Data/Frame Memory PE 0 PE 1 PE 2 PE 3 PE N Control Instruction Memory Interconnect The SIMD Concept.
1. Mul’ples have skewed distribu’ons…adamodar/podcasts/valfall15/valsession17.pdf · Making...
Transcript of 1. Mul’ples have skewed distribu’ons…adamodar/podcasts/valfall15/valsession17.pdf · Making...
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1.Mul'pleshaveskeweddistribu'ons…
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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
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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
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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
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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
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PEra'osglobally:July2014
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Example3:PEra'osfortheS&P500over'me
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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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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
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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?
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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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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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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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