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DCFChoices:EquityValuationversusFirmValuation
Assets Liabilities
Assets in Place Debt
Equity
Fixed Claim on cash flowsLittle or No role in managementFixed MaturityTax Deductible
Residual Claim on cash flowsSignificant Role in managementPerpetual Lives
Growth Assets
Existing InvestmentsGenerate cashflows todayIncludes long lived (fixed) and
short-lived(working capital) assets
Expected Value that will be created by future investments
Equity valuation: Value just the equity claim in the business
Firm Valuation: Value the entire business
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EquityValuation
Assets Liabilities
Assets in Place Debt
EquityDiscount rate reflects only the cost of raising equity financingGrowth Assets
Figure 5.5: Equity Valuation
Cash flows considered are cashflows from assets, after debt payments and after making reinvestments needed for future growth
Present value is value of just the equity claims on the firm
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FirmValuation
Assets Liabilities
Assets in Place Debt
Equity
Discount rate reflects the cost of raising both debt and equity financing, in proportion to their use
Growth Assets
Figure 5.6: Firm Valuation
Cash flows considered are cashflows from assets, prior to any debt paymentsbut after firm has reinvested to create growth assets
Present value is value of the entire firm, and reflects the value of all claims on the firm.
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FirmValueandEquityValue
¨ Togetfromfirmvaluetoequityvalue,whichofthefollowingwouldyouneedtodo?
a. Subtractoutthevalueoflongtermdebtb. Subtractoutthevalueofalldebtc. Subtractthevalueofanydebtthatwasincludedinthecostof
capitalcalculationd. Subtractoutthevalueofallliabilitiesinthefirm¨ Doingso,willgiveyouavaluefortheequitywhichisa. greaterthanthevalueyouwouldhavegotinanequityvaluationb. lesserthanthevalueyouwouldhavegotinanequityvaluationc. equaltothevalueyouwouldhavegotinanequityvaluation
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CashFlowsandDiscountRates
¨ Assumethatyouareanalyzingacompanywiththefollowingcashflows forthenextfiveyears.Year CFtoEquity InterestExp (1-taxrate) CFtoFirm1 $50 $40 $902 $60 $40 $1003 $68 $40 $1084 $76.2 $40 $116.25 $83.49 $40 $123.49TerminalValue $1603.0 $2363.008
¨ Assumealsothatthecostofequityis13.625%andthefirmcanborrowlongtermat10%.(Thetaxrateforthefirmis50%.)
¨ Thecurrentmarketvalueofequityis$1,073andthevalueofdebtoutstandingis$800.
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EquityversusFirmValuation
¨ Method1:DiscountCFtoEquityatCostofEquitytogetvalueofequity¤ CostofEquity=13.625%¤ ValueofEquity=50/1.13625+60/1.136252 +68/1.136253 +
76.2/1.136254 +(83.49+1603)/1.136255 =$1073¨ Method2:DiscountCFtoFirmatCostofCapitaltogetvalue
offirm¤ CostofDebt=Pre-taxrate(1- taxrate)=10%(1-.5)=5%CostofCapital=13.625%(1073/1873)+5%(800/1873)=9.94%¤ PVofFirm=90/1.0994+100/1.09942 +108/1.09943 +116.2/1.09944 +
(123.49+2363)/1.09945 =$1873¤ ValueofEquity=ValueofFirm- MarketValueofDebt
=$1873- $800=$1073
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FirstPrincipleofValuation
¨ DiscountingConsistencyPrinciple:Nevermixandmatchcashflowsanddiscountrates.
¨ Mismatchingcashflowstodiscountratesisdeadly.¤ Discountingcashflowsafterdebtcashflows(equitycashflows)attheweightedaveragecostofcapitalwillleadtoanupwardlybiasedestimateofthevalueofequity
¤ Discountingpre-debtcashflows(cashflowstothefirm)atthecostofequitywillyieldadownwardbiasedestimateofthevalueofthefirm.
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TheEffectsofMismatchingCashFlowsandDiscountRates
¨ Error1:DiscountCFtoEquityatCostofCapitaltogetequityvalue¤ PVofEquity=50/1.0994+60/1.09942 +68/1.09943+76.2/1.09944 +
(83.49+1603)/1.09945 =$1248¤ Valueofequityisoverstatedby$175.
