DISCOUNTRATES

TheDintheDCF..

Aswath Damodaran 20

21

EstimatingInputs:DiscountRates

¨ WhilediscountratesobviouslymatterinDCFvaluation,theydon’tmatterasmuchasmostanalyststhinktheydo.

¨ Atanintuitivelevel,thediscountrateusedshouldbeconsistentwithboththeriskinessandthetypeofcashflowbeingdiscounted.¤ EquityversusFirm:Ifthecashflowsbeingdiscountedarecashflowsto

equity,theappropriatediscountrateisacostofequity.Ifthecashflowsarecashflowstothefirm,theappropriatediscountrateisthecostofcapital.

¤ Currency:Thecurrencyinwhichthecashflowsareestimatedshouldalsobethecurrencyinwhichthediscountrateisestimated.

¤ NominalversusReal:Ifthecashflowsbeingdiscountedarenominalcashflows(i.e.,reflectexpectedinflation),thediscountrateshouldbenominal

Aswath Damodaran

21

22

RiskintheDCFModel

Risk Adjusted Cost of equity

Risk free rate in the currency of analysis

Relative risk of company/equity in

questiion

Equity Risk Premium required for average risk

equity+ X=

Aswath Damodaran

22

23

Notallriskiscreatedequal…

¨ EstimationversusEconomicuncertainty¤ Estimationuncertaintyreflectsthepossibilitythatyoucouldhavethe“wrong

model”orestimatedinputsincorrectlywithinthismodel.¤ Economicuncertaintycomesthefactthatmarketsandeconomiescanchangeover

timeandthateventhebestmodelswillfailtocapturetheseunexpectedchanges.¨ MicrouncertaintyversusMacrouncertainty

¤ Microuncertaintyreferstouncertaintyaboutthepotentialmarketforafirm’sproducts,thecompetitionitwillfaceandthequalityofitsmanagementteam.

¤ Macrouncertaintyreflectstherealitythatyourfirm’sfortunescanbeaffectedbychangesinthemacroeconomicenvironment.

¨ Discreteversuscontinuousuncertainty¤ Discreterisk:Risksthatliedormantforperiodsbutshowupatpointsintime.

(Examples:AdrugworkingitswaythroughtheFDApipelinemayfailatsomestageoftheapprovalprocessoracompanyinVenezuelamaybenationalized)

¤ Continuousrisk:Riskschangesininterestratesoreconomicgrowthoccurcontinuouslyandaffectvalueastheyhappen.

Aswath Damodaran

23

24

RiskandCostofEquity:Theroleofthemarginalinvestor

¨ Notallriskcounts:Whilethenotionthatthecostofequityshouldbehigherforriskierinvestmentsandlowerforsaferinvestmentsisintuitive,whatriskshouldbebuiltintothecostofequityisthequestion.

¨ Riskthroughwhoseeyes? Whileriskisusuallydefinedintermsofthevarianceofactualreturnsaroundanexpectedreturn,riskandreturnmodelsinfinanceassumethattheriskthatshouldberewarded(andthusbuiltintothediscountrate)invaluationshouldbetheriskperceivedbythemarginalinvestorintheinvestment

¨ Thediversificationeffect:Mostriskandreturnmodelsinfinancealsoassumethatthemarginalinvestoriswelldiversified,andthattheonlyriskthatheorsheperceivesinaninvestmentisriskthatcannotbediversifiedaway(i.e,marketornon-diversifiablerisk).Ineffect,itisprimarilyeconomic,macro,continuousriskthatshouldbeincorporatedintothecostofequity.

Aswath Damodaran

24

25

TheCostofEquity:Competing“MarketRisk”Models

Model ExpectedReturn InputsNeededCAPM E(R)=Rf +b (Rm- Rf) Riskfree Rate

BetarelativetomarketportfolioMarketRiskPremium

APM E(R)=Rf +Sbj (Rj- Rf) Riskfree Rate;#ofFactors;BetasrelativetoeachfactorFactorriskpremiums

Multi E(R)=Rf +Sbj (Rj- Rf) Riskfree Rate;Macrofactorsfactor Betasrelativetomacrofactors

MacroeconomicriskpremiumsProxy E(R)=a+S bj Yj Proxies

Regressioncoefficients

Aswath Damodaran

25

26

ClassicRisk&Return:CostofEquity

¨ IntheCAPM,thecostofequity:CostofEquity=Riskfree Rate+EquityBeta*(EquityRiskPremium)

¨ InAPMorMulti-factormodels,youstillneedariskfreerate,aswellasbetasandriskpremiumstogowitheachfactor.

¨ Touseanyriskandreturnmodel,youneed¨ Ariskfreerateasabase¨ Asingleequityriskpremium(intheCAPM)orfactorrisk

premiums,inthethemulti-factormodels¨ Abeta(intheCAPM)orbetas(inmulti-factormodels)

Aswath Damodaran

26

TheRiskFreeRate

DiscountRates:I27

Aswath Damodaran

28

TheRiskFreeRate:LayingtheFoundations

¨ Onariskfree investment,theactualreturnisequaltotheexpectedreturn.Therefore,thereisnovariancearoundtheexpectedreturn.

¨ Foraninvestmenttoberiskfree,then,ithastohave¤ Nodefaultrisk¤ Noreinvestmentrisk

¤ Itfollowsthenthatifaskedtoestimateariskfreerate:1. Timehorizonmatters:Thus,theriskfree ratesinvaluationwill

dependuponwhenthecashflowisexpectedtooccurandwillvaryacrosstime.

2. Currenciesmatter:Ariskfreerateiscurrency-specificandcanbeverydifferentfordifferentcurrencies.

3. Notallgovernmentsecuritiesareriskfree:Somegovernmentsfacedefaultriskandtheratesonbondsissuedbythemwillnotberiskfree.

Aswath Damodaran

28

29

Test1:AriskfreerateinUSdollars!

¨ Invaluation,weestimatecashflowsforever(oratleastforverylongtimeperiods).TherightriskfreeratetouseinvaluingacompanyinUSdollarswouldbea. Athree-monthTreasurybillrate(0.2%)b. Aten-yearTreasurybondrate(2%)c. Athirty-yearTreasurybondrate(3%)d. ATIPs(inflation-indexedtreasury)rate(1%)e. Noneoftheabove

¨ WhatareweimplicitlyassumingabouttheUStreasurywhenweuseanyofthetreasurynumbers?

Aswath Damodaran

29

30

Test2:ARiskfreeRateinEuros

Aswath Damodaran

30

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

10.00%

EuroGovernmentBondRates- January1,2016

31

Test3:ARiskfreeRateinIndianRupees

¨ TheIndiangovernmenthad10-yearRupeebondsoutstanding,withayieldtomaturityofabout7.73%onJanuary1,2016.

¨ InJanuary2016,theIndiangovernmenthadalocalcurrencysovereignratingofBaa3.Thetypicaldefaultspread(overadefaultfreerate)forBaa3ratedcountrybondsinearly2016was2.44%.TheriskfreerateinIndianRupeesisa. Theyieldtomaturityonthe10-yearbond(7.73%)b. Theyieldtomaturityonthe10-yearbond+Defaultspread(10.17%)c. Theyieldtomaturityonthe10-yearbond– Defaultspread(5.29%)d. Noneoftheabove

Aswath Damodaran

31

32

SovereignDefaultSpread:Threepathstothesamedestination…

¨ Sovereigndollaroreurodenominatedbonds:FindsovereignbondsdenominatedinUSdollars,issuedbyanemergingsovereign.¤ Defaultspread=EmergingGovt BondRate(inUS$)– USTreasuryBondratewithsamematurity.

