Download discount rates

Aswath Damodaran
DISCOUNTRATES
TheDintheDCF..
20
EstimatingInputs:DiscountRates
21
¨
¨
WhilediscountratesobviouslymatterinDCFvaluation,they
don’tmatterasmuchasmostanalyststhinktheydo.
Atanintuitivelevel,thediscountrateusedshouldbe
consistentwithboththeriskinessandthetypeofcashflow
beingdiscounted.
¤
¤
¤
EquityversusFirm:Ifthecashflowsbeingdiscountedarecashflowsto
equity,theappropriatediscountrateisacostofequity.Ifthecash
flowsarecashflowstothefirm,theappropriatediscountrateisthe
costofcapital.
Currency:Thecurrencyinwhichthecashflowsareestimatedshould
alsobethecurrencyinwhichthediscountrateisestimated.
NominalversusReal:Ifthecashflowsbeingdiscountedarenominal
cashflows(i.e.,reflectexpectedinflation),thediscountrateshouldbe
nominal
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RiskintheDCFModel
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Risk Adjusted
Cost of equity
=
Aswath Damodaran
Risk free rate in the
currency of analysis
+
Relative risk of
company/equity in
questiion
X
Equity Risk Premium
required for average risk
equity
22
Notallriskiscreatedequal…
23
¨
EstimationversusEconomicuncertainty
¤
¤
¨
MicrouncertaintyversusMacrouncertainty
¤
¤
¨
Estimationuncertaintyreflectsthepossibilitythatyoucouldhavethe“wrong
model”orestimatedinputsincorrectlywithinthismodel.
Economicuncertaintycomesthefactthatmarketsandeconomiescanchangeover
timeandthateventhebestmodelswillfailtocapturetheseunexpectedchanges.
Microuncertaintyreferstouncertaintyaboutthepotentialmarketforafirm’s
products,thecompetitionitwillfaceandthequalityofitsmanagementteam.
Macrouncertaintyreflectstherealitythatyourfirm’sfortunescanbeaffectedby
changesinthemacroeconomicenvironment.
Discreteversuscontinuousuncertainty
¤
¤
Discreterisk:Risksthatliedormantforperiodsbutshowupatpointsintime.
(Examples:AdrugworkingitswaythroughtheFDApipelinemayfailatsomestage
oftheapprovalprocessoracompanyinVenezuelamaybenationalized)
Continuousrisk:Riskschangesininterestratesoreconomicgrowthoccur
continuouslyandaffectvalueastheyhappen.
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RiskandCostofEquity:Theroleofthemarginal
investor
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¨
¨
¨
Notallriskcounts:Whilethenotionthatthecostofequityshould
behigherforriskierinvestmentsandlowerforsaferinvestmentsis
intuitive,whatriskshouldbebuiltintothecostofequityisthe
question.
Riskthroughwhoseeyes? Whileriskisusuallydefinedintermsof
thevarianceofactualreturnsaroundanexpectedreturn,riskand
returnmodelsinfinanceassumethattheriskthatshouldbe
rewarded(andthusbuiltintothediscountrate)invaluationshould
betheriskperceivedbythemarginalinvestorintheinvestment
Thediversificationeffect:Mostriskandreturnmodelsinfinance
alsoassumethatthemarginalinvestoriswelldiversified,andthat
theonlyriskthatheorsheperceivesinaninvestmentisriskthat
cannotbediversifiedaway(i.e,marketornon-diversifiablerisk).In
effect,itisprimarilyeconomic,macro,continuousriskthatshould
beincorporatedintothecostofequity.
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TheCostofEquity:Competing“MarketRisk”Models
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Model ExpectedReturn
CAPM E(R)=Rf +b (Rm- Rf)
APM
E(R)=Rf +Sbj (Rj- Rf)
Multi
factor
E(R)=Rf +Sbj (Rj- Rf)
Proxy
E(R)=a+S bj Yj
Aswath Damodaran
InputsNeeded
Riskfree Rate
Betarelativetomarketportfolio
MarketRiskPremium
Riskfree Rate;#ofFactors;
Betasrelativetoeachfactor
Factorriskpremiums
Riskfree Rate;Macrofactors
Betasrelativetomacrofactors
Macroeconomicriskpremiums
Proxies
Regressioncoefficients
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ClassicRisk&Return:CostofEquity
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¨
IntheCAPM,thecostofequity:
CostofEquity=Riskfree Rate+EquityBeta*(EquityRisk
Premium)
¨
¨
InAPMorMulti-factormodels,youstillneedarisk
freerate,aswellasbetasandriskpremiumstogo
witheachfactor.
Touseanyriskandreturnmodel,youneed
¨
¨
¨
Ariskfreerateasabase
Asingleequityriskpremium(intheCAPM)orfactorrisk
premiums,inthethemulti-factormodels
Abeta(intheCAPM)orbetas(inmulti-factormodels)
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27
DiscountRates:I
TheRiskFreeRate
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TheRiskFreeRate:LayingtheFoundations
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¨
¨
Onariskfree investment,theactualreturnisequaltotheexpected
return.Therefore,thereisnovariancearoundtheexpectedreturn.
Foraninvestmenttoberiskfree,then,ithastohave
¤
¤
¤
1.
2.
3.
Nodefaultrisk
Noreinvestmentrisk
Itfollowsthenthatifaskedtoestimateariskfreerate:
Timehorizonmatters:Thus,theriskfree ratesinvaluationwill
dependuponwhenthecashflowisexpectedtooccurandwill
varyacrosstime.
Currenciesmatter:Ariskfreerateiscurrency-specificandcanbe
verydifferentfordifferentcurrencies.
Notallgovernmentsecuritiesareriskfree:Somegovernments
facedefaultriskandtheratesonbondsissuedbythemwillnot
beriskfree.
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Test1:AriskfreerateinUSdollars!
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¨
Invaluation,weestimatecashflowsforever(oratleast
forverylongtimeperiods).Therightriskfreeratetouse
invaluingacompanyinUSdollarswouldbe
a.
b.
d.
Athirty-yearTreasurybondrate(3%)
ATIPs(inflation-indexedtreasury)rate(1%)
e.
Noneoftheabove
c.
¨
Athree-monthTreasurybillrate(0.2%)
Aten-yearTreasurybondrate(2%)
WhatareweimplicitlyassumingabouttheUStreasury
whenweuseanyofthetreasurynumbers?
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Test2:ARiskfreeRateinEuros
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EuroGovernmentBondRates- January1,2016
10.00%
9.00%
8.00%
7.00%
6.00%
5.00%
4.00%
3.00%
2.00%
1.00%
0.00%
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Test3:ARiskfreeRateinIndianRupees
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¨
¨
TheIndiangovernmenthad10-yearRupeebonds
outstanding,withayieldtomaturityofabout7.73%on
January1,2016.
InJanuary2016,theIndiangovernmenthadalocalcurrency
sovereignratingofBaa3.Thetypicaldefaultspread(overa
defaultfreerate)forBaa3ratedcountrybondsinearly2016
was2.44%.TheriskfreerateinIndianRupeesis
a.
b.
c.
d.
Theyieldtomaturityonthe10-yearbond(7.73%)
Theyieldtomaturityonthe10-yearbond+Defaultspread(10.17%)
Theyieldtomaturityonthe10-yearbond– Defaultspread(5.29%)
Noneoftheabove
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SovereignDefaultSpread:Threepathsto
thesamedestination…
32
¨
Sovereigndollaroreurodenominatedbonds:Find
sovereignbondsdenominatedinUSdollars,issuedbyan
emergingsovereign.
¤
¨
CDSspreads:Obtainthetradedvalueforasovereign
CreditDefaultSwap(CDS)fortheemerginggovernment.
¤
¨
Defaultspread=EmergingGovt BondRate(inUS$)– US
TreasuryBondratewithsamematurity.
Defaultspread=SovereignCDSspread(withperhapsan
adjustmentforCDSmarketfrictions).
Sovereign-ratingbasedspread:Forcountrieswhichdon’t
issuedollardenominatedbondsorhaveaCDSspread,
youhavetousetheaveragespreadforothercountries
withthesamesovereign rating.
