copy of the IRS tax table for an individual from a recent year. Often, tax tables are presented in this format.

IF TAXABLE INCOME IS OVER: BUT NOT OVER: THE TAX IS :

$           0

     9,275

   37,650

   91,150

 190,150

 413,350

 415,050

$  9,275

    37,650

    91,150

  190,150

  413,350

  415,050

10% of the amount over $0

$927.50 plus 15% of the amount over $9,275

$5,183.75 plus 25% of the amount over $37,650

$18,558.75 plus 28% of the amount over $91,150

$46,278.75 plus 33% of the amount over $190,150

$119,934.75 plus 35% of the amount over $413,350

$120,529.75 plus 39.6% of the amount over $415,050

In reading this table, the marginal tax rate for taxable income less than $9,275 is 10 percent. If the taxable income is between $9,275 and $37,650, the tax bill is $927.50 plus the marginal taxes. The marginal taxes are calculated as the taxable income minus $9,275 times the marginal tax rate of 15 percent.

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CASH FLOWS AT EAST COAST YACHTS Because of the dramatic growth at East Coast Yachts, Larissa decided that the company should be reorganized as a corporation (see our Chapter 1 Closing Case for more detail). Time has passed and, today, the company is publicly traded under the ticker symbol “ECY”.

Dan Ervin was recently hired by East Coast Yachts to assist the company with its short-term financial planning and also to evaluate the com- pany’s financial performance. Dan graduated from college five years ago with a finance degree, and he has been employed in the treasury depart- ment of a Fortune 500 company since then.

The company’s past growth has been some- what hectic, in part due to poor planning. In antic- ipation of future growth, Larissa has asked Dan to analyze the company’s cash flows. The company’s financial statements are prepared by an outside auditor. Nearby you will find the most recent income statement and the balance sheets for the past two years.

Larissa has also provided the following information. During the year, the company raised $40 million in new long-term debt and retired $22.6 million in long-term debt. The company also sold $24.2 million in new stock and repurchased $35.64 million. The company purchased $59.5 million in fixed assets, and sold $6,718,200 in fixed assets.

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CHAPTER 2 Financial Statements and Cash Flow 41

Below, we have the corporate tax table as shown in Table 2.3.

IF TAXABLE INCOME IS GREATER THAN OR EQUAL TO: BUT LESS THAN: THE TAX RATE IS :

$                  0

           50,001

           75,001

         100,001

         335,001

   10,000,001

   15,000,001

   18,333,334

$        50,000

          75,000

        100,000

        335,000

   10,000,000

   15,000,000

   18,333,333

  15%

25   

34   

39   

34   

35   

38   

35   

a. Create a tax table in Excel for corporate taxes similar to the individual tax table shown above. Your spreadsheet should then calculate the marginal tax rate, the average tax rate, and the tax bill for any level of taxable income input by a user.

b. For a taxable income of $1,350,000, what is the marginal tax rate?

c. For a taxable income of $1,350,000, what is the total tax bill?

d. For a taxable income of $1,350,000, what is the average tax rate?

CLOSING CASE

EAST COAST YACHTS

2017 Income Statement

Sales

Cost of goods sold

Selling, general, and administrative

Depreciation

EBIT

Interest expense

EBT

Taxes

Net income

Dividends

Retained earnings

$611,582,000

431,006,000

73,085,700

19,958,400

$ 87,531,900

11,000,900

$ 76,531,000

30,612,400

$ 45,918,600

17,374,500

$ 28,544,100

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Larissa has asked Dan to prepare the financial statement of cash flows and the accounting statement of cash flows. She has also asked you to answer the following questions:

1. How would you describe East Coast Yachts’ cash flows?

2. Which cash flows statement more accurately describes the cash flows at the company?

3. In light of your previous answers, comment on Larissa’s expansion plans.

EAST COAST YACHTS Balance Sheet

2016 2017 2016 2017

Current assets

Cash and equivalents

Accounts receivable

Inventories

Other

Total current assets

Fixed assets

Property, plant, and equipment

Less accumulated depreciation

Net property, plant, and equipment

Intangible assets and others

Total fixed assets

Total assets

$ 10,644,500 

18,924,800

17,090,100 

1,097,700

$ 47,757,100

$404,727,800

(93,887,500)

$310,840,300

6,772,000

$317,612,300

$365,369,400

$ 11,119,700

18,681,500

20,149,650

1,172,200

$ 51,123,050

$457,509,600

(113,845,900)

$343,663,700

6,772,000

$350,435,700

$ 401,558,750

Current liabilities

Accounts payable

Accrued expenses

Total current liabilities

Long-term debt

Total long-term liabilities

Stockholders’ equity

Preferred stock

Common stock

Capital surplus

Accumulated retained earnings

Less treasury stock

Total equity

Total liabilities and shareholders’ equity

$  43,482,200

      5,417,300

$  48,899,500

$151,860,000

$151,860,000

$    1,970,000

29,700,000

11,800,000

133,019,900

    (11,880,000)

$164,609,900

$365,369,400

$ 44,461,550

6,123,200

$ 50,584,750

$169,260,000

$169,260,000

$ 1,970,000

37,583,700

28,116,300

161,564,000

   (47,520,000)

$181,714,000

$401,558,750

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CHAPTER 3 Financial Statements Analysis and Financial Models 43

The price of a share of common stock in expensive groceries retailer Whole Foods closed at

about $29 on February 5, 2015. At that price, Whole Foods had a price−earnings (PE) ratio of 20. That is, investors were willing to pay $20 for every dollar in income earned by Whole

Foods. At the same time, investors were willing to pay $10, $12, and $402 for each dollar

earned by Ford, Cisco Systems, and Amazon.com, respectively. At the other extreme were

General Electric (GE) and Anadarko Petroleum. Each had negative earnings for the previous

year, yet GE was priced at about $29 per share and Anadarko Petroleum at about $41 per

share. Because they had negative earnings, their PE ratios would have been negative, so

they were not reported. At the time, the typical stock in the S&P 500 Index of large-company

stocks was trading at a PE of about 17, or about 17 times earnings, as they say on Wall Street.

Price-to-earnings comparisons are examples of the use of financial ratios. As we will see

in this chapter, there are a wide variety of financial ratios, all designed to summarize spe-

cific aspects of a firm’s financial position. In addition to discussing how to analyze financial

statements and compute financial ratios, we will have quite a bit to say about who uses this

information and why.

Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.

OPENING CASE

Financial Statements Analysis and Financial Models

3

3.1 FINANCIAL STATEMENTS ANALYSIS In Chapter 2, we discussed some of the essential concepts of financial statements and cash flows. This chapter continues where our earlier discussion left off. Our goal here is to expand your understanding of the uses (and abuses) of financial statement information.

A good working knowledge of financial statements is desirable because such statements, and numbers derived from those statements, are the primary means of communicating financial information both within the firm and outside the firm. In short, much of the lan- guage of business finance is rooted in the ideas we discuss in this chapter.

Clearly, one important goal of the accountant is to report financial information to the user in a form useful for decision making. Ironically, the information frequently does not come to the user in such a form. In other words, financial statements don’t come with a user’s guide. This chapter is a first step in filling this gap.

Standardizing Statements One obvious thing we might want to do with a company’s financial statements is to compare them to those of other, similar companies. We would immediately have a prob- lem, however. It’s almost impossible to directly compare the financial statements for two companies because of differences in size.

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44

For example, Tesla and GM are obviously serious rivals in the auto market, but GM is larger, so it is difficult to compare them directly. For that matter, it’s difficult even to compare financial statements from different points in time for the same company if the company’s size has changed. The size problem is compounded if we try to compare GM and, say, Toyota. If Toyota’s financial statements are denominated in yen, then we have size and currency differences.

To start making comparisons, one obvious thing we might try to do is to somehow standardize the financial statements. One common and useful way of doing this is to work with percentages instead of total dollars. The resulting financial statements are called common-size statements. We consider these next.

Common-Size Balance Sheets For easy reference, Prufrock Corporation’s 2016 and 2017 balance sheets are provided in Table 3.1. Using these, we construct common-size balance sheets by expressing each item as a percentage of total assets. Prufrock’s 2016 and 2017 common-size balance sheets are shown in Table 3.2.

Notice that some of the totals don’t check exactly because of rounding errors. Also notice that the total change has to be zero because the beginning and ending numbers must add up to 100 percent.

In this form, financial statements are relatively easy to read and compare. For exam- ple, just looking at the two balance sheets for Prufrock, we see that current assets were 19.7  percent of total assets in 2017, up from 19.0 percent in 2016. Current liabilities declined from 16.1 percent to 15.1 percent of total liabilities and equity over that same time. Similarly, total equity rose from 68.2 percent of total liabilities and equity to 72.2 percent.

Overall, Prufrock’s liquidity, as measured by current assets compared to current liabilities, increased over the year. Simultaneously, Prufrock’s indebtedness diminished as a percentage of total assets. We might be tempted to conclude that the balance sheet has grown “stronger.”

PRUFROCK CORPORATION Balance Sheets as of December 31 , 2016 and 2017

($ in mi l l ions)

Assets

Current assets

Cash

Accounts receivable

Inventory

Total

Fixed assets

Net plant and equipment

Total assets

2016

$       84

165

      393

$      642

$ 2,731

$ 3,373

2017

$       98

188

     422

$ 708

$ 2,880

$ 3,588

Liabilities and Owners’ Equity

Current liabilities

Accounts payable

Notes payable

Total

Long-term debt

Owners’ equity

Common stock and paid-in surplus

Retained earnings

Total

Total liabilities and owners’ equity

$      312

      231

$      543

$      531

$      500

1,799

$ 2,299

$ 3,373

$      344

     196

$      540

$      457

$      550

    2,041

$ 2,591

$ 3,588

TABLE 3.1

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Common-Size Income Statements Table 3.3 describes some commonly used measures of earnings. A useful way of standard- izing the income statement shown in Table 3.4 is to express each item as a percentage of total sales, as illustrated for Prufrock in Table 3.5.

Investors and analysts look closely at the income statement for clues on how well a company has performed during a particular year. Here are some commonly used measures of earnings (numbers in millions).

Net Income The so-called bottom line, defined as total revenue minus total expenses. Net income for Prufrock in the latest period is $363 million. Net income reflects differences in a firm’s capital structure and taxes as well as operating income. Interest expense and taxes are subtracted from operating income in computing net income. Shareholders look closely at net income because dividend payout and retained earnings are closely linked to net income.

EPS Net income divided by the number of shares outstanding. It expresses net income on a per-share basis. For Prufrock, the EPS = (Net income)/(Shares outstanding) = $363/33 = $11.

EBIT Earnings before interest expense and taxes. EBIT is usually called “income from operations” on the income statement and is income before unusual items, discontinued operations, or extraordinary items. To calculate EBIT, operating expenses are subtracted from total opera- tions revenues. Analysts like EBIT because it abstracts from differences in earnings from a firm’s capital structure (interest expense) and taxes. For Prufrock, EBIT is $691 million.

EBITDA Earnings before interest expense, taxes, depreciation, and amortization. EBITDA = EBIT + depreciation and amortization. Here amortization refers to a noncash expense similar to depre- ciation except it applies to an intangible asset (such as a patent), rather than a tangible asset (such as a machine). The word amortization here does not refer to the payment of debt. There is no amortization in Prufrock’s income statement. For Prufrock, EBITDA = $691 + 276 = $967 million. Analysts like to use EBITDA because it adds back two noncash items (depreciation and amortization) to EBIT and thus is a better measure of before-tax operating cash flow.

Sometimes these measures of earnings are preceded by the letters LTM, meaning the last twelve months. For example, LTM EPS is the last 12 months of EPS and LTM EBITDA is the last 12 months of EBITDA. At other times, the letters TTM are used, meaning trailing 12 months. Needless to say, LTM is the same as TTM.

TABLE 3.3 Measures of Earnings

PRUFROCK CORPORATION Common-Size Balance Sheets December 31, 2016 and 2017

Assets

Current assets

Cash

Accounts receivable

Inventory

Total

Fixed assets

Net plant and equipment

Total assets

2016

2.5%

4.9

11.7

19.0

81.0

100.0%

2017

2.7%

5.2

11.8

19.7

80.3

100.0%

Change

+ .2% + .3 + .1 + .7

− .7 .0%

Liabilities and Owners’ Equity

Current liabilities

Accounts payable

Notes payable

Total

Long-term debt

Owners’ equity

Common stock and paid-in surplus

Retained earnings

Total

Total liabilities and owners’ equity

9.2%

6.8

16.1

15.7

14.8

53.3

68.2

100.0%

9.6%

5.5

15.1

12.7

15.3

56.9

72.2

100.0%

+ .3% −1.4 −1.0 −3.0

+ .5 +3.5 +4.1 .0%

TABLE 3.2

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PRUFROCK CORPORATION 2017 Income Statement

($ in mi l l ions)

Sales

Cost of goods sold

Depreciation

Earnings before interest and taxes

Interest paid

Taxable income

Taxes (34%)

Net income

Dividends

Addition to retained earnings

$121

242

$2,311

1,344

276

$ 691

141

$ 550

187

$ 363

TABLE 3.4

PRUFROCK CORPORATION Common-Size Income Statement 2017

Sales

Cost of goods sold

Depreciation

Earnings before interest and taxes

Interest paid

Taxable income

Taxes (34%)

Net income

Dividends

Addition to retained earnings

5.2%

10.5

100.0%

58.2

11.9

29.9

6.1

23.8

8.1

15.7%

TABLE 3.5

This income statement tells us what happens to each dollar in sales. For Prufrock, inter- est expense eats up $.061 out of every sales dollar, and taxes take another $.081. When all is said and done, $.157 of each dollar flows through to the bottom line (net income), and that amount is split into $.105 retained in the business and $.052 paid out in dividends.

These percentages are useful in comparisons. For example, a relevant figure is the cost percentage. For Prufrock, $.582 of each $1.00 in sales goes to pay for goods sold. It would be interesting to compute the same percentage for Prufrock’s main competitors to see how Prufrock stacks up in terms of cost control.

3.2 RATIO ANALYSIS Another way of avoiding the problems involved in comparing companies of different sizes is to calculate and compare financial ratios. Such ratios are ways of comparing and inves- tigating the relationships between different pieces of financial information. We cover some of the more common ratios next (there are many others we don’t discuss here).

One problem with ratios is that different people and different sources frequently don’t compute them in exactly the same way, and this leads to much confusion. The specific definitions we use here may or may not be the same as ones you have seen or will see else- where. If you are using ratios as tools for analysis, you should be careful to document how you calculate each one; and, if you are comparing your numbers to those of another source, be sure you know how their numbers are computed.

ExcelMaster coverage online

www.mhhe.com/RossCore5e

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We will defer much of our discussion of how ratios are used and some problems that come up with using them until later in the chapter. For now, for each ratio we discuss, sev- eral questions come to mind:

1. How is it computed? 2. What is it intended to measure, and why might we be interested? 3. What is the unit of measurement? 4. What might a high or low value be telling us? How might such values be

misleading? 5. How could this measure be improved?

Financial ratios are traditionally grouped into the following categories:

1. Short-term solvency, or liquidity, ratios. 2. Long-term solvency, or financial leverage, ratios. 3. Asset management, or turnover, ratios. 4. Profitability ratios. 5. Market value ratios.

We will consider each of these in turn. In calculating these numbers for Prufrock, we will use the ending balance sheet (2017) figures unless we explicitly say otherwise.

Short-Term Solvency or Liquidity Measures As the name suggests, short-term solvency ratios as a group are intended to provide infor- mation about a firm’s liquidity, and these ratios are sometimes called liquidity measures. The primary concern is the firm’s ability to pay its bills over the short run without undue stress. Consequently, these ratios focus on current assets and current liabilities.

For obvious reasons, liquidity ratios are particularly interesting to short-term creditors. Because financial managers are constantly working with banks and other short-term lend- ers, an understanding of these ratios is essential.

One advantage of looking at current assets and liabilities is that their book values and market values are likely to be similar. Often (though not always), these assets and liabilities just don’t live long enough for the two to get seriously out of step. On the other hand, like any type of near-cash, current assets and liabilities can and do change fairly rapidly, so today’s amounts may not be a reliable guide to the future.

CURRENT RATIO One of the best-known and most widely used ratios is the current ratio. As you might guess, the current ratio is defined as

Current ratio = Current assets _______________ Current liabilities

[3.1]

For Prufrock, the 2017 current ratio is

Current ratio = $708 _____ $540

= 1.31 times

Because current assets and liabilities are, in principle, converted to cash over the follow- ing 12 months, the current ratio is a measure of short-term liquidity. The unit of measurement is either dollars or times. So, we could say Prufrock has $1.31 in current assets for every $1 in current liabilities, or we could say Prufrock has its current liabilities covered 1.31 times over.

To a creditor, particularly a short-term creditor such as a supplier, the higher the cur- rent ratio, the better. To the firm, a high current ratio indicates liquidity, but it also may indicate an inefficient use of cash and other short-term assets. Absent some extraordinary

Go to www.reuters.com/ finance/stocks and find the “Financials” link to examine comparative ratios for a huge number of companies.

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circumstances, we would expect to see a current ratio of at least 1; a current ratio of less than 1 would mean that net working capital (current assets less current liabilities) is nega- tive. This would be unusual in a healthy firm, at least for most types of businesses.

The current ratio, like any ratio, is affected by various types of transactions. For exam- ple, suppose the firm borrows over the long term to raise money. The short-run effect would be an increase in cash from the issue proceeds and an increase in long-term debt. Current liabilities would not be affected, so the current ratio would rise.

E X

A M

P L

E

3 .1

Suppose a firm were to pay off some of its suppliers and short-term creditors. What would happen to the current ratio? Suppose a firm buys some inventory. What happens in this case? What happens if a firm sells some merchandise?

The first case is a trick question. What happens is that the current ratio moves away from 1. If it is greater than 1 (the usual case), it will get bigger, but if it is less than 1, it will get smaller. To see this, suppose the firm has $4 in current assets and $2 in current liabilities for a current ratio of 2. If we use $1 in cash to reduce current liabilities, the new current ratio is ($4 − 1)/($2 − 1) = 3. If we reverse the original situation to $2 in current assets and $4 in current liabilities, the change will cause the current ratio to fall to 1/3 from 1/2.

The second case is not quite as tricky. Nothing happens to the current ratio because cash goes down while inventory goes up—total current assets are unaffected.

In the third case, the current ratio would usually rise because inventory is normally shown at cost and the sale would normally be at something greater than cost (the difference is the markup). The increase in either cash or receivables is therefore greater than the decrease in inventory. This increases current assets, and the current ratio rises.

Current Events

Finally, note that an apparently low current ratio may not be a bad sign for a company with a large reserve of untapped borrowing power.

QUICK (OR ACID-TEST) RATIO Inventory is often the least liquid current asset. It’s also the one for which the book values are least reliable as measures of market value because the quality of the inventory isn’t considered. Some of the inventory may later turn out to be damaged, obsolete, or lost.

More to the point, relatively large inventories are often a sign of short-term trouble. The firm may have overestimated sales and overbought or overproduced as a result. In this case, the firm may have a substantial portion of its liquidity tied up in slow-moving inventory.

To further evaluate liquidity, the quick, or acid-test, ratio is computed just like the cur- rent ratio, except inventory is omitted:

Quick ratio = Current assets − Inventory _____________________ Current liabilities

[3.2]

Notice that using cash to buy inventory does not affect the current ratio, but it reduces the quick ratio. Again, the idea is that inventory is relatively illiquid compared to cash. For Prufrock, this ratio in 2017 was

Quick ratio = $708 − 422 _________ $540

= .53 times

The quick ratio here tells a somewhat different story than the current ratio because inven- tory accounts for more than half of Prufrock’s current assets. To exaggerate the point, if this inventory consisted of, say, unsold nuclear power plants, then this would be a cause for concern.

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To give an example of current versus quick ratios, based on recent financial statements, Walmart and Manpower, Inc., had current ratios of .93 and 1.47, respectively. However, Manpower carries no inventory to speak of, whereas Walmart’s current assets are virtually all inventory. As a result, Walmart’s quick ratio was only .20, and Manpower’s was 1.47, the same as its current ratio.

CASH RATIO A very short-term creditor might be interested in the cash ratio:

Cash ratio = Cash _______________ Current liabilities

[3.3]

You can verify that this works out to be .18 times for Prufrock.

Long-Term Solvency Measures Long-term solvency ratios are intended to address the firm’s long-run ability to meet its obligations or, more generally, its financial leverage. These ratios are sometimes called financial leverage ratios or just leverage ratios. We consider three commonly used mea- sures and some variations.

TOTAL DEBT RATIO The total debt ratio takes into account all debts of all maturities to all creditors. It can be defined in several ways, the easiest of which is this:

Total debt ratio = Total assets − Total equity ______________________ Total assets

[3.4]

= $3,588 − 2,591 _____________ $3,588

= .28 times

In this case, an analyst might say that Prufrock uses 28 percent debt.1 Whether this is high or low or whether it even makes any difference depends on whether capital structure mat- ters, a subject we discuss in a later chapter.

Prufrock has $.28 in debt for every $1 in assets. Therefore, there is $.72 in equity (= $1 − .28) for every $.28 in debt. With this in mind, we can define two useful variations on the total debt ratio, the debt−equity ratio and the equity multiplier:

Debt–equity ratio = Total debt∕Total equity [3.5] = $28∕$.72 = .39 times

Equity multiplier = Total assets∕Total equity [3.6] = $1∕$.72 = 1.39 times

The fact that the equity multiplier is 1 plus the debt−equity ratio is not a coincidence:

Equity multiplier = Total assets/Total equity = $1/$.72 = 1.39 times = (Total equity + Total debt)/Total equity = 1 + Debt–equity ratio = 1.39 times

The thing to notice here is that given any one of these three ratios, you can immediately calculate the other two, so they all say exactly the same thing.

The online Women’s Business Center has more information about financial statements, ratios, and small busi- ness topics at www.sba. gov/content/womens- business-resources.

1 Total equity here includes preferred stock, if there is any. An equivalent numerator in this ratio would be (Current liabilities + Long-term debt).

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TIMES INTEREST EARNED Another common measure of long-term solvency is the times interest earned (TIE) ratio. Once again, there are several possible (and common) defini- tions, but we’ll stick with the most traditional:

Times interest earned ratio = EBIT _______ Interest

[3.7]

= $691 _____ $141

= 4.90 times

As the name suggests, this ratio measures how well a company has its interest obligations covered, and it is often called the interest coverage ratio. For Prufrock, the interest bill is covered 4.9 times over.

CASH COVERAGE A problem with the TIE ratio is that it is based on EBIT, which is not really a measure of cash available to pay interest. The reason is that depreciation and amor- tization, noncash expenses, have been deducted out. Because interest is most definitely a cash outflow (to creditors), one way to define the cash coverage ratio is

Cash coverage ratio = EBIT + (Depreciation and amortization) _______________________________ Interest

[3.8]

= $691 + 276 ___________ $141

= $967 _____ $141

= 6.86 times

The numerator here, EBIT plus depreciation and amortization, is often abbreviated EBITDA (earnings before interest, taxes, depreciation, and amortization). It is a basic measure of the firm’s ability to generate cash from operations, and it is frequently used as a measure of cash flow available to meet financial obligations.

More recently another long-term solvency measure is increasingly seen in financial state- ment analysis and in debt covenants. It uses EBITDA and interest bearing debt. Specifically, for Prufrock:

Interest bearing debt _________________ EBITDA

= $196 million + 457 million _______________________ $967 million

= .68 times

Here we include notes payable (most likely notes payable is bank debt) and long-term debt in the numerator and EBITDA in the denominator. Values below 1 on this ratio are considered very strong and values above 5 are considered weak. However, a careful comparison with other comparable firms is necessary to properly interpret the ratio.

Asset Management or Turnover Measures We next turn our attention to the efficiency with which Prufrock uses its assets. The mea- sures in this section are sometimes called asset management or utilization ratios. The spe- cific ratios we discuss can all be interpreted as measures of turnover. What they are intended to describe is how efficiently, or intensively, a firm uses its assets to generate sales. We first look at two important current assets: inventory and receivables.

INVENTORY TURNOVER AND DAYS’ SALES IN INVENTORY During the year, Prufrock had a cost of goods sold of $1,344. Inventory at the end of the year was $422. With these num- bers, inventory turnover can be calculated as

Inventory turnover = Cost of goods sold ________________ Inventory

[3.9]

= $1,344 _______ $422

= 3.18 times

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In a sense, we sold off, or turned over, the entire inventory 3.18 times during the year. As long as we are not running out of stock and thereby forgoing sales, the higher this ratio is, the more efficiently we are managing inventory.

If we know that we turned our inventory over 3.18 times during the year, we can imme- diately figure out how long it took us to turn it over on average. The result is the average days’ sales in inventory:

Days’ sales in inventory = 365 days ________________ Inventory turnover

[3.10]

= 365 _____ 3.18

= 114.61 days

This tells us that, roughly speaking, inventory sits about 115 days on average before it is sold. Alternatively, assuming we used the most recent inventory and cost figures, it will take about 115 days to work off our current inventory.

For example, in December 2015, General Motors had an 82-day supply of vehicles in inventory, more than the 60-day supply considered normal. This figure means that at the then-current rate of sales, it would have taken General Motors 82 days to deplete the available supply, or, equivalently, that General Motors had 82 days of sales in inventory. At the same time, Ford had a 59-day inventory supply and Toyota’s inventory level stood at 45 days. Of course, we could also examine these numbers on a per-segment basis. For example, there was only a 26-day inventory for compact trucks and an inventory period of 44 days for midrange luxury SUVs. At the other end, van and large car inventory levels stood at 93 days and 98 days, respectively.

RECEIVABLES TURNOVER AND DAYS’ SALES IN RECEIVABLES Our inventory measures give some indication of how fast we can sell products. We now look at how fast we col- lect on those sales. The receivables turnover is defined in the same way as inventory turnover:

Receivables turnover = Sales _________________ Accounts receivable

[3.11]

= $2,311 _______ $188

= 12.29 times

Loosely speaking, we collected our outstanding credit accounts and lent the money again 12.29 times during the year.2

This ratio makes more sense if we convert it to days, so the days’ sales in receivables is

Days’ sales in receivables = 365 days __________________ Receivables turnover

[3.12]

= 365 ______ 12.29

= 29.69 days

Therefore, on average, we collect on our credit sales in about 30 days. For obvious reasons, this ratio is frequently called the average collection period (ACP). Also note that if we are using the most recent figures, we can also say that we have 30 days’ worth of sales currently uncollected.

2 Here we have implicitly assumed that all sales are credit sales. If they were not, we would use total credit sales in these calculations, not total sales. Also, in making this calculation, we use the value of accounts receivable at the end of the accounting period. A common alterna- tive is to use the average value of accounts receivable over the accounting period. The important point is to be consistent in your method of calculation over time and across firms.

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TOTAL ASSET TURNOVER Moving away from specific accounts like inventory or receiv- ables, we can consider an important “big picture” ratio, the total asset turnover ratio. As the name suggests, total asset turnover is

Total asset turnover = Sales __________ Total assets

[3.13]

= $2,311 _______ $3,588

= .64 times

In other words, for every dollar in assets, we generated $.64 in sales.

Profitability Measures The three types of measures we discuss in this section are probably the best-known and most widely used of all financial ratios. In one form or another, they are intended to measure how efficiently the firm uses its assets and how efficiently the firm manages its operations.

PROFIT MARGIN Companies pay a great deal of attention to their profit margin:

Profit margin = Net income __________ Sales

[3.14]

= $363 ______ $2,311

= .157, or 15.7%

This tells us that Prufrock, in an accounting sense, generates a little less than 16 cents in net income for every dollar in sales.

Here is a variation on the receivables collection period. How long, on average, does it take for Prufrock Corporation to pay its bills? To answer, we need to calculate the accounts payable turnover rate using cost of goods sold. We will assume that Prufrock purchases everything on credit.

The cost of goods sold is $1,344, and accounts payable are $344. The turnover is therefore $1,344/$344 = 3.91 times. So, payables turned over about every 365/3.91 = 93.42 days. On average, then, Prufrock takes about 93 days to pay. As a potential creditor, we might take note of this fact.

Payables Turnover

E X

A M

P L

E 3

.2

Suppose you find that a particular company generates $.40 in annual sales for every dollar in total assets. How often does this company turn over its total assets?

The total asset turnover here is .40 times per year. It takes 1/.40 = 2.5 years to turn assets over completely. The 2.5 number is frequently referred to as the firm’s capital intensity.

More Turnover

E X

A M

P L

E 3

.3

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EBITDA MARGIN Another commonly used measure of profitability is the EBITDA margin. As mentioned, EBITDA is a measure of before-tax operating cash flow. It adds back noncash expenses and does not include taxes or interest expense. As a consequence, EBITDA margin looks more directly at operating cash flows than does net income and does not include the effect of capital structure or taxes. For Prufrock, EBITDA margin is

EBITDA ______ Sales

= $967 million _____________ $2,311 million

= .418, or 41.8%

All other things being equal, a relatively high margin is obviously desirable. This situation corresponds to low expense ratios relative to sales. However, we hasten to add that other things are often not equal.

For example, lowering our sales price will usually increase unit volume but will nor- mally cause margins to shrink. Total profit (or, more importantly, operating cash flow) may go up or down, so the fact that margins are smaller isn’t necessarily bad. After all, isn’t it possible that, as the saying goes, “Our prices are so low that we lose money on every- thing we sell, but we make it up in volume”?3

Margins are very different for different industries. Grocery stores have a notoriously low profit margin, generally around 2 percent. In contrast, the profit margin for the phar- maceutical industry is about 18 percent. So, for example, it is not surprising that recent profit margins for Kroger and Pfizer were about 1.6 percent and 17.6 percent, respectively.

RETURN ON ASSETS Return on assets (ROA) is a measure of profit per dollar of assets. It can be defined several ways,4 but the most common is

Return on assets = Net income __________ Total assets

[3.15]

= $363 ______ $3,588

= .101, or 10.1%

RETURN ON EQUITY Return on equity (ROE) is a measure of how the stockholders fared during the year. Because benefiting shareholders is our goal, ROE is, in an accounting sense, the true bottom-line measure of performance. ROE is usually measured as

Return on equity = Net income __________ Total equity

[3.16]

= $363 ______ $2,591

= .140, or 14.0%

Therefore, for every dollar in equity, Prufrock generated 14 cents in profit; but, again, this is correct only in accounting terms.

Because ROA and ROE are such commonly cited numbers, we stress that it is important to remember they are accounting rates of return. For this reason, these measures should properly be called return on book assets and return on book equity.

The fact that ROE exceeds ROA reflects Prufrock’s use of financial leverage. We will examine the relationship between these two measures in the next section.

3 No, it’s not. 4 For example, we might want a return on assets measure that is neutral with respect to capital structure (interest expense) and taxes. Such a measure for Prufrock would be:

EBIT ___________ Total assets

= $691 _______ $3,588

= 19.3%

This measure has a very natural interpretation. If 19.3 percent exceeds Prufrock’s borrowing rate, Prufrock will earn more money on its investments than it will pay out to its creditors. The surplus will be available to Prufrock’s shareholders after adjusting for taxes.

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Market Value Measures Our final group of measures is based, in part, on information not necessarily contained in financial statements—the market price per share of the stock. Obviously, these measures can be calculated directly only for publicly traded companies.

We assume that Prufrock has 33 million shares outstanding and the stock sold for $88 per share at the end of the year. If we recall that Prufrock’s net income was $363  million, then we can calculate that its earnings per share (EPS) was

EPS = Net income ________________ Shares outstanding

= $363 _____ 33

[3.17]

PRICE–EARNINGS RATIO The first of our market value measures, the price−earnings or PE ratio (or multiple), is defined as

PE ratio = Price per share ________________ Earnings per share

[3.18]

= $88 ____ $11

= 8 times

In the vernacular, we would say that Prufrock shares sell for eight times earnings, or we might say that Prufrock shares have, or “carry,” a PE multiple of 8.

Because the PE ratio measures how much investors are willing to pay per dollar of cur- rent earnings, higher PEs are often taken to mean that the firm has significant prospects for future growth. Of course, if a firm had no or almost no earnings, its PE would probably be quite large; so, as always, care is needed in interpreting this ratio.

MARKET-TO-BOOK RATIO A second commonly quoted measure is the market-to-book ratio:

Market-to-book ratio = Market value per share ___________________ Book value per share

[3.19]

= $88 _________ $2,591/33

= $88 ______ $78.5

= 1.12 times

Notice that book value per share is total equity (not just common stock) divided by the number of shares outstanding.

Book value per share is an accounting number that reflects historical costs. In a loose sense, the market-to-book ratio therefore compares the market value of the firm’s invest- ments to their cost. A value less than 1 could mean that the firm has not been successful overall in creating value for its stockholders.

MARKET CAPITALIZATION The market capitalization of a public firm is equal to the firm’s stock market price per share multiplied by the number of shares outstanding. For Prufrock, this is:

Price per share × Shares outstanding = $88 × 33 million = $2,904 million

This is a useful number for potential buyers of Prufrock. A prospective buyer of all of the outstanding shares of Prufrock (in a merger or acquisition) would need to come up with at least $2,904 million plus a premium.

ENTERPRISE VALUE Enterprise value (EV) is a measure of firm value that is very closely related to market capitalization. Instead of focusing on only the market value of outstanding

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shares of stock, it measures the market value of outstanding shares of stock plus the market value of outstanding interest bearing debt less cash on hand. We know the market capital- ization of Prufrock but we do not know the market value of its outstanding interest bearing debt. In this situation, the common practice is to use the book value of outstanding inter- est bearing debt less cash on hand as an approximation. For Prufrock, enterprise value is (in millions)

EV

=

Market capitalization + Market value of interest bearing debt − Cash

= $2,904 + ( $196 + 457 ) − $98 = $3,459 million

[3.20]

The purpose of the EV measure is to better estimate how much it would take to buy all of the outstanding stock of a firm and also to pay off the debt. The adjustment for cash is to recognize that if we were a buyer the cash could be used immediately to buy back debt or pay a dividend.

ENTERPRISE VALUE MULTIPLES Financial analysts use valuation multiples based upon a firm’s enterprise value when the goal is to estimate the value of the firm’s total business rather than just focusing on the value of its equity. To form an appropriate multiple, enter- prise value is divided by EBITDA. For Prufrock, the enterprise value multiple is

EV ________ EBITDA

= $3,459  ___________ $967 million

= 3.58 times

The multiple is especially useful because it allows comparison of one firm with another when there are differences in capital structure (interest expense), taxes, or capital spend- ing. The multiple is not directly affected by these differences.

Similar to PE ratios, we would expect a firm with high growth opportunities to have high EV multiples.

This completes our definition of some common ratios. We could tell you about more of them, but these are enough for now. We’ll leave it here and go on to discuss some ways of using these ratios instead of just how to calculate them. Table 3.6 summarizes some of the ratios we’ve discussed.

TABLE 3.6 Common Financial Ratios

I. Short-Term Solvency, or Liquidity, Ratios

Current ratio = Current assets _______________ Current liabilities

Days’ sales in receivables = 365 days __________________ Receivables turnover

Quick ratio = Current assets − Inventory _____________________ Current liabilities

Total asset turnover = Sales __________ Total assets

Cash ratio = Cash _______________ Current liabilities

Capital intensity = Total assets __________ Sales

II. Long-Term Solvency, or Financial Leverage, Ratios IV. Profitability Ratios

Total debt ratio = Total assets − Total equity _____________________ Total assets

Profit margin = Net income __________ Sales

Debt–equity ratio = Total debt _________ Total equity

Return on assets (ROA) = Net income __________ Total assets

Equity multiplier = Total assets __________ Total equity

Return on equity (ROE) = Net income __________ Total equity

Times interest earned ratio = EBIT _______ Interest

ROE = Net income __________ Sales

× Sales ______ Assets

× Assets ______ Equity

Cash coverage ratio = EBITDA ________ Interest

(continued )

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III. Asset Utilization, or Turnover, Ratios V. Market Value Ratios

Inventory turnover = Cost of goods sold ________________ Inventory

Price–earnings ratio = Price per share ________________ Earnings per share

Days’ sales in inventory = 365 days ________________ Inventory turnover

Market-to-book ratio = Market value per share ___________________ Book value per share

Receivables turnover = Sales _________________ Accounts receivable

EV multiple = Enterprise value ______________ EBITDA

TABLE  3.6 (continued)

E X

A M

P L

E

3 .4

Consider the following 2017 data for Atlantic’s Companies and Pacific Depot (billions except for price and earnings per share):

ATLANTIC’S COMPANIES, INC. PACIFIC DEPOT, INC.

Sales $48.3 $77.3

EBIT $ 4.8 $ 7.3

Net income $ 2.8 $ 4.4

Cash $ .5 $ .5

Depreciation $ 1.5 $ 1.9

Interest bearing debt $ 6.7 $13.4

Total assets $30.9 $44.3

Price per share $24 $27

Shares outstanding 1.5 1.7

Shareholder equity $16.1 $17.7

Earnings per share $ 1.87 $ 2.6

1. Determine the profit margin, ROE, market capitalization, enterprise value, PE multiple, and EV multiple for both Atlantic’s and Pacific Depot.

ATLANTIC’S COMPANIES, INC. PACIFIC DEPOT, INC.

Equity multiplier 30.9/16.1 = 1.9 44.3/17.7 = 2.5 Asset turnover 48.3/30.9 = 1.6 77.3/44.3 = 1.7 Profit margin 2.8/48.3 = 5.8% 4.4/77.3 = 5.7% ROE 2.8/16.1 = 17.4% 4.4/17.7 = 24.9% Market capitalization 1.5 × 24 = $36 billion 1.7 × 27 = $45.9 billion Enterprise value (1.5 × 24) + 6.7 − .5 = $42.2 billion (1.7 × 27) + 13.4 − .5 = $58.8 billion PE multiple 24/1.87 = 12.8 27/2.6 = 10.4 EBITDA 4.8 + 1.5 = $6.3 7.3 + 1.9 = $9.2 EV multiple 42.2/6.3 = 6.7 58.8/9.2 = 6.4

2. How would you describe these two companies from a financial point of view? These are simi- larly situated companies. In 2017, Pacific Depot had a higher ROE (partially because of using more debt and higher turnover), but Atlantic’s had slightly higher PE and EV multiples. Both companies’ multiples were somewhat below the general market, raising questions about future growth prospects.

Atlantic and Pacific

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3.3 THE DUPONT IDENTITY As we mentioned in discussing ROA and ROE, the difference between these two prof- itability measures reflects the use of debt financing or financial leverage. We illustrate the relationship between these measures in this section by investigating a famous way of decomposing ROE into its component parts.

A Closer Look at ROE To begin, let’s recall the definition of ROE:

Return on equity = Net income __________ Total equity

If we were so inclined, we could multiply this ratio by Assets/Assets without changing anything:

Return on equity = Net income __________ Total equity

= Net income __________ Total equity

× Assets ______ Assets

= Net income __________ Assets

× Assets __________ Total equity

Notice that we have expressed the ROE as the product of two other ratios—ROA and the equity multiplier:

ROE = ROA × Equity multiplier = ROA × ( 1 + Debt–equity ratio )

Looking back at Prufrock, for example, we see that the debt–equity ratio was .39 and ROA was 10.1 percent. Our work here implies that Prufrock’s ROE, as we previously calcu- lated, is

ROE = 10.1% × 1.39 = 14.0%

The difference between ROE and ROA can be substantial, particularly for certain busi- nesses. For example, based on recent financial statements, Wells Fargo has an ROA of only 1.29 percent, which is actually fairly typical for a bank. However, banks tend to borrow a lot of money, and, as a result, have relatively large equity multipliers. For Wells Fargo, ROE is about 11.83 percent, implying an equity multiplier of 9.17.

We can further decompose ROE by multiplying the top and bottom by total sales:

ROE = Sales _____ Sales

× Net income __________ Assets

× Assets __________ Total equity

If we rearrange things a bit, ROE is

ROE = Net income __________ Sales

× Sales ______ Assets

× Assets __________ Total equity

[3.21]

= Profit margin × Total asset turnover × Equity multiplier Return on assets

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What we have now done is to partition ROA into its two component parts, profit margin and total asset turnover. The last expression of the preceding equation is called the DuPont identity after the DuPont Corporation, which popularized its use.

We can check this relationship for Prufrock by noting that the profit margin was 15.7 percent and the total asset turnover was .64. ROE should thus be

ROE

= Profit margin

× Total asset turnover

× Equity multiplier

= .157 ×            .64 ×          1.39

= .140, or 14.0%

This 14.0 percent ROE is exactly what we had before (aside from a small rounding error). The DuPont identity tells us that ROE is affected by three things:

1. Operating efficiency (as measured by profit margin). 2. Asset use efficiency (as measured by total asset turnover). 3. Financial leverage (as measured by the equity multiplier).

Weakness in either operating or asset use efficiency (or both) will show up in a diminished return on assets, which will translate into a lower ROE.

Considering the DuPont identity, it appears that the ROE could be leveraged up by increasing the amount of debt in the firm. However, notice that increasing debt also increases interest expense, which reduces profit margins, which acts to reduce ROE. So, ROE could go up or down, depending. More important, the use of debt financing has a number of other effects, and, as we discuss at some length in later chapters, the amount of leverage a firm uses is governed by its capital structure policy.

The decomposition of ROE we’ve discussed in this section is a convenient way of sys- tematically approaching financial statement analysis. If ROE is unsatisfactory by  some measure, then the DuPont identity tells you where to start looking for the reasons.

Yahoo! and Alphabet (formerly Google) are among the most important Internet com- panies in the world. They may be good examples of how DuPont analysis can be useful in helping to ask the right questions about a firm’s financial performance. The DuPont break- downs for Yahoo! and Alphabet are summarized in Table 3.7.

As can be seen, in 2015, Yahoo! had an ROE of .001 percent (excluding non- recurring charges), down from its ROE in 2013 of 12.6 percent. In 2015, Alphabet

Yahoo!

TWELVE MONTHS ENDING ROE = PROFIT MARGIN × TOTAL ASSET TURNOVER × EQUITY MULTIPLIER

12/15 .001% = .01% × .110 × 1.56 12/14 .4% = 3.1% × .075 × 1.60 12/13 4.5% = 12.6% × .279 × 1.29

Alphabet

TWELVE MONTHS ENDING ROE = PROFIT MARGIN × TOTAL ASSET TURNOVER × EQUITY MULTIPLIER

12/15 12.3% = 22.9% × .430 × 1.24 12/14 13.8% = 21.9% × .503 × 1.25 12/13 15.3% = 24.0% × .501 × 1.27

TABLE 3.7 The DuPont Breakdown for Yahoo! and Alphabet

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had an ROE of 12.3 percent, down from its ROE in 2013 of 15.3 percent. Given this information, how is it possible that Alphabet’s ROE could be so much higher than the ROE of Yahoo! during this period of time, and what accounts for the decline in Yahoo!’s ROE?

On close inspection of the DuPont breakdown, we see that Yahoo!’s profit margin in 2015 was .01 percent. Meanwhile Alphabet’s profit margin was 22.9 percent in 2015. Yet Yahoo! and Alphabet have similar financial leverage. What can account for Alphabet’s advantage over Yahoo! in ROE? Clearly, it is profit margin and asset utilization. Asset utilization can come from higher volumes, higher prices, and/or lower costs. It is clear that the big difference in ROE between the two firms can be attributed to the difference in these two ratios.

Problems with Financial Statement Analysis We continue our chapter by discussing some additional problems that can arise in using financial statements. In one way or another, the basic problem with financial statement analysis is that there is no underlying theory to help us identify which quantities to look at and to guide us in establishing benchmarks.

As we discuss in other chapters, there are many cases in which financial theory and eco- nomic logic provide guidance in making judgments about value and risk. Little such help exists with financial statements. This is why we can’t say which ratios matter the most and what a high or low value might be.

One particularly severe problem is that many firms are conglomerates, owning more or less unrelated lines of business. GE is a well-known example. The consolidated financial statements for such firms don’t really fit any neat industry category. More generally, the kind of peer group analysis we have been describing is going to work best when the firms are strictly in the same line of business, the industry is competitive, and there is only one way of operating.

Another problem that is becoming increasingly common is that major competitors and natural peer group members in an industry may be scattered around the globe. The auto- mobile industry is an obvious example. The problem here is that financial statements from outside the United States do not necessarily conform to GAAP. The existence of dif- ferent standards and procedures makes it difficult to compare financial statements across national borders.

