Damodaran Book on Investment Valuation, 2nd Edition
INVESTMENT VALUATION: SECOND EDITION I will be putting my entire second edition online, while the book goes through the printing process – it will be available at the end of the year.This may seem like a bit of a free lunch, and I guess it is.I hope, though, that you can do me a favor as you go through the manuscript.
If you find any mistakes – mathematical or grammatical – could you please let me know? It would help me ensure that the typos do not find their way into the final version.
Chapter 1: Introduction to Valuation Chapter 2: Approaches to Valuation Chapter 3: Understanding Financial Statements Chapter 4: The Basics of Risk Chapter 5: Option Pricing Theory and Models Chapter 6: Market Efficiency: Theory and Models Chapter 7: Riskless Rates and Risk Premiums Chapter 8: Estimating Risk Parameters and Costs of Financing Chapter 9: Measuring Earnings Chapter 10: From Earnings to Cash Flows Chapter 11: Estimating Growth Chapter 12: Closure in Valuation: Estimating Terminal Value Chapter 13: Dividend Discount Models Chapter 14: Free Cashflow to Equity Models Chapter 15: Firm Valuation: Cost of Capital and APV Approaches
Chapter 16: Estimating Equity Value Per Share Chapter 17: Fundamental Principles of Relative Valuation Chapter 18: Earnings Multiples Chapter 19: Book Value Multiples Chapter 20: Revenue and Sector-Specific Multiples Chapter 21: Valuing Financial Service Firms Chapter 22: Valuing Firms with Negative Earnings Chapter 23: Valuing Young and Start-up Firms Chapter 24: Valuing Private Firms Chapter 25: Acquisitions and Takeovers Chapter 26: Valuing Real Estate Chapter 27: Valuing Other Assets Chapter 28: The Option to Delay and Valuation Implications Chapter 29: The Option to Expand and Abandon: Valuation Implications Chapter 30: Valuing Equity in Distressed Firms Chapter 31: Value Enhancement: A Discounted Cashflow Framework Chapter 32: Value Enhancement: EVA, CFROI and Other Tools Chapter 33: Valuing Bonds Chapter 34: Valuing Forward and Futures Contracts Chapter 35: Overview and Conclusions References 1 CHAPTER 1 INTRODUCTION TO VALUATION Every asset, financial as well as real, has a value. The key to successfully nvesting in and managing these assets lies in understanding not only what the value is but also the sources of the value. Any asset can be valued, but some assets are easier to value than others and the details of valuation will vary from case to case. Thus, the valuation of a share of a real estate property will require different information and follow a different format than the valuation of a publicly traded stock. What is surprising, however, is not the differences in valuation techniques across assets, but the degree of similarity in basic principles. There is undeniably uncertainty associated with valuation. Often that uncertainty comes from the asset being valued, though the valuation model may add to that uncertainty.
This chapter lays out a philosophical basis for valuation, together with a discussion of how valuation is or can be used in a variety of frameworks, from portfolio management to corporate finance. A philosophical basis for valuation It was Oscar Wilde who described a cynic as one who “knows the price of everything, but the value of nothing”. He could very well have been describing some equity research analysts and many investors, a surprising number of whom subscribe to the ‘bigger fool’ theory of investing, which argues that the value of an asset is irrelevant as long as there is a ‘bigger fool’ willing to buy the asset from them. While this may provide a basis for some profits, it is a dangerous game to play, since there is no guarantee 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 asset than its worth. This statement may seem logical and obvious, but it is forgotten and rediscovered at some time in every generation and in every market. There are those who are disingenuous enough to argue that value is in the eyes of the beholder, and that 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 a painting or a sculpture, but investors do not (and should not) buy most assets for aesthetic or emotional reasons; 2 financial assets are acquired for the cashflows expected on them.
Consequently, perceptions of value have to be backed up by reality, which implies that the price paid for any asset should reflect the cashflows that it is expected to generate. The models of valuation described in this book attempt to relate value to the level and expected growth in these cashflows. There are many areas in valuation where there is room for disagreement, including how to estimate true value and how long it will take for prices to adjust to true value. But there is one point on which there can be no disagreement. Asset prices cannot be justified by merely using the argument that there will be other investors around willing to pay a higher price in the future.
Generalities about Valuation Like all analytical disciplines, valuation has developed its own set of myths over time. 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 nor the objective search for the true value that idealists would like it to become. The models that we use in valuation may be quantitative, but the inputs leave plenty of room for subjective judgments. Thus, the final value that we obtain from these models is colored by the bias that we bring into the process. In fact, in many valuations, 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 information, analyses and opinions about a firm, it is unlikely that we embark on most valuations without some bias.There are two ways of reducing the bias in the process. The first is to avoid taking strong public positions on the value of a firm before the valuation is complete. In far too many cases, the decision on whether a firm is under or over valued precedes the actual 3 valuation1, leading to seriously biased analyses. The second is to minimize the stake we have in whether the firm is under or over valued, prior to the valuation.
Institutional concerns also play a role in determining the extent of bias in valuation. For instance, it is an acknowledged fact that equity research analysts are more likely to issue buy rather than sell recommendations,2 i. e. , that they are more likely to find firms to be undervalued than overvalued. This can be traced partly to the difficulties they face in obtaining access and collecting information on firms that they have issued sell recommendations and to the pressure that they face from portfolio managers, some of whom might have large positions in the stock. In recent years, this trend has been exacerbated by the pressure on equity research analysts to deliver investment banking business.
