1. mul’ples have skewed distribu’ons…adamodar/podcasts/valfall15/valsession17.pdf · making...

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1.Mul'pleshaveskeweddistribu'ons…

Aswath Damodaran

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0.

100.

200.

300.

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500.

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700.

0.01To4

4To8 8To12 12To16

16To20

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40To50

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75To100

More

PERa&osforUSstocks:January2015

Current

Trailing

Forward

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2.Makingsta's'cs“dicey”

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Current PE Trailing PE Forward PE

Number of firms 7887 7887 7887

Number with PE 3403 3398 2820

Average 72.13 60.49 35.25

Median 20.88 19.74 18.32

Minimum 0.25 0.4 1.15

Maximum 23,100. 23,100. 5,230.91

Standard deviation 509.6 510.41 139.75

Standard error 8.74 8.76 2.63

Skewness 31. 32.77 25.04

25th percentile 13.578 13.2 14.32

75th percentile 33.86 31.16 25.66

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3.Marketshavealotincommon:ComparingGlobalPEs

Aswath Damodaran

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0.00%

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0.01To4

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PERa&oDistribu&on:GlobalComparisoninJanuary2015

Aus,Ca&NZ

US

EmergMkts

Europe

Japan

Global

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3a.Andthedifferencesaresome'mesrevealing…PricetoBookRa'osacrossglobe–January2013

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4.Simplis'crulesalmostalwaysbreakdown…6'mesEBITDAwasnotcheapin2010…

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Butitmaybein2015,unlessyouareinJapan,AustraliaorCanada

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0.00%

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<2 2To4 4To6 6To8 8To10

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EV/EBITDA:AGlobalComparison-January2015

US

A,C&NZ

EmergMkts

Europe

Japan

Global

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Analy'calTests

¨  Whatarethefundamentalsthatdetermineanddrivethesemul'ples?¤  Proposi'on2:Embeddedineverymul'pleareallofthevariablesthat

driveeverydiscountedcashflowvalua'on-growth,riskandcashflowpaberns.

¨  Howdochangesinthesefundamentalschangethemul'ple?¤  Therela'onshipbetweenafundamental(likegrowth)andamul'ple

(suchasPE)isalmostneverlinear.¤  Proposi'on3:Itisimpossibletoproperlycomparefirmsonamul'ple,

ifwedonotknowhowfundamentalsandthemul'plemove.

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ASimpleAnaly'caldevice

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Equity Multiple or Firm Multiple

Equity Multiple Firm Multiple

1. Start with an equity DCF model (a dividend or FCFE model)

2. Isolate the denominator of the multiple in the model3. Do the algebra to arrive at the equation for the multiple

1. Start with a firm DCF model (a FCFF model)

2. Isolate the denominator of the multiple in the model3. Do the algebra to arrive at the equation for the multiple

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I.PERa'os

¨  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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UsingtheFundamentalModeltoEs'matePEForaHighGrowthFirm

¨  Theprice-earningsra'oforahighgrowthfirmcanalsoberelatedtofundamentals.Inthespecialcaseofthetwo-stagedividenddiscountmodel,thisrela'onshipcanbemadeexplicitfairlysimply:

¤  Forafirmthatdoesnotpaywhatitcanaffordtoindividends,subs'tuteFCFE/Earningsforthepayoutra'o.

¨  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

¨  Assumethatyouhavebeenaskedtoes'matethePEra'oforafirmwhichhasthefollowingcharacteris'cs:

Variable HighGrowthPhase StableGrowthPhaseExpectedGrowthRate 25% 8%PayoutRa'o 20% 50%Beta 1.00 1.00Numberofyears 5years Foreverajeryear5Riskfreerate=T.BondRate=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%thereajer

PE Ratios and Expected Growth: Interest Rate Scenarios

0

20

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5% 10% 15% 20% 25% 30% 35% 40% 45% 50%

Expected Growth Rate

PE

Rati

o 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

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25

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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:ComparingPEra'osacrossEmergingMarkets-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

¨  TheregressionofPEra'osonthesevariablesprovidesthefollowing–PE=16.16 -7.94InterestRates

+154.40GrowthinGDP -0.1116CountryRisk

RSquared=73%

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PredictedPERa'os

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

Aswath Damodaran

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PEra'osglobally:July2014

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Example3:PEra'osfortheS&P500over'me

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0.00

5.00

10.00

15.00

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35.00

40.00

45.00

50.00

1969

1970

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PERa&osfortheS&P500:1969-2014

PE

NormalizedPE

CAPE

OnJan1,2015PE=17.95NormalizedPE-=24.16CAPE=21.62

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Islow(high)PEcheap(expensive)?