¨ CDSspreads:ObtainthetradedvalueforasovereignCreditDefaultSwap(CDS)fortheemerginggovernment.¤ Defaultspread=SovereignCDSspread(withperhapsanadjustmentforCDSmarketfrictions).

¨ Sovereign-ratingbasedspread:Forcountrieswhichdon’tissuedollardenominatedbondsorhaveaCDSspread,youhavetousetheaveragespreadforothercountrieswiththesamesovereign rating.

Aswath Damodaran

32

33

LocalCurrencyGovernmentBondRates–January2016

Aswath Damodaran

33

34

Approach1:DefaultspreadfromGovernmentBonds

The Brazil Default SpreadBrazil 2021 Bond: 6.83%US 2021 T.Bond: 2.00%Spread: 4.83%

35

Approach2:CDSSpreads– January2016

Aswath Damodaran

35

36

Approach3:TypicalDefaultSpreads:January2016

Aswath Damodaran

36

37

Gettingtoariskfreerateinacurrency:Example

¨ TheBraziliangovernmentbondrateinnominalreaisonJanuary1,2016was16.51%.Togettoariskfreerateinnominalreais,wecanuseoneofthreeapproaches.¨ Approach1:GovernmentBondspread

¤ The2021Brazilbond,denominatedinUSdollars,hasaspreadof4.83%overtheUStreasurybondrate.

¤ Riskfreeratein$R=16.51%- 4.83%=11.68%¨ Approach2:TheCDSSpread

¤ TheCDSspreadforBrazil,adjustedfortheUSCDSspreadwas5.19%.

¤ Riskfreeratein$R=16.51%- 5.19%=11.32%¨ Approach3:TheRatingbasedspread

¤ BrazilhasaBaa3localcurrencyratingfromMoody’s.Thedefaultspreadforthatratingis2.44%

¤ Riskfreeratein$R=16.51%- 2.44%=14.07%

Aswath Damodaran

37

38

Test4:ARealRiskfreeRate

¨ Insomecases,youmaywantariskfree rateinrealterms(inrealterms)ratherthannominalterms.

¨ Togetarealriskfree rate,youwouldlikeasecuritywithnodefaultriskandaguaranteedrealreturn.Treasuryindexedsecuritiesofferthiscombination.

¨ InJanuary2016,theyieldona10-yearindexedtreasurybondwas0.75%.Whichofthefollowingstatementswouldyousubscribeto?a. This(0.75%)istherealriskfree ratetouse,ifyouarevaluing

UScompaniesinrealterms.b. This(0.75%)istherealriskfree ratetouse,anywhereinthe

worldExplain.

Aswath Damodaran

38

39

Whydoriskfreeratesvaryacrosscurrencies?January2016Riskfreerates

Aswath Damodaran

39

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%JapaneseYen

CzechKo

runa

SwissFranc

Taiwanese$

BulgarianLev

Euro

Hun

garianForin

t

ThaiBaht

DanishKron

e

SwedishKron

a

HK$

CroatianKu

na

IsraeliShekel

RomanianLeu

Canadian$

NorwegianKron

e

BritishPou

nd

KoreanW

on

PakistaniRup

ee

PhillipinePeso

PolishZloty

VietnameseDon

g

ChineseYuan

US$

Singapore$

MalyasianRinggit

Australian$

NZ$

IcelandKron

a

ChileanPeso

MexicanPeso

IndianRup

ee

PeruvianSol

ColombianPeso

Indo

nesianRup

iah

VenezuelanBolivar

RussianRu

ble

NigerianNaira

TurkishLira

SouthAfricanRand

KenyanShilling

BrazilianReai

RiskfreeRates- January2016

RiskfreeRate DefaultSpreadbasedonrating

40

RiskfreeRate:Don’thaveortrustthegovernmentbondrate?1. Buildupapproach:Theriskfreerateinanycurrencycanbe

writtenasthesumoftwovariables:Riskfreerate=ExpectedInflationincurrency+Expectedrealinterestrate

Theexpectedrealinterestratecanbecomputedinoneoftwoways:fromtheUSTIPsrateorsetequaltorealgrowthintheeconomy.Thus,iftheexpectedinflationrateinacountryisexpectedtobe15%andtheTIPsrateis1%,theriskfreerateis16%.

2. US$Rate&DifferentialInflation:Alternatively,youcanscaleuptheUS$riskfreeratebythedifferentialinflationbetweentheUS$andthecurrencyinquestion:

RiskfreerateCurrency=

Thus,iftheUS$riskfreerateis2.00%,theinflationrateintheforeigncurrencyis15%andtheinflationrateinUS$is1.5%,theforeigncurrencyriskfreerateisasfollows:Riskfreerate= 1.02 !.!"

!.!"# − 1=15.57%

41

Onemoretestonriskfreerates…

¨ OnJanuary1,2016,the10-yeartreasurybondrateintheUnitedStateswas2.27%,ahistoriclow.AssumethatyouwerevaluingacompanyinUSdollarsthen,butwerewaryabouttheriskfreeratebeingtoolow.Whichofthefollowingshouldyoudo?a. Replacethecurrent10-yearbondratewithamorereasonable

normalizedriskfreerate(theaverage10-yearbondrateoverthelast30yearshasbeenabout5-6%)

b. Usethecurrent10-yearbondrateasyourriskfreeratebutmakesurethatyourotherassumptions(aboutgrowthandinflation)areconsistentwiththeriskfreerate

c. Somethingelse…

Aswath Damodaran

41

42

Someperspectiveonriskfreerates

Aswath Damodaran

42

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%1954

1955

1956

1957

1958

1959

1960

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

Interestratefundamentals:T.Bondrates,Realgrowthandinflation

Inflationrate RealGDPgrowth Ten-yearT.Bondrate

43

NegativeInterestRates?

¨ In2016,therewereatleastthreecurrencies(SwissFranc,JapaneseYen,Euro)withnegativeinterestrates.Usingthefundamentals(inflationandrealgrowth)approach,howwouldyouexplainnegativeinterestrates?

¨ Hownegativecanratesget?(Isthereabound?)¨ Wouldyouusethesenegativeinterestratesasriskfreerates?¤ Ifno,whynotandwhatwouldyoudoinstead?¤ Ifyes,whatelsewouldyouhavetodoinyourvaluationtobeinternallyconsistent?

Aswath Damodaran

43

TheEquityRiskPremium

DiscountRates:II44

Aswath Damodaran

45

Theubiquitoushistoricalriskpremium

¨ Thehistoricalpremiumisthepremiumthatstockshavehistoricallyearnedoverrisklesssecurities.

¨ Whiletheusersofhistoricalriskpremiumsactasifitisafact(ratherthananestimate),itissensitiveto¤ Howfarbackyougoinhistory…¤ WhetheryouuseT.billratesorT.Bondrates¤ Whetheryouusegeometricorarithmeticaverages.

¨ Forinstance,lookingattheUS:

Aswath Damodaran

45

46

Theperilsoftrustingthepast…….

