Aswath Damodaran 1

Valuation Models

Aswath Damodaran

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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.

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Approaches to Valuation

Valuation Models

Asset BasedValuation

Discounted CashflowModels

Relative Valuation Contingent Claim Models

LiquidationValue

ReplacementCost

Equity ValuationModels

Firm ValuationModels

Cost of capitalapproach

APVapproach

Excess ReturnModels

Stable

Two-stage

Three-stageor n-stage

Current

Normalized

Equity

Firm

Earnings BookValue

Revenues Sectorspecific

Sector

Market

Option todelay

Option toexpand

Option toliquidate

Patent UndevelopedReserves

Youngfirms

Undevelopedland

Equity introubledfirm

Dividends

Free Cashflowto Firm

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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.

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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.

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Discounted Cashflow Valuation: Basis for Approach

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.

Value = CFt

(1+ r)tt =1

t = n

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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

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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.

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.

Value of Equity = CF to Equityt

(1+ ke )tt=1

t=n

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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.

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

Value of Firm = CF to Firm t

(1+ WACC) tt =1

t= n

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Generic DCF Valuation Model

Cash flowsFirm: Pre-debt cash flowEquity: After debt cash flows

Expected GrowthFirm: Growth in Operating EarningsEquity: Growth in Net Income/EPS

CF1 CF2 CF3 CF4 CF5

Forever

Firm is in stable growth:Grows at constant rateforever

Terminal ValueCFn.........

Discount RateFirm:Cost of Capital

Equity: Cost of Equity

ValueFirm: Value of Firm

Equity: Value of Equity

DISCOUNTED CASHFLOW VALUATION

Length of Period of High Growth

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DividendsEPS = 1.54 Eur * Payout Ratio 58.44%DPS = 0.90 Eur

Expected Growth41.56% *16% = 6.65%

0.96 Eur 1.02 Eur 1.09 Eur 1.16 Eur 1.24 Eur

Forever

g =4%: ROE = 8.95%(=Cost of equity)Beta = 1.00Payout = (1- 4/8.95) = .553

Terminal Value= EPS 6*Payout/(r-g)= (2.21*.553)/(.0895-.04) = 24.69

.........

Cost of Equity4.95% + 0.95 (4%) = 8.75%

Discount at Cost of Equity

Value of Equity per share = 20.48 Eur

Riskfree Rate:Long term bond rate in Euros4.95% +

Beta0.95 X

Risk Premium4%

Average beta for European banks = 0.95 Mature Market

4%Country Risk0%

VALUING ABN AMRORetention Ratio = 41.56%

ROE = 16%

DPSEPS 1.64 Eur 1.75 Eur 1.87 Eur 1.99 Eur 2.12 Eur

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Current Cashflow to FirmEBIT(1-t) : $ 404- Nt CpX 23 - Chg WC 9= FCFF $ 372Reinvestment Rate = 32/404= 7.9%

Expected Growth in EBIT (1-t).2185*.2508=.05485.48%

Stable Growthg = 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%

Terminal Value5= 288/(.0876-.0417) = 6272

Cost of Equity10.52%

Cost of Debt(4.17%+1%+4%)(1-.34)= 6.05%

WeightsE = 84% D = 16%

Discount at $ Cost of Capital (WACC) = 10.52% (.84) + 6.05% (0.16) = 9.81%

Op. Assets $ 5,272+ Cash: 795- Debt 717- Minor. Int. 12=Equity 5,349-Options 28Value/Share $7.47

R$ 21.75

Riskfree Rate:$ Riskfree Rate= 4.17% +

Beta 1.07 X

Mature market premium 4 %

Unlevered Beta for Sectors: 0.95

Firm’s D/ERatio: 19%

Embraer: Status Quo ($) Reinvestment Rate 25.08%

Return on Capital21.85%

Term Yr 549 - 261= 288

Avg Reinvestment rate = 25.08%

Year 1 2 3 4 5EBIT(1-t) 426 449 474 500 527 - Reinvestment 107 113 119 126 132 = FCFF 319 336 355 374 395

