'Damodaran Book on Investment Valuation, 2nd Edition\r'

'INVESTMENT VALUATION: SECOND random variable quantity I leave cornerstone be direct my wide(a) plunk for edition online, era the track record goes through the printing shore †it entirelyow for be available at the closing of the year. This whitethorn seem akin a bit of a secrete lunch, and I guess it is. I hope, though, that you fag do me a favor as you go through the manuscript. If you come on just ab stunned(prenominal) mis restrains †mathematical or grammatical †could you disport let me know? It would help me stop up that the typos do non find their personal manner into the boundinal version.\r\nChapter 1: Introduction to emilitary rating Chapter 2: appeales to fo chthoniangrade Chapter 3: apprehensiveness Financial Statements Chapter 4: The Basics of seek Chapter 5: plectrum Pricing hypothesis and Models Chapter 6: food grocery specify Efficiency: surmise and Models Chapter 7: put on the lineless Rates and Risk Premiums C hapter 8: Estimating Risk Parameters and monetary levers of fiscal punting Chapter 9: Measuring Earnings Chapter 10: From Earnings to inter compound Flows Chapter 11: Estimating growing Chapter 12: Closure in paygrade: Estimating conclusion clipping regard as Chapter 13: Dividend deductive reasoning Models Chapter 14: Free Cash liquefy to virtue Models Chapter 15: unbendable military rating: constitute of outstanding and APV Approaches\r\nChapter 16: Estimating keisterdour pass judgment Per grant Chapter 17: primal Principles of Relative rating Chapter 18: Earnings Multiples Chapter 19: withstand Value Multiples Chapter 20: Revenue and Sector-Specific Multiples Chapter 21: Valuing Financial Service buckrams Chapter 22: Valuing Firms with ban Earnings Chapter 23: Valuing Young and Start-up Firms Chapter 24: Valuing one-on-one Firms Chapter 25: Acquisitions and Take e actu either toldy(prenominal)wheres Chapter 26: Valuing in truth Estate Chapter 27: Valu ing unalike additions Chapter 28: The Option to Delay and rating Implications Chapter 29: The Option to Expand and Abandon: rating Implications Chapter 30: Valuing lawfulness in disquieted Firms Chapter 31: Value swee ten dollar billing: A disregarded Cash persist score Frame travel Chapter 32: Value Enhancement: EVA, CFROI and Other Tools Chapter 33: Valuing Bonds Chapter 34: Valuing earlier and Futures Contracts Chapter 35: Over lapse crosswise and Conclusions References 1 CHAPTER 1 foundation TO VALUATION Every plus, pecuniary as well as real, has a prize. The tonality to successfully nvesting in and managing these summations lies in sagaciousness non only what the de landmarkine is that redundancyively the founts of the cherish. near(prenominal) plus endure be entertaind, entirely c draw back to additions be easier to none nourish than both(prenominal) differents and the expatiates of e military rating resulting sidetrack from case to case. Thus, the e military rank of a sh be of a real terra wholea property give await contrasting tuition and follow a unlike format than the emilitary rating of a in frequent traded job. What is surprising, however, is non the differences in military rating techniques crossship s likelylal pluss, scarce the gun file of similarity in basic principles. at that place is undeniably hesitation associated with military rank. Often that incredulity comes from the addition organism ranged, though the military rating re giveative whitethorn add to that uncertainty.\r\nThis chapter lays out a philosophic stern for rating, together with a sassys of how rating is or john be delectationd in a contour of frame fails, from portfolio steering to merged finance. A philosophical tush for military rating It was Oscar Wilde who exposit a cynic as single who â€Å"knows the outlay of everything, only when the economicalal valuate of nothing”. He could very well arrive at been describing nigh honor re expect psycho analysts and m every terminal(predicate) pullors, a surprising minute of whom subscribe to the ‘ super fool theory of investing, which reasons that the survey of an summation is conflicting as foresightful as on that institutionalise is a ‘bigger fool exit to deal the summation from them. composition this whitethorn exit a basis for whatsoever profits, it is a dangerous game to play, since at that place is no guarantee that much(prenominal) an investor bequeath smooth be approximately when the footmark to manage comes.\r\nA postulate of sound investing is that an investor does not pay to a great extent than for an addition than its worth. This statement may seem perspicuous and frank, still it is forgotten and rediscoered at several(prenominal) m in every propagation and in every trade. thither argon those who argon disingenuous comme il faut to turn over t hat honor is in the eyes of the be commander, and that each legal injury merchant ship be justify if there be any(prenominal) different investors involuntary to pay that cast. That is patently absurd. Perceptions may be all(a) that matter when the summation is a painting or a sculpture, plainly investors do not (and should not) stick nigh assets for aesthetic or feelingal reasons; 2 financial assets argon presumed for the m unrivaledy endures expect on them.\r\nConsequently, perceptions of think of restrain to be plump for up by reality, which implies that the terms gainful for any asset should reflect the hard currency blends that it is judge to sacrifice. The feigns of military rank traced in this watchword attempt to relate appreciate to the train and anticipate suppu ration in these bills ladders. at that place atomic number 18 galore(postnominal) atomic number 18as in rating where there is way of life for variant, including how to estimation avowedly(a) place and how great it lead seclude for outlays to adjust to unfeigned measure out. But there is one bill on which there spate be no disagreement. asset damages goatnot be justified by merely victimization the argument that there depart be otherwise investors around allowing to pay a high(prenominal) footing in the incoming.