¨ Noisyestimates:Evenwithlongtimeperiodsofhistory,theriskpremiumthatyouderivewillhavesubstantialstandarderror.Forinstance,ifyougobackto1928(about80yearsofhistory)andyouassumeastandarddeviationof20%inannualstockreturns,youarriveatastandarderrorofgreaterthan2%:

StandardErrorinPremium=20%/√80=2.26%¨ SurvivorshipBias:UsinghistoricaldatafromtheU.S.equitymarketsoverthetwentiethcenturydoescreateasamplingbias.Afterall,theUSeconomyandequitymarketswereamongthemostsuccessfuloftheglobaleconomiesthatyoucouldhaveinvestedinearlyinthecentury.

Aswath Damodaran

46

47

RiskPremiumforaMatureMarket?Broadeningthesampleto1900-2015

Aswath Damodaran

47

Country GeometricERP ArithmeticERP StandardErrorAustralia 5.00% 6.60% 1.70%Austria 2.60% 21.50% 14.30%Belgium 2.40% 4.50% 2.00%Canada 3.30% 4.90% 1.70%Denmark 2.30% 3.80% 1.70%Finland 5.20% 8.80% 2.80%France 3.00% 5.40% 2.10%Germany 5.10% 9.10% 2.70%Ireland 2.80% 4.80% 1.80%Italy 3.10% 6.50% 2.70%Japan 5.10% 9.10% 3.00%Netherlands 3.30% 5.60% 2.10%New Zealand 4.00% 5.50% 1.70%Norway 2.30% 5.20% 2.60%South Africa 5.40% 7.20% 1.80%Spain 1.80% 3.80% 1.90%Sweden 3.10% 5.40% 2.00%Switzerland 2.10% 3.60% 1.60%U.K. 3.60% 5.00% 1.60%U.S. 4.30% 6.40% 1.90%Europe 3.20% 4.50% 1.50%World-ex U.S. 2.80% 3.90% 1.40%World 3.20% 4.40% 1.40%

48

Thesimplestwayofestimatinganadditionalcountryriskpremium:Thecountrydefaultspread

¨ Defaultspreadforcountry:Inthisapproach,thecountryequityriskpremiumissetequaltothedefaultspreadforthecountry,estimatedinoneofthreeways:¤ Thedefaultspreadonadollardenominatedbondissuedbythecountry.

(InJanuary2016,thatspreadwas4.83%fortheBrazilian$bond)¤ ThesovereignCDSspreadforthecountry.InJanuary2016,thetenyear

CDSspreadforBrazil,adjustedfortheUSCDS,was5.19%.¤ Thedefaultspreadbasedonthelocalcurrencyratingforthecountry.

Brazil’ssovereignlocalcurrencyratingisBaa3andthedefaultspreadforaBaa3ratedsovereignwasabout2.44%inJanuary2016.

¨ Addthedefaultspreadtoa“mature”marketpremium:ThisdefaultspreadisaddedontothematuremarketpremiumtoarriveatthetotalequityriskpremiumforBrazil,assumingamaturemarketpremiumof6.00%.¤ CountryRiskPremiumforBrazil=2.44%¤ TotalERPforBrazil=6.00%+2.44%=8.44%

Aswath Damodaran

48

Aswath Damodaran

49

AnequityvolatilitybasedapproachtoestimatingthecountrytotalERP

¨ Thisapproachdrawsonthestandarddeviationoftwoequitymarkets,theemergingmarketinquestionandabasemarket(usuallytheUS).Thetotalequityriskpremiumfortheemergingmarketisthenwrittenas:¤ Totalequityriskpremium=RiskPremiumUS*sCountry Equity/sUS Equity

¨ ThecountryequityriskpremiumisbaseduponthevolatilityofthemarketinquestionrelativetoU.Smarket.¤ AssumethattheequityriskpremiumfortheUSis6.00%.¤ AssumethatthestandarddeviationintheBovespa (Brazilianequity)is

30%andthatthestandarddeviationfortheS&P500(USequity)is18%.

¤ TotalEquityRiskPremiumforBrazil=6.00%(30%/18%)=10.0%¤ CountryequityriskpremiumforBrazil=10.00%- 6.00%=4.00%

Aswath Damodaran

49

50

Ameldedapproachtoestimatingtheadditionalcountryriskpremium

¨ Countryratingsmeasuredefaultrisk.Whiledefaultriskpremiumsandequityriskpremiumsarehighlycorrelated,onewouldexpectequityspreadstobehigherthandebtspreads.

¨ Anotheristomultiplythebonddefaultspreadbytherelativevolatilityofstockandbondpricesinthatmarket.UsingthisapproachforBrazilinJanuary2016,youwouldget:¤ CountryEquityriskpremium=Defaultspreadoncountrybond*sCountry

Equity /sCountry Bondn 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%

Aswath Damodaran

50

51

ATemplateforCountryRisk

Aswath Damodaran

51

Black #: Total ERPRed #: Country risk premiumAVG: GDP weighted average

ERP

: Jan

201

6

53

FromCountryEquityRiskPremiumstoCorporateEquityRiskpremiums

¨ Approach1:Assumethateverycompanyinthecountryisequallyexposedtocountryrisk.Inthiscase,¤ E(Return)=RiskfreeRate+CRP+Beta(MatureERP)¤ Implicitly,thisiswhatyouareassumingwhenyouusethelocalGovernment’s

dollarborrowingrateasyourriskfreerate.¨ Approach2:Assumethatacompany’sexposuretocountryriskissimilar

toitsexposuretoothermarketrisk.¤ E(Return)=RiskfreeRate+Beta(MatureERP+CRP)

¨ Approach3:Treatcountryriskasaseparateriskfactorandallowfirmstohavedifferentexposurestocountryrisk(perhapsbasedupontheproportionoftheirrevenuescomefromnon-domesticsales)¤ E(Return)=RiskfreeRate+b (MatureERP)+l (CRP)

MatureERP=MaturemarketEquityRiskPremiumCRP=Additionalcountryriskpremium

Aswath Damodaran

53

54

Approaches1&2:Estimatingcountryriskpremiumexposure

¨ LocationbasedCRP:Thestandardapproachinvaluationistoattachacountryriskpremiumtoacompanybaseduponitscountryofincorporation.Thus,ifyouareanIndiancompany,youareassumedtobeexposedtotheIndiancountryriskpremium.Adevelopedmarketcompanyisassumedtobeunexposedtoemergingmarketrisk.

¨ Operation-basedCRP:Thereisamorereasonablemodifiedversion.Thecountryriskpremiumforacompanycanbecomputedasaweightedaverageofthecountryriskpremiumsofthecountriesthatitdoesbusinessin,withtheweightsbaseduponrevenuesoroperatingincome.Ifacompanyisexposedtoriskindozensofcountries,youcantakeaweightedaverageoftheriskpremiumsbyregion.

Aswath Damodaran

54

55

OperationbasedCRP:SingleversusMultipleEmergingMarkets

¨ Singleemergingmarket:Embraer,in2004,reportedthatitderived3%ofitsrevenuesinBrazilandthebalancefrommaturemarkets.ThematuremarketERPin2004was5%andBrazil’sCRPwas7.89%.

¨ Multipleemergingmarkets:Ambev,theBrazilian-basedbeveragecompany,reportedrevenuesfromthefollowingcountriesduring2011.

Aswath Damodaran

55

56

Extendingtoamultinational:RegionalbreakdownCocaCola’srevenuebreakdownandERPin2012

Things to watch out for1. Aggregation across regions. For instance, the Pacific region often includes Australia & NZ with Asia2. Obscure aggregations including Eurasia and Oceania

56

57

Twoproblemswiththeseapproaches..