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LocalCurrencyGovernmentBondRates–
January2016
33
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Approach1:Defaultspreadfrom
GovernmentBonds
The Brazil Default Spread
Brazil 2021 Bond: 6.83%
US 2021 T.Bond: 2.00%
Spread:
4.83%
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Approach2:CDSSpreads– January2016
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Approach3:TypicalDefaultSpreads:
January2016
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Gettingtoariskfreerateinacurrency:Example
37
¨
TheBraziliangovernmentbondrateinnominalreaison
January1,2016was16.51%.Togettoariskfreeratein
nominalreais,wecanuseoneofthreeapproaches.
¨
¨
¨
Approach1:GovernmentBondspread
¤ The2021Brazilbond,denominatedinUSdollars,hasaspreadof
4.83%overtheUStreasurybondrate.
¤ Riskfreeratein$R=16.51%- 4.83%=11.68%
Approach2:TheCDSSpread
¤ TheCDSspreadforBrazil,adjustedfortheUSCDSspreadwas
5.19%.
¤ Riskfreeratein$R=16.51%- 5.19%=11.32%
Approach3:TheRatingbasedspread
¤ BrazilhasaBaa3localcurrencyratingfromMoody’s.Thedefault
spreadforthatratingis2.44%
¤ Riskfreeratein$R=16.51%- 2.44%=14.07%
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Test4:ARealRiskfreeRate
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¨
¨
¨
Insomecases,youmaywantariskfree rateinrealterms
(inrealterms)ratherthannominalterms.
Togetarealriskfree rate,youwouldlikeasecuritywith
nodefaultriskandaguaranteedrealreturn.Treasury
indexedsecuritiesofferthiscombination.
InJanuary2016,theyieldona10-yearindexedtreasury
bondwas0.75%.Whichofthefollowingstatements
wouldyousubscribeto?
This(0.75%)istherealriskfree ratetouse,ifyouarevaluing
UScompaniesinrealterms.
b.
This(0.75%)istherealriskfree ratetouse,anywhereinthe
world
Explain.
a.
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JapaneseYen
0.00%
Aswath Damodaran
RiskfreeRate
BrazilianReai
KenyanShilling
SouthAfricanRand
TurkishLira
Nigerian Naira
RussianRuble
Venezuelan Bolivar
IndonesianRupiah
ColombianPeso
PeruvianSol
IndianRupee
MexicanPeso
ChileanPeso
IcelandKrona
NZ$
Australian$
MalyasianRinggit
Singapore $
US$
ChineseYuan
Vietnamese Dong
PolishZloty
PhillipinePeso
PakistaniRupee
KoreanWon
BritishPound
Norwegian Krone
Canadian$
RomanianLeu
Israeli Shekel
CroatianKuna
HK$
SwedishKrona
DanishKrone
Thai Baht
HungarianForint
Euro
Bulgarian Lev
Taiwanese $
SwissFranc
CzechKoruna
Whydoriskfreeratesvaryacrosscurrencies?
January2016Riskfreerates
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RiskfreeRates- January2016
20.00%
15.00%
10.00%
5.00%
-5.00%
DefaultSpreadbasedonrating
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RiskfreeRate:Don’thaveortrustthe
governmentbondrate?
1.
Buildupapproach:Theriskfreerateinanycurrencycanbe
writtenasthesumoftwovariables:
Riskfreerate=ExpectedInflationincurrency+Expectedrealinterestrate
Theexpectedrealinterestratecanbecomputedinoneoftwoways:from
theUSTIPsrateorsetequaltorealgrowthintheeconomy.Thus,ifthe
expectedinflationrateinacountryisexpectedtobe15%andtheTIPsrate
is1%,theriskfreerateis16%.
2.
US$Rate&DifferentialInflation:Alternatively,youcanscaleup
theUS$riskfreeratebythedifferentialinflationbetweentheUS
$andthecurrencyinquestion:
RiskfreerateCurrency=
Thus,iftheUS$riskfreerateis2.00%,theinflationrateintheforeign
currencyis15%andtheinflationrateinUS$is1.5%,theforeigncurrencyrisk
freerateisasfollows:
Riskfreerate= 1.02 !.!" − 1=15.57%
!.!"#
40
Onemoretestonriskfreerates…
41
¨
OnJanuary1,2016,the10-yeartreasurybondratein
theUnitedStateswas2.27%,ahistoriclow.Assumethat
youwerevaluingacompanyinUSdollarsthen,butwere
waryabouttheriskfreeratebeingtoolow.Whichofthe
followingshouldyoudo?
a.
b.
c.
Replacethecurrent10-yearbondratewithamorereasonable
normalizedriskfreerate(theaverage10-yearbondrateover
thelast30yearshasbeenabout5-6%)
Usethecurrent10-yearbondrateasyourriskfreeratebut
makesurethatyourotherassumptions(aboutgrowthand
inflation)areconsistentwiththeriskfreerate
Somethingelse…
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0.00%
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Someperspectiveonriskfreerates
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Interestratefundamentals:T.Bondrates,Realgrowthandinflation
20.00%
15.00%
10.00%
5.00%
-5.00%
Inflationrate
Aswath Damodaran
RealGDPgrowth
Ten-yearT.Bondrate
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NegativeInterestRates?
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¨
¨
¨
In2016,therewereatleastthreecurrencies(Swiss
Franc,JapaneseYen,Euro)withnegativeinterest
rates.Usingthefundamentals(inflationandreal
growth)approach,howwouldyouexplainnegative
interestrates?
Hownegativecanratesget?(Isthereabound?)
Wouldyouusethesenegativeinterestratesasrisk
freerates?
Ifno,whynotandwhatwouldyoudoinstead?
¤ Ifyes,whatelsewouldyouhavetodoinyourvaluationto
beinternallyconsistent?
¤
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44
DiscountRates:II
TheEquityRiskPremium
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Theubiquitoushistoricalriskpremium
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¨
¨
¨
Thehistoricalpremiumisthepremiumthatstockshavehistorically
earnedoverrisklesssecurities.
Whiletheusersofhistoricalriskpremiumsactasifitisafact(ratherthan
anestimate),itissensitiveto
¤
Howfarbackyougoinhistory…
¤
WhetheryouuseT.billratesorT.Bondrates
¤
Whetheryouusegeometricorarithmeticaverages.
Forinstance,lookingattheUS:
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Theperilsoftrustingthepast…….
46
¨
¨
Noisyestimates:Evenwithlongtimeperiodsofhistory,
theriskpremiumthatyouderivewillhavesubstantial
standarderror.Forinstance,ifyougobackto1928
(about80yearsofhistory)andyouassumeastandard
deviationof20%inannualstockreturns,youarriveata
standarderrorofgreaterthan2%:
StandardErrorinPremium=20%/√80=2.26%
SurvivorshipBias:UsinghistoricaldatafromtheU.S.
equitymarketsoverthetwentiethcenturydoescreatea
samplingbias.Afterall,theUSeconomyandequity
marketswereamongthemostsuccessfuloftheglobal
economiesthatyoucouldhaveinvestedinearlyinthe
century.
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RiskPremiumforaMatureMarket?Broadening
thesampleto1900-2015
47
Country
Australia
Austria
Belgium
Canada
Denmark
Finland
France
Germany
Ireland
Italy
Japan
Netherlands
New Zealand
Norway
South Africa
Spain
Sweden
Switzerland
U.K.
U.S.
Europe
World-ex U.S.
World
Aswath Damodaran
GeometricERP
5.00%
2.60%
2.40%
3.30%
2.30%
5.20%
3.00%
5.10%
2.80%
3.10%
5.10%
3.30%
4.00%
2.30%
5.40%
1.80%
3.10%
2.10%
3.60%
4.30%
3.20%
2.80%
3.20%
ArithmeticERP
6.60%
21.50%
4.50%
4.90%
3.80%
8.80%
5.40%
9.10%
4.80%
6.50%
9.10%
5.60%
5.50%
5.20%
7.20%
3.80%
5.40%
3.60%
5.00%
6.40%
4.50%
3.90%
4.40%
StandardError
1.70%
14.30%
2.00%
1.70%
1.70%
2.80%
2.10%
2.70%
1.80%
2.70%
3.00%
2.10%
1.70%
2.60%
1.80%
1.90%
2.00%
1.60%
1.60%
1.90%
1.50%
1.40%
1.40%
47
Thesimplestwayofestimatinganadditional
countryriskpremium:Thecountrydefaultspread
48
¨
Defaultspreadforcountry:Inthisapproach,thecountryequityrisk
premiumissetequaltothedefaultspreadforthecountry,
estimatedinoneofthreeways:
¤
¤
¤
¨
Thedefaultspreadonadollardenominatedbondissuedbythecountry.
