example 3: pe ratios for the s&p 500 over...
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Example3:PEratiosfortheS&P500overtime
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1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015
PERatiosfortheS&P500:1969-2016
PEforS&P500 NormalizedPEforS&P500 CAPEforS&P500
PE NormalizedPE CAPE1969-2016 16.18 20.80 18.031986-2016 18.63 24.04 21.551996-2016 19.72 25.60 23.402006-2016 17.36 21.27 19.662009-2016 16.88 20.72 19.24Jan-17 20.57 25.00 23.91
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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
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2012
2014
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EarningstoPriceversusInterestRates:S&P500
Bond-Bill
EarningsYield
T.BondRate
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RegressionResults
¨ Inthefollowingregression,using1960-2016data,weregressE/PratiosagainstthelevelofT.Bond ratesandatermstructurevariable(T.Bond - T.Bill rate)EPRatio=0.0351+0.5609T.Bond Rate- 0.1391(T.Bond Rate- T.Bill Rate)
(5.21) (6.39) (-0.67)Rsquared=42.31%
¨ 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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Correlation between E?P and interest rates
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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
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#$
%
&'
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
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#$
%
&'
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
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%
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.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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III.PricetoBookRatio
¨ Goingbacktoasimpledividenddiscountmodel,
¨ Definingthereturnonequity(ROE)=EPS0/BookValueofEquity,thevalueofequitycanbewrittenas:
¨ Ifthereturnonequityisbaseduponexpectedearningsinthenexttimeperiod,thiscanbesimplifiedto,
P0 =DPS1r −gn
P0 = BV0*ROE*Payout Ratio*(1+gn )r-gn
P0
BV0
= PBV= ROE*Payout Ratio*(1+gn )r-gn
P0
BV0
= PBV= ROE*Payout Ratior-gnAswath Damodaran
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PriceBookValueRatio:StableGrowthFirmAnotherPresentation
¨ Thisformulationcanbesimplifiedevenfurtherbyrelatinggrowthtothereturnonequity:
g=(1- Payoutratio)*ROE¨ SubstitutingbackintotheP/BVequation,
¨ Theprice-bookvalueratioofastablefirmisdeterminedbythedifferentialbetweenthereturnonequityandtherequiredrateofreturnonitsprojects.
¨ Buildingonthisequation,acompanythatisexpectedtogenerateaROEhigher(lowerthan,equalto)itscostofequityshouldtradeatapricetobookratiohigher(lessthan,equalto)one.
P0
BV0
= PBV= ROE - gn
r-gn
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NowchangingtoanEnterprisevaluemultipleEV/BookCapital
¨ Toseethedeterminantsofthevalue/bookratio,considerthesimplefreecashflowtothefirmmodel:
¨ Dividingbothsidesbythebookvalue,weget:
¨ Ifwereplace,FCFF=EBIT(1-t)- (g/ROC)EBIT(1-t),weget:
V0 = FCFF1 WACC - g
V0
BV= FCFF1/BV
WACC-g
V0
BV= ROC - g
WACC-g
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IV.EVtoEBITDA- Determinants
¨ Thevalueoftheoperatingassetsofafirmcanbewrittenas:
¨ Nowthevalueofthefirmcanberewrittenas
¨ DividingbothsidesoftheequationbyEBITDA,
¨ ThedeterminantsofEV/EBITDAare:¤ Thecostofcapital¤ Expectedgrowthrate¤ Taxrate¤ Reinvestmentrate(orROC)
€
EV0 = FCFF1 WACC - g
€
EV = EBITDA (1- t) + Depr (t) - Cex - Δ Working Capital
WACC - g
€
EVEBITDA
= (1- t)
WACC - g +
Depr (t)/EBITDAWACC - g
- CEx/EBITDA
WACC - g -
Δ Working Capital/EBITDAWACC - g
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ASimpleExample
¨ Considerafirmwiththefollowingcharacteristics:¤ TaxRate=36%¤ CapitalExpenditures/EBITDA=30%¤ Depreciation/EBITDA=20%¤ CostofCapital=10%¤ Thefirmhasnoworkingcapitalrequirements¤ Thefirmisinstablegrowthandisexpectedtogrow5%ayearforever.