¨ Focusjustonrevenues:Totheextentthatrevenuesaretheonlyvariablethatyouconsider,whenweightingriskexposureacrossmarkets,youmaybemissingotherexposurestocountryrisk.Forinstance,anemergingmarketcompanythatgetsthebulkofitsrevenuesoutsidethecountry(inadevelopedmarket)maystillhaveallofitsproductionfacilitiesintheemergingmarket.

¨ Exposurenotadjustedorbaseduponbeta:Totheextentthatthecountryriskpremiumismultipliedbyabeta,weareassumingthatbetainadditiontomeasuringexposuretoallothermacroeconomicriskalsomeasuresexposuretocountryrisk.

Aswath Damodaran

57

58

AProduction-basedERP:RoyalDutchShellin2015

Aswath Damodaran

58

Country Oil&GasProduction %ofTotal ERPDenmark 17396 3.83% 6.20%Italy 11179 2.46% 9.14%Norway 14337 3.16% 6.20%UK 20762 4.57% 6.81%RestofEurope 874 0.19% 7.40%Brunei 823 0.18% 9.04%Iraq 20009 4.40% 11.37%Malaysia 22980 5.06% 8.05%Oman 78404 17.26% 7.29%Russia 22016 4.85% 10.06%RestofAsia&ME 24480 5.39% 7.74%Oceania 7858 1.73% 6.20%Gabon 12472 2.75% 11.76%Nigeria 67832 14.93% 11.76%RestofAfrica 6159 1.36% 12.17%USA 104263 22.95% 6.20%Canada 8599 1.89% 6.20%Brazil 13307 2.93% 9.60%RestofLatinAmerica 576 0.13% 10.78%RoyalDutchShell 454326 100.00% 8.26%

59

Approach3:Estimatealambdaforcountryrisk

¨ Countryriskexposureisaffectedbywhereyougetyourrevenuesandwhereyourproductionhappens,butthereareahostofothervariablesthatalsoaffectthisexposure,including:¤ Useofriskmanagementproducts:Companiescanusebothoptions/futures

marketsandinsurancetohedgesomeorasignificantportionofcountryrisk.¤ Government“national”interests:Therearesectorsthatareviewedasvitalto

thenationalinterests,andgovernmentsoftenplayakeyroleinthesecompanies,eitherofficiallyorunofficially.Thesesectorsaremoreexposedtocountryrisk.

¨ Itisconceivablethatthereisarichermeasureofcountryriskthatincorporatesallofthevariablesthatdrivecountryriskinonemeasure.ThatwaymyrationalewhenIdevised“lambda”asmymeasureofcountryriskexposure.

Aswath Damodaran

59

60

ARevenue-basedLambda

¨ Thefactor“l” measurestherelativeexposureofafirmtocountryrisk.Onesimplisticsolutionwouldbetodothefollowing:l =%ofrevenuesdomesticallyfirm/%ofrevenuesdomesticallyaverage firm

¨ Considertwofirms– TataMotorsandTataConsultingServices,bothIndiancompanies.In2008-09,TataMotorsgotabout91.37%ofitsrevenuesinIndiaandTCSgot7.62%.TheaverageIndianfirmgetsabout80%ofitsrevenuesinIndia:l TataMotors=91%/80%=1.14l TCS=7.62%/80%=0.09

¨ Therearetwoimplications¤ Acompany’sriskexposureisdeterminedbywhereitdoesbusinessand

notbywhereitisincorporated.¤ Firmsmightbeabletoactivelymanagetheircountryriskexposures

61

APrice/ReturnbasedLambda

Embraer versus C Bond: 2000-2003

Return on C-Bond

20100-10-20-30

Ret

urn

on E

mbr

aer

40

20

0

-20

-40

-60

Embratel versus C Bond: 2000-2003

Return on C-Bond

20100-10-20-30

Ret

urn

on E

mb r

a tel

100

80

60

40

20

0

-20

-40

-60

-80

ReturnEmbraer = 0.0195 + 0.2681 ReturnC BondReturnEmbratel = -0.0308 + 2.0030 ReturnC Bond

Aswath Damodaran

61

62

EstimatingaUSDollarCostofEquityforEmbraer- September2004

¨ AssumethatthebetaforEmbraeris1.07,andthattheUS$riskfreerateusedis4%.AlsoassumethattheriskpremiumfortheUSis5%andthecountryriskpremiumforBrazilis7.89%.Finally,assumethatEmbraergets3%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

63

ValuingEmergingMarketCompanieswithsignificantexposureindevelopedmarkets

¨ Theconventionalpracticeininvestmentbankingistoaddthecountryequityriskpremiumontothecostofequityforeveryemergingmarketcompany,notwithstandingitsexposuretoemergingmarketrisk.Thus,in2004,Embraerwouldhavebeenvaluedwithacostofequityof17-18%eventhoughitgetsonly3%ofitsrevenuesinBrazil.Asaninvestor,whichofthefollowingconsequencesdoyouseefromthisapproach?

a. Emergingmarketcompanieswithsubstantialexposureindevelopedmarketswillbesignificantlyovervaluedbyequityresearchanalysts.

b. Emergingmarketcompanieswithsubstantialexposureindevelopedmarketswillbesignificantlyundervaluedbyequityresearchanalysts.Canyouconstructaninvestmentstrategytotakeadvantageofthemisvaluation?Whatwouldneedtohappenforyoutomakemoneyofthisstrategy?

Aswath Damodaran

63

64

ImpliedEquityPremiums

¨ Let’sstartwithageneralproposition.Ifyouknowthepricepaidforanassetandhaveestimatesoftheexpectedcashflowsontheasset,youcanestimatetheIRRofthesecashflows.Ifyoupaidtheprice,thisiswhatyouhavepricedtheassettoearn(asanexpectedreturn).

¨ Ifyouassumethatstocksarecorrectlypricedintheaggregateandyoucanestimatetheexpectedcashflowsfrombuyingstocks,youcanestimatetheexpectedrateofreturnonstocksbyfindingthatdiscountratethatmakesthepresentvalueequaltothepricepaid.Subtractingouttheriskfreerateshouldyieldanimpliedequityriskpremium.

¨ Thisimpliedequitypremiumisaforwardlookingnumberandcanbeupdatedasoftenasyouwant(everyminuteofeveryday,ifyouaresoinclined).

Aswath Damodaran

64

65

ImpliedEquityPremiums:January2008

¨ Wecanusetheinformationinstockpricestobackouthowriskaversethemarketisandhowmuchofariskpremiumitisdemanding.

¨ Ifyoupaythecurrentleveloftheindex,youcanexpecttomakeareturnof8.39%onstocks(whichisobtainedbysolvingforrinthefollowingequation)

¨ ImpliedEquityriskpremium=Expectedreturnonstocks- Treasurybondrate=8.39%- 4.02%=4.37%

€

1468.36 =61.98(1+ r)

+65.08(1+ r)2

+68.33(1+ r)3

+71.75(1+ r)4

+75.34(1+ r)5

+75.35(1.0402)

(r − .0402)(1+ r)5

January 1, 2008S&P 500 is at 1468.364.02% of 1468.36 = 59.03

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

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).