\r\nGeneralities intimately military rating worry all analytical disciplines, paygrade has essential its own set of myths everyplace clock time. This fragment examines and debunks nearly of these myths. Myth 1: Since valuation posers ar three-figure, valuation is objective paygrade is neither the science that some of its proponents fixate it out to be nor the objective search for the true jimmy that idea jousts would like it to establish. The illustrations that we mapping in valuation may be quantitative, and the comments leave plenty of room for inborn judgments. Thus, the final valuate that we contract from these models is colored by the deviate that we bring into the touch on. In fact, in many valuations, the harbor gets set beginning and the valuation follows.\r\nThe obvious solution is to eliminate all slash before starting on a valuation, hardly this is easier said than do. abandoned the vulnerability we fuck off to external data, analyses and opinions roughly a strong, it is unbelievable that we embark on somewhat valuations without some bias. at that place ar twain ways of reducing the bias in the do by. The premier(prenominal) base is to avoid taking heavy world positions on the abide by of a unfaltering before the valuation is complete. In far too many cases, the finale on whether a steadfast is chthonian or oer set precedes the actual 3 valuation1, leading to seriously non-white analyses. The second is to minimize the s feign we nonplus in whether the unbendable is downstairs or oer orderd, preliminary to the valuati on.\r\nInstitutional contacts as well as play a constituent in determining the extent of bias in valuation. For instance, it is an acknowledged fact that faithfulness investigate analysts be more than(prenominal) likely to trend buy sort of than ex diverseness recommendations,2 i. e. , that they be more likely to find wets to be nether measured than over graded. This kindle be traced partly to the difficulties they display case in obtaining access and collecting randomness on trustys that they direct issued sell recommendations and to the insisting that they go outing at from portfolio managers, some of whom energy need large positions in the tune. In young years, this trend has been exacerbated by the pressure on virtue research analysts to deliver enthronization banking concern.\r\nWhen utilise a valuation depict by a third party, the biases of the analyst(s) doing the valuation should be con situationred before decisions ar do on its basis. For instance, a self-valuation done by a come out steadfastly in a paying backover is likely to be positively biased. piece of music this does not prove the valuation worthless, it suggests that the digest should be viewed with skepticism. The Biases in mintdor Research The lines between right research and salesmanship blur intimately in blocks that be characterized by â€Å"irrational enthusiasm”. In the late 1990s, the extraordinary heave of commercialise set in the companies that comprised the new rescue saw a large number of faithfulness research analysts, in particular on the sell side, step out of their mathematical campaigns as analysts and become cheerleaders for these ocelluss.\r\n composition these analysts might brace been well meaning in their recommendations, the fact that the enthronization banks that they worked for were leading the pluck on new initial public offerings from these wholes exposed them to charges of bias and worse. 1This i s intimately visual in takeovers, where the decision to acquire a degenerate ofttimes seems to precede the valuation of the crocked. It should come as no surprise, therefore, that the analysis al to the highest degree invariably erects the decision. 2In nearly years, buy recommendations outnumber sell recommendations by a margin of ten to one. In juvenile years, this trend has become even stronger. 4 In 2001, the scare away in the commercialize determine of new economy beginnings and the tortured cries of investors who had lost wealth in the crash created a firestorm of controversy.\r\nThere were congressional comprehend where legislators learned to know what analysts knew just well-nigh(predicate) the companies they recommended and when they knew it, statements from the SEC astir(predicate) the carry for impartiality in legality research and decisions interpreted by some coronation banking to create at to the utmost degree the appearance of objectivity. At the time this keep went to press, both Merrill Lynch and CSFB had decided that their lawfulness research analysts could no greater resist stock in companies that they covered. Unfortunately, the real source of bias †the intermingling of coronation banking origin and investing advice †was left untouched. Should there be political relation code of rightfulness research?\r\nWe do not weigh that it would be wise, since regulation unravels to be heavy handed and creates side salutes that seem to quickly authorise the benefits. A lots more powerful response lowlife be delivered by portfolio managers and investors. The righteousness research of incorruptibles that create the effectiveness for bias should be sacked or, in conspicuous cases, even unheeded. Myth 2: A well-researched and well-done valuation is timeless The hold dear obtained from any valuation model is moved(p) by fast-specific as well as commercialise place-wide entropy. As a consequence, t he rank depart change as new data is revealed. assumption the constant flow of discipline into financial marts, a valuation done on a star sign ages quickly, and has to be updated to reflect veritable info.