¨ Inthiscase,theValue/EBITDAmultipleforthisfirmcanbeestimatedasfollows:
ValueEBITDA
= (1- .36) .10 -.05
+ (0.2)(.36).10 -.05
- 0.3.10 - .05
- 0.10 - .05
= 8.24
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TheDeterminantsofEV/EBITDA
¨TaxRates Reinvestment
Needs
ExcessReturns
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V.EV/SalesRatio
¨ Ifpre-taxoperatingmarginsareused,theappropriatevalueestimateisthatofthefirm.Inparticular,ifonemakesthereplacestheFCFFwiththeexpandedversion:¤ FreeCashFlowtotheFirm=EBIT(1- taxrate)(1- ReinvestmentRate)
¨ ThentheValueoftheFirmcanbewrittenasafunctionoftheafter-taxoperatingmargin=(EBIT(1-t)/Sales
g=Growthrateinafter-taxoperatingincomeforthefirstnyearsgn=Growthrateinafter-taxoperatingincomeafternyearsforever(Stablegrowthrate)RIRGrowth,Stable=ReinvestmentrateinhighgrowthandstableperiodsWACC=Weightedaveragecostofcapital
Value Sales0
=After-tax Oper. Margin*(1-RIRgrowth )(1+g)* 1− (1+g)n
(1+WACC)n
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WACC-g+ (1-RIRstable )(1+g)n*(1+gn )
(WACC-gn )(1+WACC)n
(
)
****
+
,
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Thevalueofabrandname
¨ Oneofthecritiquesoftraditionalvaluationisthatisfailstoconsiderthevalueofbrandnamesandotherintangibles.
¨ Theapproachesusedbyanalyststovaluebrandnamesareoftenad-hocandmaysignificantlyoverstateorunderstatetheirvalue.
¨ Oneofthebenefitsofhavingawell-knownandrespectedbrandnameisthatfirmscanchargehigherpricesforthesameproducts,leadingtohigherprofitmarginsandhencetohigherprice-salesratiosandfirmvalue.Thelargerthepricepremiumthatafirmcancharge,thegreateristhevalueofthebrandname.
¨ Ingeneral,thevalueofabrandnamecanbewrittenas:¤ Valueofbrandname={(V/S)b-(V/S)g }*Sales¤ (V/S)b =ValueofFirm/Salesratiowiththebenefitofthebrandname¤ (V/S)g =ValueofFirm/Salesratioofthefirmwiththegenericproduct
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ValuingBrandName
CocaCola WithCott MarginsCurrentRevenues= $21,962.00 $21,962.00Lengthofhigh-growthperiod 10 10ReinvestmentRate= 50% 50%OperatingMargin(after-tax) 15.57% 5.28%Sales/Capital(Turnoverratio) 1.34 1.34Returnoncapital(after-tax) 20.84% 7.06%Growthrateduringperiod(g)= 10.42% 3.53%CostofCapitalduringperiod= 7.65% 7.65%StableGrowthPeriodGrowthrateinsteadystate= 4.00% 4.00%Returnoncapital= 7.65% 7.65%ReinvestmentRate= 52.28% 52.28%CostofCapital= 7.65% 7.65%ValueofFirm= $79,611.25 $15,371.24
Valueofbrandname=$79,611-$15,371=$64,240million
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TheDeterminantsofMultiples…
Value of Stock = DPS 1/(ke - g)
PE=Payout Ratio (1+g)/(r-g)
PEG=Payout ratio (1+g)/g(r-g)
PBV=ROE (Payout ratio) (1+g)/(r-g)
PS= Net Margin (Payout ratio)(1+g)/(r-g)
Value of Firm = FCFF 1/(WACC -g)
Value/FCFF=(1+g)/(WACC-g)
Value/EBIT(1-t) = (1+g) (1- RIR)/(WACC-g)
Value/EBIT=(1+g)(1-RiR)/(1-t)(WACC-g)
VS= Oper Margin (1-RIR) (1+g)/(WACC-g)
Equity Multiples
Firm Multiples
PE=f(g, payout, risk) PEG=f(g, payout, risk) PBV=f(ROE,payout, g, risk) PS=f(Net Mgn, payout, g, risk)
V/FCFF=f(g, WACC) V/EBIT(1-t)=f(g, RIR, WACC) V/EBIT=f(g, RIR, WACC, t) VS=f(Oper Mgn, RIR, g, WACC)
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ApplicationTests
¨ Giventhefirmthatwearevaluing,whatisa“comparable” firm?¤ Whiletraditionalanalysisisbuiltonthepremisethatfirmsinthesamesectorarecomparablefirms,valuationtheorywouldsuggestthatacomparablefirmisonewhichissimilartotheonebeinganalyzedintermsoffundamentals.
