Valuation Models Aswath Damodaran Aswath Damodaran 1 Misconceptions about Valuation Myth 1: A valuation is an objective search for “true” value • Truth 1.1: All valuations are biased. The only questions are how much and in which direction. • Truth 1.2: The direction and magnitude of the bias in your valuation is directly proportional to who pays you and how much you are paid. Myth 2.: A good valuation provides a precise estimate of value • Truth 2.1: There are no precise valuations • Truth 2.2: The payoff to valuation is greatest when valuation is least precise. Myth 3: . The more quantitative a model, the better the valuation • Truth 3.1: One’s understanding of a valuation model is inversely proportional to the number of inputs required for the model. • Truth 3.2: Simpler valuation models do much better than complex ones. Aswath Damodaran 2 Approaches to Valuation Valuation Models Asset Based Valuation Discounted Cashflow Models Relative Valuation Liquidation Value Equity Stable Current Contingent Claim Models Sector Two-stage Three-stage or n-stage Equity Valuation Models Normalized Earnings Book Revenues Value Sector specific Patent Aswath Damodaran Option to liquidate Young firms Equity in troubled firm Undeveloped land Firm Valuation Models Dividends Free Cashflow to Firm Option to expand Firm Market Replacement Cost Option to delay Cost of capital approach APV approach Undeveloped Reserves Excess Return Models 3 Basis for all valuation approaches The use of valuation models in investment decisions (i.e., in decisions on which assets are under valued and which are over valued) are based upon • a perception that markets are inefficient and make mistakes in assessing value • an assumption about how and when these inefficiencies will get corrected In an efficient market, the market price is the best estimate of value. The purpose of any valuation model is then the justification of this value. Aswath Damodaran 4 Discounted Cash Flow Valuation What is it: In discounted cash flow valuation, the value of an asset is the present value of the expected cash flows on the asset. Philosophical Basis: Every asset has an intrinsic value that can be estimated, based upon its characteristics in terms of cash flows, growth and risk. Information Needed: To use discounted cash flow valuation, you need • to estimate the life of the asset • to estimate the cash flows during the life of the asset • to estimate the discount rate to apply to these cash flows to get present value Market Inefficiency: Markets are assumed to make mistakes in pricing assets across time, and are assumed to correct themselves over time, as new information comes out about assets. Aswath Damodaran 5 Discounted Cashflow Valuation: Basis for Approach t = n CF t Value = t t =1 (1+ r) where CFt is the cash flow in period t, r is the discount rate appropriate given the riskiness of the cash flow and t is the life of the asset. Proposition 1: For an asset to have value, the expected cash flows have to be positive some time over the life of the asset. Proposition 2: Assets that generate cash flows early in their life will be worth more than assets that generate cash flows later; the latter may however have greater growth and higher cash flows to compensate. Aswath Damodaran 6 Equity Valuation versus Firm Valuation Value just the equity stake in the business Value the entire business, which includes, besides equity, the other claimholders in the firm Aswath Damodaran 7 I.Equity Valuation The value of equity is obtained by discounting expected cashflows to equity, i.e., the residual cashflows after meeting all expenses, tax obligations and interest and principal payments, at the cost of equity, i.e., the rate of return required by equity investors in the firm. Value of Equity = t=n CF t=1 to Equity t (1+ k e )t where, CF to Equityt = Expected Cashflow to Equity in period t ke = Cost of Equity Forms: The dividend discount model is a specialized case of equity valuation, and the value of a stock is the present value of expected future dividends. In the more general version, you can consider the cashflows left over after debt payments and reinvestment needs as the free cashflow to