Even companies that are clearly in the same line of business may not be comparable. For example, electric utilities engaged primarily in power generation are all classified in the same group. This group is often thought to be relatively homogeneous. However, most utilities operate as regulated monopolies, so they don’t compete much with each other, at least not historically. Many have stockholders, and many are organized as cooperatives with no stockholders. There are several different ways of generating power, ranging from hydroelectric to nuclear, so the operating activities of these utilities can differ quite a bit. Finally, profitability is strongly affected by the regulatory environment, so utilities in dif- ferent locations can be similar but show different profits.

Several other general problems frequently crop up. First, different firms use different accounting procedures—for inventory, for example. This makes it difficult to compare statements. Second, different firms end their fiscal years at different times. For firms in seasonal businesses (such as a retailer with a large Christmas season), this can lead to difficulties in comparing balance sheets because of fluctuations in accounts during the year. Finally, for any particular firm, unusual or transient events, such as a one-time profit from an asset sale, may affect financial performance. Such events can give mis- leading signals as we compare firms. The nearby Finance Matters box discusses some issues along these lines.

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WHAT’S IN A RATIO? Abraham Briloff, a well-known financial commentator, famously remarked that “financial statements are like fine per- fume; to be sniffed but not swallowed.” As you have probably figured out by now, his point is that information gleaned from financial statements—and ratios and growth rates computed from that information—should be taken with a grain of salt.

For example, in early 2016, shares in network and logistics technology company Descartes Systems Group had a PE ratio of about 67 times earnings. You would expect that this stock would have a high growth rate, and indeed ana- lysts thought so. The estimated earnings growth rate for Descartes for the next year was 33 percent. At the same time, Churchill Downs, Inc., owner of, among other things, the Kentucky Derby, had a PE ratio of about 50, but analysts esti- mated an earnings growth rate of only 7 percent for the next year. Why is the PE so high? The answer is that Churchill Downs had low earnings the previous year. So, caution is warranted when looking at PE ratios.

AK Steel Holdings illustrates another issue. If you calculated its ROE in 2014, you would get about 22 percent, which is quite good. What’s strange is the company reported a loss of about $96.9 million dollars during 2014! What’s going on is that AK Steel had a book value of equity balance of negative $492 million. In this situation, the more AK Steel loses, the higher the ROE becomes. Of course, AK Steel’s market-to-book and PE ratios are also both negative. How do you inter- pret a negative PE? We’re not really sure, either. Whenever a company has a negative book value of equity, it means that losses have been so large that book equity has been wiped out. In such cases, the ROE, PE ratio, and market-to-book ratio are often not reported because they are meaningless.

Even if a company’s book equity is positive, you still have to be careful. For example, consider The Clorox Company, which had a market-to-book ratio of about 125 in early 2016. Since the market-to-book ratio measures the value cre- ated by the company for shareholders, this would seem to be a good sign. But a closer look shows that Clorox’s book value of equity per share was negative $1.04 in 2012 and had only risen to $.92 in 2016. This decline had to do with accounting for stock repurchases made by the company, not gains or losses, but it nonetheless dramatically increased the market-to-book ratio.

Financial ratios are important tools used in evaluating companies of all types, but you cannot take a number as given. Instead, before doing any analysis, the first step is to ask whether the number actually makes sense.

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3.4 FINANCIAL MODELS Financial planning is another important use of financial statements. Most financial plan- ning models output pro forma financial statements, where pro forma means “as a matter of form.” In our case, this means that financial statements are the form we use to summarize the projected future financial status of a company.

A Simple Financial Planning Model We can begin our discussion of financial planning models with a relatively simple exam- ple. The Computerfield Corporation’s financial statements from the most recent year are shown below.

Unless otherwise stated, the financial planners at Computerfield assume that all vari- ables are tied directly to sales and current relationships are optimal. This means that all items will grow at exactly the same rate as sales. This is obviously oversimplified; we use this assumption only to make a point.

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Suppose sales increase by 20 percent, rising from $1,000 to $1,200. Planners would then also forecast a 20 percent increase in costs, from $800 to $800 × 1.2 = $960. The pro forma income statement would thus look like this:

COMPUTERFIELD CORPORATION F inancia l Statements

Income Statement Balance Sheet

Sales

Costs

Net income

$1,000

    800

$     200

Assets

Total

$500

$500

Debt

Equity

Total

$250

           250

$500

Pro Forma Income Statement

Sales

Costs

Net income

$1,200  

     960  

$   240  

Pro Forma Balance Sheet

Assets

Total

             $600 (+100)                        

             $600 (+100)

Debt

Equity

Total

$300   (+50)     300   (+50)   $600 (+100)  

PRO FORMA BALANCE SHEET

Assets

Total

            $600 (+100)                     

            $600 (+100)

Debt

Equity

Total

$110 (−140)     490 (+240)   $600 (+100)  

The assumption that all variables will grow by 20 percent lets us easily construct the pro forma balance sheet as well:

Notice we have increased every item by 20 percent. The numbers in parentheses are the dollar changes for the different items.

Now we have to reconcile these two pro forma statements. How, for example, can net income be equal to $240 and equity increase by only $50? The answer is that Computerfield must have paid out the difference of $240 − 50 = $190, possibly as a cash dividend. In this case dividends are the “plug” variable.

Suppose Computerfield does not pay out the $190. In this case, the addition to retained earnings is the full $240. Computerfield’s equity will thus grow to $250 (the starting amount) plus $240 (net income), or $490, and debt must be retired to keep total assets equal to $600.

With $600 in total assets and $490 in equity, debt will have to be $600 − 490 = $110. Because we started with $250 in debt, Computerfield will have to retire $250 − 110 = $140 in debt. The resulting pro forma balance sheet would look like this:

Planware provides insight into cash flow forecasting at www.planware.org.

In this case, debt is the plug variable used to balance projected total assets and liabilities. This example shows the interaction between sales growth and financial policy. As sales

increase, so do total assets. This occurs because the firm must invest in net working capital

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and fixed assets to support higher sales levels. Because assets are growing, total liabilities and equity, the right side of the balance sheet, will grow as well.

The thing to notice from our simple example is that the way the liabilities and owners’ equity change depends on the firm’s financing policy and its dividend policy. The growth in assets requires that the firm decide on how to finance that growth. This is strictly a man- agerial decision. Note that in our example the firm needed no outside funds. This won’t usually be the case, so we explore a more detailed situation in the next section.

The Percentage of Sales Approach In the previous section, we described a simple planning model in which every item increased at the same rate as sales. This may be a reasonable assumption for some elements. For oth- ers, such as long-term borrowing, it probably is not: The amount of long-term borrowing is set by management, and it does not necessarily relate directly to the level of sales.

In this section, we describe an extended version of our simple model. The basic idea is to separate the income statement and balance sheet accounts into two groups, those that vary directly with sales and those that do not. Given a sales forecast, we will then be able to calculate how much financing the firm will need to support the predicted sales level.

The financial planning model we describe next is based on the percentage of sales approach. Our goal here is to develop a quick and practical way of generating pro forma statements. We defer discussion of some “bells and whistles” to a later section.

THE INCOME STATEMENT We start out with the most recent income statement for the Rosengarten Corporation, as shown in Table 3.8. Notice that we have still simplified things by including costs, depreciation, and interest in a single cost figure.

Rosengarten has projected a 25 percent increase in sales for the coming year, so we are anticipating sales of $1,000 × 1.25 = $1,250. To generate a pro forma income statement, we assume that total costs will continue to run at $800/1,000 = 80 percent of sales. With this assumption, Rosengarten’s pro forma income statement is as shown in Table 3.9. The effect here of assuming that costs are a constant percentage of sales is to assume that the profit mar- gin is constant. To check this, notice that the profit margin was $132/1,000 = 13.2 percent. In our pro forma statement, the profit margin is $165/1,250 = 13.2 percent; so it is unchanged.

Next, we need to project the dividend payment. This amount is up to Rosengarten’s management. We will assume Rosengarten has a policy of paying out a constant fraction of

ROSENGARTEN CORPORATION Pro Forma Income Statement

Sales (projected)

Costs (80% of sales)

Taxable income

Taxes (34%)

Net income

$1,250  

  1,000  

$      250  

           85  

$     165  

TABLE 3.9

ROSENGARTEN CORPORATION Income Statement

Sales

Costs

Taxable income

Taxes (34%)

Net income

Dividends

Addition to retained earnings

$44   

88   

$1,000  

     800  

$   200  

       68  

$   132  

TABLE 3.8

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net income in the form of a cash dividend. For the most recent year, the dividend payout ratio was

Dividend payout ratio

=

Cash dividends / Net income 

= $44 /132 = 33 1 / 3%

[3.22]

We can also calculate the ratio of the addition to retained earnings to net income:

Addition to retained earnings/Net income = $88 / 132 = 66 2 / 3%

This ratio is called the retention ratio or plowback ratio, and it is equal to 1 minus the dividend payout ratio because everything not paid out is retained. Assuming that the payout ratio is constant, the projected dividends and addition to retained earnings will be

Projected dividends paid to shareholders = $165 × 1/3 = $ 55 Projected addition to retained earnings = $165 × 2/3 = 110 $165

THE BALANCE SHEET To generate a pro forma balance sheet, we start with the most recent statement, as shown in Table 3.10.

On our balance sheet, we assume that some items vary directly with sales and others do not. For those items that vary with sales, we express each as a percentage of sales for the year just completed. When an item does not vary directly with sales, we write “n/a” for “not applicable.”

For example, on the asset side, inventory is equal to 60 percent of sales (=$600/1,000) for the year just ended. We assume this percentage applies to the coming year, so for each $1 increase in sales, inventory will rise by $.60. More generally, the ratio of total assets to sales for the year just ended is $3,000/1,000 = 3, or 300 percent.

This ratio of total assets to sales is sometimes called the capital intensity ratio. It tells us the amount of assets needed to generate $1 in sales; the higher the ratio is, the more capital intensive is the firm. Notice also that this ratio is just the reciprocal of the total asset turnover ratio we defined previously.

ROSENGARTEN CORPORATION Balance Sheet

Assets Liabilities and Owners’ Equity

$ PERCENTAGE

OF SALES $ PERCENTAGE

OF SALES

Current assets

Cash

Accounts receivable

Inventory

Total

Fixed assets

Net plant and equipment

Total assets

$   160

     440

     600

$1,200

$1,800

$3,000

  16%

44 

  60   

120   

180

300%

Current liabilities

Accounts payable

Notes payable

Total

Long-term debt

Owners’ equity

Common stock and paid-in surplus

Retained earnings

Total

Total liabilities and owners’ equity

$ 300

   100

$ 400

$ 800

$   800

  1,000

$1,800

$3,000

30%

n/a  

n/a  

n/a  

n/a  

n/a  

n/a  

n/a  

TABLE 3.10

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For Rosengarten, assuming that this ratio is constant, it takes $3 in total assets to gen- erate $1 in sales (apparently Rosengarten is in a relatively capital-intensive business). Therefore, if sales are to increase by $100, Rosengarten will have to increase total assets by three times this amount, or $300.

On the liability side of the balance sheet, we show accounts payable varying with sales. The reason is that we expect to place more orders with our suppliers as sales volume increases, so payables will change “spontaneously” with sales. Notes payable, on the other hand, represents short-term debt such as bank borrowing. This will not vary unless we take specific actions to change the amount, so we mark this item as “n/a.”

Similarly, we use “n/a” for long-term debt because it won’t automatically change with sales. The same is true for common stock and paid-in surplus. The last item on the right side, retained earnings, will vary with sales, but it won’t be a simple percentage of sales. Instead, we will explicitly calculate the change in retained earnings based on our projected net income and dividends.

We can now construct a partial pro forma balance sheet for Rosengarten. We do this by using the percentages we have just calculated wherever possible to calculate the projected amounts. For example, net fixed assets are 180 percent of sales; so, with a new sales level of $1,250, the net fixed asset amount will be 1.80 × $1,250 = $2,250, representing an increase of $2,250 − 1,800 = $450 in plant and equipment. It is important to note that for items that don’t vary directly with sales, we initially assume no change and write in the original amounts. The result is shown in Table 3.11. Notice that the change in retained earnings is equal to the $110 addition to retained earnings we calculated earlier.

Inspecting our pro forma balance sheet, we notice that assets are projected to increase by $750. However, without additional financing, liabilities and equity will increase by only $185, leaving a shortfall of $750 − 185 = $565. We label this amount external financing needed (EFN).

Rather than create pro forma statements, if we were so inclined, we could calculate EFN directly as follows:

EFN

= Assets ______

Sales × ΔSales − Spontaneous liabilities ___________________

Sales × ΔSales − PM 

× Projected sales × (1 − d) [3.23]

ROSENGARTEN CORPORATION Part ia l Pro Forma Balance Sheet

Assets Liabilities and Owners’ Equity

NEXT YEAR

CHANGE FROM CURRENT YEAR

NEXT YEAR

CHANGE FROM CURRENT YEAR

Current assets

Cash

Accounts receivable

Inventory

Total

Fixed assets

Net plant and equipment

Total assets

$   200

     550

     750

$1,500

$2,250

$3,750

$  40

  110

  150

$300

$450

$750

Current liabilities

Accounts payable

Notes payable

Total

Long-term debt

Owners’ equity

Common stock and paid-in surplus

Retained earnings

Total

Total liabilities and owners’ equity

External financing needed

$   375

     100

$   475

$   800

$   800

  1,110

$1,910

$3,185

$   565

$  75

          0

$  75

$       0

$       0

  110

$110

$185

$565

TABLE  3.11

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In this expression, “ΔSales” is the projected change in sales (in dollars). In our example projected sales for next year are $1,250, an increase of $250 over the previous year, so ΔSales = $250. By “Spontaneous liabilities,” we mean liabilities that naturally move up and down with sales. For Rosengarten, the spontaneous liabilities are the $300 in accounts payable. Finally, PM and d are the profit margin and dividend payout ratios, which we pre- viously calculated as 13.2 percent and 33 1/3 percent, respectively. Total assets and sales are $3,000 and $1,000, respectively, so we have

EFN = $3,000 ______ 1,000

× $250 − $300 _____ 1,000

× $250 − .132 × $1,250 × ( 1 − 1 _ 3

) = $565

In this calculation, notice that there are three parts. The first part is the projected increase in assets, which is calculated using the capital intensity ratio. The second is the spontane- ous increase in liabilities. The third part is the product of profit margin and projected sales, which is projected net income, multiplied by the retention ratio. Thus, the third part is the projected addition to retained earnings.

A PARTICULAR SCENARIO Our financial planning model now reminds us of one of those good news–bad news jokes. The good news is we’re projecting a 25 percent increase in sales. The bad news is this isn’t going to happen unless Rosengarten can somehow raise $565 in new financing.

This is a good example of how the planning process can point out problems and poten- tial conflicts. If, for example, Rosengarten has a goal of not borrowing any additional funds and not selling any new equity, then a 25 percent increase in sales is probably not feasible.

If we take the need for $565 in new financing as given, we know that Rosengarten has three possible sources: short-term borrowing, long-term borrowing, and new equity. The choice of some combination among these three is up to management; we will illustrate only one of the many possibilities.

Suppose Rosengarten decides to borrow the needed funds. In this case, the firm might choose to borrow some over the short term and some over the long term. For example, cur- rent assets increased by $300 whereas current liabilities rose by only $75. Rosengarten could borrow $300 − 75 = $225 in short-term notes payable and leave total net working capital unchanged. With $565 needed, the remaining $565 − 225 = $340 would have to come from long-term debt. Table 3.12 shows the completed pro forma balance sheet for Rosengarten.

We have used a combination of short- and long-term debt as the plug here, but we emphasize that this is just one possible strategy; it is not necessarily the best one by any means. We could (and should) investigate many other scenarios. The various ratios we dis- cussed earlier come in handy here. For example, with the scenario we have just examined, we would surely want to examine the current ratio and the total debt ratio to see if we were comfortable with the new projected debt levels.

AN ALTERNATIVE SCENARIO The assumption that assets are a fixed percentage of sales is convenient, but it may not be suitable in many cases. In particular, note that we effectively assumed that Rosengarten was using its fixed assets at 100 percent of capacity because any increase in sales led to an increase in fixed assets. For most businesses, there would be some slack or excess capacity, and production could be increased by perhaps running an extra shift. According to the Federal Reserve, the overall capacity utilization for U.S. manufacturing com- panies in December 2015 was 76.5 percent, up from a recent low of 64.4 percent in June 2009.

If we assume that Rosengarten is operating at only 70 percent of capacity, then the need for external funds will be quite different. When we say “70 percent of capacity,” we mean that the current sales level is 70 percent of the full-capacity sales level:

Current sales = $1,000 = .70 × Full-capacity sales

Full-capacity sales = $1,000 / .70 = $1,429

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66

ROSENGARTEN CORPORATION Pro Forma Balance Sheet

Assets Liabilities and Owners’ Equity

NEXT YEAR

CHANGE FROM CURRENT YEAR

NEXT YEAR

CHANGE FROM CURRENT YEAR

Current assets

Cash

Accounts receivable

Inventory

Total

Fixed assets

Net plant and equipment

Total assets

$   200

     550

     750

$1,500

$2,250

$3,750

$  40

   110

  150

$300

$450

$750

Current liabilities

Accounts payable

Notes payable

Total

Long-term debt

Owners’ equity

Common stock and paid-in surplus

Retained earnings

Total

Total liabilities and owners’ equity

$   375

     325

$   700

$1,140

$   800

  1,110

$1,910

$3,750

$  75

  225

$300

$340

$    0

  110

$110

$750

TABLE 3.12

E X

A M

P L

E

3 .5

Suppose Rosengarten is operating at 90 percent capacity. What would sales be at full capacity? What is the capital intensity ratio at full capacity? What is EFN in this case?

Full-capacity sales would be $1,000/.90 = $1,111. From Table 3.10, we know that fixed assets are $1,800. At full capacity, the ratio of fixed assets to sales is thus:

Fixed assets ________________ Full-capacity sales

= $1,800 ______ 1,111

= 1.62

So, Rosengarten needs $1.62 in fixed assets for every $1 in sales once it reaches full capacity. At the projected sales level of $1,250, then, it needs $1,250 × 1.62 = $2,025 in fixed assets. Compared to the $2,250 we originally projected, this is $225 less, so EFN is $565 − 225 = $340.

Current assets would still be $1,500, so total assets would be $1,500 + 2,025 = $3,525. The capital intensity ratio would thus be $3,525/1,250 = 2.82, which is less than our original value of 3 because of the excess capacity.

The Capital Intensity Ratio

This tells us that sales could increase by almost 43 percent—from $1,000 to $1,429— before any new fixed assets would be needed.

In our previous scenario, we assumed it would be necessary to add $450 in net fixed assets. In the current scenario, no spending on net fixed assets is needed because sales are projected to rise only to $1,250, which is substantially less than the $1,429 full-capacity level.

As a result, our original estimate of $565 in external funds needed is too high. We estimated that $450 in net new fixed assets would be needed. Instead, no spending on new net fixed assets is necessary. Thus, if we are currently operating at 70 percent capacity, we need only $565 − 450 = $115 in external funds. The excess capacity thus makes a consid- erable difference in our projections.

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3.5 EXTERNAL FINANCING AND GROWTH Growth and the need for external financing are obviously related. All other things staying the same, the higher the rate of growth in sales or assets, the greater will be the need for external financing. In the previous section, we took a growth rate as given, and then we

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determined the amount of external financing needed to support that growth. In this sec- tion, we turn things around a bit. We will take the firm’s financial policy as given and then examine the relationship between that financial policy and the firm’s ability to finance new investments and thereby grow.

We emphasize that we are focusing on growth not because growth is an appropriate goal; instead, for our purposes, growth is a convenient means of examining the interactions between investment and financing decisions. In effect, we assume that the use of growth as a basis for planning is just a reflection of the very high level of aggregation used in the planning process.

EFN and Growth The first thing we need to do is establish the relationship between EFN and growth. To do this, we introduce the simplified income statement and balance sheet for the Hoffman Company in Table 3.13. Notice that we have simplified the balance sheet by combining short-term and long-term debt into a single total debt figure. Effectively, we are assuming that none of the current liabilities vary spontaneously with sales. This assumption isn’t as restrictive as it sounds. If any current liabilities (such as accounts payable) vary with sales, we can assume that any such accounts have been netted out in current assets. Also, we con- tinue to combine depreciation, interest, and costs on the income statement.

Suppose the Hoffman Company is forecasting next year’s sales level at $600, a $100 increase. Notice that the percentage increase in sales is $100/500 = 20 percent. Using the percentage of sales approach and the figures in Table 3.13, we can prepare a pro forma income statement and balance sheet as in Table 3.14. As Table 3.14 illustrates, at a 20  percent growth rate, Hoffman needs $100 in new assets. The projected addition to retained earnings is $52.8, so the external financing needed, EFN, is $100 − 52.8 = $47.2.

Notice that the debt−equity ratio for Hoffman was originally (from Table 3.13) equal to $250/250 = 1.0. We will assume that the Hoffman Company does not wish to sell new equity. In this case, the $47.2 in EFN will have to be borrowed. What will the new debt−equity ratio be? From Table 3.14, we know that total owners’ equity is projected at $302.8. The new total debt will be the original $250 plus $47.2 in new borrowing, or $297.2 total. The debt−equity ratio thus falls slightly from 1.0 to $297.2/302.8 = .98.

HOFFMAN COMPANY Income Statement and Balance Sheet

INCOME STATEMENT

Sales

Costs

Taxable income

Taxes (34%)

Net income

Dividends

Addition to retained earnings

$22                 

44                 

$500

  400

$100

     34

$  66

BALANCE SHEET

Assets Liabilities and Owners’ Equity

$ PERCENTAGE OF SALES $ PERCENTAGE OF SALES

Current assets

Net fixed assets

Total assets

$200

           300

$500

40%

  60   

100%

Total debt

Owners’ equity

Total liabilities and owners’ equity

$250

  250

$500

n/a

n/a

n/a

TABLE 3.13

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68

Table 3.15 shows EFN for several different growth rates. The projected addition to retained earnings and the projected debt−equity ratio for each scenario are also given (you should probably calculate a few of these for practice). In determining the debt−equity ratios, we assumed that any needed funds were borrowed, and we also assumed any sur- plus funds were used to pay off debt. Thus, for the zero growth case the debt falls by $44, from $250 to $206. In Table 3.15, notice that the increase in assets required is equal to the original assets of $500 multiplied by the growth rate. Similarly, the addition to retained earnings is equal to the original $44 plus $44 times the growth rate.

Table 3.15 shows that for relatively low growth rates, Hoffman will run a surplus, and its debt−equity ratio will decline. Once the growth rate increases to about 10 percent, how- ever, the surplus becomes a deficit. Furthermore, as the growth rate exceeds approximately 20 percent, the debt−equity ratio passes its original value of 1.0.

Figure 3.1 illustrates the connection between growth in sales and external financing needed in more detail by plotting asset needs and additions to retained earnings from Table 3.15 against the growth rates. As shown, the need for new assets grows at a much faster rate than the addition to retained earnings, so the internal financing provided by the addition to retained earnings rapidly disappears.

PROJECTED SALES

GROWTH

INCREASE IN ASSETS REQUIRED

ADDITION TO RETAINED EARNINGS

EXTERNAL F INANCING

NEEDED, EFN

PROJECTED DEBT–EQUITY

RATIO

    0%  

5  

 10     

15    

20    

25    

 $   0   

    25  

   50  

   75  

  100   

  125   

$44.0    

46.2  

48.4  

50.6  

52.8  

55.0  

–$44.0   

–21.2 

    1.6 

  24.4 

  47.2 

  70.0 

.70  

.77  

.84  

.91  

.98  

1.05    

TABLE 3.15 Growth and Projected EFN for the Hoffman Company

TABLE 3.14

HOFFMAN COMPANY Pro Forma Income Statement and Balance Sheet

INCOME STATEMENT

Sales (projected)

Costs (80% of sales)

Taxable income

Taxes (34%)

Net income

Dividends

Addition to retained earnings

$26.4                 

52.8                 

$600.0

         480.0

$120.0

         40.8

$      79.2

BALANCE SHEET

Assets Liabilities and Owners’ Equity

$ PERCENTAGE OF SALES

$ PERCENTAGE OF SALES

Current assets

Net fixed assets

Total assets

$240.0

  360.0

$600.0

40%

    60   

100%

Total debt

Owners’ equity

Total liabilities and owners’ equity

External financing needed

$250.0

  302.8

$552.8

$  47.2

n/a

n/a

n/a

n/a

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As this discussion shows, whether a firm runs a cash surplus or deficit depends on growth. Microsoft is a good example. Its revenue growth in the 1990s was amazing, averaging well over 30 percent per year for the decade. Growth slowed down noticeably over the 2000–2015 period, but, nonetheless, Microsoft’s combination of growth and sub- stantial profit margins led to enormous cash surpluses. In part because Microsoft paid relatively low dividends, the cash really piled up; in 2016, Microsoft’s cash and short-term investment hoard exceeded $102 billion.

Financial Policy and Growth Based on our discussion just preceding, we see that there is a direct link between growth and external financing. In this section, we discuss two growth rates that are particularly useful in long-range planning.

THE INTERNAL GROWTH RATE The first growth rate of interest is the maximum growth rate that can be achieved with no external financing of any kind. We will call this the internal growth rate because this is the rate the firm can maintain with internal financ- ing only. In Figure 3.1, this internal growth rate is represented by the point where the two lines cross. At this point, the required increase in assets is exactly equal to the addition to retained earnings, and EFN is therefore zero. We have seen that this happens when the growth rate is slightly less than 10 percent. With a little algebra (see Problem 28 at the end of the chapter), we can define this growth rate more precisely as

Internal growth rate = ROA × b __________ 1 − ROA × b

[3.24]

where ROA is the return on assets we discussed earlier, and b is the plowback, or retention, ratio also defined earlier in this chapter.

For the Hoffman Company, net income was $66 and total assets were $500. ROA is thus $66/500 = 13.2 percent. Of the $66 net income, $44 was retained, so the plowback ratio, b, is $44/66 = 2/3. With these numbers, we can calculate the internal growth rate as

Internal growth rate

=

ROA × b __________ 1 − ROA × b

= .132 × (2 / 3) _______________ 1 − .132 × (2 / 3)

= 9.65%

FIGURE 3.1 Growth and Related Financing Needed for the Hoffman Company

5 10

Increase in assets required

Projected addition to retained earnings

EFN < 0 (surplus)

Projected growth in sales (%)

As se

t n ee

ds a

nd re

ta in

ed e

ar ni

ng s

($ )

25

50 44

75

100

125

15 20 25

EFN > 0 (deficit)

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70

Thus, the Hoffman Company can expand at a maximum rate of 9.65 percent per year with- out external financing.

THE SUSTAINABLE GROWTH RATE We have seen that if the Hoffman Company wishes to grow more rapidly than at a rate of 9.65 percent per year, external financing must be arranged. The second growth rate of interest is the maximum growth rate a firm can achieve with no external equity financing while it maintains a constant debt−equity ratio. This rate is commonly called the sustainable growth rate because it is the maximum rate of growth a firm can maintain without increasing its financial leverage.

There are various reasons why a firm might wish to avoid equity sales. For example, new equity sales can be expensive because of the substantial fees that may be involved. Alternatively, the current owners may not wish to bring in new owners or contribute additional equity. Why a firm might view a particular debt−equity ratio as optimal is dis- cussed in later chapters; for now, we will take it as given.

Based on Table 3.15, the sustainable growth rate for Hoffman is approximately 20  percent because the debt−equity ratio is near 1.0 at that growth rate. The precise value can be calculated as follows (see Problem 28 at the end of the chapter):

Sustainable growth rate = ROE × b ___________ 1 − ROE × b

[3.25]

This is identical to the internal growth rate except that ROE, return on equity, is used instead of ROA.

For the Hoffman Company, net income was $66 and total equity was $250; ROE is thus $66/250 = 26.4 percent. The plowback ratio, b, is still 2/3, so we can calculate the sustain- able growth rate as

Sustainable growth rate

= ROE × b ____________ 1 − ROE × b

= .264 × (2 / 3) _______________

1 − .264 × (2 / 3)

= 21.36%

Thus, the Hoffman Company can expand at a maximum rate of 21.36 percent per year without external equity financing.

E X

A M

P L

E 3

.6

Suppose Hoffman grows at exactly the sustainable growth rate of 21.36 percent. What will the pro forma statements look like?

At a 21.36 percent growth rate, sales will rise from $500 to $606.8. The pro forma income statement will look like this:

HOFFMAN COMPANY Pro Forma Income Statement

Sales (projected) $606.8

Costs (80% of sales) 485.4

Taxable income $121.4

Taxes (34%) 41.3

Net income $ 80.1

Dividends $26.7

Addition to retained earnings 53.4

Sustainable Growth

(continued )

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DETERMINANTS OF GROWTH Earlier in this chapter, we saw that the return on equity, ROE, could be decomposed into its various components using the DuPont identity. Because ROE appears so prominently in the determination of the sustainable growth rate, it is obvious that the factors important in determining ROE are also important determinants of growth.

From our previous discussions, we know that ROE can be written as the product of three factors:

ROE = Profit margin × Total asset turnover × Equity multiplier

If we examine our expression for the sustainable growth rate, we see that anything that increases ROE will increase the sustainable growth rate by making the top bigger and the bottom smaller. Increasing the plowback ratio will have the same effect.

Putting it all together, what we have is that a firm’s ability to sustain growth depends explicitly on the following four factors:

1. Profit margin: An increase in profit margin will increase the firm’s ability to generate funds internally and thereby increase its sustainable growth.

2. Dividend policy: A decrease in the percentage of net income paid out as divi- dends will increase the retention ratio. This increases internally generated equity and thus increases sustainable growth.

3. Financial policy: An increase in the debt−equity ratio increases the firm’s finan- cial leverage. Because this makes additional debt financing available, it increases the sustainable growth rate.

4. Total asset turnover: An increase in the firm’s total asset turnover increases the sales generated for each dollar in assets. This decreases the firm’s need for new assets as sales grow and thereby increases the sustainable growth rate. Notice that increasing total asset turnover is the same thing as decreasing capital intensity.

The sustainable growth rate is a very useful planning number. What it illustrates is the explicit relationship between the firm’s four major areas of concern: its operating effi- ciency as measured by profit margin, its asset use efficiency as measured by total asset turnover, its dividend policy as measured by the retention ratio, and its financial policy as measured by the debt−equity ratio.

We construct the balance sheet just as we did before. Notice, in this case, that owners’ equity will rise from $250 to $303.4 because the addition to retained earnings is $53.4.

HOFFMAN COMPANY Pro Forma Balance Sheet

Assets Liabilities and Owners’ Equity

$ PERCENTAGE

OF SALES $ PERCENTAGE

OF SALES

Current assets $242.7 40% Total debt $250.0 n/a

Net fixed assets 364.1 60 Owners’ equity 303.4 n/a

Total assets $606.8 100% Total liabilities and owners’ equity

$553.4 n/a

External financing needed

$ 53.4 n/a

As illustrated, EFN is $53.4. If Hoffman borrows this amount, then total debt will rise to $303.4, and the debt−equity ratio will be exactly 1.0, which verifies our earlier calculation. At any other growth rate, something would have to change.

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72

If a firm does not wish to sell new equity and its profit margin, dividend policy, financial pol- icy, and total asset turnover (or capital intensity) are all fixed, then there is only one possible growth rate.

I. Internal Growth Rate

Internal growth rate = ROA × b ____________ 1 − ROA × b

where

ROA = Return on assets = Net income/Total assets b = Plowback (retention) ratio b = Addition to retained earnings/Net income The internal growth rate is the maximum growth rate that can be achieved with no external financing of any kind.

II. Sustainable Growth Rate

Sustainable growth rate = ROE × b ____________ 1 − ROE × b

where

ROE = Return on equity = Net income/Total equity b = Plowback (retention) ratio b = Addition to retained earnings/Net income The sustainable growth rate is the maximum growth rate that can be achieved with no external equity financing while maintaining a constant debt–equity ratio.

TABLE 3.16 Summary of Internal and Sustainable Growth Rates

E X

A M

P L

E

3 .7

The Sandar Co. has a debt–equity ratio of .5, a profit margin of 3 percent, a dividend payout ratio of 40 percent, and a capital intensity ratio of 1. What is its sustainable growth rate? If Sandar desired a 10 percent sustainable growth rate and planned to achieve this goal by improving profit margins, what would you think?

ROE is .03 × 1 × 1.5 = 4.5 percent. The retention ratio is 1 − .40 = .60 Sustainable growth is thus .045(.60)/[1 − .045(.60)] = 2.77 percent.

For the company to achieve a 10 percent growth rate, the profit margin will have to rise. To see this, assume that sustainable growth is equal to 10 percent and then solve for profit margin, PM:

.10 = PM (1.5) (.6) / [ 1 − PM (1.5) (.6) ] PM = .1/.99 = 10.1%

For the plan to succeed, the necessary increase in profit margin is substantial, from below 3 percent to about 10 percent. This may not be feasible.

Profit Margins and Sustainable Growth

Given values for all four of these, there is only one growth rate that can be achieved. This is an important point, so it bears restating:

One of the primary benefits of financial planning is that it ensures internal consistency among the firm’s various goals. The concept of the sustainable growth rate captures this element nicely. Also, we now see how a financial planning model can be used to test the feasibility of a planned growth rate. If sales are to grow at a rate higher than the sus- tainable growth rate, the firm must increase profit margins, increase total asset turnover, increase financial leverage, increase earnings retention, or sell new shares.

The two growth rates, internal and sustainable, are summarized in Table 3.16.

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A Note about Sustainable Growth Rate Calculations Very commonly, the sustainable growth rate is calculated using just the numerator in our expression, ROE × b. This causes some confusion, which we can clear up here. The issue has to do with how ROE is computed. Recall that ROE is calculated as net income divided by total equity. If total equity is taken from an ending balance sheet (as we have done consistently, and is commonly done in practice), then our formula is the right one. However, if total equity is from the beginning of the period, then the simpler formula is the correct one.

In principle, you’ll get exactly the same sustainable growth rate regardless of which way you calculate it (as long as you match up the ROE calculation with the right formula). In reality, you may see some differences because of accounting-related complications. By the way, if you use the average of beginning and ending equity (as some advocate), yet another formula is needed. Also, all of our comments here apply to the internal growth rate as well.

3.6 SOME CAVEATS REGARDING FINANCIAL PLANNING MODELS

Financial planning models do not always ask the right questions. A primary reason is that they tend to rely on accounting relationships and not financial relationships. In particular, the three basic elements of firm value tend to get left out—namely, cash flow size, risk, and timing.

Because of this, financial planning models sometimes do not produce output that gives the user many meaningful clues about what strategies will lead to increases in value. Instead, they divert the user’s attention to questions concerning the association of, say, the debt−equity ratio and firm growth.

The financial model we used for the Hoffman Company was simple—in fact, too simple. Our model, like many in use today, is really an accounting statement generator at heart. Such models are useful for pointing out inconsistencies and reminding us of finan- cial needs, but they offer little guidance concerning what to do about these problems.

In closing our discussion, we should add that financial planning is an iterative process. Plans are created, examined, and modified over and over. The final plan will be a result negotiated between all the different parties to the process. In fact, long-term financial plan- ning in most corporations relies on what might be called the Procrustes approach.5 Upper- level management has a goal in mind, and it is up to the planning staff to rework and to ultimately deliver a feasible plan that meets that goal.

The final plan will therefore implicitly contain different goals in different areas and also satisfy many constraints. For this reason, such a plan need not be a dispassionate assessment of what we think the future will bring; it may instead be a means of recon- ciling the planned activities of different groups and a way of setting common goals for the future.

However it is done, the important thing to remember is that financial planning should not become a purely mechanical exercise. If it does, it will probably focus on the wrong things. Nevertheless, the alternative to planning is stumbling into the future. Perhaps the immortal Yogi Berra (the baseball catcher, not the cartoon character), said it best: “Ya gotta watch out if you don’t know where you’re goin’. You just might not get there.”6

5 In Greek mythology, Procrustes is a giant who seizes travelers and ties them to an iron bed. He stretches them or cuts off their legs as needed to make them fit the bed. 6 Were not exactly sure what this means, either, but we like the sound of it.

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PART 1 Overview74

This chapter focuses on working with information contained in financial statements. Specifically, we studied standardized financial statements, ratio analysis, and long-term financial planning.

1. We explained that differences in firm size make it difficult to compare financial statements, and we dis- cussed how to form common-size statements to make comparisons easier and more meaningful.

2. Evaluating ratios of accounting numbers is another way of comparing financial statement information. We defined a number of the most commonly used ratios, and we discussed the famous DuPont identity.

3. We showed how pro forma financial statements can be generated and used to plan for future financing needs.

After you have studied this chapter, we hope that you have some perspective on the uses and abuses of financial statement information. You should also find that your vocabulary of business and financial terms has grown substantially.

SUMMARY AND CONCLUSIONS

1. Financial Ratio Analysis A financial ratio by itself tells us little about a company since financial ratios vary a great deal across industries. There are two basic methods for analyzing financial ratios for a company: time trend analysis and peer group analysis. Why might each of these analysis methods be useful? What does each tell you about the company’s financial health?

2. Industry-Specific Ratios So-called “same-store sales” are a very important measure for companies as diverse as McDonald’s and Sears. As the name suggests, examining same-store sales means comparing revenues from the same stores or restaurants at two different points in time. Why might companies focus on same-store sales rather than total sales?

3. Sales Forecast Why do you think most long-term financial planning begins with sales forecasts? Put differently, why are future sales the key input?

4. Sustainable Growth In the chapter, we used Rosengarten Corporation to demonstrate how to calculate EFN. The ROE for Rosengarten is about 7.3 percent, and the plowback ratio is about 67 percent. If you calculate the sustainable growth rate for Rosengarten, you will find it is only 5.14 percent. In our calculation for EFN, we used a growth rate of 25 percent. Is this possible? (Hint: Yes. How?)

5. EFN and Growth Rate Broslofski Co. maintains a positive retention ratio and keeps its debt–equity ratio constant every year. When sales grow by 20 percent, the firm has a negative projected EFN. What does this tell you about the firm’s sustainable growth rate? Do you know, with certainty, if the internal growth rate is greater than or less than 20 percent? Why? What happens to the projected EFN if the retention ratio is increased? What if the retention ratio is decreased? What if the retention ratio is zero?

6. Common-Size Financials One tool of financial analysis is common-size financial statements. Why do you think common-size income statements and balance sheets are used? Note that the accounting statement of cash flows is not converted into a common-size statement. Why do you think this is?

7. Asset Utilization and EFN One of the implicit assumptions we made in calculating the external funds needed was that the company was operating at full capacity. If the company is operating at less than full capacity, how will this affect the external funds needed?

Use the following information to answer the next five questions: A small business called The Grandmother Calendar Company began selling personalized photo calendar kits. The kits were a hit, and sales soon sharply exceeded forecasts. The rush of orders created a huge backlog, so the company leased more space and expanded capacity, but it still could not keep up with demand. Equipment failed from overuse and quality suffered. Working capital was drained to expand production, and, at the same time, payments from customers were often delayed until the product was shipped. Unable to deliver on orders, the company became so strapped for cash that employee paychecks began to bounce. Finally, out of cash, the company ceased operations entirely three years later.

CONCEPT QUESTIONS

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CHAPTER 3 Financial Statements Analysis and Financial Models 75

8. Product Sales Do you think the company would have suffered the same fate if its product had been less popular? Why or why not?

9. Cash Flow The Grandmother Calendar Company clearly had a cash flow problem. In the context of the cash flow analysis we developed in Chapter 2, what was the impact of customers not paying until orders were shipped?

10. Corporate Borrowing If the firm was so successful at selling, why wouldn’t a bank or some other lender step in and provide it with the cash it needed to continue?

11. Cash Flow Which is the biggest culprit here: too many orders, too little cash, or too little production capacity?

12. Cash Flow What are some of the actions that a small company like The Grandmother Calendar Company can take (besides expansion of capacity) if it finds itself in a situation in which growth in sales outstrips production?

13. Comparing ROE and ROA Both ROE and ROA measure profitability. Which one is more useful for comparing two companies? Why?

14. Ratio Analysis Consider the ratio EBITDA/Assets. What does this ratio tell us? Why might it be more useful than ROA in comparing two companies?

QUESTIONS AND PROBLEMS

1. DuPont Identity If Harley, Inc., has an equity multiplier of 1.35, total asset turnover of 2.15, and a profit margin of 6.08 percent, what is its ROE?

2. Equity Multiplier and Return on Equity Quinn Company has a debt–equity ratio of .75. Return on assets is 8.6 percent, and total equity is $975,000. What is the equity multiplier? Return on equity? Net income?

3. Using the DuPont Identity Y3K, Inc., has sales of $6,180, total assets of $3,680, and a debt–equity ratio of .45. If its return on equity is 15 percent, what is its net income?

4. EFN The most recent financial statements for Cornell, Inc., are shown here:

INCOME STATEMENT BALANCE SHEET

Sales

Costs

Taxable income

Taxes (34%)

Net income

$43,000

  30,200

$12,800

    4,352

$  8,448

Assets

Total

$104,500

$104,500

Debt

Equity

Total

$  28,200

    76,300

$104,500

Assets and costs are proportional to sales. Debt and equity are not. A dividend of $2,600 was paid, and the company wishes to maintain a constant payout ratio. Next year’s sales are projected to be $50,310. What is the external financing needed?

5. Sales and Growth The most recent financial statements for Weyland Co. are shown here:

INCOME STATEMENT BALANCE SHEET

Sales

Costs

Taxable income

Taxes (34%)

Net income

$67,400

  39,600

$27,800

    9,452

$18,348

Current assets

Fixed assets

Total

$  19,000

  141,000

$160,000

Long term debt

Equity

Total

$   51,000 

  109,000 

$160,000 

Basic (Questions 1–10)

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PART 1 Overview76

Assets and costs are proportional to sales. The company maintains a constant 30 percent dividend payout ratio and a constant debt–equity ratio. What is the maximum increase in sales that can be sustained assuming no new equity is issued?

6. Sustainable Growth If the SGS Corp. has an ROE of 14.5 percent and a payout ratio of 25 percent, what is its sustainable growth rate?

7. Sustainable Growth Assuming the following ratios are constant, what is the sustainable growth rate?

Total asset turnover

Profit margin

Equity multiplier

Payout ratio

= 3.20 = 7.4% = 1.45 = 60%

8. Calculating EFN The most recent financial statements for Incredible Edibles, Inc., are shown here (assuming no income taxes):

INCOME STATEMENT BALANCE SHEET

Sales

Costs

Net income

$12,100

    8,760

$  3,340

Assets

Total

$28,300

$28,300

Debt

Equity

Total

$ 7,400

  20,900

$28,300

Assets and costs are proportional to sales. Debt and equity are not. No d ividends are paid. Next year’s sales are projected to be $14,399. What is the external financing needed?

9. External Funds Needed Cheryl Colby, CFO of Charming Florist Ltd., has created the firm’s pro forma balance sheet for the next fiscal year. Sales are projected to grow by 15 percent to $211.6 million. Current assets, fixed assets, and short-term debt are 20 percent, 90 percent, and 15 percent of sales, respectively. The company pays out 40 percent of its net income in dividends. The company currently has $32 million of long-term debt, and $16 million in common stock par value. The profit margin is 10 percent.

a. Construct the current balance sheet for the firm using the projected sales figure.

b. Based on the sales growth forecast, how much does the company need in external funds for the upcoming fiscal year?

c. Construct the firm’s pro forma balance sheet for the next fiscal year and confirm the external funds needed that you calculated in part (b).

10. Sustainable Growth Rate The Dent Company has an ROE of 13.15 percent and a payout ratio of 30 percent.

a. What is the company’s sustainable growth rate?

b. Can the company’s actual growth rate be different from its sustainable growth rate? Why or why not?

c. How can the company increase its sustainable growth rate?

11. Return on Equity Firm A and Firm B have debt/total asset ratios of 35 percent and 30 percent and returns on total assets of 8 percent and 9 percent, respectively. Which firm has a greater return on equity?

12. Ratios and Foreign Companies Prince Albert Canning PLC had a net loss of £17,218 on sales of £153,875. What was the company’s profit margin? Does the fact that these figures are quoted in a foreign currency make any difference? Why? In dollars, sales were $223,180. What was the net loss in dollars?

