TheCostofCapital:TheSwissArmyKnifeofFinance

AswathDamodaranApril2016

Abstract

Thereisnonumberinfinancethatisusedinmoreplacesorinmorecontextsthanthecostofcapital.Incorporatefinance,itisthehurdlerateoninvestments,anoptimizingtoolforcapitalstructure and a divining rod for dividends. In valuation, it plays the role of discount rate indiscountedcashflowvaluationandasacontrolvariable,whenpricingassets.Notwithstandingits wide use, or perhaps because of it, the cost of capital is also widely misunderstood,misestimatedandmisused.Inthispaper,IlookatwhatthecostofcapitalistryingtomeasureandhowbesttoavoidthepitfallsthatIseeinpractice.

What is the costof capital? If youaskedadozen investors,managersor analysts thisquestion,youare likely togetadozendifferentanswers.Somewilldescribe itas thecostofraisingfundingforabusiness,fromdebtandequity.Otherswillarguethatitisthehurdlerateusedbybusinessestodeterminewhethertoinvestinnewprojects.Afewmayuseitasametricthatdriveswhethertoreturncash,andifyes,howmuchtoreturntoinvestorsindividendsandstockbuybacks.Manywillpointto itasthediscountratethat isusedwhenvaluinganentirebusinessandsomemaycharacterizeitasanoptimizingtoolforthedecidingontherightmixofdebtandequityforacompany.TheyareallrightandthatisthereasonthecostofcapitalistheSwissArmyknifeofFinance,muchusedandoftentimesmisused.

TheMechanics Thecostofcapital, initsmostbasicform,isaweightedaverageofthecostsofraisingfunding for an investmentor abusiness,with that funding taking the formof eitherdebtorequity.Thecostofequitywillreflecttheriskthatequityinvestorsseeintheinvestmentandthecostofdebtwillreflectthedefaultriskthatlendersperceivefromthatsameinvestment.Theweightsoneachcomponentwillreflecthowmuchofeachsourcewillbeusedinfinancingtheinvestment.Figure1capturesthekeyingredients.

Figure 1: Cost of Capital Ingredients

Thisrelativelysimpleconstructhasestimationquestionsembeddedinit,includinghowequityinvestorsperceiveriskandconvertthatriskintoarequiredreturnandwhatlendersconsiderinmakingtheirjudgmentsonthedefaultspread.Therearealsoquestionsaboutwhattaxrate,theeffectiveorthemarginal,touseintheassessmenttobestcapturethetiltinthetaxcodetowardsdebt.

Ifyoumakeitthroughthemechanicsofcomputingcostofcapital,youwillseeitdescribedasanopportunitycost,adiscountrateandahurdlerateforinvestmentsanditisalloftheabovedependinguponwhereitisbeingusedandbywhom,asdelineatedinfigure2:

Figure 2: The Cost of Capital as Swiss Army Knife

Forinvestorsincompanies,thecostofcapitalisanopportunitycostinthesensethatitistherateofreturnthattheywouldexpecttomakeinotherinvestmentsofequivalentrisk.Forthecompaniesthemselves, itbecomesacostof financing,sincetheyhavetodeliverreturnsthatbeatoratleastmatchthecostofcapitaltokeepinvestorshappy.Finally,withinthecompany,especiallyifitisinmultiplebusinesses,thecostofcapitalcantaketheformofahurdlerateoninvestments, though it can be different for different businesses, if they have different riskprofiles.

RoleinCorporateFinance All businesses have to decide whether and where to invest scarce resources (theinvestment decision), what mix of debt and equity to use in funding these businesses (thefinancingdecision) andhowmuch cash (if any) to return to theowners of thebusiness (thedividenddecisions).Ifcorporatefinanceisthedisciplinethatlooksatthesedecisions,thecostofcapitalisanessentialtoolineachone.

InvestmentAnalysis Itisundeniablethatgreatbusinessesgetbuiltfrommakinggoodinvestmentjudgmentsandthatgoodbusinessescanbedestroyedbybadones.Butwhatseparatesagoodinvestmentfromabadone?Inthecorporatefinanceworld,itisthecostofcapitalthatisthebenchmarkthathastobebeatenforaninvestmenttobecategorizedasagoodinvestment,thoughthereisstillsomedisagreementabouthowbesttomeasurethereturnonaninvestment.Therearesome

who prefer to stick with accounting numbers and estimate a return on invested capital,computedastheratioofoperatingincometoinvestedcapita,andcomparingthatreturntothecostofcapital.Thereareotherswhoputtheirfaithincashflowsandestimateanetpresentvalueforaninvestment,wherethecostofcapitalisusedtodiscountfuturecashflowstothepresent.Therearestillotherswhocomputean internalrateofreturnonthecashflowsandcomparethosetothecostofcapital.

