I . PE Ratiospeople.stern.nyu.edu/adamodar/pdfiles/eqnotes/pe.pdf · 24 I . PE Ratios ¨ To...
Transcript of I . PE Ratiospeople.stern.nyu.edu/adamodar/pdfiles/eqnotes/pe.pdf · 24 I . PE Ratios ¨ To...
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I.PERatios
¨ Tounderstandthefundamentals,startwithabasicequitydiscountedcashflowmodel.¤ Withthedividenddiscountmodel,
¤ Dividingbothsidesbythecurrentearningspershare,
¤ IfthishadbeenaFCFEModel,
P0 =DPS1r −gn
P0
EPS0
= PE= Payout Ratio*(1+gn )
r-gn
P0 =FCFE1r −gn
P0
EPS0
= PE= (FCFE/Earnings)*(1+gn )
r-gnAswath Damodaran
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UsingtheFundamentalModeltoEstimatePEForaHighGrowthFirm
¨ Theprice-earningsratioforahighgrowthfirmcanalsoberelatedtofundamentals.Inthespecialcaseofthetwo-stagedividenddiscountmodel,thisrelationshipcanbemadeexplicitfairlysimply:
¤ Forafirmthatdoesnotpaywhatitcanaffordtoindividends,substituteFCFE/Earningsforthepayoutratio.
¨ Dividingbothsidesbytheearningspershare:
P0 =EPS0*Payout Ratio*(1+g)* 1− (1+g)n
(1+r)n
"
#$
%
&'
r-g+ EPS0*Payout Ration*(1+g)n*(1+gn )
(r-gn )(1+r)n
P0EPS0
=Payout Ratio * (1 + g) * 1 − (1 + g)n
(1+ r)n"
# $ %
& '
r - g+
Payout Ratio n *(1+ g)n * (1 + gn )(r - gn )(1+ r)n
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ASimpleExample
¨ AssumethatyouhavebeenaskedtoestimatethePEratioforafirmwhichhasthefollowingcharacteristics:
Variable HighGrowthPhase StableGrowthPhaseExpectedGrowthRate 25% 8%PayoutRatio 20% 50%Beta 1.00 1.00Numberofyears 5years Foreverafteryear5
Riskfree rate=T.Bond Rate=6%Requiredrateofreturn=6%+1(5.5%)=11.5%
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P0
EPS0
=.20*(1.25)* 1− (1.25)5
(1.115)5
"
#$
%
&'
.115-.25+ .50*(1.25)5*(1.08)
(.115-.08)(1.115)5 = 28.75
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a.PEandGrowth:Firmgrowsatx%for5years,8%thereafter
PE Ratios and Expected Growth: Interest Rate Scenarios
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5% 10% 15% 20% 25% 30% 35% 40% 45% 50%
Expected Growth Rate
PE
Ratio r=4%
r=6%
r=8%
r=10%
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b.PEandRisk:AFollowupExample
PE Ratios and Beta: Growth Scenarios
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0.75 1.00 1.25 1.50 1.75 2.00
Beta
PE
Rati
o g=25%
g=20%
g=15%
g=8%
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Example1:ComparingPEratiosacrossEmergingMarkets- March2014(pre- Ukraine)
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Russia looks really cheap, right?
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Example2:AnOldExamplewithEmergingMarkets:June2000
Country PE Ratio Interest Rates
GDP Real Growth
Country Risk
Argentina 14 18.00% 2.50% 45Brazil 21 14.00% 4.80% 35Chile 25 9.50% 5.50% 15Hong Kong 20 8.00% 6.00% 15India 17 11.48% 4.20% 25Indonesia 15 21.00% 4.00% 50Malaysia 14 5.67% 3.00% 40Mexico 19 11.50% 5.50% 30Pakistan 14 19.00% 3.00% 45Peru 15 18.00% 4.90% 50Phillipines 15 17.00% 3.80% 45Singapore 24 6.50% 5.20% 5South Korea 21 10.00% 4.80% 25Thailand 21 12.75% 5.50% 25Turkey 12 25.00% 2.00% 35Venezuela 20 15.00% 3.50% 45
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RegressionResults
¨ TheregressionofPEratiosonthesevariablesprovidesthefollowing–PE=16.16 - 7.94InterestRates
+154.40GrowthinGDP- 0.1116CountryRisk
RSquared=73%
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PredictedPERatios
Country PE Ratio Interest Rates
GDP Real Growth
Country Risk
Predicted PE
Argentina 14 18.00% 2.50% 45 13.57Brazil 21 14.00% 4.80% 35 18.55Chile 25 9.50% 5.50% 15 22.22Hong Kong 20 8.00% 6.00% 15 23.11India 17 11.48% 4.20% 25 18.94Indonesia 15 21.00% 4.00% 50 15.09Malaysia 14 5.67% 3.00% 40 15.87Mexico 19 11.50% 5.50% 30 20.39Pakistan 14 19.00% 3.00% 45 14.26Peru 15 18.00% 4.90% 50 16.71Phillipines 15 17.00% 3.80% 45 15.65Singapore 24 6.50% 5.20% 5 23.11South Korea 21 10.00% 4.80% 25 19.98Thailand 21 12.75% 5.50% 25 20.85Turkey 12 25.00% 2.00% 35 13.35Venezuela 20 15.00% 3.50% 45 15.35
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Example3:PEratiosfortheS&P500overtime
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0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00
50.00
1969
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PERatiosfortheS&P500:1969-2015
PE NormalizedPE CAPE
PE NormalizedPE CAPE1969-2015 16.06 20.70 17.081986-2015 18.52 24.00 20.341996-2015 19.61 25.61 22.292006-2015 16.90 20.88 18.45
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Islow(high)PEcheap(expensive)?