¨  AmarketstrategistarguesthatstocksareexpensivebecausethePEra'otodayishighrela'vetotheaveragePEra'oacross'me.Doyouagree?a.  Yesb.  No¤  Ifyoudonotagree,whatfactorsmightexplainthehigherPEra'otoday?

¤ WouldyouresponddifferentlyifthemarketstrategisthasaNobelPrizeinEconomics?

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34

E/PRa'os,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%

EarningstoPriceversusInterestRates:S&P500

EarningsYield

T.BondRate

Bond-Bill

35

RegressionResults

¨  Thereisastrongposi'verela'onshipbetweenE/Pra'osandT.Bondrates,asevidencedbythecorrela'onof0.65betweenthetwovariables.,

¨  Inaddi'on,thereisevidencethatthetermstructurealsoaffectsthePEra'o.¨  Inthefollowingregression,using1960-2014data,weregressE/Pra'osagainst

thelevelofT.Bondratesandatermstructurevariable(T.Bond-T.Billrate)E/P=3.47%+0.5661T.BondRate–0.1428(T.BondRate-T.BillRate)

(4.93) (6.15) (-0.67) Rsquared=40.94[%

¨  Goingbackto2008,thisiswhattheregressionlookedlike:E/P=2.56%+0.7044T.BondRate–0.3289(T.BondRate-T.BillRate)

(4.71) (7.10) (1.46) Rsquared=50.71%TheR-squaredhasdroppedandtheT.Bondrateandthedifferen'alwiththeT.Billratehavenothlostsignificance.Howwouldyoureadthisresult?

Aswath Damodaran

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II.PEGRa'o

¨  PEGRa'o=PEra'o/ExpectedGrowthRateinEPS¤  Forconsistency,youshouldmakesurethatyourearningsgrowth

reflectstheEPSthatyouuseinyourPEra'ocomputa'on.¤  Thegrowthratesshouldpreferablybeoverthesame'meperiod.

¨  TounderstandthefundamentalsthatdeterminePEGra'os,letusreturnagaintoa2-stageequitydiscountedcashflowmodel:

¨  Dividingbothsidesoftheequa'onbytheearningsgivesustheequa'onforthePEra'o.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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PEGRa'osandFundamentals

¨  Riskandpayout,whichaffectPEra'os,con'nuetoaffectPEGra'osaswell.¤  Implica'on:WhencomparingPEGra'osacrosscompanies,wearemakingimplicitorexplicitassump'onsaboutthesevariables.

¨  DividingPEbyexpectedgrowthdoesnotneutralizetheeffectsofexpectedgrowth,sincetherela'onshipbetweengrowthandvalueisnotlinearandfairlycomplex(evenina2-stagemodel)

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ASimpleExample

¨  Assumethatyouhavebeenaskedtoes'matethePEGra'oforafirmwhichhasthefollowingcharacteris'cs:

Variable HighGrowthPhase StableGrowthPhaseExpectedGrowthRate 25% 8%PayoutRa'o 20% 50%Beta 1.00 1.00¨  Riskfreerate=T.BondRate=6% ¨  Requiredrateofreturn=6%+1(5.5%)=11.5%¨  ThePEGra'oforthisfirmcanbees'matedasfollows:

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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PEGRa'osandRisk

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PEGRa'osandQualityofGrowth

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PERa'osandExpectedGrowth

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PEGRa'osandFundamentals:Proposi'ons

¨  Proposi'on1:HighriskcompanieswilltradeatmuchlowerPEGra'osthanlowriskcompanieswiththesameexpectedgrowthrate.¤  Corollary1:ThecompanythatlooksmostundervaluedonaPEGra'o

basisinasectormaybetheriskiestfirminthesector¨  Proposi'on2:Companiesthatcanabaingrowthmoreefficiently

byinves'nglessinbeberreturnprojectswillhavehigherPEGra'osthancompaniesthatgrowatthesameratelessefficiently.¤  Corollary2:CompaniesthatlookcheaponaPEGra'obasismaybe

companieswithhighreinvestmentratesandpoorprojectreturns.¨  Proposi'on3:Companieswithveryloworveryhighgrowthrates

willtendtohavehigherPEGra'osthanfirmswithaveragegrowthrates.Thisbiasisworseforlowgrowthstocks.¤  Corollary3:PEGra'osdonotneutralizethegrowtheffect.