61.98 65.08 68.33 71.75 75.34

Aswath Damodaran

65

66

Ayearthatmadeadifference..TheimpliedpremiuminJanuary2009

Year Market value of index Dividends Buybacks Cash to equity Dividend yield Buyback yield Total yield2001 1148.09 15.74 14.34 30.08 1.37% 1.25% 2.62%2002 879.82 15.96 13.87 29.83 1.81% 1.58% 3.39%2003 1111.91 17.88 13.70 31.58 1.61% 1.23% 2.84%2004 1211.92 19.01 21.59 40.60 1.57% 1.78% 3.35%2005 1248.29 22.34 38.82 61.17 1.79% 3.11% 4.90%2006 1418.30 25.04 48.12 73.16 1.77% 3.39% 5.16%2007 1468.36 28.14 67.22 95.36 1.92% 4.58% 6.49%2008 903.25 28.47 40.25 68.72 3.15% 4.61% 7.77%

Normalized 903.25 28.47 24.11 52.584 3.15% 2.67% 5.82%

January 1, 2009S&P 500 is at 903.25Adjusted Dividends & Buybacks for 2008 = 52.58

In 2008, the actual cash returned to stockholders was 68.72. However, there was a 41% dropoff in buybacks in Q4. We reduced the total buybacks for the year by that amount.

Analysts expect earnings to grow 4% a year for the next 5 years. We will assume that dividends & buybacks will keep pace..Last year’s cashflow (52.58) growing at 4% a year

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).

54.69 56.87 59.15 61.52 63.98

Expected Return on Stocks (1/1/09) = 8.64%Riskfree rate = 2.21%Equity Risk Premium = 6.43%

903.25 = 54.69(1+ r)

+56.87(1+ r)2 +

59.15(1+ r)3 +

61.52(1+ r)4 +

63.98(1+ r)5 +

63.98(1.0221)(r −.0221)(1+ r)5

Aswath Damodaran

66

67

TheAnatomyofaCrisis:ImpliedERPfromSeptember12,2008toJanuary1,2009

Aswath Damodaran

67

68

AnUpdatedEquityRiskPremium:January2016

Aswath Damodaran

68

Base year cash flow (last 12 mths)Dividends (TTM): 42.66+ Buybacks (TTM): 63.43

= Cash to investors (TTM): 106.09

Expected growth in next 5 yearsTop down analyst estimate of earnings

growth for S&P 500: 5.55%

Risk free rate = T.Bond rate on 1/1/16= 2.27%

r = Implied Expected Return on Stocks = 8.39%

S&P 500 on 1/1/16= 2043.94

Minus

Implied Equity Risk Premium (1/1/16) = 8.39% - 2.27% = 6.12%

Equals

Earnings and Cash flows grow @2.27% (set equal to risk free rate) a year forever.

Payout ratio assumed to stay stable. 106.09 growing @ 5.55% a year

Last12mths 1 2 3 4 5 TerminalYearDividends+Buybacks 106.09 111.99$ 118.21$ 124.77$ 131.70$ 139.02$ 142.17

2043.94 = 111.99(1 + ,) +118.21(1 + ,)/ +

124.77(1 + ,)1 +

131.70(1 + ,)2 +

139.02(1 + ,)3 +

142.17(, − .0227)(1 + ,)3

You have to solve for the discount rate (r). I

used the solver or Goal seek function in Excel

69

ImpliedPremiumsintheUS:1960-2015

Aswath Damodaran

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

19601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982198319841985198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012201320142015

Impl

ied

Prem

ium

Year

Implied Premium for US Equity Market: 1960-2015

70

ABuybackAdjustedVersionoftheUSERP

Aswath Damodaran

70

71

ImpliedPremiumversusRiskFreeRate

Aswath Damodaran

71

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%19

6119

6219

6319

6419

6519

6619

6719

6819

6919

7019

7119

7219

7319

7419

7519

7619

7719

7819

7919

8019

8119

8219

8319

8419

8519

8619

8719

8819

8919

9019

9119

9219

9319

9419

9519

9619

9719

9819

9920

0020

0120

0220

0320

0420

0520

0620

0720

0820

0920

1020

1120

1220

1320

1420

15

Implied ERP and Risk free Rates

Implied Premium (FCFE)

T. Bond Rate

Expected Return on Stocks = T.Bond Rate + Equity Risk Premium

Since 2008, the expected return on stocks has stagnated at about 8%, but the risk free rate has dropped dramatically.

72

EquityRiskPremiumsandBondDefaultSpreads

Aswath Damodaran

72

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

ERP

/ Baa

Spr

ead

Pre

miu

m (

Sp

rea

d)

Equity Risk Premiums and Bond Default Spreads

ERP/Baa Spread Baa - T.Bond Rate ERP

73

EquityRiskPremiumsandCapRates(RealEstate)

Aswath Damodaran

73

-8.00%

-6.00%

-4.00%

-2.00%

0.00%

2.00%

4.00%

6.00%

8.00%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

Figure18:EquityRiskPremiums,CapRatesandBondSpreads

ERP

BaaSpread

CapRatepremium

74

Whyimpliedpremiumsmatter?

¨ Inmanyinvestmentbanks,itiscommonpractice(especiallyincorporatefinancedepartments)tousehistoricalriskpremiums(andarithmeticaveragesatthat)asriskpremiumstocomputecostofequity.Ifallanalystsinthedepartmentusedthearithmeticaveragepremium(forstocksoverT.Bills)for1928-2015of7.92%tovaluestocksinJanuary2014,giventheimpliedpremiumof6.12%,whataretheylikelytofind?

a. Thevaluestheyobtainwillbetoolow(moststockswilllookovervalued)

b. Thevaluestheyobtainwillbetoohigh(moststockswilllookundervalued)

c. Thereshouldbenosystematicbiasaslongastheyusethesamepremiumtovalueallstocks.

Aswath Damodaran

74

75

Whichequityriskpremiumshouldyouuse?

Ifyouassume this Premium touse

Premiumsrevertbacktohistoricalnormsandyourtimeperiodyieldsthesenorms

Historical riskpremium

Marketiscorrect intheaggregateorthatyourvaluationshouldbemarketneutral

Current impliedequityriskpremium

Marker makesmistakesevenintheaggregatebutiscorrectovertime

Averageimpliedequity riskpremiumovertime.

Aswath Damodaran

75

Predictor Correlation with implied

premium next year

Correlation with actual

return- next 5 years

Correlation with actual return

– next 10 years

Current implied premium 0.750 0.475 0.541

Average implied premium: Last 5

years

0.703 0.541 0.747

Historical Premium -0.476 -0.442 -0.469

Default Spread based premium 0.035 0.234 0.225

76

AnERPfortheSensex

¨ Inputsforthecomputation¤ Sensexon9/5/07=15446¤ Dividendyieldonindex=3.05%¤ Expectedgrowthrate- next5years=14%¤ Growthratebeyondyear5=6.76%(setequaltoriskfree rate)

¨ Solvingfortheexpectedreturn:

¨ Expectedreturnonstocks=11.18%¨ ImpliedequityriskpremiumforIndia=11.18%- 6.76%=

4.42%€

15446 =537.06(1+ r)

+612.25(1+ r)2

+697.86(1+ r)3

+795.67(1+ r)4

+907.07(1+ r)5

+907.07(1.0676)(r − .0676)(1+ r)5

Aswath Damodaran

76

77

ChangingCountryRisk:BrazilCRP&TotalERPfrom2000to2015

Aswath Damodaran

77

78

TheevolutionofEmergingMarketRisk

Aswath Damodaran

78

StartofyearPBV

DevelopedPBV

EmergingROE

DevelopedROE

EmergingUST.Bond

rate

GrowthRate

Developed

GrowthRate

Emerging

CostofEquity

(Developed)