equity. Aswath Damodaran 8 II. Firm Valuation Cost of capital approach: The value of the firm is obtained by discounting expected cashflows to the firm, i.e., the residual cashflows after meeting all operating expenses and taxes, but prior to debt payments, 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 = CF to Firm t (1+ WACC) t t =1 APV approach: The value of the firm can also be written as the sum of the value of the unlevered firm and the effects (good and bad) of debt. Firm Value = Unlevered Firm Value + PV of tax benefits of debt - Expected Bankruptcy Cost Aswath Damodaran 9 Generic DCF Valuation Model DISCOUNTED CASHFLOW VALUATION Expected Growth Firm: Growth in Operating Earnings Equity: Growth in Net Income/EPS Cash flows Firm: Pre-debt cash flow Equity: After debt cash flows Firm is in stable growth: Grows at constant rate forever Terminal Value Value Firm: Value of Firm CF1 CF2 CF3 CF4 CF5 CFn ......... Forever Equity: Value of Equity Length of Period of High Growth Discount Rate Firm:Cost of Capital Equity: Cost of Equity Aswath Damodaran 10 VALUING ABN AMRO Retention Ratio = 41.56% Dividends EPS = 1.54 Eur * Payout Ratio 58.44% DPS = 0.90 Eur ROE = 16% Expected Growth 41.56% * 16% = 6.65% g =4%: ROE = 8.95%(=Cost of equity) Beta = 1.00 Payout = (1- 4/8.95) = .553 Terminal Value= EPS 6*Payout/(r-g) = (2.21*.553)/(.0895-.04) = 24.69 Value of Equity per share = 20.48 Eur EPS 1.64 Eur DPS 0.96 Eur 1.75 Eur 1.02 Eur 1.87 Eur 1.09 Eur 1.99 Eur 1.16 Eur 2.12 Eur 1.24 Eur ......... Forever Discount at Cost of Equity Cost of Equity 4.95% + 0.95 (4%) = 8.75% Riskfree Rate: Long term bond rate in Euros 4.95% + Beta 0.95 X Average beta for European banks = 0.95 Aswath Damodaran Risk Premium 4% Mature Market 4% Country Risk 0% 11 Aswath Damodaran 12 Avg Reinvestment rate = 25.08% Embraer: Status Quo ($) Reinvestment Rate 25.08% Current Cashflow to Firm EBIT(1-t) : $ 404 - Nt CpX 23 - Chg WC 9 = FCFF $ 372 Reinvestment Rate = 32/404= 7.9% Return on Capital 21.85% Stable Growth g = 4.17%; Beta = 1.00; Country Premium= 5% Cost of capital = 8.76% ROC= 8.76%; Tax rate=34% Reinvestment Rate=g/ROC =4.17/8.76= 47.62% Expected Growth in EBIT (1-t) .2185*.2508=.0548 5.48 % Terminal Value5= 288/(.0876-.0417) = 6272 $ Cashflows Op. Assets $ 5,272 + Cash: 795 - Debt 717 - Minor. Int. 12 =Equity 5,349 -Options 28 Value/Share $7.47 R$ 21.75 Year EBIT(1-t) - Reinvestment = FCFF 1 426 107 319 3 474 119 355 4 500 126 374 Term Yr 549 - 261 = 288 5 527 132 395 Discount at$ Cost of Capital (WACC) = 10.52% (.84) + 6.05% (0.16) = 9.81% Cost of Equity 10.52 % Riskfree Rate : $ Riskfree Rate= 4.17% On October 6, 2003 Embraer Price = R$15.51 Cost of Debt (4.17%+1%+4%)(1-.34) = 6.05% + Beta 1.07 Unlevered Beta for Sectors: 0.95 Aswath Damodaran 2 449 113 336 X Weights E = 84% D = 16% Mature market premium 4% Firm’s D/E Ratio: 19% + Lambda 0.27 X Country Equity Risk Premium 7.67% Country Default Spread 6.01% X Rel Equity Mkt Vol 1.28 13 Current Revenue $ 3,804 Current Margin: -49.82% Stable Growth Cap ex growth slows and net cap ex decreases EBIT -1895m Revenue Growth: 13.33% NOL: 2,076m Stable Revenue Growth: 5% EBITDA/Sales -> 30% Stable EBITDA/ Sales 30% Stable ROC=7.36% Reinvest 67.93% Terminal Value= 677(.0736-.05) =$ 28,683 Value of Op Assets $ 5,530 + Cash & Non-op $ 2,260 = Value of Firm $ 7,790 - Value of Debt $ 4,923 = Value of Equity $ 2867 - Equity Options $ 14 Value per share $ 3.22 Revenues EBITDA EBIT EBIT (1-t) + Depreciation - Cap Ex - Chg WC FCFF $3,804 ($95) ($1,675) ($1,675) $1,580 $3,431 $0 ($3,526) 1 $5,326 $0 ($1,738) ($1,738) $1,738 $1,716 $46 ($1,761) 2 $6,923 $346 ($1,565) ($1,565) $1,911 $1,201 $48 ($903) 3 $8,308 $831 ($1,272) ($1,272) $2,102 $1,261 $42 ($472) 4 $9,139 $1,371 $320 $320 $1,051 $1,324 $25 $22 5 $10,053 $11,058 $11,942 $12,659 $13,292 $1,809 $2,322 $2,508 $3,038 $3,589 $1,074 $1,550 $1,697 $2,186 $2,694 $1,074 $1,550 $1,697 $2,186 $2,276 $736 $773 $811 $852 $894 $1,390 $1,460 $1,533 $1,609 $1,690 $27 $30 $27 $21 $19 $392 $832 $949 $1,407 $1,461 6 7 8 9 10 Beta Cos t of Equity Cos t of Debt Debt Ratio Cos t of Capital 3.00 16.80% 12.80% 74.91% 13.80% 3.00 16.80% 12.80% 74.91% 13.80% 3.00 16.80% 12.80% 74.91% 