(InJanuary2016,thatspreadwas4.83%fortheBrazilian$bond)
ThesovereignCDSspreadforthecountry.InJanuary2016,thetenyear
CDSspreadforBrazil,adjustedfortheUSCDS,was5.19%.
Thedefaultspreadbasedonthelocalcurrencyratingforthecountry.
Brazil’ssovereignlocalcurrencyratingisBaa3andthedefaultspreadfora
Baa3ratedsovereignwasabout2.44%inJanuary2016.
Addthedefaultspreadtoa“mature”marketpremium:Thisdefault
spreadisaddedontothematuremarketpremiumtoarriveatthe
totalequityriskpremiumforBrazil,assumingamaturemarket
premiumof6.00%.
¤
¤
CountryRiskPremiumforBrazil=2.44%
TotalERPforBrazil=6.00%+2.44%=8.44%
Aswath
Damodaran
Aswath
Damodaran
48
Anequityvolatilitybasedapproachto
estimatingthecountrytotalERP
49
¨
Thisapproachdrawsonthestandarddeviationoftwoequity
markets,theemergingmarketinquestionandabasemarket
(usuallytheUS).Thetotalequityriskpremiumforthe
emergingmarketisthenwrittenas:
¤
¨
Totalequityriskpremium=RiskPremiumUS*sCountry Equity/sUS Equity
Thecountryequityriskpremiumisbaseduponthevolatility
ofthemarketinquestionrelativetoU.Smarket.
¤
¤
¤
¤
AssumethattheequityriskpremiumfortheUSis6.00%.
AssumethatthestandarddeviationintheBovespa (Brazilianequity)is
30%andthatthestandarddeviationfortheS&P500(USequity)is
18%.
TotalEquityRiskPremiumforBrazil=6.00%(30%/18%)=10.0%
CountryequityriskpremiumforBrazil=10.00%- 6.00%=4.00%
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49
Ameldedapproachtoestimatingtheadditional
countryriskpremium
50
¨
¨
Countryratingsmeasuredefaultrisk.Whiledefaultriskpremiums
andequityriskpremiumsarehighlycorrelated,onewouldexpect
equityspreadstobehigherthandebtspreads.
Anotheristomultiplythebonddefaultspreadbytherelative
volatilityofstockandbondpricesinthatmarket.Usingthis
approachforBrazilinJanuary2016,youwouldget:
¤
¤
¤
CountryEquityriskpremium=Defaultspreadoncountrybond*sCountry
Equity /sCountry Bond
n StandardDeviationinBovespa (Equity)=30%
n StandardDeviationinBrazilgovernmentbond=20%
n DefaultspreadforBrazil=2.44%
BrazilCountryRiskPremium=2.44%(30%/20%)=3.66%
BrazilTotalERP=MatureMarketPremium+CRP=6.00%+3.66%=9.66%
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ATemplateforCountryRisk
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ERP : Jan 2016
Black #: Total ERP
Red #: Country risk premium
AVG: GDP weighted average
FromCountryEquityRiskPremiumsto
CorporateEquityRiskpremiums
53
¨
Approach1:Assumethateverycompanyinthecountryisequally
exposedtocountryrisk.Inthiscase,
¤
¤
¨
Approach2:Assumethatacompany’sexposuretocountryriskissimilar
toitsexposuretoothermarketrisk.
¤
¨
E(Return)=RiskfreeRate+CRP+Beta(MatureERP)
Implicitly,thisiswhatyouareassumingwhenyouusethelocalGovernment’s
dollarborrowingrateasyourriskfreerate.
E(Return)=RiskfreeRate+Beta(MatureERP+CRP)
Approach3:Treatcountryriskasaseparateriskfactorandallowfirmsto
havedifferentexposurestocountryrisk(perhapsbaseduponthe
proportionoftheirrevenuescomefromnon-domesticsales)
¤
E(Return)=RiskfreeRate+b (MatureERP)+l (CRP)
MatureERP=MaturemarketEquityRiskPremium
CRP=Additionalcountryriskpremium
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Approaches1&2:Estimatingcountryrisk
premiumexposure
54
¨
¨
LocationbasedCRP:Thestandardapproachinvaluationisto
attachacountryriskpremiumtoacompanybaseduponits
countryofincorporation.Thus,ifyouareanIndiancompany,
youareassumedtobeexposedtotheIndiancountryrisk
premium.Adevelopedmarketcompanyisassumedtobe
unexposedtoemergingmarketrisk.
Operation-basedCRP:Thereisamorereasonablemodified
version.Thecountryriskpremiumforacompanycanbe
computedasaweightedaverageofthecountryrisk
premiumsofthecountriesthatitdoesbusinessin,withthe
weightsbaseduponrevenuesoroperatingincome.Ifa
companyisexposedtoriskindozensofcountries,youcan
takeaweightedaverageoftheriskpremiumsbyregion.
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OperationbasedCRP:SingleversusMultiple
EmergingMarkets
55
¨
¨
Singleemergingmarket:Embraer,in2004,reportedthatitderived3%of
itsrevenuesinBrazilandthebalancefrommaturemarkets.Themature
marketERPin2004was5%andBrazil’sCRPwas7.89%.
Multipleemergingmarkets:Ambev,theBrazilian-basedbeverage
company,reportedrevenuesfromthefollowingcountriesduring2011.
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55
Extendingtoamultinational:Regionalbreakdown
CocaCola’srevenuebreakdownandERPin2012
56
Things to watch out for
1. Aggregation across regions. For instance, the Pacific region often includes Australia & NZ with Asia
2. Obscure aggregations including Eurasia and Oceania
56
Twoproblemswiththeseapproaches..
57
¨
¨
Focusjustonrevenues:Totheextentthatrevenuesare
theonlyvariablethatyouconsider,whenweightingrisk
exposureacrossmarkets,youmaybemissingother
exposurestocountryrisk.Forinstance,anemerging
marketcompanythatgetsthebulkofitsrevenues
outsidethecountry(inadevelopedmarket)maystill
haveallofitsproductionfacilitiesintheemerging
market.
Exposurenotadjustedorbaseduponbeta:Totheextent
thatthecountryriskpremiumismultipliedbyabeta,we
areassumingthatbetainadditiontomeasuring
exposuretoallothermacroeconomicriskalsomeasures
exposuretocountryrisk.
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AProduction-basedERP:RoyalDutchShell
in2015
58
Country
Denmark
Italy
Norway
UK
RestofEurope
Brunei
Iraq
Malaysia
Oman
Russia
RestofAsia&ME
Oceania
Gabon
Nigeria
RestofAfrica
USA
Canada
Brazil
RestofLatinAmerica
RoyalDutchShell
Aswath Damodaran
Oil&GasProduction
17396
11179
14337
20762
874
823
20009
22980
78404
22016
24480
7858
12472
67832
6159
104263
8599
13307
576
454326
%ofTotal
3.83%
2.46%
3.16%
4.57%
0.19%
0.18%
4.40%
5.06%
17.26%
4.85%
5.39%
1.73%
2.75%
14.93%
1.36%
22.95%
1.89%
2.93%
0.13%
100.00%
ERP
6.20%
9.14%
6.20%
6.81%
7.40%
9.04%
11.37%
8.05%
7.29%
10.06%
7.74%
6.20%
11.76%
11.76%
12.17%
6.20%
6.20%
9.60%
10.78%
8.26%
58
Approach3:Estimatealambdaforcountryrisk
59
¨
Countryriskexposureisaffectedbywhereyougetyour
revenuesandwhereyourproductionhappens,butthereare
ahostofothervariablesthatalsoaffectthisexposure,
including:
¤
¤
¨
Useofriskmanagementproducts:Companiescanusebothoptions/futures
marketsandinsurancetohedgesomeorasignificantportionofcountryrisk.