13. External Funds Needed The Optical Scam Company has forecast a sales growth rate of 18 percent for next year. The current financial statements are shown below. Current assets, fixed assets, and short-term debt are proportional to sales.

Intermediate (Questions 11–23)

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CHAPTER 3 Financial Statements Analysis and Financial Models 77

INCOME STATEMENT

Sales

Costs

Taxable income

Taxes

Net income

Dividends

Addition to retained earnings

$1,450,000  

3,067,500  

$ 31,600,000    

   24,650,000    

$   6,950,000    

     2,432,500    

$   4,517,500    

BALANCE SHEET

Assets Liabilities and Equity

Current assets

Fixed assets

Total assets

$10,750,000

  32,100,000

$42,850,000

Short-term debt

Long-term debt

Common stock

Accumulated retained earnings

Total equity

Total liabilities and equity

$   5,150,000

$   7,700,000

$   3,100,000

  26,900,000

$30,000,000

$42,850,000

a. Using the equation from the chapter, calculate the external funds needed for next year.

b. Construct the firm’s pro forma balance sheet for next year and confirm the external funds needed you calculated in part (a).

c. Calculate the sustainable growth rate for the company.

d. Can the company eliminate the need for external funds by changing its dividend policy? What other options are available to the company to meet its growth objectives?

14. Days’ Sales in Receivables A company has net income of $263,000, a profit margin of 7.4 percent, and an accounts receivable balance of $165,700. Assuming 80 percent of sales are on credit, what is the company’s days’ sales in receivables?

15. Ratios and Fixed Assets The Arkham Company has a ratio of long-term debt to long-term debt plus equity of .45 and a current ratio of 1.25. Current liabilities are $1,215, sales are $9,360, profit margin is 7.5 percent, and ROE is 15.3 percent. What is the amount of the firm’s net fixed assets?

16. Calculating the Cash Coverage Ratio PVA Inc.’s net income for the most recent year was $21,460. The tax rate was 34 percent. The firm paid $7,340 in total interest expense and deducted $8,720 in depreciation expense. What was the cash coverage ratio for the year?

17. Cost of Goods Sold Sexton Corp. has current liabilities of $263,000, a quick ratio of .75, inventory turnover of 10.35, and a current ratio of 1.25. What is the cost of goods sold for the company?

18. Common-Size and Common-Base-Year Financial Statements In addition to common-size financial statements, common-base-year financial statements are often used. Common-base-year financial statements are constructed by dividing the current-year account value by the base-year account value. Thus, the result shows the growth rate in the account. Using the financial statements below, construct the common-size balance sheet and common-base-year balance sheet for the company. Use 2016 as the base year.

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PART 1 Overview78

JARROW CORPORATION 2016 and 2017 Balance Sheets

ASSETS LIABILITIES AND OWNERS’ EQUITY

2016 2017 2013 2014

Current assets

Cash

Accounts receivable

Inventory

Total

Fixed assets

Net plant and equipment

Total assets

$  17,928

28,565

    48,607

$  95,100

$422,852

$517,952

$  22,608

32,170

    57,173

$111,951

$488,184

$600,135

Current liabilities

Accounts receivable

Notes payable

Total

Long-term debt

Owners’ equity

Common stock and paid-in surplus

Accumulated retained earnings

Total

Total liabilities and owners’ equity

$  25,192

    32,379

$  57,571

$  46,200

$  55,000

  359,181

$414,181

$517,952

$  32,198

    39,476

$  71,674

$  70,000

$  55,000

  403,461

$458,461

$600,135

19. Full-Capacity Sales Breyfolge Mfg., Inc., is currently operating at only 92 percent of fixed asset capacity. Current sales are $905,000. How fast can sales grow before any new fixed assets are needed?

20. Fixed Assets and Capacity Usage For the company in the previous problem, suppose fixed assets are currently $895,000 and sales are projected to grow to $997,000. How much in new fixed assets is required to support this growth in sales? Assume the company operates at full capacity.

21. Calculating EFN The most recent financial statements for Retro Machine, Inc., follow. Sales for 2017 are projected to grow by 20 percent. Interest expense will remain constant; the tax rate and the dividend payout rate will also remain constant. Costs, other expenses, current assets, fixed assets, and accounts payable increase spontaneously with sales. If the firm is operating at full capacity and no new debt or equity are issued, what is the external financing needed to support the 20 percent growth rate in sales?

RETRO MACHINE INC 2016 Income Statement

Sales

Costs

Other expenses

Earnings before interest and taxes

Interest paid

Taxable income

Taxes (35%)

Net income

Dividends

Addition to retained earnings

$594,600

462,700

    12,200

$119,700

      8,960

$110,740

    38,759

 $  71,981

$  28,792

43,189

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CHAPTER 3 Financial Statements Analysis and Financial Models 79

RETRO MACHINE, INC Balance Sheet as of December 31 , 2016

ASSETS LIABILITIES AND OWNERS’ EQUITY

Current assets

Cash

Accounts receivable

Inventory

Total

Fixed assets

Net plant and equipment

Total assets

$  17,070

24,560

    58,650

$100,280

$278,780

$379,060

Current liabilities

Accounts payable

Notes payable

Total

Long-term debt

Owners’ equity

Common stock and paid-in surplus

Accumulated retained earnings

Total

Total liabilities and owners’ equity

$  45,900

    11,480

$  57,380

$106,000

$  95,000

120,680

$215,680

$379,060

22. Capacity Usage and Growth In the previous problem, suppose the firm was operating at only 85 percent capacity in 2016. What is EFN now?

23. Calculating EFN In Problem 21, suppose the firm wishes to keep its debt–equity ratio constant. What is EFN now?

24. EFN and Internal Growth Redo Problem 21 using sales growth rates of 15 and 25 percent in addition to 20 percent. Illustrate graphically the relationship between EFN and the growth rate, and use this graph to determine the relationship between them.

25. EFN and Sustainable Growth Redo Problem 23 using sales growth rates of 30 and 35 percent in addition to 20 percent. Illustrate graphically the relationship between EFN and the growth rate, and use this graph to determine the relationship between them.

26. Constraints on Growth Dahlia, Inc., wishes to maintain a growth rate of 9 percent per year and a debt–equity ratio of .40. The profit margin is 7.2 percent, and the ratio of total assets to sales is constant at 2.25. Is this growth rate possible? To answer, determine what the dividend payout ratio must be. How do you interpret the result?

27. EFN Define the following:

S = Previous year’s sales A = Total assets E = Total equity g = Projected growth in sales PM = Profit margin b = Retention (plowback) ratio

Assuming that all debt is constant, show that EFN can be written as

EFN = −PM(S)b + [A − PM(S)b] × g

Hint: Asset needs will equal A × g. The addition to retained earnings will equal PM(S)b × (1 + g).

28. Sustainable Growth Rate Based on the results in Problem 27, show that the internal and sustainable growth rates can be calculated as shown in equations 3.24 and 3.25. Hint: For the internal growth rate, set EFN equal to zero and solve for g.

29. Sustainable Growth Rate In the chapter, we discussed one calculation of the sustainable growth rate as

Sustainable growth rate = ROE × b __________ 1 − ROE × b

Challenge (Questions 24–30)

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PART 1 Overview80

In practice, probably the most commonly used calculation of the sustainable growth rate is ROE × b. This equation is identical to the two sustainable growth rate equations presented in the chapter if the ROE is calculated using the beginning of period equity. Derive this equation from the equation presented in the chapter.

30. Sustainable Growth Rate Use the sustainable growth rate equations from the previous problem to answer the following questions. Grendl, Inc., had total assets of $410,000 and equity of $265,000 at the beginning of the year. At the end of the year, the company had total assets of $460,000. During the year the company sold no new equity. Net income for the year was $75,000 and dividends were $32,000. What is the approximate sustainable growth rate for the company? What is the exact sustainable growth rate? What is the approximate sustainable growth rate if you calculate ROE based on the beginning of period equity? Is this number too high or too low? Why?

RATIOS AND FINANCIAL PLANNING AT EAST COAST YACHTS After Dan’s analysis of East Coast Yachts’ cash flow (at the end of our previous chapter), Larissa approached Dan about the company’s performance and future growth plans. First, Larissa wants to find out how East Coast Yachts is performing relative to its peers. Additionally, she wants to find out the future financing necessary to fund the company’s growth. In the past, East Coast Yachts experienced difficulty in financing its growth plan, in large part because of poor planning. In fact, the company had to turn down several large jobs because its facilities were unable to handle the additional demand. Larissa hoped that Dan would be able to estimate the amount of capital the company would have to raise next year so that East Coast Yachts would be better pre- pared to fund its expansion plans.

To get Dan started with his analyses, Larissa provided the following financial statements. Dan then gath- ered the industry ratios for the yacht manufacturing industry.

WHAT’S ON THE WEB? 1. DuPont Identity You can find financial statements for Walt Disney Company at Disney’s home page,

disney.com. For the three most recent years, calculate the DuPont identity for Disney. How has ROE changed over this period? How have changes in each component of the DuPont identity affected ROE over this period?

2. Ratio Analysis You want to examine the financial ratios for Starwood Hotels & Resorts. Go to www. reuters.com and type in the ticker symbol for the company (HOT). Now find financial ratios for Starwood and the industry and sector averages for each ratio.

a. What do TTM and MRQ mean? b. How do Starwood’s recent profitability ratios compare to their values over the past five years? To the

industry averages? To the sector averages? Which is the better comparison group for Starwood: the industry or sector averages? Why?

c. In what areas does Starwood seem to outperform its competitors based on the financial ratios? Where does Starwood seem to lag behind its competitors?

3. Applying Percentage of Sales    Locate the most recent annual financial statements for DuPont at www.dupont.com under the “Investors” link. Locate the annual report. Using the growth in sales for the most recent year as the projected sales growth for next year, construct a pro forma income statement and balance sheet. Based on these projections, what are the external funds needed?

4. Growth Rates    You can find the home page for Caterpillar, Inc., at www.cat.com. Go to the web page and find the most recent annual report. Using the information from the financial statements, what is the sustainable growth rate?

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CHAPTER 3 Financial Statements Analysis and Financial Models 81

EAST COAST YACHTS 2017 Income Statement

Sales

Cost of goods sold

Selling, general, and administrative

Depreciation

EBIT

Interest expense

EBT

Taxes

Net income

Dividends

Retained earnings

$611,582,000   

431,006,000   

73,085,700   

       19,958,400   

$    87,531,900   

       11,000,900   

$    76,531,000   

       30,612,400   

$    45,918,600   

$    17,374,500   

$    28,544,100   

EAST COAST YACHTS 2017 Balance Sheet

Current assets

Cash and equivalents

Accounts receivable

Inventory

Other

Total current assets

Fixed assets

Property, plant, and equipment

Less accumulated depreciation

Net property, plant, and equipment

Intangible assets and others

Total fixed assets

Total assets

$        11,119,700 

18,681,500 

20,149,650 

              1,172,200 

$            51,123,050 

$457,509,600 

    (113,845,900)

$343,663,700 

          6,772,000 

$350,435,700 

$401,558,750 

Current liabilities

Accounts payable

Accrued expenses

Total current liabilities

Long-term debt

Total long-term liabilities

Stockholders’ equity

Preferred stock

Common stock

Capital surplus

Accumulated retained earnings

Less treasury stock

Total equity

Total liabilities and shareholders’ equity

$        44,461,550   

              6,123,200   

$       50,584,750   

$169,260,000   

$169,260,000   

$      1,970,000   

37,583,700   

28,116,300   

161,564,000   

     (47,520,000)   

$181,714,000   

$401,558,750   

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PART 1 Overview82

1. East Coast Yachts uses a small percentage of preferred stock as a source of financing. In calculating the ratios for the company, should preferred stock be included as part of the company’s total equity?

2. Calculate all of the ratios listed in the industry table for East Coast Yachts.

3. Compare the performance of East Coast Yachts to the industry as a whole. For each ratio, comment on why it might be viewed as positive or negative relative to the industry. Suppose you create an inventory ratio calculated as inventory divided by current liabilities. How would you interpret this ratio? How does East Coast Yachts compare to the industry average for this ratio?

4. Calculate the sustainable growth rate for East Coast Yachts. Calculate external funds needed (EFN) and prepare pro forma income statements and balance sheets assuming growth at precisely this rate. Recalculate the ratios in the previous question. What do you observe?

5. As a practical matter, East Coast Yachts is unlikely to be willing to raise external equity capital, in part because the shareholders don’t want to dilute their existing ownership and control positions. However, East Coast Yachts is planning for a growth rate of 20 percent next year. What are your conclusions and recommendations about the feasibility of East Coast’s expansion plans?

6. Most assets can be increased as a percentage of sales. For instance, cash can be increased by any amount. However, fixed assets often must be increased in specific amounts since it is impossible, as a practical matter, to buy part of a new plant or machine. In this case, a company has a “staircase” or “lumpy” fixed cost structure. Assume that East Coast Yachts is currently producing at 100 percent of capacity and sales are expected to grow at 20 percent. As a result, to expand production, the company must set up an entirely new line at a cost of $95,000,000. Prepare the pro forma income statement and balance sheet. What is the new EFN with these assumptions? What does this imply about capacity utilization for East Coast Yachts next year?

Yacht Industry Rat ios

LOWER QUARTILE MEDIAN UPPER QUARTILE

Current ratio   .86 1.51  1.97

Quick ratio   .43  .75 1.01

Total asset turnover 1.10  1.27  1.46

Inventory turnover 12.18    14.38    16.43  

Receivables turnover 10.25    17.65    22.43  

Debt ratio  .32  .56   .61

Debt–equity ratio  .83 1.13  1.44 

Equity multiplier 1.83  2.13  2.44 

Interest coverage 5.72  8.21  10.83   

Profit margin   5.02%   7.48%   9.05%

Return on assets   7.05% 10.67% 14.16%

Return on equity 14.06% 19.32% 26.41%

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CHAPTER 4 Discounted Cash Flow Valuation 83

The signing of big-name athletes is often accompanied by great fanfare, but the numbers are often

misleading. For example, in late 2015, catcher Matt Weiters reached a one-year deal with the Baltimore

Orioles, signing a contract with a reported value of $15.8 million. Not bad, especially for someone who

makes a living using the “tools of ignorance” (jock jargon for a catcher’s equipment). Another example

is the contract signed by David Price of the Boston Red Sox, which had a stated value of $217 million.

It looks like Matt and David did pretty well, but the Orioles weren’t done as they signed

first baseman Chris Davis to a contract that has a stated value of $161 million, but this amount

was actually payable over several years. The contract called for $17 million per year for the

first six years, plus $42 million in future salary to be paid in the years 2023 through 2037.

David Price’s payments were similarly spread over time, although his payments were only

for seven years. Because two of the three contracts called for payments that are made at

future dates, we must consider the time value of money, which means none of these players

received the quoted amounts. How much did they really get? This chapter gives you the “tools

of knowledge” to answer this question.

Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.

OPENING CASE

Discounted Cash Flow Valuation 4 PART TWO: VALUATION AND CAPITAL BUDGETING

4.1 VALUATION: THE ONE-PERIOD CASE Keith Vaughan is trying to sell a piece of raw land in Alaska. Yesterday, he was offered $10,000 for the property. He was about ready to accept the offer when another indi- vidual offered him $11,424. However, the second offer was to be paid a year from now. Keith has satisfied himself that both buyers are honest and financially solvent, so he has no fear that the offer he selects will fall through. These two offers are pictured as cash flows in Figure 4.1. Which offer should Mr. Vaughan choose?

Jim Ellis, Keith’s financial adviser, points out that if Keith takes the first offer, he could invest the $10,000 in a bank at an insured rate of 12 percent.1 At the end of one year, he would have:

$10,000 + (.12 × $10,000) = $10,000 × 1.12 = $11,200 Return of Interest principal

Because this is less than the $11,424 Keith could receive from the second offer, Mr. Ellis recommends that he take the latter. This analysis uses the concept of future value, or compound value, which is the value of a sum after investing over one or more periods. The compound, or future value, of $10,000 at 12 percent is $11,200.

An alternative method employs the concept of present value. One can determine present value by asking the following question: How much money must Keith put in 1 At this point, the savvy reader could ask where one could actually find guaranteed debt yielding 12%. One example is Puerto Rico’s recent constitutionally guaranteed debt yielding a similar rate. However, in general, we concede that government guaranteed debt yielding double digit is very unusual and we should point out that Puerto Rico defaulted on its debt in July 2016.

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84

the bank today at 12 percent so that he will have $11,424 next year? We can write this algebraically as:

PV × 1.12 = $11,424

We want to solve for present value (PV), the amount of money that yields $11,424 if invested at 12 percent today. Solving for PV, we have:

PV = $11,424 _______ 1.12

= $10,200

The formula for PV can be written as:

Present Value of Investment:

PV = C 1 ______ 1 + r

[4.1]

where C1 is cash flow at Date 1 and r is the rate of return that Keith Vaughan requires on his land sale. It is sometimes referred to as the discount rate.

Present value analysis tells us that a payment of $11,424 to be received next year has a present value of $10,200 today. In other words, at a 12 percent interest rate, Mr. Vaughan is indifferent between $10,200 today or $11,424 next year. If you gave him $10,200 today, he could put it in the bank and receive $11,424 next year.

Because the second offer has a present value of $10,200, whereas the first offer is for only $10,000, present value analysis also indicates that Mr. Vaughan should take the second offer. In other words, both future value analysis and present value analysis lead to the same decision. As it turns out, present value analysis and future value analysis must always lead to the same decision.

As simple as this example is, it contains the basic principles that we will be working with over the next few chapters. We now use another example to develop the concept of net present value.

0 1

$10,000 $11,424Alternative sale prices

Year

FIGURE 4.1 Cash Flow for Mr. Vaughan’s Sale

E X

A M

P L

E

Diane Badame, a financial analyst at Kaufman & Broad, a leading real estate firm, is thinking about rec- ommending that Kaufman & Broad invest in a piece of land that costs $85,000. She is certain that next year the land will be worth $91,000, a sure $6,000 gain. Given that the guaranteed interest rate in the bank is 10 percent, should Kaufman & Broad undertake the investment in land? Ms. Badame’s choice is described in Figure 4.2 with the cash flow time chart.

Present Value

FIGURE 4.2 Cash Flows for Land Investment

0 1

-$85,000

$91,000Cash inflow

Time

Cash outflow

4 .1

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CHAPTER 4 Discounted Cash Flow Valuation 85

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A moment’s thought should be all it takes to convince her that this is not an attractive business deal. By investing $85,000 in the land, she will have $91,000 available next year. Suppose, instead, that Kaufman & Broad puts the same $85,000 into the bank. At the interest rate of 10 percent, this $85,000 would grow to:

(1 + .10) × $85,000 = $93,500 next year.

It would be foolish to buy the land when investing the same $85,000 in the financial market would produce an extra $2,500 (that is, $93,500 from the bank minus $91,000 from the land investment).

This is a future value calculation. Alternatively, she could calculate the present value of the sale price next year as:

Present value = $91,000 _______ 1.10

= $82,727.27

Because the present value of next year’s sales price is less than this year’s purchase price of $85,000, present value analysis also indicates that she should not recommend purchasing the property.

Frequently, business people want to determine the exact cost or benefit of a decision. The decision to buy this year and sell next year can be evaluated as

Net Present Value of Investment:

–$2,273 = –$85,000 + $91,000 ________ 1.10

Cost of land today

Present value of next year’s sales price

The formula for NPV can be written as:

NPV = –Cost + PV [4.2]

Equation 4.2 says that the value of the investment is –$2,273, after stating all the benefits and all the costs as of Date 0. We say that –$2,273 is the net present value (NPV) of the investment. That is, NPV is the present value of future cash flows minus the present value of the cost of the investment. Because the net present value is negative, Diane Badame should not recommend purchasing the land.

Both the Vaughan and the Badame examples deal with perfect certainty. That is, Keith Vaughan knows with perfect certainty that he could sell his land for $11,424 next year. Similarly, Diane Badame knows with perfect certainty that Kaufman & Broad could receive $91,000 for selling its land. Unfortunately, business people frequently do not know future cash flows. This uncertainty is treated in the next example.

Professional Artworks, Inc., is a firm that speculates in modern paintings. The manager is thinking of buying an original Picasso for $400,000 with the intention of selling it at the end of one year. The manager expects that the painting will be worth $480,000 in one year. The relevant cash flows are depicted in Figure 4.3.

Of course, this is only an expectation—the painting could be worth more or less than $480,000. Suppose the guaranteed interest rate granted by banks is 10 percent. Should the firm purchase the piece of art?

Our first thought might be to discount at the interest rate, yielding:

$480,000

_________ 1.10

= $436,364

Uncertainty and Valuation

(continued )

E X

A M

P L

E 4

.2

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86

Because $436,364 is greater than $400,000, it looks at first glance as if the painting should be purchased. However, 10 percent is the return we have assumed one can earn on a riskless investment. Because the painting is quite risky, a higher discount rate is called for. The manager chooses a rate of 25 percent to reflect this risk. In other words, he argues that a 25 percent expected return is fair compensation for an investment as risky as this painting.

The present value of the painting becomes:

$480,000

_________ 1.25

= $384,000

Thus, the manager believes that the painting is currently overpriced at $400,000 and does not make the purchase.

FIGURE 4.3 Cash Flows for Investment in Painting

0 1

-$400,000

$480,000Expected cash inflow

Time

Cash outflow

The preceding analysis is typical of decision making in today’s corporations, though real-world examples are, of course, much more complex. Unfortunately, any example with risk poses a problem not faced by a riskless example. In an example with riskless cash flows, the appropriate required return (i.e., discount rate) can be determined by checking the current returns on U.S. Treasury securities. Conceptually, the correct discount rate for a risky expected cash flow is the expected return available in the market on other invest- ments of the same risks. This is the correct discount rate to apply because it represents the economic opportunity cost to investors. It is the expected return they will require before committing funding to an investment. However, the actual selection of the discount rate for a risky investment is quite a difficult task. We don’t know at this point whether the discount rate on the painting should be 11 percent, 25 percent, 52 percent, or some other percentage.

Because the choice of a discount rate is so difficult, we merely wanted to broach the subject here. We must wait until the specific material on risk and return is covered in later chapters before a risk-adjusted analysis can be presented.

4.2 THE MULTIPERIOD CASE The previous section presented the calculation of future value and present value for one period only. We will now perform the calculations for the multiperiod case.

Future Value and Compounding Suppose an individual were to make a loan of $1. At the end of the first year, the borrower would owe the lender the principal amount of $1 plus the interest on the loan at the interest rate of r. For the specific case where the interest rate is, say, 9 percent, the borrower owes the lender:

$1 × (1 + r ) = $1 × 1.09 = $1.09

At the end of the year, though, the lender has two choices. She can either take the $1.09— or, more generally, (1 + r)—out of the financial market, or she can leave it in and lend it again for a second year. The process of leaving the money in the financial market and lending it for another year is called compounding.

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Suppose that the lender decides to compound her loan for another year. She does this by taking the proceeds from her first one-year loan, $1.09, and lending this amount for the next year. At the end of next year, then, the borrower will owe her:

$1 × (1 + r) × (1 + r) = $1 × (1 + r)2 = 1 + 2r + r2

$1 × (1.09) × (1.09) = $1 × (1.09)2 = $1 + $.18 + $.0081 = $1.1881

This is the total she will receive two years from now by compounding the loan. In other words, by providing a ready opportunity for lending, the capital market enables

the investor to transform $1 today into $1.1881 at the end of two years. At the end of three years, the total cash will be $1 × (1.09)3 = $1.2950.

The most important point to notice is that the total amount that the lender receives is not just the $1 that she lent out plus two years’ worth of interest on $1:

2 × r = 2 × $.09 = $.18

The lender also gets back an amount r2, which is the interest in the second year on the interest that was earned in the first year. The term, 2 × r, represents simple interest over the two years, and the term, r2, is referred to as the interest on interest. In our example this latter amount is exactly:

r2 = $.092 = $.0081

When cash is invested at compound interest, each interest payment is reinvested. With simple interest, the interest is not reinvested. Benjamin Franklin’s statement, “Money makes money and the money that money makes makes more money,” is a colorful way of explaining compound interest. The difference between compound interest and simple interest is illustrated in Figure 4.4. In this example, the difference does not amount to much because the loan is for $1. If the loan were for $1 million, the lender would receive $1,188,100 in two years’ time. Of this amount, $8,100 is interest on interest. The lesson is that those small numbers beyond the decimal point can add up to big dollar amounts when the transactions are for big amounts. In addition, the longer-lasting the loan, the more important interest on interest becomes.

The general formula for an investment over many periods can be written as:

Future Value of an Investment:

FV = C0 × (1 + r )T [4.3]

FIGURE 4.4 Simple and Compound Interest

$1.295 $1.270

$1.188 $1.180

$1.09

$1

1 year 2 years 3 years The purple-shaded area represents the initial investment. The green-shaded area represents the simple interest. The blue-shaded area represents interest on interest.

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where C0 is the cash to be invested at Date 0 (i.e., today), r is the interest rate per period, and T is the number of periods over which the cash is invested.

Suh-Pyng Ku has put $500 in a savings account at the First National Bank of Kent. The account earns 7 percent, compounded annually. How much will Ms. Ku have at the end of three years?

$500 × 1.07 × 1.07 × 1.07 = $500 × (1.07)3 = $612.52

Figure 4.5 illustrates the growth of Ms. Ku’s account.

Interest on Interest

FIGURE 4.5 Suh-Pyng Ku’s Savings Account

0 01 12 23 3

$612.52

$500D ol

la rs

Time Time

$612.52

-$500

Jay Ritter invested $1,000 in the stock of the SDH Company. The company pays a current dividend of $2, which is expected to grow by 20 percent per year for the next two years. What will the dividend of the SDH Company be after two years?

$2 × (1.20)2 = $2.88

Figure 4.6 illustrates the increasing value of SDH’s dividends.

Compound Growth

FIGURE 4.6 The Growth of the SDH Dividends

0 21

$2.00

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Time Time 0 1 2

$2.88

$2.40

$2.88 $2.40

$2.00 Cash inflows

The two previous examples can be calculated in any one of four ways. The computa- tions could be done by hand, by calculator, by spreadsheet, or with the help of a table. The appropriate table is Table A.3, which appears in the back of the text. This table presents future value of $1 at the end of T periods. The table is used by locating the appropriate interest rate on the horizontal axis and the appropriate number of periods on the vertical axis.

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For example, Suh-Pyng Ku would look at the following portion of Table A.3:

INTEREST RATE

PERIOD 6% 7% 8%

1 1.0600 1.0700 1.0800

2 1.1236 1.1449 1.1664

3 1.1910 1.2250 1.2597

4 1.2625 1.3108 1.3605

She could calculate the future value of her $500 as:

$500  ×  1.2250  = $612.50 Initial investment   Future value of $1 

In the example concerning Suh-Pyng Ku, we gave you both the initial investment and the interest rate and then asked you to calculate the future value. Alternatively, the interest rate could have been unknown, as shown in the following example:

Gareth James, who recently won $10,000 in the lottery, wants to buy a car in five years. Gareth estimates that the car will cost $16,105 at that time. His cash flows are displayed in Figure 4.7.

What interest rate must he earn to be able to afford the car?

Finding the Rate

The ratio of purchase price to initial cash is:

$16,105

________ $10,000

 = 1.6105

Thus, he must earn an interest rate that allows $1 to become $1.6105 in five years. Table A.3 tells us that an interest rate of 10 percent will allow him to purchase the car.

One can express the problem algebraically as:

$10,000 × (1 × r )5 = $16,105 where r is the interest rate needed to purchase the car. Because $16,105/$10,000 = 1.6105, we have (1 + r )5 = 1.6105 Either the table or a calculator solves for r.

FIGURE 4.7 Cash Flows for Purchase of Gareth James’ Car

0 5

-$16,105

Cash inflow

Time

Cash outflow

$10,000

The Power of Compounding: A Digression Most people who have had any experience with compounding are impressed with its power over long periods of time. In fact, compound interest has been described as the “eighth wonder of the world” and “the most powerful force in the universe.”2 Take the 2 These quotes are often attributed to Albert Einstein (particularly the second one), but whether he really said either is not known. The first quote is also often attributed to Baron Rothschild, John Maynard Keynes, Benjamin Franklin, and others.

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stock market, for example. Ibbotson and Sinquefield have calculated what the stock market returned as a whole from 1926 through 2015.3 They find that one dollar placed in these stocks at the beginning of 1926 would have been worth $5,384.08 at the end of 2015. This is 10.02 percent compounded annually for 90 years, i.e., ($1.1002)90 = $5,384.08, ignoring a small rounding error.

The example illustrates the great difference between compound and simple interest. At 10.02 percent, simple interest on $1 is .1002 cents a year (i.e., $.1002). Simple interest over 90 years is $9.01 (90 × $.1002). That is, an individual withdrawing .1002 cents every year would have withdrawn $9.01 (90 × $.1002) over 90 years. This is quite a bit below the $5,384.08 that was obtained by reinvestment of all principal and interest.

The results are more impressive over even longer periods of time. A person with no experience in compounding might think that the value of $1 at the end of 180 years would be twice the value of $1 at the end of 90 years, if the yearly rate of return stayed the same. Actually the value of $1 at the end of 180 years would be the square of the value of $1 at the end of 90 years. That is, if the annual rate of return remained the same, a $1 investment in common stocks should be worth $28,988,317.45 [$1 × (5,384.08 × 5,384.08)].

A few years ago, an archaeologist unearthed a relic stating that Julius Caesar lent the Roman equivalent of one penny to someone. Since there was no record of the penny ever being repaid, the archaeologist wondered what the interest and principal would be if a descendant of Caesar tried to collect from a descendant of the borrower in the 20th century. The archaeologist felt that a rate of 6 percent might be appropriate. To his sur- prise, the principal and interest due after more than 2,000 years was vastly greater than the entire wealth on earth.

The power of compounding can explain why the parents of well-to-do families fre- quently bequeath wealth to their grandchildren rather than to their children. That is, they skip a generation. The parents would rather make the grandchildren very rich than make the children moderately rich. We have found that in these families the grandchildren have a more positive view of the power of compounding than do the children.

3 Stocks, Bonds, Bills, and Inflation [SBBI]. 2016 Yearbook, Ibbotson Associates, Chicago, 2016.

Present Value and Discounting We now know that an annual interest rate of 9 percent enables the investor to transform $1 today into $1.1881 two years from now. In addition, we would like to know:

How much would an investor need to lend today so that she could receive $1 two years from today?

Some people have said that it was the best real estate deal in history. Peter Minuit, director-general of New Netherlands, the Dutch West India Company’s colony in North America, in 1626 allegedly bought Manhattan Island from native Americans for 60 guilders’ worth of trinkets. This sounds cheap, but did the Dutch really get the better end of the deal? It is reported that 60 guilders was worth about $24 at the prevailing exchange rate. If the native Americans had sold the trinkets at a fair market value and invested the $24 at 5 percent (tax-free), it would now, about 390 years later, be worth about $4.4 billion. Today, Manhattan is undoubtedly worth more than $4.4 billion, and so, at a 5 percent rate of return, the native Americans got the worst of the deal. However, if invested at 10 percent, the amount of money they received would be worth about:

$24(1 + r )T = 24 × 1.1390 = $330.7 quadrillion

This is a lot of money. In fact, $330.7 quadrillion is more than all the real estate in the world is worth today. Note that no one in the history of the world has ever been able to find an investment yielding 10 percent every year for 390 years.

How Much for That Island?

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Algebraically, we can write this as:

PV × (1.09)2 = $1

In the preceding equation, PV stands for present value, the amount of money we must lend today in order to receive $1 in two years’ time.

Solving for PV in this equation, we have:

PV = $1 _______ 1.1881

= $.84

This process of calculating the present value of a future cash flow is called discounting. It is the opposite of compounding. The difference between compounding and discounting is illustrated in Figure 4.8.

To be certain that $.84 is in fact the present value of $1 to be received in two years, we must check whether or not, if we loaned out $.84 and rolled over the loan for two years, we would get exactly $1 back. If this were the case, the capital markets would be saying that $1 received in two years’ time is equivalent to having $.84 today. Checking the exact numbers, we get:

$.84168 × 1.09 × 1.09 = $1

In other words, when we have capital markets with a sure interest rate of 9 percent, we are indifferent between receiving $.84 today or $1 in two years. We have no reason to treat these two choices differently from each other, because if we had $.84 today and loaned it out for two years, it would return $1 to us at the end of that time. The value [1/(1.09)2] is called the present value factor. It is the factor used to calculate the present value of a future cash flow.

In the multiperiod case, the formula for PV can be written as:

Present Value of Investment:

PV = CT ______ (1 + r)T

[4.4]

where CT is cash flow at Date T and r is the appropriate discount rate.

FIGURE 4.8 Compounding and Discounting

D ol

la rs

Future years

$1,000

101

Compounding at 9%

$2,367.36 Compound interest

Discounting at 9%

$422.41

$1,900 Simple interest

$1,000

2 3 4 5 6 7 8 9

The top line shows the growth of $1,000 at compound interest with the funds invested at 9 percent: $1,000 × (1.09)10 = $2,367.36. Simple interest is shown on the next line. It is $1,000 + [10 × ($1,000 × .09)] = $1,900. The bottom line shows the discounted value of $1,000 if the interest rate is 9 percent.

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In the preceding example, we gave both the interest rate and the future cash flow. Alternatively, the interest rate could have been unknown.

Harry DeAngelo will receive $10,000 three years from now. Harry can earn 8 percent on his investments, so the appropriate discount rate is 8 percent. What is the present value of his future cash flow?

PV = $10,000 ×  ( 1 _____

1.08 )

3

= $10,000 × .7938

= $7,938

Figure 4.9 illustrates the application of the present value factor to Harry’s investment.

When his investments grow at an 8 percent rate of interest, Harry DeAngelo is equally inclined toward receiving $7,938 now and receiving $10,000 in three years’ time. After all, he could convert the $7,938 he receives today into $10,000 in three years by lending it at an interest rate of 8 percent.

Harry DeAngelo could have reached his present value calculation in one of three ways. The computation could have been done by hand, by calculator, or with the help of Table A.1, which appears in the back of the text. This table presents present value of $1 to be received after T periods. The table is used by locating the appropriate interest rate on the horizontal and the appropriate number of periods on the vertical. For example, Harry De Angelo would look at the following portion of Table A.1:

INTEREST RATE

PERIOD 7% 8% 9%

1 .9346 .9259 .9174

2 .8734 .8573 .8417

3 .8163 .7938 .7722

4 .7629 .7350 .7084

The appropriate present value factor is .7938.

Multiperiod Discounting

FIGURE 4.9 Discounting Harry DeAngelo’s Opportunity

0 1 2

$7,938D ol

la rs

Time

0 3

$10,000

$10,000

Cash inflows

1 2 3 Time

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A customer of the Beatty Corp. wants to buy a tugboat today. Rather than paying immediately, he will pay $50,000 in three years. It will cost the Beatty Corp. $38,610 to build the tugboat immediately. The relevant cash flows to Beatty Corp. are displayed in Figure 4.10. By charging what interest rate would the Beatty Corp. neither gain nor lose on the sale?

Finding the Rate

FIGURE 4.10 Cash Flows for Tugboat

0

-$38,610

$50,000Cash inflows

Time

Cash outflows

3

The ratio of construction cost to sale price is:

$38,610

________ $50,000

= .7722

We must determine the interest rate that allows $1 to be received in three years to have a present value of $.7722. Table A.1 tells us that 9 percent is that interest rate.

Dennis Draper has won the Kentucky state lottery and will receive the following set of cash flows over the next two years:

YEAR CASH FLOW

1 $2,000

2 5,000

Mr. Draper can currently earn 6 percent in his money market account, so, the appropriate discount rate is 6 percent. The present value of the cash flows is:

YEAR CASH FLOW × PRESENT VALUE FACTOR = PRESENT VALUE

1 $2,000 × 1 _____ 1.06

 = $2,000 × .943 = $1,887

2 $5,000 × ( 1 _____

1.06 )

2 = $5,000 × .890 = 4,450

Total  $6,337

In other words, Mr. Draper is equally inclined toward receiving $6,337 today and receiving $2,000 and $5,000 over the next two years.

Cash Flow Valuation

Frequently, an investor or a business will receive more than one cash flow. The present value of the set of cash flows is the sum of the present values of the individual cash flows. This is illustrated in the following examples:

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Finance.com has an opportunity to invest in a new high-speed computer that costs $50,000. The com- puter will generate cash flows (from cost savings) of $25,000 one year from now, $20,000 two years from now, and $15,000 three years from now. The computer will be worthless after three years, and no additional cash flows will occur. Finance.com has determined that the appropriate discount rate is 7 percent for this investment. Should Finance.com make this investment in a new high-speed computer? What is the present value of the investment?

The cash flows and present value factors of the proposed computer are as follows:

CASH FLOWS PRESENT VALUE FACTOR

Year 0 –$50,000 1   =  1

1 25,000 1 ____

1.07     = .9346

2 20,000 ( 1 _____

1.07 )

2   = .8734

3 15,000 ( 1 _____

1.07 )

3

  = .8163

The present values of the cash flows are: Cash flows × Present value factor = Present value

Year 0 –$50,000 × 1 = –$50,000.00 1 $25,000 ×    .9346 = 23,364.49 2 $20,000 ×    .8734 = 17,468.77 3 $15,000 ×    .8163 = 12,244.47

Total $  3,077.73

Finance.com should invest in a new high-speed computer because the present value of its future cash flows is greater than its cost. The NPV is $3,077.73.

NPV

The Algebraic Formula To derive an algebraic formula for the net present value of a cash flow, recall that the PV of receiving a cash flow one year from now is:

PV = C1/(1 + r)

and the PV of receiving a cash flow two years from now is:

PV = C2 /(1 + r )2

We can write the NPV of a T-period project as:

NPV = −C0 + C1 _____

1 + r  +  C2 ______

(1 + r)2  + . . . +  CT ______

(1 + r)T  = −C0 + ∑

t =1 

T Ci ______

(1 + r)T [4.5]

The initial flow, −C0, is assumed to be negative because it represents an investment. The Σ is shorthand for the sum of the series.

We will close this section by answering the question we posed at the beginning of the chapter concerning baseball player Chris Davis’ contract. The terms of the contract called for $17 million per year for 2016 through 2022, $3.5 million per year for 2023 through

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2032, and $1.4 million per year for 2033 through 2037. If 12 percent is the appropriate interest rate, what kind of deal did the Oriole’s first baseman snag?

To answer, we can calculate the present value by discounting each year’s salary back to the present as follows (notice we assume that all the payments are made at year-end and that 12 percent is the appropriate discount rate):

Year 1 (2016): $17,000,000 × 1/1.121 = $15,178,571.43 Year 2 (2017): $17,000,000 × 1/1.122 = $13,552,295.92 Year 3 (2018): $17,000,000 × 1/1.123 = $12,100,264.21 . . . . Year 8 (2023): $ 3,500,000 × 1/1.128 = $ 1,413,591.30 . . . . Year 22 (2037): $ 1,400,000 × 1/1.1222 = $ 115,699.51

If you fill in the missing rows and then add (do it for practice), you will see that Chris’ contract had a present value of about $87.3 million, or only about 54 percent of the stated $161 million value (but still pretty good).

As you have probably noticed, doing extensive present value calculations can get to be pretty tedious, so a nearby Spreadsheet Techniques box shows how we recommend doing them. As an application, we take a look at lottery payouts in a nearby Finance Matters box.

We can set up a basic spreadsheet to calculate the present values of the individual cash flows as follows. Notice that we have calculated the present values one at a time and added them up:

1

2

3 4 5 6 7 8 9

1 0 1 1 1 2 1 3 1 4 1 5

1 6 1 7 1 8 1 9 2 0 2 1 2 2

A B C D E

What is the present value of $200 in one year, $400 the next year, $600 the next year, and $800 the last year if the discount rate is 12 percent?

Rate: .12

Year Cash flows Present values Formula used

1 $200 $178.57 =PV($B$7,A10,0,-B10) 2 $400 $318.88 =PV($B$7,A11,0,-B11) 3 $600 $427.07 =PV($B$7,A12,0,-B12) 4 $800 $508.41 =PV($B$7,A13,0,-B13)

Total PV: $1,432.93 =SUM(C10:C13)

Notice the negative signs inserted in the PV formulas. These just make the present values have positive signs. Also, the discount rate in cell B7 is entered as $B$7 (an "absolute" reference) because it is used over and over. We could have just entered ".12" instead, but our approach is more flexible.

Using a spreadsheet to value multiple future cash flows

How to Calculate Present Values wi th Mult ip le Future Cash F lows Using a Spreadsheet

SPREADSHEET TECHNIQUES

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JACKPOT! If you or someone you know is a regular lottery player, you probably already understand that you are 1,300 times more likely to get struck by lightning than you are to win a big lottery jackpot. What are your odds of winning? Below you will find a table with your chances of winning the Mega Millions Lottery compared to other events.

Odds of winning a Mega Millions jackpot 1:175,711,536*

Odds of being killed in a fireworks discharge 1:652,046 

Odds of being killed by a dog 1:144,899 

Odds of being killed by lightning 1:134,906 

Odds of being killed in an earthquake 1:97,807 

Odds of being killed by bees 1:79,842 

Odds of being killed by air transport 1:7,178 

Odds of being killed by or in a car 1:368 

*Source: Mega Millions Lottery website. All other odds from the National Safety Council.

Sweepstakes may have different odds than lotteries, but these odds may not be much better. At one time, the larg- est advertised potential grand prize ever was Pepsi’s “Play for a Billion,” which, you guessed it, had a $1 billion (billion!) prize. Not bad for a day’s work, but you still have to read the fine print. It turns out that the winner would be paid $5 million per year for the next 20 years, $10 million per year for years 21 through 39, and a lump sum $710 million in 40 years. From what you have learned, you know the value of the sweepstakes wasn’t even close to $1 billion. In fact, at an interest rate of 10 percent, the present value is about $70.7 million.

In January 2016, three winners split the record $1.584 billion Powerball jackpot. Each winner was given the option of receiving the jackpot as $328 million immediately or $7.9 million per year for the next 30 years, with the first payment to be made immediately. In a unique twist, the payments will increase at 5 percent pear year. So, what discount rate does this imply? After you learn about growing annuities in the next section, see if you don’t agree that the interest rate is about 2.79 percent.

Some lotteries make your decision a little tougher. The Ontario Lottery will pay you either $2,000 a week for the rest of your life or $1.3 million now. (That’s in Canadian dollars, or “loonies,” by the way.) Of course, there is the chance you might die in the near future, so the lottery guarantees that your heirs will collect the $2,000 weekly payments until the 20th anniversary of the first payment, or until you would have turned 91, whichever comes first. This payout scheme complicates your decision quite a bit. If you live for only the 20-year minimum, the break-even interest rate between the two options is about 5.13 percent per year, compounded weekly. If you expect to live longer than the 20-year minimum, you might be better off accepting $2,000 per week for life. Of course, if you manage to invest the $1.3 million lump sum at a rate of return of about 8 percent per year (compounded weekly), you can have your cake and eat it too because the investment will return $2,000 at the end of each week forever! Taxes complicate the deci- sion in this case because the lottery payments are all on an after-tax basis. Thus, the rates of return in this example would have to be after-tax as well.

FINANCE MATTERS

4.3 COMPOUNDING PERIODS So far we have assumed that compounding and discounting occur yearly. Sometimes compounding may occur more frequently than just once a year. For example, imagine that a bank pays a 10 percent interest rate “compounded semiannually.” This means that a $1,000 deposit in the bank would be worth $1,000 × 1.05 = $1,050 after six months, and $1,050 × 1.05 = $1,102.50 at the end of the year.

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4 By law, lenders are required to report the APR on all loans. In this text, we compute the APR as the interest rate per period multiplied by the number of periods in a year. According to federal law, the APR is a measure of the cost of consumer credit expressed as a yearly rate and it includes interest and certain noninterest charges and fees. In practice, the APR can be much higher than the interest rate on the loan if the lender charges substantial fees that must be included in the federally mandated APR calculation.

The end-of-the-year wealth can be written as:

$1,000  (1 + .10 ___ 2

) 2 = $1,000 × (1.05)2 = $1,102.50

Of course, a $1,000 deposit would be worth $1,100 (= $1,000 × 1.10) with yearly compounding. Note that the future value at the end of one year is greater with semian- nual compounding than with yearly compounding. With yearly compounding, the original $1,000 remains the investment base for the full year. The original $1,000 is the investment base only for the first six months with semiannual compounding. The base over the second six months is $1,050. Hence, one gets interest on interest with semiannual compounding.