Figure3:TheCostofCapitalasHurdleRate

Note the two cautionary notes at the bottom of the table, capturing common mistakes ininvestment analysis. The first is when a company insists on using its cost of capital on allinvestments,eveniftheseinvestmentsareindifferentbusinessesandhavedifferentriskprofiles.Thatwillleadtosafebusinessessubsidizingriskybusinesseswithinthecompanyandovertime,the company itself will get riskier. The other is when a specific project is fundeddisproportionatelywithdebt,andthecostofcapitaliscomputedusingthatdebtratio.Inthiscase,projectsthatarefundedwithlessdebtwillsubsidizetheonesthatarefundedwithmore.

CapitalStructure The second component in corporate finance is finding a financingmix that optimizesbusinessvalue.Ofcourse,youcouldtaketheMiller-Modiglianitheoremtoheartandarguethatdebt isof littleconsequencetovalue,but thatview is indefensible inaworldwith taxesanddefaultrisk.Putdifferently,ifyouaccepttheargumentthatsomefirmscanborrowtoomuchandotherstoolittle,itfollowsthatthereisanoptimalmixofdebtandequityforabusinessandtheonlyquestionishowyoudeterminethatoptimal.Here,thecostofcapitalcanoperateasanoptimizingtool,wherethemixofdebtandequitythatminimizescostofcapitalistheonethatthebusinessshouldaspiretohave,since,ineffect,itmaximizesthevalueofthebusiness. Tousethecostofcapitalasanoptimizingtool,though,youhavetobeabletoincorporatetheeffectsofborrowingmoreintobothyourcostofequityandyourcostofdebt,sincebotharelikelytoincreaseasthedebtratiogoesup,theformerbecauseequityinvestorswillbeexposed

tomorevolatileequityearnings,afterinterestpayments,andthelatterbecausedefaultriskwillincreasewiththedebt.Figure4includestheseeffects:

Figure4:CostofCapitalasOptimizingTool

Whiletheconventionalcostofcapitalapproachisbuiltaroundtheassumptionthattheoperatingincome of a company is unaffected by its debt policy, a simple extension would allow theoperating incometochange(droppingasacompany’sdefaultrisk increases)andtheoptimaldebtratiothenwouldbetheonethatmaximizesfirmvalue(ratherthanminimizecostofcapital).

DividendPolicy Thefinalpieceofthecorporatefinancepuzzleisdividendpolicy,withthecostofcapitalagainplayinga key role. Specifically, if all the investments that abusinesshas available to itgeneratereturnsthatarelessthattheirrespectivecostsofcapital,thecashshouldbereturnedto investors (as dividends or in the form of stock buybacks). While this proposition seemsunremarkable,itisastonishinghowmanycompaniesseemtoviolateitacrosstheglobe.Atthestartof2016,for instance, Iassessedthereturnsoncapitalandcostsofcapitalofmorethan40,000publiclytradedcompaniesgloballyandcametotheconclusionthatmorethanhalfofthemgeneratedreturnsontheirinvestmentsthat,atleastintheaggregate,werelowerthanthecostsofcapitalofthesecompanies.Infigure5,Isummarizethoseresults:

As you borrow more, he equity in the firm will become more risky as financial leverage magnifies business risk. The cost of equity will increase.

Cost of EquityWeight of

equityPre-tax cost of debt (1- tax

rate)Weight of Debt

X + X

As you borrow more, your default risk as a firm will increase pushing up your cost of debt.

At some level of borrowing, your tax benefits may be put at risk, leading to a lower tax rate.

Bankruptcy costs are built into both the cost of equity the pre-tax cost of debt

Tax benefit ishere

The trade off: As you use more debt, you replace more expensive equity with cheaper debt but you also increase the costs of equity and debt. The net effect will determine whether

the cost of capital will increase, decrease or be unchanged as debt ratio changes.

Itistruethatthisisjustoneyear’sresults,butmyanalyseseachyearforthepreviousthreeyearsyieldnumbersthatareverysimilar.Putsimply,growth,acrosstheglobe,ismorelikelytodestroyvaluethantoaddit,inacompanyandweshouldbemorecautiousaboutpushingcompaniestogoformoregrowth.