¨ Error2:DiscountCFtoFirmatCostofEquitytogetfirmvalue¤ PVofFirm=90/1.13625+100/1.136252 +108/1.136253 +
116.2/1.136254 +(123.49+2363)/1.136255 =$1613¤ PVofEquity=$1612.86- $800=$813¤ ValueofEquityisunderstatedby$260.
¨ Error3:DiscountCFtoFirmatCostofEquity,forgettosubtractoutdebt,andgettoohighavalueforequity¤ ValueofEquity=$1613¤ ValueofEquityisoverstatedby$540
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DiscountedCashFlowValuation:TheSteps
1. Estimatethediscountrateorratestouseinthevaluation1. Discountratecanbeeitheracostofequity(ifdoingequityvaluation)oracostof
capital(ifvaluingthefirm)2. Discountratecanbeinnominaltermsorrealterms,dependinguponwhether
thecashflowsarenominalorreal3. Discountratecanvaryacrosstime.
2. Estimatethecurrentearningsandcashflowsontheasset,toeitherequityinvestors(CFtoEquity)ortoallclaimholders(CFtoFirm)
3. Estimatethefutureearningsandcashflowsonthefirmbeingvalued,generallybyestimatinganexpectedgrowthrateinearnings.
4. Estimatewhenthefirmwillreach“stablegrowth” andwhatcharacteristics(risk&cashflow)itwillhavewhenitdoes.
5. ChoosetherightDCFmodelforthisassetandvalueit.
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GenericDCFValuationModel
Cash flowsFirm: Pre-debt cash flowEquity: After debt cash flows
Expected GrowthFirm: Growth in Operating EarningsEquity: Growth in Net Income/EPS
CF1 CF2 CF3 CF4 CF5
Forever
Firm is in stable growth:Grows at constant rateforever
Terminal ValueCFn.........
Discount RateFirm:Cost of Capital
Equity: Cost of Equity
ValueFirm: Value of Firm
Equity: Value of Equity
DISCOUNTED CASHFLOW VALUATION
Length of Period of High Growth
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Sameingredients,differentapproaches…
Input DividendDiscountModel
FCFE (Potentialdividend)discountmodel
FCFF (firm)valuationmodel
Cashflow Dividend Potential dividends=FCFE=Cashflowsaftertaxes,reinvestmentneedsanddebtcashflows
FCFF=Cash flowsbeforedebtpaymentsbutafterreinvestmentneedsandtaxes.
Expected growth Inequityincomeanddividends
InequityincomeandFCFE
InoperatingincomeandFCFF
Discountrate Costofequity Costofequity Costofcapital
Steadystate Whendividendsgrowatconstantrateforever
When FCFEgrowatconstantrateforever
WhenFCFFgrowatconstant rateforever
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Starteasy:TheDividendDiscountModel
Net Income* Payout ratio= Dividends
Cost of Equity
Expected dividends = Expected net income * (1- Retention ratio)
Length of high growth period: PV of dividends during high growth Stable Growth
When net income and dividends grow at constant rate forever.
Value of equity
Rate of return demanded by equity investors
Expected growth in net income
Retention ratio needed to sustain growth
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Movingonup:The“potentialdividends”orFCFEmodel
Free Cashflow to EquityNon-cash Net Income- (Cap Ex - Depreciation)- Change in non-cash WC- (Debt repaid - Debt issued)= Free Cashflow to equity
Cost of equity
Expected FCFE = Expected net income * (1- Equity Reinvestment rate)
Length of high growth period: PV of FCFE during high growth Stable Growth
When net income and FCFE grow at constant rate forever.
Value of Equity in non-cash Assets+ Cash = Value of equity
Rate of return demanded by equity investors
Expected growth in net income
Equity reinvestment needed to sustain growth
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Tovaluingtheentirebusiness:TheFCFFmodel
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Free Cashflow to FirmAfter-tax Operating Income- (Cap Ex - Depreciation)- Change in non-cash WC= Free Cashflow to firm
Cost of capital
Expected FCFF= Expected operating income * (1- Reinvestment rate)
Length of high growth period: PV of FCFF during high growth Stable Growth
When operating income and FCFF grow at constant rate forever.