CostofEquity

(Emerging)Differential

ERP2004 2.00 1.19 10.81% 11.65% 4.25% 3.75% 5.25% 7.28% 10.63% 3.35%2005 2.09 1.27 11.12% 11.93% 4.22% 3.72% 5.22% 7.26% 10.50% 3.24%2006 2.03 1.44 11.32% 12.18% 4.39% 3.89% 5.39% 7.55% 10.11% 2.56%2007 1.67 1.67 10.87% 12.88% 4.70% 4.20% 5.70% 8.19% 10.00% 1.81%2008 0.87 0.83 9.42% 11.12% 4.02% 3.52% 5.02% 10.30% 12.37% 2.07%2009 1.20 1.34 8.48% 11.02% 2.21% 1.71% 3.21% 7.35% 9.04% 1.69%2010 1.39 1.43 9.14% 11.22% 3.84% 3.34% 4.84% 7.51% 9.30% 1.79%2011 1.12 1.08 9.21% 10.04% 3.29% 2.79% 4.29% 8.52% 9.61% 1.09%2012 1.17 1.18 9.10% 9.33% 1.88% 1.38% 2.88% 7.98% 8.35% 0.37%2013 1.56 1.63 8.67% 10.48% 1.76% 1.26% 2.76% 6.02% 7.50% 1.48%2014 1.95 1.50 9.27% 9.64% 3.04% 2.54% 4.04% 6.00% 7.77% 1.77%2015 1.88 1.56 9.69% 9.75% 2.17% 1.67% 3.17% 5.94% 7.39% 1.45%2016 1.89 1.59 9.24% 10.16% 2.27% 1.77% 3.27% 5.72% 7.60% 1.88%

RelativeRiskMeasures

DiscountRates:III79

Aswath Damodaran

80

TheCAPMBeta:TheMostUsed(andMisused)RiskMeasure

¨ Thestandardprocedureforestimatingbetasistoregressstockreturns(Rj)againstmarketreturns(Rm)-Rj =a+bRmwhereaistheinterceptandbistheslopeoftheregression.

¨ Theslopeoftheregressioncorrespondstothebetaofthestock,andmeasurestheriskinessofthestock.

¨ Thisbetahasthreeproblems:• Ithashighstandarderror• Itreflectsthefirm’sbusinessmixovertheperiodofthe

regression,notthecurrentmix• Itreflectsthefirm’saveragefinancialleverageovertheperiod

ratherthanthecurrentleverage.

Aswath Damodaran

80

81

Unreliable,whenitlooksbad..

Aswath Damodaran

81

82

Orwhenitlooksgood..

Aswath Damodaran

82

Onesliceofhistory..83

Aswath Damodaran

During this time period, Valeant was a stock under siege, without a CEO, under legal pressure & lacking financials.

Andsubjecttogameplaying84

Aswath Damodaran

85

MeasuringRelativeRisk:Youdon’tlikebetasormodernportfoliotheory?Noproblem.

Aswath Damodaran

85

86

Don’tlikethediversifiedinvestorfocus,butokaywithprice-basedmeasures

1. RelativeStandardDeviation• RelativeVolatility=Std devofStock/AverageStd devacrossallstocks• Capturesallrisk,ratherthanjustmarketrisk

2. ProxyModels• Lookathistoricalreturnsonallstocksandlookforvariablesthat

explaindifferencesinreturns.• Youare,ineffect,runningmultipleregressionswithreturnson

individualstocksasthedependentvariableandfundamentalsaboutthesestocksasindependentvariables.

• Thisapproachstartedwithmarketcap(thesmallcapeffect)andoverthelasttwodecadeshasaddedothervariables(momentum,liquidityetc.)

3. CAPMPlusModels• StartwiththetraditionalCAPM(Rf +Beta(ERP))andthenaddother

premiumsforproxies.

Aswath Damodaran

86

87

Don’tliketheprice-basedapproach..

1. Accountingriskmeasures:Totheextentthatyoudon’ttrustmarket-pricedbasedmeasuresofrisk,youcouldcomputerelativeriskmeasuresbasedon• Accountingearningsvolatility:Computeanaccountingbetaorrelative

volatility• Balancesheetratios:Youcouldcomputeariskscorebaseduponaccounting

ratioslikedebtratiosorcashholdings(akintodefaultriskscoresliketheZscore)

2. QualitativeRiskModels:Inthesemodels,riskassessmentsarebasedatleastpartiallyonqualitativefactors(qualityofmanagement).

3. Debtbasedmeasures:Youcanestimateacostofequity,baseduponanobservablecostsofdebtforthecompany.• Costofequity=Costofdebt*Scalingfactor• Thescalingfactorcanbecomputedfromimpliedvolatilities.

Aswath Damodaran

87

88

DeterminantsofBetas&RelativeRisk

Beta of Firm (Unlevered Beta)

Beta of Equity (Levered 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.

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

Implications1. Cyclical companies should have higher betas than non-cyclical 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.

Implications1. 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.

ImplciationsHighly levered firms should have highe betas than firms with less debt.Equity Beta (Levered beta) = Unlev Beta (1 + (1- t) (Debt/Equity Ratio))

Aswath Damodaran

88

89

Inaperfectworld…wewouldestimatethebetaofafirmbydoingthefollowing

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 firmLevered Beta = Unlevered Beta ( 1 + (1- tax rate) (Debt/Equity))

Aswath Damodaran

89

90

Adjustingforoperatingleverage…

¨ Withinanybusiness,firmswithlowerfixedcosts(asapercentageoftotalcosts)shouldhavelowerunleveredbetas.Ifyoucancomputefixedandvariablecostsforeachfirminasector,youcanbreakdowntheunleveredbetaintobusinessandoperatingleveragecomponents.¤ Unleveredbeta=Purebusinessbeta*(1+(Fixedcosts/Variablecosts))

¨ Thebiggestproblemwithdoingthisisinformational.Itisdifficulttogetinformationonfixedandvariablecostsforindividualfirms.

¨ Inpractice,wetendtoassumethattheoperatingleverageoffirmswithinabusinessaresimilarandusethesameunleveredbetaforeveryfirm.

Aswath Damodaran

90

91

Adjustingforfinancialleverage…

¨ Conventionalapproach:Ifweassumethatdebtcarriesnomarketrisk(hasabetaofzero),thebetaofequityalonecanbewrittenasafunctionoftheunleveredbetaandthedebt-equityratiobL =bu (1+((1-t)D/E))Insomeversions,thetaxeffectisignoredandthereisno(1-t)intheequation.

¨ DebtAdjustedApproach:Ifbetacarriesmarketriskandyoucanestimatethebetaofdebt,youcanestimatetheleveredbetaasfollows:bL =bu (1+((1-t)D/E))-bdebt (1-t)(D/E)Whilethelatterismorerealistic,estimatingbetasfordebtcanbedifficulttodo.

Aswath Damodaran

91

92

Bottom-upBetas

Step 1: Find the business or businesses that your firm operates in.

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))

If you can, adjust this beta for differencesbetween your firm and the comparablefirms on operating leverage and product characteristics.

Step 3: Estimate how much value your firm derives from each of the different businesses it is in.

While revenues or operating income are often used as weights, it is better to try to estimate the value of each business.

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))

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.

Possible Refinements

Aswath Damodaran

92

93

Whybottom-upbetas?