13.80% 3.00 16.80% 12.80% 74.91% 13.80% 3.00 16.80% 12.80% 74.91% 13.80% 2.60 15.20% 11.84% 67.93% 12.92% Cost of Equity 16.80% Cost of Debt 4.8%+8.0%=12.8% Tax rate = 0% -> 35% Riskfree Rate : T. Bond rate = 4.8% + Beta 3.00> 1.10 Internet/ Retail Aswath Damodaran 2.20 13.60% 10.88% 60.95% 11.94% Operating Leverage X 1.80 12.00% 9.92% 53.96% 10.88% 1.40 10.40% 8.96% 46.98% 9.72% Forever 1.00 8.80% 6.76% 40.00% 7.98% Weights Debt= 74.91% -> 40% Global Crossing November 2001 Stock price = $1.86 Risk Premium 4% Current D/E: 441% Term. Year $13,902 $ 4,187 $ 3,248 $ 2,111 $ 939 $ 2,353 $ 20 $ 677 Base Equity Premium Country Risk Premium 14 Valuing Global Crossing with Distress Probability of distress • Price of 8 year, 12% bond issued by Global Crossing = $ 653 120(1 Distress) t 1000(1 Distress) 8 (1.05) t (1.05) 8 t1 t 8 653 • Probability of distress = 13.53% a year • Cumulative probability of survival over 10 years = (1- .1353)10 = 23.37% Distress sale value of equity • • • • Book value of capital = $14,531 million Distress sale value = 15% of book value = .15*14531 = $2,180 million Book value of debt = $7,647 million Distress sale value of equity = $ 0 Distress adjusted value of equity • Value of Global Crossing = $3.22 (.2337) + $0.00 (.7663) = $0.75 Aswath Damodaran 15 Adjusted Present Value Model In the adjusted present value approach, the value of the firm is written as the sum of the value of the firm without debt (the unlevered firm) and the effect of debt on firm value Firm Value = Unlevered Firm Value + (Tax Benefits of Debt Expected Bankruptcy Cost from the Debt) • The unlevered firm value can be estimated by discounting the free cashflows to the firm at the unlevered cost of equity • The tax benefit of debt reflects the present value of the expected tax benefits. In its simplest form, Tax Benefit = Tax rate * Debt • The expected bankruptcy cost is a function of the probability of bankruptcy and the cost of bankruptcy (direct as well as indirect) as a percent of firm value. Aswath Damodaran 16 Excess Return Models You can present any discounted cashflow model in terms of excess returns, with the value being written as: • Value = Capital Invested + Present value of excess returns on current investments + Present value of excess returns on future investments This model can be stated in terms of firm value (EVA) or equity value. Aswath Damodaran 17 EQUITY VALUATION WITH EQUITY EVA Current EVA Net Income = - Equity cost = Equity EVA = Expected Growth .60 * 20% =12% $ 3104 $ 1645 $ 1459 Net Income $3,599 - Equity Cost (see below) $1,908 Excess Equity Return $1,692 Book Equity= 17997 + PV of EVA= 38334 = Equity EVA=56331 Value/sh = $50.26 $4,031 $2,137 $1,895 Firm is in stable growth: Growth rate = 5% Return on Equity = 15% Cost of equity =9.40% Terminal Value= $2220/(.094-.05)=50,459 $4,515 $5,057 $5,664 $2,393 $2,680 $3,002 $2,122 $2,377 $2,662 Forever Discount atCost of Equity Cost of Equity 10.60% Riskfree Rate : 5.00% + Beta 1.40 X Risk Premium 4.00% Base Equity Premium = 4% Aswath Damodaran Country Risk Premium=0% 18 Choosing the right Discounted Cashflow Model Can you estimate cash flows? Yes No Is leverage stable or likely to change over time? Use dividend discount model Are the current earnings positive & normal? Yes No Use current earnings as base < Growth rate of economy Is the cause temporary? Yes Stable leverage Unstable leverage FCFE FCFF What rate is the firm growing at currently? Are the firm’s competitive advantges time limited? Stable growth model No Replace current earnings with normalized earnings Is the firm likely to survive? Yes 2-stage model Yes No 3-stage or n-stage model No Adjust margins over time to nurse firm to financial health Does the firm have a lot of debt? Yes Value Equity as an option to liquidate Aswath Damodaran > Growth rate of economy No Estimate liquidation value 19 Relative Valuation What is it?: The value of any asset can be estimated by looking at how the market prices “similar” or ‘comparable” assets. Philosophical Basis: The intrinsic value of an asset is impossible (or close to impossible) to estimate. The value of an asset is whatever the market is willing to pay for it (based upon