Because $1,000 × 1.1025 = $1,102.50, 10 percent compounded semiannually is the same as 10.25 percent compounded annually. In other words, a rational investor could not care less whether she is quoted a rate of 10 percent compounded semiannually or a rate of 10.25 percent compounded annually.

Quarterly compounding at 10 percent yields wealth at the end of one year of:

$1,000 (1 + .10 ___ 4

) 4 = $1,103.81

More generally, compounding an investment m times a year provides end-of-year wealth of:

C0 (1 + r __

m )

m

[4.6]

where C0 is one’s initial investment and r is the annual percentage rate (APR). The APR is the annual interest rate without consideration of compounding. Banks and other financial institutions may use other names for the APR.4

What is the end-of-year wealth if Fernando Zapatero receives an annual percentage rate of 24 percent compounded monthly on a $1 investment?

Using Equation 4.6, his wealth is:

$1  (1 +  .24

____ 12

) 12

 = $1 × (1.02)12

= $1.2682 The annual rate of return is 26.82 percent. This annual rate of return is either called the effective annual rate (EAR) or the effective annual yield (EAY). Due to compounding, the effective annual interest rate is greater than the annual percentage rate of 24 percent. Algebraically, we can rewrite the effective annual interest rate as:

Effective Annual Rate:

(1 + r __

m )

m

− 1 [4.7]

Students are often bothered by the subtraction of 1 in Equation 4.7. Note that end-of-year wealth is composed of both the interest earned over the year and the original principal. We remove the original principal by subtracting 1 in Equation 4.7.

EARs

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Distinction between Annual Percentage Rate and Effective Annual Rate The distinction between the annual percentage rate (APR) and the effective annual rate (EAR) is frequently quite troubling to students. One can reduce the confusion by noting that the APR becomes meaningful only if the compounding interval is given. For example, for an APR of 10 percent, the future value at the end of one year with semiannual compounding is [1 + (.10/2)]2 = 1.1025. The future value with quarterly compounding is [1 + (.10/4)]4 = 1.1038. If the APR is 10 percent but no compounding interval is given, one cannot calculate future value. In other words, one does not know whether to compound semiannually, quarterly, or over some other interval.

By contrast, the EAR is meaningful without a compounding interval. For example, an EAR of 10.25 percent means that a $1 investment will be worth $1.1025 in one year. One can think of this as an APR of 10 percent with semiannual compounding or an APR of 10.25 percent with annual compounding, or some other possibility.

There can be a big difference between an APR and an EAR when interest rates are high. For example, consider “payday loans.” Payday loans are short-term loans made to consumers, often for less than two weeks. They are offered by companies such as Check Into Cash and AmeriCash Platinum. The loans work like this: You write a check today that is postdated. When the check date arrives, you go to the store and either pay the cash for the check or the company cashes the check. For example, in one particular state, Check Into Cash allows you to write a check for $115 dated 14 days in the future, for which they give you $100 today. So what are the APR and EAR of this arrange- ment? First, we need to find the interest rate, which we can find by the FV equation as follows:

FV = PV × (1 + r)1

$115 = $100 × (1 + r)1

1.15 = (1 + r) r = .15, or 15%

If an annual percentage rate of 8 percent is compounded quarterly, what is the effective annual rate? Using Equation 4.7, we have:

(1 + r __

m )

m

− 1 =  (1 + .08

____ 4

) 4

− 1 = .0824 = 8.24%

Referring back to our earlier example where C0 = $1,000 and r = 10%, we can generate the following table:

C 0 COMPOUNDING FREQUENCY (m ) C 1

EFFECTIVE ANNUAL

RATE = (1 + r __

m )

m

− 1

$1,000 Yearly (m = 1) $1,100.00 .10  1,000 Semiannually (m = 2)  1,102.50 .1025  1,000 Quarterly (m = 4)  1,103.81 .10381  1,000 Daily (m = 365)  1,105.16 .10516

Compounding Frequencies

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That doesn’t seem too bad until you remember this is the interest rate for 14 days! The APR of the loan is:

APR = .15 × 365/14 APR = 3.9107, or 391.07%

And the EAR for this loan is:

EAR = (1 + Quoted rate/m)m − 1 EAR = (1 + .15)365/14 − 1 EAR = 37.2366, or 3,723.66%

Now that’s an interest rate! Just to see what a difference a small variation in fees can make, AmeriCash Platinum will make you write a check for $117.50 for the same amount today. Check for yourself that the APR of this arrangement is 456.25 percent and the EAR is 6,598.65 percent. Definitely not a loan we would like to take out!

By law, lenders are required to report the APR on all loans. In this text, we compute the APR as the interest rate per period multiplied by the number of periods in a year. According to federal law, the APR is a measure of the cost of consumer credit expressed as a yearly rate, and it includes interest and certain noninterest charges and fees. In practice, the APR can be much higher than the interest rate on the loan if the lender charges substan- tial fees that must be included in the federally mandated APR calculation.

Compounding over Many Years Formula 4.6 applies for an investment over one year. For an investment over one or more (T) years, the formula becomes:

Future Value with Compounding:

FV = C0 (1 + r __

m )

mT [4.8]

Continuous Compounding The previous discussion shows that one can compound much more frequently than once a year. One could compound semiannually, quarterly, monthly, daily, hourly, each minute, or even more often. The limiting case would be to compound every infinitesimal instant, which is commonly called continuous compounding. Surprisingly, banks and other financial institutions sometimes quote continuously compounded rates, which is why we study them.

Though the idea of compounding this rapidly may boggle the mind, a simple formula is involved. With continuous compounding, the value at the end of T years is expressed as:

C0 × erT [4.9]

Harry DeAngelo is investing $5,000 at an annual percentage rate of 12 percent per year, compounded quarterly, for five years. What is his wealth at the end of five years?

Using Equation 4.8, his wealth is:

$5,000 × (1 + . 12

___ 4

) 4 ×5

= $5,000 × (1.03)20 = $5,000 × 1.8061 = $9,030.50

Multiyear Compounding

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where C0 is the initial investment, r is the annual percentage rate, and T is the number of years over which the investment runs. The number e is a constant and is approximately equal to 2.718. It is not an unknown like C0, r, and T.

Linda DeFond invested $1,000 at a continuously compounded rate of 10 percent for one year. What is the value of her wealth at the end of one year?

From Equation 4.9, we have:

$1,000 × e.10 = $1,000 × 1.1052 = $1,105.20

This number can easily be read from our Table A.5. One merely sets r, the value on the horizontal dimension, to 10 percent and T, the value on the vertical dimension, to 1. For this problem, the relevant portion of the table is:

PERIOD (T )

CONTINUOUSLY COMPOUNDED RATE ( r )

9% 10% 11%

1 1.0942 1.1052 1.1163

2 1.1972 1.2214 1.2461

3 1.3100 1.3499 1.3910

Note that a continuously compounded rate of 10 percent is equivalent to an annually compounded rate of 10.52 percent. In other words, Linda DeFond would not care whether her bank quoted a continuously compounded rate of 10 percent or a 10.52 percent rate, compounded annually.

Continuous Compounding

Linda DeFond’s brother, Mark, invested $1,000 at a continuously compounded rate of 10 percent for two years.

The appropriate equation here is:

$1,000 × e.10×2 = $1,000 × e.20 = $1,221.40

Using the portion of the table of continuously compounded rates reproduced above, we find the value to be 1.2214.

Continuous Compounding, Continued

The Michigan state lottery is going to pay you $1,000 at the end of four years. If the annual continuously compounded rate of interest is 8 percent, what is the present value of this payment?

$1,000 × 1 _____ e.08×4

= $1,000 × 1 _______ 1.3771

= $726.15

Present Value with Continuous Compounding

Figure 4.11 illustrates the relationship among annual, semiannual, and continuous compounding. Semiannual compounding gives rise to both a smoother curve and a higher ending value than does annual compounding. Continuous compounding has both the smoothest curve and the highest ending value of all.

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FIGURE 4.11 Annual, Semiannual, and Continuous Compounding

0 1 5

1

D ol

la rs

D ol

la rs

D ol

la rs

2

3

2 3 4

4 Interest earned

Annual compounding

1

2

3

4 Interest earned

Years

Semiannual compounding

1

2

3

4

Interest earned

Continuous compounding

0 1 52 3 4 Years

0 1 52 3 4 Years

4.4 SIMPLIFICATIONS The first part of this chapter has examined the concepts of future value and present value. Although these concepts allow one to answer a host of problems concerning the time value of money, the human effort involved can frequently be excessive. For example, consider a bank calculating the present value on a 20-year monthly mortgage. Because this mortgage has 240 (= 20 × 12) payments, a lot of time is needed to perform a conceptually simple task.

Because many basic finance problems are potentially so time-consuming, we search out simplifications in this section. We provide simplifying formulas for four classes of cash flow streams: 1. Perpetuity 2. Growing perpetuity 3. Annuity 4. Growing annuity

Perpetuity A perpetuity is a constant stream of cash flows without end. If you are thinking that perpetuities have no relevance to reality, it will surprise you that there is a well-known case of an unending cash flow stream: the British bonds called consols. An investor purchasing a consol is entitled to receive yearly interest from the British government forever.

How can the price of a consol be determined? Consider a consol that pays a coupon of C dollars each year and will do so forever. Applying the PV formula gives us:

PV =  C _____ 1 + r

 +  C ______ (1 + r)2

 +  C ______ (1 + r)3

 + . . .

where the dots at the end of the formula stand for the infinite string of terms that continues the formula. Series like the preceding one are called geometric series. It is well known that even though they have an infinite number of terms, the whole series has a finite sum because each term is only a fraction of the preceding term. Before turning to our calculus books, though, it is worth going back to our original principles to see if a bit of financial intuition can help us find the PV.

The present value of the consol is the present value of all of its future coupons. In other words, it is an amount of money that, if an investor had it today, would enable him to achieve the same pattern of expenditures that the consol and its coupons would. Suppose that an investor wanted to spend exactly C dollars each year. If he had the consol, he could do this. How much money must he have today to spend the same amount? Clearly he would need exactly enough so that the interest on the money would be C dollars per year. If he had any more, he could spend more than C dollars each year. If he had any less, he would eventually run out of money spending C dollars per year.

ExcelMaster coverage online

www.mhhe.com/RossCore5e

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The amount that will give the investor C dollars each year, and therefore the present value of the consol, is: 

PV =  C __ r [4.10]

To confirm that this is the right answer, notice that if we lend the amount C/r, the interest it earns each year will be:

Interest =  C __ r  × r = C

which is exactly the consol payment. To sum up, we have shown that for a consol:

Formula for Present Value of Perpetuity:

PV =  C _____ 1 + r

 +  C ______ (1 + r)2

 +  C ______ (1 + r)3

 + . . . [4.11]

=  C __ r

It is comforting to know how easily we can use a bit of financial intuition to solve this mathematical problem.

Growing Perpetuity Imagine an apartment building where cash flows to the landlord after expenses will be $100,000 next year. These cash flows are expected to rise at 5 percent per year. Assuming that this rise will continue indefinitely, the cash flow stream is termed a growing perpetuity. The relevant interest rate is 11 percent. Therefore, the appropriate discount rate is 11 percent and the present value of the cash flows can be represented as:

PV =  $100,000 _________ 1.11

 +  $100,000(1.05) ______________ (1.11)2

 +  $100,000(1.05) 2 ______________

(1.11)3  + . . .

+  $100,000(1.05) N −1 ________________

(1.11)N  + . . .

Algebraically, we can write the formula as:

PV =  C _____ 1 + r

 +  C × (1 + g) _________ (1 + r)2

  +  C × (1 + g) 2 __________

(1 + r)3  + . . . +  C × (1 + g)

N−1 ____________

(1 + r)N  + . . .

where C is the cash flow to be received one period hence, g is the rate of growth per period, expressed as a percentage, and r is the appropriate discount rate.

Consider a perpetuity paying $100 a year. If the relevant interest rate is 8 percent, what is the value of the consol?

Using Equation 4.10, we have:

PV =  $100 _____ .08

 = $1,250

Now suppose that interest rates fall to 6 percent. Using [4.10], the value of the perpetuity is:

PV =  $100 _____ .06

 = $1,666.67

Note that the value of the perpetuity rises with a drop in the interest rate. Conversely, the value of the perpetuity falls with a rise in the interest rate.

Perpetuities

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Fortunately, this formula reduces to the following simplification:

Formula for Present Value of Growing Perpetuity:

PV = C _____ r − g

[4.12]

From Formula 4.12, the present value of the cash flows from the apartment building is:

$100,000 _________ .11 − .05

 = $1,666,667

There are three important points concerning the growing perpetuity formula:

1. The Numerator. The numerator in Formula 4.12 is the cash flow one period hence, not at Date 0. Consider the following example:

Rothstein Corporation is just about to pay a dividend of $3.00 per share. Investors anticipate that the annual dividend will rise by 6 percent a year forever. The applicable discount rate is 11 percent. What is the price of the stock today?

The numerator in Formula 4.12 is the cash flow to be received next period. Since the growth rate is 6 percent, the dividend next year is $3.18 (= $3.00 × 1.06). The price of the stock today is:

$66. = $3.00

Imminent dividend

+ $3.18 ________ .11 − .06

Present value of all dividends beginning

a year from now

The price of $66.60 includes both the dividend to be received immediately and the present value of all dividends beginning a year from now. Formula 4.12 only makes it possible to calculate the present value of all dividends beginning a year from now. Be sure you understand this example; test questions on this subject always seem to trip up a few of our students.

Paying Dividends

2. The Discount Rate and the Growth Rate. The discount rate r must be greater than the growth rate g for the growing perpetuity formula to work. Consider the case in which the growth rate approaches the discount rate in magnitude. Then the denominator in the growing perpetuity formula gets infinitesimally small and the present value grows infinitely large. The present value is in fact undefined when r is less than g.

3. The Timing Assumption. Cash generally flows into and out of real-world firms both randomly and nearly continuously. However, Formula 4.12 assumes that cash flows are received and disbursed at regular and discrete points in time. In the example of the apartment, we assumed that the net cash flows of $100,000 only occurred once a year. In reality, rent checks are commonly received every month. Payments for maintenance and other expenses may occur anytime within the year.

The growing perpetuity formula [4.12] can be applied only by assuming a regular and discrete pattern of cash flow. Although this assumption is sensible because the formula saves so much time, the user should never forget that it is an assumption. This point will be mentioned again in the chapters ahead.

A few words should be said about terminology. Authors of financial textbooks generally use one of two conventions to refer to time. A minority of financial writers treat cash flows as being received on exact dates, for example Date 0, Date 1, and so forth. Under this convention,

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Date 0 represents the present time. However, because a year is an interval, not a specific moment in time, the great majority of authors refer to cash flows that occur at the end of a year (or alternatively, the end of a period). Under this end-of-the-year convention, the end of Year 0 is the present, the end of Year 1 occurs one period hence, and so on. (The beginning of Year 0 has already passed and is not generally referred to.)5

The interchangeability of the two conventions can be seen from the following chart:

Date 0 Date 1 Date 2 Date 3 Now

End of Year 0 End of Year 1 End of Year 2 End of Year 3 Now

We strongly believe that the dates convention reduces ambiguity. However, we use both conventions because you are likely to see the end-of-year convention in later courses. In fact, both conventions may appear in the same example for the sake of practice.

Annuity An annuity is a level stream of regular payments that lasts for a fixed number of periods. Not surprisingly, annuities are among the most common kinds of financial instruments. The pensions that people receive when they retire are often in the form of an annuity. Leases and mortgages are also often annuities.

To figure out the present value of an annuity we need to evaluate the following equation:

C _____

1 + r  +  C  ______

(1 + r)2  +  C  ______

(1 + r)3  + . . . +  C ______

(1 + r)T  

The present value of only receiving the coupons for T periods must be less than the present value of a consol, but how much less? To answer this we have to look at consols a bit more closely.

Consider the following time chart:

woN

Date (or end of year) 0 1 2 3 T (T 1) (T 2)

Consol 1 C C C . . . C C C . . .

Consol 2 C C . . .

Annuity C C C . . . C

Consol 1 is a normal consol with its first payment at Date 1. The first payment of Consol 2 occurs at Date T + 1.

The present value of having a cash flow of C at each of T dates is equal to the present value of Consol 1 minus the present value of Consol 2. The present value of Consol 1 is given by:

PV = C __ r [4.13]

Consol 2 is just a consol with its first payment at Date T + 1. From the perpetuity formula, this consol will be worth C/r at Date T.6 However, we do not want the value at Date T.

5 Sometimes financial writers merely speak of a cash flow in Year x. Although this terminology is ambiguous, such writers generally mean the end of Year x. 6 Students frequently think that C/r is the present value at Date T + 1 because the consol’s first payment is at Date T + 1. However, the formula values the annuity as of one period prior to the first payment.

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The term we use to compute the present value of the stream of level payments, C, for T years is called an annuity factor. The annuity factor in the current example is 9.8181. Because the annuity factor is used so often in PV calculations, we have included it in Table A.2 in the back of this book. The table gives the values of these factors for a range of interest rates, r, and maturity dates, T.

The annuity factor as expressed in the brackets of Formula 4.15 is a complex formula. For simplification, we may from time to time refer to the present value annuity factor as:

PVIFAr,T

That is, the above expression stands for the present value of $1 a year for T years at an interest rate of r.

We want the value now; in other words, the present value at Date 0. We must discount C/r back by T periods. Therefore, the present value of Consol 2 is:

PV =  C __ r     [

1 ______ (1 + r)T

] [4.14]

The present value of having cash flows for T years is the present value of a consol with its first payment at Date 1 minus the present value of a consol with its first payment at Date T + 1. Thus, the present value of an annuity is Formula 4.13 minus Formula 4.14. This can be written as:

C

__ r   −   C __

r     [

1 ______ (1 + r)T

]

This simplifies to:

Formula for Present Value of Annuity:

PV = C  [ 1 __ r  −  1 _______

r (1 + r)T ] [4.15]

This can also be written as:

PV = C 

⎡

⎢ ⎣ 1 −  1 ______

(1 + r)T __________

r

⎤

⎥ ⎦

Mark Young has just won the state lottery, paying $50,000 a year for 20 years. He is to receive his first payment a year from now. The state advertises this as the Million Dollar Lottery because $1,000,000 = $50,000 × 20. If the interest rate is 8 percent, what is the true value of the lottery?

Equation 4.15 yields:

Present value of  Million Dollar Lottery = $50,000 × 

⎡

⎢ ⎣ 1 −  1 _______

(1.08)20 ____________

.08

⎤

⎥ ⎦ Periodic payment = $50,000  = $490,907.37

× Annuity factor 9.8181

Rather than being overjoyed at winning, Mr. Young sues the state for misrepresentation and fraud. His legal brief states that he was promised $1 million but received only $490,907.37.

Lottery Valuation

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Our experience is that annuity formulas are not hard, but tricky, for the beginning student. We present four tricks below.

TRICK 1: A DELAYED ANNUITY One of the tricks in working with annuities or perpetuities is getting the timing exactly right. This is particularly true when an annuity or perpetuity begins at a date many periods in the future. We have found that even the brightest begin- ning student can make errors here. Consider the following example:

We can also provide a formula for the future value of an annuity:

FV = C  [ (1 + r)T

______ r  −  1 __

r ]  = C  [

(1 + r)T − 1 __________ r ] [4.16]

As with present value factors for annuities, we have compiled future value factors in Table A.4 in the back of this book. Of course, you can also use a spreadsheet as we illustrate in the nearby Spreadsheet Techniques box.

SPREADSHEET TECHNIQUESAnnui ty Present Values

Using a spreadsheet to find annuity present values goes like this:

1

2

3 4 5 6 7 8 9

1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7

A B C D E F G

What is the present value of $500 per year for 3 years if the discount rate is 10 percent? We need to solve for the unknown present value, so we use the formula PV(rate, nper, pmt, fv).

Payment amount per period: $500 Number of payments: 3

Discount rate: .1

Annuity present value: $1,243.43

The formula entered in cell B11 is =PV(B9,B8,-B7,0); notice that fv is zero and that pmt has a negative sign on it. Also notice that rate is entered as a decimal, not a percentage.

Using a spreadsheet to find annuity present values

Suppose you put $3,000 per year into a Roth IRA. The account pays 6 percent per year. How much will you have when you retire in 30 years?

This question asks for the future value of an annuity of $3,000 per year for 30 years at 6 percent, which we can calculate as follows:

FV = C   [ (1 + r)T − 1

___________ r ]  = $3,000 ×  [

1.0630 − 1 __________

.06 ]

= $3,000 × 79.0582 = $237,174.56

So, you’ll have close to a quarter million dollars in the account.

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TRICK 2: ANNUITY DUE The annuity formula of Formula 4.15 assumes that the first annuity payment begins a full period hence. This type of annuity is sometimes called an annuity in arrears or an ordinary annuity. What happens if the annuity begins today, in other words, at Date 0?

Danielle Caravello will receive a four-year annuity of $500 per year, beginning at Date 6. If the interest rate is 10 percent, what is the present value of her annuity? This situation can be graphed as:

0 1 2 3 4 5 6 7 8 9 10

$500 $500 $500 $500

The analysis involves two steps:

1. Calculate the present value of the annuity using Formula 4.15. This is:

Present Value of Annuity at Date 5:

$500 × 

⎡

⎢ ⎣ 1 − 1 _______

(1.10)4 ___________

.10

⎤

⎥ ⎦  = $500 × PVIFA10%,4 = $500 × 3.1699 = $1,584.93

Note that $1,584.93 represents the present value at Date 5. Students frequently think that $1,584.93 is the present value at Date 6, because the annuity begins

at Date 6. However, our formula values the annuity as of one period prior to the first payment. This can be seen in the most typical case where the first payment occurs at Date 1. The equation values the annuity as of Date 0 in that case.

2. Discount the present value of the annuity back to Date 0. That is:

Present Value at Date 0:

$1,584.93

__________ (1.10)5

 = $984.12

Again, it is worthwhile mentioning that, because the annuity formula brings Danielle’s annuity back to Date 5, the second calculation must discount over the remaining 5 periods. The two-step proce- dure is graphed in Figure 4.12.

FIGURE 4.12 Discounting Danielle Caravello’s Annuity

109Date Cash flow

$984.13 $1,584.93

$500 $500 $500 $500 876543210

Step one: Discount the four payments back to Date 5 by using the annuity formula. Step two: Discount the present value at Date 5 ($1,584.93) back to present value at Date 0.

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In a previous example, Mark Young received $50,000 a year for 20 years from the state lottery. In that example, he was to receive the first payment a year from the winning date. Let us now assume that the first payment occurs immediately. The total number of payments remains 20.

Under this new assumption, we have a 19-date annuity with the first payment occurring at Date 1—plus an extra payment at Date 0. The present value is:

$50,000  +  $50,000 × PVIFA8%,19 Payment at Date 0  19 − year annuity

 = $50,000 + ($50,000 × 9.6036) = $530,180

The present value in this example, $530,180, is greater than $490,907.37, the present value in the earlier lottery example. This is to be expected because the annuity of the current example begins earlier. An annuity with an immediate initial payment is called an annuity in advance or, more commonly, an annuity due. Always remember that Formula 4.15 and Table A.2 in this book refer to an ordinary annuity.

Annuity Due

Ms. Ann Chen receives an annuity of $450, payable once every two years. The annuity stretches out over 20 years. The first payment occurs at Date 2, that is, two years from today. The annual interest rate is 6 percent.

The trick is to determine the interest rate over a two-year period. The interest rate over two years is:

(1.06 × 1.06) − 1 = 12.36%

That is, $100 invested over two years will yield $112.36. What we want is the present value of a $450 annuity over 10 periods, with an interest rate of 12.36

percent per period. This is:

$450 × 

⎡

⎢ ⎣ 1 − 1 ____________

(1 + .1236)10 _________________

.1236

⎤

⎥ ⎦  = $450 × PVIFA12.36%,10 = $2,505.57

Infrequent Annuities

TRICK 3: THE INFREQUENT ANNUITY The following example treats an annuity with pay- ments occurring less frequently than once a year.

TRICK 4: EQUATING PRESENT VALUE OF TWO ANNUITIES The following example equates the present value of inflows with the present value of outflows.

Harold and Helen Nash are saving for the college education of their newborn daughter, Susan. The Nashes estimate that college expenses will run $30,000 per year when their daughter reaches college in 18 years. The annual interest rate over the next few decades will be 14 percent. How much money must they deposit in the bank each year so that their daughter will be completely supported through four years of college?

To simplify the calculations, we assume that Susan is born today. Her parents will make the first of her four annual tuition payments on her 18th birthday. They will make equal bank deposits on each of her first 17 birthdays, but no deposit at Date 0. This is illustrated as:

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Date 0 1 2 . . . 17 18 19 20 21

Susan’s Parents’ Parents’ . . . Parents’ Tuition Tuition Tuition Tuition birth 1st 2nd 17th and payment payment payment payment deposit deposit last 1 2 3 4 deposit

Mr. and Ms. Nash will be making deposits to the bank over the next 17 years. They will be withdraw- ing $30,000 per year over the following four years. We can be sure they will be able to withdraw fully $30,000 per year if the present value of the deposits is equal to the present value of the four $30,000 withdrawals.

This calculation requires three steps. The first two determine the present value of the withdraw- als. The final step determines yearly deposits that will have a present value equal to that of the withdrawals.

1. We calculate the present value of the four years at college using the annuity formula:

$30,000 × 

⎡

⎢ ⎣ 1 − 1 _______

(1.14)4 ___________

.14

⎤

⎥ ⎦  = $30,000 × PVIFA14%,4 = $30,000 × 2.9137 = $87,411.37

We assume that Susan enters college on her 18th birthday. Given our discussion in Trick 1, $87,411.37 represents the present value at Date 17.

2. We calculate the present value of the college education at Date 0 as:

$87,411.37

___________ (1.14)17

 = $9,422.92

3. Assuming that Helen and Harold Nash make deposits to the bank at the end of each of the 17 years, we calculate the annual deposit that will yield a present value of all deposits of $9,422.92. This is calculated as:

C  × PVIFA14%,17 = $9,422.92

Because PVIFA14%,17 = 6.3729

C  =  $9,422.92 __________ 6.3729

 = $1,478.60

Thus, deposits of $1,478.60 made at the end of each of the first 17 years and invested at 14 percent will provide enough money to make tuition payments of $30,000 over the following four years. Alternatively, we could have set $84,411.37 as the future value of an annuity and solved for the payment that way. Do this yourself and see if you don’t get the same annuity payment.

An alternative method would be to (1) calculate the present value of the tuition pay- ments at Susan’s 18th birthday and (2) calculate annual deposits such that the future value of the deposits at her 18th birthday equals the present value of the tuition payments at that date. Although this technique can also provide the right answer, we have found that it is more likely to lead to errors. Therefore, we only equate present values in our presentation.

Growing Annuity Cash flows in business are very likely to grow over time, due either to real growth or to inflation. The growing perpetuity, which assumes an infinite number of cash flows, pro- vides one formula to handle this growth. We now consider a growing annuity, which is a

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finite number of growing cash flows. Because perpetuities of any kind are rare, a formula for a growing annuity would be useful indeed. The formula is:

Formula for Present Value of Growing Annuity:

PV = C  [ 1 _____

r − g  −  1 _____

r − g  ×  (

1 + g _____

1 + r )

T    ] = C 

⎛

⎜ ⎝ 1 − (

1 + g _____

1 + r )

T ____________

r − g

⎞

⎟ ⎠ [4.17]

where, as before, C is the payment to occur at the end of the first period, r is the interest rate, g is the rate of growth per period, expressed as a percentage, and T is the number of periods for the annuity.

Stuart Gabriel, a second-year MBA student, has just been offered a job at $80,000 a year. He antici- pates his salary increasing by 9 percent a year until his retirement in 40 years. Given an interest rate of 20 percent, what is the present value of his lifetime salary?

We simplify by assuming he will be paid his $80,000 salary exactly one year from now, and that his salary will continue to be paid in annual installments. From [4.17], the calculation is:

Present value  of Stuart’s 

lifetime salary  = $80,000 × 

⎡

⎢ ⎣ 1 − (

1.09 _____

1.20 )

40

______________

.20 − .09

⎤

⎥ ⎦  = $711,731

Though the growing annuity is quite useful, it is more tedious than the other simplifying formulas. Whereas most sophisticated calculators have special programs for perpetuity, growing perpetuity, and annuity, there is no special program for growing annuity. Hence, one must calculate all the terms in Formula 4.17 directly.

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In a previous example, Harold and Helen Nash planned to make 17 identical payments in order to fund the college education of their daughter, Susan. Alternatively, imagine that they planned to increase their payments at 4 percent per year. What would their first payment be?

The first two steps of the previous Nash family example showed that the present value of the college costs was $9,422.92. These two steps would be the same here. However, the third step must be altered. Now we must ask, How much should their first payment be so that, if payments increase by 4 percent per year, the present value of all payments will be $9,422.92?

We set the growing annuity formula equal to $9,422.92 and solve for C.

C  

⎡

⎢ ⎣ 1 − (

1 + g ______

1 + r )

T

______________

r − g   

⎤

⎥ ⎦  = C   ⎡

⎢ ⎣ 1 − (

1.04 _____

1.14 )

17

______________

.14 − .04

⎤

⎥ ⎦  = $9,422.92

Here, C = $1,192.75. Thus, the deposit on their daughter’s first birthday is $1,192.75, the deposit on the second birthday is $1,240.46 (= 1.04 × $1,192.75), and so on.

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4.5 LOAN TYPES AND LOAN AMORTIZATION Whenever a lender extends a loan, some provision will be made for repayment of the prin- cipal (the original loan amount). A loan might be repaid in equal installments, for example, or it might be repaid in a single lump sum. Because the way that the principal and interest are paid is up to the parties involved, there are actually an unlimited number of possibilities.

In this section, we describe a few forms of repayment that come up quite often, and more complicated forms can usually be built up from these. The three basic types of loans are pure discount loans, interest-only loans, and amortized loans. Working with these loans is a very straightforward application of the present value principles that we have already developed.

Pure Discount Loans The pure discount loan is the simplest form of loan. With such a loan, the borrower receives money today and repays a single lump sum at some time in the future. A one-year, 10 percent pure discount loan, for example, would require the borrower to repay $1.10 in one year for every dollar borrowed today.

Because a pure discount loan is so simple, we already know how to value one. Suppose a borrower was able to repay $25,000 in five years. If we, acting as the lender, wanted a 12 percent interest rate on the loan, how much would we be willing to lend? Put another way, what value would we assign today to that $25,000 to be repaid in five years? Based on our previous work we know the answer is just the present value of $25,000 at 12 percent for five years:

Present value = $25,000/1.125

= $25,000/1.7623 = $14,186

Pure discount loans are common when the loan term is short, say a year or less. In recent years, they have become increasingly common for much longer periods.

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Interest-Only Loans A second type of loan repayment plan calls for the borrower to pay interest each period and to repay the entire principal (the original loan amount) at some point in the future. Loans with such a repayment plan are called interest-only loans. Notice that if there is just one period, a pure discount loan and an interest-only loan are the same thing.

For example, with a three-year, 10 percent, interest-only loan of $1,000, the borrower would pay $1,000 × .10 = $100 in interest at the end of the first and second years. At the

When the U.S. government borrows money on a short-term basis (a year or less), it does so by selling what are called Treasury bills, or T-bills for short. A T-bill is a promise by the government to repay a fixed amount at some time in the future—for example, 3 months or 12 months.

Treasury bills are pure discount loans. If a T-bill promises to repay $10,000 in 12 months, and the market interest rate is 7 percent, how much will the bill sell for in the market?

Because the going rate is 7 percent, the T-bill will sell for the present value of $10,000 to be repaid in one year at 7 percent:

Present value = $10,000/1.07 = $9,345.79

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end of the third year, the borrower would return the $1,000 along with another $100 in interest for that year. Similarly, a 50-year interest-only loan would call for the borrower to pay interest every year for the next 50 years and then repay the principal. In the extreme, the borrower pays the interest every period forever and never repays any principal. As we discussed earlier in the chapter, the result is a perpetuity.

Most corporate bonds have the general form of an interest-only loan. Because we will be considering bonds in some detail in the next chapter, we will defer further discussion of them for now.

Amortized Loans With a pure discount or interest-only loan, the principal is repaid all at once. An alterna- tive is an amortized loan, with which the lender may require the borrower to repay parts of the loan amount over time. The process of providing for a loan to be paid off by making regular principal reductions is called amortizing the loan.

A simple way of amortizing a loan is to have the borrower pay the interest each period plus some fixed amount. This approach is common with medium-term business loans. For example, suppose a business takes out a $5,000, five-year loan at 9 percent. The loan agreement calls for the borrower to pay the interest on the loan balance each year and to reduce the loan balance each year by $1,000. Because the loan amount declines by $1,000 each year, it is fully paid in five years.

In the case we are considering, notice that the total payment will decline each year. The reason is that the loan balance goes down, resulting in a lower interest charge each year, whereas the $1,000 principal reduction is constant. For example, the interest in the first year will be $5,000 × .09 = $450. The total payment will be $1,000 + 450 = $1,450. In the second year, the loan balance is $4,000, so the interest is $4,000 × .09 = $360, and the total payment is $1,360. We can calculate the total payment in each of the remaining years by preparing a simple amortization schedule as follows:

YEAR BEGINNING

BALANCE TOTAL

PAYMENT INTEREST

PAID PRINCIPAL

PAID ENDING

BALANCE

1 $5,000 $1,450 $ 450 $1,000 $4,000

2 4,000 1,360 360 1,000 3,000

3 3,000 1,270 270 1,000 2,000

4 2,000 1,180 180 1,000 1,000

5 1,000 1,090 90 1,000 0

Totals $6,350 $1,350 $5,000

Notice that in each year, the interest paid is given by the beginning balance multiplied by the interest rate. Also notice that the beginning balance is given by the ending balance from the previous year.

Probably the most common way of amortizing a loan is to have the borrower make a single, fixed payment every period. Almost all consumer loans (such as car loans) and mortgages work this way. For example, suppose our five-year, 9 percent, $5,000 loan was amortized this way. How would the amortization schedule look?

We first need to determine the payment. From our discussion earlier in the chapter, we know that this loan’s cash flows are in the form of an ordinary annuity. In this case, we can solve for the payment as follows:

$5,000 = C × {[1 − (1/1.095)]/.09} = C × [(1 − .6499)/.09]

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This gives us:

C = $5,000/3.8897 = $1,285.46

The borrower will therefore make five equal payments of $1,285.46. Will this pay off the loan? We will check by filling in an amortization schedule.

In our previous example, we knew the principal reduction each year. We then calculated the interest owed to get the total payment. In this example, we know the total payment. We will thus calculate the interest and then subtract it from the total payment to calculate the principal portion in each payment.

In the first year, the interest is $450, as we calculated before. Because the total payment is $1,285.46, the principal paid in the first year must be:

Principal paid = $1,285.46 − 450 = $835.46

The ending loan balance is thus:

Ending balance = $5,000 − 835.46 = $4,164.54

The interest in the second year is $4,164.54 × .09 = $374.81, and the loan balance declines by $1,285.46 – 374.81 = $910.65. We can summarize all of the relevant calculations in the following schedule:

YEAR BEGINNING

BALANCE TOTAL

PAYMENT INTEREST

PAID PRINCIPAL

PAID ENDING

BALANCE

1 $5,000.00 $1,285.46 $ 450.00 $ 835.46 $4,164.54

2 4,164.54 1,285.46 374.81 910.65 3,253.88

3 3,253.88 1,285.46 292.85 992.61 2,261.27

4 2,261.27 1,285.46 203.51 1,081.95 1,179.32

5 1,179.32 1,285.46 106.14  1,179.32 0.00

Totals $6,427.30 $1,427.31  $5,000.00

Because the loan balance declines to zero, the five equal payments do pay off the loan. Notice that the interest paid declines each period. This isn’t surprising because the loan balance is going down. Given that the total payment is fixed, the principal paid must be rising each period. To see how to calculate this loan in Excel, see the upcoming Spreadsheet Techniques box.

If you compare the two loan amortizations in this section, you will see that the total interest is greater for the equal total payment case: $1,427.31 versus $1,350. The reason for this is that the loan is repaid more slowly early on, so the interest is somewhat higher. This doesn’t mean that one loan is better than the other; it means that one is effectively paid off faster than the other. For example, the principal reduction in the first year is $835.46 in the equal total payment case as compared to $1,000 in the first case.

A common arrangement in real estate lending might call for a 5-year loan with, say, a 15-year amortiza- tion. What this means is that the borrower makes a payment every month of a fixed amount based on a 15-year amortization. However, after 60 months, the borrower makes a single, much larger payment called a “balloon” or “bullet” to pay off the loan. Because the monthly payments don’t fully pay off the loan, the loan is said to be partially amortized.

Partial Amortization, or “Bite the Bullet”

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Suppose we have a $100,000 commercial mortgage with a 12 percent APR and a 20-year (240- month) amortization. Further suppose the mortgage has a five-year balloon. What will the monthly payment be? How big will the balloon payment be?

The monthly payment can be calculated based on an ordinary annuity with a present value of $100,000. There are 240 payments, and the interest rate is 1 percent per month. The payment is:

$100,000 = C × [(1 − 1/1.01240 ) /.01] = C × 90.8194

C = $1,101.09

Now, there is an easy way and a hard way to determine the balloon payment. The hard way is to actually amortize the loan for 60 months to see what the balance is at that time. The easy way is to recognize that after 60 months, we have a 240 – 60 = 180-month loan. The payment is still $1,101.09 per month, and the interest rate is still 1 percent per month. The loan balance is thus the present value of the remaining payments:

Loan balance = $1,101.09 × [(1 − 1/1.01180 )/.01] = $1,101.09 × 83.3217 = $91,744.69

The balloon payment is a substantial $91,744. Why is it so large? To get an idea, consider the first payment on the mortgage. The interest in the first month is $100,000 × .01 = $1,000. Your payment is $1,101.09, so the loan balance declines by only $101.09. Because the loan balance declines so slowly, the cumulative “pay down” over five years is not great.

We will close this section with an example that may be of particular relevance. Federal Stafford loans are an important source of financing for many college students, helping to cover the cost of tuition, books, new cars, condominiums, and many other things. Sometimes students do not seem to fully realize that Stafford loans have a serious draw- back: They must be repaid in monthly installments, usually beginning six months after the student leaves school.

Some Stafford loans are subsidized, meaning that the interest does not begin to accrue until repayment begins (this is a good thing). If you are a dependent undergraduate student under this particular option, the total debt you can run up is, at most, $23,000. For loans between July 2015 and July 2016, the interest rate is 4.29 percent, or 4.29/12 = .3575 percent per month. Under the “standard repayment plan,” the loans are amortized over 10 years (subject to a minimum payment of $50).

Suppose you max out borrowing under this program and also get stuck paying the maximum interest rate. Beginning six months after you graduate (or otherwise depart the ivory tower), what will your monthly payment be? How much will you owe after making payments for four years?

Given our earlier discussions, see if you don’t agree that your monthly payment assum- ing a $23,000 total loan is $236.05 per month. Also, as explained in Example 4.28, after making payments for four years, you still owe the present value of the remaining payments. There are 120 payments in all. After you make 48 of them (the first four years), you have 72 to go. By now, it should be easy for you to verify that the present value of $236.05 per month for 72 months at .3575 percent per month is just under $15,000, so you still have a long way to go.

Of course, it is possible to rack up much larger debts. According to the Association of American Medical Colleges, students who borrowed to attend medical school and gradu- ated in 2014 had an average student loan balance of $176,000. Ouch! How long will it take the average student to pay off her medical school loans?

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Let’s say she makes a monthly payment of $1,200, and the loan has an interest rate of 7 percent per year, or .5833 percent per month. See if you agree that it will take 333 months, or just about 28 years, to pay off the loan. Maybe MD really stands for “mucho debt!”

4.6 WHAT IS A FIRM WORTH? Suppose you are in the business of trying to determine the value of small companies. (You are a business appraiser.) How can you determine what a firm is worth? One way to think about the question of how much a firm is worth is to calculate the present value of its future cash flows.

Let us consider the example of a firm that is expected to generate net cash flows (cash inflows minus cash outflows) of $5,000 in the first year and $2,000 for each of the next five years. The firm can be sold for $10,000 seven years from now. The owners of the firm would like to be able to make 10 percent on their investment in the firm.

Loan amortization is a common spreadsheet application. To illustrate, we will set up the problem that we examined earlier: a five-year, $5,000, 9 percent loan with constant payments. Our spreadsheet looks like this:

1 2 3 4 5 6 7 8 9

1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0 3 1

A B C D E F G H

Loan amount: $5,000 Interest rate: .09

Loan term: 5 Loan payment: $1,285.46

Note: Payment is calculated using PMT(rate, nper, -pv, fv). Amortization table:

Year Beginning Total Interest Principal Ending Balance Payment Paid Paid Balance

1 $5,000.00 $1,285.46 $450.00 $835.46 $4,164.54 2 4,164.54 1,285.46 374.81 910.65 3,253.88 3 3,253.88 1,285.46 292.85 992.61 2,261.27 4 2,261.27 1,285.46 203.51 1,081.95 1,179.32 5 1,179.32 1,285.46 106.14 1,179.32 0.00

Totals 6,427.31 1,427.31 5,000.00

Formulas in the amortization table:

Year Beginning Total Interest Principal Ending Balance Payment Paid Paid Balance

1 =+D4 =$D$7 =+$D$5*C13 =+D13-E13 =+C13-F13 2 =+G13 =$D$7 =+$D$5*C14 =+D14-E14 =+C14-F14 3 =+G14 =$D$7 =+$D$5*C15 =+D15-E15 =+C15-F15 4 =+G15 =$D$7 =+$D$5*C16 =+D16-E16 =+C16-F16 5 =+G16 =$D$7 =+$D$5*C17 =+D17-E17 =+C17-F17

Note: Totals in the amortization table are calculated using the SUM formula.

Using a spreadsheet to amortize a loan

Loan Amort izat ion Using a Spreadsheet SPREADSHEET TECHNIQUES

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The value of the firm is found by multiplying the net cash flows by the appropriate present value factor. The value of the firm is the sum of the present values of the individual net cash flows.

The present value of the net cash flows is given next.

END OF YEAR

THE PRESENT VALUE OF THE F IRM

NET CASH FLOW OF THE F IRM

PRESENT VALUE FACTOR (10%)

PRESENT VALUE OF NET CASH FLOWS

1 $ 5,000 .90909 $ 4,545.45

2 2,000 .82645 1,652.89

3 2,000 .75131 1,502.63

4 2,000 .68301 1,366.03

5 2,000 .62092 1,241.84

6 2,000 .56447 1,128.95

7 10,000 .51316 5,131.58

Present value of firm $16,569.38

We can also use the simplifying formula for an annuity to give us:

$5,000 _______ 1.1

+ (2,000 × PVIFA10%,5 ) _________________

1.1 + 10,000 _______

(1.1)7 = $16,569.38

Suppose you have the opportunity to acquire the firm for $12,000. Should you acquire the firm? The answer is yes because the NPV is positive.

NPV = PV − Cost $4,569.38 = $16,569.38 − 12,000

The incremental value (NPV) of acquiring the firm is $4,569.38.

The Trojan Pizza Company is contemplating investing $1 million in four new outlets in Los Angeles. Andrew Lo, the firm’s chief financial officer (CFO), has estimated that the investments will pay out cash flows of $200,000 per year for nine years and nothing thereafter. (The cash flows will occur at the end of each year and there will be no cash flow after Year 9.) Mr. Lo has determined that the relevant discount rate for this investment is 15 percent. This is the rate of return that the firm can earn at comparable projects. Should the Trojan Pizza Company make the investments in the new outlets?

The decision can be evaluated as:

NPV = −$1,000,000 + $200,000 _________ 1.15

+ $200,000 _________ (1.15)2

+ . . . +  $200,000 _________ (1.15)9

= −$1,000,000 + $200,000 × PVIFA15%,9 = −$1,000,000 + $954,316.78 = −$45,683.22

The present value of the four new outlets is only $954,316.78. The outlets are worth less than they cost. The Trojan Pizza Company should not make the investment because the NPV is −$45,683.22. If the Trojan Pizza Company requires a 15 percent rate of return, the new outlets are not a good investment.

