Discounted Cash Flow Valuation: The Inputs

Discounted Cash Flow Valuation:The InputsAswath Damodaran1

The Key Inputs in DCF ValuationlDiscount Rate– Cost of Equity, in valuing equity– Cost of Capital, in valuing the firmlCash Flows– Cash Flows to Equity– Cash Flows to FirmlGrowth (to get future cash flows)– Growth in Equity Earnings– Growth in Firm Earnings (Operating Income)2

I. Estimating Discount RatesDCF Valuation3

Estimating Inputs: Discount RatesllCritical ingredient in discounted cashflow valuation. Errors inestimating the discount rate or mismatching cashflows and discountrates can lead to serious errors in valuation.At an intuitive level, the discount rate used should be consistent withboth the riskiness and the type of cashflow being discounted.– Equity versus Firm: If the cash flows being discounted are cash flows toequity, the appropriate discount rate is a cost of equity. If the cash flowsare cash flows to the firm, the appropriate discount rate is the cost ofcapital.– Currency: The currency in which the cash flows are estimated should alsobe the currency in which the discount rate is estimated.– Nominal versus Real: If the cash flows being discounted are nominal cashflows (i.e., reflect expected inflation), the discount rate should be nominal4

I. Cost of EquitylThe cost of equity is the rate of return that investors require to make anequity investment in a firm. There are two approaches to estimatingthe cost of equity;– a dividend-growth model.– a risk and return modelllThe dividend growth model (which specifies the cost of equity to bethe sum of the dividend yield and the expected growth in earnings) isbased upon the premise that the current price is equal to the value. Itcannot be used in valuation, if the objective is to find out if an asset iscorrectly valued.A risk and return model, on the other hand, tries to answer twoquestions:– How do you measure risk?– How do you translate this risk measure into a risk premium?5

What is Risk?lRisk, in traditional terms, is viewed as a ‘negative’. Webster’sdictionary, for instance, defines risk as “exposing to danger or hazard”.The Chinese symbols for risk are reproduced below:lThe first symbol is the symbol for “danger”, while the second is thesymbol for “opportunity”, making risk a mix of danger andopportunity.6

Risk and Return ModelsStep 1: Defining RiskThe risk in an investment can be measured by the variance in actual returns around anexpected returnRiskless InvestmentLow Risk InvestmentHigh Risk InvestmentE(R)E(R)E(R)Step 2: Differentiating between Rewarded and Unrewarded RiskRisk that is specific to investment (Firm Specific)Risk that affects all investments (Market Risk)Can be diversified away in a diversified portfolioCannot be diversified away since most assets1. each investment is a small proportion of portfolioare affected by it.2. risk averages out across investments in portfolioThe marginal investor is assumed to hold a “diversified” portfolio. Thus, only market risk willbe rewarded and priced.Step 3: Measuring Market RiskThe CAPMIf there is1. no private information2. no transactions costthe optimal diversifiedportfolio includes everytraded asset. Everyonewill hold this market portfolioMarket Risk Riskadded by any investmentto the market portfolio:Beta of asset relative toMarket portfolio (froma regression)The APMIf there are noarbitrage opportunitiesthen the market risk ofany asset must becaptured by betasrelative to factors thataffect all investments.Market Risk Riskexposures of anyasset to marketfactorsMulti-Factor ModelsSince market risk affectsmost or all investments,it must come frommacro economic factors.Market Risk Riskexposures of anyasset to macroeconomic factors.Betas of asset relativeto unspecified marketfactors (from a factoranalysis)Betas of assets relativeto specified macroeconomic factors (froma regression)Proxy ModelsIn an efficient market,differences in returnsacross long periods mustbe due to market riskdifferences. Looking forvariables correlated withreturns should then giveus proxies for this risk.Market Risk Captured by theProxy Variable(s)Equation relatingreturns to proxyvariables (from aregression)7

Comparing Risk ModelsModelCAPMAPMMultifactorProxyExpected ReturnE(R) Rf β (Rm- Rf)Inputs NeededRiskfree RateBeta relative to market portfolioMarket Risk PremiumE(R) Rf Σj 1 βj (Rj- Rf) Riskfree Rate; # of Factors;Betas relative to each factorFactor risk premiumsE(R) Rf Σj 1,,N βj (Rj- Rf) Riskfree Rate; Macro factorsBetas relative to macro factorsMacro economic risk premiumsE(R) a Σj 1.N bj YjProxiesRegression coefficients8

Beta’s PropertiesllBetas are standardized around one.Ifβ 1β 1β 1β 0l. Average risk investment. Above Average risk investment. Below Average risk investment. Riskless investmentThe average beta across all investments is one.9

Limitations of the CAPMll1. The model makes unrealistic assumptions2. The parameters of the model cannot be estimated precisely– - Definition of a market index– - Firm may have changed during the 'estimation' period'l3. The model does not work well– - If the model is right, there should bell* a linear relationship between returns and betas* the only variable that should explain returns is betas– - The reality is thatll* the relationship between betas and returns is weak* Other variables (size, price/book value) seem to explain differences inreturns better.10

Inputs required to use the CAPM (a) the current risk-free rate(b) the expected return on the market index and(c) the beta of the asset being analyzed.11

Riskfree Rate in ValuationloooThe correct risk free rate to use in a risk and return model isa short-term Government Security rate (eg. T.Bill), since it has nodefault risk or price riska long-term Government Security rate, since it has no default riskother: specify - 12