Value of Operatng Assets+ Cash & non-operating assets- Debt= Value of equity
Weighted average of costs of equity and debt
Expected growth in operating ncome
Reinvestment needed to sustain growth
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EstimatingInputs:DiscountRates
¨ WhilediscountratesobviouslymatterinDCFvaluation,theydon’tmatterasmuchasmostanalyststhinktheydo.
¨ Atanintuitivelevel,thediscountrateusedshouldbeconsistentwithboththeriskinessandthetypeofcashflowbeingdiscounted.¤ EquityversusFirm:Ifthecashflowsbeingdiscountedarecashflowsto
equity,theappropriatediscountrateisacostofequity.Ifthecashflowsarecashflowstothefirm,theappropriatediscountrateisthecostofcapital.
¤ Currency:Thecurrencyinwhichthecashflowsareestimatedshouldalsobethecurrencyinwhichthediscountrateisestimated.
¤ NominalversusReal:Ifthecashflowsbeingdiscountedarenominalcashflows(i.e.,reflectexpectedinflation),thediscountrateshouldbenominal
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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=
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Notallriskiscreatedequal…
¨ EstimationversusEconomicuncertainty¤ Estimationuncertaintyreflectsthepossibilitythatyoucouldhavethe“wrong
model”orestimatedinputsincorrectlywithinthismodel.¤ Economicuncertaintycomesthefactthatmarketsandeconomiescanchangeover
timeandthateventhebestmodelswillfailtocapturetheseunexpectedchanges.¨ MicrouncertaintyversusMacrouncertainty
¤ Microuncertaintyreferstouncertaintyaboutthepotentialmarketforafirm’sproducts,thecompetitionitwillfaceandthequalityofitsmanagementteam.
¤ Macrouncertaintyreflectstherealitythatyourfirm’sfortunescanbeaffectedbychangesinthemacroeconomicenvironment.
¨ Discreteversuscontinuousuncertainty¤ Discreterisk:Risksthatliedormantforperiodsbutshowupatpointsintime.
(Examples:AdrugworkingitswaythroughtheFDApipelinemayfailatsomestageoftheapprovalprocessoracompanyinVenezuelamaybenationalized)
¤ Continuousrisk:Riskschangesininterestratesoreconomicgrowthoccurcontinuouslyandaffectvalueastheyhappen.
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RiskandCostofEquity:Theroleofthemarginalinvestor
¨ Notallriskcounts:Whilethenotionthatthecostofequityshouldbehigherforriskierinvestmentsandlowerforsaferinvestmentsisintuitive,whatriskshouldbebuiltintothecostofequityisthequestion.
¨ Riskthroughwhoseeyes? Whileriskisusuallydefinedintermsofthevarianceofactualreturnsaroundanexpectedreturn,riskandreturnmodelsinfinanceassumethattheriskthatshouldberewarded(andthusbuiltintothediscountrate)invaluationshouldbetheriskperceivedbythemarginalinvestorintheinvestment
¨ Thediversificationeffect:Mostriskandreturnmodelsinfinancealsoassumethatthemarginalinvestoriswelldiversified,andthattheonlyriskthatheorsheperceivesinaninvestmentisriskthatcannotbediversifiedaway(i.e,marketornon-diversifiablerisk).Ineffect,itisprimarilyeconomic,macro,continuousriskthatshouldbeincorporatedintothecostofequity.
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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
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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)
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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.
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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?
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Test2:ARiskfreeRateinEuros
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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
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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
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SovereignDefaultSpread:Threepathstothesamedestination…
¨ Sovereigndollaroreurodenominatedbonds:FindsovereignbondsdenominatedinUSdollars,issuedbyanemergingsovereign.¤ Defaultspread=EmergingGovt BondRate(inUS$)– USTreasuryBondratewithsamematurity.
¨ CDSspreads:ObtainthetradedvalueforasovereignCreditDefaultSwap(CDS)fortheemerginggovernment.¤ Defaultspread=SovereignCDSspread(withperhapsanadjustmentforCDSmarketfrictions).
¨ Sovereign-ratingbasedspread:Forcountrieswhichdon’tissuedollardenominatedbondsorhaveaCDSspread,youhavetousetheaveragespreadforothercountrieswiththesamesovereign rating.
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Approach1:DefaultspreadfromGovernmentBonds
The Brazil Default SpreadBrazil 2021 Bond: 6.83%US 2021 T.Bond: 2.00%Spread: 4.83%
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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%
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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.
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