When using a valuation done by a third party, the biases of the analyst(s) doing the valuation 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. While this does not make the valuation worthless, it suggests that the analysis should be viewed with skepticism. The Biases in Equity Research The lines between equity research and salesmanship blur most in periods that are characterized by “irrational exuberance”. In the late 1990s, the extraordinary surge of market values in the companies that comprised the new economy 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 the charge on new initial public offerings from these firms exposed them to charges of bias and worse. 1This 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. 2In most years, buy recommendations outnumber sell recommendations by a margin of ten to one. In recent years, this trend has become even stronger. 4 In 2001, the crash in the market values of new economy stocks and the anguished cries of investors who had lost wealth in the crash created a firestorm of controversy.
There were congressional hearing where legislators demanded to know what analysts knew about the companies they recommended and when they knew it, statements from the SEC about the need for impartiality in equity research and decisions taken by some investment banking to create at least the appearance of objectivity. At the time this book went to press, both Merrill Lynch and CSFB had decided that their equity research analysts could no longer hold stock in companies that they covered. Unfortunately, the real source of bias – the intermingling of investment banking business and investment advice – was left untouched. Should there be government regulation of equity research?
We do not believe that it would be wise, since regulation tends to be heavy handed and creates side costs that seem to quickly exceed the benefits. A much more effective response can be delivered by portfolio managers and investors. The equity research of firms that create the potential for bias should be discounted or, in egregious cases, even ignored. 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 as market-wide information. As a consequence, the value will change as new information is revealed. Given the constant flow of information into financial markets, a valuation done on a firm ages quickly, and has to be updated to reflect current information.
This information may be specific to the firm, affect an entire sector or alter expectations for all firms in the market. The most common example of firm-specific information is an earnings report that contains news not only about a firm’s performance in the most recent time period but, more importantly, about the business model that the firm has adopted. 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 business models that could deliver customers but not earnings, even in the long term. In some cases, new information can affect the valuations of all firms in a sector.
Thus, pharmaceutical companies that were valued highly in early 1992, on the assumption that the high growth from the eighties would continue into the future, were valued much less in early 1993, as the prospects of 5 health reform and price controls dimmed future prospects. With the benefit of hindsight, the valuations of these companies (and the analyst recommendations) made in 1992 can be criticized, but they were reasonable, given the information available at that time. Finally, information about the state of the economy and the level of interest rates affect 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 are likely to be largest at cyclical firms.
Similarly, an increase in interest rates will affect all investments, though to varying degrees. When analysts change their valuations, they will undoubtedly be asked to justify them. In some cases, the fact that valuations change over time is viewed as a problem. The best response may be the one that Lord Keynes gave when he was criticized for changing his position on a major economic issue: “When the facts change, I change my mind. And what do you do, sir? ” 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 uncertainty about the final numbers, colored as they are by the assumptions that we make about the future of the company and the economy.
It is unrealistic to expect or demand absolute certainty in valuation, since cash flows and discount rates are estimated with error. This also means that you have to give yourself 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 usually be much more precise than the valuation of a young company, in a sector that is in turmoil. If this company happens to operate in an emerging market, with additional disagreement about the future of the market thrown into the mix, the uncertainty is magnified.
Later in this book, we will argue that the difficulties associated with valuation can be related to where a firm is in the life cycle. Mature firms tend to be easier to value than growth firms, and young start-up companies are more difficult to value than companies with established produces and markets. The problems are not with the valuation models we use, though, but with the difficulties we run into in making estimates for the future. 6 Many investors and analysts use the uncertainty 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 yield better valuations, but it is not necessarily so. As models become more complex, the number of inputs needed to value a firm increases, bringing with it the potential for input errors. These problems are compounded when models become so complex that they become ‘black boxes’ where analysts feed in numbers into one end and valuations emerge from the other. All too often the blame gets attached to the model rather than the analyst when a valuation fails. The refrain becomes “It was not my fault. The model did it. ” There are three oints we will emphasize in this book on all valuation. The first is the principle of parsimony, which essentially states that you do not use more inputs than you absolutely need to value an asset. The second is that the there is a trade off between the benefits of building in more detail and the estimation costs (and error) with providing the detail. The third is that the models don’t value companies: you do. In a world where the problem that we often face in valuations is not too little information but too much, separating 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 that markets are inefficient Implicit often in the act of valuation is the assumption that markets make mistakes and that we can find these mistakes, often using information that tens of thousands of other investors can access. Thus, the argument, that those who believe that markets are inefficient should spend their time and resources on valuation whereas those who believe that markets are efficient should take the market price as the best estimate of value, seems to be reasonable. This statement, though, does not reflect the internal contradictions in both positions. Those who believe that markets are efficient may still feel that valuation has something to contribute, especially when they are called upon to value the effect of a change in the way a firm is run or to understand why market prices change over time. Furthermore, it is not clear how markets would become efficient in the first place, if investors did not attempt to find under and over valued stocks and trade on these valuations. In other words, a pre-condition for market efficiency seems to be the existence of millions of investors who believe that markets are not. On the other hand, those who believe that markets make mistakes and buy or sell stocks on that basis ultimately must believe that markets will correct these mistakes, i. e. become efficient, because that is how they make their money. This is a fairly self-serving definition of inefficiency – markets are inefficient until you take a large position in the stock that you believe to be mispriced but they become efficient after you take the position. We approach the issue of market efficiency as wary skeptics.
On the one hand, we believe that markets make mistakes but, on the other, finding these mistakes requires a combination of skill and luck. This view of markets leads us to the following conclusions. First, if something looks too good to be true – a stock looks obviously under valued or over valued – it is probably not true. Second, when the value from an analysis is significantly different from the market price, we start off with the presumption that the market is correct and we have to convince ourselves that this is not the case before we conclude that something is over or under valued. This higher standard may lead us to be more cautious in following through on valuations.
