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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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25

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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28

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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29

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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32

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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35

-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

36

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?

Aswath Damodaran

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37

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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38

PEGRatiosandFundamentals

¨ Riskandpayout,whichaffectPEratios,continuetoaffectPEGratiosaswell.¤ Implication:WhencomparingPEGratiosacrosscompanies,wearemakingimplicitorexplicitassumptionsaboutthesevariables.

¨ DividingPEbyexpectedgrowthdoesnotneutralizetheeffectsofexpectedgrowth,sincetherelationshipbetweengrowthandvalueisnotlinearandfairlycomplex(evenina2-stagemodel)

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39

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

Aswath Damodaran

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40

PEGRatiosandRisk

Aswath Damodaran

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41

PEGRatiosandQualityofGrowth

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42

PERatiosandExpectedGrowth

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PEGRatiosandFundamentals:Propositions

¨ Proposition1:HighriskcompanieswilltradeatmuchlowerPEGratiosthanlowriskcompanieswiththesameexpectedgrowthrate.¤ Corollary1:ThecompanythatlooksmostundervaluedonaPEGratio

basisinasectormaybetheriskiestfirminthesector¨ Proposition2:Companiesthatcanattaingrowthmoreefficiently

byinvestinglessinbetterreturnprojectswillhavehigherPEGratiosthancompaniesthatgrowatthesameratelessefficiently.¤ Corollary2:CompaniesthatlookcheaponaPEGratiobasismaybe

companieswithhighreinvestmentratesandpoorprojectreturns.¨ Proposition3:Companieswithveryloworveryhighgrowthrates

willtendtohavehigherPEGratiosthanfirmswithaveragegrowthrates.Thisbiasisworseforlowgrowthstocks.¤ Corollary3:PEGratiosdonotneutralizethegrowtheffect.

Aswath Damodaran

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