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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
0
20
40
60
80
100
120
140
160
180
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
0
5
10
15
20
25
30
35
40
45
50
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
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
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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35
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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