Given the historic difficulty of beating the market, this is not an undesirable outcome. Myth 6: The product of valuation (i. e. , the value) is what matters; The process of valuation is not important. As valuation models are introduced in this book, there is the risk of focusing exclusively on the outcome, i. e. , the value of the company, and whether it is under or over valued, and missing some valuable insights that can be obtained from the process of the valuation. The process can tell us a great deal about the determinants of value and help us answer some fundamental questions — What is the appropriate price to pay for high growth? What is a brand name worth? How important is it to improve returns on projects?
What is the effect of profit margins on value? Since the process is so 8 informative, even those who believe that markets are efficient (and that the market price is therefore the best estimate of value) should be able to find some use for valuation models. The Role of Valuation Valuation 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 in portfolio management, acquisition analysis and corporate finance. 1. Valuation and 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 in portfolio management for a passive investor, whereas it plays a larger role for an active investor. Even among active investors, the nature and the role of valuation is different for different types of active investment. Market timers use valuation much less than investors who pick stocks, and the focus is on market valuation rather than on firm-specific valuation. Among security selectors, valuation plays a central role in portfolio management for fundamental analysts and a peripheral role for technical analysts. The following sub-section describes, in broad terms, different investment philosophies and the role played by valuation in each. 1.
Fundamental Analysts: The underlying theme in fundamental analysis is that the true value of the firm can be related to its financial characteristics — its growth prospects, risk profile and cashflows. Any deviation from this true value is a sign that a stock is under or overvalued. It is a long term investment strategy, and the assumptions underlying it are: (a) the relationship between value and the underlying financial factors can be measured. (b) the relationship is stable over time. (c) deviations from the relationship are corrected in a reasonable time period. Valuation is the central focus in fundamental analysis. Some analysts use discounted cashflow models to value firms, while others use multiples such as the priceearnings and price-book value ratios.
Since investors using this approach hold a large number of ‘undervalued’ stocks in their portfolios, their hope is that, on average, these portfolios will do better than the market. 9 2. Franchise Buyer: The philosophy of a franchise buyer is best expressed by an investor who has been very successful at it — Warren Buffett. “We try to stick to businesses we believe we understand,” Mr. Buffett writes3. “That means they must be relatively simple and stable in character. If a business is complex and subject to constant change, we’re not smart enough to predict future cash flows. ” Franchise buyers concentrate on a few businesses they understand well, and attempt to acquire undervalued firms.
Often, as in the case of Mr. Buffett, franchise buyers wield influence on the management of these firms and can change financial and investment policy. As a long term strategy, the underlying assumptions are that : (a) Investors who understand a business well are in a better position to value it correctly. (b) These undervalued businesses can be acquired without driving the price above the true value. Valuation plays a key role in this philosophy, since franchise buyers are attracted to a particular business because they believe it is undervalued. They are also interested in how much additional value they can create by restructuring the business and running it right. 3.
Chartists: Chartists believe that prices are driven as much by investor psychology as by any underlying financial variables. The information available from trading — price movements, trading volume, short sales, etc. — gives an indication of investor psychology and future price movements. The assumptions here are that prices move in predictable patterns, that there are not enough marginal investors taking advantage of these patterns to eliminate them, and that the average investor in the market is driven more by emotion rather than by rational analysis. While valuation does not play much of a role in charting, there are ways in which an enterprising chartist can incorporate it into analysis.
For instance, valuation can be used to determine support and resistance lines4 on price charts. 3This is extracted from Mr. Buffett’s letter to stockholders in Berkshire Hathaway for 1993. 4On 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 10 4. Information Traders: Prices move on information about the firm. Information traders attempt to trade in advance of new information or shortly after it is revealed to financial markets, buying on good news and selling on bad.
The underlying assumption is that these traders can anticipate information announcements and gauge the market reaction to them better than the average investor in the market. For an information trader, the focus is on the relationship between information and changes in value, rather than on value, per se. Thus an information trader may buy an ‘overvalued’ firm if he believes that the next information announcement is going to cause the price to go up, because it contains better than expected news. If there is a relationship between how undervalued or overvalued a company is and how its stock price reacts to new information, then valuation could play a role in investing for an information trader. 5.
Market Timers: Market timers note, with some legitimacy, that the payoff to calling turns in markets is much greater than the returns from stock picking. They argue that it is easier to predict market movements than to select stocks and that these predictions can be based upon factors that are observable. 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: (a) The overall market itself can be valued and compared to the current level. (b) A valuation model can be used to value all stocks, and the results from the crosssection can be used to determine whether the market is over or under valued.
For example, as the number of stocks that are overvalued, using the dividend discount model, increases relative to the number that are undervalued, there may be reason to believe that the market is overvalued. 6. Efficient Marketers: Efficient marketers believe that the market price at any point in time represents the best estimate of the true value of the firm, and that any attempt to exploit perceived market efficiencies will cost more than it will make in excess profits. They assume that markets aggregate information quickly and accurately, that marginal of values obtained from a valuation model can be used to determine these levels, i. e. the maximum value will become the resistance level and the minimum value will become the support line. 11 investors promptly exploit any inefficiencies and that any inefficiencies in the market are caused by friction, such as transactions costs, and cannot be arbitraged away. For efficient marketers, valuation is a useful exercise to determine why a stock sells for the price that it does. Since the underlying assumption is that the market price is the best estimate of the true value of the company, the objective becomes determining what assumptions about growth and risk are implied in this market price, rather than on finding under or over valued firms. . Valuation in Acquisition Analysis Valuation should play a central part of acquisition analysis. The bidding firm or individual has to decide on a fair value for the target firm before making a bid, and the target firm has to determine a reasonable value for itself before deciding to accept or reject the offer. There are also special factors to consider in takeover valuation. First, the effects 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 that synergy is impossible to value and should not be considered in quantitative terms are wrong.