¨ AmarketstrategistarguesthatstocksareexpensivebecausethePEratiotodayishighrelativetotheaveragePEratioacrosstime.Doyouagree?a. Yesb. No
¨ Ifyoudonotagree,whatfactorsmightexplainthehigherPEratiotoday?
¨ WouldyouresponddifferentlyifthemarketstrategisthasaNobelPrizeinEconomics?
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E/PRatios,T.BondRatesandTermStructure
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-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014
EarningstoPriceversusInterestRates:S&P500
EarningsYield T.BondRate Bond-Bill
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RegressionResults
¨ ThereisastrongpositiverelationshipbetweenE/PratiosandT.Bond rates,asevidencedbythecorrelationof0.66betweenthetwovariables.,
¨ Inaddition,thereisevidencethatthetermstructurealsoaffectsthePEratio.¨ Inthefollowingregression,using1960-2014data,weregressE/Pratiosagainst
thelevelofT.Bond ratesandatermstructurevariable(T.Bond - T.Bill rate)E/P=3.51%+0.5598T.Bond Rate– 0.1374(T.Bond Rate-T.Bill Rate)
(4.93) (6.23) (-0.65)Rsquared=41.28%
¨ Goingbackto2008,thisiswhattheregressionlookedlike:E/P=2.56%+0.7044T.Bond Rate– 0.3289(T.Bond Rate-T.Bill Rate)
(4.71) (7.10) (1.46)Rsquared=50.71%TheR-squaredhasdroppedandtheT.Bond rateandthedifferentialwiththeT.Billratehavenoth lostsignificance.Howwouldyoureadthisresult?
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II.PEGRatio
¨ PEGRatio=PEratio/ExpectedGrowthRateinEPS¤ Forconsistency,youshouldmakesurethatyourearningsgrowth
reflectstheEPSthatyouuseinyourPEratiocomputation.¤ Thegrowthratesshouldpreferablybeoverthesametimeperiod.
¨ TounderstandthefundamentalsthatdeterminePEGratios,letusreturnagaintoa2-stageequitydiscountedcashflowmodel:
¨ DividingbothsidesoftheequationbytheearningsgivesustheequationforthePEratio.Dividingitagainbytheexpectedgrowth‘g:
P0 =EPS0*Payout Ratio*(1+g)* 1− (1+g)n
(1+r)n
"
#$
%
&'
r-g+ EPS0*Payout Ration*(1+g)n*(1+gn )
(r-gn )(1+r)n
PEG=Payout Ratio*(1+g)* 1− (1+g)n
(1+r)n
"
#$
%
&'
g(r-g)+ Payout Ration*(1+g)n*(1+gn )
g(r-gn )(1+r)n
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PEGRatiosandFundamentals
¨ Riskandpayout,whichaffectPEratios,continuetoaffectPEGratiosaswell.¤ Implication:WhencomparingPEGratiosacrosscompanies,wearemakingimplicitorexplicitassumptionsaboutthesevariables.
¨ DividingPEbyexpectedgrowthdoesnotneutralizetheeffectsofexpectedgrowth,sincetherelationshipbetweengrowthandvalueisnotlinearandfairlycomplex(evenina2-stagemodel)
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ASimpleExample
¨ AssumethatyouhavebeenaskedtoestimatethePEGratioforafirmwhichhasthefollowingcharacteristics:
Variable HighGrowthPhase StableGrowthPhaseExpectedGrowthRate 25% 8%PayoutRatio 20% 50%Beta 1.00 1.00¨ Riskfree rate=T.Bond Rate=6%
¨ Requiredrateofreturn=6%+1(5.5%)=11.5%¨ ThePEGratioforthisfirmcanbeestimatedasfollows:
PEG =0.2 * (1.25) * 1− (1.25)5
(1.115)5
"
#$
%
&'
.25(.115 - .25)+ 0.5 * (1.25)5*(1.08)
.25(.115-.08) (1.115)5 = 115 or 1.15
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PEGRatiosandRisk
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PEGRatiosandQualityofGrowth
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PERatiosandExpectedGrowth
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PEGRatiosandFundamentals:Propositions
¨ Proposition1:HighriskcompanieswilltradeatmuchlowerPEGratiosthanlowriskcompanieswiththesameexpectedgrowthrate.¤ Corollary1:ThecompanythatlooksmostundervaluedonaPEGratio
basisinasectormaybetheriskiestfirminthesector¨ Proposition2:Companiesthatcanattaingrowthmoreefficiently
byinvestinglessinbetterreturnprojectswillhavehigherPEGratiosthancompaniesthatgrowatthesameratelessefficiently.¤ Corollary2:CompaniesthatlookcheaponaPEGratiobasismaybe
companieswithhighreinvestmentratesandpoorprojectreturns.¨ Proposition3:Companieswithveryloworveryhighgrowthrates
willtendtohavehigherPEGratiosthanfirmswithaveragegrowthrates.Thisbiasisworseforlowgrowthstocks.¤ Corollary3:PEGratiosdonotneutralizethegrowtheffect.
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