Government“national”interests:Therearesectorsthatareviewedasvitalto
thenationalinterests,andgovernmentsoftenplayakeyroleinthese
companies,eitherofficiallyorunofficially.Thesesectorsaremoreexposedto
countryrisk.
Itisconceivablethatthereisarichermeasureofcountryrisk
thatincorporatesallofthevariablesthatdrivecountryriskin
onemeasure.ThatwaymyrationalewhenIdevised
“lambda”asmymeasureofcountryriskexposure.
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59
ARevenue-basedLambda
¨
Thefactor“l” measurestherelativeexposureofafirmtocountry
risk.Onesimplisticsolutionwouldbetodothefollowing:
l =%ofrevenuesdomesticallyfirm/%ofrevenuesdomesticallyaverage firm
¨
Considertwofirms– TataMotorsandTataConsultingServices,
bothIndiancompanies.In2008-09,TataMotorsgotabout91.37%
ofitsrevenuesinIndiaandTCSgot7.62%.TheaverageIndianfirm
getsabout80%ofitsrevenuesinIndia:
l TataMotors=91%/80%=1.14
l TCS=7.62%/80%=0.09
¨
Therearetwoimplications
¤
¤
Acompany’sriskexposureisdeterminedbywhereitdoesbusinessand
notbywhereitisincorporated.
Firmsmightbeabletoactivelymanagetheircountryriskexposures
60
APrice/ReturnbasedLambda
61
ReturnEmbraer = 0.0195 + 0.2681 ReturnC Bond
ReturnEmbratel = -0.0308 + 2.0030 ReturnC Bond
Embraer versus C Bond: 2000-2003
Embratel versus C Bond: 2000-2003
40
100
80
60
Return on Embrat el
Return on Embraer
20
0
-20
40
20
0
-20
-40
-40
-60
-60
-30
-80
-20
-10
0
Return on C-Bond
Aswath Damodaran
10
20
-30
-20
-10
0
10
20
Return on C-Bond
61
EstimatingaUSDollarCostofEquityfor
Embraer- September2004
62
¨
¨
AssumethatthebetaforEmbraeris1.07,andthattheUS$riskfreerate
usedis4%.AlsoassumethattheriskpremiumfortheUSis5%andthe
countryriskpremiumforBrazilis7.89%.Finally,assumethatEmbraer
gets3%ofitsrevenuesinBrazil&therestintheUS.
Therearefiveestimatesof$costofequityforEmbraer:
¤
¤
¤
¤
¤
Approach1:ConstantexposuretoCRP,LocationCRP
n E(Return)=4%+1.07(5%)+7.89%=17.24%
Approach2:ConstantexposuretoCRP,OperationCRP
n E(Return)=4%+1.07(5%)+(0.03*7.89%+0.97*0%)=9.59%
Approach3:BetaexposuretoCRP,LocationCRP
n E(Return)=4%+1.07(5%+7.89%)=17.79%
Approach4:BetaexposuretoCRP,OperationCRP
n E(Return)=4%+1.07(5%+(0.03*7.89%+0.97*0%))=9.60%
Approach5:LambdaexposuretoCRP
n E(Return)=4%+1.07(5%)+0.27(7.89%)=11.48%
Aswath Damodaran
62
ValuingEmergingMarketCompanieswith
significantexposureindevelopedmarkets
63
¨
a.
b.
Theconventionalpracticeininvestmentbankingistoaddthecountry
equityriskpremiumontothecostofequityforeveryemergingmarket
company,notwithstandingitsexposuretoemergingmarketrisk.Thus,in
2004,Embraerwouldhavebeenvaluedwithacostofequityof17-18%
eventhoughitgetsonly3%ofitsrevenuesinBrazil.Asaninvestor,which
ofthefollowingconsequencesdoyouseefromthisapproach?
Emergingmarketcompanieswithsubstantialexposureindeveloped
marketswillbesignificantlyovervaluedbyequityresearchanalysts.
Emergingmarketcompanieswithsubstantialexposureindeveloped
marketswillbesignificantlyundervaluedbyequityresearchanalysts.
Canyouconstructaninvestmentstrategytotakeadvantageofthemisvaluation?
Whatwouldneedtohappenforyoutomakemoneyofthisstrategy?
Aswath Damodaran
63
ImpliedEquityPremiums
64
¨
¨
¨
Let’sstartwithageneralproposition.Ifyouknowtheprice
paidforanassetandhaveestimatesoftheexpectedcash
flowsontheasset,youcanestimatetheIRRofthesecash
flows.Ifyoupaidtheprice,thisiswhatyouhavepricedthe
assettoearn(asanexpectedreturn).
Ifyouassumethatstocksarecorrectlypricedintheaggregate
andyoucanestimatetheexpectedcashflowsfrombuying
stocks,youcanestimatetheexpectedrateofreturnonstocks
byfindingthatdiscountratethatmakesthepresentvalue
equaltothepricepaid.Subtractingouttheriskfreerate
shouldyieldanimpliedequityriskpremium.
Thisimpliedequitypremiumisaforwardlookingnumberand
canbeupdatedasoftenasyouwant(everyminuteofevery
day,ifyouaresoinclined).
Aswath Damodaran
64
ImpliedEquityPremiums:January2008
65
¨
Wecanusetheinformationinstockpricestobackouthowriskaversethemarketisandhowmuchofarisk
premiumitisdemanding.
Between 2001 and 2007
dividends and stock
buybacks averaged 4.02%
of the index each year.
Analysts expect earnings to grow 5% a year for the next 5 years. We
will assume that dividends & buybacks will keep pace..
Last year’s cashflow (59.03) growing at 5% a year
61.98
65.08
68.33
71.75
After year 5, we will assume that
earnings on the index will grow at
4.02%, the same rate as the entire
economy (= riskfree rate).
75.34
January 1, 2008
S&P 500 is at 1468.36
4.02% of 1468.36 = 59.03
¨
Ifyoupaythecurrentleveloftheindex,youcanexpecttomakeareturnof8.39%onstocks(whichisobtainedby
solvingforrinthefollowingequation)
1468.36 =
¨
61.98 65.08
68.33
71.75
75.34
75.35(1.0402)
+
+
+
+
+
(1+ r) (1+ r) 2 (1+ r) 3 (1+ r) 4 (1+ r) 5 (r − .0402)(1+ r) 5
ImpliedEquityriskpremium=Expectedreturnonstocks- Treasurybondrate=8.39%- 4.02%=4.37%
€
Aswath Damodaran
65
Ayearthatmadeadifference..Theimplied
premiuminJanuary2009
66
Year
2001
2002
2003
2004
2005
2006
2007
2008
Normalized
Market value of index
1148.09
879.82
1111.91
1211.92
1248.29
1418.30
1468.36
903.25
903.25
Dividends
15.74
15.96
17.88
19.01
22.34
25.04
28.14
28.47
28.47
Buybacks
14.34
13.87
13.70
21.59
38.82
48.12
67.22
40.25
24.11
Cash to equity Dividend yield Buyback yield
30.08
1.37%
1.25%
29.83
1.81%
1.58%
31.58
1.61%
1.23%
40.60
1.57%
1.78%
61.17
1.79%
3.11%
73.16
1.77%
3.39%
95.36
1.92%
4.58%
68.72
3.15%
4.61%
52.584
3.15%
2.67%
In 2008, the actual cash
returned to stockholders was
68.72. However, there was a
Analysts expect earnings to grow 4% a year for the next 5 years. We
41% dropoff in buybacks in
will assume that dividends & buybacks will keep pace..
Q4. We reduced the total
buybacks for the year by that Last year’s cashflow (52.58) growing at 4% a year
amount.
54.69
56.87
59.15
61.52
January 1, 2009
S&P 500 is at 903.25
Adjusted Dividends &
Buybacks for 2008 = 52.58
Aswath Damodaran
903.25 =
Total yield
2.62%
3.39%
2.84%
3.35%
4.90%
5.16%
6.49%
7.77%
5.82%
After year 5, we will assume that
earnings on the index will grow at
2.21%, the same rate as the entire
economy (= riskfree rate).