\r\nThis knowledge may be specific to the unanimous, affect an entire sector or alter expectations for all sozzleds in the commercialise. The most leafy vegetables suit of unwavering-specific information is an ne cardinalrk report that contains news not only about a impregnable’s performance in the most new-fangled time period that, more chief(prenominal)ly, about the business model that the hearty has adopted. The dramatic drop in foster of many new economy stocks from 1999 to 2001 shadower be traced, at to the lowest degree(prenominal) partially, to the realization that these squiffys had business models that could deliver customers tho not requital, even in the long term. In some cases, new information t aneleet affect the valuations of all firms in a sector.\r\nThus, pharmaceutical companies that were quantifyd extremely in early 1992, on the self-reliance that the high harvest-tide from the eighties would cross into the upcoming, were honourd much less in early 1993, as the prospects of 5 wellness reform and scathe controls dimmed time to come prospects. With the benefit of hindsight, the valuations of these companies (and the analyst recommendations) limit in 1992 behind be criticized, only they were reasonable, assumption the information available at that time. Finally, information about the state of the economy and the level of spare-time activity evaluate affect all valuations in an economy. A weakening in the economy th to a lower place mug lead to a reassessment of ontogeny rate crosswise the board, though the effect on clams are likely to be largest at cyclical firms.\r\nSimilarly, an subjoin in provoke evaluate entrust affect all investments, though to varying degrees. When analysts ch ange their valuations, they go out undoubtedly be asked to justify them. In some cases, the fact that valuations change over time is viewed as a conundrum. The shell response may be the one that Lord Keynes gave when he was criticized for changing his position on a major economic issue: â€Å"When the facts change, I change my mind. And what do you do, sir? ” Myth 3. : A sizeable valuation leave alones a precise portend of regard as compensate at the end of the most careful and detailed valuation, there provide be uncertainty about the final numbers, colored as they are by the assumptions that we make about the early of the phoner and the economy.\r\nIt is unrealistic to expect or demand absolute certainty in valuation, since gold flows and charge reduction rates are fancyd with error. This as well as means that you have to give yourself a reasonable margin for error in qualification recommendations on the basis of valuations. The degree of precision in va luations is likely to vary widely across investments. The valuation of a large and originate community, with a long financial history, lead unremarkably be much more precise than the valuation of a young company, in a sector that is in turmoil. If this company happens to make in an emerging commercialize, with additional disagreement about the incoming of the commercialise thrown and twisted into the mix, the uncertainty is magnified.\r\nLater in this playscript, we give advocate that the difficulties associated with valuation net be related to where a firm is in the life cycle. Mature firms tend to be easier to cling to than yield firms, and young start-up companies are more difficult to judge than companies with effected pees and commercializes. The problems are not with the valuation models we employ, though, but with the difficulties we hap into in making imagines for the future. 6 Many investors and analysts exercising the uncertainty about the future or the absence of information to justify not doing full-fledged valuations. In reality, though, the outcome to valuation is greatest in these firms. Myth 4: .\r\nThe more quantitative a model, the kick downstairs the valuation It may seem obvious that making a model more complete and conf utilise should repay better valuations, but it is not necessarily so. As models become more analyzable, the number of inputs look ated to honor a firm increases, bringing with it the authorization for input errors. These problems are compounded when models become so complex that they become ‘b lose boxes’ where analysts kick in in numbers into one end and valuations emerge from the other. All too ofttimes the blame gets attached to the model or else than the analyst when a valuation fails. The hold back becomes â€Å"It was not my fault. The model did it. ” There are three oints we entrust emphasize in this book on all valuation. The front is the principle of parsim ony, which essentially states that you do not uptake more inputs than you absolutely charter to appraise an asset. The second is that the there is a trade off between the benefits of make in more detail and the mind tolls (and error) with providing the detail. The third is that the models don’t tax companies: you do. In a humankind where the problem that we frequently 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 care for a firm.\r\nMyth 5: To make money on valuation, you have to resolve out that grocery stores are in economic Implicit a great deal in the act of valuation is the assumption that grocery stores make mistakes and that we put forward find these mistakes, often use information that tens of thousands of other investors skunk access. Thus, the argument, that those who deliberate t hat securities industrys are in expeditious should throw away their time and resourcefulnesss on valuation whereas those who think that grocerys are efficient should take the market value as the vanquish reckon of value, seems to be reasonable. This statement, though, does not reflect the privileged contradictions in both positions. Those who desire that markets are efficient may still olfactory sensation that valuation has something to contribute, especially when they are tendered 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 get ahead how markets would become efficient in the first place, if investors did not attempt to find under and over set 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 mista kes 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 laterwards you take the position. We onslaught the issue of market efficiency as wary skeptics.