Investment valuation tools and techniques for determining the value of any asset 3rd by damonaran

Investment valuation tools and techniques for determining the value of any asset 3rd by damonaran Investment valuation tools and techniques for determining the value of any asset 3rd by damonaran Investment valuation tools and techniques for determining the value of any asset 3rd by damonaran Investment valuation tools and techniques for determining the value of any asset 3rd by damonaran Investment valuation tools and techniques for determining the value of any asset 3rd by damonaran

Investment Valuation

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Investment Valuation

Tools and Techniques for

Determining the Value of Any Asset

Third Edition

ASWATH DAMODARAN

www.damodaran.com

WILEY John Wiley & Sons, Inc.

Copyright © 2012 by Aswath Damodaran All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

ISBN 978-1-118-01152-2 (cloth); ISBN 978-1-118-20654-6 (ebk);

ISBN 978-1-118-20655-3 (ebk); ISBN 978-1-118-20656-0 (ebk) ISBN 978-1-118-13073-5 (paper); ISBN 978-1-118-20657-7 (ebk);

ISBN 978-1-118-20658-4 (ebk); ISBN 978-1-118-20659-1 (ebk)

1 Corporations—Valuation—Mathematical models I Title

HG4028.V3 D353 2012

10 9 8 7 6 5 4 3 2 1

I would like to dedicate this book to Michele, whose patience and support made it possible, and to my four children— Ryan, Brendan, Kendra, and Kiran—who provided the inspiration.

Preface to the Third Edition

and real assets It is a fundamental precept of this book that any asset can be ued, albeit imprecisely in some cases I have attempted to provide a sense of notonly the differences between the models used to value different types of assets, butalso the common elements in these models

val-The past decade has been an eventful one for those interested in valuation forseveral reasons First, the growth of Asian and Latin American markets broughtemerging market companies into the forefront, and you will see the increased focus

on these companies in this edition Second, we saw the havoc wreaked by economic factors on company valuations during the bank crisis of 2008, and a blur-ring of the lines between developed and emerging markets The lessons I learnedabout financial fundamentals during the crisis about risk-free rates, risk premiumsand cash flow estimation are incorporated into the text Third, the past year has seenthe influx of social media companies, with small revenues and outsized market capi-talizations, in an eerie replay of the dot-com boom from the late 1990s More thanever, it made clear that the more things change, the more they stay the same Finally,the entry of new players into equity markets (hedge funds, private equity investorsand high-frequency traders) has changed markets and investing dramatically Witheach shift, the perennial question arises: “Is valuation still relevant in this market?”and my answer remains unchanged, “Absolutely and more than ever.”

macro-As technology increasingly makes the printed page an anachronism, I have tried

to adapt in many ways First, this book will be available in e-book format, andhopefully will be just as useful as the print edition (if not more so) Second, everyvaluation in this book will be put on the web site that will accompany this book(www.damodaran.com), as will a significant number of datasets and spreadsheets

In fact, the valuations in the book will be updated online, allowing the book to have

a much closer link to real-time valuations

In the process of presenting and discussing the various aspects of valuation, Ihave tried to adhere to four basic principles First, I have attempted to be as com-prehensive as possible in covering the range of valuation models that are available

to an analyst doing a valuation, while presenting the common elements in thesemodels and providing a framework that can be used to pick the right model for anyvaluation scenario Second, the models are presented with real-world examples,warts and all, so as to capture some of the problems inherent in applying thesemodels There is the obvious danger that some of these valuations will appear to behopelessly wrong in hindsight, but this cost is well worth the benefits Third, inkeeping with my belief that valuation models are universal and not market-specific,illustrations from markets outside the United States are interspersed throughout thebook Finally, I have tried to make the book as modular as possible, enabling areader to pick and choose sections of the book to read, without a significant loss ofcontinuity

vii

CHAPTER 1

CHAPTER 5

ix

Option Pricing Models 90

CHAPTER 6

CHAPTER 8

CHAPTER 10

CHAPTER 13

CHAPTER 14

CHAPTER 15

Firm Valuation: Cost of Capital and Adjusted Present Value Approaches 380

Firm Valuation: The Adjusted Present Value Approach 398

CHAPTER 16

CHAPTER 17

Conclusion 577

CHAPTER 21

New Paradigms or Old Principles:

CHAPTER 24

CHAPTER 26

The Options to Expand and to Abandon: Valuation Implications 805

CHAPTER 30

CHAPTER 31

Value Enhancement: A Discounted Cash Flow Valuation Framework 841

CHAPTER 32

Value Enhancement: Economic Value Added, Cash Flow Return on Investment,

Investment Valuation

CHAPTER 1

Introduction to Valuation

in and managing these assets lies in understanding not only what the value is, butthe sources of the value Every asset can be valued, but some assets are easier tovalue than others, and the details of valuation will vary from case to case Thus,valuing of a real estate property will require different information and follow a dif-ferent format than valuing a publicly traded stock What is surprising, however, isnot the differences in techniques across assets, but the degree of similarity in thebasic principles of valuation There is uncertainty associated with valuation Oftenthat uncertainty comes from the asset being valued, though the valuation modelmay add to that uncertainty

This chapter lays out a philosophical basis for valuation, together with a sion of how valuation is or can be used in a variety of frameworks, from portfoliomanagement to corporate finance

discus-A PHILOSOPHICdiscus-AL Bdiscus-ASIS FOR Vdiscus-ALUdiscus-ATION

It was Oscar Wilde who described a cynic as one who “knows the price of thing, but the value of nothing.” He could very well have been describing some ana-lysts and many investors, a surprising number of whom subscribe to the “biggerfool” theory of investing, which argues that the value of an asset is irrelevant as long

every-as there is a “bigger fool” around willing to buy the every-asset from them While this mayprovide a basis for some profits, it is a dangerous game to play, since there is no guar-antee that such an investor will still be around when the time to sell comes