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III.PricetoBookRa'o

¨  Goingbacktoasimpledividenddiscountmodel,

¨  Definingthereturnonequity(ROE)=EPS0/BookValueofEquity,thevalueofequitycanbewribenas:

¨  Ifthereturnonequityisbaseduponexpectedearningsinthenext'me

period,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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PriceBookValueRa'o:StableGrowthFirmAnotherPresenta'on

¨  Thisformula'oncanbesimplifiedevenfurtherbyrela'nggrowthtothereturnonequity:

g=(1-Payoutra'o)*ROE¨  Subs'tu'ngbackintotheP/BVequa'on,

¨  Theprice-bookvaluera'oofastablefirmisdeterminedbythedifferen'albetweenthereturnonequityandtherequiredrateofreturnonitsprojects.

¨  Buildingonthisequa'on,acompanythatisexpectedtogenerateaROEhigher(lowerthan,equalto)itscostofequityshouldtradeatapricetobookra'ohigher(lessthan,equalto)one.

P0

BV0

= PBV= ROE - gn

r-gn

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NowchangingtoanEnterprisevaluemul'pleEV/BookCapital

¨  Toseethedeterminantsofthevalue/bookra'o,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

¨  Thevalueoftheopera'ngassetsofafirmcanbewribenas:

¨  Nowthevalueofthefirmcanberewribenas

¨  Dividingbothsidesoftheequa'onbyEBITDA,

¨  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

¨  Considerafirmwiththefollowingcharacteris'cs:¤  TaxRate=36%¤  CapitalExpenditures/EBITDA=30%¤  Deprecia'on/EBITDA=20%¤  CostofCapital=10%¤  Thefirmhasnoworkingcapitalrequirements¤  Thefirmisinstablegrowthandisexpectedtogrow5%ayearforever.

¨  Inthiscase,theValue/EBITDAmul'pleforthisfirmcanbees'matedasfollows:

Value

EBITDA = (1- .36)

.10 -.05 + (0.2)(.36)

.10 -.05 - 0.3

.10 - .05 - 0

.10 - .05 = 8.24

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48

TheDeterminantsofEV/EBITDA

¨  TaxRates Reinvestment

Needs

ExcessReturns

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V.EV/SalesRa'o

¨  Ifpre-taxopera'ngmarginsareused,theappropriatevaluees'mateisthatofthefirm.Inpar'cular,ifonemakesthereplacestheFCFFwiththeexpandedversion:¤  FreeCashFlowtotheFirm=EBIT(1-taxrate)(1-ReinvestmentRate)

¨  ThentheValueoftheFirmcanbewribenasafunc'onoftheajer-taxopera'ngmargin=(EBIT(1-t)/Sales

g=Growthrateinajer-taxopera'ngincomeforthefirstnyearsgn=Growthrateinajer-taxopera'ngincomeajernyearsforever(Stablegrowthrate)RIRGrowth,Stable=ReinvestmentrateinhighgrowthandstableperiodsWACC=Weightedaveragecostofcapital

Value Sales0

=After-tax Oper. Margin*(1-RIRgrowth )(1+g)* 1− (1+g)n

(1+WACC)n

"

#$

%

&'

WACC-g+ (1-RIRstable )(1+g)n*(1+gn )

(WACC-gn )(1+WACC)n

(

)

****

+

,

----

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50

Thevalueofabrandname

¨  Oneofthecri'quesoftradi'onalvalua'onisthatisfailstoconsiderthevalueofbrandnamesandotherintangibles.

¨  Theapproachesusedbyanalyststovaluebrandnamesareojenad-hocandmaysignificantlyoverstateorunderstatetheirvalue.

¨  Oneofthebenefitsofhavingawell-knownandrespectedbrandnameisthatfirmscanchargehigherpricesforthesameproducts,leadingtohigherprofitmarginsandhencetohigherprice-salesra'osandfirmvalue.Thelargerthepricepremiumthatafirmcancharge,thegreateristhevalueofthebrandname.

¨  Ingeneral,thevalueofabrandnamecanbewribenas:¤  Valueofbrandname={(V/S)b-(V/S)g}*Sales¤  (V/S)b=ValueofFirm/Salesra'owiththebenefitofthebrandname¤  (V/S)g=ValueofFirm/Salesra'oofthefirmwiththegenericproduct

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ValuingBrandName

CocaCola WithCoEMarginsCurrentRevenues= $21,962.00 $21,962.00Lengthofhigh-growthperiod 10 10ReinvestmentRate= 50% 50%Opera'ngMargin(ajer-tax) 15.57% 5.28%Sales/Capital(Turnoverra'o) 1.34 1.34Returnoncapital(ajer-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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TheDeterminantsofMul'ples…

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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