RoleinValuation Ifthecostofcapitalisakeyplayerinalmosteveryaspectofcorporatefinance,itshouldcomeasnosurprisethatitisjustascriticalaninputintovaluationaswell.Inparticular,whenvaluingabusiness,thecostofcapitalisthediscountratethatyouusetodiscountbackthecashflows to the firm (i.e., cash flows before debt cash flows) to arrive at value today. Figure 6illustratesthemechanics:

Figure6:CostofCapitalinValuation

Itshouldcomeasnosurprisethatthecostofcapitalthatfindsitsplaceinvaluationisthesamecost of capital that played the role of hurdle rate, capital structure optimizer and dividenddeterminant.Theonlydifferenceisthatitisnowtheinvestorswhoareusingthecostofcapitaltovaluetheentirebusiness. Inthiscontext,itisworthaskingthequestionastowhotheseinvestorsare.Afterall,apubliclytradedcompanyhasmany,manyinvestorsandeachmayhaveadifferentperceptionoftheriskinessofthecompany(anditscostofcapital).Therulethatwefollow,butnotjustherebutwhereverweusethecostofcapital,isthattheriskinabusinessisseenthroughtheeyesofthemarginalinvestorinthestock,i.e.,aninvestorwhosetspricesatthemargin.Thateffectivelyrequiresthisinvestortoownsubstantialnumbersofsharesandtradethoseshares. Therearesomewhowouldarguethatforcingthediscountratetobeartheburdenofcarryingtheburdenofriskisnotonlyaskingtoomuchofit,butistooconstricting.Theyarguethatitismuchmoreexpansivetobringriskintothecashflows(perhapsriskadjustingthecashflowsforcertaintypesofrisk)andperhapsevenafteryouhavecompletedyourvaluation,aspost-valuediscountstovalue.Infact,whenvaluingaprivatebusiness,theygofurther,arguingthat the discount rate itself should be higher for these businesses because owners are notdiversified. I don't disagree with this contention, but it is important that you decide whichcomponentofyourvaluationisbestsuitedtocarryagivenrisk,andmakesurethatyoudon’tdoublecountarisk(inthecashflowsandthediscountrateorinyourdiscountrateandinapost-valuationdiscount).Infigure7,Iprovideabreakdownofrisksinabusinessandwhereeachtypeofriskshouldbeincorporated,inmyview,invaluation.

Figure7:ARiskAdjustmentTemplate

Insummary,withapubliccompany,thediscountrateisavehicleforreflectingmacroeconomicormarketrisksthatcannotbediversifiedaway,companyspecificriskgetadjustedforinexpectedcashflows(withtheresultthatthereisnodiscountinvaluefortheserisks)anddiscreteriskssuchasdistressandnationalizationarebestadjustedforusingprobabilities,afterthevaluation.Withaprivatebusiness,adiscountratewillhavetobehighertoincorporatecompany-specificrisks,sincetheowneroftheprivatebusinesswilltendnottobediversifiedandtheremayalsohave to be a post-valuation adjustment for the illiquidity associated with investing in thebusiness. Inclosing,thecostofcapitalinavaluationisnotareturnthatyouwouldliketomakeonthecompanythatyouarevaluinganditisnotareceptacleforyourhopesandfears,whereyourespondtodiscomfortwithuncertaintybyincreasingyourdiscountrate.Itshouldnotbe,thoughitoftenis,amechanismforreverseengineeringapre-determinedvalue.

CostofEquity:KeyInputs Togettothecostsofequity,debtandcapital,youhavetoencounterandestimatekeyinputsalongtheway.Inparticular,youcannotestimateanyofthesenumberswithoutariskfreerateasabaseandriskpremiums(intheformsofequityriskpremiumsanddefaultspreads).Inthissection,wewilllookateachoftheseinputs.

RiskfreeRate Theriskfreerateisthestartingpointforbothyourcostofequityandcostofdebt.Ifyoudefine it, as I do, as the rate of return you would expect to make on an investment withguaranteedreturns,an investmentcanberisk freeonly if theentitymakingtheguarantee isdefaultfreeandifyouarenotexposedtoreinvestmentrisk.Specifically,asix-monthtreasurybillisnotriskfree,ifyourtimehorizonisfiveyearsandagovernmentbondisnotriskfree,ifthegovernmentisitselfperceivedashavingdefaultrisk.