A postulate of sound investing is that an investor does not pay more for an assetthan it’s worth This statement may seem logical and obvious, but it is forgotten andrediscovered at some time in every generation and in every market There are thosewho are disingenuous enough to argue that value is in the eye of the beholder, andthat any price can be justified if there are other investors willing to pay that price.That is patently absurd Perceptions may be all that matter when the asset is apainting or a sculpture, but investors do not (and should not) buy most assets foraesthetic or emotional reasons; financial assets are acquired for the cash flows ex-pected on them Consequently, perceptions of value have to be backed up by reality,which implies that the price that is paid for any asset should reflect the cash flows it

is expected to generate The models of valuation described in this book attempt torelate value to the level and expected growth of these cash flows

There are many areas in valuation where there is room for disagreement, includinghow to estimate true value and how long it will take for prices to adjust to true value

1

But there is one point on which there can be no disagreement: Asset prices cannot bejustified by merely using the argument that there will be other investors around willing

to pay those prices

GENERALITIES ABOUT VALUATIONLike all analytical disciplines, valuation has developed its own set of myths overtime This section examines and debunks some of these myths

Myth 1: Since valuation models are quantitative, valuation

is objective

Valuation is neither the science that some of its proponents make it out to be northe objective search for true value that idealists would like it to become The mod-els that we use in valuation may be quantitative, but the inputs leave plenty ofroom for subjective judgments Thus, the final value that we obtain from thesemodels is colored by the bias that we bring into the process In fact, in many valua-tions, the price gets set first and the valuation follows

The obvious solution is to eliminate all bias before starting on a valuation,but this is easier said than done Given the exposure we have to external informa-tion, analyses, and opinions about a firm, it is unlikely that we embark on mostvaluations without some bias There are two ways of reducing the bias in theprocess The first is to avoid taking strong public positions on the value of a firmbefore the valuation is complete In far too many cases, the decision on whether a

biased analyses The second is to minimize, prior to the valuation, the stake wehave in whether the firm is under- or overvalued

Institutional concerns also play a role in determining the extent of bias in ation For instance, it is an acknowledged fact that equity research analysts are

likely to find firms to be undervalued than overvalued) This can be traced partly tothe difficulties analysts face in obtaining access and collecting information on firmsthat they have issued sell recommendations on, and partly to pressure that they facefrom portfolio managers, some of whom might have large positions in the stock Inrecent years, this trend has been exacerbated by the pressure on equity research an-alysts to deliver investment banking business

When using a valuation done by a third party, the biases of the analyst(s)should be considered before decisions are made on its basis For instance, a self-valuation done by a target firm in a takeover is likely to be positively biased Whilethis does not make the valuation worthless, it suggests that the analysis should beviewed with skepticism

1 This is most visible in takeovers, where the decision to acquire a firm often seems to precede the valuation of the firm It should come as no surprise, therefore, that the analysis almost invariably supports the decision.

2 In most years buy recommendations outnumber sell recommendations by a margin of 10 to

1 In recent years this trend has become even stronger.

Myth 2: A well-researched and well-done valuation

is timeless

The value obtained from any valuation model is affected by firm-specific as well asmarketwide information As a consequence, the value will change as new informa-tion is revealed Given the constant flow of information into financial markets, avaluation done on a firm ages quickly and has to be updated to reflect current in-formation This information may be specific to the firm, affect an entire sector, oralter expectations for all firms in the market

The most common example of firm-specific information is an earnings reportthat contains news not only about a firm’s performance in the most recent time pe-riod but, even more importantly, about the business model that the firm hasadopted The dramatic drop in value of many new economy stocks from 1999 to

2001 can be traced, at least partially, to the realization that these firms had businessmodels that might deliver customers but not earnings, even in the long term Wehave seen social media companies like Linkedin and Zynga received enthusiasticmarket responses in 2010, and it will be interesting to see if history repeats itself

BIAS IN EQUITY RESEARCHThe lines between equity research and salesmanship blur most in periods thatare characterized by “irrational exuberance.” In the late 1990s, the extraordi-nary surge of market values in the companies that comprised the new econ-omy saw a large number of equity research analysts, especially on the sell side,step out of their roles as analysts and become cheerleaders for these stocks.While these analysts might have been well-meaning in their recommendations,the fact that the investment banks that they worked for were leading thecharge on initial public offerings from these firms exposed them to charges ofbias and worse

In 2001, the crash in the market values of new economy stocks and the guished cries of investors who had lost wealth in the crash created a firestorm ofcontroversy There were congressional hearings where legislators demanded toknow what analysts knew about the companies they recommended and whenthe knew it, statements from the Securities and Exchange Commision (SEC)about the need for impartiality in equity research, and decisions taken by someinvestment banks to create at least the appearance of objectivity Investmentbanks even created Chinese walls to separate their investment bankers from theirequity research analysts While that technical separation has helped, the realsource of bias—the intermingling of banking business, trading, and investmentadvice—has not been touched

an-Should there be government regulation of equity research? It would not

be wise, since regulation tends to be heavy-handed and creates side costs thatseem quickly to exceed the benefits A much more effective response can bedelivered by portfolio managers and investors Equity research that creates thepotential for bias should be discounted or, in egregious cases, even ignored.Alternatively, new equity research firms that deliver only investment advicecan meet a need for unbiased valuations

These companies offer tremendous promise because of their large member bases,but they are still in the nascent stages of commercializing that promise.