¨ Thestandarderrorinabottom-upbetawillbesignificantlylowerthanthestandarderrorinasingleregressionbeta.Roughlyspeaking,thestandarderrorofabottom-upbetaestimatecanbewrittenasfollows:

Stderrorofbottom-upbeta=

¨ Thebottom-upbetacanbeadjustedtoreflectchangesinthefirm’sbusinessmixandfinancialleverage.Regressionbetasreflectthepast.

¨ Youcanestimatebottom-upbetasevenwhenyoudonothavehistoricalstockprices.Thisisthecasewithinitialpublicofferings,privatebusinessesordivisionsofcompanies.

€

Average Std Error across BetasNumber of firms in sample

Aswath Damodaran

93

94

EstimatingBottomUpBetas&CostsofEquity:Vale

Aswath Damodaran

Business' Sample'Sample'size'

Unlevered'beta'of'business' Revenues'

Peer'Group'EV/Sales'

Value'of'Business'

Proportion'of'Vale'

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%'

Logistics'Global'transportation'firms' 223' 0.75' $1,644' 1.14' $1,874' 1.76%'

Vale'Operations' '' '' 0.8440' $47,151' '' $106,543' 100.00%'

95

Embraer’sBottom-upBeta

Business UnleveredBeta D/ERatio LeveredbetaAerospace 0.95 18.95% 1.07

¨ LeveredBeta=UnleveredBeta(1+(1- taxrate)(D/ERatio)=0.95(1+(1-.34)(.1895))=1.07

¨ CananunleveredbetaestimatedusingU.S.andEuropeanaerospacecompaniesbeusedtoestimatethebetaforaBrazilianaerospacecompany?

a. Yesb. No

Whatconcernswouldyouhaveinmakingthisassumption?

Aswath Damodaran

95

96

GrossDebtversusNetDebtApproaches

¨ AnalystsinEuropeandLatinAmericaoftentakethedifferencebetweendebtandcash(netdebt)whencomputingdebtratiosandarriveatverydifferentvalues.

¨ ForEmbraer,usingthegrossdebtratio¤ GrossD/ERatioforEmbraer=1953/11,042=18.95%¤ LeveredBetausingGrossDebtratio=1.07

¨ Usingthenetdebtratio,weget¤ NetDebtRatioforEmbraer=(Debt- Cash)/MarketvalueofEquity

=(1953-2320)/11,042=-3.32%¤ LeveredBetausingNetDebtRatio=0.95(1+(1-.34)(-.0332))=0.93

¨ ThecostofEquityusingnetdebtleveredbetaforEmbraerwillbemuchlowerthanwiththegrossdebtapproach.ThecostofcapitalforEmbraerwillevenoutsincethedebtratiousedinthecostofcapitalequationwillnowbeanetdebtratioratherthanagrossdebtratio.

Aswath Damodaran

96

97

TheCostofEquity:ARecap

Cost of Equity = Riskfree Rate + Beta * (Risk Premium)

Has to be in the samecurrency as cash flows, and defined in same terms(real or nominal) as thecash flows

Preferably, a bottom-up beta,based upon other firms in thebusiness, and firmʼs own financialleverage

Historical Premium1. Mature Equity Market Premium:Average premium earned bystocks over T.Bonds in U.S.2. Country risk premium =Country Default Spread* ( σEquity/σCountry bond)

Implied PremiumBased on how equitymarket is priced todayand a simple valuationmodel

or

Aswath Damodaran

97

Moppingup

DiscountRates:IV98

Aswath Damodaran

99

EstimatingtheCostofDebt

¨ Thecostofdebtistherateatwhichyoucanborrowatcurrently,Itwillreflectnotonlyyourdefaultriskbutalsothelevelofinterestratesinthemarket.

¨ Thetwomostwidelyusedapproachestoestimatingcostofdebtare:¤ Lookinguptheyieldtomaturityonastraightbondoutstandingfrom

thefirm.Thelimitationofthisapproachisthatveryfewfirmshavelongtermstraightbondsthatareliquidandwidelytraded

¤ Lookinguptheratingforthefirmandestimatingadefaultspreadbasedupontherating.Whilethisapproachismorerobust,differentbondsfromthesamefirmcanhavedifferentratings.Youhavetouseamedianratingforthefirm

¨ Whenintrouble(eitherbecauseyouhavenoratingsormultipleratingsforafirm),estimateasyntheticratingforyourfirmandthecostofdebtbaseduponthatrating.

Aswath Damodaran

99

100

EstimatingSyntheticRatings

¨ Theratingforafirmcanbeestimatedusingthefinancialcharacteristicsofthefirm.Initssimplestform,theratingcanbeestimatedfromtheinterestcoverageratioInterestCoverageRatio=EBIT/InterestExpenses

¨ ForEmbraer’sinterestcoverageratio,weusedtheinterestexpensesfrom2003andtheaverageEBITfrom2001to2003.(Theaircraftbusinesswasbadlyaffectedby9/11anditsaftermath.In2002and2003,Embraerreportedsignificantdropsinoperatingincome)InterestCoverageRatio=462.1/129.70=3.56

Aswath Damodaran

100

101

InterestCoverageRatios,RatingsandDefaultSpreads:2003&2004

IfInterestCoverageRatiois EstimatedBondRating DefaultSpread(2003) DefaultSpread(2004)>8.50 (>12.50) AAA 0.75% 0.35%6.50- 8.50 (9.5-12.5) AA 1.00% 0.50%5.50- 6.50 (7.5-9.5) A+ 1.50% 0.70%4.25- 5.50 (6-7.5) A 1.80% 0.85%3.00- 4.25 (4.5-6) A– 2.00% 1.00%2.50- 3.00 (4-4.5) BBB 2.25% 1.50%2.25- 2.50 (3.5-4) BB+ 2.75% 2.00%2.00- 2.25 ((3-3.5) BB 3.50% 2.50%1.75- 2.00 (2.5-3) B+ 4.75% 3.25%1.50- 1.75 (2-2.5) B 6.50% 4.00%1.25- 1.50 (1.5-2) B– 8.00% 6.00%0.80- 1.25 (1.25-1.5) CCC 10.00% 8.00%0.65- 0.80 (0.8-1.25) CC 11.50% 10.00%0.20- 0.65 (0.5-0.8) C 12.70% 12.00%<0.20 (<0.5) D 15.00% 20.00%

¨ Thefirstnumberunderinterestcoverageratiosisforlargermarketcapcompaniesandthesecondinbracketsisforsmallermarketcapcompanies.ForEmbraer,Iusedtheinterestcoverageratiotableforsmaller/riskierfirms(thenumbersinbrackets)whichyieldsalowerratingforthesameinterestcoverageratio.

Aswath Damodaran

101

102

CostofDebtcomputations

¨ Companiesincountrieswithlowbondratingsandhighdefaultriskmightbeartheburdenofcountrydefaultrisk,especiallyiftheyaresmallerorhavealloftheirrevenueswithinthecountry.

¨ Largercompaniesthatderiveasignificantportionoftheirrevenuesinglobalmarketsmaybelessexposedtocountrydefaultrisk.Inotherwords,theymaybeabletoborrowataratelowerthanthegovernment.

