117

AnImpliedERP

Aswath Damodaran

Base year cash flow (last 12 mths)Dividends (TTM): 42.66+ Buybacks (TTM): 63.43

= Cash to investors (TTM): 106.09

Expected growth in next 5 yearsTop down analyst estimate of earnings

growth for S&P 500: 5.55%

Risk free rate = T.Bond rate on 1/1/16= 2.27%

r = Implied Expected Return on Stocks = 8.39%

S&P 500 on 1/1/16= 2043.94

Minus

Implied Equity Risk Premium (1/1/16) = 8.39% - 2.27% = 6.12%

Equals

Earnings and Cash flows grow @2.27% (set equal to risk free rate) a year forever.

Payout ratio assumed to stay stable. 106.09 growing @ 5.55% a year

Last12mths 1 2 3 4 5 TerminalYearDividends+Buybacks 106.09 111.99$ 118.21$ 124.77$ 131.70$ 139.02$ 142.17

2043.94 = 111.99(1 + ,) +118.21(1 + ,)/ +

124.77(1 + ,)1 +

131.70(1 + ,)2 +

139.02(1 + ,)3 +

142.17(, − .0227)(1 + ,)3

You have to solve for the discount rate (r). I

used the solver or Goal seek function in Excel

118

ImpliedPremiumsintheUS:1960-2015

Aswath Damodaran

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

19601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982198319841985198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012201320142015

Impl

ied

Prem

ium

Year

Implied Premium for US Equity Market: 1960-2015

Black #: Total ERPRed #: Country risk premiumAVG: GDP weighted average

ERP

: Jan

201

6

120

Applica?onTest:Es?ma?ngaMarketRiskPremium

AswathDamodaran

120

¨  Foryourcompany,getthegeographicalbreakdownofrevenuesinthemostrecentyear.Baseduponthisrevenuebreakdownandthemostrecentcountryriskpremiums,es?matetheequityriskpremiumthatyouwoulduseforyourcompany.

¨  Thiscomputa?onwasbaseden?relyonrevenues.Withyourcompany,whatconcernswouldyouhaveaboutyoures?matebeingtoohighortoolow?

121

Es?ma?ngBeta

AswathDamodaran

121

¨  Thestandardprocedurefores?ma?ngbetasistoregressstockreturns(Rj)againstmarketreturns(Rm):

Rj=a+bRmwhereaistheinterceptandbistheslopeoftheregression.

¨  Theslopeoftheregressioncorrespondstothebetaofthestock,andmeasurestheriskinessofthestock.

¨  TheRsquared(R2)oftheregressionprovidesanes?mateofthepropor?onoftherisk(variance)ofafirmthatcanbeaWributedtomarketrisk.Thebalance(1-R2)canbeaWributedtofirmspecificrisk.

122

Es?ma?ngPerformance

AswathDamodaran

122

¨  Theinterceptoftheregressionprovidesasimplemeasureofperformanceduringtheperiodoftheregression,rela?vetothecapitalassetpricingmodel.Rj =Rf+b(Rm-Rf)

=Rf(1-b)+bRm ........... CapitalAssetPricingModelRj =a +bRm ........... RegressionEqua?on

¨  If a>Rf(1-b)....StockdidbeWerthanexpectedduringregressionperioda=Rf(1-b)....Stockdidaswellasexpectedduringregressionperioda<Rf(1-b)....Stockdidworsethanexpectedduringregressionperiod

¨  ThedifferencebetweentheinterceptandRf(1-b)isJensen'salpha.Ifitisposi?ve,yourstockdidperformbeWerthanexpectedduringtheperiodoftheregression.

123

Se_ngupfortheEs?ma?on

AswathDamodaran

123

¨  Decideonanes?ma?onperiod¤  Servicesuseperiodsrangingfrom2to5yearsfortheregression¤  Longeres?ma?onperiodprovidesmoredata,butfirmschange.¤  Shorterperiodscanbeaffectedmoreeasilybysignificantfirm-specific

eventthatoccurredduringtheperiod¤  Decideonareturninterval-daily,weekly,monthly

¤  Shorterintervalsyieldmoreobserva?ons,butsufferfrommorenoise.¤  Noiseiscreatedbystocksnottradingandbiasesallbetastowardsone.

¨  Es?matereturns(includingdividends)onstock¤  Return=(PriceEnd-PriceBeginning+DividendsPeriod)/PriceBeginning¤  Includeddividendsonlyinex-dividendmonth

¨  Chooseamarketindex,andes?matereturns(inclusiveofdividends)ontheindexforeachintervalfortheperiod.