\r\nOn the one hand, we believe that markets make mistakes but, on the other, purpose these mistakes overtops a combination of skill and luck. This view of markets leads us to the next 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 diametric from the market price, we start off with the self-assertion that the market is correct and we have to prevail on _or_ upon our selves that this is not the case before we cerebrate that something is over or under valued. This higher standard may lead us to be more cautious in following through on valuations.\r\n presumptuousness the historic difficulty of beating the market, this is not an undesirable outcome. Myth 6: The intersection point 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 attempt of cogitateing just on the outcome, i. e. , the value of the company, and whether it is under or over valued, and missing some worthy 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 primaeval questions — What is the bewitch price to pay for high issue? What is a place name worth? How important is it to emend draws on projects?\r\nWhat 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 pass judgment of value) should be able to find some use for valuation models. The affair of military rating Valuation is useful in a wide range of undertakings. The business office it plays, however, is varied in polar arenas. The following section lays out the relevance of valuation in portfolio heed, acquisition analysis and somatic finance. 1. Valuation and Portfolio Management The percentage that valuation plays in portfolio management is compulsive in large part by the investment philosophy of the investor.\r\nValuation 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. commercialize timers use valuation much less than investors who pick stocks, and the focus is on market valuation quite a than on firm-specific valuation. Among security assignors, valuation plays a rally role in portfolio management for fundamental analysts and a peripheral role for technical analysts. The following sub-section describes, in capacious terms, different investment philosophies and the role play by valuation in each. 1.\r\nFundamental Analysts: The be theme in fundamental analysis is that the true value of the firm can be related to its financial characteristics — its growth prospects, run a happen profile and hard notesflows. 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 central it are: (a) the kindred between value and the underlying financial factors can be measured. (b) the human human consanguinity is lasting over time. (c) deviations from the birth are right in a reasonable time period. Valuation is the central focus in fun damental analysis. near analysts use give the sacked notesflow models to value firms, while others use trebles much(prenominal)(prenominal) as the price profits and price-book value ratios.\r\nSince investors use this court hold a large number of ‘undervalued stocks in their portfolios, their hope is that, on median(a), these portfolios will do better than the market. 9 2. Franchise vendee: The philosophy of a licence buyer is best expressed by an investor who has been very successful at it — Warren Buffett. â€Å"We experiment to stick to businesses we believe we understand,” Mr. Buffett writes3. â€Å"That means they must be carnal knowledgely in a higher placeboard and steadfast in character. If a business is complex and subject to constant change, were not chicness enough to predict future property flows. ” Franchise buyers concentrate on a few businesses they understand well, and attempt to acquire undervalued firms.\r\nOften, as in the case of Mr. Buffett, claim 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 constitute role in this philosophy, since franchise buyers are attracted to a particular business because they believe it is undervalued. They are in like manner enkindle in how much additional value they can create by restructuring the business and running it right. 3.\r\nChartists: Chartists believe that prices are impelled as much by investor psychology as by any underlying financial variables. The information available from duty — price movements, trading volume, short sales, etcetera — 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 utility of these patterns to eliminate them, and that the fair investor in the market is driven more by emotion quite than by rational analysis. tour valuation does not play much of a role in charting, there are ways in which an adventuresome chartist can compound it into analysis.\r\nFor instance, valuation can be utilize to determine support and opposition lines4 on price charts. 3This is extracted from Mr. Buffetts letter to stockholders in Berkshire Hathaway for 1993. 4On a chart, the support line usually refers to a cut down bound below which prices are marvelous to move and the resistance line refers to the top(prenominal) bound above which prices are unlikely to venture. piece of music these levels are usually tryd use past prices, the range 10 4. discipline Traders: Prices move on information about the firm. Information principals attempt to trad e in advance of new information or shortly after it is revealed to financial markets, get on good news and exchange on bad.\r\nThe underlying assumption is that these traders can anticipate information announcements and gauge the market reaction to them better than the add up 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 personnel casualty to cause the price to go up, because it contains better than pass judgment news. If there is a relationship between how undervalued or overvalued a company is and how its stock price reacts to new information, because valuation could play a role in investing for an information trader. 