63.98
54.69 56.87 59.15 61.52 63.98
63.98(1.0221)
+
+
+
+
+
2
3
4
5
(1+ r) (1+ r) (1+ r) (1+ r) (1+ r) (r −.0221)(1+ r)5
Expected Return on Stocks (1/1/09) = 8.64%
Riskfree rate
= 2.21%
Equity Risk Premium
= 6.43%
66
TheAnatomyofaCrisis:ImpliedERPfrom
September12,2008toJanuary1,2009
67
Aswath Damodaran
67
AnUpdatedEquityRiskPremium:January
2016
68
Base year cash flow (last 12 mths)
Dividends (TTM):
42.66
+ Buybacks (TTM):
63.43
= Cash to investors (TTM): 106.09
Payout ratio assumed to stay stable. 106.09
growing @ 5.55% a year
Expected growth in next 5 years
Top down analyst estimate of earnings
growth for S&P 500: 5.55%
Last12mths 1
2
3
4
5 TerminalYear
Dividends+Buybacks 106.09 $111.99 $118.21 $124.77 $131.70 $139.02 142.17
Earnings and Cash
flows grow @2.27%
(set equal to risk free
rate) a year forever.
S&P 500 on 1/1/16=
2043.94
111.99
118.21
124.77
131.70
139.02
142.17
2043.94 = +
+
+
+
+
/
1
2
3
(1 + ,) (1 + ,)
(1 + ,)
(1 + ,)
(1 + ,)
(, − .0227)(1 + ,)3
You have to solve for
the discount rate (r). I
used the solver or Goal
seek function in Excel
r = Implied Expected Return on Stocks = 8.39%
Minus
Risk free rate = T.Bond rate on 1/1/16= 2.27%
Equals
Implied Equity Risk Premium (1/1/16) = 8.39% - 2.27% = 6.12%
Aswath Damodaran
68
4.00%
3.00%
Implied Premium
ImpliedPremiumsintheUS:1960-2015
Implied Premium for US Equity Market: 1960-2015
7.00%
6.00%
5.00%
2.00%
1.00%
0.00%
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
Year
69
Aswath Damodaran
ABuybackAdjustedVersionoftheUSERP
70
Aswath Damodaran
70
ImpliedPremiumversusRiskFreeRate
71
Implied ERP and Risk free Rates
25.00%
Expected Return on Stocks = T.Bond Rate + Equity Risk Premium
20.00%
15.00%
Implied Premium (FCFE)
Since 2008, the expected return on
stocks has stagnated at about 8%,
but the risk free rate has dropped
dramatically.
10.00%
5.00%
T. Bond Rate
1961
1962
1963
1964
1965
1966
1967
1968
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
0.00%
Aswath Damodaran
71
EquityRiskPremiumsandBondDefaultSpreads
72
Equity Risk Premiums and Bond Default Spreads
7.00%
9.00
8.00
6.00%
7.00
6.00
4.00%
5.00
4.00
3.00%
ERP / Baa Spread
Premium (Spread)
5.00%
3.00
2.00%
2.00
1.00%
1.00
0.00%
0.00
ERP/Baa Spread
Aswath Damodaran
Baa - T.Bond Rate
ERP
72
EquityRiskPremiumsandCapRates(Real
Estate)
73
Figure18:EquityRiskPremiums,CapRatesandBondSpreads
8.00%
6.00%
4.00%
2.00%
ERP
BaaSpread
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
0.00%
CapRatepremium
-2.00%
-4.00%
-6.00%
-8.00%
Aswath Damodaran
73
Whyimpliedpremiumsmatter?
74
¨
a.
b.
c.
Inmanyinvestmentbanks,itiscommonpractice(especially
incorporatefinancedepartments)tousehistoricalrisk
premiums(andarithmeticaveragesatthat)asriskpremiums
tocomputecostofequity.Ifallanalystsinthedepartment
usedthearithmeticaveragepremium(forstocksoverT.Bills)
for1928-2015of7.92%tovaluestocksinJanuary2014,given
theimpliedpremiumof6.12%,whataretheylikelytofind?
Thevaluestheyobtainwillbetoolow(moststockswilllook
overvalued)
Thevaluestheyobtainwillbetoohigh(moststockswilllook
undervalued)
Thereshouldbenosystematicbiasaslongastheyusethe
samepremiumtovalueallstocks.
Aswath Damodaran
74
Whichequityriskpremiumshouldyouuse?
75
Ifyouassume this
Premium touse
Premiumsrevertbacktohistoricalnorms
andyourtimeperiodyieldsthesenorms
Historical riskpremium
Marketiscorrect intheaggregateorthat Current impliedequityriskpremium
yourvaluationshouldbemarketneutral
Marker makesmistakeseveninthe
aggregatebutiscorrectovertime
Predictor
Averageimpliedequity riskpremiumover
time.
Correlation with implied Correlation with actual Correlation with actual return
premium next year
return- next 5 years
– next 10 years
Current implied premium
0.750
0.475
0.541
Average implied premium: Last 5
0.703
0.541
0.747
Historical Premium
-0.476
-0.442
-0.469
Default Spread based premium
0.035
0.234
0.225
years
Aswath Damodaran
75
AnERPfortheSensex
76
¨
Inputsforthecomputation
¤
¤
¤
¤
¨
Sensexon9/5/07=15446
Dividendyieldonindex=3.05%
Expectedgrowthrate- next5years=14%
Growthratebeyondyear5=6.76%(setequaltoriskfree rate)
Solvingfortheexpectedreturn:
15446 =
¨
€
¨
537.06 612.25 697.86 795.67 907.07
907.07(1.0676)
+
+
+
+
+
(1+ r) (1+ r) 2 (1+ r) 3 (1+ r) 4 (1+ r) 5 (r − .0676)(1+ r) 5
Expectedreturnonstocks=11.18%
ImpliedequityriskpremiumforIndia=11.18%- 6.76%=
4.42%
Aswath Damodaran
76
ChangingCountryRisk:BrazilCRP&Total
ERPfrom2000to2015
77
Aswath Damodaran
77
TheevolutionofEmergingMarketRisk
78
PBV
Startofyear Developed
2004
2.00
2005
2.09
2006
2.03
2007
1.67
2008
0.87
2009
1.20
2010
1.39
2011
1.12
2012
1.17
2013
1.56
2014
1.95
2015
1.88
2016
1.89
Aswath Damodaran
PBV
Emerging
1.19
1.27
1.44
1.67
0.83
1.34
1.43
1.08
1.18
1.63
1.50
1.56
1.59
ROE
Developed
10.81%
11.12%
11.32%
10.87%
9.42%
8.48%
9.14%
9.21%
9.10%
8.67%
9.27%
9.69%
9.24%
ROE
Emerging
11.65%
11.93%
12.18%
12.88%
11.12%
11.02%
11.22%
10.04%
9.33%
10.48%
9.64%
9.75%
10.16%
Growth
Rate
UST.Bond
Developed
rate
4.25%
3.75%
4.22%
3.72%
4.39%
3.89%
4.70%
4.20%
4.02%
3.52%
2.21%
1.71%
3.84%
3.34%
3.29%
2.79%
1.88%
1.38%
1.76%
1.26%
3.04%
2.54%
2.17%
1.67%
2.27%
1.77%
Growth
Costof
Costof
Rate
Equity
Equity Differential
Emerging (Developed) (Emerging)
ERP
5.25%
7.28%
10.63%
3.35%
5.22%
7.26%
10.50%
3.24%
5.39%
7.55%
10.11%
2.56%
5.70%
8.19%
10.00%
1.81%
5.02%
10.30%
12.37%
2.07%
3.21%
7.35%
9.04%
1.69%
4.84%
7.51%
9.30%
1.79%
4.29%
8.52%
9.61%
1.09%
2.88%
7.98%
8.35%
0.37%
2.76%
6.02%
7.50%
1.48%
4.04%
6.00%
7.77%
1.77%
3.17%
5.94%
7.39%
1.45%
3.27%
5.72%
7.60%
1.88%
78
79
DiscountRates:III
RelativeRiskMeasures
Aswath Damodaran
TheCAPMBeta:TheMostUsed(and
Misused)RiskMeasure
80
¨
Thestandardprocedureforestimatingbetasistoregress
stockreturns(Rj)againstmarketreturns(Rm)Rj =a+bRm
whereaistheinterceptandbistheslopeoftheregression.