its characteristics) Information Needed: To do a relative valuation, you need • an identical asset, or a group of comparable or similar assets • a standardized measure of value (in equity, this is obtained by dividing the price by a common variable, such as earnings or book value) • and if the assets are not perfectly comparable, variables to control for the differences Market Inefficiency: Pricing errors made across similar or comparable assets are easier to spot, easier to exploit and are much more quickly corrected. Aswath Damodaran 20 Variations on Multiples Equity versus Firm Value • • Scaling variable • • • • Earnings (EPS, Net Income, EBIT, EBITDA) Book value (Book value of equity, Book value of assets, Book value of capital) Revenues Sector specific variables Base year • • • • Equity multiples (Price per share or Market value of equity) Firm value multiplies (Firm value or Enterprise value) Most recent financial year (Current) Last four quarters (Trailing) Average over last few years (Normalized) Expected future year (Forward) Comparables • • Aswath Damodaran Sector Market 21 Definitional Tests Is the multiple consistently defined? • Proposition 1: Both the value (the numerator) and the standardizing variable ( the denominator) should be to the same claimholders in the firm. In other words, the value of equity should be divided by equity earnings or equity book value, and firm value should be divided by firm earnings or book value. Is the multiple uniformally estimated? • The variables used in defining the multiple should be estimated uniformly across assets in the “comparable firm” list. • If earnings-based multiples are used, the accounting rules to measure earnings should be applied consistently across assets. The same rule applies with book-value based multiples. Aswath Damodaran 22 An Example: Price Earnings Ratio: Definition PE = Market Price per Share / Earnings per Share There are a number of variants on the basic PE ratio in use. They are based upon how the price and the earnings are defined. Price: is usually the current price is sometimes the average price for the year EPS: earnings per share in most recent financial year earnings per share in trailing 12 months (Trailing PE) forecasted earnings per share next year (Forward PE) forecasted earnings per share in future year Aswath Damodaran 23 Descriptive Tests What is the average and standard deviation for this multiple, across the universe (market)? What is the median for this multiple? • The median for this multiple is often a more reliable comparison point. How large are the outliers to the distribution, and how do we deal with the outliers? • Throwing out the outliers may seem like an obvious solution, but if the outliers all lie on one side of the distribution (they usually are large positive numbers), this can lead to a biased estimate. Are there cases where the multiple cannot be estimated? Will ignoring these cases lead to a biased estimate of the multiple? How has this multiple changed over time? Aswath Damodaran 24 PE Ratio: Descriptive Statistics Aswath Damodaran 25 PE: Deciphering the Distribution Mean Standard Error Median Standard Deviation Skewness Minimum Maximum Count Largest(500) Smallest(500) Aswath Damodaran Current PE 36.04 1.94 18.25 123.36 23.13 0.65 5103.50 4024 48.00 9.38 Trailing PE 34.14 2.93 17.25 176.34 28.40 1.35 6914.50 3627 39.60 9.62 Forward PE 30.79 1.15 18.52 57.56 13.66 3.30 1414.00 2491 34.49 12.94 26 8 Times EBITDA is not cheap… Aswath Damodaran 27 Analytical Tests What are the fundamentals that determine and drive these multiples? • Proposition 2: Embedded in every multiple are all of the variables that drive every discounted cash flow valuation - growth, risk and cash flow patterns. • In fact, using a simple discounted cash flow model and basic algebra should yield the fundamentals that drive a multiple How do changes in these fundamentals change the multiple? • The relationship between a fundamental (like growth) and a multiple (such as PE) is seldom linear. For example, if firm A has twice the growth rate of firm B, it will generally not trade at twice its PE ratio • Proposition 3: It is impossible to properly compare