¨ ThesyntheticratingforEmbraerisA-.Usingthe2004defaultspreadof1.00%,weestimateacostofdebtof9.29%(usingariskfree rateof4.29%andaddingintwothirdsofthecountrydefaultspreadof6.01%):

Costofdebt=Riskfree rate+2/3(Brazilcountrydefaultspread)+Companydefaultspread=4.29%+4.00%+1.00%=9.29%

Aswath Damodaran

102

103

SyntheticRatings:SomeCaveats

¨ Therelationshipbetweeninterestcoverageratiosandratings,developedusingUScompanies,tendstotravelwell,aslongasweareanalyzinglargemanufacturingfirmsinmarketswithinterestratesclosetotheUSinterestrate

¨ TheyaremoreproblematicwhenlookingatsmallercompaniesinmarketswithhigherinterestratesthantheUS.Onewaytoadjustforthisdifferenceismodifytheinterestcoverageratiotabletoreflectinterestratedifferences(Forinstances,ifinterestratesinanemergingmarketaretwiceashighasratesintheUS,halvetheinterestcoverageratio.

Aswath Damodaran

103

104

DefaultSpreads:Theeffectofthecrisisof2008..Andtheaftermath

Default spread over treasury

Rating 1-Jan-08 12-Sep-08 12-Nov-08 1-Jan-09 1-Jan-10 1-Jan-11Aaa/AAA 0.99% 1.40% 2.15% 2.00% 0.50% 0.55%Aa1/AA+ 1.15% 1.45% 2.30% 2.25% 0.55% 0.60%Aa2/AA 1.25% 1.50% 2.55% 2.50% 0.65% 0.65%Aa3/AA- 1.30% 1.65% 2.80% 2.75% 0.70% 0.75%A1/A+ 1.35% 1.85% 3.25% 3.25% 0.85% 0.85%A2/A 1.42% 1.95% 3.50% 3.50% 0.90% 0.90%A3/A- 1.48% 2.15% 3.75% 3.75% 1.05% 1.00%

Baa1/BBB+ 1.73% 2.65% 4.50% 5.25% 1.65% 1.40%Baa2/BBB 2.02% 2.90% 5.00% 5.75% 1.80% 1.60%

Baa3/BBB- 2.60% 3.20% 5.75% 7.25% 2.25% 2.05%Ba1/BB+ 3.20% 4.45% 7.00% 9.50% 3.50% 2.90%Ba2/BB 3.65% 5.15% 8.00% 10.50% 3.85% 3.25%Ba3/BB- 4.00% 5.30% 9.00% 11.00% 4.00% 3.50%B1/B+ 4.55% 5.85% 9.50% 11.50% 4.25% 3.75%B2/B 5.65% 6.10% 10.50% 12.50% 5.25% 5.00%B3/B- 6.45% 9.40% 13.50% 15.50% 5.50% 6.00%

Caa/CCC+ 7.15% 9.80% 14.00% 16.50% 7.75% 7.75%ERP 4.37% 4.52% 6.30% 6.43% 4.36% 5.20%

104

105

UpdatedDefaultSpreads- January2016

Aswath Damodaran

105

0.75% 1.00% 1.10% 1.25%1.75%

2.25%

3.25%

4.25%

5.50%

6.50%

7.50%

9.00%

12.00%

16.00%

20.00%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

Aaa/AAA Aa2/AA A1/A+ A2/A A3/A- Baa2/BBB Ba1/BB+ Ba2/BB B1/B+ B2/B B3/B- Caa/CCC Ca2/CC C2/C D2/D

DefaultSpreadsfor10-yearCorporateBonds:January2015vsJanuary2016

Spread:2016 Spread:2015

106

SubsidizedDebt:Whatshouldwedo?

¨ AssumethattheBraziliangovernmentlendsmoneytoEmbraeratasubsidizedinterestrate(say6%indollarterms).IncomputingthecostofcapitaltovalueEmbraer,shouldbeweusethecostofdebtbasedupondefaultriskorthesubsidizedcostofdebt?

a. Thesubsidizedcostofdebt(6%).Thatiswhatthecompanyispaying.

b. Thefaircostofdebt(9.25%).Thatiswhatthecompanyshouldrequireitsprojectstocover.

c. Anumberinthemiddle.

Aswath Damodaran

106

107

WeightsfortheCostofCapitalComputation

¨ Incomputingthecostofcapitalforapubliclytradedfirm,thegeneralruleforcomputingweightsfordebtandequityisthatyouusemarketvalueweights(andnotbookvalueweights).Why?a. Becausethemarketisusuallyrightb. Becausemarketvaluesareeasytoobtainc. Becausebookvaluesofdebtandequityaremeaninglessd. Noneoftheabove

Aswath Damodaran

107

108

EstimatingCostofCapital:Embraerin2004

¨ Equity¤ CostofEquity=4.29%+1.07(4%)+0.27(7.89%)=10.70%¤ MarketValueofEquity=11,042millionBR($3,781million)

¨ Debt¤ Costofdebt=4.29%+4.00%+1.00%=9.29%¤ MarketValueofDebt=2,083millionBR($713million)

¨ CostofCapitalCostofCapital=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

109

Ifyouhadtodoit….ConvertingaDollarCostofCapitaltoaNominalRealCostofCapital

¨ Approach1:UseaBRriskfree rateinallofthecalculationsabove.Forinstance,iftheBRriskfree ratewas12%,thecostofcapitalwouldbecomputedasfollows:¤ 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%

Costofcapital=

=1.0997(1.08/1.02)-1=0.1644or16.44%

€

(1+ Cost of Capital$) 1+ InflationBR1+ Inflation$

"

# $

%

& '

Aswath Damodaran

109

110

DealingwithHybridsandPreferredStock

¨ Whendealingwithhybrids(convertiblebonds,forinstance),breakthesecuritydownintodebtandequityandallocatetheamountsaccordingly.Thus,ifafirmhas$125millioninconvertibledebtoutstanding,breakthe$125millionintostraightdebtandconversionoptioncomponents.Theconversionoptionisequity.

¨ Whendealingwithpreferredstock,itisbettertokeepitasaseparatecomponent.Thecostofpreferredstockisthepreferreddividendyield.(Asaruleofthumb,ifthepreferredstockislessthan5%oftheoutstandingmarketvalueofthefirm,lumpingitinwithdebtwillmakenosignificantimpactonyourvaluation).

Aswath Damodaran

110

111

Decomposingaconvertiblebond…

¨ Assumethatthefirmthatyouareanalyzinghas$125millioninfacevalueofconvertibledebtwithastatedinterestrateof4%,a10yearmaturityandamarketvalueof$140million.IfthefirmhasabondratingofAandtheinterestrateonA-ratedstraightbondis8%,youcanbreakdownthevalueoftheconvertiblebondintostraightdebtandequityportions.¤ Straightdebt=(4%of$125million)(PVofannuity,10years,8%)+125

million/1.0810=$91.45million¤ Equityportion=$140million- $91.45million=$48.55million

¨ Thedebtportion($91.45million)getsaddedtodebtandtheoptionportion($48.55million)getsaddedtothemarketcapitalizationtogettothedebtandequityweightsinthecostofcapital.

Aswath Damodaran

111

112

RecappingtheCostofCapital

Cost of Capital = Cost of Equity (Equity/(Debt + Equity)) + Cost of Borrowing (1-t) (Debt/(Debt + Equity))

Cost of borrowing should be based upon(1) synthetic or actual bond rating(2) default spreadCost of Borrowing = Riskfree rate + Default spread

Marginal tax rate, reflectingtax benefits of debt

Weights should be market value weightsCost of equitybased upon bottom-upbeta

Aswath Damodaran

112