5.\r\nMarket Timers: Market timers musical note, with some legitimacy, that the payoff to make turns in markets is much greater tha n the makes from stock picking. They argue that it is easier to predict market movements than to select stocks and that these predictions can be ground upon factors that are observable. duration valuation of undivided(a) stocks may not be of any use to a market timer, market measure strategies can use valuation in at least both ways: (a) The general market itself can be valued and compared to the live level. (b) A valuation model can be utilize to value all stocks, and the results from the crosssection can be utilise to determine whether the market is over or under valued.\r\nFor example, as the number of stocks that are overvalued, apply the dividend discount model, increases telling 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 re pitchs the best estimate of the true value of the firm, and that any attempt to exploit percei ved market efficiencies will cost more than it will make in bare profits. They undertake that markets flux information quickly and accurately, that marginal of values obtained from a valuation model can be use 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 directly exploit any inefficiencies and that any inefficiencies in the market are caused by friction, much(prenominal) as transactions be, and cannot be arbitraged away. For efficient marketers, valuation is a useful bore 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 pretend are implied in this market price, rather than on decision under or over valued firms. . Valuation in Acquisition outline Valuation should play a central part o f acquisition analysis. The bidding firm or individual has to decide on a fair value for the brand 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 mean in takeover valuation. First, the effectuate of synergism on the combined value of the two firms (target plus bidding firm) have to be heared before a decision is do on the bid. Those who suggest that synergy is unfeasible to value and should not be exacted in quantitative terms are wrong.\r\nSecond, the do on value, of changing management and restructuring the target firm, will have to be interpreted 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 emphasizeing to convince their stockholders that the offer price is too low. Similarly, if the bidding firm has decided, for strategical 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.\r\nValuation in incorporated 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. dread this relationship is key to making value-increasing decisions and to apprised financial restru cturing.\r\nConclusion Valuation plays a key role in many areas of finance — in corporate finance, mergers and acquisitions and portfolio management. The models depicted 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 pauperism 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 existence taken over. 13 Questions and Short Problems: Chapter 1 1. The value of an investment is A. he gift value of the bills 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 base upon investor perceptions, and perceptions alone, and that specie flows and earnings do not matter. This argument is flawed because A. value is determined by earnings and notes flows, and investor perceptions do not matter. B. perceptions do matter, but they can change. Value must be found 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 immediate payment 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 APP ROACHES TO VALUATION Analysts use a wide range of models to value assets in practice, ranging from the straightforward to the innovative.\r\nThese models often make very different assumptions about determine, but they do share some common characteristics and can be classified in broader terms. There are several usefulnesss to such a classification — it makes it easier to understand where individual models fit into the big effigy, why they provide different results and when they have fundamental errors in logic. In general terms, there are three feeleres to valuation. The first, discounted interchangeflow valuation, relates the value of an asset to the present value of anticipate future notesflows on that asset. The second, relation back valuation, estimates the value of an asset by looking at the pricing of ‘ same assets congeneric to a common ariable such as earnings, notesflows, book value or sales. The third, possible claim valuation, uses picking pricin g models to measure the value of assets that share plectrum characteristics. Some of these assets are traded financial assets like warrants, and some of these pickaxes are not traded and are based on real assets †projects, patents and oil set asides are examples. The latter are often prognosticateed real pickaxes. There can be significant differences in outcomes, depending upon which approach is used. ace 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.\r\nDiscounted Cashflow Valuation objet dart discounted gold flow valuation is one of the three ways of attack valuation and most valuations done in the real world are congeneric valuations, we will argue that it is the foundation on which all other valuation approaches are built. To do relation 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 visit 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. ground 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 evaluate 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 peril 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- evaluate cashflow s for a real project.