firms on a multiple, if we do not know the nature of the relationship between fundamentals and the multiple. Aswath Damodaran 28 Relative Value and Fundamentals Value of Stock = DPS 1/(ke - g) PE=Payout Ratio (1+g)/(r-g) PE=f(g, payout, risk) PEG=Payout ratio (1+g)/g(r-g) PBV=ROE (Payout ratio) (1+g)/(r-g) PEG=f(g, payout, risk) PBV=f(ROE,payout, g, risk) PS= Net Margin (Payout ratio) (1+g)/(r-g) PS=f(Net Mgn, payout, g, risk) Equity Multiples Firm Multiples V/FCFF=f(g, WACC) Value/FCFF=(1+g)/ (WACC-g) V/EBIT(1-t)=f(g, RIR, WACC) Value/EBIT(1-t) = (1+g) (1- RIR)/(WACC-g) V/EBIT=f(g, RIR, WACC, t) Value/EBIT=(1+g)(1RiR)/(1-t)(WACC-g) VS=f(Oper Mgn, RIR, g, WACC) VS= Oper Margin (1RIR) (1+g)/(WACC-g) Value of Firm = FCFF 1/(WACC -g) Aswath Damodaran 29 What to control for... Multiple Variables that determine it… PE Ratio PBV Ratio PS Ratio EVV/EBITDA EV/ Sales Expected Growth, Risk, Payout Ratio Return on Equity, Expected Growth, Risk, Payout Net Margin, Expected Growth, Risk, Payout Ratio Expected Growth, Reinvestment rate, Cost of capital Operating Margin, Expected Growth, Risk, Reinvestment Aswath Damodaran 30 Application Tests Given the firm that we are valuing, what is a “comparable” firm? • While traditional analysis is built on the premise that firms in the same sector are comparable firms, valuation theory would suggest that a comparable firm is one which is similar to the one being analyzed in terms of fundamentals. • Proposition 4: There is no reason why a firm cannot be compared with another firm in a very different business, if the two firms have the same risk, growth and cash flow characteristics. Given the comparable firms, how do we adjust for differences across firms on the fundamentals? • Proposition 5: It is impossible to find an exactly identical firm to the one you are valuing. Aswath Damodaran 31 Comparing PE Ratios across a Sector Comp any Name PT Indosat ADR Te leb ras ADR Te lecom Corp orati on o f New Zeala nd ADR Te lecom Arg enti na Stet - France Telecom SA ADR B Hell enic Te lecommu nicatio n Organ ization SA ADR Te lecomun ica cio nes de Ch ile ADR Swisscom AG ADR Asia Sa tell ite Tele com Holdi ngs ADR Portugal Tel eco m SA ADR Te lefo nos de Me xico ADR L Mata v RT ADR Te lstra ADR Gila t Comm unicati ons Deutsche Telek om AG ADR British Tel eco mmun ica tion s PL C ADR Te le Dan mark AS ADR Te leko muni kasi Ind onesia ADR Cab le & Wi reless PLC ADR APT Satel lite Holdi ngs ADR Te lefo nica SA ADR Royal KPN NV ADR Te lecom Italia SPA ADR Nipp on Teleg raph & Tel epho ne ADR Fra nce Tel eco m SA ADR Kore a Te lecom ADR Aswath Damodaran PE 7.8 8.9 11 .2 12 .5 12 .8 16 .6 18 .3 19 .6 20 .8 21 .1 21 .5 21 .7 22 .7 24 .6 25 .7 27 28 .4 29 .8 31 32 .5 35 .7 42 .2 44 .3 45 .2 71 .3 Growth 0.06 0.075 0.11 0.08 0.12 0.08 0.11 0.16 0.13 0.14 0.22 0.12 0.31 0.11 0.07 0.09 0.32 0.14 0.33 0.18 0.13 0.14 0.2 0.19 0.44 32 PE, Growth and Risk Dependent variable is: R squared = 66.2% PE R squared (adjusted) = 63.1% Variable Coefficient SE t-ratio Constant 13.1151 3.471 3.78 Growth rate 121.223 19.27 6.29 Emerging Market -13.8531 3.606 -3.84 Emerging Market is a dummy: 1 if emerging market 0 if not Aswath Damodaran prob 0.0010 ≤ 0.0001 0.0009 33 Is Telebras under valued? Predicted PE = 13.12 + 121.22 (.075) - 13.85 (1) = 8.35 At an actual price to earnings ratio of 8.9, Telebras is slightly overvalued. Aswath Damodaran 34 PE Ratio without a constant - US Stocks Mo d e l Su mm a ry Mo de l 1 a R R Sq ua r e .8 5 6 b .73 3 Adjus t e d R Sq ua r e .73 2 St d. Er ro r o f th e Es tim a te 13 5 0.6 77 6 1 93 1 3 a . Fo r r e g re ss io n t hr ou gh th e or igin (th e n o - int e rc e pt m od e l), R Squ a r e m e a su r e s t he pr o po rt ion of t he va r ia b ility in th e de p e n de n t va ria ble a b ou t th e o rig in ex pla ine d b y r e gr e s sion . T his CANNOT b e c o m p ar ed to R Sq ua r e fo r m od e ls whic h inc lu d e a n int er c e p t. b . Pr e d ic tor s: Valu e Line Bet a , P a you t Ra tio , Ex pe c te d Gr owt h in EPS: ne x t 5 ye a rs Co e f fici e n ts a,b ,c Uns t an d ar d iz ed Coe f fic ie nt s Mo de l 1 B Exp e ct e d Gro wth in EPS: n e xt 5 ye ar s Pa yo ut Ra tio Va lu e Lin e Be ta Std . Er r or St a nd a r diz e d C oe ffic ie n ts Be t a 9 5% Co nf ide n ce Int e rva l f or B t Sig . Lo wer Bo un d Up pe r Bo un d 1 .2 28 .05 5 .51 4 22 .1 87 .0 0 0 1 .1 19 1.3 3 6 - 1 .1 E- 0 2 .01 4 - .01 3 - .7 68 .4 4 3 - .03 9 .0 1 7 1 1. 