+ Lambda0.27

XCountry Equity RiskPremium7.67%

Country Default Spread6.01%

XRel Equity Mkt Vol

1.28

On October 6, 2003Embraer Price = R$15.51

$ Cashflows

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Forever

Terminal Value= 677(.0736-.05)=$ 28,683

Cost of Equity16.80%

Cost of Debt4.8%+8.0%=12.8%Tax rate = 0% -> 35%

WeightsDebt= 74.91% -> 40%

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 $ 14Value per share $ 3.22

Riskfree Rate:T. Bond rate = 4.8%

+Beta3.00> 1.10 X

Risk Premium4%

Internet/Retail

Operating Leverage

Current D/E: 441%

Base EquityPremium

Country RiskPremium

CurrentRevenue$ 3,804

CurrentMargin:-49.82%

Revenue Growth:13.33%

EBITDA/Sales -> 30%

Stable Growth

StableRevenueGrowth: 5%

StableEBITDA/Sales 30%

Stable ROC=7.36%Reinvest 67.93% EBIT

-1895m

NOL:2,076m

$13,902$ 4,187$ 3,248$ 2,111$ 939$ 2,353$ 20$ 677

Term. Year

2 431 5 6 8 9 107

Global CrossingNovember 2001Stock price = $1.86

Cap ex growth slows and net cap ex decreases

Beta 3.00 3.00 3.00 3.00 3.00 2.60 2.20 1.80 1.40 1.00Cost of Equity 16.80% 16.80% 16.80% 16.80% 16.80% 15.20% 13.60% 12.00% 10.40% 8.80%Cost of Debt 12.80% 12.80% 12.80% 12.80% 12.80% 11.84% 10.88% 9.92% 8.96% 6.76%Debt Ratio 74.91% 74.91% 74.91% 74.91% 74.91% 67.93% 60.95% 53.96% 46.98% 40.00%Cost of Capital 13.80% 13.80% 13.80% 13.80% 13.80% 12.92% 11.94% 10.88% 9.72% 7.98%

Revenues $3,804 $5,326 $6,923 $8,308 $9,139 $10,053 $11,058 $11,942 $12,659 $13,292 EBITDA ($95) $ 0 $346 $831 $1,371 $1,809 $2,322 $2,508 $3,038 $3,589 EBIT ($1,675) ($1,738) ($1,565) ($1,272) $320 $1,074 $1,550 $1,697 $2,186 $2,694 EBIT (1-t) ($1,675) ($1,738) ($1,565) ($1,272) $320 $1,074 $1,550 $1,697 $2,186 $2,276 + Depreciation $1,580 $1,738 $1,911 $2,102 $1,051 $736 $773 $811 $852 $894 - Cap Ex $3,431 $1,716 $1,201 $1,261 $1,324 $1,390 $1,460 $1,533 $1,609 $1,690 - Chg WC $ 0 $46 $48 $42 $25 $27 $30 $27 $21 $19 FCFF ($3,526) ($1,761) ($903) ($472) $22 $392 $832 $949 $1,407 $1,461

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Valuing Global Crossing with Distress

Probability of distress• Price of 8 year, 12% bond issued by Global Crossing = $ 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

653 120(1 Distress)

t

(1.05)tt1

t8

1000(1 Distress)

8

(1.05)8

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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.

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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.

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Current EVANet Income = $ 3104 - Equity cost = $ 1645Equity EVA = $ 1459

Expected Growth.60 * 20% =12%

Forever

Firm is in stable growth:Growth rate = 5%Return on Equity = 15%Cost of equity =9.40%

Terminal Value= $2220/(.094-.05)=50,459

Cost of Equity10.60%

Discount at Cost of Equity

Riskfree Rate:5.00% +

Beta1.40 X

Risk Premium4.00%

Base EquityPremium = 4%

Country RiskPremium=0%

EQUITY VALUATION WITH EQUITY EVA

Book Equity= 17997+ PV of EVA= 38334= Equity EVA=56331Value/sh = $50.26

Net Income $3,599 $4,031 $4,515 $5,057 $5,664 - Equity Cost (see below) $1,908 $2,137 $2,393 $2,680 $3,002Excess Equity Return $1,692 $1,895 $2,122 $2,377 $2,662

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Choosing the right Discounted Cashflow Model

Can you estimate cash flows?

Yes No

Use dividend discount model

Is leverage stable or likely to change over time?

Stable leverage

Unstable leverage

Are the current earnings positive & normal?

Yes

Use current earnings as base

No

Is the cause temporary?

Yes No

Replace current earnings with normalized earnings

Is the firm likely to survive?