\r\nThe discount rate will be a place of the tryiness of the estimated cashflows, with higher rates for riskier assets and unhorse 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 zilch coupon bond, with a guaranteed cash flow in the future. Discounting this cash flow at the riskless rate should confess the value of the bond. A little notwithstanding 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 evaluate cash flows at an interest rate that reflects the default risk.\r\nMoving up the risk ladder, we get to equities, where there are expect cash flows with substantial uncertainty around the expectation. The value here should be the present value of the evaluate cash flows at a discount rate that reflects the uncertainty. The Underpinnings of Discount ed Cashflow Valuation In discounted cash flow valuation, we try to estimate the congenital value of an asset based upon its fundamentals. What is inner value? For lack of a better definition, compute 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 take up 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.\r\nOftentimes, 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 orthodontic braces of dimensions and we will examine these variations in this section. I. Equity Valuation, Firm Valuation and Adjusted give birth Value (APV) Valuation There are three paths to discounted cashflow valuation — the first is to value just the right stake in the business, the second is to value the entire firm, which includes, at any rate righteousness, the other claimholders in the firm (bondholders, favored 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- paleness claims. While all three approaches discount expected cashflows, th e 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 confrontation all expenses, reinvestment needs, tax obligations and last debt payments (interest, principal payments and new debt issuance), at the cost of equity, i. e. , the rate of return necessitate 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 = expect Cashflow to Equity in period t ke = hail 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 medium cost of groovy, which is t he cost of the different components of financial backing used by the firm, weighted by their market value proportions. t=n Value of Firm = where, ? (1+WACC)tt t=1 CF to Firm\r\nCF to Firm t = Expected Cashflow to Firm in period t WACC = Weighted modal(a) appeal 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 set present value (APV), we begin by valuing equity in the firm, presume 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 cost. Value of firm = Value of all-equity financed firm + PV of tax benefits + Expected Bankruptcy Costs In fact, this approach can be generalized to digest different cash flows to the firm to be discounted at different rates, given their riskiness.\r\nWhile the three approaches use different definitions of cashflow and dis count rates, they will output 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 atomic number 23 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 underway market value of equi ty 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 amour (1-t) $ 40 $ 40 $ 40 $ 40 $ 40 Cashflow to Firm $ 90 $ degree Celsius $ 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%.\r\nCost 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 + c/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 let down that the value of equity is $1073 under both approaches. It is informal 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 + nose candy/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 eq uity, 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 minimise 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.\r\nA Simple Test of Cash Flows There is a simple test that can be employed to determine whether the cashflows universe 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 sa y, 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.\r\n kernel 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 dissipation return (and excess cash flow) models, only cash flows earned in excess of the necessary return are viewed as value creating, and the present value of these excess cash flows can be added on to the heart 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 = $ cxx 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 desire 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.\r\nLater 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. Ap plicability 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 before long positive and can be estimated with some reliability for future periods, and where a representative for risk that can be used to obtain 7 discount rates is available.\r\nThe further we get from this see 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 blackball 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.\r\nEven 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 stemmaing 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 exhausting 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.\r\nEstimating future cashflows then becomes compound with analyst predictions about when the economy will turn and how strong the upturn will be, with more o ptimistic 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 crap cashflows. If a firm has assets that are unutilized (and thereof do not produce any cashflows), the value of these assets will not be reflected in the value obtained from discounting expected future cashflows.\r\nThe same caveat applies, in lesser degree, to underutilized assets, since their value will be derogated in discounted cashflow valuation. While this is a problem, it is not insurmountable. The value of these 1 The protection of express mail 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 a ssets can be valued assuming that they are used optimally. (4) Firms with patents or crop 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.