I.PERatios
24
¨
Tounderstandthefundamentals,startwithabasic
equitydiscountedcashflowmodel.
¤
Withthedividenddiscountmodel,
P0 =
¤
DPS1
r − gn
Dividingbothsidesbythecurrentearningspershare,
P0
Payout Ratio*(1+ g n )
= PE=
EPS0
r-gn
¤
IfthishadbeenaFCFEModel,
FCFE1
r − gn
(FCFE/Earnings)*(1+ g n )
P0 =
Aswath Damodaran
P0
= PE=
EPS0
r-gn
24
UsingtheFundamentalModeltoEstimatePE
ForaHighGrowthFirm
25
¨
Theprice-earningsratioforahighgrowthfirmcanalsobe
relatedtofundamentals.Inthespecialcaseofthetwo-stage
dividenddiscountmodel,thisrelationshipcanbemade
explicitfairlysimply:
" (1+g)n %
EPS0 *Payout Ratio*(1+g)*$1−
n '
n
# (1+r) & EPS0 *Payout Ratio n *(1+g) *(1+g n )
P0 =
+
r-g
(r-g n )(1+r)n
Forafirmthatdoesnotpaywhatitcanaffordtoin
dividends,substituteFCFE/Earningsforthepayoutratio.
Dividingbothsidesbytheearningspershare:
"
¤
¨
Aswath Damodaran
(1 + g)n %
'
Payout Ratio * (1 + g) * $ 1 −
#
(1+ r) n &
P0
Payout Ratio n *(1+ g) n * (1 + gn )
=
+
EPS0
r -g
(r - g n )(1+ r) n
25
ASimpleExample
26
¨
AssumethatyouhavebeenaskedtoestimatethePEratioforafirm
whichhasthefollowingcharacteristics:
Variable
HighGrowthPhase
StableGrowthPhase
ExpectedGrowthRate
25%
8%
PayoutRatio
20%
50%
Beta
1.00
1.00
Numberofyears
5years
Foreverafteryear5
Riskfree rate=T.Bond Rate=6%
Requiredrateofreturn=6%+1(5.5%)=11.5%
"
(1.25)5 %
.20*(1.25)*$1−
5'
5
P0
# (1.115) & .50*(1.25) *(1.08)
=
+
= 28.75
EPS0
.115-.25
(.115-.08)(1.115)5
Aswath Damodaran
26
a.PEandGrowth:Firmgrowsatx%for5years,
8%thereafter
27
PE Ratios and Expected Growth: Interest Rate Scenarios
180
160
140
Ratio
100
PE
120
80
r=4%
r=6%
r=8%
r=10%
60
40
20
0
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
Expected Growth Rate
Aswath Damodaran
27
b.PEandRisk:AFollowupExample
28
PE Ratios and Beta: Growth Scenarios
50
45
40
35
g=25%
g=20%
g=15%
g=8%
25
PE
Ratio
30
20
15
10
5
0
0.75
1.00
1.25
1.50
1.75
2.00
Beta
Aswath Damodaran
28
Example1:ComparingPEratiosacross
EmergingMarkets- March2014(pre- Ukraine)
29
Russia looks really cheap, right?
Aswath Damodaran
29
Example2:AnOldExamplewithEmerging
Markets:June2000
30
Country
PE Ratio
Argentina
Brazil
Chile
Hong Kong
India
Indonesia
Malaysia
Mexico
Pakistan
Peru
Phillipines
Singapore
South Korea
Thailand
Turkey
Venezuela
14
21
25
20
17
15
14
19
14
15
15
24
21
21
12
20
Aswath Damodaran
Interest
Rates
18.00%
14.00%
9.50%
8.00%
11.48%
21.00%
5.67%
11.50%
19.00%
18.00%
17.00%
6.50%
10.00%
12.75%
25.00%
15.00%
GDP Real
Growth
2.50%
4.80%
5.50%
6.00%
4.20%
4.00%
3.00%
5.50%
3.00%
4.90%
3.80%
5.20%
4.80%
5.50%
2.00%
3.50%
Country
Risk
45
35
15
15
25
50
40
30
45
50
45
5
25
25
35
45
30
RegressionResults
31
¨
TheregressionofPEratiosonthesevariables
providesthefollowing–
PE=16.16
- 7.94InterestRates
+154.40GrowthinGDP
- 0.1116CountryRisk
RSquared=73%
Aswath Damodaran
31
PredictedPERatios
32
Country
PE Ratio
Argentina
Brazil
Chile
Hong Kong
India
Indonesia
Malaysia
Mexico
Pakistan
Peru
Phillipines
Singapore
South Korea
Thailand
Turkey
Venezuela
14
21
25
20
17
15
14
19
14
15
15
24
21
21
12
20
Aswath Damodaran
Interest
Rates
18.00%
14.00%
9.50%
8.00%
11.48%
21.00%
5.67%
11.50%
19.00%
18.00%
17.00%
6.50%
10.00%
12.75%
25.00%
15.00%
GDP Real
Growth
2.50%
4.80%
5.50%
6.00%
4.20%
4.00%
3.00%
5.50%
3.00%
4.90%
3.80%
5.20%
4.80%
5.50%
2.00%
3.50%
Country
Risk
45
35
15
15
25
50
40
30
45
50
45
5
25
25
35
45
Predicted PE
13.57
18.55
22.22
23.11
18.94
15.09
15.87
20.39
14.26
16.71
15.65
23.11
19.98
20.85
13.35
15.35
32
Example3:PEratiosfortheS&P500over
time
33
PERatiosfortheS&P500:1969-2015
50.00
1969-2015
1986-2015
1996-2015
2006-2015
45.00
40.00
PE
NormalizedPE
CAPE
16.06
18.52
19.61
16.90
20.70
24.00
25.61
20.88
17.08
20.34
22.29
18.45
35.00
30.00
25.00
20.00
15.00
10.00
0.00
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
5.00
PE
Aswath Damodaran
NormalizedPE
CAPE
33
Islow(high)PEcheap(expensive)?