Yes No

Adjust margins over time to nurse firm to financial health

Does the firm have a lot of debt?

YesNo

Value Equity as an option to liquidate

Estimate liquidation value

What rate is the firm growingat currently?

< Growth rate of economy

Stable growthmodel

> Growth rate of economy

Are the firm’s competitive advantges time limited?

Yes No

2-stage model

3-stage orn-stagemodel

FCFE FCFF

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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.

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Variations on Multiples

Equity versus Firm Value• Equity multiples (Price per share or Market value of equity)• Firm value multiplies (Firm value or Enterprise 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• Most recent financial year (Current)• Last four quarters (Trailing)• Average over last few years (Normalized)• Expected future year (Forward)

Comparables• Sector• Market

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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.

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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

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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?

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PE Ratio: Descriptive Statistics

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PE: Deciphering the Distribution

Current PE Trailing PE Forward PEMean 36.04 34.14 30.79Standard Error 1.94 2.93 1.15Median 18.25 17.25 18.52Standard Deviation 123.36 176.34 57.56Skewness 23.13 28.40 13.66Minimum 0.65 1.35 3.30Maximum 5103.50 6914.50 1414.00Count 4024 3627 2491Largest(500) 48.00 39.60 34.49Smallest(500) 9.38 9.62 12.94

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8 Times EBITDA is not cheap…

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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.

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Relative Value and Fundamentals

Value of Stock = DPS 1/(ke - g)

PE=Payout Ratio (1+g)/(r-g)

PEG=Payout ratio (1+g)/g(r-g)

PBV=ROE (Payout ratio) (1+g)/(r-g)

PS= Net Margin (Payout ratio)(1+g)/(r-g)

Value of Firm = FCFF1/(WACC -g)

Value/FCFF=(1+g)/(WACC-g)

Value/EBIT(1-t) = (1+g) (1- RIR)/(WACC-g)

Value/EBIT=(1+g)(1-RiR)/(1-t)(WACC-g)

VS= Oper Margin (1-RIR) (1+g)/(WACC-g)

Equity Multiples

Firm Multiples

PE=f(g, payout, risk) PEG=f(g, payout, risk) PBV=f(ROE,payout, g, risk) PS=f(Net Mgn, payout, g, risk)

V/FCFF=f(g, WACC) V/EBIT(1-t)=f(g, RIR, WACC) V/EBIT=f(g, RIR, WACC, t) VS=f(Oper Mgn, RIR, g, WACC)

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What to control for...

Multiple Variables that determine it…PE Ratio Expected Growth, Risk, Payout RatioPBV Ratio Return on Equity, Expected Growth, Risk, Payout PS Ratio Net Margin, Expected Growth, Risk, Payout RatioEVV/EBITDA Expected Growth, Reinvestment rate, Cost of capitalEV/ Sales Operating Margin, Expected Growth, Risk,

Reinvestment

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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.

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Comparing PE Ratios across a Sector

Company Name PE GrowthPT Indosat ADR 7.8 0.06Telebras ADR 8.9 0.075Telecom Corporation of New Zealand ADR 11.2 0.11Telecom Argentina Stet - France Telecom SA ADR B 12.5 0.08Hellenic Telecommunication Organization SA ADR 12.8 0.12Telecomunicaciones de Chile ADR 16.6 0.08Swisscom AG ADR 18.3 0.11Asia Satellite Telecom Holdings ADR 19.6 0.16Portugal Telecom SA ADR 20.8 0.13Telefonos de Mexico ADR L 21.1 0.14Matav RT ADR 21.5 0.22Telstra ADR 21.7 0.12Gilat Communications 22.7 0.31Deutsche Telekom AG ADR 24.6 0.11British Telecommunications PLC ADR 25.7 0.07Tele Danmark AS ADR 27 0.09Telekomunikasi Indonesia ADR 28.4 0.32Cable & Wireless PLC ADR 29.8 0.14APT Satellite Holdings ADR 31 0.33Telefonica SA ADR 32.5 0.18Royal KPN NV ADR 35.7 0.13Telecom Italia SPA ADR 42.2 0.14Nippon Telegraph & Telephone ADR 44.3 0.2France Telecom SA ADR 45.2 0.19Korea Telecom ADR 71.3 0.44

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PE, Growth and Risk

Dependent variable is: PE

R squared = 66.2% R squared (adjusted) = 63.1%

Variable Coefficient SE t-ratio probConstant 13.1151 3.471 3.78 0.0010Growth rate 121.223 19.27 6.29 ≤

0.0001Emerging Market -13.8531 3.606 -3.84 0.0009Emerging Market is a dummy: 1 if emerging market

0 if not

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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.