Second, the effects on value, of changing management and restructuring the target firm, will have to be taken into account in deciding on a fair price. This is of particular concern in hostile takeovers. Finally, there is a significant problem with bias in takeover valuations. Target firms may be over-optimistic in estimating value, especially when the takeover is hostile, and they are trying to convince their stockholders that the offer price is too low. Similarly, if the bidding firm has decided, for strategic reasons, to do an acquisition, there may be strong pressure on the analyst to come up with an estimate of value that backs up the acquisition. 3.
Valuation in Corporate Finance If the objective in corporate finance is the maximization of firm value5, the relationship among financial decisions, corporate strategy and firm value has to be 5Most corporate financial theory is constructed on this premise. 12 delineated. In recent years, management consulting firms have started offered companies advice on how to increase value6. Their suggestions have often provided the basis for the restructuring of these firms. The value of a firm can be directly related to decisions that it makes — on which projects it takes, on how it finances them and on its dividend policy. Understanding this relationship is key to making value-increasing decisions and to sensible financial restructuring.
Conclusion Valuation plays a key role in many areas of finance — in corporate finance, mergers and acquisitions and portfolio management. The models presented in this book will provide a range of tools that analysts in each of these areas will find useful, but the cautionary note sounded in this chapter bears repeating. Valuation is not an objective exercise; and any preconceptions and biases that an analyst brings to the process will find its way into the value. 6The 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 being taken over. 13 Questions and Short Problems: Chapter 1 1. The value of an investment is A. he 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 upon investor perceptions, and perceptions alone, and that cash flows and earnings do not matter. This argument is flawed because A. value is determined by earnings and cash flows, and investor perceptions do not matter. B. perceptions do matter, but they can change. Value must be based upon something more stable. C. investors are irrational. Therefore, their perceptions should not determine value. D. alue is determined by investor perceptions, but it is also determined by the underlying earnings and cash flows. Perceptions must be based upon reality. 3. You use a valuation model to arrive at a value of $15 for a stock. The market price 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. none of the above E. either A, B, or C. 0 CHAPTER 2 APPROACHES TO VALUATION Analysts use a wide range of models to value assets in practice, ranging from the simple to the sophisticated.
These models often make very different assumptions about pricing, but they do share some common characteristics and can be classified in broader terms. There are several advantages to such a classification — it makes it easier to understand where 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, discounted cashflow valuation, relates the value of an asset to the present value of expected future cashflows on that asset. The second, relative valuation, estimates the value of an asset by looking at the pricing of ‘comparable’ assets relative to a common ariable such as earnings, cashflows, book value or sales. The third, contingent claim valuation, uses option pricing models to measure the value of assets that share option characteristics. Some of these assets are traded financial assets like warrants, 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 options. There can be significant differences in outcomes, depending upon which approach is used. One of the objectives in this book is to explain the reasons for such differences in value across different models and to help in choosing the right model to use for a specific task.
Discounted Cashflow Valuation While discounted cash flow valuation is one of the three ways of approaching valuation and most valuations done in the real world are relative valuations, we will argue that it is the foundation on which all other valuation approaches are built. To do relative valuation correctly, we need to understand the fundamentals of discounted cash flow valuation. 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 discounted cash flow valuation. Anyone who understands its fundamentals will be able to analyze and use the other approaches. In this section, we will consider the basis of this approach, a philosophical rationale for discounted cash flow valuation and an examination of the different sub-approaches to discounted cash flow valuation. Basis for Discounted Cashflow Valuation This approach has its foundation in the present value rule, where the value of any asset is the present value of expected future cashflows that the asset generates. t=n t ? (1+r) t t=1 Value = where, CF n = Life of the asset CFt = Cashflow in period t r = Discount rate reflecting the riskiness of the estimated cashflows The cashflows will vary from asset to asset — dividends for stocks, coupons (interest) and the face value for bonds and after-tax cashflows for a real project.
The discount rate will be a function of the riskiness of the estimated cashflows, with higher rates for riskier assets and lower rates for safer projects. You can in fact think of discounted cash flow valuation on a continuum. At one end of the spectrum, you have the default-free zero coupon bond, with a guaranteed cash flow in the future. Discounting this cash flow at the riskless rate should yield the value of the bond. A little further up the spectrum are corporate bonds where the cash flows take the form of coupons and there is default risk. These bonds can be valued by discounting the expected 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 flows with substantial uncertainty around the expectation. The value here should be the present value of the expected cash flows at a discount rate that reflects the uncertainty. The Underpinnings of Discounted Cashflow Valuation In discounted cash flow valuation, we try to estimate the intrinsic value of an asset based upon 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 all-knowing analyst, who not only knows the expected cash flows for the firm but also attaches the right discount rate(s) to these cash flows and values them with absolute precision. Hopeless though the task of estimating intrinsic value may seem to be, especially when valuing young companies with substantial uncertainty about the future, we believe that these estimates can be different from the market prices attached to these companies. In other words, markets make mistakes. Does that mean we believe that markets are inefficient? Not quite. While we assume that prices can deviate from intrinsic value, estimated based upon fundamentals, we also assume that the two will converge sooner rather than latter. Categorizing Discounted Cash Flow Models There are literally thousands of discounted cash flow models in existence.