70 5 .82 5 .38 4 14 .1 84 .0 0 0 1 0. 08 7 13 .3 24 a . De p e nd e n t Va r ia b le : Cu r re nt PE b . Line a r Re g r e ss ion t hr ou gh th e Orig in c . We igh te d Le a st Sq u ar e s Re g re ss ion - We ig h te d by Ma r ke t Ca p Aswath Damodaran 35 Relative Valuation: Choosing the Right Model Aswath Damodaran 36 Contingent Claim (Option) Valuation Options have several features • They derive their value from an underlying asset, which has value • The payoff on a call (put) option occurs only if the value of the underlying asset is greater (lesser) than an exercise price that is specified at the time the option is created. If this contingency does not occur, the option is worthless. • They have a fixed life Any security that shares these features can be valued as an option. Aswath Damodaran 37 Option Payoff Diagrams Strike Price Value of Asset Put Option Call Option Aswath Damodaran 38 Underlying Theme: Searching for an Elusive Premium Traditional discounted cashflow models under estimate the value of investments, where there are options embedded in the investments to • Delay or defer making the investment (delay) • Adjust or alter production schedules as price changes (flexibility) • Expand into new markets or products at later stages in the process, based upon observing favorable outcomes at the early stages (expansion) • Stop production or abandon investments if the outcomes are unfavorable at early stages (abandonment) Put another way, real option advocates believe that you should be paying a premium on discounted cashflow value estimates. Aswath Damodaran 39 Three Basic Questions When is there a real option embedded in a decision or an asset? • • When does that real option have significant economic value? • • There has to be a clearly defined underlying asset whose value changes over time in unpredictable ways. The payoffs on this asset (real option) have to be contingent on an specified event occurring within a finite period. For an option to have significant economic value, there has to be a restriction on competition in the event of the contingency. At the limit, real options are most valuable when you have exclusivity - you and only you can take advantage of the contingency. They become less valuable as the barriers to competition become less steep. Can that value be estimated using an option pricing model? • • • Aswath Damodaran The underlying asset is traded - this yield not only observable prices and volatility as inputs to option pricing models but allows for the possibility of creating replicating portfolios An active marketplace exists for the option itself. The cost of exercising the option is known with some degree of certaint 40 Putting Natural Resource Options to the Test The Option Test: • • The Exclusivity Test: • • Natural resource reserves are limited (at least for the short term) It takes time and resources to develop new reserves The Option Pricing Test • • • Underlying Asset: Oil or gold in reserve Contingency: If value > Cost of development: Value - Dev Cost If value < Cost of development: 0 Underlying Asset: While the reserve or mine may not be traded, the commodity is. If we assume that we know the quantity with a fair degree of certainty, you can trade the underlying asset Option: Oil companies buy and sell reserves from each other regularly. Cost of Exercising the Option: This is the cost of developing a reserve. Given the experience that commodity companies have with this, they can estimate this cost with a fair degree of precision. Bottom Line: Real option pricing models work well with natural resource options. Aswath Damodaran 41 The Real Options Test: Patents and Technology The Option Test: • • Underlying Asset: Product that would be generated by the patent Contingency: If PV of CFs from development > Cost of development: PV - Cost If PV of CFs from development < Cost of development: 0 The Exclusivity Test: • • The Pricing Test • • • Patents