In some cases, new information can affect the valuations of all firms in a sector.Thus, financial service companies that were valued highly in early 2008, on the as-sumption that the high growth and returns from the prior years would continueinto the future, were valued much less in early 2009, as the banking crisis of 2008laid bare the weaknesses and hidden risks in their businesses

Finally, information about the state of the economy and the level of interestrates affects all valuations in an economy A weakening in the economy can lead to

a reassessment of growth rates across the board, though the effect on earnings islikely to be largest at cyclical firms Similarly, an increase in interest rates will affectall investments, though to varying degrees

When analysts change their valuations, they will undoubtedly be asked to tify them, and in some cases the fact that valuations change over time is viewed as aproblem The best response is the one that John Maynard Keynes gave when hewas criticized for changing his position on a major economic issue: “When the factschange, I change my mind And what do you do, sir?”

jus-Myth 3: A good valuation provides a precise estimate

of value

Even at the end of the most careful and detailed valuation, there will be uncertaintyabout the final numbers, colored as they are by assumptions that we make aboutthe future of the company and the economy It is unrealistic to expect or demandabsolute certainty in valuation, since cash flows and discount rates are estimated.This also means that analysts have to give themselves a reasonable margin for error

in making recommendations on the basis of valuations

The degree of precision in valuations is likely to vary widely across investments.The valuation of a large and mature company with a long financial history will usu-ally be much more precise than the valuation of a young company in a sector in tur-moil If this latter company happens to operate in an emerging market, withadditional disagreement about the future of the market thrown into the mix, the un-certainty is magnified Later in this book, in Chapter 23, we argue that the difficultiesassociated with valuation can be related to where a firm is in the life cycle Maturefirms tend to be easier to value than growth firms, and young start-up companies aremore difficult to value than companies with established products and markets Theproblems are not with the valuation models we use, though, but with the difficulties

we run into in making estimates for the future Many investors and analysts use theuncertainty about the future or the absence of information to justify not doing full-fledged valuations In reality, though, the payoff to valuation is greatest in these firms

Myth 4: The more quantitative a model, the better the valuation

It may seem obvious that making a model more complete and complex should yieldbetter valuations; but it is not necessarily so As models become more complex, thenumber of inputs needed to value a firm tends to increase, bringing with it the po-tential for input errors These problems are compounded when models become so

complex that they become “black boxes” where analysts feed in numbers at oneend and valuations emerge from the other All too often when a valuation fails, theblame gets attached to the model rather than the analyst The refrain becomes “Itwas not my fault The model did it.”

There are three important points that need to be made about all valuation Thefirst is to adhere to the principle of parsimony, which essentially states that you donot use more inputs than you absolutely need to value an asset The second is to rec-ognize that there is a trade-off between the additional benefits of building in moredetail and the estimation costs (and error) with providing the detail The third is to

understand that models don’t value companies—you do In a world where the

prob-lem that you often face in valuations is not too little information but too much, andseparating the information that matters from the information that does not is almost

as important as the valuation models and techniques that you use to value a firm

Myth 5: To make money on valuation, you have to assume thatmarkets are inefficient (but that they will become efficient)

Implicit in the act of valuation is the assumption that markets make mistakes andthat we can find these mistakes, often using information that tens of thousands ofother investors have access to Thus, it seems reasonable to say that those who be-lieve that markets are inefficient should spend their time and resources on valuationwhereas those who believe that markets are efficient should take the market price

as the best estimate of value

This statement, though, does not reflect the internal contradictions in both sitions Those who believe that markets are efficient may still feel that valuation hassomething to contribute, especially when they are called on to value the effect of achange in the way a firm is run or to understand why market prices change overtime Furthermore, it is not clear how markets would become efficient in the firstplace if investors did not attempt to find under- and over-valued stocks and trade

po-on these valuatipo-ons In other words, a precpo-onditipo-on for market efficiency seems to

be the existence of millions of investors who believe that markets are not efficient

On the other hand, those who believe that markets make mistakes and buy orsell stocks on that basis must believe that ultimately markets will correct these mis-takes (i.e., become efficient), because that is how they make their money This istherefore a fairly self-serving definition of inefficiency—markets are inefficient untilyou take a large position in the stock that you believe to be mispriced, but they be-come efficient after you take the position

It is best to approach the issue of market efficiency as a skeptic Recognizethat on the one hand markets make mistakes but, on the other, finding these mis-takes requires a combination of skill and luck This view of markets leads to thefollowing conclusions: First, if something looks too good to be true—a stock looks

obviously undervalued or overvalued—it is probably not true Second, when the

value from an analysis is significantly different from the market price, start offwith the presumption that the market is correct; then you have to convince your-self that this is not the case before you conclude that something is over- or under-valued This higher standard may lead you to be more cautious in followingthrough on valuations, but given the difficulty of beating the market, this is not anundesirable outcome

Myth 6: The product of valuation (i.e., the value) is whatmatters; the process of valuation is not important.