Oftentimes, we hear claims made by investment banks or consulting firms that their valuation models are better or more sophisticated than those used by their contemporaries. Ultimately, however, discounted cash flow models can vary only a couple of dimensions and we will examine these variations in this section. I. Equity Valuation, Firm Valuation and Adjusted Present Value (APV) Valuation There are three paths to discounted cashflow valuation — the first is to value just the equity stake in the business, the second is to value the entire firm, which includes, besides equity, the other claimholders in the firm (bondholders, preferred stockholders, etc. and the third is to value the firm in pieces, beginning with its operations and adding the effects on value of debt and other non-equity claims. While all three approaches discount expected cashflows, the relevant cashflows and discount rates are different under each. The value of equity is obtained by discounting expected cashflows to equity, i. e. , the residual cashflows after meeting all expenses, reinvestment needs, tax obligations and net debt payments (interest, principal payments and new debt issuance), at the cost of equity, i. e. , the rate of return required by equity investors in the firm. t=n Value of Equity = where, CF to Equity t (1+k e )t t=1 ? CF to Equityt = Expected Cashflow to Equity in period t ke = Cost of Equity The dividend discount model is a specialized case of equity valuation, where the value of the equity is the present value of expected future dividends. The value of the firm is obtained by discounting expected cashflows to the firm, i. e. , the residual cashflows after meeting all operating expenses, reinvestment needs and taxes, but prior to any payments to either debt or equity holders, at the weighted average cost of capital, which is the cost of the different components of financing used by the firm, weighted by their market value proportions. t=n Value of Firm = where, ? (1+WACC)tt t=1 CF to Firm
CF to Firm t = Expected Cashflow to Firm in period t WACC = Weighted Average Cost of Capital The value of the firm can also be obtained by valuing each claim on the firm separately. In this approach, which is called adjusted present value (APV), we begin by valuing equity in the firm, assuming that it was financed only with equity. We then consider the value added (or taken away) by debt by considering the present value of the tax benefits that flow from debt and the expected bankruptcy costs. Value of firm = Value of all-equity financed firm + PV of tax benefits + Expected Bankruptcy Costs In fact, this approach can be generalized to allow different cash flows to the firm to be discounted at different rates, given their riskiness.
While the three approaches use different definitions of cashflow and discount rates, they will yield consistent estimates of value as long as you use the same set of assumptions in valuation. The key error to avoid is mismatching cashflows and discount rates, since discounting cashflows to equity at the cost of capital will lead to an upwardly biased estimate of the value of equity, while discounting cashflows to the firm at the cost of equity will yield a downward biased estimate of the value of the firm. In the illustration 4 that follows, we will show the equivalence of equity and firm valuation. Later in this book, we will show that adjusted present value models and firm valuation models also yield the same values. Illustration 2. : Effects of mismatching cashflows and discount rates Assume that you are analyzing a company with the following cashflows 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 1 2 3 4 5 Terminal Value Cashflow to Equity $ 50 $ 60 $ 68 $ 76. 2 $ 83. 49 $ 1603. 008 Interest (1-t) $ 40 $ 40 $ 40 $ 40 $ 40 Cashflow to Firm $ 90 $ 100 $ 108 $ 116. 2 $ 123. 49 $ 2363. 008 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 = Pre-tax 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% (1073/1873) + 5% (800/1873) = 9. 94% Method 1: Discount CF to Equity at Cost of Equity to get value of equity We discount cash flows to equity at the cost of equity: PV of Equity = 50/1. 13625 + 60/1. 136252 + 68/1. 136253 + 76. 2/1. 136254 + (83. 49+1603)/1. 136255 = $1073 Method 2: Discount CF to Firm at Cost of Capital to get value of firm PV of Firm = 90/1. 0994 + 100/1. 09942 + 108/1. 09943 + 116. 2/1. 09944 + (123. 49+2363)/1. 9945 = $1873 5 PV of Equity = PV of Firm – Market Value of Debt = $ 1873 – $ 800 = $1073 Note that the value of equity is $1073 under both approaches. It is easy to make the mistake of discounting cashflows to equity at the cost of capital or the cashflows to the firm at the cost of equity. Error 1: Discount CF to Equity at Cost of Capital to get too high a value for equity PV of Equity = 50/1. 0994 + 60/1. 09942 + 68/1. 09943 + 76. 2/1. 09944 + (83. 49+1603)/1. 09945 = $1248 Error 2: Discount CF to Firm at Cost of Equity to get too low a value for the firm PV of Firm = 90/1. 13625 + 100/1. 136252 + 108/1. 136253 + 116. 2/1. 136254 + (123. 49+2363)/1. 36255 = $1613 PV of Equity = PV of Firm – Market Value of Debt = $1612. 86 – $800 = $813 The effects of using the wrong discount rate are clearly visible in the last two calculations. When the cost of capital is mistakenly used to discount the cashflows to equity, the value of equity increases by $175 over its true value ($1073). When the cashflows to the firm are erroneously discounted at the cost of equity, the value of the firm is understated by $260. We have to point out that getting the values of equity to agree with the firm and equity valuation approaches can be much more difficult in practice than in this example. We will return and consider the assumptions that we need to make to arrive at this result.