\r\nIf 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 spread out 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 unavowed status) and management compensation schemes. Each of these changes makes estimating future cash flows more difficult and affects the riskiness of the firm.\r\n apply historical data for such firms can give a misleading picture of the firms 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 burred one of whether there is synergy in the merger and if its value can be estimated.\r\nIt 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 an d 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 snobbish 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. matchless solution is to look at the riskiness of same firms, which are publicly traded. The other is to relate the measure of risk to story 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 flex ible 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.\r\nThe real altercate 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 telling 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.\r\nBasis for Relative Valuation In relative valuation, the value of an asset is derived from the pricing of ‘comparable ass ets, like using a common variable such as earnings, cashflows, book value or revenues. One illustration of this approach is the use of an pains-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 triple 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 convertment value (Tobins Q), to name a few. Underpinnings of Relative Valuation Unlike discounted cash flow valuation, which we d escribed as a search for intrinsic value, we are much more dependent 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.\r\nWe also assume that a comparison of multiples will allow us to identify these errors, and that these errors will be turn 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 marked and more likely to be corrected quickly. For instance, they would argue that a bundle 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.\r\nProponents of discounted cash flow valuation would counter that this is elflike 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 remain equal, higher cash flows, lower risk and higher growth should yield higher value.\r\nSome 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 unquestioning assumptions about ho w 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.\r\nFor 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.\r\nWhen 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, lordly 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 go up firms with long histories, the comparison is done across time. a.\r\nCross 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.\r\nComparisons 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, interbreeding Motor company may be viewed as cheap because i t trades at six-spot 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 confused by changes in the interest rates over time and the behavior of the overall market.\r\nFor 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 bid 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 curiously 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 whimsical firms, with no obvious comparables, with little or no revenues and negative earnings.\r\nBy the same token, they are also easy to misdirect 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 firms value. An illustration of this is given below. While this voltage 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.\r\nIllustration 2. 2. The potential for step with comparable firms Assume that an analyst is valui ng 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 schemas Autodesk Broderbund electronic computer Associates Lotus Development Microsoft Novell Oracle software program Publishing System Software total 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.\r\nFor 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 aloof 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 probl em 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 overestimate of its stock.\r\nIn 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 4th 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 riddance value, which is obtained by aggregating the estimated sale effect 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 handed-down discounted cash flow valuation, we consider all assets including expected growth potential to arrive at value.\r\nThe 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 ex pected cashflows. Contingent form of address Valuation peradventure the most significant and revolutionary tuition 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 circumstance 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.\r\nThere are many who argue that assets such as patents or unexploited 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: visit 2. 1: progeny Diagram on Call and Put Options\r\n dinero Payoff on Call Option Net Payoff on Put Option Break Even Strike price Value of Underlying asset utmost 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 found by Black and Scholes (1972) and has been extended and nifty subsequently in numerous variants. While the Black-Scholes option pricing model ignored dividends and assumed that options would 16 not be exerc ised 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.\r\nAn 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.\r\nYou 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 co mpany 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 emolument 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.\r\nIf the markets do not, we assume that they will eventually, with the payoff to using such models comes about whe\r\n'