As valuation models are introduced in this book, there is the risk of focusing sively on the outcome (i.e., the value of the company and whether it is under- orovervalued), and missing some valuable insights that can be obtained from theprocess of the valuation The process can tell us a great deal about the determinants

exclu-of value and help us answer some fundamental questions: What is the appropriateprice to pay for high growth? What is a brand name worth? How important is it toimprove returns on projects? What is the effect of profit margins on value? Sincethe process is so informative, even those who believe that markets are efficient (andthat the market price is therefore the best estimate of value) should be able to findsome use for valuation models

THE ROLE OF VALUATIONValuation is useful in a wide range of tasks The role it plays, however, is different

in different arenas The following section lays out the relevance of valuation inportfolio management, in acquisition analysis, and in corporate finance

Valuation in Portfolio Management

The role that valuation plays in portfolio management is determined in large part

by the investment philosophy of the investor Valuation plays a minimal role inportfolio management for a passive investor, whereas it plays a larger role for anactive investor Even among active investors, the nature and the role of valuationare different for different types of active investment Market timers should use val-uation much less than investors who pick stocks for the long term, and their focus

is on market valuation rather than on firm-specific valuation Among stock pickersvaluation plays a central role in portfolio management for fundamental analystsand a peripheral role for technical analysts

true value of the firm can be related to its financial characteristics—its growthprospects, risk profile, and cash flows Any deviation from this true value is a signthat a stock is under- or overvalued It is a long-term investment strategy, and theassumptions underlying it are:

measured

Valuation is the central focus in fundamental analysis Some analysts use counted cash flow models to value firms, while others use multiples such as theprice-earnings and price–book value ratios Since investors using this approachhold a large number of undervalued stocks in their portfolios, their hope is that, onaverage, these portfolios will do better than the market

dis-Franchise Buyers The philosophy of a franchise buyer is best expressed by aninvestor who has been very successful at it—Warren Buffett “We try to stick to

must be relatively simple and stable in character If a business is complex andsubject to constant change, we’re not smart enough to predict future cashflows.” Franchise buyers concentrate on a few businesses they understand welland attempt to acquire undervalued firms Often, as in the case of Mr Buffett,franchise buyers wield influence on the management of these firms and canchange financial and investment policy As a long-term strategy, the underlyingassumptions are that:

correctly

the true value and sometimes at a bargain

Valuation plays a key role in this philosophy, since franchise buyers are tracted to a particular business because they believe it is undervalued They are alsointerested in how much additional value they can create by restructuring the busi-ness and running it right

by any underlying financial variables The information available from trading—price movements, trading volume, short sales, and so forth—gives an indication ofinvestor psychology and future price movements The assumptions here are thatprices move in predictable patterns, that there are not enough marginal investorstaking advantage of these patterns to eliminate them, and that the average investor

in the market is driven more by emotion than by rational analysis

While valuation does not play much of a role in charting, there are ways inwhich an enterprising chartist can incorporate it into analysis For instance, valua-

traders attempt to trade in advance of new information or shortly after it is vealed to financial markets, buying on good news and selling on bad The underly-ing assumption is that these traders can anticipate information announcements andgauge the market reaction to them better than the average investor in the market.For an information trader, the focus is on the relationship between informationand changes in value, rather than on value per se Thus an information trader may

3 This is extracted from Mr Buffett’s letter to stockholders in Berkshire Hathaway for 1993.

4 On a chart, the support line usually refers to a lower bound below which prices are unlikely

to move, and the resistance line refers to the upper bound above which prices are unlikely to venture While these levels are usually estimated using past prices, the range of values ob- tained from a valuation model can be used to determine these levels (i.e., the maximum value will become the resistance line and the minimum value will become the support line).

buy stock in even an overvalued firm if he or she believes that the next informationannouncement is going to cause the price to go up because it contains better thanexpected news If there is a relationship between how undervalued or overvalued acompany is and how its stock price reacts to new information, then valuation couldplay a role in investing for an information trader.

call-ing turns in markets is much greater than the returns from stock pickcall-ing They gue that it is easier to predict market movements than to select stocks and thatthese predictions can be based on factors that are observable

ar-While valuation of individual stocks may not be of any use to a market timer,market timing strategies can use valuation in at least two ways:

1 The overall market itself can be valued and compared to the current level.

2 A valuation model can be used to value all stocks, and the results from the

across all stocks be used to determine whether the market is over- or ued For example, as the number of stocks that are overvalued, using a dis-counted cash flow model, increases relative to the number that are undervalued,there may be reason to believe that the market is overvalued

underval-Efficient Marketers Efficient marketers believe that the market price at any point in timerepresents the best estimate of the true value of the firm, and that any attempt to ex-ploit perceived market efficiencies will cost more than it will make in excess profits.They assume that markets aggregate information quickly and accurately, that marginalinvestors promptly exploit any inefficiencies, and that any inefficiencies in the marketare caused by friction, such as transaction costs, and cannot be arbitraged away.For efficient marketers, valuation is a useful exercise to determine why a stocksells for the price that it does Since the underlying assumption is that the marketprice is the best estimate of the true value of the company, the objective becomesdetermining what assumptions about growth and risk are implied in this marketprice, rather than on finding under- or overvalued firms

Valuation in Acquisition Analysis

Valuation should play a central part in acquisition analysis The bidding firm or dividual has to decide on a fair value for the target firm before making a bid, andthe target firm has to determine a reasonable value for itself before deciding to ac-cept or reject the offer

in-There are also special factors to consider in takeover valuation First, the fects of synergy on the combined value of the two firms (target plus bidding firm)have to be considered before a decision is made on the bid Those who suggest thatsynergy is impossible to value and should not be considered in quantitative termsare wrong Second, the effects on value of changing management and restructuringthe target firm will have to be taken into account in deciding on a fair price This is

ef-of particular concern in hostile takeovers

Finally, there is a significant problem with bias in takeover valuations Targetfirms may be overly optimistic in estimating value, especially when the takeoversare hostile and they are trying to convince their stockholders that the offer prices

are too low Similarly, if the bidding firm has decided for strategic reasons to do anacquisition, there may be strong pressure on the analyst to come up with an esti-mate of value that backs up the acquisition.