A Simple Test of Cash Flows There is a simple test that can be employed to determine whether the cashflows being used in a valuation are cashflows to equity or cashflows to the firm. If the cash flows that are being discounted are after interest expenses (and principal payments), they are cash flows to equity and the discount rate that should be used should be the cost of equity. If the cash flows that are discounted are before interest expenses and principal payments, they are usually cash flows to the firm. Needless to say, there are other items that need to be considered when estimating these cash flows, and we will consider them in extensive detail in the coming chapters. 6 II.
Total Cash Flow versus Excess Cash Flow Models The conventional discounted cash flow model values an asset by estimating the present value of all cash flows generated by that asset at the appropriate discount rate. In excess return (and excess cash flow) models, only cash flows earned in excess of the required return are viewed as value creating, and the present value of these excess cash flows can be added on to the amount invested in the asset to estimate its value. To illustrate, assume that you have an asset in which you invest $100 million and that you expect to generate $12 million per year in after-tax cash flows in perpetuity. Assume further that the cost of capital on this investment is 10%. With a total cash flow model, the value of this asset can be estimated as follows: Value of asset = $12 million/0. 0 = $120 million With an excess return model, we would first compute the excess return made on this asset: Excess return = Cash flow earned – Cost of capital * Capital Invested in asset = $12 million – 0. 10 * $100 million = $2 million 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/0. 10 + $100 million = $120 million Note 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 earning per se that create value, but earnings in excess of a required return.
Later in this book, we will consider special versions of these excess return models such as Economic Value Added (EVA). As in the simple example above, we will argue that, with consistent assumptions, total cash flow and excess return models are equivalent. Applicability and Limitations of DCF Valuation Discounted cashflow valuation is based upon expected future cashflows and discount rates. Given these informational requirements, this approach is easiest to use for assets (firms) whose cashflows are currently positive and can be estimated with some reliability for future periods, and where a proxy for risk that can be used to obtain 7 discount rates is available.
The further we get from this idealized setting, the more difficult discounted cashflow valuation becomes. The following list contains some scenarios where discounted cashflow valuation might run into trouble and need to be adapted. (1) Firms in trouble: A distressed firm generally has negative earnings and cashflows. It expects to lose money for some time in the future. For these firms, estimating future cashflows is difficult to do, since there is a strong probability of bankruptcy. For firms which are expected to fail, discounted cashflow valuation does not work very well, since we value the firm as a going concern providing positive cashflows to its investors.
Even for firms that are expected to survive, cashflows will have to be estimated until they turn positive, since obtaining a present value of negative cashflows will yield a negative1 value for equity or the firm. (2) Cyclical Firms: The earnings and cashflows of cyclical firms tend to follow the economy – rising during economic booms and falling during recessions. If discounted cashflow valuation is used on these firms, expected future cashflows are usually smoothed out, unless the analyst wants to undertake the onerous task of predicting the timing and duration of economic recessions and recoveries. Many cyclical firms, in the depths of a recession, look like troubled firms, with negative earnings and cashflows.
Estimating future cashflows then becomes entangled with analyst predictions about when the economy will turn and how strong the upturn will be, with more optimistic analysts arriving at higher estimates of value. This is unavoidable, but the economic biases of the analyst have to be taken into account before using these valuations. (3) Firms with unutilized assets: Discounted cashflow valuation reflects the value of all assets that produce cashflows. If a firm has assets that are unutilized (and hence do not produce any cashflows), the value of these assets will not be reflected in the value obtained from discounting expected future cashflows.
The same caveat applies, in lesser degree, to underutilized assets, since their value will be understated in discounted cashflow valuation. While this is a problem, it is not insurmountable. The value of these 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. 8 assets can always be obtained externally2, and added on to the value obtained from discounted cashflow valuation. Alternatively, the assets can be valued assuming that they are used optimally. (4) Firms with patents or product options: Firms often have unutilized patents or licenses that do not produce any current cashflows and are not expected to produce cashflows in the near future, but, nevertheless, are valuable.
If this is the case, the value obtained from discounting expected cashflows to the firm will understate the true value of the firm. Again, the problem can be overcome, by valuing these assets in the open market or by using option pricing models, and then adding on to the value obtained from discounted cashflow valuation. (5) Firms in the process of restructuring: Firms in the process of restructuring often sell some of their assets, acquire other assets, and change their capital structure and dividend policy. Some of them also change their ownership structure (going from publicly traded to private status) and management compensation schemes. Each of these changes makes estimating future cashflows more difficult and affects the riskiness of the firm.
Using historical data for such firms can give a misleading picture of the firm’s value. However, these firms can be valued, even in the 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. (6) Firms involved in acquisitions: There are at least two specific issues relating to acquisitions that need to be taken into account when using discounted cashflow valuation models to value target firms. The first is the thorny one of whether there is synergy in the merger and if its value can be estimated.
It can be done, though it does require assumptions about the form the synergy will take and its effect on cashflows. The second, especially in hostile takeovers, is the effect of changing management on cashflows and risk. Again, the effect of the change can and should be incorporated into the estimates of future cashflows and discount rates and hence into value. (7) Private Firms: The biggest problem in using discounted cashflow valuation models to value private firms is the measurement of risk (to use in estimating discount rates), since 2 If these assets are traded on external markets, the market prices of these assets can be used in the valuation. If not, the cashflows can be projected, assuming full utilization of assets, and the value can be most risk/return models require that risk parameters be estimated from historical prices on the asset being analyzed. Since securities in private firms are not traded, this is not possible. One solution is to look at the riskiness of comparable firms, which are publicly traded. The other is to relate the measure of risk to accounting variables, which are available for the private firm. The point is not that discounted cash flow valuation cannot be done in these cases, but that we have to be flexible enough to deal with them. The fact is that valuation is simple for firms with well defined assets that generate cashflows that can be easily forecasted.