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PE Ratio without a constant - US StocksModel Summary

.856b .733 .732 1350.677619313Model1

R R SquareaAdjusted R

SquareStd. Error of the

Estimate

For regression through the origin (the no- interceptmodel), R Square measures the proportion of thevariability in the dependent variable about the originexplained by regression. T his CANNOT be compared to RSquare for models which include an intercept.

a.

Predictors: Value Line Beta, Payout Ratio, ExpectedGrowth in EPS: next 5 years

b.

Coefficientsa,b,c

1.228 .055 .514 22.187 .000 1.119 1.336

- 1.1E- 02 .014 - .013 - .768 .443 - .039 .01711.705 .825 .384 14.184 .000 10.087 13.324

Expected Growth inEPS: next 5 yearsPayout RatioValue Line Beta

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig. Lower Bound Upper Bound

95% Confidence Interval forB

Dependent Variable: Current PEa. Linear Regression through the Originb. Weighted Least Squares Regression - Weighted by Market Capc.

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Relative Valuation: Choosing the Right Model

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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.

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Option Payoff Diagrams

Value of AssetStrike Price

Call OptionPut Option

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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.

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Three Basic Questions

When is there a real option embedded in a decision or an asset?• 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. When does that real option have significant economic value?

• 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?• 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

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Putting Natural Resource Options to the Test

The Option Test: • Underlying Asset: Oil or gold in reserve• Contingency: If value > Cost of development: Value - Dev Cost

If value < Cost of development: 0 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: 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.

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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 - CostIf PV of CFs from development < Cost of development: 0

The Exclusivity Test:• Patents restrict competitors from developing similar products• Patents do not restrict competitors from developing other products to treat the same disease.

The Pricing Test• 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.

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The Real Options Test for Growth (Expansion) Options

The Options Test• Underlying Asset: Expansion Project• ContingencyIf PV of CF from expansion > Expansion Cost: PV - Expansion CostIf PV of CF from expansion < Expansion Cost: 0

The Exclusivity Test• Barriers may range from strong (exclusive licenses granted by the government) to weaker

(brand name, knowledge of the market) to weakest (first mover). The Pricing Test

• 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.

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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.

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Valuation Models

Asset BasedValuation

Discounted CashflowModels

Relative Valuation Contingent Claim Models

LiquidationValue

ReplacementCost

Equity ValuationModels

Firm ValuationModels

Cost of capitalapproach

APVapproach

Excess ReturnModels

Stable

Two-stage

Three-stageor n-stage

Current

Normalized

Equity

Firm

Earnings BookValue

Revenues Sectorspecific

Sector

Market

Option todelay

Option toexpand

Option toliquidate

Patent UndevelopedReserves

Youngfirms

Undevelopedland

Equity introubledfirm

Dividends

Free Cashflowto Firm

Aswath Damodaran 46

Which approach should you use? Depends upon the asset being valued..

Mature businessesSeparable & marketable assets

Growth businessesLinked and non-marketable assets

Liquidation &Replacement costvaluation

Other valuation models

Asset Marketability and Valuation Approaches

Cashflows currently orexpected in near future

Assets that will never generate cashflows

Discounted cashflow or relative valuation models

Relative valuation models

Cash Flows and Valuation Approaches

Cashflows if a contingencyoccurs

Option pricing models

Unique asset or businessLarge number of similar assets that are priced

Discounted cashflow or option pricing models

Relative valuation models

Uniqueness of Asset and Valuation Approaches

Aswath Damodaran 47

And the analyst doing the valuation….

Very short time horizonLong Time Horizon

Liquidation value Discounted Cashflow value

Investor Time Horizon and Valuation Approaches

Option pricing models

Relative valuation

Markets are correct on average but make mistakes on individual assets

Discounted Cashflow value

Views on market and Valuation Approaches

Option pricing models

Relative valuation

Markets make mistakes but correct them over time

Asset markets and financialmarkets may diverge

Liquidation value