Estimating Discounted Rates

EstimatingDiscountedRatesDamodaranonValuationPartone:DiscountedCashFlowValuationChapter21EstimatingDiscountedRatesCostofEquityCostofDebt2CostofEquityEstimatingParametersforRiskandReturnModelsri=rRF+(rM–rRF)biRisk-freerateRiskpremiumBeta3CostofEquity—Risk-freerateArisk-freeassetisdefinedasonewheretheinvestorknowstheexpectedreturnwithcertainty.Foraninvestmenttoberiskfree,twoconditionshavetobemet:NodefaultriskNouncertaintyaboutreinvestmentrates—nointermediatecashflows(5-yearzerocoupontreasurynotes4CostofEquity—Risk-freerateTheconsistencyprincipleTherisk-freerateusedtocomeupwithexpectedreturnsshouldbemeasuredconsistentlywithhowthecashflowsaremeasured.Currencyinflation5CostofEquity—Risk-freerateRiskfreerateswhenthereisnotdefault-freeentityGovernmentsinemergingmarketsareperceivedascapableofdefaultingevenwhentheyborrowintheirlocalcurrenciesManygovernmentsdonotissuelong-termbondsdenominatedinthelocalcurrency,soalong-termrisk-freerateinthatcurrencyisnotavailable.6CostofEquity—Risk-freerateRiskfreerateswhenthereisnotdefault-freeentity(Method1)Lookatthelargestandsafestfirmsinthatmarketandusetheratethattheypayontheirlong-termborrowingsinthelocalcurrencyasbase.Usearatethatismarginallylowerthanthecorporateborrowingrate(1percent).7CostofEquity—Risk-freerateRiskfreerateswhenthereisnotdefault-freeentity(Method2)Iftherearelong-termdollar-denominatedforwardcontractsonthecurrency,usetheinterestrateparityandthetreasurybondratetoestimatetolocalborrowingrate.Example:ifthecurrentspotrateis38.10ThaibahtperUSdollar,the10-yearforwardrateis61.36bahtperdollarandthecurrent10-yearUSTreasurybondrateis5%,the10-yearThairisk-freerate(innominalbaht)canbeestimatedasfollows:61.36=38.1∗(1+𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡𝑟𝑎𝑡𝑒𝑇ℎ𝑎𝑖𝑏𝑎ℎ𝑡1+0.05)10𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡𝑟𝑎𝑡𝑒𝑇ℎ𝑎𝑖𝑏𝑎ℎ𝑡=10.12%8CostofEquity—Risk-freerateRiskfreerateswhenthereisnotdefault-freeentity(Method3)Risklessrate=Governmentbondrate–DefaultspreadExample:assumethattheBraziliangovernmentbondrate,innominalBrazilianreals(BR),is12%andthelocalcurrencyratingassignedtoBraziliangovernmentisBBB.IfthedefaultspreadforBBBisratebondsis2percent,therisklessBrazilianrealrateisRisklessBRrate=Brazilgovernmentbondrate–Defaultspread=12%-2%=10%9Costofequity—riskpremiumRiskpremiumsmeasuresRiskaversionofinvestorsRiskinessoftheaverageinvestmentEstimateriskpremiumsSurveypremiumsHistoricalpremiumsImpliedequitypremiums10Costofequity—riskpremiumSurveypremiumsSurveyinvestorsabouttheirexpectationsforthefuturereturnsVeryfewpractitionersactuallyusethesesurveypremiumsbecause:1.Noconstraintsonreasonability2.Extremelyvolatile,dependonrecentmarketmovements3.Short-termpremiums11Costofequity—riskpremiumHistoricalPremiumsEstimateissues—TimeperiodusedBenefitofshorterperiods:riskaversionofaverageinvestorsislikelytochangeovertimeandusingashorterandmorerecenttimeperiodprovidesamoreupdatedestimateCostofshorterperiods:greatererrorsintheriskpremiumestimate.EstimatePeriodsStdErrorofRiskPremiumEstimate5years205=8.94%10years2010=6.32%25years2025=4.00%50years2050=2.83%12Costofequity—riskpremiumHistoricalPremiumsEstimateissues—Choiceofrisk-freesecurityGiventhattheyieldcurveintheUShasbeenupward-slopingformostofpastdecades,theriskpremiumislargerwhenestimatedrelativetoshorter-termgovernmentsecurities(suchasTreasurybills)Therisk-freeratechosenincomputepremiumhastobeconsistentwiththerisk-freerateusedtocomputeexpectedreturns.13Costofequity—riskpremiumHistoricalPremiumsEstimateissues—ArithmeticandgeometricaveragesConventionalwisdomarguesfortheuseofthearithmeticaverage.Inreality,thegeometricaverageisbettersinceempiricalstudiesindicatethatreturnsonstocksarenegativelycorrelatedovertime.Stocks-TreasurybillsStocks-TreasuryBondsArithmeticGeometricArithmeticGeometric1928-20047.92%6.53%6.02%4.84%1964-20045.82%4.34%4.59%3.47%1994-20048.60%5.82%6.85%4.51%14Costofequity—riskpremiumHistoricalPremiums—CountryriskpremiumsInmanyemergingmarkets,thereisverylittlehistoricaldataandthedatathatexististoovolatiletoyieldameaningfulestimateoftheriskpremium.TheriskpremiuminanyequitymarketcanbewrittenasEquityriskpremium=Basepremiumformatureequitymarket+countrypremium15Costofequity—riskpremiumHistoricalPremiums—Countryriskpremiums1.CountrybonddefaultspreadsRatingassignedtoacountry’sdebtbyaratingsagency,suchasStandard&Poor’s;Example:BrazilwasratedB1inearly2005byMoody’s,andthe10-yearBrazilianC-bond,whichisdollar-denominatedbond,waspricedtoyield7.75%,3.5%morethantheinterestrate(4.25%)ona10-yearTreasurybondatthesametime.IfweassumethatthetotalequityriskpremiumfortheUSis4.84%,thentheriskpremiumforBrazilwouldbe8.34%.16Costofequity—riskpremiumHistoricalPremiums—Countryriskpremiums2.RelativestandarddeviationsEquityriskpremiumofmarketsreflectthedifferenceinequityrisk,asmeasuredbythevolatilitiesofequitiesinthesemarket.Problems:Thisapproachunderstatetheequityriskpremiuminveryriskemergingmarketsthathavelowstandarddeviationsfortheirequitymarketsbecauseofilliquidity.17Costofequity—riskpremiumHistoricalPremiums—Countryriskpremiums2