The real challenge in valuation is to extend the valuation framework to cover firms that vary to some extent or the other from this idealized framework. Much of this book is spent considering how to value such firms. Relative Valuation While we tend to focus most on discounted cash flow valuation, when discussing valuation, the reality is that most valuations are relative valuations. The value of most assets, from the house you buy to the stocks that you invest in, are based upon how similar assets are priced in the market place. We begin this section with a basis for relative valuation, move on to consider the underpinnings of the model and then consider common variants within relative valuation.
Basis for Relative Valuation In relative valuation, the value of an asset is derived from the pricing of ‘comparable’ assets, standardized using a common variable such as earnings, cashflows, book value or revenues. One illustration of this approach is the use of an industry-average price-earnings ratio to value a firm. This assumes that the other firms in the industry are comparable to the firm being valued and that the market, on average, prices these firms correctly. Another multiple in wide use is the price to book value ratio, with firms selling at a discount on book value, relative to comparable firms, being considered undervalued. The multiple of price to sales is also used to value firms, with the average rice-sales ratios of firms with similar characteristics being used for comparison. While these three multiples are among the most widely used, there are others that also play a role in estimated. 10 analysis – price to cashflows, price to dividends and market value to replacement value (Tobin’s Q), to name a few. Underpinnings of Relative Valuation Unlike discounted cash flow valuation, which we described as a search for intrinsic value, we are much more reliant on the market when we use relative valuation. In other words, we assume that the market is correct in the way it prices stocks, on average, but that it makes errors on the pricing of individual stocks.
We also assume that a comparison of multiples will allow us to identify these errors, and that these errors will be corrected over time. The assumption that markets correct their mistakes over time is common to both discounted cash flow and relative valuation, but those who use multiples and comparables to pick stocks argue, with some basis, that errors made by mistakes in pricing individual stocks in a sector are more noticeable and more likely to be corrected 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 under valued and that the correction towards the sector average should occur sooner rather than latter.
Proponents of discounted cash flow valuation would counter that this is small consolation if the entire sector is over priced by 50%. Categorizing Relative Valuation Models Analysts and investors are endlessly inventive when it comes to using relative valuation. Some compare multiples across companies, while others compare the multiple of a company to the multiples it used to trade in the past. While most relative valuations are based upon comparables, there are some relative valuations that are based upon fundamentals. I. Fundamentals versus Comparables In discounted cash flow valuation, the value 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.
Some analysts who use multiples go back to these discounted cash flow models to extract multiples. Other analysts compare multiples 11 across firms or time, and make explicit or implicit assumptions about how firms are similar or vary on fundamentals. 1. Using Fundamentals The first approach relates multiples to fundamentals about the firm being valued – growth rates in earnings and cashflows, payout ratios and risk. This approach to estimating multiples is equivalent to using discounted cashflow models, requiring the same information and yielding the same results. Its primary advantage is to show the relationship between multiples and firm characteristics, and allows us to explore how multiples change as these characteristics change.
For instance, what will be the effect of changing profit margins on the price/sales ratio? What will happen to price-earnings ratios as growth rates decrease? What is the relationship between price-book value ratios and return on equity? 2. Using Comparables The more common approach to using multiples is to compare how a firm is valued with how similar firms are priced by the market, or in some cases, with how the firm was valued in prior periods. As we will see in the later chapters, finding similar and comparable firms is often a challenge and we have to often accept firms that are different from the firm being valued on one dimension or the other.
When this is the case, we have to either explicitly or implicitly control for differences across firms on growth, risk and cash flow measures. In practice, controlling for these variables can range from the naive (using industry averages) to the sophisticated (multivariate regression models where the relevant variables are identified and we control for differences. ). II. Cross Sectional versus Time Series Comparisons In most cases, analysts price stocks on a relative basis by comparing the multiple it is trading to the multiple at which other firms in the same business are trading. In some cases, however, especially for mature firms with long histories, the comparison is done across time. a.
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 are doing relative valuation and we are making 12 cross sectional comparisons. The conclusions can vary depending upon our assumptions about the firm being valued and the comparable firms. For instance, if we assume that the firm we are valuing is similar to the average firm in the industry, we would conclude that it is cheap if it trades at a multiple that is lower than the average multiple. If, on the other hand, we assume that the firm being valued is riskier than the average firm in the industry, we might conclude that the firm should trade at a lower multiple than other firms in the business. In short, you cannot compare firms without making assumptions about their fundamentals. b.
Comparisons across time If you have a mature firm with a long history, you can compare the multiple it trades today to the multiple it used to trade in the past. Thus, Ford Motor company may be viewed as cheap because it trades at six times earnings, if it has historically traded at ten times earnings. To make this comparison, however, you have to assume that your firm has not changed its fundamentals over time. For instance, you would expect a high growth firm’s price earnings ratio to drop and its expected growth rate to decrease over time as it becomes larger. Comparing multiples across time can also be complicated by changes in the interest rates over time and the behavior of the overall market.
For instance, as interest rates fall below historical norms and the overall market increases, you would expect most companies to trade at much higher multiples of earnings and book value than they have historically. Applicability of multiples and limitations The allure of multiples is that they are simple and easy to work with. They can be used to obtain estimates of value quickly for firms and assets, and are particularly useful when there are a large number of comparable firms being traded on financial markets and the market is, on average, pricing these firms correctly. They tend to be more difficult to use to value unique firms, with no obvious comparables, with little or no revenues and negative earnings.