34
¨
Amarketstrategistarguesthatstocksareexpensive
becausethePEratiotodayishighrelativetothe
averagePEratioacrosstime.Doyouagree?
a.
b.
¨
¨
Yes
No
Ifyoudonotagree,whatfactorsmightexplainthe
higherPEratiotoday?
Wouldyouresponddifferentlyifthemarket
strategisthasaNobelPrizeinEconomics?
Aswath Damodaran
34
E/PRatios,T.BondRatesandTermStructure
35
EarningstoPriceversusInterestRates:S&P500
16.00%
14.00%
12.00%
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
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
-2.00%
EarningsYield
Aswath Damodaran
T.BondRate
Bond-Bill
35
RegressionResults
36
¨
¨
¨
ThereisastrongpositiverelationshipbetweenE/PratiosandT.Bond rates,as
evidencedbythecorrelationof0.66betweenthetwovariables.,
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.Bill
ratehavenoth lostsignificance.Howwouldyoureadthisresult?
Aswath Damodaran
36
II.PEGRatio
37
¨
¨
PEGRatio=PEratio/ExpectedGrowthRateinEPS
¤
Forconsistency,youshouldmakesurethatyourearningsgrowth
reflectstheEPSthatyouuseinyourPEratiocomputation.
¤
Thegrowthratesshouldpreferablybeoverthesametimeperiod.
TounderstandthefundamentalsthatdeterminePEGratios,letusreturn
againtoa2-stageequitydiscountedcashflowmodel:
" (1+g)n %
EPS0 *Payout Ratio*(1+g)*$1−
n '
n
# (1+r) & EPS0 *Payout Ratio n *(1+g) *(1+g n )
P0 =
+
r-g
(r-g n )(1+r)n
¨
Dividingbothsidesoftheequationbytheearningsgivesustheequation
forthePEratio.Dividingitagainbytheexpectedgrowth‘g:
" (1+g)n %
Payout Ratio*(1+g)*$1−
n '
n
# (1+r) & Payout Ratio n *(1+g) *(1+g n )
PEG=
+
g(r-g)
g(r-g n )(1+r)n
Aswath Damodaran
37
PEGRatiosandFundamentals
38
¨
Riskandpayout,whichaffectPEratios,continueto
affectPEGratiosaswell.
¤
¨
Implication:WhencomparingPEGratiosacrosscompanies,
wearemakingimplicitorexplicitassumptionsaboutthese
variables.
DividingPEbyexpectedgrowthdoesnotneutralize
theeffectsofexpectedgrowth,sincethe
relationshipbetweengrowthandvalueisnotlinear
andfairlycomplex(evenina2-stagemodel)
Aswath Damodaran
38
ASimpleExample
39
¨
AssumethatyouhavebeenaskedtoestimatethePEGratioforafirm
whichhasthefollowingcharacteristics:
Variable
HighGrowthPhase
StableGrowthPhase
ExpectedGrowthRate
25%
8%
PayoutRatio
20%
50%
Beta
1.00
1.00
¨
Riskfree rate=T.Bond Rate=6%
¨
Requiredrateofreturn=6%+1(5.5%)=11.5%
¨
ThePEGratioforthisfirmcanbeestimatedasfollows:
"
(1.25)5 %
0.2 * (1.25) * $1−
5'
0.5 * (1.25)5 *(1.08)
# (1.115) &
PEG =
+
= 115 or 1.15
5
.25(.115 - .25)
.25(.115-.08) (1.115)
Aswath Damodaran
39
PEGRatiosandRisk
40
Aswath Damodaran
40
PEGRatiosandQualityofGrowth
41
Aswath Damodaran
41
PERatiosandExpectedGrowth
42
Aswath Damodaran
42
PEGRatiosandFundamentals:Propositions
43
¨
Proposition1:HighriskcompanieswilltradeatmuchlowerPEG
ratiosthanlowriskcompanieswiththesameexpectedgrowth
rate.
¤
¨
Proposition2:Companiesthatcanattaingrowthmoreefficiently
byinvestinglessinbetterreturnprojectswillhavehigherPEG
ratiosthancompaniesthatgrowatthesameratelessefficiently.
¤
¨
Corollary1:ThecompanythatlooksmostundervaluedonaPEGratio
basisinasectormaybetheriskiestfirminthesector
Corollary2:CompaniesthatlookcheaponaPEGratiobasismaybe
companieswithhighreinvestmentratesandpoorprojectreturns.
Proposition3:Companieswithveryloworveryhighgrowthrates
willtendtohavehigherPEGratiosthanfirmswithaveragegrowth
rates.Thisbiasisworseforlowgrowthstocks.
¤
Corollary3:PEGratiosdonotneutralizethegrowtheffect.
Aswath Damodaran
43