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SUMMARY AND CONCLUSIONS 1. Two basic concepts, future value and present value, were introduced in the beginning of this chapter.

With a 10 percent interest rate, an investor with $1 today can generate a future value of $1.10 in a year, $1.21 [=$1 × (1.10)2] in two years, and so on. Conversely, present value analysis places a current value on a later cash flow. With the same 10 percent interest rate, a dollar to be received in one year has a present value of $.909 [=$1/1.10] in Year 0. A dollar to be received in two years has a present value of $.826 [=$1/(1.10)2].

2. One commonly expresses the interest rate as, say, 12 percent per year. However, one can speak of the interest rate as 3 percent per quarter. Although the annual percentage rate remains 12 percent [=3 percent × 4], the effective annual interest rate is 12.55 percent [=(1.03)4 − 1]. In other words, the compounding process increases the future value of an investment. The limiting case is continuous compounding, where funds are assumed to be reinvested every infinitesimal instant.

3. A basic quantitative technique for financial decision making is net present value analysis. The net present value formula for an investment that generates cash flows (Ci) in future periods is:

NPV = −C0 + C1 ______

(1 + r )  +  C2 _______

(1 + r)2 + . . . + CT _______

(1 + r)T  = −C0 + ∑

i =1

T

Ci _______ (1 + r )i

The formula assumes that the cash flow at Date 0 is the initial investment (a cash outflow).

4. Frequently, the actual calculation of present value is long and tedious. The computation of the present value of a long-term mortgage with monthly payments is a good example of this. We presented four simplifying formulas:

Perpetuity: PV =  C __ r

Growing perpetuity: PV = C _____ r − g

Annuity: PV = C 

⎡

⎢ ⎣ 1 −  1 _______

(1 + r)T ___________

r

⎤

⎥ ⎦

Growing annuity: PV = C 

⎡

⎢ ⎣ 1 −  (

1 + g ______

1 + r )

T

______________

r − g   

⎤

⎥ ⎦

5. We stressed a few practical considerations in the application of these formulas:

a. The numerator in each of the formulas, C, is the cash flow to be received one full period hence.

b. Cash flows are generally irregular in practice. To avoid unwieldy problems, assumptions to create more regular cash flows are made both in this textbook and in the real world.

c. A number of present value problems involve annuities (or perpetuities) beginning a few periods hence. Students should practice combining the annuity (or perpetuity) formula with the discounting formula to solve these problems.

d. Annuities and perpetuities may have periods of every two or every n years, rather than once a year. The annuity and perpetuity formulas can easily handle such circumstances.

e. One frequently encounters problems where the present value of one annuity must be equated with the present value of another annuity.

6. Many loans are annuities. The process of providing for a loan to be paid off gradually is called amortizing the loan, and we discussed how amortization schedules are prepared and interpreted.

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118 PART 2 Valuation and Capital Budgeting

1. Compounding and Period As you increase the length of time involved, what happens to future values? What happens to present values?

2. Interest Rates What happens to the future value of an annuity if you increase the rate r? What happens to the present value?

3. Present Value Suppose two athletes sign 10-year contracts for $80 million. In one case, we’re told that the $80 million will be paid in 10 equal installments. In the other case, we’re told that the $80 million will be paid in 10 installments, but the installments will increase by 5 percent per year. Who got the better deal?

4. APR and EAR Should lending laws be changed to require lenders to report EARs instead of APRs? Why or why not?

5. Time Value On subsidized Stafford loans, a common source of financial aid for college students, interest does not begin to accrue until repayment begins. Who receives a bigger subsidy, a freshman or a senior? Explain.

Use the following information for Questions 6-10:

Toyota Motor Credit Corporation (TMCC), a subsidiary of Toyota Motor Corporation, offered some securities for sale to the public on March 28, 2008. Under the terms of the deal, TMCC promised to repay the owner of one of these securities $100,000 on March 28, 2038, but investors would receive nothing until then. Investors paid TMCC $24,099 for each of these securities, so they gave up $24,099 on March 28, 2008, for the promise of a $100,000 payment 30 years later.

6. Time Value of Money Why would TMCC be willing to accept such a small amount today ($24,099) in exchange for a promise to repay about four times that amount ($100,000) in the future?

7. Call Provisions TMCC has the right to buy back the securities on the anniversary date at a price established when the securities were issued (this feature is a term of this particular deal). What impact does this feature have on the desirability of this security as an investment?

8. Time Value of Money Would you be willing to pay $24,099 today in exchange for $100,000 in 30 years? What would be the key considerations in answering yes or no? Would your answer depend on who is making the promise to repay?

9. Investment Comparison Suppose that when TMCC offered the security for $24,099 the U.S. Treasury had offered an essentially identical security. Do you think it would have had a higher or lower price? Why?

10. Length of Investment The TMCC security is bought and sold on the New York Stock Exchange. If you looked at the price today, do you think the price would exceed the $24,099 original price? Why? If you looked in the year 2019, do you think the price would be higher or lower than today’s price? Why?

CONCEPT QUESTIONS

1. Simple Interest versus Compound Interest First City Bank pays 7 percent simple interest on its savings account balances, whereas Second City Bank pays 7 percent interest compounded annually. If you made a $4,800 deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 10 years?

2. Calculating Future Values Compute the future value of $3,550 compounded annually for:

a. 10 years at 6 percent.

b. 10 years at 8 percent.

c. 20 years at 6 percent.

d. Why is the interest earned in part (c) not twice the amount earned in part (a)?

Basic (Questions 1–20)

QUESTIONS AND PROBLEMS

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CHAPTER 4 Discounted Cash Flow Valuation 119

3. Calculating Present Values For each of the following, compute the present value:

PRESENT VALUE YEARS INTEREST RATE FUTURE VALUE

9 7% $ 15,451 

13  9 51,557

16 14 886,073

24 11 550,164

4. Calculating Interest Rates Solve for the unknown interest rate in each of the following:

PRESENT VALUE YEARS INTEREST RATE FUTURE VALUE

$ 217 3 $ 293 

432 10  1,053

41,000 16 162,181

54,382 19 483,500

5. Calculating the Number of Periods Solve for the unknown number of years in each of the following:

PRESENT VALUE YEARS INTEREST RATE FUTURE VALUE

$ 625 6% $ 1,284

810 9 4,341

18,400 7 234,162

21,500 10 215,000

6. Calculating the Number of Periods At 5.75 percent interest, how long does it take to double your money? To quadruple it?

7. Calculating Present Values Imprudential, Inc., has an unfunded pension liability of $540 million that must be paid in 20 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 5.6 percent, what is the present value of this liability?

8. Calculating Rates of Return Although appealing to more refined tastes, art as a collectible has not always performed so profitably. In 2010, Deutscher-Menzies sold Arkie Under the Shower, a painting by renowned Australian painter Brett Whiteley, at auction for a price of $1,100,000. Unfortunately for the previous owner, he had purchased it three years earlier at a price of $1,680,000. What was his annual rate of return on this painting?

9. Perpetuities An investor purchasing a British consol is entitled to receive annual payments from the British government forever. What is the price of a consol that pays $80 annually if the next payment occurs one year from today? The market interest rate is 2.6 percent.

10. Continuous Compounding Compute the future value of $1,625 continuously compounded for

a. Five years at an annual percentage rate of 14 percent.

b. Three years at an annual percentage rate of 6 percent.

c. Ten years at an annual percentage rate of 8 percent.

d. Eight years at an annual percentage rate of 9 percent.

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120 PART 2 Valuation and Capital Budgeting

11. Present Value and Multiple Cash Flows Machine Co. has identified an investment project with the following cash flows. If the discount rate is 5 percent, what is the present value of these cash flows? What is the present value at 13 percent? At 18 percent?

YEAR CASH FLOW

1 $  585

2  815

3 1,630

4 2,140

12. Present Value and Multiple Cash Flows Investment X offers to pay you $4,850 per year for nine years, whereas Investment Y offers to pay you $6,775 per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 5 percent? If the discount rate is 21 percent?

13. Calculating Annuity Present Value An investment offers $5,500 per year for 15 years, with the first payment occurring one year from now. If the required return is 7.5 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever?

14. Calculating Perpetuity Values The Perpetual Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $18,000 per year forever. If the required return on this investment is 4.3 percent, how much will you pay for the policy? Suppose the company told you the policy costs $445,000. At what interest rate would this be a fair deal?

15. Calculating EAR Find the EAR in each of the following cases:

APR NUMBER OF T IMES COMPOUNDED EAR

9.8% Quarterly

12.4 Monthly

7.6 Daily

8.4 Infinite

16. Calculating APR Find the APR in each of the following cases:

APR NUMBER OF T IMES COMPOUNDED EAR

Semiannually 10.4%

Monthly 8.9

Weekly 11.6

Infinite 15.4

17. Calculating EAR First National Bank charges 15.7 percent compounded monthly on its business loans. First United Bank charges 16.2 percent compounded semiannually. As a potential borrower, which bank would you go to for a new loan?

18. Interest Rates Well-known financial writer Andrew Tobias argues that he can earn 177 percent per year buying wine by the case. Specifically, he assumes that he will consume one $10 bottle of fine Bordeaux per week for the next 12 weeks. He can either pay $10 per week or buy a case of 12 bottles today. If he buys the case, he receives a 10 percent discount, and, by doing so, earns the 177 percent. Assume he buys the wine and consumes the first bottle today. Do you agree with his analysis? Do you see a problem with his numbers?

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CHAPTER 4 Discounted Cash Flow Valuation 121

19. Calculating Number of Periods  One of your customers is delinquent on his accounts payable balance. You’ve mutually agreed to a repayment schedule of $450 per month. You will charge 1.3 percent per month interest on the overdue balance. If the current balance is $18,700, how long will it take for the account to be paid off?

20. Calculating EAR Friendly’s Quick Loans, Inc., offers you “three for four or I knock on your door.” This means you get $3 today and repay $4 when you get your paycheck in one week (or else). What’s the effective annual return Friendly’s earns on this lending business? If you were brave enough to ask, what APR would Friendly’s say you were paying?

21. Future Value What is the future value in six years of $1,500 invested in an account with an annual percentage rate of 7.2 percent

a. Compounded annually?

b. Compounded semiannually?

c. Compounded monthly?

d. Compounded continuously?

e. Why does the future value increase as the compounding period shortens?

22. Simple Interest versus Compound Interest First Simple Bank pays 7.4 percent simple interest on its investment accounts. If First Complex Bank pays interest on its accounts compounded annually, what rate should the bank set if it wants to match First Simple Bank over an investment horizon of 10 years?

23. Calculating Annuities You are planning to save for retirement over the next 30 years. To do this, you will invest $750 per month in a stock account and $325 per month in a bond account. The return of the stock account is expected to be an APR of 10.5 percent, and the bond account will earn an APR of 6.1 percent. When you retire, you will combine your money into an account with an APR of 6.9 percent. All interest rates are compounded monthly. How much can you withdraw each month from your account assuming a withdrawal period of 25 years?

24. Calculating Rates of Return Suppose an investment offers to triple your money in 12 months (don’t believe it). What rate of return per quarter are you being offered?

25. Calculating Rates of Return  You’re trying to choose between two different investments, both of which have up-front costs of $55,000. Investment G returns $105,000 in five years. Investment H returns $235,000 in 11 years. Which of these investments has the higher return?

26. Growing Perpetuities Mark Weinstein has been working on an advanced technology in laser eye surgery. His technology will be available in the near term. He anticipates his first annual cash flow from the technology to be $210,000, received three years from today. Subsequent annual cash flows will grow at 2.5 percent in perpetuity. What is the value today of the technology if the discount rate is 11 percent?

27. Perpetuities A prestigious investment bank designed a new security that pays a quarterly dividend of $1.75 in perpetuity. The first dividend occurs one quarter from today. What is the price of the security if the annual percentage rate is 5.5 percent compounded quarterly?

28. Annuity Present Values What is the value today of an annuity of $5,700 per year, with the first cash flow received 3 years from today and the last one received 25 years from today? Use a discount rate of 6.8 percent.

29. Annuity Present Values What is the value today of a 15-year annuity that pays $825 a year? The annuity’s first payment occurs six years from today. The annual interest rate is 9 percent for Years 1 through 5, and 12 percent thereafter.

30. Balloon Payments Mike Bayles has just arranged to purchase a $825,000 vacation home in the Bahamas with a 20 percent down payment. The mortgage has an APR of 5.4 percent, compounded monthly, and calls for equal monthly payments over the next 30 years. His first payment will be due one month from now. However, the mortgage has an eight-year balloon payment, meaning that the balance of the loan must be paid off at the end of Year 8. There were no other transaction costs or finance charges. How much will Mike’s balloon payment be in eight years?

Intermediate (Questions 21–52)

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122 PART 2 Valuation and Capital Budgeting

31. Calculating Interest Expense You receive a credit card application from Shady Banks Savings and Loan offering an introductory rate of 1.9 percent per year, compounded monthly for the first six months, increasing thereafter to 16 percent compounded monthly. Assuming you transfer the $7,500 balance from your existing credit card and make no subsequent payments, how much interest will you owe at the end of the first year?

32. Perpetuities Reigle Pharmaceuticals is considering a drug project that costs $1,650,000 today and is expected to generate end-of-year annual cash flows of $185,000, forever. At what discount rate would the company be indifferent between accepting or rejecting the project?

33. Growing Annuity Southern California Publishing Company is trying to decide whether or not to revise its popular textbook, Financial Psychoanalysis Made Simple. It has estimated that the revision will cost $135,000. Cash flows from increased sales will be $38,000 the first year. These cash flows will increase by 5.5 percent per year. The book will go out of print five years from now. Assume that the initial cost is paid now and revenues are received at the end of each year. If the company requires a return of 11 percent for such an investment, should it undertake the revision?

34. Growing Annuity Your job pays you only once a year, for all the work you did over the previous 12 months. Today, December 31, you just received your salary of $75,000 and you plan to spend all of it. However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 10 percent of your annual salary in an account that will earn 9.5 percent per year. Your salary will increase at 3.4 percent per year throughout your career. How much money will you have on the date of your retirement 35 years from today?

35. Present Value and Interest Rates What is the relationship between the value of an annuity and the level of interest rates? Suppose you just bought a 15-year annuity of $5,250 per year at the current interest rate of 10 percent per year. What happens to the value of your investment if interest rates suddenly drop to 5 percent? What if interest rates suddenly rise to 15 percent?

36. Calculating the Number of Payments You’re prepared to make monthly payments of $190, beginning at the end of this month, into an account that pays 8.75 percent interest compounded monthly. How many payments will you have made when your account balance reaches $25,000?

37. Calculating Annuity Present Values You want to borrow $105,000 from your local bank to buy a new sailboat. You can afford to make monthly payments of $2,025, but no more. Assuming monthly compounding, what is the highest APR you can afford on a 60-month loan?

38. Calculating Loan Payments You need a 30-year, fixed-rate mortgage to buy a new home for $225,000. Your mortgage bank will lend you the money at an APR of 5.1 percent. However, you can only afford monthly payments of $875, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments at $875?

39. Present and Future Values The present value of the following cash flow stream is $5,800 when discounted at 8 percent annually. What is the value of the missing cash flow?

YEAR CASH FLOW

1 $1,300

2 ?

3 1,900

4 2,450

40. Calculating Present Values You have just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $165,000 per year. Thus, in one year you receive $1.165 million. In two years, you get $1.33 million, and so on. If the appropriate interest rate is 7.5 percent, what is the value of your winnings today?

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CHAPTER 4 Discounted Cash Flow Valuation 123

41. EAR versus APR You have just purchased a new warehouse. To finance the purchase, you’ve arranged for a 30-year mortgage loan for 80 percent of the $3.9 million purchase price. The monthly payment on this loan will be $18,250. What is the APR on this loan? The EAR?

42. Present Value and Break-Even Interest Consider a firm with a contract to sell an asset for $150,000 three years from now. The asset costs $102,000 to produce today. Given a relevant discount rate of 11 percent per year, will the firm make a profit on this asset? At what rate does the firm just break even?

43. Present Value and Multiple Cash Flows What is the value today of $3,500 per year, at a discount rate of 7.6 percent, if the first payment is received 7 years from now and the last payment is received 30 years from now?

44. Variable Interest Rates A 15-year annuity pays $1,750 per month, and payments are made at the end of each month. If the interest rate is 11.4 percent compounded monthly for the first seven years, and 8.6 percent compounded monthly thereafter, what is the value of the annuity today?

45. Comparing Cash Flow Streams You have your choice of two investment accounts. Investment A is a 15-year annuity that features end-of-month $1,250 payments and has an interest rate of 6.15 percent compounded monthly. Investment B is a continuously compounded lump-sum investment with an interest rate of 7 percent also good for 15 years. How much money would you need to invest in B today for it to be worth as much as Investment A 15 years from now?

46. Calculating Present Value of a Perpetuity Given an interest rate of 6.4 percent per year, what is the value at t = 7 of a perpetual stream of $3,250 payments that begin at t = 15?

47. Calculating EAR A local finance company quotes an interest rate of 16.6 percent on one-year loans. So, if you borrow $23,000, the interest for the year will be $3,818. Because you must repay a total of $26,818 in one year, the finance company requires you to pay $26,818/12, or $2,234.83, per month over the next 12 months. Is the interest rate on the loan 16.6 percent? What rate would legally have to be quoted? What is the effective annual rate?

48. Calculating Present Values A 5-year annuity of 10 $6,500 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now. If the discount rate is 9 percent compounded monthly, what is the value of this annuity five years from now? What is the value three years from now? What is the current value of the annuity?

49. Calculating Annuities Due Suppose you are going to receive $17,500 per year for five years. The appropriate interest rate is 7.4 percent.

a. What is the present value of the payments if they are in the form of an ordinary annuity? What is the present value if the payments are an annuity due?

b. Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? What if the payments are an annuity due?

c. Which has the highest present value, the ordinary annuity or the annuity due? Which has the highest future value? Will this always be true?

50. Calculating Annuities Due You want to buy a new sports car from Muscle Motors for $83,000. The contract is in the form of a 60-month annuity due at an APR of 4.89 percent, compounded monthly. What will your monthly payment be?

51. Amortization with Equal Payments Prepare an amortization schedule for a three-year loan of $51,000. The interest rate is 9 percent per year, and the loan calls for equal annual payments. How much interest is paid in the third year? How much total interest is paid over the life of the loan?

52. Amortization with Equal Principal Payments Rework Problem 51 assuming that the loan agreement calls for a principal reduction of $17,000 every year instead of equal annual payments.

53. Calculating Annuities Due You want to lease a set of golf clubs from Pings Ltd. The lease contract is in the form of 24 equal monthly payments at an APR of 9.7 percent, compounded monthly. Since the clubs cost $3,100 retail, Pings wants the present value of the lease payments to equal $3,100 and your first payment is due immediately. What will your monthly lease payments be?

Challenge (Questions 53–80)

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124 PART 2 Valuation and Capital Budgeting

54. Annuities You are saving for the college education of your two children. They are two years apart in age; one will begin college 15 years from today and the other will begin 17 years from today. You estimate your children’s college expenses to be $55,000 per year per child, payable at the beginning of each school year. The annual interest rate is 9.2 percent. How much money must you deposit in an account each year to fund your children’s education? Your deposits begin one year from today. You will make your last deposit when your oldest child enters college. Assume your children will be on the four-year plan.

55. Growing Annuities Tom Adams has received a job offer from a large investment bank as a clerk to an associate banker. His base salary will be $65,000. He will receive his first annual salary payment one year from the day he begins to work. In addition, he will get an immediate $12,000 bonus for joining the company. His salary will grow at 3.2 percent each year. Each year he will receive a bonus equal to 10 percent of his salary. Mr. Adams is expected to work for 35 years. What is the present value of the offer if the discount rate is 9 percent?

56. Calculating Annuities You have recently won the super jackpot in the Set for Life Lottery. On reading the fine print, you discover that you have the following two options:

a. You will receive 31 annual payments of $400,000, with the first payment being delivered today. The income will be taxed at a rate of 36 percent. Taxes will be withheld when the checks are issued.

b. You will receive $1,000,000 now, and you will not have to pay taxes on this amount. In addition, beginning one year from today, you will receive $325,000 each year for 30 years. The cash flows from this annuity will be taxed at 36 percent.

Using a discount rate of 4.5 percent, which option should you select?

57. Calculating Growing Annuities You have 30 years left until retirement and want to retire with $2.2 million. Your salary is paid annually and you will receive $70,000 at the end of the current year. Your salary will increase at 3 percent per year, and you can earn a return of 9.7 percent on the money you invest. If you save a constant percentage of your salary, what percentage of your salary must you save each year?

58. Balloon Payments On September 1, 2014, Susan Chao bought a motorcycle for $35,000. She paid $1,000 down and financed the balance with a five-year loan at an APR of 5.8 percent compounded monthly. She started the monthly payments exactly one month after the purchase (i.e., October 1, 2014). Two years later, at the end of October 2016, Susan got a new job and decided to pay off the loan. If the bank charges her a 1 percent prepayment penalty based on the loan balance, how much must she pay the bank on November 1, 2016?

59. Calculating Annuity Values Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with a retirement income of $25,000 per month for 20 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $340,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $1,000,000 to his nephew Frodo. He can afford to save $2,200 per month for the next 10 years. If he can earn an EAR of 11 percent before he retires and an EAR of 7 percent after he retires, how much will he have to save each month in Years 11 through 30?

60. Calculating Annuity Values After deciding to get a new car, you can either lease the car or purchase it with a three-year loan. The car you wish to buy costs $38,000. The dealer has a special leasing arrangement where you pay $2,500 today and $425 per month for the next three years. If you purchase the car, you will pay it off in monthly payments over the next three years at an APR of 3.8 percent, compounded monthly. You believe that you will be able to sell the car for $24,500 in three years. Should you buy or lease the car? What break-even resale price in three years would make you indifferent between buying and leasing?

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CHAPTER 4 Discounted Cash Flow Valuation 125

61. Calculating Annuity Values An All-Pro defensive lineman is in contract negotiations. The team has offered the following salary structure:

TIME SALARY

0 $7,000,000

1 6,100,000

2 6,900,000

3 7,600,000

4 8,200,000

5 9,500,000

6 8,400,000

All salaries are to be paid in a lump sum. The player has asked you as his agent to renegotiate the terms. He wants a signing bonus of $9 million payable today and a contract value increase of $2.5 million. He also wants an equal salary paid every three months, with the first paycheck three months from now. If the interest rate is an APR of 5 percent compounded daily, what is the amount of his quarterly check? Assume 365 days in a year.

62. Discount Interest Loans This question illustrates what is known as discount interest. Imagine you are discussing a loan with a somewhat unscrupulous lender. You want to borrow $20,000 for one year. The interest rate is 14.5 percent. You and the lender agree that the interest on the loan will be .145 × $20,000 = $2,900. So the lender deducts this interest amount from the loan up front and gives you $17,100. In this case, we say that the discount is $2,900. What’s wrong here?

63. Calculating Annuity Values You are serving on a jury. A plaintiff is suing the city for injuries sustained after a freak street sweeper accident. In the trial, doctors testified that it will be five years before the plaintiff is able to return to work. The jury has already decided in favor of the plaintiff. You are the foreperson of the jury and propose that the jury give the plaintiff an award to cover the following: (1) The present value of two years’ back pay. The plaintiff’s annual salary for the last two years would have been $42,000 and $45,000, respectively. (2) The present value of five years’ future salary. You assume the salary will be $49,000 per year. (3) $150,000 for pain and suffering. (4) $25,000 for court costs. Assume that the salary payments are equal amounts paid at the end of each month. If the interest rate you choose is an EAR of 9 percent, what is the size of the settlement? If you were the plaintiff, would you like to see a higher or lower interest rate?

64. Calculating EAR with Points You are looking at a one-year loan of $10,000. The interest rate is quoted as 12.5 percent plus two points. A point on a loan is 1 percent (one percentage point) of the loan amount. Quotes similar to this one are very common with home mortgages. The interest rate quotation in this example requires the borrower to pay two points to the lender up front and repay the loan later with 12.5 percent interest. What rate would you actually be paying here?

65. Calculating EAR with Points The interest rate on a one-year loan is quoted as 9 percent plus three points (see the previous problem). What is the EAR? Is your answer affected by the loan amount?

66. EAR versus APR There are two banks in the area that offer 30-year, $225,000 mortgages at 5.4 percent compounded monthly and charge a $2,400 loan application fee. However, the application fee charged by Insecurity Bank and Trust is refundable if the loan application is denied, whereas that charged by I. M. Greedy and Sons Mortgage Bank is not. The current disclosure law requires that any fees that will be refunded if the applicant is rejected be included in calculating the APR, but this is not required with nonrefundable fees (presumably because refundable fees are part of the loan rather than a fee). What are the EARs on these two loans? What are the APRs?

67. Calculating EAR with Add-On Interest This problem illustrates a deceptive way of quoting interest rates called add-on interest. Imagine that you see an advertisement for Crazy Judy’s Stereo City that

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126 PART 2 Valuation and Capital Budgeting

reads something like this: “$2,500 Instant Credit! 17.5% Simple Interest! Three Years to Pay! Low, Low Monthly Payments!” You’re not exactly sure what all this means and somebody has spilled ink over the APR on the loan contract, so you ask the manager for clarification.

Judy explains that if you borrow $2,500 for three years at 17.5 percent interest, in three years you will owe

$2,500 × 1.1753 = $2,500 × 1.622234 = $4,055.59

Now, Judy recognizes that coming up with $4,055.59 all at once might be a strain, so she lets you make “low, low monthly payments” of $4,055.59/36 = $112.66 per month, even though this is extra bookkeeping work for her.

Is the interest rate on this loan 17.5 percent? Why or why not? What is the APR on this loan? What is the EAR? Why do you think this is called add-on interest?

68. Growing Annuities You have successfully started and operated a company for the past 10 years. You have decided that it is time to sell your company and spend time on the beaches of Hawaii. A potential buyer is interested in your company, but he does not have the necessary capital to pay you a lump sum. Instead, he has offered $500,000 today and annuity payments for the balance. The first payment will be for $220,000 in three months. The payments will increase at 2.5 percent per quarter and a total of 25 quarterly payments will be made. If you require an EAR of 11 percent, how much are you being offered for your company?

69. Calculating the Number of Periods Your Christmas ski vacation was great, but it unfortunately ran a bit over budget. All is not lost, because you just received an offer in the mail to transfer your $10,000 balance from your current credit card, which charges an annual rate of 18.2 percent, to a new credit card charging a rate of 7.9 percent. How much faster could you pay the loan off by making your planned monthly payments of $175 with the new card? What if there was a fee of 3 percent charged on any balances transferred?

70. Future Value and Multiple Cash Flows An insurance company is offering a new policy to its customers. Typically, the policy is bought by a parent or grandparent for a child at the child’s birth. The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company:

First birthday: $750

Second birthday: 750

Third birthday: 850

Fourth birthday: 850

Fifth birthday: 950

Sixth birthday: 950

After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $500,000. If the relevant interest rate is 10 percent for the first six years and 8 percent for all subsequent years, is the policy worth buying?

71. Annuity Present Values and Effective Rates You have just won the lottery. You will receive $4,000,000 today, and then receive 40 payments of $1,750,000. These payments will start one year from now and will be paid every six months. A representative from Greenleaf Investments has offered to purchase all the payments from you for $35 million. If the appropriate interest rate is an APR of 8 percent compounded daily, should you take the offer? Assume there are 365 days per year.

72. Calculating Interest Rates A financial planning service offers a college savings program. The plan calls for you to make six annual payments of $15,000 each, with the first payment occurring today, your child’s 12th birthday. Beginning on your child’s 18th birthday, the plan will provide $32,000 per year for four years. What return is this investment offering?

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CHAPTER 4 Discounted Cash Flow Valuation 127

73. Break-Even Investment Returns Your financial planner offers you two different investment plans. Plan X is a $15,000 annual perpetuity. Plan Y is a 10-year, $31,000 annual annuity. Both plans will make their first payment one year from today. At what discount rate would you be indifferent between these two plans?

74. Perpetual Cash Flows What is the value of an investment that pays $30,000 every other year forever, if the first payment occurs one year from today and the discount rate is an APR of 11 percent compounded daily? What is the value today if the first payment occurs four years from today?

75. Ordinary Annuities and Annuities Due As discussed in the text, an annuity due is identical to an ordinary annuity except that the periodic payments occur at the beginning of each period and not at the end of the period. Show that the relationship between the value of an ordinary annuity and the value of an otherwise equivalent annuity due is

Annuity due value = Ordinary annuity value × (1 + r ) Show this for both present and future values.

76. Calculating Annuities  You have just won the Life’s Downhill After 30 lottery. The lottery payments will be made for the next 30 years. The payments are slightly unusual in that you will be paid $600,000 every six months starting six months from today, for a total of 60 payments. You will also receive $900,000 every nine months starting nine months from today, for a total of 40 payments. When the payments coincide, for example 18 months from today, you will receive both payments. If the interest rate is an APR of 8.1 percent compounded monthly, what is the present value of your winnings?

77. Calculating EAR A check-cashing store is in the business of making personal loans to walk-up customers. The store makes only one-week loans at 5.5 percent interest per week.

a. What APR must the store report to its customers? What is the EAR that the customers are actually paying?

b. Now suppose the store makes one-week loans at 5.5 percent discount interest per week (see Question 62). What’s the APR now? The EAR?

c. The check-cashing store also makes one-month add-on interest loans at 5.5 percent discount interest per week. Thus, if you borrow $100 for one month (four weeks), the interest will be ($100 × 1.0554 ) − 100 = $23.88. Because this is discount interest, your net loan proceeds today will be $76.12. You must then repay the store $100 at the end of the month. To help you out, though, the store lets you pay off this $100 in installments of $25 per week. What is the APR of this loan? What is the EAR?

78. Present Value of a Growing Perpetuity What is the equation for the present value of a growing perpetuity with a payment of C one period from today if the payments grow by C each period?

79. Rule of 72 A useful rule of thumb for the time it takes an investment to double with discrete compounding is the “Rule of 72.” To use the Rule of 72, you divide 72 by the interest rate to determine the number of periods it takes for a value today to double. For example, if the interest rate is 6 percent, the Rule of 72 says it will take 72/6 = 12 years to double. This is approximately equal to the actual answer of 11.90 years. The Rule of 72 can also be applied to determine what interest rate is needed to double money in a specified period. This is a useful approximation for many interest rates and periods. At what rate is the Rule of 72 exact?

80. Rule of 69.3 A corollary to the Rule of 72 is the Rule of 69.3. The Rule of 69.3 is exactly correct except for rounding when interest rates are compounded continuously. Prove the Rule of 69.3 for continuously compounded interest.

WHAT’S ON THE WEB? 1. Calculating Future Values Go to www.dinkytown.net and follow the “Investment Calculators” link. If you

currently have $10,000 and invest this money at 9 percent, how much will you have in 30 years? Assume you will not make any additional contributions. How much will you have if you can earn 11 percent?

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128 PART 2 Valuation and Capital Budgeting

CLOSING CASE

THE MBA DECISION Ben Bates graduated from college six years ago with a finance undergraduate degree. Since graduation, he has been employed in the finance department at East Coast Yachts. Although he is satisfied with his current job, his goal is to become an investment banker. He feels that an MBA degree would allow him to achieve this goal. After examining schools, he has narrowed his choice to either Wilton University or Mount Perry College. Although internships are encouraged by both schools, to get class credit for the internship, no salary can be paid. Other than internships, neither school will allow its students to work while enrolled in its MBA program.

Ben’s annual salary at East Coast Yachts is $57,000 per year, and his salary is expected to increase at 3 percent per year until retirement. He is currently 28 years old and expects to work for 40 more years. His current job includes a fully paid health insurance plan, and his current average tax rate is 26 percent. Ben has a savings account with enough money to cover the entire cost of his MBA program.

2. Future Values and Taxes Taxes can greatly affect the future value of your investment. The website at www.fincalc.com has a financial calculator that adjusts your return for taxes. Suppose you have $50,000 to invest today. If you can earn a 12 percent return and no additional annual savings, how much will you have in 20 years? (Enter 0 percent as the tax rate.) Now, assume that your marginal tax rate is 27.5 percent. How much will you have at this tax rate?

Excel is a great tool for solving problems, but with many time value of money problems, you may still need to draw a time line. For example, consider a classic retirement problem. A friend is celebrating her birthday and wants to start saving for her anticipated retirement. She has the following years to retirement and retirement spending goals:

Years until retirement: 30

Amount to withdraw each year: $90,000

Years to withdraw in retirement: 20

Interest rate: 8%

Because your friend is planning ahead, the first withdrawal will not take place until one year after she retires. She wants to make equal annual deposits into her account for her retirement fund.

a. If she starts making these deposits in one year and makes her last deposit on the day she retires, what amount must she deposit annually to be able to make the desired withdrawals at retirement?

b. Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump-sum deposit today to cover her retirement needs. What amount does she have to deposit today?

c. Suppose your friend’s employer will contribute to the account each year as part of the company’s profit- sharing plan. In addition, your friend expects a distribution from a family trust several years from now. What amount must she deposit annually now to be able to make the desired withdrawals at retirement? The details are

Employer’s annual contribution: $1,500

Years until trust fund distribution: 20

Amount of trust fund distribution: $25,000

EXCEL MASTER IT ! PROBLEM

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CHAPTER 4 Discounted Cash Flow Valuation 129

The Ritter College of Business at Wilton University is one of the top MBA programs in the country. The MBA degree requires two years of full-time enrollment at the university. The annual tuition is $63,000, payable at the beginning of each school year. Books and other supplies are estimated to cost $2,500 per year. Ben expects that after graduation from Wilton, he will receive a job offer for about $105,000 per year, with an $18,000 signing bonus. The salary at this job will increase at 4 percent per year. Because of the higher salary, his average income tax rate will increase to 31 percent.

The Bradley School of Business at Mount Perry College began its MBA program 16 years ago. The Bradley School is smaller and less well known than the Ritter College. Bradley offers an accelerated, one-year pro- gram, with a tuition cost of $75,000 to be paid upon matriculation. Books and other supplies for the program are expected to cost $3,500. Ben thinks that after graduation from Mount Perry, he will receive an offer of $88,000 per year, with a $15,000 signing bonus. The salary at this job will increase at 3.5 percent per year. His average income tax rate at this level of income will be 29 percent.

Both schools offer a health insurance plan that will cost $3,000 per year, payable at the beginning of the year. Ben also estimates that room and board expenses will cost $2,000 more per year at both schools than his current expenses, payable at the beginning of each year. The appropriate discount rate is 6.1 percent. Assume all salaries are paid at the end of each year.

1. How does Ben’s age affect his decision to get an MBA?

2. What other, perhaps nonquantifiable factors, affect Ben’s decision to get an MBA?

3. Assuming all salaries are paid at the end of each year, what is the best option for Ben—from a strictly financial standpoint?

4. In choosing between the two schools, Ben believes that the appropriate analysis is to calculate the future value of each option. How would you evaluate this statement?

5. What initial salary would Ben need to receive to make him indifferent between attending Wilton University and staying in his current position? Assume his tax rate after graduating from Wilton University will be 31 percent regardless of his income level.

6. Suppose that instead of being able to pay cash for his MBA, Ben must borrow the money. The current borrowing rate is 5.4 percent. How would this affect his decision to get an MBA?

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PART 2 Valuation and Capital Budgeting130

5 OPENING CASE

Interest Rates and Bond Valuation 2015 and early 2016 proved to be a very unusual period for bonds. For example, in February

2016, Sweden’s central bank lowered its interest rate from negative .35 percent to negative

.5 percent! Sweden was not alone as the Eurozone, Switzerland, and Japan, among others,

all had negative interest rates set by the respective central banks. Why was this happening?

Central banks were in a race to the bot tom, lowering interest rates in an attempt to improve

their domestic economies. 

While central bank interest rates are a monetary policy tool, you would expect that the

interest rates determined by the market would never be negative. After all, why would you

accept less in the future than you would now? However, this proved to be incorrect as the yield

on the two-year Swiss government bond was negative 1.12 percent. And, in an event that had

never previously occurred, bonds issued by chocolate giant Nestlé and Deutsche Bank AG

both traded with negative yields.

This chapter takes what we have learned about the time value of money and shows how it

can be used to value one of the most common of all financial assets, a bond. It then discusses

bond features, bond types, and the operation of the bond market. What we will see is that bond

prices depend critically on interest rates, so we will go on to discuss some very fundamental

issues regarding interest rates. Clearly, interest rates are important to everybody because

they underlie what businesses of all types—small and large—must pay to borrow money.

Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.

Our goal in this chapter is to introduce you to bonds. We begin by showing how the tech- niques we developed in Chapter 4 can be applied to bond valuation. From there, we go on to discuss bond features and how bonds are bought and sold. One important thing we learn is that bond values depend, in large part, on interest rates. We therefore close out the chap- ter with an examination of interest rates and their behavior.

5.1 BONDS AND BOND VALUATION When a corporation (or government) wishes to borrow money from the public on a long-term basis, it usually does so by issuing or selling debt securities that are generi- cally called bonds. In this section, we describe the various features of corporate bonds

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and some of the terminology associated with bonds. We then discuss the cash flows associated with a bond and how bonds can be valued using our discounted cash flow procedure.

Bond Features and Prices A bond is normally an interest-only loan, meaning that the borrower will pay the interest every period, but none of the principal will be repaid until the end of the loan. For exam- ple, suppose the Beck Corporation wants to borrow $1,000 for 30 years. The interest rate on similar debt issued by similar corporations is 12 percent. Beck will thus pay .12 × $1,000 = $120 in interest every year for 30 years. At the end of 30 years, Beck will repay the $1,000. As this example suggests, a bond is a fairly simple financing arrangement. There  is, however, a rich jargon associated with bonds, so we will use this example to define some of the more important terms.

In our example, the $120 regular interest payments that Beck promises to make are called the bond’s coupons. Because the coupon is constant and paid every year, the type of bond we are describing is sometimes called a level coupon bond. The amount that will be repaid at the end of the loan is called the bond’s face value, or par value. As in our example, this par value is usually $1,000 for corporate bonds, and a bond that sells for its par value is called a par value bond. Government bonds frequently have much larger face, or par, val- ues. Finally, the annual coupon divided by the face value is called the coupon rate on the bond; in this case, because $120/1,000 = 12 percent, the bond has a 12 percent coupon rate.

The number of years until the face value is paid is called the bond’s time to maturity. A corporate bond will frequently have a maturity of 30 years when it is originally issued, but this varies. Once the bond has been issued, the number of years to maturity declines as time goes by.

Bond Values and Yields As time passes, interest rates change in the marketplace. The cash flows from a bond, how- ever, stay the same. As a result, the value of the bond will fluctuate. When interest rates rise, the present value of the bond’s remaining cash flows declines, and the bond is worth less. When interest rates fall, the bond is worth more.

To determine the value of a bond at a particular point in time, we need to know the num- ber of periods remaining until maturity, the face value, the coupon, and the market interest rate for bonds with similar features. This interest rate required in the market on a bond is called the bond’s yield to maturity (YTM). This rate is sometimes called the bond’s yield for short. Given all this information, we can calculate the present value of the cash flows as an estimate of the bond’s current market value.

For example, suppose the Xanth (pronounced “zanth”) Co. were to issue a bond with 10 years to maturity. The Xanth bond has an annual coupon of $80. (Most, but not all, straight coupon bonds in the U.S. pay interest semiannually. Practice differs around the world.) Similar bonds have a yield to maturity of 8 percent. Based on our preceding dis- cussion, the Xanth bond will pay $80 per year for the next 10 years in coupon interest. In 10 years, Xanth will pay $1,000 to the owner of the bond. The cash flows from the bond are shown in Figure 5.1 What would this bond sell for?

As illustrated in Figure 5.1, the Xanth bond’s cash flows have an annuity component (the coupons) and a lump sum (the face value paid at maturity). We thus estimate the mar- ket value of the bond by calculating the present value of these two components separately and adding the results together. First, at the going rate of 8 percent, the present value of the $1,000 paid in 10 years is:

Present value = $1,000/1.08 10 = $1,000 / 2.1589 = $463.19

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132

Second, the bond offers $80 per year for 10 years; the present value of this annuity stream is:

Annuity present value

= $80 × (1 − 1/1.0 8 10 )/.08 = $80 × (1 − 1/2.1589)/.08

= $80 × 6.7101

= $536.81

We can now add the values for the two parts together to get the bond’s value:

Total bond value = $463.19 + 536.81 = $1,000

This bond sells for exactly its face value. This is not a coincidence. The going interest rate in the market is 8 percent. Considered as an interest-only loan, what interest rate does this bond have? With an $80 coupon, this bond pays exactly 8 percent interest only when it sells for $1,000.

To illustrate what happens as interest rates change, suppose that a year has gone by. The Xanth bond now has nine years to maturity. If the interest rate in the market has risen to 10 percent, what will the bond be worth? To find out, we repeat the present value calcula- tions with 9 years instead of 10, and a 10 percent yield instead of an 8 percent yield. First, the present value of the $1,000 paid in nine years at 10 percent is:

Present value = $1,000/1.10 9 = $1,000 / 2.3579 = $424.10

Second, the bond now offers $80 per year for nine years; the present value of this annuity stream at 10 percent is:

Annuity present value

= $80 × (1 − 1/1.1 0 9 )/.10 = $80 × (1 − 1/2.3579)/.10

= $80 × 5.7590

= $460.72

We can now add the values for the two parts together to get the bond’s value:

Total bond value = $424.10 + 460.72 = $884.82

Therefore, the bond should sell for about $885. In the vernacular, we say that this bond, with its 8 percent coupon, is priced to yield 10 percent at $885.

The Xanth Co. bond now sells for less than its $1,000 face value. Why? The market interest rate is 10 percent. Considered as an interest-only loan of $1,000, this bond only pays 8 percent, its coupon rate. Because this bond pays less than the going rate, investors

A good bond site to visit is finance.yahoo.com/ bonds, which has loads of useful information.

FIGURE 5.1 Cash Flows for Xanth Co. Bond

Year

Cash flows

Coupon Face value

As shown, the Xanth bond has an annual coupon of $80 and a face, or par, value of $1,000 paid at maturity in 10 years.

$ 80 1,000

$1,080

0 1 2 3 4 5 6 7 8 9 10

$80 $80 $80 $80 $80 $80 $80 $80 $80

$80$80$80$80$80$80$80$80$80

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are willing to lend only something less than the $1,000 promised repayment. Because the bond sells for less than face value, it is said to be a discount bond.

The only way to get the interest rate up to 10 percent is to lower the price to less than $1,000 so that the purchaser, in effect, has a built-in gain. For the Xanth bond, the price of $885 is $115 less than the face value, so an investor who purchased and kept the bond would get $80 per year and would have a $115 gain at maturity as well. This gain compen- sates the lender for the below-market coupon rate.

Another way to see why the bond is discounted by $115 is to note that the $80 cou- pon is $20 below the coupon on a newly issued par value bond, based on current market conditions. The bond would be worth $1,000 only if it had a coupon of $100 per year. In a sense, an investor who buys and keeps the bond gives up $20 per year for nine years. At 10  percent, this annuity stream is worth:

Annuity present value

= $20 × (1 − 1/1. 10 9 )/.10

= $20 × 5.7590

= $115.18

This is the amount of the discount. What would the Xanth bond sell for if interest rates had dropped by 2 percent instead of

rising by 2 percent? As you might guess, the bond would sell for more than $1,000. Such a bond is said to sell at a premium and is called a premium bond.

This case is just the opposite of that of a discount bond. The Xanth bond now has a coupon rate of 8 percent when the market rate is only 6 percent. Investors are willing to pay a premium to get this extra coupon amount. In this case, the relevant discount rate is 6  percent, and there are nine years remaining. The present value of the $1,000 face amount is:

Present value of face amount = $1,000/1.06 9 = $1,000/1.6895 = $591.89

The present value of the coupon stream is:

Annuity present value

= $80 × (1 − 1/1.0 6 9 )/.06 = $80 × (1 − 1/1.6895)/.06

= $80 × 6.8017

= $544.14

We can now add the values for the two parts together to get the bond’s value:

Total bond value = $591.89 + 544.14 = $1,136.03

Total bond value is therefore about $136 in excess of par value. Once again, we can verify this amount by noting that the coupon is now $20 too high, based on current market condi- tions. The present value of $20 per year for nine years at 6 percent is:

Annuity present value

= $20 × (1 − 1/1. 6 9 )/.06

= $20 × 6.8017

= $136.03

This is just as we calculated. Based on our examples, we can now write the general expression for the value of a

bond. If a bond has (1) a face value of F paid at maturity, (2) a coupon of C paid per period, (3) T periods to maturity, and (4) a yield of r per period, its value is:

Bond value = C × [1 – 1/(1 + r ) T ]/r + F/(1 + r ) T [5.1]

Online bond calculators are available at personal .fidelity.com; interest rate information is avail- able at money.cnn.com/ data/bonds and www. bankrate.com.