¨
¨
Theslopeoftheregressioncorrespondstothebetaof
thestock,andmeasurestheriskinessofthestock.
Thisbetahasthreeproblems:
•
•
•
Ithashighstandarderror
Itreflectsthefirm’sbusinessmixovertheperiodofthe
regression,notthecurrentmix
Itreflectsthefirm’saveragefinancialleverageovertheperiod
ratherthanthecurrentleverage.
Aswath Damodaran
80
Unreliable,whenitlooksbad..
81
Aswath Damodaran
81
Orwhenitlooksgood..
82
Aswath Damodaran
82
Onesliceofhistory..
83
During this time period, Valeant was a
stock under siege, without a CEO,
under legal pressure & lacking
financials.
Aswath Damodaran
Andsubjecttogameplaying
84
Aswath Damodaran
MeasuringRelativeRisk:Youdon’tlikebetasor
modernportfoliotheory?Noproblem.
85
Aswath Damodaran
85
Don’tlikethediversifiedinvestorfocus,
butokaywithprice-basedmeasures
86
1. RelativeStandardDeviation
•
•
RelativeVolatility=Std devofStock/AverageStd devacrossallstocks
Capturesallrisk,ratherthanjustmarketrisk
2. ProxyModels
•
•
•
Lookathistoricalreturnsonallstocksandlookforvariablesthat
explaindifferencesinreturns.
Youare,ineffect,runningmultipleregressionswithreturnson
individualstocksasthedependentvariableandfundamentalsabout
thesestocksasindependentvariables.
Thisapproachstartedwithmarketcap(thesmallcapeffect)andover
thelasttwodecadeshasaddedothervariables(momentum,liquidity
etc.)
3. CAPMPlusModels
•
StartwiththetraditionalCAPM(Rf +Beta(ERP))andthenaddother
premiumsforproxies.
Aswath Damodaran
86
Don’tliketheprice-basedapproach..
87
Accountingriskmeasures:Totheextentthatyoudon’ttrust
market-pricedbasedmeasuresofrisk,youcouldcompute
relativeriskmeasuresbasedon
1.
•
•
Accountingearningsvolatility:Computeanaccountingbetaorrelative
volatility
Balancesheetratios:Youcouldcomputeariskscorebaseduponaccounting
ratioslikedebtratiosorcashholdings(akintodefaultriskscoresliketheZ
score)
QualitativeRiskModels:Inthesemodels,riskassessments
arebasedatleastpartiallyonqualitativefactors(qualityof
management).
Debtbasedmeasures:Youcanestimateacostofequity,
baseduponanobservablecostsofdebtforthecompany.
2.
3.
•
•
Costofequity=Costofdebt*Scalingfactor
Thescalingfactorcanbecomputedfromimpliedvolatilities.
Aswath Damodaran
87
DeterminantsofBetas&RelativeRisk
88
Beta of Equity (Levered Beta)
Beta of Firm (Unlevered Beta)
Nature of product or
service offered by
company:
Other things remaining equal,
the more discretionary the
product or service, the higher
the beta.
Operating Leverage (Fixed
Costs as percent of total
costs):
Other things remaining equal
the greater the proportion of
the costs that are fixed, the
higher the beta of the
company.
Implications
1. Cyclical companies should
have higher betas than noncyclical companies.
2. Luxury goods firms should
have higher betas than basic
goods.
3. High priced goods/service
firms should have higher betas
than low prices goods/services
firms.
4. Growth firms should have
higher betas.
Implications
1. Firms with high infrastructure
needs and rigid cost structures
should have higher betas than
firms with flexible cost structures.
2. Smaller firms should have higher
betas than larger firms.
3. Young firms should have higher
betas than more mature firms.
Aswath Damodaran
Financial Leverage:
Other things remaining equal, the
greater the proportion of capital that
a firm raises from debt,the higher its
equity beta will be
Implciations
Highly levered firms should have highe betas
than firms with less debt.
Equity Beta (Levered beta) =
Unlev Beta (1 + (1- t) (Debt/Equity Ratio))
88
Inaperfectworld…wewouldestimatethebetaofa
firmbydoingthefollowing
89
Start with the beta of the business that the firm is in
Adjust the business beta for the operating leverage of the firm to arrive at the
unlevered beta for the firm.
Use the financial leverage of the firm to estimate the equity beta for the firm
Levered Beta = Unlevered Beta ( 1 + (1- tax rate) (Debt/Equity))
Aswath Damodaran
89
Adjustingforoperatingleverage…
90
¨
Withinanybusiness,firmswithlowerfixedcosts(asa
percentageoftotalcosts)shouldhavelowerunlevered
betas.Ifyoucancomputefixedandvariablecostsfor
eachfirminasector,youcanbreakdowntheunlevered
betaintobusinessandoperatingleveragecomponents.
¤
¨
¨
Unleveredbeta=Purebusinessbeta*(1+(Fixedcosts/Variable
costs))
Thebiggestproblemwithdoingthisisinformational.Itis
difficulttogetinformationonfixedandvariablecostsfor
individualfirms.
Inpractice,wetendtoassumethattheoperating
leverageoffirmswithinabusinessaresimilaranduse
thesameunleveredbetaforeveryfirm.
Aswath Damodaran
90
Adjustingforfinancialleverage…
91
¨
Conventionalapproach:Ifweassumethatdebtcarries
nomarketrisk(hasabetaofzero),thebetaofequity
alonecanbewrittenasafunctionoftheunleveredbeta
andthedebt-equityratio
bL =bu (1+((1-t)D/E))
Insomeversions,thetaxeffectisignoredandthereisno(1-t)in
theequation.
¨
DebtAdjustedApproach:Ifbetacarriesmarketriskand
youcanestimatethebetaofdebt,youcanestimatethe
leveredbetaasfollows:
bL =bu (1+((1-t)D/E))- bdebt (1-t)(D/E)
Whilethelatterismorerealistic,estimatingbetasfordebtcanbe
difficulttodo.
Aswath Damodaran
91
Bottom-upBetas
92
Step 1: Find the business or businesses that your firm operates in.
Possible Refinements
Step 2: Find publicly traded firms in each of these businesses and
obtain their regression betas. Compute the simple average across
these regression betas to arrive at an average beta for these publicly
traded firms. Unlever this average beta using the average debt to
equity ratio across the publicly traded firms in the sample.
Unlevered beta for business = Average beta across publicly traded
firms/ (1 + (1- t) (Average D/E ratio across firms))
Step 3: Estimate how much value your firm derives from each of
the different businesses it is in.
Step 4: Compute a weighted average of the unlevered betas of the
different businesses (from step 2) using the weights from step 3.
Bottom-up Unlevered beta for your firm = Weighted average of the
unlevered betas of the individual business
Step 5: Compute a levered beta (equity beta) for your firm, using
the market debt to equity ratio for your firm.
Levered bottom-up beta = Unlevered beta (1+ (1-t) (Debt/Equity))
Aswath Damodaran
If you can, adjust this beta for differences
between your firm and the comparable
firms on operating leverage and product
characteristics.
While revenues or operating income
are often used as weights, it is better
to try to estimate the value of each
business.
If you expect the business mix of your
firm to change over time, you can
change the weights on a year-to-year
basis.
If you expect your debt to equity ratio to
change over time, the levered beta will
change over time.
92
Whybottom-upbetas?
93
Thestandarderrorinabottom-upbetawillbesignificantly
lowerthanthestandarderrorinasingleregressionbeta.
Roughlyspeaking,thestandarderrorofabottom-upbeta
estimatecanbewrittenasfollows:
Average Std Error across Betas
Stderrorofbottom-upbeta=
¨
Number of firms in sample
¨
¨
Thebottom-upbetacanbeadjustedtoreflectchangesinthe
firm’sbusinessmixandfinancialleverage.Regressionbetas
€
reflectthepast.