Valuation in Corporate Finance

If the objective in corporate finance is the maximization of firm value,5the ship between financial decisions, corporate strategy, and firm value has to be delin-eated In recent years, management consulting firms have started offering companies

the restructuring of these firms

The value of a firm can be directly related to decisions that it makes—on whichprojects it takes, on how it finances them, and on its dividend policy Understand-ing this relationship is key to making value-increasing decisions and to sensiblefinancial restructuring

CONCLUSIONValuation plays a key role in many areas of finance—in corporate finance, in mergersand acquisitions, and in portfolio management The models presented in this bookwill provide a range of tools that analysts in each of these areas will find of use, but thecautionary note sounded in this chapter bears repeating Valuation is not an objectiveexercise, and any preconceptions and biases that an analyst brings to the process willfind their way into the value And even the very best valuation will yield an estimate ofthe value, with a substantial likelihood of you being wrong in your assessment.QUESTIONS AND SHORT PROBLEMS

In the problems following, use an equity risk premium of 5.5 percent if none is specified.

1 The value of an investment is:

a The present value of the cash flows on the investment

b Determined by investor perceptions about it

c Determined by demand and supply

d Often a subjective estimate, colored by the bias of the analyst

e All of the above

2 There are many who claim that value is based on investor perceptions, and ceptions alone, and that cash flows and earnings do not matter This argument isflawed because:

per-a Value is determined by earnings and cash flows, and investor perceptions donot matter

b Perceptions do matter, but they can change Value must be based on thing more substantial

5 Most corporate financial theory is constructed on this premise.

6 The motivation for this has been the fear of hostile takeovers Companies have increasingly turned to “value consultants” to tell them how to restructure, increase value, and avoid be- ing taken over.

c Investors are irrational Therefore, their perceptions should not determinevalue.

d Value is determined by investor perceptions, but it is also determined by theunderlying earnings and cash flows Perceptions must be based on reality

3 You use a valuation model to arrive at a value of $15 for a stock The marketprice of the stock is $25 The difference may be explained by:

a A market inefficiency; the market is overvaluing the stock

b The use of the wrong valuation model to value the stock

c Errors in the inputs to the valuation model

d All of the above

CHAPTER 2

Approaches to Valuation

so-phisticated These models often make very different assumptions, but they doshare some common characteristics and can be classified in broader terms Thereare several advantages to such a classification: It makes it easier to understandwhere individual models fit into the big picture, why they provide different results,and when they have fundamental errors in logic

In general terms, there are three approaches to valuation The first, discountedcash flow (DCF) valuation, relates the value of an asset to the present value (PV) ofexpected future cash flows on that asset The second, relative valuation, estimatesthe value of an asset by looking at the pricing of comparable assets relative to acommon variable such as earnings, cash flows, book value, or sales The third, con-tingent claim valuation, uses option pricing models to measure the value of assetsthat share option characteristics Some of these assets are traded financial assets likewarrants, and some of these options are not traded and are based on real assets,(projects, patents, and oil reserves are examples) The latter are often called real op-tions There can be significant differences in outcomes, depending on which ap-proach is used One of the objectives in this book is to explain the reasons for suchdifferences in value across different models, and to help in choosing the right model

to use for a specific task

DISCOUNTED CASH FLOW VALUATIONWhile discounted cash flow valuation is only one of the three ways of approachingvaluation and most valuations done in the real world are relative valuations, it is thefoundation on which all other valuation approaches are built To do relative valua-tion correctly, we need to understand the fundamentals of discounted cash flow val-uation To apply option pricing models to value assets, we often have to begin with

a discounted cash flow valuation This is why so much of this book focuses on counted cash flow valuation Anyone who understands its fundamentals will be able

dis-to analyze and use the other approaches This section considers the basis of this proach, a philosophical rationale for discounted cash flow valuation, and an exami-nation of the different subapproaches to discounted cash flow valuation

ap-Basis for Discounted Cash Flow Valuation

This approach has its foundation in the present value rule, where the value of anyasset is the present value of expected future cash flows on it

11

where n = Life of the asset

r = Discount rate reflecting the riskiness of the estimated cash flowsThe cash flows will vary from asset to asset—dividends for stocks, coupons (in-terest) and the face value for bonds, and after-tax cash flows for a real project Thediscount rate will be a function of the riskiness of the estimated cash flows, withhigher rates for riskier assets and lower rates for safer projects

You can in fact think of discounted cash flow valuation on a continuum At oneend of the spectrum you have the default-free zero coupon bond, with a guaranteedcash flow in the future Discounting this cash flow at the riskless rate should yield thevalue of the bond A little further up the risk spectrum are corporate bonds where thecash flows take the form of coupons and there is default risk These bonds can be val-ued by discounting the cash flows at an interest rate that reflects the default risk.Moving up the risk ladder, we get to equities, where there are expected cash flowswith substantial uncertainty around the expectations The value here should be thepresent value of the expected cash flows at a discount rate that reflects the uncertainty

Underpinnings of Discounted Cash Flow Valuation

In discounted cash flow valuation, we try to estimate the intrinsic value of an assetbased on its fundamentals What is intrinsic value? For lack of a better definition,consider it the value that would be attached to the firm by an unbiased analyst, whonot only estimates the expected cash flows for the firm correctly, given the informa-tion available at the time, but also attaches the right discount rate to value these cashflows Hopeless though the task of estimating intrinsic value may seem to be, espe-cially when valuing young companies with substantial uncertainty about the future,making the best estimates that you can and persevering to estimate value can still payoff because markets make mistakes While market prices can deviate from intrinsicvalue (estimated based on fundamentals), you are hoping that the two will convergesooner rather than later

Categorizing Discounted Cash Flow Models

There are literally thousands of discounted cash flow models in existence ment banks or consulting firms often claim that their valuation models are better ormore sophisticated than those used by their contemporaries Ultimately, however,discounted cash flow models can vary only a couple of dimensions