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134

As we have illustrated in this section, bond prices and interest rates always move in opposite directions. When interest rates rise, a bond’s value, like any other present value, will decline. Similarly, when interest rates fall, bond values rise. Even if we are considering a bond that is riskless in the sense that the borrower is certain to make all the payments, there is still risk in owning a bond. We discuss this next.

Interest Rate Risk The risk that arises for bond owners from fluctuating interest rates is called interest rate risk. How much interest rate risk a bond has depends on how sensitive its price is to inter- est rate changes. This sensitivity directly depends on two things: the time to maturity and the coupon rate. As we will see momentarily, you should keep the following in mind when looking at a bond:

1. All other things being equal, the longer the time to maturity, the greater the interest rate risk.

2. All other things being equal, the lower the coupon rate, the greater the interest rate risk.

Learn more about bonds at investorguide.com.

E X

A M

P L

E

5 .1

In practice, bonds issued in the United States usually make coupon payments twice a year. So, if an ordi- nary bond has a coupon rate of 14 percent, then the owner will get a total of $140 per year, but this $140 will come in two payments of $70 each. Suppose we are examining such a bond. The yield to maturity is quoted at 16 percent.

Bond yields are quoted like APRs; the quoted rate is equal to the actual rate per period multiplied by the number of periods. In this case, with a 16 percent quoted yield and semiannual payments, the true yield is 8 percent per six months. The bond matures in seven years. What is the bond’s price? What is the effective annual yield on this bond?

Based on our discussion, we know the bond will sell at a discount because it has a coupon rate of 7 percent every six months when the market requires 8 percent every six months. So, if our answer exceeds $1,000, we know that we have made a mistake.

To get the exact price, we first calculate the present value of the bond’s face value of $1,000 paid in seven years. This seven-year period has 14 periods of six months each. At 8 percent per period, the value is:

Present value = $1,000/1.0814 = $1,000/2.9372 = $340.46

The coupons can be viewed as a 14-period annuity of $70 per period. At an 8 percent discount rate, the present value of such an annuity is:

Annuity present value

= $70 × (1 − 1/1.0 8 14 )/.08

= $70 × (1 − .3405)/.08

= $70 × 8.2442

= $577.10

The total present value gives us what the bond should sell for:

Total present value = $340.46 + 577.10 = $917.56

To calculate the effective yield on this bond, note that 8 percent every six months is equivalent to:

Effective annual rate = (1 + .08)2 − 1 = 16.64%

The effective yield, therefore, is 16.64 percent.

Semiannual Coupons

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We illustrate the first of these two points in Figure 5.2. As shown, we compute and plot prices under different interest rate scenarios for 10 percent coupon bonds with maturities of 1 year and 30 years. We assume coupons are paid semi-annually. Notice how the slope of the line connecting the prices is much steeper for the 30-year maturity than it is for the 1-year maturity. This steepness tells us that a relatively small change in interest rates will lead to a substantial change in the bond’s value. In comparison, the one-year bond’s price is relatively insensitive to interest rate changes.

Intuitively, we can see that the reason that shorter-term bonds have less interest rate sensi- tivity is that a large portion of a bond’s value comes from the $1,000 face amount. The pres- ent value of this amount isn’t greatly affected by a small change in interest rates if the amount is to be received in one year. Even a small change in the interest rate, however, once it is compounded for 30 years, can have a significant effect on the present value. As a result, the present value of the face amount will be much more volatile with a longer-term bond.

The other thing to know about interest rate risk is that, like most things in finance and economics, it increases at a decreasing rate. In other words, if we compared a 10-year bond to a 1-year bond, we would see that the 10-year bond has much greater interest rate risk. However, if you were to compare a 20-year bond to a 30-year bond, you would find that while the 30-year bond has somewhat greater interest rate risk because it has a longer maturity, the difference in the risk would be fairly small.

The reason that bonds with lower coupons have greater interest rate risk is essentially the same. As we discussed earlier, the value of a bond depends on the present value of its coupons and the present value of the face amount. If two bonds with different coupon rates have the same maturity, then the value of the one with the lower coupon is proportionately more dependent on the face amount to be received at maturity. As a result, all other things

FIGURE 5.2 Interest Rate Risk and Time to Maturity

1,000

2,000

1,500

500

5 Interest rate (%)

Bo nd

v al

ue ($

)

10 15 20

30-year bond

1-year bond

$501.64

$1,048.19

$1,772.72

$913.22

Value of a Bond with a 10 Percent Coupon Rate for Di�erent Interest Rates and Maturities

Time to Maturity

Interest Rate 1 Year 30 Years

5% 10 15 20

$1,048.19 1,000.00

955.11 913.22

$1,772.72 1,000.00

671.02 501.64

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136

being equal, its value will fluctuate more as interest rates change. Put another way, the bond with the higher coupon has a larger cash flow early in its life, so its value is less sensi- tive to changes in the discount rate.

Bonds are rarely issued with maturities longer than 30 years. However, low interest rates in recent years have led to the issuance of bonds with much longer terms. In the 1990s, Walt Disney issued “Sleeping Beauty” bonds with a 100-year maturity. Similarly, BellSouth, Coca-Cola, and Dutch banking giant ABN AMRO all issued bonds with 100-year maturities. These companies evidently wanted to lock in the historical low interest rates for a long time. Before these fairly recent issues, it appears the last time 100-year bonds were issued was in May 1954, by the Chicago and Eastern Railroad. And low interest rates in recent years have led to more 100-year bonds. For example, in July 2015, Brazilian oil company Petrobras issued 100-year bonds, and those weren’t the longest maturity bonds issued in 2015 as issu- ance of perpetual bonds hit a record. For example, French energy company Total issued $5.7 billion in perpetual bonds and Volkswagen issued $2.6 billion in perpetual debt.

We can illustrate the effect of interest rate risk using the 100-year BellSouth issue. The following table provides some basic information on this issue, along with its prices on December 31, 1995, July 31, 1996, and December 9, 2014.

MATURITY COUPON

RATE PRICE ON 12/31/95

PRICE ON 7/31/96

PERCENTAGE CHANGE IN PRICE 1995–96

PRICE ON 12/9/14

PERCENTAGE CHANGE IN PRICE

1996–2014

2095 7.00% $1,000.00 $800.00 −20.0% $1,235.59 +54.4%

Several things emerge from this table. First, interest rates apparently rose between December 31, 1995, and July 31, 1996 (why?). After that, however, they fell (why?). The bond’s price first lost 20 percent and then gained 54.4 percent. These swings illustrate that longer-term bonds have significant interest rate risk.

Finding the Yield to Maturity: More Trial and Error Frequently, we will know a bond’s price, coupon rate, and maturity date, but not its yield to maturity. For example, suppose we are interested in a six-year, 8 percent coupon bond with annual coupons. A broker quotes a price of $955.14. What is the yield on this bond?

We’ve seen that the price of a bond can be written as the sum of its annuity and lump- sum components. Knowing that there is an $80 coupon for six years and a $1,000 face value, we can say that the price is:

$955.14 = $80 × [1 − 1/(1 + r  ) 6  ]/ r + 1,000/(1 + r  ) 6

where r is the unknown discount rate, or yield to maturity. We have one equation here and one unknown, but we cannot solve for r explicitly. The only way to find the answer is to use trial and error.

This problem is essentially identical to the one we examined in the last chapter when we tried to find the unknown interest rate on an annuity. However, finding the rate (or yield) on a bond is even more complicated because of the $1,000 face amount.

We can speed up the trial-and-error process by using what we know about bond prices and yields. In this case, the bond has an $80 coupon and is selling at a discount. We thus know that the yield is greater than 8 percent. If we compute the price at 10 percent:

Bond value

=

$80 × (1 − 1/1. 10 6 ) /.10 + 1,000/1. 10 6

= $80 × 4.3553 + 1,000/1.7716

=

$912.89

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TABLE 5.1 Summary of Bond Valuation

At 10 percent, the value we calculate is lower than the actual price, so 10 percent is too high. The true yield must be somewhere between 8 and 10 percent. At this point, it’s “plug and chug” to find the answer. You would probably want to try 9 percent next. If you did, you would see that this is in fact the bond’s yield to maturity.

A bond’s yield to maturity should not be confused with its current yield, which is a bond’s annual coupon divided by its price. In the example we just worked, the bond’s annual coupon was $80, and its price was $955.14. Given these numbers, we see that the current yield is $80/955.14 = 8.38 percent, which is less than the yield to maturity of 9 percent. The reason the current yield is too low is that it only considers the coupon portion of your return; it doesn’t consider the built-in gain from the price discount. For a premium bond, the reverse is true, meaning that current yield would be higher because it ignores the built-in loss.

Our discussion of bond valuation is summarized in Table 5.1. A nearby Spreadsheet Techniques box shows how to find prices and yields the easy way.

Current market rates are available at www.bankrate.com.

I. Finding the Value of a Bond

Bond value = C × [1 – 1/(1 + r  ) T    ] /r + F/(1 + r ) T where

C = Coupon paid each period  r = Discount rate per period T = Number of periods F = Bond’s face value

II. Finding the Yield on a Bond

Given a bond value, coupon, time to maturity, and face value, it is possible to find the implicit discount rate, or yield to maturity, by trial and error only. To do this, try different discount rates until the calculated bond value equals the given value (or let a spreadsheet or a financial calculator do it for you). Remember that increasing the rate decreases the bond value.

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5 .2

A bond has a quoted price of $1,080.42. It has a face value of $1,000, a semiannual coupon of $30, and a maturity of five years. What is its current yield? What is its yield to maturity? Which is bigger? Why?

Notice that this bond makes semiannual payments of $30, so the annual payment is $60. The current yield is thus $60/1,080.42 = 5.55 percent. To calculate the yield to maturity, refer back to Example 5.1. Now, in this case, the bond pays $30 every six months and it has 10 six-month periods until maturity. So, we need to find r as follows:

$1,080.42 = $30 × [ 1 − 1/(1 + r  ) 10 ] /r + 1,000/(1 + r  )

10

After some trial and error, we find that r is equal to 2.1 percent. But, the tricky part is that this 2.1 percent is the yield per six months. We have to double it to get the yield to maturity, so the yield to maturity is 4.2 percent, which is less than the current yield. The reason is that the current yield ignores the built-in loss of the premium between now and maturity.

Current Events

5.2 MORE ON BOND FEATURES In this section, we continue our discussion of corporate debt by describing in some detail the basic terms and features that make up a typical long-term corporate bond. We discuss additional issues associated with long-term debt in subsequent sections.

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138

How to Calculate Bond Pr ices and Yie lds Us ing a Spreadsheet SPREADSHEET TECHNIQUES

Most spreadsheets have fairly elaborate routines available for calculating bond values and yields; many of these routines involve details that we have not discussed. However, setting up a simple spreadsheet to cal- culate prices or yields is straightforward, as our next two spreadsheets show:

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A B C D E F G H

Suppose we have a bond with 22 years to maturity, a coupon rate of 8 percent, and a yield to maturity of 9 percent. If the bond makes semiannual payments, what is its price today?

Settlement date: 1/1/00 Maturity date: 1/1/22

Annual coupon rate: .08 Yield to maturity: .09

Face value (% of par): 100 Coupons per year: 2

Bond price (% of par): 90.49

The formula entered in cell B13 is =PRICE(B7,B8,B9,B10,B11,B12); notice that face value and bond price are given as a percentage of face value.

Using a spreadsheet to calculate bond values

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A B C D E F G H

Suppose we have a bond with 22 years to maturity, a coupon rate of 8 percent, and a price of $960.17. If the bond makes semiannual payments, what is its yield to maturity?

Settlement date: 1/1/00 Maturity date: 1/1/22

Annual coupon rate: .08 Bond price (% of par): 96.017 Face value (% of par): 100

Coupons per year: 2 Yield to maturity: .084

The formula entered in cell B13 is =YIELD(B7,B8,B9,B10,B11,B12); notice that face value and bond price are entered as a percentage of face value.

Using a spreadsheet to calculate bond yields

1 7

In our spreadsheets, notice that we had to enter two dates, a settlement date and a maturity date. The settlement date is just the date you actually pay for the bond, and the maturity date is the day the bond actually matures. In most of our problems, we don’t explicitly have these dates, so we have to make them up. For example, since our bond has 22 years to maturity, we just picked 1/1/2000 (January 1, 2000) as the settlement date and 1/1/2022 (January 1, 2022) as the maturity date. Any two dates would do as long as they are exactly 22 years apart, but these are particularly easy to work with. Finally, notice that we had to enter the coupon rate and yield to maturity in annual terms and then explicitly provide the number of coupon payments per year.

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Securities issued by corporations may be classified roughly as equity securities and debt securities. At the crudest level, a debt represents something that must be repaid; it is the result of borrowing money. When corporations borrow, they gener- ally promise to make regularly scheduled interest payments and to repay the original amount borrowed (that is, the principal). The person or firm making the loan is called the creditor, or lender. The corporation borrowing the money is called the debtor, or borrower.

From a financial point of view, the main differences between debt and equity are the following:

1. Debt is not an ownership interest in the firm. Creditors generally do not have voting power.

2. The corporation’s payment of interest on debt is considered a cost of doing business and is fully tax deductible. Dividends paid to stockholders are not tax deductible.

3. Unpaid debt is a liability of the firm. If it is not paid, the creditors can legally claim the assets of the firm. This action can result in liquidation or reorganiza- tion, two of the possible consequences of bankruptcy. Thus, one of the costs of issuing debt is the possibility of financial failure. This possibility does not arise when equity is issued.

Long-Term Debt: The Basics Ultimately, all long-term debt securities are promises made by the issuing firm to pay principal when due and to make timely interest payments on the unpaid balance. Beyond this, there are a number of features that distinguish these securities from one another. We discuss some of these features next.

The maturity of a long-term debt instrument is the length of time the debt remains outstanding with some unpaid balance. Debt securities can be short term (with maturities of one year or less) or long term (with maturities of more than one year).1 Short-term debt is sometimes referred to as unfunded debt.2

Debt securities are typically called notes, debentures, or bonds. Strictly speaking, a bond is a secured debt. However, in common usage, the word bond refers to all kinds of secured and unsecured debt. We will therefore continue to use the term generically to refer to long-term debt. Also, usually, the only difference between a note and a bond is the original maturity. Issues with an original maturity of 10 years or less are often called notes. Longer-term issues are called bonds.

The two major forms of long-term debt are public issue and privately placed. We concentrate on public-issue bonds. Most of what we say about them holds true for private-issue, long-term debt as well. The main difference between public-issue and privately placed debt is that the latter is directly placed with a lender and not offered to the public. Because this is a private transaction, the specific terms are up to the par- ties involved.

There are many other dimensions to long-term debt, including such things as security, call features, sinking funds, ratings, and protective covenants. The following table illus- trates these features for a bond issued by the Walt Disney Company. If some of these terms are unfamiliar, have no fear. We will discuss them all presently.

Information for bond investors can be found at www.investinginbonds .com.

Information on individual bonds can be found at finra-markets.morning- star.com/MarketData/ Default.jsp.

1 There is no universally agreed-upon distinction between short-term and long-term debt. In addition, people often refer to intermediate-term debt, which has a maturity of more than 1 year and less than 3 to 5, or even 10, years. 2 The word funding is part of the jargon of finance. It generally refers to the long term. Thus, a firm planning to “fund” its debt requirements may be replacing short-term debt with long-term debt.

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140

Many of these features will be detailed in the bond indenture, so we discuss this first.

The Indenture The indenture is the written agreement between the corporation (the borrower) and its creditors. It is sometimes referred to as the deed of trust.3 Usually, a trustee (a bank per- haps) is appointed by the corporation to represent the bondholders. The trust company must (1) make sure the terms of the indenture are obeyed, (2) manage the sinking fund (described in the following pages), and (3) represent the bondholders in default, that is, if the company defaults on its payments to them.

The bond indenture is a legal document. It can run several hundred pages and gen- erally makes for very tedious reading. It is an important document, however, because it generally includes the following provisions:

1. The basic terms of the bonds. 2. The total amount of bonds issued. 3. A description of property used as security. 4. The repayment arrangements. 5. The call provisions. 6. Details of the protective covenants.

We discuss these features next.

TERMS OF A BOND Corporate bonds usually have a face value (that is, a denomination) of $1,000. This is called the principal value and it is stated on the bond certificate. So, if a corpo- ration wanted to borrow $1 million, 1,000 bonds would have to be sold. The par value (that is, initial accounting value) of a bond is almost always the same as the face value, and the terms are used interchangeably in practice. Although a par value of $1,000 is most common, essentially any par value is possible. For example, looking at our Walt Disney bond, the par value is $2,000.

Corporate bonds are usually in registered form. For example, the indenture might read as follows:

FEATURES OF A WALT DISNEY COMPANY BOND

TERM EXPLANATION

Amount of issue $1 billion The company issued $1 billion worth of bonds.

Date of issue 01/08/2016 The bonds were sold on 01/08/2016.

Maturity 02/13/2026 The bonds mature on 02/13/2026.

Face value $2,000 The denomination of the bonds is $2,000.

Annual coupon 3.00% Each bondholder will receive $60 per bond per year (3.00% of face value).

Offer price 99.600 The offer price will be 99.600% of the $2,000 face value, or $1,992, per bond.

Coupon payment dates 2/13, 8/13 Coupons of $60/2 = $30 will be paid on these dates. Security None The bonds are not secured by specific assets.

Sinking fund None The bonds have no sinking fund.

Call provision At any time The bonds do not have a deferred call.

Call price Treasury rate plus .15% The bonds have a “make whole” call price.

Rating Moody’s A2, Fitch A The bonds have a medium-quality credit rating.

Interest is payable semiannually on July 1 and January 1 of each year to the person in whose name the bond is registered at the close of business on June 15 or December 15, respectively.

3The words loan agreement or loan contract are usually used for privately placed debt and term loans.

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This means that the company has a registrar who will record the ownership of each bond and record any changes in ownership. The company will pay the interest and princi- pal by check mailed directly to the address of the owner of record. A corporate bond may be registered and have attached “coupons.” To obtain an interest payment, the owner must separate a coupon from the bond certificate and send it to the company registrar (the pay- ing agent).

Alternatively, the bond could be in bearer form. This means that the certificate is the basic evidence of ownership, and the corporation will “pay the bearer.” Ownership is not otherwise recorded, and, as with a registered bond with attached coupons, the holder of the bond certificate detaches the coupons and sends them to the company to receive payment.

There are two drawbacks to bearer bonds. First, they are difficult to recover if they are lost or stolen. Second, because the company does not know who owns its bonds, it cannot notify bondholders of important events. Bearer bonds were once the dominant type, but they are now much less common (in the United States) than registered bonds.

SECURITY Debt securities are classified according to the collateral and mortgages used to protect the bondholder.

Collateral is a general term that frequently means securities (for example, bonds and stocks) that are pledged as security for payment of debt. For example, collateral trust bonds often involve a pledge of common stock held by the corporation. However, the term col- lateral is commonly used to refer to any asset pledged on a debt.

Mortgage securities are secured by a mortgage on the real property of the borrower. The property involved is usually real estate, for example, land or buildings. The legal document that describes the mortgage is called a mortgage trust indenture or trust deed.

Sometimes mortgages are on specific property, for example, a railroad car. More often, blanket mortgages are used. A blanket mortgage pledges all the real property owned by the company.4

Bonds frequently represent unsecured obligations of the company. A debenture is an unsecured bond, for which no specific pledge of property is made. The term note is gener- ally used for such instruments if the maturity of the unsecured bond is less than 10 or so years when the bond is originally issued. Debenture holders have a claim only on property not otherwise pledged, in other words, the property that remains after mortgages and col- lateral trusts are taken into account.

The terminology that we use here and elsewhere in this chapter is standard in the United States. Outside the United States, these same terms can have different meanings. For exam- ple, bonds issued by the British government (“gilts”) are called treasury “stock.” Also, in the United Kingdom, a debenture is a secured obligation.

At the current time, public bonds issued in the United States by industrial and financial companies are typically debentures. However, most utility and railroad bonds are secured by a pledge of assets.

SENIORITY In general terms, seniority indicates preference in position over other lend- ers, and debts are sometimes labeled as senior or junior to indicate seniority. Some debt is subordinated, as in, for example, a subordinated debenture.

In the event of default, holders of subordinated debt must give preference to other speci- fied creditors. Usually, this means that the subordinated lenders will be paid off only after the specified creditors have been compensated. However, debt cannot be subordinated to equity.

REPAYMENT Bonds can be repaid at maturity, at which time the bondholder will receive the stated, or face, value of the bond, or they may be repaid in part or in entirety before maturity. Early repayment in some form is more typical and is often handled through a sinking fund.

The Securities Industry and Financial Markets Association (SIFMA) site is www.sifma.org.

4 Real property includes land and things “affixed thereto.” It does not include cash or inventories.

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A sinking fund is an account managed by the bond trustee for the purpose of repaying the bonds. The company makes annual payments to the trustee, who then uses the funds to retire a portion of the debt. The trustee does this by either buying up some of the bonds in the market or calling in a fraction of the outstanding bonds. This second option is dis- cussed in the next section.

There are many different kinds of sinking fund arrangements, and the details would be spelled out in the indenture. For example:

1. Some sinking funds start about 10 years after the initial issuance. 2. Some sinking funds establish equal payments over the life of the bond. 3. Some high-quality bond issues establish payments to the sinking fund that

are not sufficient to redeem the entire issue. As a consequence, there is the possibility of a large “balloon payment” at maturity.

THE CALL PROVISION A call provision allows the company to repurchase, or “call,” part or all of the bond issue at stated prices over a specific period. Corporate bonds are usually callable.

Generally, the call price is above the bond’s stated value (that is, the par value). The difference between the call price and the stated value is the call premium. The amount of the call premium may become smaller over time. One arrangement is to initially set the call premium equal to the annual coupon payment and then make it decline to zero as the call date moves closer to the time of maturity.

Call provisions are often not operative during the first part of a bond’s life. This makes the call provision less of a worry for bondholders in the bond’s early years. For example, a company might be prohibited from calling its bonds for the first 10 years. This is a deferred call provision. During this period of prohibition, the bond is said to be call protected.

In recent years, a new type of call provision, a “make-whole” call, has become very widespread in the corporate bond market. With such a feature, bondholders receive approximately what the bonds are worth if they are called. Because bondholders don’t suf- fer a loss in the event of a call, they are “made whole.”

To determine the make-whole call price, we calculate the present value of the remain- ing interest and principal payments at a rate specified in the indenture. For example, look- ing at our Walt Disney issue, we see that the discount rate is “Treasury rate plus .15%.” What this means is that we determine the discount rate by first finding a U.S. Treasury issue with the same maturity. We calculate the yield to maturity on the Treasury issue and then add on an additional .15 percent to get the discount rate we use.

Notice that, with a make-whole call provision, the call price is higher when interest rates are lower and vice versa (why?). Also notice that, as is common with a make-whole call, the Walt Disney issue does not have a deferred call feature. Why might investors not be too concerned about the absence of this feature?

PROTECTIVE COVENANTS A protective covenant is that part of the indenture or loan agreement that limits certain actions a company might otherwise wish to take during the term of the loan. Protective covenants can be classified into two types: negative covenants and positive (or affirmative) covenants.

A negative covenant is a “thou shalt not” type of covenant. It limits or prohibits actions that the company might take. Here are some typical examples:

1. The firm must limit the amount of dividends it pays according to some formula. 2. The firm cannot pledge any assets to other lenders. 3. The firm cannot merge with another firm. 4. The firm cannot sell or lease any major assets without approval by the lender. 5. The firm cannot issue additional long-term debt.

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A positive covenant is a “thou shalt” type of covenant. It specifies an action that the company agrees to take or a condition the company must abide by. Here are some examples:

1. The company must maintain its working capital at or above some specified mini- mum level.

2. The company must periodically furnish audited financial statements to the lender.

3. The firm must maintain any collateral or security in good condition.

This is only a partial list of covenants; a particular indenture may feature many different ones.

5.3 BOND RATINGS Firms frequently pay to have their debt rated. The two leading bond-rating firms are Moody’s and Standard & Poor’s (S&P). The debt ratings are an assessment of the credit- worthiness of the corporate issuer. The definitions of creditworthiness used by Moody’s and S&P are based on how likely the firm is to default and the protection creditors have in the event of a default.

It is important to recognize that bond ratings are concerned only with the possibility of default. Earlier, we discussed interest rate risk, which we defined as the risk of a change in the value of a bond resulting from a change in interest rates. Bond ratings do not address this issue. As a result, the price of a highly rated bond can still be quite volatile.

Bond ratings are constructed from information supplied by the corporation and other sources. The rating classes and some information concerning them are shown in the following table.

Want detailed information on the amount and terms of the debt issued by a particular firm? Check out its latest financial state- ments by searching SEC filings at www.sec.gov.

Want to know what cri- teria are commonly used to rate corporate and municipal bonds? Go to www.standardandpoors .com, www.moodys.com, and www.fitchratings .com.

    INVESTMENT-QUALITY BOND RATINGS LOW-QUALITY, SPECULATIVE,

AND/OR “JUNK” BOND RATINGS

HIGH GRADE

MEDIUM GRADE

LOW GRADE

LOW GRADE

STANDARD & POOR’S MOODY’S

AAA AA A BBB BB B CCC CC C D

AAA AA A BAA BA B CAA CA C

MOODY’S S&P

Aaa AAA Debt rated Aaa and AAA has the highest rating. Capacity to pay interest and principal is extremely strong.

Aa AA Debt rated Aa and AA has a very strong capacity to pay interest and repay principal. Together with the highest rat- ing, this group comprises the high-grade bond class.

A A Debt rated A has a strong capacity to pay interest and repay principal, although it is somewhat more susceptible to the adverse effects of changes in circumstances and economic conditions than debt in higher-rated categories.

Baa BBB Debt rated Baa and BBB is regarded as having an adequate capacity to pay interest and repay principal. Whereas it normally exhibits adequate protection parameters, adverse economic conditions or changing circumstances are more likely to lead to a weakened capacity to pay interest and repay principal for debt in this category than in higher-rated categories. These bonds are medium-grade obligations.

Ba;B

Caa

Ca

C

BB;B

CCC

CC

C

Debt rated in these categories is regarded, on balance, as predominantly speculative with respect to capacity to pay interest and repay principal in accordance with the terms of the obligation. BB and Ba indicate the lowest degree of speculation, and Ca, CC, and C the highest degree of speculation. Although such debt is likely to have some quality and protective characteristics, these are outweighed by large uncertainties or major risk exposures to adverse conditions. Issues rated C by Moody’s are typically in default.

D Debt rated D is in default, and payment of interest and/or repayment of principal is in arrears.

Note: At times, both Moody’s and S&P use adjustments (called notches) to these ratings. S&P uses plus and minus signs: A1 is the strongest A rating and A− the weakest. Moody’s uses a 1, 2, or 3 designation, with 1 being the highest. Moody’s has no D rating.

The highest rating a firm’s debt can have is AAA or Aaa, and such debt is judged to be the best quality and to have the lowest degree of risk. For example, as of April 2016,

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Microsoft and Johnson & Johnson were the only U.S.-based nonfinancial companies with a AAA credit rating. AA or Aa ratings indicate very good quality debt and are much more common.

A large part of corporate borrowing takes the form of low-grade, or “junk,” bonds. If these low-grade corporate bonds are rated at all, they are rated below investment grade by the major rating agencies. Investment-grade bonds are bonds rated at least BBB by S&P or Baa by Moody’s.

Rating agencies don’t always agree. For example, some bonds are known as “crossover” or “5B” bonds. The reason is that they are rated triple-B (or Baa) by one rating agency and double-B (or Ba) by another, a “split rating.” For example, in July 2015, Spanish cell tower company Cellnex issued €600 million worth of seven-year notes that were rated BBB− by Fitch and BB+ by S&P.

A bond’s credit rating can change as the issuer’s financial strength improves or dete- riorates. For example, in February 2016, S&P cut the bond rating on British mining company Anglo American from BBB- to BB, lowering the company’s bond rating from investment-grade to junk bond status. S&P’s ratings cut followed a similar ratings cut by both Moody’s and Fitch earlier that same week. Bonds that drop into junk territory like this are called fallen angels. Anglo American was downgraded because metal prices had fallen to a six-year low.

Credit ratings are important because defaults really do occur, and when they do, inves- tors can lose heavily. For example, in 2000, AmeriServe Food Distribution, Inc., which supplied restaurants such as Burger King with everything from burgers to giveaway toys, defaulted on $200 million in junk bonds. After the default, the bonds traded at just 18 cents on the dollar, leaving investors with a loss of more than $160 million.

Even worse in AmeriServe’s case, the bonds had been issued only four months earlier, thereby making AmeriServe an NCAA champion. While that might be a good thing for a college basketball team such as the University of Kentucky Wildcats, in the bond market NCAA means “No Coupon At All,” and it’s not a good thing for investors.

5.4 SOME DIFFERENT TYPES OF BONDS Thus far, we have considered only “plain vanilla” corporate bonds. In this section, we briefly look at bonds issued by governments and also at bonds with unusual features.

Government Bonds The biggest borrower in the world—by a wide margin—is everybody’s favorite fam- ily member, Uncle Sam. In early 2016, the total debt of the U.S. government was about $19 trillion, or approximately $59,000 per citizen (and growing!). When the government wishes to borrow money for more than one year, it sells what are known as Treasury notes and bonds to the public (in fact, it does so every month). Currently, outstanding Treasury notes and bonds have original maturities ranging from 2 to 30 years.

Most U.S. Treasury issues are just ordinary coupon bonds. There are two important things to keep in mind, however. First, U.S. Treasury issues, unlike essentially all other bonds, have no default risk because (we hope) the Treasury can always come up with the money to make the payments. Second, Treasury issues are exempt from state income taxes (though not federal income taxes). In other words, the coupons you receive on a Treasury note or bond are only taxed at the federal level.

State and local governments also borrow money by selling notes and bonds. Such issues are called municipal notes and bonds, or just “munis.” Unlike Treasury issues, munis have varying degrees of default risk, and, in fact, they are rated much like corporate issues. Also, they are almost always callable. The most intriguing thing about munis is that their coupons are exempt from federal income taxes (though not necessarily state income taxes), which makes them very attractive to high-income, high-tax bracket investors.

Another good bond market site is money. cnn.com.

If you’re nervous about the level of debt piled up by the U.S. government, don’t go to www.treasury .gov/resource-center or to www.brillig.com/ debt_clock! Learn all about government bonds at www.newyorkfed.org.

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Because of the enormous tax break they receive, the yields on municipal bonds are much lower than the yields on taxable bonds. For example, in February 2016, long-term AAA-rated corporate bonds were yielding about 3.65 percent. At the same time, long- term AAA munis were yielding about 3.21 percent. Suppose an investor was in a 30  percent tax bracket. All else being the same, would this investor prefer a AAA corporate bond or a AAA municipal bond?

To answer, we need to compare the aftertax yields on the two bonds. Ignoring state and local taxes, the muni pays 3.21 percent on both a pretax and an aftertax basis. The corporate issue pays 3.65 percent before taxes, but it pays .0365 × (1 – .30) = .0256, or 2.56 percent, once we account for the 30 percent tax bite. Given this, the muni bond has a better yield.

For information on munic- ipal bonds, including prices, checkout emma .msrb.org.

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Suppose taxable bonds are currently yielding 8 percent, while at the same time, munis of comparable risk and maturity are yielding 6 percent. Which is more attractive to an investor in a 40 percent tax bracket? What is the break-even tax rate? How do you interpret this rate?

For an investor in a 40 percent tax bracket, a taxable bond yields 8 × (1 – .40) = 4.8 percent after taxes, so the muni is much more attractive. The break-even tax rate is the tax rate at which an investor would be indifferent between a taxable and a nontaxable issue. If we let t* stand for the break-even tax rate, then we can solve for it as follows:

.08 × (1 − t *) = .06 1 − t * = .06/.08 = .75

t * = .25

Thus, an investor in a 25 percent tax bracket would make 6 percent after taxes from either bond.

Taxable versus Municipal Bonds

Zero Coupon Bonds A bond that pays no coupons at all must be offered at a price that is much lower than its stated value. Such bonds are called zero coupon bonds, or just zeroes.5

Suppose the Eight-Inch Nails (EIN) Company issues a $1,000 face value, five-year zero coupon bond. The initial price is set at $508.35. Even though no interest payments are made on the bond, zero coupon bond calculations use semiannual periods to be consistent with coupon bond calculations. Using semiannual periods, it is straightforward to verify that, at this price, the bond yields 14 percent to maturity. The total interest paid over the life of the bond is $1,000 – 508.35 = $491.65.

For tax purposes, the issuer of a zero coupon bond deducts interest every year even though no interest is actually paid. Similarly, the owner must pay taxes on interest accrued every year, even though no interest is actually received.

The way in which the yearly interest on a zero coupon bond is calculated is governed by tax law. Before 1982, corporations could calculate the interest deduction on a straight-line basis, For EIN, the annual interest deduction would have been $491.65/5 = $98.33 per year.

Under current tax law, the implicit interest is determined by amortizing the loan. We do this by first calculating the bond’s value at the beginning of each year. For example, after one year, the bond will have four years until maturity, so it will be worth $1,000/1.078 = $582.01; the value in two years will be $1,000/1.076 = $666.34; and so on. The implicit interest each year is the change in the bond’s value for the year.

Notice that under the old rules, zero coupon bonds were more attractive for corporations because the deductions for interest expense were larger in the early years (compare the implicit interest expense with the straight-line expense).

5 A bond issued with a very low coupon rate (as opposed to a zero coupon rate) is an original-issue discount (OID) bond.

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Under current tax law, EIN could deduct $73.66 (= $582.01 – 508.35) in interest paid the first year, and the owner of the bond would pay taxes on $73.66 of taxable income (even though no interest was actually received). This second tax feature makes taxable zero cou- pon bonds less attractive to individuals. However, they are still a very attractive investment for tax-exempt investors with long-term dollar-denominated liabilities, such as pension funds, because the future dollar value is known with relative certainty.

Some bonds are zero coupon bonds for only part of their lives. For example, at one time, General Motors had a debenture outstanding that for the first 20 years of its life, no coupon payments would be made, but after 20 years, it would begin paying coupons at a rate of 7.75 percent per year, payable semiannually.

Floating-Rate Bonds The conventional bonds we have talked about in this chapter have fixed-dollar obliga- tions because the coupon rate is set as a fixed percentage of the par value. Similarly, the principal is set equal to the par value. Under these circumstances, the coupon payment and principal are completely fixed.

With floating-rate bonds (floaters), the coupon payments are adjustable. The adjust- ments are tied to an interest rate index such as the Treasury bill interest rate or the 30-year Treasury bond rate.

The value of a floating-rate bond depends on exactly how the coupon payment adjust- ments are defined. In most cases, the coupon adjusts with a lag to some base rate. For exam- ple, suppose a coupon rate adjustment is made on June 1. The adjustment might be based on the simple average of Treasury bond yields during the previous three months. In addition, the majority of floaters have the following features:

1. The holder has the right to redeem his/her note at par on the coupon payment date after some specified amount of time. This is called a put provision, and it is discussed in the following section.

2. The coupon rate has a floor and a ceiling, meaning that the coupon is subject to a minimum and a maximum. In this case, the coupon rate is said to be “capped,” and the upper and lower rates are sometimes called the collar.

A particularly interesting type of floating-rate bond is an inflation-linked bond. Such bonds have coupons that are adjusted according to the rate of inflation (the principal amount may be adjusted as well). The U.S. Treasury began issuing such bonds in January of 1997. The issues are sometimes called “TIPS,” or Treasury Inflation-Protected Securities. Other countries, including Canada, Israel, and Britain, have issued similar securities.

Other Types of Bonds Many bonds have unusual or exotic features. For example, at one time, Berkshire Hathaway, the company run by the legendary Warren Buffett, issued bonds with a negative coupon. The buyers of these bonds also received the right to purchase shares of stock in Berkshire at a fixed price per share over the subsequent five years. Such a right, which is called a warrant, would be very valuable if the stock price climbed substantially (a later chapter discusses this subject in greater depth).

Bond features are really only limited by the imaginations of the parties involved. Unfortunately, there are far too many variations for us to cover in detail here. We there- fore close out this section by mentioning only a few of the more common types. A nearby Finance Matters box has some additional discussion on more exotic bonds.

Income bonds are similar to conventional bonds, except that coupon payments are dependent on company income. Specifically, coupons are paid to bondholders only if the firm’s income is sufficient. This would appear to be an attractive feature, but income bonds are not very common.

Official information on U.S. inflation- indexed bonds is at www.treasurydirect.gov.

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A convertible bond can be swapped for a fixed number of shares of stock anytime before maturity at the holder’s option. Convertibles are relatively common, but the number has been decreasing in recent years.

A put bond allows the holder to force the issuer to buy the bond back at a stated price. For example, International Paper Co. has bonds outstanding that allow the holder to force International Paper to buy the bonds back at 100 percent of the face value given that cer- tain “risk” events happen. One such event is a change in credit rating from investment grade to lower than investment grade by Moody’s or S&P. The put feature is therefore just the reverse of the call provision.

BEAUTY IS IN THE EYE OF THE BONDHOLDER Many bonds have unusual or exotic features. One of the most common types is an asset-backed, or securitized, bond. Mortgage-backed securities were big news in 2007. For several years, there had been rapid growth in so-called sub- prime mortgage loans, which are mortgages made to individuals with less than top-quality credit. However, a combina- tion of cooling (and in some places dropping) housing prices and rising interest rates caused mortgage delinquencies and foreclosures to rise. This increase in problem mortgages caused a significant number of mortgage-backed securities to drop sharply in value and created huge losses for investors. Bondholders of a securitized bond receive interest and principal payments from a specific asset (or pool of assets) rather than a specific company. For example, at one point rock legend David Bowie sold $55 million in bonds backed by future royalties from his albums and songs (that’s some serious ch-ch-ch-change!). Owners of these “Bowie” bonds received the royalty payments, so if Bowie’s record sales fell, there was a possibility the bonds could have defaulted. Other artists have sold bonds backed by future royalties, includ- ing James Brown, Iron Maiden, and the estate of the legendary Marvin Gaye.

Mortgage-backs are the best known type of asset-backed security. With a mortgage-backed bond, a trustee pur- chases mortgages from banks and merges them into a pool. Bonds are then issued, and the bondholders receive pay- ments derived from payments on the underlying mortgages. One unusual twist with mortgage bonds is that if interest rates decline, the bonds can actually decrease in value. This can occur because homeowners are likely to refinance at the lower rates, paying off their mortgages in the process. Securitized bonds are usually backed by assets with long-term payments, such as mortgages. However, there are bonds securitized by car loans and credit card payments, among other assets, and a growing market exists for bonds backed by automobile leases.

The reverse convertible is a relatively new type of structured note. This type generally offers a high coupon rate, but the redemption at maturity can be paid in cash at par value or paid in shares of stock. For example, one recent General Motors (GM) reverse convertible had a coupon rate of 16 percent, which is a very high coupon rate in today’s interest rate environment. However, at maturity, if GM’s stock declined sufficiently, bondholders would receive a fixed number of GM shares that were worth less than par value. So, while the income portion of the bond return would be high, the potential loss in par value could easily erode the extra return.

CAT bonds are issued to cover insurance companies against natural catastrophes. The type of natural catastrophe is outlined in the bond’s indenture. For example, about 30 percent of all CAT bonds protect against a North Atlantic hurricane. The way these issues are structured is that the borrowers can suspend payment temporarily (or even perma- nently) if they have significant hurricane-related losses. These CAT bonds may seem like pretty risky investments, but to date, only three such bonds have not made their scheduled payments, courtesy of the massive destruction caused by Hurricane Katrina, the 2011 Japanese tsunami, and an unusually active 2011 tornado season.

Perhaps the most unusual bond (and certainly the most ghoulish) is the “death bond.” Companies such as Stone Street Financial purchase life insurance policies from individuals who are expected to die within the next 10 years. They then sell bonds that are paid off from the life insurance proceeds received when the policyholders pass away. The return on the bonds to investors depends on how long the policyholders live. A major risk is that if medical treat- ment advances quickly, it will raise the life expectancy of the policyholders, thereby decreasing the return to the bondholder.

FINANCE MATTERS

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Structured notes are bonds that are based on stocks, bonds, commodities, or curren- cies. One particular type of structured note has a return based on a stock market index. At expiration, if the stock index has declined, the bond returns the principal. However, if the stock index has increased, the bond will return a portion of the stock index return, say 80  percent. Another type of structured note will return twice the stock index return, but with the potential for loss of principal.

A given bond may have many unusual features. Two of the most recent exotic bonds are CoCo bonds, which have a coupon payment, and NoNo bonds, which are zero coupon bonds. CoCo and NoNo bonds are contingent convertible, putable, callable, subordinated bonds. The contingent convertible clause is similar to the normal conversion feature, except the contingent feature must be met. For example, a contingent feature may require that the company stock trade at 110 percent of the conversion price for 20 out of the most recent 30 days. Valuing a bond of this sort can be quite complex, and the yield to maturity calculation is often meaningless.

5.5 BOND MARKETS Bonds are bought and sold in enormous quantities every day. You may be surprised to learn that the trading volume in bonds on a typical day is many, many times larger than the trading volume in stocks (by trading volume, we mean the amount of money that changes hands). Here is a finance trivia question: What is the largest securities market in the world? Most people would guess the New York Stock Exchange. In fact, the largest securities mar- ket in the world in terms of trading volume is the U.S. Treasury market, with an average daily volume over $500 billion.

How Bonds Are Bought and Sold Most trading in bonds takes place over the counter, or OTC. Recall that this means that there is no particular place where buying and selling occur. Instead, dealers around the country (and around the world) stand ready to buy and sell. The various dealers are con- nected electronically.

One reason the bond markets are so big is that the number of bond issues far exceeds the number of stock issues. There are two reasons for this. First, a corporation would typically have only one common stock issue outstanding (there are exceptions to this that we discuss in our next chapter). However, a single large corporation could easily have a dozen or more note and bond issues outstanding. Beyond this, federal, state, and local borrowing is enormous. For example, even a small city would usually have a wide variety of notes and bonds outstanding, representing money borrowed to pay for things like roads, sewers, and schools. When you think about how many small cities there are in the United States, you begin to get the picture!

Because the bond market is almost entirely OTC, it has historically had little or no transparency. A financial market is transparent if it is possible to easily observe its prices and trading volume. On the New York Stock Exchange, for example, it is possible to see the price and quantity for every single transaction. In contrast, in the bond market, it is often not possible to observe either. Transactions are privately negotiated between parties, and there is little or no centralized reporting of transactions.

Although the total volume of trading in bonds far exceeds that in stocks, only a very small fraction of the total bond issues that exist actually trade on a given day. This fact, combined with the lack of transparency in the bond market, means that getting up-to-date prices on individual bonds can be difficult or impossible, particularly for smaller corporate or munici- pal issues. Instead, a variety of sources of estimated prices exist and are very commonly used.

Bond Price Reporting In 2002, transparency in the corporate bond market began to improve dramatically. Under new regulations, corporate bond dealers are now required to report trade information

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through what is known as the Trade Report and Compliance Engine (TRACE). By 2010, transaction and price data were reported on more than 29,000 corporate bonds, which is essentially all publicly traded corporate bonds.

TRACE bond quotes are available at http://finra-markets.morningstar.com/MarketData /Default.jsp. We went to the site and entered “Deere” for the well-known manufacturer of green tractors. We found a total of eight bond issues outstanding. Below you can see the information we found for all of these bonds.

To learn more about TRACE, visit www.finra .org.

If you go to the website and click on a particular bond, you will get a lot of information about the bond, including the credit rating, the call schedule, original issue information, and trade information. For example, when we checked, the first bond listed had not traded for two weeks.

As shown in Figure 5.3, the Financial Industry Regulatory Authority (FINRA) provides a daily snapshot of the data from TRACE by reporting the most active issues. The infor- mation reported is largely self-explanatory. Notice that the price of the first Apple bond listed increased about 1.681 percent on this day. What do you think happened to the yield to maturity for this bond? Figure 5.3 focuses on the most active bonds with investment- grade ratings, but the most active high-yield and convertible bonds are also available on the website.