Youcanestimatebottom-upbetasevenwhenyoudonot
havehistoricalstockprices.Thisisthecasewithinitialpublic
offerings,privatebusinessesordivisionsofcompanies.
Aswath Damodaran
93
EstimatingBottomUpBetas&Costsof
Equity:Vale
Sample'
Sample'
size'
Metals'&'
Mining'
Global'firms'in'metals'&'
mining,'Market'cap>$1'
billion'
48'
0.86'
$9,013'
1.97'
$17,739'
16.65%'
Iron'Ore'
Global'firms'in'iron'ore'
78'
0.83'
$32,717'
2.48'
$81,188'
76.20%'
Fertilizers'
Global'specialty'
chemical'firms'
693'
0.99'
$3,777'
1.52'
$5,741'
5.39%'
Global'transportation'
firms'
223'
0.75'
$1,644'
1.14'
$1,874'
1.76%'
''
0.8440'
$47,151'
''
$106,543'
100.00%'
Business'
Logistics'
Vale'
Operations'
''
Aswath Damodaran
Unlevered'beta'
of'business'
Revenues'
Peer'Group'
EV/Sales'
Value'of'
Business'
Proportion'of'
Vale'
94
Embraer’sBottom-upBeta
95
Business
Aerospace
¨
¨
a.
b.
UnleveredBeta D/ERatio
0.95
18.95%
Leveredbeta
1.07
LeveredBeta =UnleveredBeta(1+(1- taxrate)(D/ERatio)
=0.95(1+(1-.34)(.1895))=1.07
CananunleveredbetaestimatedusingU.S.andEuropean
aerospacecompaniesbeusedtoestimatethebetaforaBrazilian
aerospacecompany?
Yes
No
Whatconcernswouldyouhaveinmakingthisassumption?
Aswath Damodaran
95
GrossDebtversusNetDebtApproaches
96
¨
¨
AnalystsinEuropeandLatinAmericaoftentakethedifferencebetween
debtandcash(netdebt)whencomputingdebtratiosandarriveatvery
differentvalues.
ForEmbraer,usingthegrossdebtratio
¤
¤
¨
Usingthenetdebtratio,weget
¤
¤
¨
GrossD/ERatioforEmbraer=1953/11,042=18.95%
LeveredBetausingGrossDebtratio=1.07
NetDebtRatioforEmbraer=(Debt- Cash)/MarketvalueofEquity
=(1953-2320)/11,042=-3.32%
LeveredBetausingNetDebtRatio=0.95(1+(1-.34)(-.0332))=0.93
ThecostofEquityusingnetdebtleveredbetaforEmbraerwillbemuch
lowerthanwiththegrossdebtapproach.ThecostofcapitalforEmbraer
willevenoutsincethedebtratiousedinthecostofcapitalequationwill
nowbeanetdebtratioratherthanagrossdebtratio.
Aswath Damodaran
96
TheCostofEquity:ARecap
97
Preferably, a bottom-up beta,
based upon other firms in the
business, and firmʼs own financial
leverage
Cost of Equity =
Riskfree Rate
Has to be in the same
currency as cash flows,
and defined in same terms
(real or nominal) as the
cash flows
Aswath Damodaran
+
Beta *
(Risk Premium)
Historical Premium
1. Mature Equity Market Premium:
Average premium earned by
stocks over T.Bonds in U.S.
2. Country risk premium =
Country Default Spread* ( σEquity/σCountry bond)
or
Implied Premium
Based on how equity
market is priced today
and a simple valuation
model
97
98
DiscountRates:IV
Moppingup
Aswath Damodaran
EstimatingtheCostofDebt
99
¨
¨
Thecostofdebtistherateatwhichyoucanborrowat
currently,Itwillreflectnotonlyyourdefaultriskbutalsothe
levelofinterestratesinthemarket.
Thetwomostwidelyusedapproachestoestimatingcostof
debtare:
¤
¤
¨
Lookinguptheyieldtomaturityonastraightbondoutstandingfrom
thefirm.Thelimitationofthisapproachisthatveryfewfirmshave
longtermstraightbondsthatareliquidandwidelytraded
Lookinguptheratingforthefirmandestimatingadefaultspread
basedupontherating.Whilethisapproachismorerobust,different
bondsfromthesamefirmcanhavedifferentratings.Youhavetousea
medianratingforthefirm
Whenintrouble(eitherbecauseyouhavenoratingsor
multipleratingsforafirm),estimateasyntheticratingfor
yourfirmandthecostofdebtbaseduponthatrating.
Aswath Damodaran
99
EstimatingSyntheticRatings
100
¨
Theratingforafirmcanbeestimatedusingthefinancial
characteristicsofthefirm.Initssimplestform,therating
canbeestimatedfromtheinterestcoverageratio
InterestCoverageRatio=EBIT/InterestExpenses
¨
ForEmbraer’sinterestcoverageratio,weusedthe
interestexpensesfrom2003andtheaverageEBITfrom
2001to2003.(Theaircraftbusinesswasbadlyaffected
by9/11anditsaftermath.In2002and2003,Embraer
reportedsignificantdropsinoperatingincome)
InterestCoverageRatio=462.1/129.70=3.56
Aswath Damodaran
100
InterestCoverageRatios,RatingsandDefault
Spreads:2003&2004
101
¨
IfInterestCoverageRatiois
EstimatedBondRating
DefaultSpread(2003)
DefaultSpread(2004)
>8.50
6.50- 8.50
5.50- 6.50
4.25- 5.50
3.00- 4.25
2.50- 3.00
2.25- 2.50
2.00- 2.25
1.75- 2.00
1.50- 1.75
1.25- 1.50
0.80- 1.25
0.65- 0.80
0.20- 0.65
<0.20 (<0.5)
AAA
AA
A+
A
A–
BBB
BB+
BB
B+
B
B–
CCC
CC
C
0.75%
1.00%
1.50%
1.80%
2.00%
2.25%
2.75%
3.50%
4.75%
6.50%
8.00%
10.00%
11.50%
12.70%
15.00%
0.35%
0.50%
0.70%
0.85%
1.00%
1.50%
2.00%
2.50%
3.25%
4.00%
6.00%
8.00%
10.00%
12.00%
20.00%
(>12.50)
(9.5-12.5)
(7.5-9.5)
(6-7.5)
(4.5-6)
(4-4.5)
(3.5-4)
((3-3.5)
(2.5-3)
(2-2.5)
(1.5-2)
(1.25-1.5)
(0.8-1.25)
(0.5-0.8)
D
Thefirstnumberunderinterestcoverageratiosisforlargermarketcapcompaniesandthesecondin
bracketsisforsmallermarketcapcompanies.ForEmbraer,Iusedtheinterestcoverageratiotablefor
smaller/riskierfirms(thenumbersinbrackets)whichyieldsalowerratingforthesameinterestcoverage
ratio.
Aswath Damodaran
101
CostofDebtcomputations
102
Companiesincountrieswithlowbondratingsandhighdefaultrisk
mightbeartheburdenofcountrydefaultrisk,especiallyiftheyare
smallerorhavealloftheirrevenueswithinthecountry.
¨ Largercompaniesthatderiveasignificantportionoftheirrevenues
inglobalmarketsmaybelessexposedtocountrydefaultrisk.In
otherwords,theymaybeabletoborrowataratelowerthanthe
government.
¨ ThesyntheticratingforEmbraerisA-.Usingthe2004default
spreadof1.00%,weestimateacostofdebtof9.29%(usinga
riskfree rateof4.29%andaddingintwothirdsofthecountry
defaultspreadof6.01%):
Costofdebt
=Riskfree rate+2/3(Brazilcountrydefaultspread)+Companydefault
spread=4.29%+4.00%+1.00%=9.29%
¨
Aswath Damodaran
102
SyntheticRatings:SomeCaveats
103
¨
¨
Therelationshipbetweeninterestcoverageratiosand
ratings,developedusingUScompanies,tendstotravel
well,aslongasweareanalyzinglargemanufacturing
firmsinmarketswithinterestratesclosetotheUS
interestrate
Theyaremoreproblematicwhenlookingatsmaller
companiesinmarketswithhigherinterestratesthanthe
US.Onewaytoadjustforthisdifferenceismodifythe
interestcoverageratiotabletoreflectinterestrate
differences(Forinstances,ifinterestratesinan
emergingmarketaretwiceashighasratesintheUS,
halvetheinterestcoverageratio.