The first is to value just the equity stake in the business, while the second is to valuethe entire business, which includes, besides equity, the other claimholders in thefirm (bondholders, preferred stockholders) While both approaches discount ex-pected cash flows, the relevant cash flows and discount rates are different undereach Figure 2.1 captures the essence of the two approaches

r

t t

t 1

t n

=+

=

=

The value of equity is obtained by discounting expected cash flows to equity(i.e., the residual cash flows after meeting all expenses, reinvestment needs, taxobligations, and interest and principal payments) at the cost of equity (i.e., the rate

of return required by equity investors in the firm)

ke= Cost of equityThe dividend discount model is a special case of equity valuation, where the value

of equity is the present value of expected future dividends

The value of the firm is obtained by discounting expected cash flows to thefirm (i.e., the residual cash flows after meeting all operating expenses, reinvest-ment needs, and taxes, but prior to any payments to either debt or equity

Equity Valuation

Cash flows considered are cash flows from assets, after debt payments and after making

reinvestments needed for future growth

Present value is value of just the equity claims on the firm

Growth Assets

Firm Valuation

Cash flows considered are cash flows from assets, prior to any debt payments but after firm has reinvested to create growth assets

Present value is value of the entire firm, and reflects the value of all claims on the firm

holders) at the weighted average cost of capital (WACC), which is the cost of thedifferent components of financing used by the firm, weighted by their marketvalue proportions.

WACC = Weighted average cost of capitalWhile these approaches use different definitions of cash flow and discountrates, they will yield consistent estimates of value for equity as long as you are con-sistent in your assumptions in valuation The key error to avoid is mismatchingcash flows and discount rates, since discounting cash flows to equity at the cost

of capital will lead to an upwardly biased estimate of the value of equity, while counting cash flows to the firm at the cost of equity will yield a downwardly biasedestimate of the value of the firm Illustration 2.1 shows the equivalence of equityand firm valuation

Assume that you are analyzing a company with the following cash flows for the next five years Assume also that the cost of equity is 13.625% and the firm can borrow long term at 10% (The tax rate for the firm is 50%.) The current market value of equity is $1,073, and the value of debt outstanding is $800 Year Cash Flow to Equity Interest (Long-Term) Cash Flow to Firm

The cost of equity is given as an input and is 13.625%, and the after-tax cost of debt is 5%.

Cost of debt = Pretax rate(1 – Tax rate) = 10%(1 – 5) = 5%

Given the market values of equity and debt, we can estimate the cost of capital.

WACC = Cost of equity[Equity/(Debt + Equity)] + Cost of debt[Debt/(Debt + Equity)]

= 13.625%(1,073/1,873) + 5%(800/1,873) = 9.94%

We discount cash flows to equity at the cost of equity:

t 1

t n

=+

=

=

M ETHOD 2: D ISCOUNT C ASH F LOWS TO F IRM AT C OST OF C APITAL TO G ET V ALUE OF F IRM

PV of firm = 90/1.0994 + 100/1.0994 2 + 108/1.0994 3 + 116.2/1.0994 4

+ (123.49 + $2,363)/1.0994 5 = $1,873

PV of equity = PV of firm – Market value of debt

= $1,873 – $800 = $1,073 Note that the value of equity is $1,073 under both approaches It is easy to make the mistake of discounting cash flows to equity at the cost of capital or the cash flows to the firm at the cost of equity.

its assets, using either equity or debt What are the effects of using debt on value?

On the plus side, the tax deductibility of interest expenses provides a tax subsidy

or benefit to the firm, which increases with the tax rate faced by the firm on its come On the minus side, debt does increase the likelihood that the firm will default

in-on its commitments and be forced into bankruptcy The net effect can be positive,neutral or negative In the cost of capital approach, we capture the effects of debt inthe discount rate:

+Pretax cost of debt (1 −Tax rate) (Proportion of debt used to fund business)The cash flows discounted are predebt cash flows and do not include any of the taxbenefits of debt (since that would be double counting)

In a variation, called the adjusted present value (APV) approach, we separate

the effects on value of debt financing from the value of the assets of a business.Thus, we start by valuing the business as if it were all equity funded and assess the

effect of debt separately, by first valuing the tax benefits from the debt and thensubtracting out the expected bankruptcy costs

While the two approaches take different tacks to evaluating the value added or stroyed by debt, they will provide the same estimate of value, if we are consistent inour assumptions about cash flows and risk In chapter 15, we will return to exam-ine these approaches in more detail

flow model values an asset by estimating the present value of all cash flows ated by that asset at the appropriate discount rate In excess return (and excess cashflow) models, only cash flows earned in excess of the required return are viewed asvalue creating, and the present value of these excess cash flows can be added to theamount invested in the asset to estimate its value To illustrate, assume that youhave an asset in which you invested $100 million and that you expect to generate

gener-$12 million in after-tax cash flows in perpetuity Assume further that the cost ofcapital on this investment is 10 percent With a total cash flow model, the value ofthis asset can be estimated as follows:

Value of asset = $12 million /.1 = $120 million

With an excess return model, we would first compute the excess return made onthis asset:

A SIMPLE TEST OF CASH FLOWSThere is a simple test that can be employed to determine whether the cashflows being used in a valuation are cash flows to equity or cash flows to thefirm If the cash flows that are being discounted are after interest expenses(and principal payments), they are cash flows to equity and the discount rateused should be the cost of equity If the cash flows that are discounted are be-fore interest expenses and principal payments, they are usually cash flows tothe firm Needless to say, there are other items that need to be consideredwhen estimating these cash flows, and they are considered in extensive detail

in the coming chapters

We then add the present value of these excess returns to the investment in the asset:Value of asset = Present value of excess return + Investment in the asset

