360 365 loan calculator dinkytown

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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

Chief Product Officer, SVP Products & Markets: G. Scott Virkler Vice President, Portfolio and Learning Content: Mike Ryan Vice President, Content Design & Delivery: Betsy Whalen Managing Director: Tim Vertovec Brand Manager: Chuck Synovec Director, Product Development: Rose Koos Product Developer: Jennifer Upton Lead Product Developer: Michele Janicek Marketing Manager: Trina Maurer Market Development Manager: Julie Wolfe Digital Product Developer: Tobi Philips Director, Content Design & Delivery: Linda Avenarius Program Manager: Mark Christianson Content Project Managers: Kathryn D. Wright, Bruce Gin, and Karen Jozefowicz Buyer: Laura M. Fuller Design: Matt Diamond Content Licensing Specialists: Beth Thole and Melissa Homer Cover Image: © darekm101/Getty Images Compositor: SPi Global Printer: LSC Communications

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 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

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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?