¤ Proposition4:Thereisnoreasonwhyafirmcannotbecomparedwithanotherfirminaverydifferentbusiness,ifthetwofirmshavethesamerisk,growthandcashflowcharacteristics.
¨ Giventhecomparablefirms,howdoweadjustfordifferencesacrossfirmsonthefundamentals?¤ Proposition5:Itisimpossibletofindanexactlyidenticalfirmtotheoneyouarevaluing.
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Valuingonecompanyrelativetoothers…Relativevaluationwithcomparables
¨ Ideally,youwouldliketofindlotsofpubliclytradedfirmsthatlookjustlikeyourfirm,intermsoffundamentals,andcomparethepricingofyourfirmtothepricingoftheseotherpubliclytradedfirms.Since,theyarealljustlikeyourfirm,therewillbenoneedtocontrolfordifferences.
¨ Inpractice,itisverydifficult(andperhapsimpossible)tofindfirmsthatsharethesamerisk,growthandcashflowcharacteristicsofyourfirm.Evenifyouareabletofindsuchfirms,theywillveryfewinnumber.Thetradeoffthenbecomes:
Small sample of firms that are “just like” your firm
Large sample of firms that are similar in some dimensions but different on others
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Techniquesforcomparingacrossfirms
1. Directcomparisons:Ifthecomparablefirmsare“justlike” yourfirm,youcancomparemultiplesdirectlyacrossthefirmsandconcludethatyourfirmisexpensive(cheap)ifittradesatamultiplehigher(lower)thantheotherfirms.
2. Storytelling:Ifthereisakeydimensiononwhichthefirmsvary,youcantellastorybaseduponyourunderstandingofhowvaluevariesonthatdimension.Anexample:Thiscompanytradesat12timesearnings,whereastherestofthesectortradesat10timesearnings,butIthinkitischeapbecauseithasamuchhighergrowthratethantherestofthesector.
3. Modifiedmultiple:Youcanmodifythemultipletoincorporatethedimensiononwhichtherearedifferencesacrossfirms.
4. Statisticaltechniques:Ifyourfirmsvaryonmorethanonedimension,youcantryusingmultipleregressions(orvariantsthereof)toarriveata“controlled” estimateforyourfirm.
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Example1:Let’strysomestorytellingComparingPEratiosacrossfirmsinasector
CompanyName TrailingPE ExpectedGrowth StandardDeviationCoca-ColaBottling 29.18 9.50% 20.58%MolsonInc.Ltd.'A' 43.65 15.50% 21.88%Anheuser-Busch 24.31 11.00% 22.92%CorbyDistilleriesLtd. 16.24 7.50% 23.66%Chalone WineGroup 21.76 14.00% 24.08%AndresWinesLtd.'A'8.96 3.50% 24.70%Todhunter Int'l 8.94 3.00% 25.74%Brown-Forman'B'10.07 11.50% 29.43%Coors(Adolph)'B' 23.02 10.00% 29.52%PepsiCo,Inc. 33.00 10.50% 31.35%Coca-Cola 44.33 19.00% 35.51%BostonBeer'A' 10.59 17.13% 39.58%WhitmanCorp. 25.19 11.50% 44.26%Mondavi (Robert)'A'16.47 14.00% 45.84%Coca-ColaEnterprises37.14 27.00% 51.34%HansenNaturalCorp9.70 17.00% 62.45%
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AQuestion
¨ Youarereadinganequityresearchreportonthissector,andtheanalystclaimsthatAndresWineandHansenNaturalareundervaluedbecausetheyhavelowPEratios.Wouldyouagree?a. Yesb. No
¨ Whyorwhynot?