= $2 million /.1 + $100 million = $120 millionNote that the answers in the two approaches are equivalent Why, then,would we want to use an excess return model? By focusing on excess returns,this model brings home the point that it is not earnings per se that create value,but earnings in excess of a required return Chapter 32 considers special versions

of these excess return models As in this simple example, with consistent sumptions, total cash flow and excess return models are equivalent

as-Applicability and Limitations of Discounted Cash Flow Valuation

Discounted cash flow valuation is based on expected future cash flows and count rates Given these estimation requirements, this approach is easiest to usefor assets (firms) whose cash flows are currently positive and can be estimatedwith some reliability for future periods, and where a proxy for risk that can beused to obtain discount rates is available The further we get from this idealizedsetting, the more difficult (and more useful) discounted cash flow valuation be-comes Here are some scenarios where discounted cash flow valuation might runinto trouble and need to be adapted

and expects to lose money for some time in the future For these firms, ing future cash flows is difficult to do, since there is a strong probability of bank-ruptcy For firms that are expected to fail, discounted cash flow valuation doesnot work very well, since the method values the firm as a going concern provid-ing positive cash flows to its investors Even for firms that are expected to sur-vive, cash flows will have to be estimated until they turn positive, since obtaining

for the firm We will examine these firms in more detail in chapters 22 and 30

economy—rising during economic booms and falling during recessions If counted cash flow valuation is used on these firms, expected future cash flows areusually smoothed out, unless the analyst wants to undertake the onerous task ofpredicting the timing and duration of economic recessions and recoveries In thedepths of a recession many cyclical firms look like troubled firms, with negativeearnings and cash flows Estimating future cash flows then becomes entangled withanalyst predictions about when the economy will turn and how strong the upturnwill be, with more optimistic analysts arriving at higher estimates of value This is

1 The protection of limited liability should ensure that no stock will sell for less than zero The price of such a stock can never be negative.

unavoidable, but the economic biases of the analysts have to be taken into accountbefore using these valuations.

all assets that produce cash flows If a firm has assets that are unutilized (and hence

do not produce any cash flows), the value of these assets will not be reflected in thevalue obtained from discounting expected future cash flows The same caveat ap-plies, in lesser degree, to underutilized assets, since their value will be understated

in discounted cash flow valuation While this is a problem, it is not

value obtained from discounted cash flow valuation Alternatively, the assets can bevalued as though they are used optimally

licenses that do not produce any current cash flows and are not expected to duce cash flows in the near future, but are valuable nevertheless If this is the case,the value obtained from discounting expected cash flows to the firm will understatethe true value of the firm Again, the problem can be overcome, by valuing these as-sets in the open market or by using option pricing models, and then adding thevalue obtained from discounted cash flow valuation Chapter 28 examines the use

pro-of option pricing models to value patents

some of their assets, acquire other assets, and change their capital structure anddividend policy Some of them also change their ownership structure (going frompublicly traded to private status and vice versa) and management compensationschemes Each of these changes makes estimating future cash flows more difficultand affects the riskiness of the firm Using historical data for such firms can give amisleading picture of the firm’s value However, these firms can be valued, even inthe light of the major changes in investment and financing policy, if future cashflows reflect the expected effects of these changes and the discount rate is adjusted

to reflect the new business and financial risk in the firm Chapter 31 takes a closerlook at how value can be altered by changing the way a business is run

ac-quisitions that need to be taken into account when using discounted cash flow uation models to value target firms The first is the thorny one of whether there issynergy in the merger and how its value can be estimated To do so will require as-sumptions about the form the synergy will take and its effect on cash flows Thesecond, especially in hostile takeovers, is the effect of changing management oncash flows and risk Again, the effect of the change can and should be incorpo-rated into the estimates of future cash flows and discount rates and hence intovalue Chapter 25 looks at the value of synergy and control in acquisitions

val-2 If these assets are traded on external markets, the market prices of these assets can be used

in the valuation If not, the cash flows can be projected, assuming full utilization of assets, and the value can be estimated.

Private Firms The biggest problem in using discounted cash flow valuation els to value private firms is the measurement of risk (to use in estimating discountrates), since most risk/return models require that risk parameters be estimated fromhistorical prices on the asset being analyzed and make assumptions about the pro-files of investors in the firm that may not fit private businesses One solution is tolook at the riskiness of comparable firms that are publicly traded The other is torelate the measure of risk to accounting variables, which are available for the pri-vate firm Chapter 24 looks at adaptations to valuation models that are needed tovalue private businesses.

mod-The point is not that discounted cash flow valuation cannot be done in these cases,but that we have to be flexible enough to adapt our models The fact is that valua-tion is simple for firms with well-defined assets that generate cash flows that can beeasily forecasted The real challenge in valuation is to extend the valuation frame-work to cover firms that vary to some extent or the other from this idealized frame-work Much of this book is spent considering how to value such firms

RELATIVE VALUATIONWhile we tend to focus most on discounted cash flow valuation when discussingvaluation, the reality is that most valuations are relative valuations The values ofmost assets, from the house you buy to the stocks you invest in, are based on howsimilar assets are priced in the marketplace This section begins with a basis for rel-ative valuation, moves on to consider the underpinnings of the model, and thenconsiders common variants within relative valuation