By the same token, they are also easy to misuse and manipulate, especially when comparable firms are used. Given that no two firms are exactly similar in terms of risk and 13 growth, the definition of ‘comparable’ firms is a subjective one. Consequently, a biased analyst can choose a group of comparable firms to confirm his or her biases about a firm’s value. An illustration of this is given below. While this potential for bias exists with discounted cashflow valuation as well, the analyst in DCF valuation is forced to be much more explicit about the assumptions which determine the final value. With multiples, these assumptions are often left unstated.
Illustration 2. 2. The potential for misuse with comparable firms Assume that an analyst is valuing an initial public offering of a firm that manufactures computer software. At the same time, the price-earnings multiples of other publicly traded firms manufacturing software are as follows:3 Firm Adobe Systems Autodesk Broderbund Computer Associates Lotus Development Microsoft Novell Oracle Software Publishing System Software Average PE Ratio Multiple 23. 2 20. 4 32. 8 18. 0 24. 1 27. 4 30. 0 37. 8 10. 6 15. 7 24. 0 While the average PE ratio using the entire sample listed above is 24, it can be changed markedly by removing a couple of firms from the group.
For instance, if the two firms with the lowest PE ratios in the group (Software Publishing and System Software) are eliminated from the sample, the average PE ratio increases to 27. If the two firms with the highest PE ratios in the group (Broderbund and Oracle) are removed from the group, the average PE ratio drops to 21. 3 These were the PE ratios for these firms at the end of 1992. 14 The other problem with using multiples based upon comparable firms is that it builds in errors (over valuation or under valuation) that the market might be making in valuing these firms. In illustration 2. 2, for instance, if the market has overvalued all computer software firms, using the average PE ratio of these firms to value an initial public offering will lead to an overvaluation of its stock.
In contrast, discounted cashflow valuation is based upon firm-specific growth rates and cashflows, and is less likely to be influenced by market errors in valuation. Asset Based Valuation Models There are some who add a fourth approach to valuation to the three that we describe in this chapter. They argue that you can argue the individual assets owned by a firm and use that to estimate its value – asset based valuation models. In fact, there are several variants on asset based valuation models. The first is liquidation value, which is obtained by aggregating the estimated sale proceeds of the assets owned by a firm. The second is replacement cost, where you evaluate what it would cost you to replace all of the assets that a firm has today. While analysts may use sset-based valuation approaches to estimate value, we do not consider them to be alternatives to discounted cash flow, relative or option pricing models since both replacement and liquidation values have to be obtained using one or more of these approaches. Ultimately, all valuation models attempt to value assets – the differences arise in how we identify the assets and how we attach value to each asset. In liquidation valuation, we look only at assets in place and estimate their value based upon what similar assets are priced at in the market. In traditional discounted cash flow valuation, we consider all assets including expected growth potential to arrive at value.
The two approaches may, in fact, yield the same values if you have a firm that has no growth assets and the market assessments of value reflect expected cashflows. Contingent Claim Valuation Perhaps the most significant and revolutionary development in valuation is the acceptance, at least in some cases, that the value of an asset may not be greater than the present value of expected cash flows if the cashflows are contingent on the occurrence or 15 non-occurrence of an event. This acceptance has largely come about because of the development of option pricing models. While these models were initially used to value traded options, there has been an attempt, in recent years, to extend the reach of these models into more traditional valuation.
There are many who argue that assets such as patents or undeveloped reserves are really options and should be valued as such, rather than with traditional discounted cash flow models. Basis for Approach A contingent claim or option pays off only under certain contingencies – if the value of the underlying asset exceeds a pre-specified value for a call option, or is less than a pre-specified value for a put option. Much work has been done in the last twenty years in developing models that value options, and these option pricing models can be used to value any assets that have option-like features. The following diagram illustrates the payoffs on call and put options as a function of the value of the underlying asset: Figure 2. 1: Payoff Diagram on Call and Put Options
Net Payoff on Call Option Net Payoff on Put Option Break Even Strike price Value of Underlying asset Maximum Loss Break Even An option can be valued as a function of the following variables – the current value, the variance in value of the underlying asset, the strike price, the time to expiration of the option and the riskless interest rate. This was first established by Black and Scholes (1972) and has been extended and refined subsequently in numerous variants. While the Black-Scholes option pricing model ignored dividends and assumed that options would 16 not be exercised early, it can be modified to allow for both. A discrete-time variant, the Binomial option pricing model, has also been developed to price options.
An asset can be valued as an option if the payoffs are a function of the value of an underlying asset. It can be valued as a call option if the payoff is contingent on the value of the asset exceeding a pre-specified level.. It can be valued as a put option if the payoff increases as the value of the underlying asset drops below a pre-specified level. Underpinnings for Contingent Claim Valuation The fundamental premise behind the use of option pricing models is that discounted cash flow models tend to understate the value of assets that provide payoffs that are contingent on the occurrence of an event. As a simple example, consider an undeveloped oil reserve belonging to Exxon.
You could value this reserve based upon expectations of oil prices in the future, but this estimate would miss the two nonexclusive facts. 1. The oil company will develop this reserve if oil prices go up and will not if oil prices decline. 2. The oil company will develop this reserve if development costs go down because of technological improvement and will not if development costs remain high. An option pricing model would yield a value that incorporates these rights. When we use option pricing models to value assets such as patents and undeveloped natural resource reserves, we are assuming that markets are sophisticated enough to recognize such options and to incorporate them into the market price.
If the markets do not, we assume that they will eventually, with the payoff to using such models comes about whe