restrict competitors from developing similar products Patents do not restrict competitors from developing other products to treat the same disease. Underlying Asset: Patents are not traded. Not only do you therefore have to estimate the present values and volatilities yourself, you cannot construct replicating positions or do arbitrage. Option: Patents are bought and sold, though not as frequently as oil reserves or mines. Cost of Exercising the Option: This is the cost of converting the patent for commercial production. Here, experience does help and drug firms can make fairly precise estimates of the cost. Bottom Line: Use real option pricing arguments with caution. Aswath Damodaran 42 The Real Options Test for Growth (Expansion) Options The Options Test • Underlying Asset: Expansion Project • Contingency If PV of CF from expansion > Expansion Cost: PV - Expansion Cost If PV of CF from expansion < Expansion Cost: 0 The Exclusivity Test • The Pricing Test • • • Barriers may range from strong (exclusive licenses granted by the government) to weaker (brand name, knowledge of the market) to weakest (first mover). Underlying Asset: As with patents, there is no trading in the underlying asset and you have to estimate value and volatility. Option: Licenses are sometimes bought and sold, but more diffuse expansion options are not. Cost of Exercising the Option: Not known with any precision and may itself evolve over time as the market evolves. Bottom Line: Using option pricing models to value expansion options will not only yield extremely noisy estimates, but may attach inappropriate premiums to discounted cashflow estimates. Aswath Damodaran 43 Summarizing the Real Options Argument There are real options everywhere. Most of them have no significant economic value because there is no exclusivity associated with using them. When options have significant economic value, the inputs needed to value them in a binomial model can be used in more traditional approaches (decision trees) to yield equivalent value. The real value from real options lies in • Recognizing that building in flexibility and escape hatches into large decisions has value • Insights we get on understanding how and why companies behave the way they do in investment analysis and capital structure choices. Aswath Damodaran 44 Valuation Models Asset Based Valuation Discounted Cashflow Models Relative Valuation Liquidation Value Equity Stable Current Contingent Claim Models Sector Two-stage Three-stage or n-stage Equity Valuation Models Normalized Earnings Book Revenues Value Sector specific Dividends Cost of capital approach Aswath Damodaran Option to liquidate Young firms Equity in troubled firm Undeveloped land Firm Valuation Models Patent Free Cashflow to Firm Option to expand Firm Market Replacement Cost Option to delay APV approach Undeveloped Reserves Excess Return Models 45 Which approach should you use? Depends upon the asset being valued.. Asset Marketability and Valuation Approaches Mature businesses Separable & marketable assets Growth businesses Linked and non-marketable assets Liquidation & Replacement cost valuation Other valuation models Cash Flows and Valuation Approaches Cashflows currently or expected in near future Discounted cashflow or relative valuation models Cashflows if a contingency occurs Option pricing models Assets that will never generate cashflows Relative valuation models Uniqueness of Asset and Valuation Approaches Unique asset or business Discounted cashflow or option pricing models Aswath Damodaran Large number of similar assets that are priced Relative valuation models 46 And the analyst doing the valuation…. Investor Time Horizon and Valuation Approaches Very short time horizon Liquidation value Long Time Horizon Relative valuation Option pricing models Discounted Cashflow value Views on market and Valuation Approaches Markets are correct on average but make mistakes on individual assets Relative valuation Asset markets and financial markets may diverge Liquidation value Markets make mistakes but correct them over time Discounted Cashflow value Option pricing models Aswath Damodaran 47

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