124

ChoosingtheParameters:Disney

¨  Periodused:5years¨  ReturnInterval=Monthly¨  MarketIndex:S&P500Index.¨  Forinstance,tocalculatereturnsonDisneyinDecember2009,

¤  PriceforDisneyatendofNovember2009=$30.22¤  PriceforDisneyatendofDecember2009=$32.25¤  Dividendsduringmonth=$0.35(Itwasanex-dividendmonth)¤  Return=($32.25-$30.22+$0.35)/$30.22=7.88%

¨  Toes?matereturnsontheindexinthesamemonth¤  IndexlevelatendofNovember2009=1095.63¤  IndexlevelatendofDecember2009=1115.10¤  DividendsonindexinDecember2009=1.683¤  Return=(1115.1–1095.63+1.683)/1095.63=1.78%

Aswath Damodaran

Disney’sHistoricalBeta

!ReturnonDisney=.0071+1.2517ReturnonMarketR²=0.73386

(0.10)

126

AnalyzingDisney’sPerformance

¨  Intercept=0.712%¤  Thisisaninterceptbasedonmonthlyreturns.Thus,ithastobe

comparedtoamonthlyriskfreerate.¤  Between2008and2013

n  AverageAnnualizedT.Billrate=0.50%n MonthlyRiskfreeRate=0.5%/12=0.042%n  RiskfreeRate(1-Beta)=0.042%(1-1.252)=-.0105%

¨  TheComparisonisthenbetween¤  Intercept versus RiskfreeRate(1-Beta)¤  0.712% versus 0.0105%¤  Jensen’sAlpha=0.712%-(-0.0105)%=0.723%

¨  Disneydid0.723%beWerthanexpected,permonth,betweenOctober2008andSeptember2013¤  Annualized,Disney’sannualexcessreturn=(1.00723)12-1=9.02%

Aswath Damodaran

127

MoreonJensen’sAlpha

AswathDamodaran

127

¨  Ifyoudidthisanalysisoneverystocklistedonanexchange,whatwouldtheaverageJensen’salphabeacrossallstocks?a.  Dependuponwhetherthemarketwentupordownduringtheperiodb.  Shouldbezeroc.  Shouldbegreaterthanzero,becausestockstendtogoupmoreopenthandown.

¨  Disneyhasaposi?veJensen’salphaof9.02%ayearbetween2008and2013.Thiscanbeviewedasasignthatmanagementinthefirmdidagoodjob,managingthefirmduringtheperiod.a.  Trueb.  False

¨  Disneyhashadaposi?veJensen’salphabetween2008and2013.Ifyouwereaninvestorinearly2014,lookingatthestock,youwouldviewthisasasignthatthestockwillbea:a.  Goodinvestmentforthefutureb.  Badinvestmentforthefuturec.  Noinforma?onaboutthefuture

128

Es?ma?ngDisney’sBeta

¨  SlopeoftheRegressionof1.25isthebeta¨  Regressionparametersarealwayses?matedwitherror.Theerroriscapturedinthestandarderrorofthebetaes?mate,whichinthecaseofDisneyis0.10.

¨  AssumethatIaskedyouwhatDisney’struebetais,aperthisregression.¤  Whatisyourbestpointes?mate?

¤  Whatrangewouldyougiveme,with67%confidence?

¤  Whatrangewouldyougiveme,with95%confidence?

Aswath Damodaran

129

TheDirtySecretof“StandardError”

Distribution of Standard Errors: Beta Estimates for U.S. stocks

0

200

400

600

800

1000

1200

1400

1600

<.10 .10 - .20 .20 - .30 .30 - .40 .40 -.50 .50 - .75 > .75

Standard Error in Beta Estimate

Num

ber o

f Firm

s

Aswath Damodaran

130

BreakingdownDisney’sRisk

¨  RSquared=73%¨  Thisimpliesthat

¤  73%oftheriskatDisneycomesfrommarketsources¤  27%,therefore,comesfromfirm-specificsources

¨  Thefirm-specificriskisdiversifiableandwillnotberewarded.

¨  TheR-squaredforcompanies,globally,hasincreasedsignificantlysince2008.Whymightthisbehappening?

¨  Whataretheimplica?onsforinvestors?

Aswath Damodaran

131

TheRelevanceofRSquared

AswathDamodaran

131

¨  YouareadiversifiedinvestortryingtodecidewhetheryoushouldinvestinDisneyorAmgen.Theybothhavebetasof1.25,butDisneyhasanRSquaredof73%whileAmgen’sRsquaredisonly25%.Whichonewouldyouinvestin?¤  Amgen,becauseithasthelowerRsquared¤ Disney,becauseithasthehigherRsquared¤  Youwouldbeindifferent

¨  Wouldyouranswerbedifferentifyouwereanundiversifiedinvestor?

132

BetaEs?ma?on:UsingaService(Bloomberg)

Aswath Damodaran