Aswath Damodaran
103
DefaultSpreads:Theeffectofthecrisisof
2008..Andtheaftermath
104
Default spread over treasury
Rating
Aaa/AAA
Aa1/AA+
Aa2/AA
Aa3/AAA1/A+
A2/A
A3/A-
1-Jan-08
0.99%
1.15%
1.25%
1.30%
1.35%
1.42%
1.48%
12-Sep-08
1.40%
1.45%
1.50%
1.65%
1.85%
1.95%
2.15%
12-Nov-08
2.15%
2.30%
2.55%
2.80%
3.25%
3.50%
3.75%
1-Jan-09
2.00%
2.25%
2.50%
2.75%
3.25%
3.50%
3.75%
1-Jan-10
0.50%
0.55%
0.65%
0.70%
0.85%
0.90%
1.05%
1-Jan-11
0.55%
0.60%
0.65%
0.75%
0.85%
0.90%
1.00%
Baa1/BBB+
Baa2/BBB
1.73%
2.02%
2.65%
2.90%
4.50%
5.00%
5.25%
5.75%
1.65%
1.80%
1.40%
1.60%
Baa3/BBBBa1/BB+
Ba2/BB
Ba3/BBB1/B+
B2/B
B3/B-
2.60%
3.20%
3.65%
4.00%
4.55%
5.65%
6.45%
3.20%
4.45%
5.15%
5.30%
5.85%
6.10%
9.40%
5.75%
7.00%
8.00%
9.00%
9.50%
10.50%
13.50%
7.25%
9.50%
10.50%
11.00%
11.50%
12.50%
15.50%
2.25%
3.50%
3.85%
4.00%
4.25%
5.25%
5.50%
2.05%
2.90%
3.25%
3.50%
3.75%
5.00%
6.00%
Caa/CCC+
ERP
7.15%
4.37%
9.80%
4.52%
14.00%
6.30%
16.50%
6.43%
7.75%
4.36%
7.75%
5.20%104
UpdatedDefaultSpreads- January2016
105
DefaultSpreadsfor10-yearCorporateBonds:January2015vsJanuary2016
25.00%
20.00%
20.00%
16.00%
15.00%
12.00%
10.00%
9.00%
7.50%
6.50%
5.50%
5.00%
4.25%
3.25%
0.75%
1.00%
1.10%
1.25%
1.75%
2.25%
0.00%
Aaa/AAA
Aa2/AA
A1/A+
A2/A
A3/A-
Baa2/BBB Ba1/BB+
Spread: 2016
Aswath Damodaran
Ba2/BB
B1/B+
B2/B
B3/B-
Caa/CCC
Ca2/CC
C2/C
D2/D
Spread: 2015
105
SubsidizedDebt:Whatshouldwedo?
106
¨
a.
b.
c.
AssumethattheBraziliangovernmentlendsmoneyto
Embraeratasubsidizedinterestrate(say6%indollar
terms).Incomputingthecostofcapitaltovalue
Embraer,shouldbeweusethecostofdebtbasedupon
defaultriskorthesubsidizedcostofdebt?
Thesubsidizedcostofdebt(6%).Thatiswhatthe
companyispaying.
Thefaircostofdebt(9.25%).Thatiswhatthecompany
shouldrequireitsprojectstocover.
Anumberinthemiddle.
Aswath Damodaran
106
WeightsfortheCostofCapitalComputation
107
¨
Incomputingthecostofcapitalforapubliclytraded
firm,thegeneralruleforcomputingweightsfordebt
andequityisthatyouusemarketvalueweights(and
notbookvalueweights).Why?
a.
b.
c.
d.
Becausethemarketisusuallyright
Becausemarketvaluesareeasytoobtain
Becausebookvaluesofdebtandequityaremeaningless
Noneoftheabove
Aswath Damodaran
107
EstimatingCostofCapital:Embraerin2004
108
¨
Equity
¤
¤
¨
Debt
¤
¤
¨
CostofEquity=4.29%+1.07(4%)+0.27(7.89%)=10.70%
MarketValueofEquity=11,042millionBR($3,781million)
Costofdebt=4.29%+4.00%+1.00%=9.29%
MarketValueofDebt=2,083millionBR($713million)
CostofCapital
CostofCapital=10.70%(.84)+9.29%(1- .34)(0.16))=9.97%
¤
¤
¤
ThebookvalueofequityatEmbraeris3,350millionBR.
ThebookvalueofdebtatEmbraeris1,953millionBR;Interest
expenseis222milBR;Averagematurityofdebt=4years
Estimatedmarketvalueofdebt=222million(PVofannuity,4years,
9.29%)+$1,953million/1.09294 =2,083millionBR
Aswath Damodaran
108
Ifyouhadtodoit….ConvertingaDollarCostof
CapitaltoaNominalRealCostofCapital
109
¨
Approach1:UseaBRriskfree rateinallofthecalculations
above.Forinstance,iftheBRriskfree ratewas12%,thecost
ofcapitalwouldbecomputedasfollows:
¤
¤
¤
¨
CostofEquity=12%+1.07(4%)+0.27(7.89%)=18.41%
CostofDebt=12%+1%=13%
(Thisassumestheriskfree ratehasnocountryriskpremium
embeddedinit.)
Approach2:Usethedifferentialinflationratetoestimatethe
costofcapital.Forinstance,iftheinflationrateinBRis8%
andtheinflationrateintheU.S.is2%
" 1 + Inflation %
BR
(1
+
Cost
of
Capital
)
$
'
$
Costofcapital=
# 1 + Inflation$ &
=1.0997(1.08/1.02)-1=0.1644or16.44%
Aswath Damodaran
€
109
DealingwithHybridsandPreferredStock
110
¨
¨
Whendealingwithhybrids(convertiblebonds,for
instance),breakthesecuritydownintodebtandequity
andallocatetheamountsaccordingly.Thus,ifafirmhas
$125millioninconvertibledebtoutstanding,breakthe
$125millionintostraightdebtandconversionoption
components.Theconversionoptionisequity.
Whendealingwithpreferredstock,itisbettertokeepit
asaseparatecomponent.Thecostofpreferredstockis
thepreferreddividendyield.(Asaruleofthumb,ifthe
preferredstockislessthan5%oftheoutstandingmarket
valueofthefirm,lumpingitinwithdebtwillmakeno
significantimpactonyourvaluation).
Aswath Damodaran
110
Decomposingaconvertiblebond…
111
¨
Assumethatthefirmthatyouareanalyzinghas$125million
infacevalueofconvertibledebtwithastatedinterestrateof
4%,a10yearmaturityandamarketvalueof$140million.If
thefirmhasabondratingofAandtheinterestrateonAratedstraightbondis8%,youcanbreakdownthevalueof
theconvertiblebondintostraightdebtandequityportions.
¤
¤
¨
Straightdebt=(4%of$125million)(PVofannuity,10years,8%)+125
million/1.0810=$91.45million
Equityportion=$140million- $91.45million=$48.55million
Thedebtportion($91.45million)getsaddedtodebtandthe
optionportion($48.55million)getsaddedtothemarket
capitalizationtogettothedebtandequityweightsinthecost
ofcapital.
Aswath Damodaran
111
RecappingtheCostofCapital
112
Cost of borrowing should be based upon
(1) synthetic or actual bond rating
(2) default spread
Cost of Borrowing = Riskfree rate + Default spread
Cost of Capital =
Cost of Equity (Equity/(Debt + Equity))
Cost of equity
based upon bottom-up
beta
Aswath Damodaran
+
Cost of Borrowing
(1-t)
Marginal tax rate, reflecting
tax benefits of debt
(Debt/(Debt + Equity))
Weights should be market value weights
112