As we mentioned before, the U.S. Treasury market is the largest securities market in the world. As with bond markets in general, it is an OTC market, so there is limited

FIGURE 5.3 Sample TRACE Bond Quotations Source: FINRA reported TRACE prices.

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transparency. However, unlike the situation with bond markets in general, trading in Treasury issues, particularly recently issued ones, is very heavy. Each day, representative prices for outstanding Treasury issues are reported.

Figure 5.4 shows a portion of the daily Treasury bond listings from the website wsj.com. Examine the entry that begins “02/15/2026.” Reading from left to right, the “02/15/2026” tells us that the bond’s maturity is February 15, 2026. The 1.625 is the bond’s coupon rate.

The next two pieces of information are the bid and asked prices. In general, in any OTC or dealer market, the bid price represents what a dealer is willing to pay for a security, and the asked price (or just “ask” price) is what a dealer is willing to take for it. The difference between the two prices is called the bid-ask spread (or just “spread”), and it represents the dealer’s profit.

Treasury prices are quoted as a percentage of face value. The bid price, or what a dealer is willing to pay, on the 02/15/2026 bond is 98.875. With a $1,000 face value, this quote represents $988.75. The asked price, or the price at which the dealer is willing to sell the bond, is 98.8906, or $988.906.

The next number quoted is the change in the asked price from the previous day, mea- sured as a percentage of face value, so this issue’s asked price rose by .1172 percent, or $1.172, in value from the previous day. Finally, the last number reported is the yield to maturity, based on the asked price. Notice that this is a discount bond because it sells for less than its face value. Not surprisingly, its yield to maturity (1.747 percent) is greater than its coupon rate (1.625 percent).

The Federal Reserve Bank of St. Louis main- tains dozens of online files containing macro- economic data as well as rates on U.S. Treasury issues. Go to research .stlouisfed.org/fred2/.

FIGURE 5.4 Sample Wall Street Journal U.S. Treasury Bond Prices

Source: The Wall Street Journal, February 19, 2016. 3/31/2016 2.375 100.1953 100.2109 -0.0313 0.34

1/31/2017 0.875 100.2813 100.2969 0.0078 0.558 4/15/2018 0.75 99.9219 99.9375 -0.0547 0.779 4/30/2018 0.625 99.6328 99.6484 -0.0703 0.787 5/15/2019 3.125 106.8984 106.9141 -0.0625 0.945 5/31/2020 1.375 100.8594 100.875 -0.0625 1.164 6/30/2021 2.125 104.1563 104.1719 0.0156 1.315 8/15/2022 7.25 135.8906 135.9063 -0.0313 1.429 8/15/2023 2.5 106.8125 106.8281 0.0625 1.531 11/15/2024 2.25 104.5078 104.5234 0.125 1.69 8/15/2025 6.875 145.0703 145.0859 0.0469 1.705 2/15/2026 1.625 98.875 98.8906 0.1172 1.747 2/15/2027 6.625 147.7656 147.8281 0.1094 1.804 8/15/2028 5.5 139.5156 139.5781 0.1406 1.919 2/15/2029 5.25 137.6094 137.6719 0.1328 1.951 5/15/2030 6.25 152.7344 152.7969 0.1641 1.975 2/15/2031 5.375 143.5625 143.625 0.2422 1.992 2/15/2036 4.5 138.2656 138.3281 0.3906 2.134 2/15/2037 4.75 142.6641 142.7266 0.3594 2.197 2/15/2038 4.375 136.2188 136.2813 0.4375 2.269 8/15/2039 4.5 138.0625 138.125 0.4688 2.373 5/15/2040 4.375 135.6797 135.7109 0.3984 2.419 11/15/2041 3.125 112.1641 112.1953 0.4766 2.481 8/15/2042 2.75 104.0234 104.0547 0.5156 2.539 5/15/2044 3.375 116.7656 116.7969 0.5859 2.538 8/15/2045 2.875 105.6484 105.6797 0.5781 2.598 11/15/2045 3 108.4844 108.5156 0.6016 2.588 2/15/2046 2.5 97.8281 97.8594 0.5391 2.603

Treasury Bonds

Coupon Bid Asked Chg Asked yieldMaturity

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SELECTED INTERNATIONAL GOVERNMENT 10-YEAR BOND YIELDS

YIELD (%)

Switzerland

Japan

Germany

United Kingdom

United States

Australia

Mexico

Brazil

Greece

  –.36     .00

    .20

  1.41

  1.75

  2.43

  3.96

  6.87

10.25

Source: www.bloomberg.com, February 19, 2016.

The last bond listed, the 02/15/2046, is often called the “bellwether” bond. This bond’s yield is the one that is usually reported in the evening news. So, for example, when you hear that long-term interest rates rose, what is really being said is that the yield on this bond went up (and its price went down).

If you examine the yields on the various issues in Figure 5.4, you will clearly see that they vary by maturity. Why this occurs and what it might mean are some of the things we discuss in our next section. Government (referred to as “sovereign”) bond yields also vary by country of origin. Below we show the 10-year bond yields of several countries. The yields vary according to default risks and foreign exchange risks (to be discussed later in the text).

Current and historical Treasury yield information is available at www. publicdebt.treas.gov/.

A Note on Bond Price Quotes If you buy a bond between coupon payment dates, the price you pay is usually more than the price you are quoted. The reason is that standard convention in the bond market is to quote prices net of “accrued interest,” meaning that accrued interest is deducted to arrive at the quoted price. This quoted price is called the clean price. The price you actually pay, however, includes the accrued interest. This price is the dirty price, also known as the “full” or “invoice” price.

An example is the easiest way to understand these issues. Suppose you buy a bond with a 12 percent annual coupon, payable semiannually. You actually pay $1,080 for this bond, so $1,080 is the dirty, or invoice, price. Further, on the day you buy it, the next coupon is due in four months, so you are between coupon dates. Notice that the next coupon will be $60.

Locate the Treasury issue in Figure 5.4 that matures on May 15, 2019. What is its coupon rate? What is its bid price? What was the previous day’s asked price?

The bond listed as 05/15/2019 is the one we seek. Its coupon rate is 3.125 percent of face value. The bid price is 106.8984, or 106.8984 percent of face value. The ask price is 106.9141, which is down by .0625 from the previous day. This means that the ask price on the previous day was equal to 106.9141 + .0625 = 106.9766.

Treasury Quotes

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The accrued interest on a bond is calculated by taking the fraction of the coupon period that has passed, in this case two months out of six, and multiplying this fraction by the next coupon, $60. So, the accrued interest in this example is 2/6 × $60 = $20. The bond’s quoted price (i.e., its clean price) would be $1,080 – 20 = $1,060.6

5.6 INFLATION AND INTEREST RATES So far, we haven’t considered the role of inflation in our various discussions of interest rates, yields, and returns. Because this is an important consideration, we discuss the impact of inflation next.

Real versus Nominal Rates In examining interest rates, or any other financial market rates such as discount rates, bond yields, rates of return, and required returns, it is often necessary to distinguish between real rates and nominal rates. Nominal rates are called nominal because they have not been adjusted for inflation. Real rates are rates that have been adjusted for inflation.

To see the effect of inflation, suppose prices are currently rising by 5 percent per year. In other words, the rate of inflation is 5 percent. An investment is available that will be worth $115.50 in one year. It costs $100 today. Notice that with a present value of $100 and a future value in one year of $115.50, this investment has a 15.5 percent rate of return. In calculating this 15.5 percent return, we did not consider the effect of inflation, however, so this is the nominal return.

What is the impact of inflation here? To answer, suppose pizzas cost $5 apiece at the beginning of the year. With $100, we can buy 20 pizzas. Because the inflation rate is 5 percent, pizzas will cost 5 percent more, or $5.25, at the end of the year. If we take the investment, how many pizzas can we buy at the end of the year? Measured in pizzas, what is the rate of return on this investment?

Our $115.50 from the investment will buy us $115.50/5.25 = 22 pizzas. This is up from 20 pizzas, so our pizza rate of return is 10 percent. What this illustrates is that even though the nominal return on our investment is 15.5 percent, our buying power goes up by only 10 percent because of inflation. Put another way, we are really only 10 percent richer. In this case, we say that the real return is 10 percent.

Alternatively, we can say that with 5 percent inflation, each of the $115.50 nominal dollars we get is worth 5 percent less in real terms, so the real dollar value of our investment in a year is:

$115.50/1.05 = $110

What we have done is to deflate the $115.50 by 5 percent. Because we give up $100 in current buying power to get the equivalent of $110, our real return is again 10 percent. Because we have removed the effect of future inflation here, this $110 is said to be mea- sured in current dollars.

The difference between nominal and real rates is important and bears repeating:

The nominal rate on an investment is the percentage change in the number of dollars you have. The real rate on an investment is the percentage change in how much you can buy with your dollars, in other words, the percentage change in your buying power.

6 The way accrued interest is calculated actually depends on the type of bond being quoted, for example, Treasury or corporate. The differ- ence has to do with exactly how the fractional coupon period is calculated. In our example above, we implicitly treated the months as having exactly the same length (i.e., 30 days each, 360 days in a year), which is consistent with the way corporate bonds are quoted. In contrast, for Treasury bonds, actual day counts are used.

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The Fisher Effect Our discussion of real and nominal returns illustrates a relationship often called the Fisher effect (after the great economist Irving Fisher). Because investors are ultimately concerned with what they can buy with their money, they require compensation for infla- tion. Let R stand for the nominal rate and r stand for the real rate. The Fisher effect tells us that the relationship between nominal rates, real rates, and inflation can be written as:

1 + R = ( 1 + r  ) × ( 1 + h  ) [5.2]

where h is the inflation rate. In the preceding example, the nominal rate was 15.50 percent and the inflation rate was

5 percent. What was the real rate? We can determine it by plugging in these numbers:

1 + .1550

=

(1 + r) × (1 + .05)

1 + r = 1.1550/1.05 = 1.10 r =

.10, or 10%

This real rate is the same as we had before. If we take another look at the Fisher effect, we can rearrange things a little as follows:

1 + R

= (1 + r)   × (1 + h)

R = r + h + r × h

[5.3]

What this tells us is that the nominal rate has three components. First, there is the real rate on the investment, r. Next, there is the compensation for the decrease in the value of the money originally invested because of inflation, h. The third component represents compensation for the fact that the dollars earned on the investment are also worth less because of the inflation.

This third component is usually small, so it is often dropped. The nominal rate is then approximately equal to the real rate plus the inflation rate:

R ≈ r + h [5.4]

Fisher’s thinking is that investors are not foolish. They know that inflation reduces pur- chasing power, and therefore, they will demand an increase in the nominal rate before lend- ing money. Fisher’s hypothesis, typically called the Fisher effect, can be stated as:

A rise in the rate of inflation causes the nominal rate to rise just enough so that the real rate of interest is unaffected. In other words, the real rate is invariant to the rate of inflation.

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If investors require a 2 percent real rate of return, and the inflation rate is 8 percent, what must be the approximate nominal rate? The exact nominal rate?

First of all, the nominal rate is approximately equal to the sum of the real rate and the inflation rate: 2 percent + 8 percent = 10 percent. From the Fisher effect, we have:

1 + R

=

(1 + r)  × (1 + h)

= 1.02 × 1.08

= 1.1016

Therefore, the nominal rate will actually be closer to 10.16 percent. In this example, you can also see how negative nominal interests can come about, e.g., in the unusual situation when inflation rates are expected to be sufficiently negative.

The Fisher Effect

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It is important to note that financial rates, such as interest rates, discount rates, and rates of return, are almost always quoted in nominal terms. To remind you of this, we will hence- forth use the symbol R instead of r in most of our discussions about such rates.

5.7 DETERMINANTS OF BOND YIELDS We are now in a position to discuss the determinants of a bond’s yield. As we will see, the yield on any particular bond is a reflection of a variety of factors, some common to all bonds and some specific to the issue under consideration.

The Term Structure of Interest Rates At any point in time, short-term and long-term interest rates will generally be different. Sometimes short-term rates are higher, sometimes lower. Figure 5.5 gives us a long-range perspective on this by showing about two centuries of short- and long-term U.S. Treasury interest rates. As shown, through time, the difference between short- and long-term rates has ranged from essentially zero to up to several percentage points, both positive and negative.

The relationship between short- and long-term interest rates is known as the term structure of interest rates. To be a little more precise, the term structure of interest rates tells us what nominal interest rates are on default-free, pure discount bonds of all maturi- ties. These rates are, in essence, “pure” interest rates because they involve no risk of default and a single, lump-sum future payment. In other words, the term structure tells us the pure time value of money for different lengths of time.

When long-term rates are higher than short-term rates, we say that the term structure is upward sloping, and, when short-term rates are higher, we say it is downward sloping. The term structure can also be “humped.” When this occurs, it is usually because rates increase at first, but then begin to decline as we look at longer- and longer-term rates. The most

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2

4

6

8

10

12

14

16

0 1800 1820 1840 1860 1880 1900

Year

In te

re st

ra te

(% )

1920 1940 1960 1980 2000

Long-term rates Short-term rates

2020

FIGURE 5.5 U.S. Interest Rates: 1800–2015

Source: Jeremy J. Siegel, Stocks for the Long Run, 4th edition, © McGraw-Hill, 2008, updated by the authors.

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common shape of the term structure, particularly in modern times, is upward sloping, but the degree of steepness has varied quite a bit.

What determines the shape of the term structure? There are three basic components. The first two are the ones we discussed in our previous section, the real rate of interest and the rate of inflation. The real rate of interest is the compensation investors demand for forgoing the use of their money. You can think of it as the pure time value of money after adjusting for the effects of inflation.

The real rate of interest is the basic component underlying every interest rate, regardless of the time to maturity. When the real rate is high, all interest rates will tend to be higher, and vice versa. Thus, the real rate doesn’t really determine the shape of the term structure; instead, it mostly influences the overall level of interest rates.

In contrast, the prospect of future inflation very strongly influences the shape of the term structure. Investors thinking about loaning money for various lengths of time recog- nize that future inflation erodes the value of the dollars that will be returned. As a result, investors demand compensation for this loss in the form of higher nominal rates. This extra compensation is called the inflation premium.

If investors believe that the rate of inflation will be higher in the future, then long-term nominal interest rates will tend to be higher than short-term rates. Thus, an upward-sloping term structure may be a reflection of anticipated increases in inflation. Similarly, a downward- sloping term structure probably reflects the belief that inflation will be falling in the future.

The third, and last, component of the term structure has to do with interest rate risk. As we discussed earlier in the chapter, longer-term bonds have much greater risk of loss resulting from changes in interest rates than do shorter-term bonds. Investors recognize this risk, and they demand extra compensation in the form of higher rates for bearing it. This extra compensation is called the interest rate risk premium. The longer the term to maturity, the greater is the interest rate risk, so the interest rate risk premium increases with maturity. However, as we discussed earlier, interest rate risk increases at a decreasing rate, so the interest rate risk premium does as well.7

Putting the pieces together, we see that the term structure reflects the combined effect of the real rate of interest, the inflation premium, and the interest rate risk premium. Figure 5.6 shows how these can interact to produce an upward-sloping term structure (in the top part of Figure 5.6) or a downward-sloping term structure (in the bottom part).

In the top part of Figure 5.6, notice how the rate of inflation is expected to rise gradually. At the same time, the interest rate risk premium increases at a decreasing rate, so the com- bined effect is to produce a pronounced upward-sloping term structure. In the bottom part of Figure 5.6, the rate of inflation is expected to fall in the future, and the expected decline is enough to offset the interest rate risk premium and produce a downward-sloping term struc- ture. Notice that if the rate of inflation was expected to decline by only a small amount, we could still get an upward-sloping term structure because of the interest rate risk premium.

We assumed in drawing Figure 5.6 that the real rate would remain the same. Actually, expected future real rates could be larger or smaller than the current real rate. Also, for simplicity, we used straight lines to show expected future inflation rates as rising or declin- ing, but they do not necessarily have to look like this. They could, for example, rise and then fall, leading to a humped yield curve.

Bond Yields and the Yield Curve: Putting It All Together Going back to Figure 5.4, recall that we saw that the yields on Treasury notes and bonds of different maturities are not the same. Each day, in addition to the Treasury prices and yields shown in Figure 5.4, the U.S Treasury Department website provides a plot of Treasury

Online yield curve infor- mation is available at www.bloomberg.com/ markets.

7 In days of old, the interest rate risk premium was called a “liquidity” premium. Today, the term liquidity premium has an altogether differ- ent meaning, which we explore in our next section. Also, the interest rate risk premium is sometimes called a maturity risk premium. Our terminology is consistent with the modern view of the term structure.

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156

yields relative to maturity. This plot is called the Treasury yield curve (or just the yield curve). Figure 5.7 shows the yield curve as of February 2016. Note, the yield curve avail- able on the U.S Treasury website will display both the nominal and real yield curves.

As you probably now suspect, the shape of the yield curve is a reflection of the term structure of interest rates. In fact, the Treasury yield curve and the term structure of interest rates are almost the same thing. The only difference is that the term structure is based on pure discount bonds, whereas the yield curve is based on coupon bond yields. As a result, Treasury yields depend on the three components that underlie the term structure—the real rate, expected future inflation, and the interest rate risk premium.

Treasury notes and bonds have three important features that we need to remind you of: they are default-free, they are taxable, and they are highly liquid. This is not true of bonds in general, so we need to examine what additional factors come into play when we look at bonds issued by corporations or municipalities.

The first thing to consider is credit risk, that is, the possibility of default. Investors recognize that issuers other than the Treasury may or may not make all the promised pay- ments on a bond, so they demand a higher yield as compensation for this risk. This extra compensation is called the default risk premium. Earlier in the chapter, we saw how bonds were rated based on their credit risk. What you will find if you start looking at bonds of different ratings is that lower-rated bonds have higher yields.

To see the current Treasury yield curve, check out the Data and Charts Center at: www. treasury.gov.

FIGURE 5.6 The Term Structure of Interest Rates

Time to maturity

Inflation premium

Real rate

Interest rate risk premium

Nominal interest rate

In te

re st

ra te

A. Upward-sloping term structure

Nominal interest rate

Time to maturity

In te

re st

ra te

B. Downward-sloping term structure

Inflation premium

Interest rate risk premium

Real rate

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An important thing to recognize about a bond’s yield is that it is calculated assuming that all the promised payments will be made. As a result, it is really a promised yield, and it may or may not be what you will earn. In particular, if the issuer defaults, your actual yield will be lower, probably much lower. This fact is particularly important when it comes to junk bonds. Thanks to a clever bit of marketing, such bonds are now commonly called high-yield bonds, which has a much nicer ring to it; but now you recognize that these are really high promised yield bonds.

Next, recall that we discussed earlier how municipal bonds are free from most taxes and, as a result, have much lower yields than taxable bonds. Investors demand the extra yield on a taxable bond as compensation for the unfavorable tax treatment. This extra com- pensation is the taxability premium.

Finally, bonds have varying degrees of liquidity. As we discussed earlier, there are an enormous number of bond issues, most of which do not trade on a regular basis. As a result, if you wanted to sell quickly, you would probably not get as good a price as you could otherwise. Investors prefer liquid assets to illiquid ones, so they demand a liquidity premium on top of all the other premiums we have discussed. As a result, all else being the same, less liquid bonds will have higher yields than more liquid bonds.

Conclusion If we combine all of the things we have discussed regarding bond yields, we find that bond yields represent the combined effect of no fewer than six things. The first is the real rate of interest. On top of the real rate are five premiums representing compensation for (1) expected future inflation, (2) interest rate risk, (3) default risk, (4) taxability, and (5)  lack of liquidity. As a result, determining the appropriate yield on a bond requires careful analysis of each of these effects.

FIGURE 5.7 The Treasury Yield Curve: February 19, 2016Treasury Yield Curve

Month(s) Years

02/19/2015

02/19/2016

1 3 6 1 2 3 5 7 10 20 30

3.00%

2.00%

1.00%

0.00%

02/19/2016

Maturity

02/19/2015

Source: https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/Historic-Yield-Data-Visualization. aspx, February 19, 2016.

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SUMMARY AND CONCLUSIONS

This chapter has explored bonds, bond yields, and interest rates. We saw that

1. Determining bond prices and yields is an application of basic discounted cash flow principles.

2. Bond values move in the direction opposite that of interest rates, leading to potential gains or losses for bond investors.

3. Bonds have a variety of features spelled out in a document called the indenture.

4. Bonds are rated based on their default risk. Some bonds, such as Treasury bonds, have no risk of default, whereas so-called junk bonds have substantial default risk.

5. A wide variety of bonds exist, many of which contain exotic or unusual features.

6. Almost all bond trading is OTC, with little or no market transparency in many cases. As a result, bond price and volume information can be difficult to find for some types of bonds.

7. Bond yields and interest rates reflect the effects of six different factors: the real interest rate and five premiums that investors demand as compensation for inflation, interest rate risk, default risk, taxability, and lack of liquidity.

CONCEPT QUESTIONS

 1. Treasury Bonds Is it true that a U.S. Treasury security is risk free?

 2. Interest Rate Risk Which has greater interest rate risk, a 30-year Treasury bond or a 30-year BB corporate bond?

 3. Treasury Pricing With regard to bid and ask prices on a Treasury bond, is it possible for the bid price to be higher? Why or why not?

 4. Yield to Maturity Treasury bid and ask quotes are sometimes given in terms of yields, so there would be a bid yield and an ask yield. Which do you think would be larger? Explain.

 5. Call Provisions A company is contemplating a long-term bond issue. It is debating whether or not to include a call provision. What are the benefits to the company from including a call provision? What are the costs? How do these answers change for a put provision?

 6. Coupon Rate How does a bond issuer decide on the appropriate coupon rate to set on its bonds? Explain the difference between the coupon rate and the required return on a bond.

 7. Real and Nominal Returns Are there any circumstances under which an investor might be more concerned about the nominal return on an investment than the real return?

 8. Bond Ratings Companies pay rating agencies such as Moody’s and S&P to rate their bonds, and the costs can be substantial. However, companies are not required to have their bonds rated in the first place; doing so is strictly voluntary. Why do you think they do it?

 9. Bond Ratings Often, junk bonds are not rated. Why?

10. Term Structure What is the difference between the term structure of interest rates and the yield curve?

11. Crossover Bonds Looking back at the crossover bonds we discussed in the chapter, why do you think split ratings such as these occur?

12. Municipal Bonds Why is it that municipal bonds are not taxed at the federal level but are taxable across state lines? Why is it that U.S. Treasury bonds are not taxable at the state level? (You may need to dust off the history books for this one.)

13. Bond Market What are the implications for bond investors of the lack of transparency in the bond market?

14. Treasury Market Take a look back at Figure 5.4. Notice the wide range of coupon rates. Why are they so different?

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CHAPTER 5 Interest Rates and Bond Valuation 159

15. Rating Agencies A controversy erupted regarding bond-rating agencies when some agencies began to provide unsolicited bond ratings. Why do you think this is controversial?

16. Bonds as Equity The 100-year bonds we discussed in the chapter have something in common with junk bonds. Critics charge that, in both cases, the issuers are really selling equity in disguise. What are the issues here? Why would a company want to sell “equity in disguise”?

17. Bond Prices versus Yields

a. What is the relationship between the price of a bond and its YTM?

b. Explain why some bonds sell at a premium over par value while other bonds sell at a discount. What do you know about the relationship between the coupon rate and the YTM for premium bonds? What about for discount bonds? For bonds selling at par value?

c. What is the relationship between the current yield and YTM for premium bonds? For discount bonds? For bonds selling at par value?

18. Interest Rate Risk All else being the same, which has more interest rate risk, a long-term bond or a short-term bond? What about a low coupon bond compared to a high coupon bond? What about a long-term, high coupon bond compared to a short-term, low coupon bond?

1. Valuing Bonds What is the dollar price of a zero coupon bond with 17 years to maturity, semiannual compounding, and a par value of $1,000, if the YTM is

a. 4 percent

b. 10 percent

c. 14 percent

2. Valuing Bonds Microhard has issued a bond with the following characteristics:

Par: $1,000

Time to maturity: 23 years

Coupon rate: 7 percent

Semiannual payments

Calculate the price of this bond if the YTM is

a. 7 percent

b. 9 percent

c. 5 percent

3. Bond Yields Skolits Corp. issued 15-year bonds two years ago at a coupon rate of 5.1 percent. The bonds make semiannual payments. If these bonds currently sell for 105 percent of par value, what is the YTM?

  4. Coupon Rates Lydic Corporation has bonds on the market with 12.5 years to maturity, a YTM of 6.4 percent, a par value of $1,000, and a current price of $1,040. The bonds make semiannual payments. What must the coupon rate be on these bonds?

  5. Valuing Bonds Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company has a bond outstanding with a par value of €1,000, 16 years to maturity, and a coupon rate of 4.7 percent paid annually. If the yield to maturity is 3.4 percent, what is the current price of the bond?

  6. Bond Yields A Japanese company has a bond outstanding that sells for 103.25 percent of its ¥100,000 par value. The bond has a coupon rate of 4.9 percent paid annually and matures in 18 years. What is the yield to maturity of this bond?

Basic (Questions 1–15)

QUESTIONS AND PROBLEMS

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 7. Calculating Real Rates of Return If Treasury bills are currently paying 4.8 percent and the inflation rate is 2.7 percent, what is the approximate real rate of interest? The exact real rate?

  8. Inflation and Nominal Returns Suppose the real rate is 1.8 percent and the inflation rate is 3.4 percent. What rate would you expect to see on a Treasury bill?

  9. Nominal and Real Returns An investment offers a total return of 12.1 percent over the coming year. Alan Wingspan thinks the total real return on this investment will be only 7.6 percent. What does Alan believe the inflation rate will be over the next year?

  10. Nominal versus Real Returns Say you own an asset that had a total return last year of 11.4 percent. If the inflation rate last year was 3.9 percent, what was your real return?

11. Zero Coupon Bonds You find a zero coupon bond with a par value of $10,000 and 17 years to maturity. If the yield to maturity on this bond if 4.9 percent, what is the dollar price of the bond? Assume semiannual compounding periods.

12. Valuing Bonds Mycroft Corp. has a $2,000 par value bond outstanding with a coupon rate of 4.9 percent paid semiannually and 13 years to maturity. The yield to maturity of the bond is 3.8 percent. What is the dollar price of the bond?

13. Valuing Bonds Union Local School District has bonds outstanding with a coupon rate of 3.7 percent paid semiannually and 16 years to maturity. The yield to maturity on these bonds is 3.9 percent and the bonds have a par value of $5,000. What is the price of the bonds?

  14. Using Treasury Quotes Locate the Treasury bond in Figure 5.4 that matures in August 2028. What is its coupon rate? What is its bid price? What was the previous day’s asked price? Assume a par value of $1,000.

15. Using Treasury Quotes Locate the Treasury bond in Figure 5.4 that matures in August 2039. Is this a premium or a discount bond? What is its current yield? What is its yield to maturity? What is the bid-ask spread in dollars? Assume a $1,000 par value.

  16. Bond Price Movements Miller Corporation has a premium bond making semiannual payments. The bond has a coupon rate of 8.2 percent, a YTM of 6.2 percent, and 13 years to maturity. The Modigliani Company has a discount bond making semiannual payments. This bond has a coupon rate of 6.2 percent, a YTM of 8.2 percent, and also has 13 years to maturity. If interest rates remain unchanged, what do you expect the price of these bonds to be 1 year from now assuming both bonds have a par value of $1,000? In 3 years? In 8 years? In 12 years? In 13 years? What’s going on here? Illustrate your answers by graphing bond prices versus time to maturity.

  17. Interest Rate Risk Laurel, Inc., and Hardy Corp. both have 6.5 percent coupon bonds outstanding, with semiannual interest payments, and both are currently priced at the par value of $1,000. The Laurel, Inc., bond has 4 years to maturity, whereas the Hardy Corp. bond has 23 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? If interest rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of these bonds be then? Illustrate your answers by graphing bond prices versus YTM. What does this problem tell you about the interest rate risk of longer-term bonds?

  18. Interest Rate Risk The Faulk Corp. has a bond with a coupon rate of 5.7 percent outstanding. The Gonas Company has a bond with a coupon rate of 12.3 percent outstanding. Both bonds have 14 years to maturity, make semiannual payments, and have a YTM of 9 percent. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? What if interest rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower coupon bonds?

  19. Bond Yields Bonino Software has 6.4 percent coupon bonds on the market with 11 years to maturity. The bonds make semiannual payments and currently sell for 108 percent of par. What is the current yield on the bonds? The YTM? The effective annual yield?

  20. Bond Yields Hagelin Co. wants to issue new 20-year bonds for some much-needed expansion projects. The company currently has 6.4 percent coupon bonds on the market that sell for $1,121.80,

Intermediate (Questions 16–26)

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CHAPTER 5 Interest Rates and Bond Valuation 161

make semiannual payments, and mature in 20 years. What coupon rate should the company set on its new bonds if it wants them to sell at par? Both bonds have a par value of $1,000.

21. Accrued Interest You purchase a bond with an invoice price of $945. The bond has a coupon rate of 6.8 percent, and there are two months to the next semiannual coupon date. What is the clean price of the bond?

  22. Accrued Interest You purchase a bond with a coupon rate of 7.6 percent and a clean price of $1,060. If the next semiannual coupon payment is due in four months, what is the invoice price?

  23. Finding the Bond Maturity Cavo Corp. has 6.3 percent coupon bonds making annual payments with a YTM of 7.14 percent. The current yield on these bonds is 6.95 percent. How many years do these bonds have left until they mature?

  24. Using Bond Quotes Suppose the following bond quote for IOU Corporation appears in the financial page of today’s newspaper. Assume the bond has a face value of $1,000 and the current date is

April 15, 2016. What is the yield to maturity of the bond? What is the current yield?

COMPANY (T ICKER) COUPON MATURITY LAST PRICE LAST YIELD EST VOL (000s)

IOU (IOU) 5.400 Apr 15, 2029 104.355 ?? 1,827

  25. Finding the Maturity You’ve just found a 10 percent coupon bond on the market that sells for par value. What is the maturity on this bond?

26. Components of Bond Returns Bond P is a premium bond with a coupon of 8.4 percent. Bond D has a coupon rate of 5.6 percent and is currently selling at a discount. Both bonds make annual payments, have a YTM of 7 percent, and have eight years to maturity. What is the current yield for Bond P? For Bond D? If interest rates remain unchanged, what is the expected capital gains yield over the next year for Bond P? For Bond D? Explain your answers and the interrelationship among the various types of yields.

  27. Holding Period Yield You will earn the YTM on a bond if you hold the bond until maturity and if interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY).

a. Suppose that today you buy a bond with an annual coupon rate of 5.5 percent for $865. The bond has 21 years to maturity. What rate of return do you expect to earn on your investment?

b. Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for? What is the HPY on your investment? Compare this yield to the YTM when you first bought the bond. Why are they different?

  28. Valuing Bonds The Grimm Corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $800 every six months over the subsequent eight years, and finally pays $1,000 every six months over the last six years. Bond N also has a face value of $20,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. If the required return on both these bonds is 5.9 percent compounded semiannually, what is the current price of Bond M? Of Bond N?

  29. Valuing the Call Feature At one point, some Treasury bonds were callable. Consider the prices on the following three Treasury issues as of February 24, 2016:

5.50

7.60

8.40

May 20

May 20

May 20

106.32150

103.12000

107.98750

106.37500

103.50000

108.21875

–.406 –.094 –.406

5.28

5.24

5.32

The bond in the middle is callable in February 2017. What is the implied value of the call feature? (Hint: Is there a way to combine the two noncallable issues to create an issue that has the same coupon as the callable bond?)

Challenge (Questions 27–34)

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30. Treasury Bonds The following Treasury bond quote appeared in The Wall Street Journal on May 11, 2004:

9.125 May 09 100:03 100:04 . . . –2.15

Why would anyone buy this Treasury bond with a negative yield to maturity? How is this possible?

31. Real Cash Flows An engineer earned $22,400 per year when he began his career. Thirty years later, his annual salary was $97,500. The inflation index over this same period grew from 415.23 to 1,021.39. What was his real annual salary increase? What is his current salary in real terms?

32. Real Cash Flows When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh flowers on her grave every Sunday as long as he lived. The week after she died in 1962, a bunch of fresh flowers that the former baseball player thought appropriate for the star cost about $5. Based on actuarial tables, “Joltin’ Joe” could expect to live for 30 years after the actress died. Assume that the EAR is 5.5 percent. Also, assume that the price of the flowers will increase at 2.9 percent per year, when expressed as an EAR. Assuming that each year has exactly 52 weeks, what is the present value of this commitment? Joe began purchasing flowers the week after Marilyn died.

  33. Real Cash Flows You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $700 per month in a stock account in real dollars and $325 per month in a bond account in real dollars. The effective annual return of the stock account is expected to be 12 percent, and the bond account will have an annual return of 7 percent. When you retire, you will combine your money into an account with an effective annual return of 8 percent. The inflation rate over this period is expected to be 4 percent. How much can you withdraw each month from your account in real terms assuming a 25-year withdrawal period? What is the nominal dollar amount of your last withdrawal?

  34. Real Cash Flows Paul Adams owns a health club in downtown Los Angeles. He charges his customers an annual fee of $800 and has an existing customer base of 525. Paul plans to raise the annual fee by 6 percent every year and expects the club membership to grow at a constant rate of 3 percent for the next five years. The overall expenses of running the health club are $80,000 a year and are expected to grow at the inflation rate of 2 percent annually. After five years, Paul plans to buy a luxury boat for $400,000, close the health club, and travel the world in his boat for the rest of his life. What is the annual amount that Paul can spend while on his world tour if he will have no money left in the bank when he dies? Assume Paul has a remaining life of 25 years and earns 9 percent on his savings.

WHAT’S ON THE WEB? 1. Bond Quotes    You can find current bond prices at finra-markets.morningstar.com/MarketData/Default

.jsp. You want to find the bond prices and yields for bonds issued by Georgia Pacific. You can enter the ticker symbol “GP” to do a search. What is the shortest maturity bond issued by Georgia Pacific that is outstanding? What is the longest maturity bond? What is the credit rating for Georgia Pacific’s bonds? Do all of the bonds have the same credit rating? Why do you think this is?

2. Yield Curves    You can find information regarding the most current bond yields at money.cnn.com. Find the yield curve for U.S. Treasury bonds. What is the general shape of the yield curve? What does this imply about expected future inflation? Now graph the yield curve for AAA, AA, and A rated corporate bonds. Is the corporate yield curve the same shape as the Treasury yield curve? Why or why not?

3. Default Premiums     The Federal Reserve Bank of St. Louis has files listing historical interest rates on its website www.stlouisfed.org. Find the link for “FRED” data. You will find listings for Moody’s Seasoned Aaa Corporate Bond Yield and Moody’s Seasoned Baa Corporate Bond Yield. A default premium can be calculated as the difference between the Aaa bond yield and the Baa bond yield. Calculate the default premium using these two bond indexes for the most recent 36 months. Is the default premium the same for every month? Why do you think this is?

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EXCEL MASTER IT ! PROBLEM Companies often buy bonds to meet a future liability or cash outlay. Such an investment is called a dedicated portfolio because the proceeds of the portfolio are dedicated to the future liability. In such a case, the port- folio is subject to reinvestment risk. Reinvestment risk occurs because the company will be reinvesting the coupon payments it receives. If the YTM on similar bonds falls, these coupon payments will be reinvested at a lower interest rate, which will result in a portfolio value that is lower than desired at maturity. Of course, if interest rates increase, the portfolio value at maturity will be higher than needed.

Suppose Ice Cubes, Inc., has the following liability due in five years. The company is going to buy five-year bonds today to meet the future obligation. The liability and current YTM are below:

Amount of liability:

Current YTM:

$100,000,000

8%

a. At the current YTM, what is the face value of the bonds the company has to purchase today to meet its future obligation? Assume that the bonds in the relevant range will have the same coupon rate as the current YTM and these bonds make semiannual coupon payments.

b. Assume the interest rates remain constant for the next five years. Thus, when the company reinvests the coupon payments, it will reinvest at the current YTM. What is the value of the portfolio in five years?

c. Assume that immediately after the company purchases the bonds, interest rates either rise or fall by 1 percent. What is the value of the portfolio in five years under these circumstances?

One way to eliminate reinvestment risk is called immunization. Rather than buying bonds with the same maturity as the liability, the company instead buys bonds with the same duration as the liability. If you think about the ded- icated portfolio, if the interest rate falls, the future value of the reinvested coupon payments decreases. However, as interest rates fall, the price of bonds increases. These effects offset each other in an immunized portfolio.

Another advantage of using duration to immunize a portfolio is that the duration of a portfolio is the weighted average of the duration of the assets in the portfolio. In other words, to find the duration of a portfo- lio, you simply take the weight of each asset multiplied by its duration and then sum the results.

d. What is the duration of the liability for Ice Cubes, Inc.?

e. Suppose the two bonds shown below are the only bonds available to immunize the liability. What face amount of each bond will the company need to purchase to immunize the portfolio?

FINANCING EAST COAST YACHTS’ EXPANSION PLANS WITH A BOND ISSUE After Dan’s EFN analysis for East Coast Yachts (see the Closing Case in Chapter 3), Larissa has decided to expand the company’s operations. She has asked Dan to enlist an underwriter to help sell $45 million in new 30-year bonds to finance new construction. Dan has entered into discussions with Renata Harper, an underwriter from the firm of Crowe & Mallard, about which bond features East Coast Yachts should consider and also what coupon

CLOSING CASE

BOND A BOND B

Settlement

Maturity

Coupon rate

YTM

Coupons per year

1/1/2000

1/1/2003

    7.00%

    7.50%

           2

1/1/2000

1/1/2008

    8.00%

    9.00%

           2

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rate the issue will likely have. Although Dan is aware of bond features, he is uncertain as to the costs and benefits of some of them, so he isn’t clear on how each feature would affect the coupon rate of the bond issue.

1. You are Renata’s assistant, and she has asked you to prepare a memo to Dan describing the effect of each of the following bond features on the coupon rate of the bond. She would also like you to list any advantages or disadvantages of each feature.

a. The security of the bond, that is, whether or not the bond has collateral.

b. The seniority of the bond.

c. The presence of a sinking fund.

d. A call provision with specified call dates and call prices.

e. A deferred call accompanying the above call provision.

f. A make-whole call provision.

g. Any positive covenants. Also, discuss several possible positive covenants East Coast Yachts might consider.

h. Any negative covenants. Also, discuss several possible negative covenants East Coast Yachts might consider.

i. A conversion feature (note that East Coast Yachts is not a publicly traded company).

j. A floating rate coupon.

Dan is also considering whether to issue coupon-bearing bonds or zero coupon bonds. The YTM on either bond issue will be 5.5 percent. The coupon bond would have a 5.5 percent coupon rate. The company’s tax rate is 35 percent.

2. How many of the coupon bonds must East Coast Yachts issue to raise the $45 million? How many of the zeroes must it issue?

3. In 30 years, what will be the principal repayment due if East Coast Yachts issues the coupon bonds? What if it issues the zeroes?

4. What are the company’s considerations in issuing a coupon bond compared to a zero coupon bond?

5. Suppose East Coast Yachts issues the coupon bonds with a make-whole call provision. The make-whole call rate is the Treasury rate plus .40 percent. If East Coast calls the bonds in seven years when the Treasury rate is 4.8 percent, what is the call price of the bond? What if it is 6.2 percent?

6. Are investors really made whole with a make-whole call provision?

7. After considering all the relevant factors, would you recommend a zero coupon issue or a regular coupon issue? Why? Would you recommend an ordinary call feature or a make-whole call feature? Why?

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CHAPTER 6 Stock Valuation 165

6 OPENING CASE

Stock Valuation When the stock market closed on February 19, 2016, the common stock of heavy equip-

ment manufacturer Caterpillar was selling for $65.40 per share. On that same day, Marriott

International, the well-known hotel company, closed at $65.71 per share, and software com-

pany Red Hat closed at $65.90. Since the stock prices of these three companies were so

similar, you might expect that they would be offering similar dividends to their stockholders,

but you would be wrong. In fact, Caterpillar’s annual dividend was $3.01 per share, Marriott’s

was $.95 per share, and Red Hat paid no dividends at all!

As we will see in this chapter, dividends currently being paid are one of the primary factors

we look at when attempting to value common stocks. However, it is obvious from looking at

Red Hat that current dividends are not the end of the story. This chapter explores dividends,

stock values, and the connection between the two.

Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.

In our previous chapter, we introduced you to bonds and bond valuation. In this chapter, we turn to the other major source of financing for corporations, common and preferred stock. We first describe the cash flows associated with a share of stock and then go on to develop a very famous result, the dividend growth model. From there, we move on to examine various important features of common and preferred stock, focusing on shareholder rights. We close out the chapter with a discussion of how shares of stock are traded and how stock prices and other important information are reported in the financial press.

6.1 THE PRESENT VALUE OF COMMON STOCKS Dividends versus Capital Gains Our goal in this section is to value common stocks. We learned in Chapter 5 that an asset’s value is determined by the present value of its future cash flows. Investing in a stock can provide two kinds of cash flows. First, many stocks pay dividends on a regular basis. Second, the stockholder receives the sale price when she sells the stock. Thus, in order to value common stocks, we need to answer an interesting question: Is the value of a stock equal to:

1. The discounted present value of the sum of next period’s dividend plus next period’s stock price, or

2. The discounted present value of all future dividends?

This is the kind of question that students would love to see on a multiple-choice exam, because both (1) and (2) are right.

ExcelMaster coverage online

www.mhhe.com/RossCore5e

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To see that (1) and (2) are the same, let’s start with an individual who will buy the stock and hold it for one year. In other words, she has a one-year holding period. In addition, she is willing to pay P0 for the stock today. That is, she calculates:

P 0 = Div 1 _____

1 + R + P 1 _____

1 + R [6.1]

Div1 is the dividend paid at year’s end and P1 is the price at year’s end. P0 is the present value of the common stock investment. The term in the denominator, R, is the appropriate discount rate for the stock.

That seems easy enough, but where does P1 come from? P1 is not pulled out of thin air. Rather, there must be a buyer at the end of Year 1 who is willing to purchase the stock for P1. This buyer determines the price by:

P 1 = Div 2 _____

1 + R + P 2 _____

1 + R [6.2]

Substituting the value of P1 from Equation 6.2 into Equation 6.1 yields:

P 0 = 1 ____

1 + R [ Div 1 + (

Div 2 + P 2 ________ 1 + R

) ] [6.3]

= Div 1 ____ 1 + R

+ Div 2 _______ (1 + R) 2

+ P 2 _______ (1 + R) 2

We can ask a similar question for Formula 6.3: Where does P2 come from? An investor at the end of Year 2 is willing to pay P2 because of the dividend and stock price at Year 3. This process can be repeated ad nauseam.1 At the end, we are left with:

P 0  = Div 1 _____

1 + R + Div 2 ________

(1 + R) 2 + Di v 3 ________

(1 + R) 3 + . . . = ∑

t=1

*   Di v t _______

(1 + R) t [6.4]

Thus the value of a firm’s common stock to the investor is equal to the present value of all of the expected future dividends.

This is a very useful result. A common objection to applying present value analysis to stocks is that investors are too shortsighted to care about the long-run stream of dividends. These critics argue that an investor will generally not look past his or her time horizon. Thus, prices in a market dominated by short-term investors will reflect only near-term dividends. However, our discussion shows that a long-run dividend discount model holds even when investors have short-term time horizons. Although an investor may want to cash out early, she must find another investor who is willing to buy. The price this second inves- tor pays is dependent on dividends after his date of purchase.

Valuation of Different Types of Stocks The above discussion shows that the value of the firm is the present value of its future dividends. How do we apply this idea in practice? Equation 6.4 represents a very general model and is applicable regardless of whether the level of expected dividends is growing, fluctuating, or constant. The general model can be simplified if the firm’s dividends are expected to follow some basic patterns: (1) zero growth, (2) constant growth, and (3) dif- ferential growth. These cases are illustrated in Figure 6.1.

1 This procedure reminds us of the physicist lecturing on the origins of the universe. He was approached by an elderly gentleman in the audience who disagreed with the lecture. The attendee said that the universe rests on the back of a huge turtle. When the physicist asked what the turtle rested on, the gentleman said another turtle. Anticipating the physicist’s objections, the attendee said, “Don’t tire yourself out, young fellow. It’s turtles all the way down.”