Basis for Relative Valuation

In relative valuation, the value of an asset is derived from the pricing of ble assets, standardized using a common variable such as earnings, cash flows,book value, or revenues One illustration of this approach is the use of an industry-average price-earnings ratio to value a firm, the assumption being that the otherfirms in the industry are comparable to the firm being valued and that the market,

compara-on average, prices these firms correctly Another multiple in wide use is theprice–book value ratio, with firms selling at a discount on book value relative tocomparable firms being considered undervalued Revenue multiple are also used tovalue firms, with the average price-sales ratios of firms with similar characteristicsbeing used for comparison While these three multiples are among the most widelyused, there are others that also play a role in analysis—EV to EBITDA, EV to in-vested capital, and market value to replacement value (Tobin’s Q), to name a few

Underpinnings of Relative Valuation

Unlike discounted cash flow valuation, which is a search for intrinsic value, tive valuation relies much more on the market being right In other words, we as-sume that the market is correct in the way it prices stocks on average, but that itmakes errors on the pricing of individual stocks We also assume that a compari-son of multiples will allow us to identify these errors, and that these errors will becorrected over time

The assumption that markets correct their mistakes over time is common toboth discounted cash flow and relative valuation, but those who use multiplesand comparables to pick stocks argue, with some basis, that errors made in pric-ing individual stocks in a sector are more noticeable and more likely to be cor-rected quickly For instance, they would argue that a software firm that trades at

a price-earnings ratio of 10 when the rest of the sector trades at 25 times earnings

is clearly undervalued and that the correction toward the sector average shouldoccur sooner rather than later Proponents of discounted cash flow valuationwould counter that this is small consolation if the entire sector is overpriced by

50 percent

Categorizing Relative Valuation Models

Analysts and investors are endlessly inventive when it comes to using relative ation Some compare multiples across companies, while other compare the multiple

valu-of a company to the multiples it used to trade at in the past While most relativevaluations are based on the pricing of comparable assets at the same time, there aresome relative valuations that are based on fundamentals

of a firm is determined by its expected cash flows Other things remaining equal,higher cash flows, lower risk, and higher growth should yield higher value Someanalysts who use multiples go back to these discounted cash flow models to ex-tract multiples Other analysts compare multiples across firms or time and makeexplicit or implicit assumptions about how firms are similar or vary on funda-mentals

Using Fundamentals The first approach relates multiples to fundamentals about

the firm being valued—growth rates in earnings and cash flows, reinvestmentand risk This approach to estimating multiples is equivalent to using discountedcash flow models, requiring the same information and yielding the same results.Its primary advantage is that it shows the relationship between multiples andfirm characteristics, and allows us to explore how multiples change as thesecharacteristics change For instance, what will be the effect of changing profitmargins on the price-sales ratio? What will happen to price-earnings ratios asgrowth rates decrease? What is the relationship between price–book value ratiosand return on equity?

Using Comparables The more common approach to using multiples is to

com-pare how a firm is valued with how similar firms are priced by the market or, insome cases, with how the firm was valued in prior periods As we see in the laterchapters, finding similar and comparable firms is often a challenge, and frequently

we have to accept firms that are different from the firm being valued on one sion or the other When this is the case, we have to either explicitly or implicitlycontrol for differences across firms on growth, risk, and cash flow measures Inpractice, controlling for these variables can range from the naive (using industry av-erages) to the sophisticated (multivariate regression models where the relevant vari-ables are identified and controlled for)

dimen-Cross-Sectional versus Time Series Comparisons In most cases, analysts pricestocks on a relative basis, by comparing the multiples they are trading at to themultiples at which other firms in the same business are trading at contemporane-ously In some cases, however, especially for mature firms with long histories, thecomparison is done across time.

Cross-Sectional Comparisons When we compare the price-earnings ratio of a

software firm to the average price-earnings ratio of other software firms, we aredoing relative valuation and we are making cross-sectional comparisons The con-clusions can vary depending on our assumptions about the firm being valued andthe comparable firms For instance, if we assume that the firm we are valuing issimilar to the average firm in the industry, we would conclude that it is cheap if ittrades at a multiple that is lower than the average multiple If, however, we assumethat the firm being valued is riskier than the average firm in the industry, we mightconclude that the firm should trade at a lower multiple than other firms in thebusiness In short, you cannot compare firms without making assumptions abouttheir fundamentals

Comparisons across Time If you have a mature firm with a long history, you can

compare the multiple it trades at today to the multiple it used to trade at in thepast Thus, Ford Motor Company may be viewed as cheap because it trades at sixtimes earnings, if it has historically traded at 10 times earnings To make this com-parison, however, you have to assume that your firm’s fundamentals have notchanged over time For instance, you would expect a high-growth firm’s price-earnings ratio to drop over time and its expected growth rate to decrease as it be-comes larger Comparing multiples across time can also be complicated by changes

in interest rates and the behavior of the overall market For instance, as interestrates fall below historical norms and the overall market increases in value, youwould expect most companies to trade at much higher multiples of earnings andbook value than they have historically

Applicability and Limitations of Multiples

The allure of multiples is that they are simple and easy to relate to They can beused to obtain estimates of value quickly for firms and assets, and are particularlyuseful when a large number of comparable firms are traded on financial markets,and the market is, on average, pricing these firms correctly They tend to be moredifficult to use to value unique firms with no obvious comparables, with little or norevenues, and with negative earnings

By the same token, multiples are also easy to misuse and manipulate, cially when comparable firms are used Given that no two firms are exactly alike

espe-in terms of risk and growth, the defespe-inition of comparable firms is a subjectiveone Consequently, a biased analyst can choose a group of comparable firms toconfirm his or her biases about a firm’s value Illustration 2.2 shows an example.While this potential for bias exists with discounted cash flow valuation as well,the analyst in DCF valuation is forced to be much more explicit about the as-sumptions that determine the final value With multiples, these assumptions areoften left unstated