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Example2:Fact-basedstorytellingComparingPERatiosacrossaSector:PE
Company Name PE GrowthPT Indosat ADR 7.8 0.06Telebras ADR 8.9 0.075Telecom Corporation of New Zealand ADR 11.2 0.11Telecom Argentina Stet - France Telecom SA ADR B 12.5 0.08Hellenic Telecommunication Organization SA ADR 12.8 0.12Telecomunicaciones de Chile ADR 16.6 0.08Swisscom AG ADR 18.3 0.11Asia Satellite Telecom Holdings ADR 19.6 0.16Portugal Telecom SA ADR 20.8 0.13Telefonos de Mexico ADR L 21.1 0.14Matav RT ADR 21.5 0.22Telstra ADR 21.7 0.12Gilat Communications 22.7 0.31Deutsche Telekom AG ADR 24.6 0.11British Telecommunications PLC ADR 25.7 0.07Tele Danmark AS ADR 27 0.09Telekomunikasi Indonesia ADR 28.4 0.32Cable & Wireless PLC ADR 29.8 0.14APT Satellite Holdings ADR 31 0.33Telefonica SA ADR 32.5 0.18Royal KPN NV ADR 35.7 0.13Telecom Italia SPA ADR 42.2 0.14Nippon Telegraph & Telephone ADR 44.3 0.2France Telecom SA ADR 45.2 0.19Korea Telecom ADR 71.3 0.44
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PE,GrowthandRisk
Dependentvariableis: PERsquared=66.2%Rsquared(adjusted)=63.1%
Variable Coefficient SE t-ratio ProbabilityConstant 13.1151 3.471 3.78 0.0010Growthrate121.223 19.27 6.29 ≤0.0001EmergingMarket -13.8531 3.606 -3.84 0.0009
EmergingMarketisadummy: 1ifemergingmarket0ifnot
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IsTelebrasundervalued?
¨ PredictedPE=13.12+121.22(.075)- 13.85(1)=8.35
¨ Atanactualpricetoearningsratioof8.9,Telebrasisslightlyovervalued.
¨ Bottomline:JustbecauseacompanytradesatalowPEratiodoesnotmakeitcheap.
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Example3:AnEyeballingExercisewithP/BVRatiosEuropeanBanksin2010
Name PBV Ratio Return on Equity Standard DeviationBAYERISCHE HYPO-UND VEREINSB 0.80 -1.66% 49.06%COMMERZBANK AG 1.09 -6.72% 36.21%DEUTSCHE BANK AG -REG 1.23 1.32% 35.79%BANCA INTESA SPA 1.66 1.56% 34.14%BNP PARIBAS 1.72 12.46% 31.03%BANCO SANTANDER CENTRAL HISP 1.86 11.06% 28.36%SANPAOLO IMI SPA 1.96 8.55% 26.64%BANCO BILBAO VIZCAYA ARGENTA 1.98 11.17% 18.62%SOCIETE GENERALE 2.04 9.71% 22.55%ROYAL BANK OF SCOTLAND GROUP 2.09 20.22% 18.35%HBOS PLC 2.15 22.45% 21.95%BARCLAYS PLC 2.23 21.16% 20.73%UNICREDITO ITALIANO SPA 2.30 14.86% 13.79%KREDIETBANK SA LUXEMBOURGEOI 2.46 17.74% 12.38%ERSTE BANK DER OESTER SPARK 2.53 10.28% 21.91%STANDARD CHARTERED PLC 2.59 20.18% 19.93%HSBC HOLDINGS PLC 2.94 18.50% 19.66%LLOYDS TSB GROUP PLC 3.33 32.84% 18.66%Average 2.05 12.54% 24.99%Median 2.07 11.82% 21.93%
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Themediantest…
¨ Wearelookingforstocksthattradeatlowpricetobookratios,whilegeneratinghighreturnsonequity,withlowrisk.Butwhatisalowpricetobookratio?Orahighreturnonequity?Oralowrisk
¨ Onesimplemeasureofwhatisparforthesectorarethemedianvaluesforeachofthevariables.Asimplisticdecisionruleonunderandovervaluedstockswouldthereforebe:¤ Undervaluedstocks:Tradeatpricetobookratiosbelowthemedianfor
thesector,(2.07),generatereturnsonequityhigherthanthesectormedian(11.82%)andhavestandarddeviationslowerthanthemedian(21.93%).
¤ Overvaluedstocks:Tradeatpricetobookratiosabovethemedianforthesectorandgeneratereturnsonequitylowerthanthesectormedian.
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Howaboutthismechanism?
¨ Wearelookingforstocksthattradeatlowpricetobookratios,whilegeneratinghighreturnsonequity.Butwhatisalowpricetobookratio?Orahighreturnonequity?
¨ Takingthesampleof18banks,weranaregressionofPBVagainstROEandstandarddeviationinstockprices(asaproxyforrisk).
PBV= 2.27 + 3.63ROE - 2.68Std dev(5.56) (3.32) (2.33)
Rsquaredofregression=79%
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Andthesepredictions?
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AfollowuponUSBanks
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