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CASE 1 (ZERO GROWTH) The value of a stock with a constant dividend is given by:

P 0 = Div 1 ____

1 + R + Div 2 _______

(1 + R) 2 + . . . = Div ____

R

Here it is assumed that Div1 = Div2 = . . . = Div. This is just an application of the perpetu- ity formula from a previous chapter.

CASE 2 (CONSTANT GROWTH) Dividends grow at rate g, as follows:

End of Year D iv idend

1 2 3 4 . . .

Div Div(1 + g) Div(1 + g)2 Div(1 + g)3

Note that Div is the dividend at the end of the first period.

FIGURE 6.1 Zero Growth, Constant Growth, and Differential Growth Patterns

Di�erential growth

Constant growth

High growth g1

Low growth g2

g1 > g2

Zero growth g = 0

Years

Dividend growth models

Zero growth: P0 = Div R

1 10

D iv

id en

ds p

er s

ha re

2 3 4 5 6 7 8 9

Constant growth: P0 = Div

R - g

Di�erential growth: P0 = Σ + t = 1

T Div(1 + g1)t

(1 + R)t R - g 2 (1 + R)T

DivT + 1

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6 .1

Hampshire Products will pay a dividend of $4 per share a year from now. Financial analysts believe that dividends will rise at 6 percent per year for the foreseeable future. What is the dividend per share at the end of each of the first five years?

End of Year Div idend

1 2 3 4 5

$4.00 $4 × (1.06) = $4.24

$4 × (1.06)2 = $4.4944

$4 × (1.06)3 = $4.7641

$4 × (1.06)4 = $5.0499

Projected Dividends

(continued )

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The assumption of steady dividend growth might strike you as peculiar. Why would the dividend grow at a constant rate? The reason is that, for many companies, steady growth in dividends is an explicit goal. For example, in 2016, Procter & Gamble, the Cincinnati- based maker of personal care and household products, increased its annual dividend by about 1 percent to $2.68 per share; this increase was notable because it was the 60th in a row. The subject of dividend growth falls under the general heading of dividend policy, so we will defer further discussion of it to a later chapter.

CASE 3 (DIFFERENTIAL GROWTH) In this case, an algebraic formula would be too unwieldy. Instead, we present examples.

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6 .2

Suppose an investor is considering the purchase of a share of the Utah Mining Company. The stock will pay a $3 dividend a year from today. This dividend is expected to grow at 10 percent per year (g = 10%) for the foreseeable future. The investor thinks that the required return (R) on this stock is 15 percent, given her assessment of Utah Mining’s risk. (We also refer to R as the discount rate of the stock.) What is the value of a share of Utah Mining Company’s stock?

Using the constant growth formula of Case 2, we assess the value to be $60:

$60 = $3 ________

.15 − .10

P0 is quite dependent on the value of g. If g had been estimated to be 12.5 percent, the value of the share would have been:

$120 = $3 _________ .15 − .125

The stock price doubles (from $60 to $120) when g only increases 25 percent (from 10 percent to 12.5 percent). Because of P0’s dependency on g, one must maintain a healthy sense of skepticism when using this constant growth of dividends model.

Furthermore, note that P0 is equal to infinity when the growth rate, g, equals the discount rate, R. Because stock prices do not grow infinitely, an estimate of g greater than R implies an error in estimation. More will be said of this point later.

Stock Valuation

The value of a common stock with dividends growing at a constant rate is:

P 0 = Div

____ 1 + R +

Div (1 + g) ________

(1 + R) 2 + Div  (1 + g)

2 _________

(1 + R) 3 + Div  (1 + g)

3 _________

(1 + R) 4 + . . .  = Div ____

R − g

where g is the growth rate. Div is the dividend on the stock at the end of the first period. This is the formula for the present value of a growing perpetuity, which we derived in a previous chapter.

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6 .3

Consider the stock of Elixir Drug Company, which has a new back-rub ointment and is enjoying rapid growth. The dividend for a share of stock a year from today will be $1.15. During the next four years, the dividend will grow at 15 percent per year (g1 = 15%). After that, growth (g2) will be equal to 10 percent per year. Can you calculate the present value of the stock if the required return (R) is 15 percent?

Figure 6.2 displays the growth in the dividends. We need to apply a two-step process to discount these dividends. We first calculate the present value of the dividends growing at 15 percent per annum. That is, we first calculate the present value of the dividends at the end of each of the first five years. Second, we calculate the present value of the dividends beginning at the end of Year 6.

Differential Growth

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Calculate Present Value of First Five Dividends The present value of dividend payments in Years 1 through 5 is as follows:

FUTURE YEAR

GROWTH RATE (g 1)

EXPECTED DIVIDEND

PRESENT VALUE

1 .15 $1.1500 $1

2 .15 1.3225  1

3 .15 1.5209  1

4 .15 1.7490  1

5 .15 2.0114  1

Years 1–5 The present value of dividends = $5

The growing annuity formula of the previous chapter could normally be used in this step. However, note that dividends grow at 15 percent, which is also the discount rate. Since g = R, the growing annuity for- mula cannot be used in this example.

Calculate Present Value of Dividends Beginning at End of Year 6 This is the procedure for deferred perpetuities and deferred annuities that we mentioned in a previous chapter. The dividends beginning at the end of Year 6 are:

End of Year Div idend

6 7 8 9

Div5 × (1 + g2) $2.0114 × 1.10

= $2.2125

Div5 × (1 + g2)2 $2.0114 × (1.10)2

= $2.4338

Div5 × (1 + g2)3 $2.0114 × (1.10)3

= $2.6771

Div5 × (1 + g2)4 $2.0114 × (1.10)4

= $2.9448

As stated in the previous chapter, the growing perpetuity formula calculates present value as of one year prior to the first payment. Because the payment begins at the end of Year 6, the present value formula calculates present value as of the end of Year 5.

The price at the end of Year 5 is given by:

P 5 = Div 6 _____

R − g 2 = $2.2125 ________

.15 − .10 = $44.25

FIGURE 6.2 Growth in Dividends for Elixir Drug Company

D iv

id en

ds

End of year

15% growth rate

$1.15 $1.3225

$1.5209

$1.7490

$2.0114 $2.2125 $2.4338

$2.6772 $2.9449

10% growth rate

9 1087654321

(continued )

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6.2 ESTIMATES OF PARAMETERS IN THE DIVIDEND DISCOUNT MODEL

The value of the firm is a function of its growth rate, g, and its discount rate, R. How does one estimate these variables?

Where Does g Come From? The previous discussion on stocks assumed that dividends grow at the rate g. We now want to estimate this rate of growth. This section extends the discussion of growth contained in Chapter 3. Consider a business whose earnings next year are expected to be the same as earnings this year unless a net investment is made. This situation is likely to occur, because net investment is equal to gross, or total, investment less depreciation. A net investment of zero occurs when total investment equals depreciation. If total investment is equal to depre- ciation, the firm’s physical plant is maintained, consistent with no growth in earnings.

Net investment will be positive only if some earnings are not paid out as dividends, that is, only if some earnings are retained.2 This leads to the following equation:

Earnings next year

= Earnings this year

+ Retained earnings this year

× Return on retained earnings

Increase in earnings

The increase in earnings is a function of both the retained earnings and the return on the retained earnings.

We now divide both sides of Equation 6.5 by earnings this year, yielding:

Earnings next year ________________ Earnings this year

 =  Earnings this year _______________ Earnings this year

 +  Retained earnings this year _______________________ Earnings this year

[6.6]

× Return on retained earnings

The left-hand side of Equation 6.6 is one plus the growth rate in earnings, which we write as 1 + g. The ratio of retained earnings to earnings is called the retention ratio. Thus, we can write:

1 + g = 1 + Retention ratio × Return on retained earnings [6.7]

It is difficult for a financial analyst to determine the return to be expected on currently retained earnings, because the details on forthcoming projects are not generally public information. However, it is frequently assumed that the projects selected in the current year have an anticipated return equal to returns from projects in other years. Here, we can esti- mate the anticipated return on current retained earnings by the historical return on equity or ROE. After all, ROE is the return on the firm’s entire equity, which is the return on the cumulation of all the firm’s past projects.

[6.5]

The present value of P5 at the end of Year 0 is:

P 5 _______

(1 + R  ) 5 = $44.25 _______

(1.15  ) 5  = $22

The present value of all dividends as of the end of Year 0 is $27 (= $22 + 5).

2 We ignore the possibility of the issuance of stocks or bonds in order to raise capital. These possibilities are considered in later chapters.

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From Equation 6.7, we have a simple way to estimate growth:

Formula for Firm’s Growth Rate : g = Retention ratio × Return on retained earnings  (ROE) [6.8]

Previously g referred to growth in dividends. However, the growth in earnings is equal to the growth rate in dividends in this context, because as we will presently see, the ratio of dividends to earnings is held constant. In fact, as you have probably figured out, g is the sustainable growth rate we introduced in Chapter 3.

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6 .4

Pagemaster Enterprises just reported earnings of $2 million. It plans to retain 40 percent of its earnings. The historical return on equity (ROE) has been 16 percent, a figure that is expected to continue into the future. How much will earnings grow over the coming year?

We first perform the calculation without reference to Equation 6.8. Then we use [6.8] as a check.

Calculation without Reference to Equation 6.8 The firm will retain $800,000 (= 40% × $2 million). Assuming that historical ROE is an appropriate estimate for future returns, the anticipated increase in earnings is:

$800, 000 × .16 = $128, 000

The percentage growth in earnings is:

Change in earnings

________________ Total earnings

= $128, 000 _________ $2 million

= .064

This implies that earnings in one year will be $2,128,000 (= $2,000,000 × 1.064).

Check Using Equation 6.8 We use g = Retention ratio × ROE. We have:

g = .4 × .16 = .064

Earnings Growth

Where Does R Come From? Thus far, we have taken the required return, or discount rate R, as given. We will have quite a bit to say on this subject in later chapters. For now, we want to examine the implications of the dividend growth model for this required return. Earlier, we calculated P0 as:

P 0 = Div / (R − g)

Now let’s assume we know P0. If we rearrange this equation to solve for R, we get:

R − g

= Div / P 0

R = Div / P 0 + g

[6.9]

This tells us that the total return, R, has two components. The first of these, Div/P0, is called the expected dividend yield. Because this is calculated as the expected cash dividend divided by the current price, it is conceptually similar to the current yield on a bond.

The second part of the total return is the growth rate, g. As we will verify shortly, the dividend growth rate is also the rate at which the stock price grows. Thus, this growth rate can be interpreted as the capital gains yield, that is, the rate at which the value of the investment grows.

To illustrate the components of the required return, suppose we observe a stock selling for $20 per share. The next dividend will be $1 per share. You think that the dividend will

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grow by 10 percent per year more or less indefinitely. What return does this stock offer you if this is correct?

The dividend growth model calculates total return as:

R

= Dividend yield + Capital gains yield

R = Div / P 0 + g

In this case, total return works out to be:

R

= $1/20 + 10%

= 5 % + 10% = 15%

This stock, therefore, has an expected return of 15 percent. We can verify this answer by calculating the price in one year, P1, using 15 percent as

the required return. Based on the dividend growth model, this price is:

P 1

= Div × (1 + g) / (R − g)

= $1 × 1.10/ (.15 − .10)

= $1.10/ .05

Notice that this $22 is $20 × 1.1, so the stock price has grown by 10 percent as it should. If you pay $20 for the stock today, you will get a $1 dividend at the end of the year, and you will have a $22 − 20 = $2 gain. Your dividend yield is thus $1/20 = 5 percent. Your capital gains yield is $2/20 = 10 percent, so your total return would be 5 percent + 10 percent = 15 percent.

To get a feel for actual numbers in this context, consider that, according to the 2016 Value Line Investment Survey, Procter & Gamble’s dividends were expected to grow by 4 percent over the next 5 or so years, compared to a historical growth rate of 8.5  percent over the preceding 5 years and 10 percent over the preceding 10 years. In 2016, the projected dividend for the coming year was given as $2.75. The stock price at that time was about $82 per share. What is the return investors require on P&G? Here, the dividend yield is 3.4 percent and the capital gains yield is 4 percent, giving a total required return of 7.4  percent on P&G stock.

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6 .5

Pagemaster Enterprises, the company examined in the previous example, has 1,000,000 shares of stock outstanding. The stock is selling at $10. What is the required return on the stock?

Because the retention ratio is 40 percent, the payout ratio is 60 percent (= 1 − Retention ratio). The payout ratio is the ratio of dividends/earnings. Because earnings a year from now will be $2,128,000 (=$2,000,000 × 1.064), dividends will be $1,276,800 (=60 × $2,128,000). Dividends per share will be $1.28 (=$1,276,800/1,000,000). Given our previous result that g =.064, we calculate R from [6.9] as follows:

.192 = $1.28 ______ 10.00

+ .064

Calculating the Required Return

A Healthy Sense of Skepticism It is important to emphasize that our approach merely estimates g; our approach does not determine g precisely. We mentioned earlier that our estimate of g is based on a number of assumptions. For example, we assume that the return on reinvestment of future retained

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CHAPTER 6 Stock Valuation 173

earnings is equal to the firm’s past ROE. We assume that the future retention ratio is equal to the past retention ratio. Our estimate for g will be off if these assumptions prove to be wrong. 3D Systems, a 3-D printer manufacturer, is an example of a firm whose historical growth rate will not equal future growth rates. The company had total revenues of about $112.8 million in 2009 compared to about $663 million in 2015. That works out to a growth rate of a remarkable 34.3 percent per year! How likely is it that the company can continue to grow at this rate? If it did, it would have revenues of about $17 trillion in just 11 years, which is about the same as the gross domestic product (GDP) of the United States. Obviously, 3D Systems’ growth rate will slow substantially in the next several years.

Unfortunately, the determination of R is highly dependent on g. In the Pagemaster Enterprises example, if g is estimated to be 0, R equals 12.8 percent (=$1.28/10.00). If g is estimated to be 12 percent, R equals 24.8 percent (=$1.28/10.00 + 12%). Thus, one should view estimates of R with a healthy sense of skepticism.

Because of the preceding, some financial economists generally argue that the estima- tion error for R for a single security is too large to be practical. Therefore, they suggest calculating the average R for an entire industry. This R would then be used to discount the dividends of a particular stock in the same industry.

One should be particularly skeptical of two polar cases when estimating R for individual securities. First, consider a firm currently paying no dividend. The stock price will be above zero because investors believe that the firm may initiate a dividend at some point or the firm may be acquired at some point. However, when a firm goes from no dividends to a positive number of dividends, the implied growth rate is infinite. Thus, Equation 6.9 must be used with extreme caution here, if at all—a point we emphasize later in this chapter.

Second, we mentioned earlier that the value of the firm is infinite when g is equal to R. Because prices for stocks do not grow infinitely, an analyst whose estimate of g for a

HOW FAST IS TOO FAST? Growth rates are an important tool for evaluating a company and, as we have seen, an important part of valuing a com- pany’s stock. When you’re thinking about (and calculating) growth rates, a little common sense goes a long way. For example, in 2015, retailing giant Walmart had about 777 million square feet of stores, distribution centers, and so forth in the U.S. The company expected to increase its square footage by about 4 percent over the next year. This doesn’t sound too outrageous, but can Walmart grow its square footage at 4 percent indefinitely?

Using the compound growth calculation we discussed in an earlier chapter, see if you agree that if Walmart grows at 4 percent per year over the next 300 years, the company will have more than 100 trillion square feet under roof, which is about the total land mass of the entire United States! In other words, if Walmart keeps growing at 4 percent, the entire country will eventually be one big Walmart. Scary.

What about growth in cash flow? As of its fiscal year-end in September 2015, Apple had grown its operating cash flow at an annual rate of about 41.4 percent for the previous six years. The company generated about $81.3 billion in cash flow for 2015. If the company were to grow its cash flow at that same rate for the next nine years, it would generate over $1.83 trillion per year, which is greater than total amount of U.S. currency in the world.

As these examples show, growth rates shouldn’t just be extrapolated into the future. It is fairly easy for a small com- pany to grow very fast. If a company has $100 in sales, it only has to increase sales by another $100 to have a 100 percent increase in sales. If the company’s sales are $10 billion, it has to increase sales by another $10 billion to achieve the same 100 percent increase. So, long-term growth rate estimates must be chosen very carefully. As a rule of thumb, for really long- term growth rate estimates, you should probably assume that a company will not grow much faster than the economy as a whole, which is probably noticeably less than 5 percent (inflation adjusted).

FINANCE MATTERS

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particular firm is equal to or above R must have made a mistake. Most likely, the analyst’s high estimate for g is correct for the next few years. However, firms cannot maintain an abnormally high growth rate forever. The analyst’s error was to use a short-run estimate of g in a model requiring a perpetual growth rate. A nearby Finance Matters box discusses the consequences of long-term growth at unrealistic rates.

The No-Payout Firm Students frequently ask the following question: If the dividend discount model is correct, why aren’t no-payout stocks selling at zero? This is a good question and gets at the goals of the firm. A firm with many growth opportunities is faced with a dilemma. The firm can pay out cash now, or it can forgo cash payments now so that it can make investments that will generate even greater payouts in the future.3 This is often a painful choice, because a strategy of deferment may be optimal yet unpopular among certain stockholders.

Many firms choose to pay no cash to stockholders—and these firms sell at positive prices. For example, many Internet firms, such as Alphabet, pay no cash to stockholders. Rational shareholders believe that they will either receive a payout at some point or they will receive something just as good. That is, the firm will be acquired in a merger, with the stockholders receiving either cash or shares of stock at that time.

Of course, the actual application of the dividend discount model is difficult for firms of this type. Clearly, the model for constant growth of payouts does not exactly apply. Though the differential growth model can work in theory, the difficulties of estimating the date of the first payout, the growth rate of payouts after that date, and the ultimate merger price make application of the model quite difficult in reality.

Empirical evidence suggests that firms with high growth rates are likely to have lower pay- outs, a result consistent with the above analysis. For example, consider Microsoft Corporation. The company started in 1975 and grew rapidly for many years. It paid its first dividend in 2003, though it was a billion-dollar company (in both sales and market value of stockholders’ equity) prior to that date. Why did it wait so long to pay a dividend? It waited because it had so many positive growth opportunities, that is, new software products, to take advantage of.

6.3 COMPARABLES So far in this chapter, we have valued stocks by discounting dividends (or total payouts). In addition to this approach, practitioners commonly value stocks by comparables. The com- parables approach is similar to valuation in real estate. If your neighbor’s home just sold for $200,000 and it has similar size and amenities to your home, your home is probably worth around $200,000 also. In the stock market, comparable firms are assumed to have similar multiples. To see how the comparables approach works, let’s look at perhaps the most common multiple, the price-to-earnings (PE) multiple, or PE ratio.

Price-to-Earnings Ratio Recall that a stock’s price-to-earnings ratio is the ratio of the stock’s price to its earn- ings per share. For example, if the stock of Sun Aerodynamic Systems (SAS) is selling at $27.00 per share and its earnings per share over the last year was $4.50, SAS’s PE ratio would be 6 (= $27/4.50).

It is generally assumed that similar firms have similar PE ratios. For example, imagine the average price-to-earnings (PE) ratio across all publicly traded companies in the specialty retail industry is 12 and a particular company in the industry has earnings of $10  million. If this company is judged to be similar to the rest of the industry, one might estimate that company’s value to be $120 million (= 12 × $10 million). 3 A third alternative is to issue stock so that the firm has enough cash both to pay dividends and to invest. This possibility is explored in a later chapter.

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Valuation via PE certainly looks easier than valuation via discounted cash flow (DCF), since the DCF approach calls for estimates of future cash flows. But is the PE approach better? That depends on the similarity across comparables.

On February 19, 2016, Alphabet’s stock price was $701 and its EPS was $23.59, imply- ing a PE ratio of about 29.7.4 On the same day, Hewlett-Packard’s PE was 10.2, Microsoft’s was 36.7, and Apple’s was 10.2. Why would stocks in the same industry trade at different PE ratios?

The dividend discount model (in Examples 6.1 and 6.2) implies that the PE ratio is related to growth opportunities.5 As an example, consider two firms, each having just reported earnings per share of $1. However, one firm has many valuable growth opportuni- ties, while the other firm has no growth opportunities at all. The firm with growth oppor- tunities should sell at a higher price, because an investor is buying both current income of $1 and growth opportunities. Suppose that the firm with growth opportunities sells for $16 and the other firm sells for $8. The $1 earnings per share number appears in the denomina- tor of the PE ratio for both firms. Thus, the PE ratio is 16 for the firm with growth oppor- tunities, but only 8 for the firm without the opportunities.

There are at least two additional factors explaining the PE ratio. The first is the discount rate, R. Since R appears in the denominator of the dividend discount model, the formula implies that the PE ratio is negatively related to the firm’s discount rate. We have already suggested that the discount rate is positively related to the stock’s risk or variability. Thus, the PE ratio is negatively related to the stock’s risk. To see that this is a sensible result, con- sider two firms, A and B, behaving as cash cows. The stock market expects both firms to have annual earnings of $1 per share forever. However, the earnings of Firm A are known with certainty while the earnings of Firm B are quite variable. A rational stockholder is likely to pay more for a share of Firm A because of the absence of risk. If a share of Firm A sells at a higher price and both firms have the same EPS, the PE ratio of Firm A must be higher.

The second additional factor concerns the firm’s accounting method. As an example, consider two identical firms, C and D. Firm C uses LIFO and reports earnings of $2 per share.6 Firm D uses the less conservative accounting assumptions of FIFO and reports earnings of $3 per share. The market knows that both firms are identical and prices both at $18 per share. The price–earnings ratio is 9 (= $18/2) for Firm C and 6 (= $18/3) for Firm D. Thus, the firm with the more conservative principles has the higher PE ratio.

In conclusion, we have argued that a stock’s PE ratio is likely a function of three factors:

1. Growth opportunities. Companies with significant growth opportunities are likely to have high PE ratios.

2. Risk. Low-risk stocks are likely to have high PE ratios. 3. Accounting practices. Firms following conservative accounting practices will

likely have high PE ratios.

4 We just calculated PE as the ratio of current price to last year’s EPS. Alternatively, PE can be computed as the ratio of current price to projected EPS over the next year. 5 We can also use the constant growth version of the dividend discount model to solve for the price–earnings ratio. Recall that

Price per share = Div ____ R − g

If Div can be expressed as EPS1 × (1 − b), where EPS1 is earnings per share in time 1 and b is the plowback ratio (where 1 − b is the dividend payout ratio), and EPS0 (1 + g) 5 EPS1, then

Price per share = EP S 0 (1 + g)(1 − b) ________________ R − g

dividing by EPS0 yields

Price per share __________ EP S 0

= (1 + g)(1 − b)

_________ R − g

6 Recall from your accounting courses that in an inflationary environment, FIFO (first-in, first-out) accounting understates the true cost of inventory and hence inflates reported earnings. Inventory is valued according to more recent costs under LIFO (last-in, first-out), implying that reported earnings are lower here than they would be under FIFO. Thus, LIFO inventory accounting is a more conservative method than FIFO. Similar accounting leeway exists for construction costs (completed contracts versus percentage-of-completion methods) and deprecia- tion (accelerated depreciation versus straight-line depreciation).

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Which of these factors is most important in the real world? The consensus among finance professionals is that growth opportunities typically have the biggest impact on PE ratios. For example, high-tech companies generally have higher PE ratios than, say, utilities, because utilities have fewer opportunities for growth, even though utilities typically have lower risk. And, within industries, differences in growth opportunities also generate the biggest differences in PE ratios. In our example at the beginning of this section, Alphabet’s high PE is almost certainly due to its growth opportunities, not its low risk or its accounting conservatism. In fact, due to its relative youth, the risk of Alphabet is likely higher than the risk of many of its competitors. Hewlett-Packard’s PE is lower than Alphabet’s PE because Hewlett-Packard’s growth opportunities are a small fraction of its existing business lines. However, Hewlett-Packard had a much higher PE decades ago, when it had huge growth opportunities but little in the way of existing business.

Thus, while multiples such as the PE ratio can be used to price stocks, care must be taken. Firms in the same industry are likely to have different multiples if they have differ- ent growth rates, risk levels, and accounting treatments. Average multiples should not be calculated across all firms in any industry. Rather, an average multiple should be calculated only across those firms in an industry with similar characteristics.

Enterprise Value Ratios The PE ratio is an equity ratio. That is, the numerator is the price per share of stock and the denominator is the earnings per share of stock. In addition, practitioners often use ratios involving both equity and debt. Perhaps the most common is the enterprise value (EV) to EBITDA ratio. Enterprise value is equal to the market value of the firm’s equity plus the market value of the firm’s debt minus cash. Recall, EBITDA stands for earnings before interest, taxes, depreciation, and amortization.

For example, imagine that Illinois Food Products Co. (IFPC) has equity worth $800  million, debt worth $300 million, and cash of $100 million. The enterprise value here is $1 billion (= $800 + 300 − 100). Further imagine the firm has the following income statement:

ILL INOIS FOOD PRODUCTS CO. Income Statement ($ in mi l l ions)

Revenue $700.00

Cost of goods sold −500.00

Earnings before interest, taxes, depreciation, and amortization     $200.00

(EBITDA)

Depreciation and amortization −100.00 Interest      − 24.00 Pretax income 76.00

Taxes (@ 30%)      − 22.80 Profit after taxes  $ 53.20

The EV to EBITDA ratio is 5 (= $1 billion/200 million). Note that all the items in the income statement below EBITDA are ignored when calculating this ratio.

As with PE ratios, it is generally assumed that similar firms have similar EV/EBITDA ratios. For example, imagine that the average EV/EBITDA ratio in an industry is 6. If QRT Corporation, a firm in the industry with EBITDA of $50 million, is judged to be similar to the rest of the industry, its enterprise value might be estimated at $300 million (= 6 × $50). Now imagine that QRT has $75 million of debt and $25 million of cash. Given our estimate of QRT’s enterprise value, QRT’s stock would be worth $250 million (= $300 − 75 + 25).

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A number of questions arise with value ratios:

1. Is there any advantage to the EV/EBITDA ratio over the PE ratio? Yes. Companies in the same industry may differ by leverage, i.e., the ratio of debt to equity. As you will learn in Chapter 14, leverage increases the risk of equity, impacting the discount rate, R. Thus, while firms in the same industry may be otherwise comparable, they are likely to have different PE ratios if they have dif- ferent degrees of leverage. Since enterprise value includes debt and equity, the impact of leverage on the EV/EBITDA ratio is less.7

2. Why is EBITDA used in the denominator? The numerator and denominator of a ratio should be consistent. Since the numerator of the PE ratio is the price of a share of stock, it makes sense that the denominator is the earnings per share (EPS) of stock. That is, interest is specifically subtracted before EPS is calculated. By contrast, since EV involves the sum of debt and equity, it is sensible that the denominator is unaffected by interest payments. This is the case with EBITDA since, as its name implies, earnings are calculated before interest is taken out.

3. Why does the denominator ignore depreciation and amortization? Many practi- tioners argue that, since depreciation and amortization are not cash flows, earn- ings should be calculated before taking out depreciation and amortization. In other words, depreciation and amortization merely reflect the sunk cost of a pre- vious purchase. However, this view is by no means universal. Others point out that depreciable assets will eventually be replaced in an ongoing business. Since depreciation charges reflect the cost of future replacement, it can be argued that these charges should be considered in a calculation of income.

4. What other denominators are used in value ratios? Among others, practitioners may use EBIT (earnings before interest and taxes), EBITA (earnings before interest, taxes, and amortization), and free cash flow.

5. Why is cash subtracted out? Many firms seem to hold amounts of cash well in excess of what is needed. For example, Microsoft held tens of billions of dol- lars in cash and short-term investments throughout the last decade, far more than many analysts believed was optimal. Since an enterprise value ratio should reflect the ability of productive assets to create earnings or cash flow, cash should be subtracted out when calculating the ratio. However, the viewpoint that all cash should be ignored can be criticized. Some cash holdings are necessary to run a business, and this amount of cash should be included in EV.

6.4 VALUING STOCKS USING FREE CASH FLOWS So far in this chapter, we have discounted cash payouts to value a single share of stock and used the method of comparables. As an alternative, one can value stocks by discounting their cash flows using a “top down” approach.

As an example, consider Global Harmonic Control Systems (GHCS). Revenues, which are forecasted to be $500 million in one year, are expected to grow at 10 percent per year for the two years after that, 8 percent per year for the next two years, and 6 percent per year after that. Expenses including depreciation are 60 percent of revenues. Net invest- ment, including net working capital and capital spending less depreciation, is 10 percent of revenues. Because all costs are proportional to revenues, net cash flow (sometimes referred to as free cash flow) grows at the same rate as do revenues. GHCS is an all-equity firm with 12 million shares outstanding. A discount rate of 16 percent is appropriate for a firm of GHCS’s risk.

7 However, leverage does impact the ratio of EV to EBITDA to some extent. As we discuss in Chapter 14, leverage creates a tax shield, increasing EV. Since leverage should not impact EBITDA, the ratio should increase with leverage.

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The relevant numbers for the first five years, rounded to two decimals, are:

YEAR ($000,000) 1 2 3 4 5

Revenues 500.00 550.00 605.00 653.40 705.67

Expenses 300.00 330.00 363.00 392.04 423.40

Earnings before taxes 200.00 220.00 242.00 261.36 282.27

Taxes (40%) 80.00 88.00 96.80 104.54 112.91

Earnings after taxes 120.00 132.00 145.20 156.82 169.36

Net investment 50.00 55.00 60.50 65.34 70.57

Net cash flow 70.00 77.00 84.70 91.48 98.79

Since net cash flow grows at 6 percent per year after Year 5, net cash flow in Year 6 is forecasted to be $104.72 (= $98.79 × 1.06). Using the growing perpetuity formula, we can calculate the present value as of Year 5 of all future cash flows to be $1,047.22 million [= $104.72/(.16 − .06)].

The present value as of today of that terminal value is:

$1, 047.22 × 1 _______ (1.16) 5

= $498.59 million

The present value of the net cash flows during the first five years is:

$70 _____ 1.16

+ $77 _______ (1.16) 2

+ $84.7 _______ (1.16) 3

+ $91.48 _______ (1.16) 4

+ $98.79 _______ (1.16) 5

= $269.39 million

Adding in the terminal value, today’s value of the firm is $767.98 million (=  $269.39 +  498.59). Given the number of shares outstanding, the price per share is $64.00 (= $767.98/12).

The above calculation assumes a growing perpetuity after Year 5. However, we pointed out in the previous section that stocks are often valued by multiples. An investor might estimate the terminal value of GHCS via a multiple, rather than the growing perpetuity for- mula. For example, suppose that the price–earnings ratio for comparable firms in GHCS’s industry is 7.

Since earnings after tax in Year 5 are $169.36. Using the PE multiple of 7, the value of the firm at Year 5 would be estimated as $1,185.52 million (= $169.36 × 7).

The firm’s value today is:

$70 _____ 1.16

+ $77 _______ (1.16) 2

+ $84.7 _______ (1.16) 3

+ $91.48 _______ (1.16) 4

+ $98.79 _______ (1.16) 5

+ $1,185.52 _________ (1.16) 5

= $833.83

With 12 million shares outstanding, the price per share of GHCS would be $69.49 (= $833.83/12).

Now we have two estimates of the value of a share of equity in GHCS. The differ- ent estimates reflect the different ways of calculating terminal value. Using the constant growth discounted cash flow method for terminal value, our estimate of the equity value per share of GHCS is $64; using the PE comparable method, our estimate is $69.49. There is no best method. If the comparable firms were all identical to GHCS, perhaps the PE method would be best. Unfortunately, firms are not identical. On the other hand, if we were very sure of the terminal date and the growth in subsequent cash flows, perhaps the constant growth method would be best. In practice, both methods are used.

Conceptually, the dividend discount model, the comparables method, and the free cash flow model are mutually consistent and can be used to determine the value of a share

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of stock. In practice, the dividend discount model is especially useful for firms paying very steady dividends and the comparables method is useful for firms with similar growth opportunities. The free cash flow model is helpful for non-dividend-paying firms with external financing needs.

6.5 SOME FEATURES OF COMMON AND PREFERRED STOCKS

In discussing common stock features, we focus on shareholder rights and dividend pay- ments. For preferred stock, we explain what the “preferred” means, and we also debate whether preferred stock is really debt or equity.

Common Stock Features The term common stock means different things to different people, but it is usually applied to stock that has no special preference either in receiving dividends or in bankruptcy.

SHAREHOLDER RIGHTS The conceptual structure of the corporation assumes that sharehold- ers elect directors who, in turn, hire management to carry out their directives. Shareholders, therefore, control the corporation through the right to elect the directors. Generally, only shareholders have this right.

Directors are elected each year at an annual meeting. Although there are exceptions (discussed next), the general idea is “one share, one vote” (not one shareholder, one vote). Corporate democracy is thus very different from our political democracy. With corporate democracy, the “golden rule” prevails absolutely.8

Directors are elected at an annual shareholders’ meeting by a vote of the holders of a majority of shares who are present and entitled to vote. However, the exact mechanism for electing directors differs across companies. The most important difference is whether shares must be voted cumulatively or voted straight.

To illustrate the two different voting procedures, imagine that a corporation has two share- holders: Smith with 20 shares and Jones with 80 shares. Both want to be a director. Jones does not want Smith, however. We assume there are a total of four directors to be elected.

The effect of cumulative voting is to permit minority participation.9 If cumulative vot- ing is permitted, the total number of votes that each shareholder may cast is determined first. This is usually calculated as the number of shares (owned or controlled) multiplied by the number of directors to be elected.

With cumulative voting, the directors are elected all at once. In our example, this means that the top four vote getters will be the new directors. A shareholder can distribute votes however he/she wishes.

Will Smith get a seat on the board? If we ignore the possibility of a five-way tie, then the answer is yes. Smith will cast 20 × 4 = 80 votes, and Jones will cast 80 × 4 = 320 votes. If Smith gives all his votes to himself, he is assured of a directorship. The reason is that Jones can’t divide 320 votes among four candidates in such a way as to give all of them more than 80 votes, so Smith will finish fourth at worst.

In general, if there are N directors up for election, then 1/(N + 1) percent of the stock plus one share will guarantee you a seat. In our current example, this is 1/(4 + 1) = 20 percent. So the more seats that are up for election at one time, the easier (and cheaper) it is to win one.

With straight voting, the directors are elected one at a time. Each time, Smith can cast 20 votes and Jones can cast 80. As a consequence, Jones will elect all of the candidates.

8 The golden rule: Whosoever has the gold makes the rules. 9 By minority participation, we mean participation by shareholders with relatively small amounts of stock.

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The only way to guarantee a seat is to own 50 percent plus one share. This also guarantees that you will win every seat, so it’s really all or nothing.

As we’ve illustrated, straight voting can “freeze out” minority shareholders; that is the reason many states have mandatory cumulative voting. In states where cumulative voting is mandatory, devices have been worked out to minimize its impact.

One such device is to stagger the voting for the board of directors. With staggered elec- tions, only a fraction of the directorships are up for election at a particular time. Thus, if only two directors are up for election at any one time, it will take 1/(2 + 1) = 33.33 percent of the stock plus one share to guarantee a seat.

Overall, staggering has two basic effects:

1. Staggering makes it more difficult for a minority to elect a director when there is cumulative voting because there are fewer directors to be elected at one time.

2. Staggering makes takeover attempts less likely to be successful because it makes it more difficult to vote in a majority of new directors.

We should note that staggering may serve a beneficial purpose. It provides “institutional memory,” that is, continuity on the board of directors. This may be important for corpora- tions with significant long-range plans and projects.

PROXY VOTING A proxy is the grant of authority by a shareholder to someone else to vote his/her shares. For convenience, much of the voting in large public corporations is actually done by proxy.

As we have seen, with straight voting, each share of stock has one vote. The owner of 10,000 shares has 10,000 votes. Large companies have hundreds of thousands or even mil- lions of shareholders. Shareholders can come to the annual meeting and vote in person, or they can transfer their right to vote to another party.

Obviously, management always tries to get as many proxies as possible transferred to it. However, if shareholders are not satisfied with management, an “outside” group of share- holders can try to obtain votes via proxy. They can vote by proxy in an attempt to replace management by electing enough directors. The resulting battle is called a proxy fight.

CLASSES OF STOCK Some firms have more than one class of common stock. Often, the classes are created with unequal voting rights. The Ford Motor Company, for example, has Class B common stock, which is not publicly traded (it is held by Ford family interests and trusts). This class has 40 percent of the voting power, even though it represents less than 10 percent of the total number of shares outstanding.

There are many other cases of corporations with different classes of stock. For example, Adolph Coors Class B shares, which were owned by the public, had no votes at all except in the case of a merger. (Adolph Coors later merged with Molson.) The CEO of cable TV giant Comcast, Brian Roberts, owned about .4 percent of the company’s equity, but he

Stock in JRJ Corporation sells for $20 per share and features cumulative voting. There are 10,000 shares outstanding. If three directors are up for election, how much does it cost to ensure yourself a seat on the board?

The question here is how many shares of stock it will take to get a seat. The answer is 2,501, so the cost is 2,501 × $20 = $50,020. Why 2,501? Because there is no way the remaining 7,499 votes can be divided among three people to give all of them more than 2,501 votes. For example, sup- pose two people receive 2,502 votes and the first two seats. A third person can receive at most 10,000 − 2,502 − 2,502 − 2,501 = 2,495, so the third seat is yours.

Buying the Election

E X

A M

P L

E 6

.6

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had a third of all the votes, thanks to a special class of stock. Another good example is Alphabet, formerly Google. Alphabet initially had two classes of common stock, A and B (it has recently added a third class). The Class A shares are held by the public, and each share has one vote. The Class B shares are held by company insiders, and each Class B share has 10 votes. As a result, Google’s founders and management control the company.

Historically, the New York Stock Exchange did not allow companies to create classes of publicly traded common stock with unequal voting rights. Exceptions (e.g., Ford) appear to have been made. In addition, many non-NYSE companies have dual classes of common stock.

A primary reason for creating dual or multiple classes of stock has to do with control of the firm. If such stock exists, management of a firm can raise equity capital by issuing nonvoting or limited-voting stock while maintaining control.

The subject of unequal voting rights is controversial in the United States, and the idea of one share, one vote has a strong following and a long history. Interestingly, however, shares with unequal voting rights are quite common in the United Kingdom and elsewhere around the world.

OTHER RIGHTS The value of a share of common stock in a corporation is directly related to the general rights of shareholders. In addition to the right to vote for directors, share- holders usually have the following rights:

1. The right to share proportionally in dividends paid. 2. The right to share proportionally in assets remaining after liabilities have been

paid in a liquidation. 3. The right to vote on stockholder matters of great importance, such as a merger.

Voting is usually done at the annual meeting or a special meeting.

In addition, stockholders sometimes have the right to share proportionally in any new stock sold. This is called the preemptive right.

Essentially, a preemptive right means that a company that wishes to sell stock must first offer it to the existing stockholders before offering it to the general public. The purpose is to give a stockholder the opportunity to protect his/her proportionate ownership in the corporation.

DIVIDENDS A distinctive feature of corporations is that they have shares of stock on which they are authorized by law to pay dividends to their shareholders. Dividends paid to shareholders represent a return on the capital directly or indirectly contributed to the corporation by the shareholders. The payment of dividends is at the discretion of the board of directors.

Some important characteristics of dividends include the following:

1. Unless a dividend is declared by the board of directors of a corporation, it is not a liability of the corporation. A corporation cannot default on an undeclared dividend. As a consequence, corporations cannot become bankrupt because of nonpayment of dividends. The amount of the dividend and even whether it is paid are decisions based on the business judgment of the board of directors.

2. The payment of dividends by the corporation is not a business expense. Dividends are not deductible for corporate tax purposes. In short, dividends are paid out of the corporation’s aftertax profits.

3. Dividends received by individual shareholders are taxable. However, corporations that own stock in other corporations are permitted to exclude 70 percent of the dividend amounts they receive and are taxed only on the remaining 30 percent.10

10 For the record, the 70 percent exclusion applies when the recipient owns less than 20 percent of the outstanding stock In a corporation. If a corporation owns more than 20 percent but less than 80 percent, the exclusion is 80 percent. If more than 80 percent is owned, the corporation can file a single “consolidated” return and the exclusion is effectively 100 percent.

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Preferred Stock Features Preferred stock differs from common stock because it has preference over common stock in the payment of dividends and in the distribution of corporation assets in the event of liquidation. Preference means only that the holders of the preferred shares must receive a dividend (in the case of an ongoing firm) before holders of common shares are entitled to anything.

Preferred stock is a form of equity from a legal and tax standpoint. It is important to note, however, that holders of preferred stock sometimes have no voting privileges.

STATED VALUE Preferred shares have a stated liquidating value, usually $100 per share. The cash dividend is described in terms of dollars per share. For example, a Ford “$5 pre- ferred” easily translates into a dividend yield of 5 percent of stated value.

CUMULATIVE AND NONCUMULATIVE DIVIDENDS A preferred dividend is not like interest on a bond. The board of directors may decide not to pay the dividends on preferred shares, and their decision may have nothing to do with the current net income of the corporation.

Dividends payable on preferred stock are either cumulative or noncumulative; most are cumulative. If preferred dividends are cumulative and are not paid in a particular year, they will be carried forward as an arrearage. Usually, both the accumulated (past) preferred dividends and the current preferred dividends must be paid before the common sharehold- ers can receive anything.

Unpaid preferred dividends are not debts of the firm. Directors elected by the common shareholders can defer preferred dividends indefinitely. However, in such cases, common share- holders must also forgo dividends. In addition, holders of preferred shares are sometimes granted voting and other rights if preferred dividends have not been paid for some time.

IS PREFERRED STOCK REALLY DEBT? A good case can be made that preferred stock is really debt in disguise, a kind of equity bond. Preferred shareholders receive a stated dividend only, and if the corporation is liquidated, preferred shareholders get a stated value. Often, preferred stocks carry credit ratings much like those of bonds. Furthermore, preferred stock is sometimes convertible into common stock, and preferred stocks are often callable.

In addition, many issues of preferred stock have obligatory sinking funds. The exis- tence of such a sinking fund effectively creates a final maturity because it means that the entire issue will ultimately be retired. For these reasons, preferred stock seems to be a lot like debt. However, for tax purposes, preferred dividends are treated like common stock dividends.

In the 1990s, firms began to sell securities that look a lot like preferred stock but are treated as debt for tax purposes. The new securities were given interesting acronyms like TOPrS (trust-originated preferred securities, or toppers), MIPS (monthly income preferred securities), and QUIPS (quarterly income preferred securities), among others. Because of various specific features, these instruments can be counted as debt for tax purposes, mak- ing the interest payments tax deductible. Payments made to investors in these instruments are treated as interest for personal income taxes for individuals. Until 2003, interest pay- ments and dividends were taxed at the same marginal tax rate. When the tax rate on divi- dend payments was reduced, these instruments were not included, so individuals must still pay their higher income tax rate on dividend payments received from these instruments.

6.6 THE STOCK MARKETS Stock markets consist of a primary market and a secondary market. In the primary, or new-issue market, shares of stock are first brought to the market and sold to investors. In the secondary market, existing shares are traded among investors.

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In the primary market, companies sell securities to raise money. We will discuss this pro- cess in detail in a later chapter. We therefore focus mainly on secondary market activity in this section. We conclude with a discussion of how stock prices are quoted in the financial press.

Dealers and Brokers Because most securities transactions involve dealers and brokers, it is important to under- stand exactly what is meant by the terms dealer and broker. A dealer maintains an inven- tory and stands ready to buy and sell at any time. In contrast, a broker brings buyers and sellers together, but does not maintain an inventory. Thus, when we speak of used car deal- ers and real estate brokers, we recognize that the used car dealer maintains an inventory, whereas the real estate broker does not.

In the securities markets, a dealer stands ready to buy securities from investors wishing to sell them and sell securities to investors wishing to buy them. Recall from our previous chapter that the price the dealer is willing to pay is called the bid price. The price at which the dealer will sell is called the ask price (sometimes called the asked, offered, or offer- ing price). The difference between the bid and ask prices is called the spread, and it is the basic source of dealer profits.

Dealers exist in all areas of the economy, not just the stock markets. For example, your local college bookstore is probably both a primary and a secondary market textbook dealer. If you buy a new book, this is a primary market transaction. If you buy a used book, this is a se