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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:THEINPUTS

Thedevilisinthedetails..

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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

DISCOUNTRATES

TheDintheDCF..

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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

DiscountRates:I27

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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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LocalCurrencyGovernmentBondRates–January2016

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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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Approach2:CDSSpreads– January2016

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Approach3:TypicalDefaultSpreads:January2016

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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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