The Riskfree RatelllOn a riskfree asset, the actual return is equal to the expected return.Therefore, there is no variance around the expected return.For an investment to be riskfree, i.e., to have an actual return be equalto the expected return, two conditions have to be met –– There has to be no default risk, which generally implies that the securityhas to be issued by the government. Note, however, that not allgovernments can be viewed as default free.– There can be no uncertainty about reinvestment rates, which implies that itis a zero coupon security with the same maturity as the cash flow beinganalyzed.13

Riskfree Rate in PracticelllThe riskfree rate is the rate on a zero coupon government bondmatching the time horizon of the cash flow being analyzed.Theoretically, this translates into using different riskfree rates for eachcash flow - the 1 year zero coupon rate for the cash flow in year 2, the2-year zero coupon rate for the cash flow in year 2 .Practically speaking, if there is substantial uncertainty about expectedcash flows, the present value effect of using time varying riskfree ratesis small enough that it may not be worth it.14

The Bottom Line on Riskfree RateslllUsing a long term government rate (even on a coupon bond) as theriskfree rate on all of the cash flows in a long term analysis will yield aclose approximation of the true value.For short term analysis, it is entirely appropriate to use a short termgovernment security rate as the riskfree rate.If the analysis is being done in real terms (rather than nominal terms)use a real riskfree rate, which can be obtained in one of two ways –– from an inflation-indexed government bond, if one exists– set equal, approximately, to the long term real growth rate of the economyin which the valuation is being done.15

Riskfree Rate in ValuationlooooYou are valuing a Brazilian company in nominal U.S. dollars. Thecorrect riskfree rate to use in this valuation is:the U.S. treasury bond ratethe Brazilian C-Bond rate (the rate on dollar denominated Brazilianlong term debt)the local riskless Brazilian Real rate (in nominal terms)the real riskless Brazilian Real rate16

Measurement of the risk premiumllThe risk premium is the premium that investors demand for investingin an average risk investment, relative to the riskfree rate.As a general proposition, this premium should be– greater than zero– increase with the risk aversion of the investors in that market– increase with the riskiness of the “average” risk investment17

Risk Aversion and Risk PremiumslllIf this were the capital market line, the risk premium would be aweighted average of the risk premiums demanded by each and everyinvestor.The weights will be determined by the magnitude of wealth that eachinvestor has. Thus, Warren Bufffet’s risk aversion counts moretowards determining the “equilibrium” premium than yours’ and mine.As investors become more risk averse, you would expect the“equilibrium” premium to increase.18

Estimating Risk Premiums in PracticelllSurvey investors on their desired risk premiums and use the averagepremium from these surveys.Assume that the actual premium delivered over long time periods isequal to the expected premium - i.e., use historical dataEstimate the implied premium in today’s asset prices.19

The Survey ApproachlllSurveying all investors in a market place is impractical.However, you can survey a few investors (especially the largerinvestors) and use these results. In practice, this translates into surveysof money managers’ expectations of expected returns on stocks overthe next year.The limitations of this approach are:– there are no constraints on reasonability (the survey could producenegative risk premiums or risk premiums of 50%)– they are extremely volatile– they tend to be short term; even the longest surveys do not go beyond oneyear20

The Historical Premium ApproachllThis is the default approach used by most to arrive at the premium touse in the modelIn most cases, this approach does the following– it defines a time period for the estimation (1926-Present, 1962-Present.)– it calculates average returns on a stock index during the period– it calculates average returns on a riskless security over the period– it calculates the difference between the two– and uses it as a premium looking forwardlThe limitations of this approach are:– it assumes that the risk aversion of investors has not changed in asystematic way across time. (The risk aversion may change from year toyear, but it reverts back to historical averages)– it assumes that the riskiness of the “risky” portfolio (stock index) has notchanged in a systematic way across time.21

Historical Average Premiums for the UnitedStatesHistorical period Stocks - T.BillsArith Geom1926-19968.76% 6.95%1962-19965.74% 4.63%1981-199610.34% 9.72%What is the right premium?Stocks - T.BondsArith Geom7.57% 5.91%5.16% 4.46%9.22% 8.02%22

What about historical premiums for othermarkets?llHistorical data for markets outside the United States tends to be sketchand unreliable.Ibbotson, for instance, estimates the following premiums for majormarkets from 45%Risk 5%23

Risk Premiums for Latin raguayPeruUruguayRatingBBBBBAAA BBB BBBBBBBRisk Premium5.5% 1.75% 7.25%5.5% 2% 7.5%5.5% 0.75% 6.25%5.5% 1.25% 6.75%5.5% 1.5% 7%5.5% 1.75% 7.25%5.5% 2.5% 8%5.5% 1.75% 7.25%24

Risk Premiums for kistanPhillipinesSingaporeTaiwanThailandRatingBBB BBBBB AAAAAA B BB AAAAA ARisk Premium5.5% 1.5% 7.00%5.5% 1.75% 7.25%5.5% 2.00% 7.50%5.5% 0.00% 5.50%5.5% 1.00% 6.50%5.5% 1.25% 6.75%5.5% 2.75% 8.25%5.5% 2.00% 7.50%5.5% 0.00% 7.50%5.5% 0.50% 6.00%5.5% 1.35% 6.85%25