Onesimplerulethatwillsaveyoubothtimeandaggravationinestimatingriskfreeratesistostickwithalong-termrate,witheitherten-yearorthirty-yearbondsrepresentingacceptablechoices.Youshoulddothisevenifthecompanyinquestionchoosestoborrowshortterm,sinceitisfoolhardytoloweracompany’scostofdebt(andcapital)forplayingthetermstructure.TotheCFOwhoarguesthatthisisnotfair,sinceheorshecanborrowmoneycheapershortterm,theresponseshouldbethatthecostofcapitalisnotadeviceforrewardingcompaniesforplayingtermstructuregames. Toestimateariskfreerateincurrencieswherethereisatleastoneentitythatisviewedasdefaultfreeissuinglongtermbonds,youcouldusetheinterestrateonthesebondsasyourriskfreerate.ItisthisrationalethatallowsustousetheUStreasurybondrateastheriskfreeinUSdollarsandthatrateontheten-yearGermanEurobondastheriskfreerateinEuros.HowdoweknowthattheUSandGermangovernmentsaredefaultfree?Wedonothaveanyguarantees,butitisnotbaseduponthestandarddefensethatgovernmentscanprintmorecurrencytostaveoffdefault,sincetheGermangovernmentnolongerhasthatoptionwiththeEuro.Instead,Iwillfallbackonthedefense,weakthoughtitmightbe,thatthesegovernmentsareviewedasdefaultfree(AaaorAAA)bythebondratingsagencies.1

Ifyouareworkinginacurrency,wheretherearenodefaultfreeentitieswithbondsinthatcurrency,youhavetobecomemorecreativeinestimatingriskfree.Oneapproachistostartwithagovernmentbondrate in thecurrency,but to thennetout thedefault spread for thegovernmentinvolved,toarriveariskfreerate.Thesedefaultspreadscanbeobtainedinoneofthreeways:byfindinggovernmentbondsissuedinUSdollarsorEurosbythatgovernmentandnettingouteithertheUST.Bondrate(forUSdollars)ortheGermanEurobondrate(forEuros),by using sovereign CDS spreads or by using the local currency sovereign ratings to estimatespreads.2Figure8summarizesriskfreeratesinglobalcurrenciesinJanuary2016:

1 With the US government, even this argument is weakened by the fact that at least one ratings agency (S&P) has assigned a rating below AAA to the government. 2 See my website (Damodaran.com) for a lookup table that relates default spreads for sovereign ratings.

Therearetwothingsinnoteinthisgraph.1. Lowriskfreerates:Notethattherearethreecurrencieswheretheriskfreeislessthan

zero,amind-bendingchallengeforthoseofuswhohavebeentaughtthattheinterestrate is compensation for lenders giving up current consumption and several othercurrencieswhereriskfreeratesareverylow,relativetohistoricalnorms.3Therearesomewhoargue thatyoushouldnormalize risk free rates,usingperhapsanaverageacrosstime.Thatisadangerouspractice,sincetheriskfreerateoperatesasanopportunitycost,andifriskfreeratesaretoolow,youarestuckinvestingatthoserates,nomatterhowlowyouthinktheyare.

2. Theriskfreeratesarehigherinsomecurrencies(liketheBrazilianReaiandtheRussianRuble)thaninothers(theUSdollar,theEuro.Atfirstsight,thesedifferencesinriskfreeratesmayleadyoutobelievethatvaluingacompanyinalowriskfreeratecurrencywillgiveyouahighervalue,becauseitwillgiveyoualowercostofcapital,butyouwouldbewrong.Thedifferencesinriskfreerates,giventhattheyarecleansedondefaultrisk,canbeattributedalmostentirelytodifferencesinexpectedinflationacrosscurrencies,withhigherinflationcurrencieshavinghigherrates.Sinceyoushouldmatchthecurrencyinwhichyoudoyourcashflowstothecurrencyinwhichyouestimateyourdiscountrate,

3 Damodaran, Aswath, 2010, Into the Abyss: What if nothing is risk free? http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1648164

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Figure8:RiskfreeRates- January2016

RiskfreeRate DefaultSpreadbasedonrating

The defaultspreadsforacurrencyarecalculatedbasedonthelocalcurrencysovereignratingsforthegovernmentissuingbondsinthatcurrency.ForAAAratedgovernments,thedefault

choosingalowinflationcurrency,whileloweringyourdiscountrate,willalsolowertheexpectednominalgrowthrateinyourcashflows,yieldingoffsettingeffects.Thebottomline:itdoesnotmatterwhatcurrencyyouchoosetovalueacompanyin,aslongasyoustay consistent in your inflation assumptions. In fact, you couldmake your valuationcurrency-freebyestimatingarealriskfreerate(suchastheTIPsrate)andrealcashflowsandyourvalueshouldmatchuptoaUSdollaroranominalBrazilianReaivaluation.

Theriskfreerateinavaluationthereforehaslesstodowithwhereacompanyisincorporated,orwhatcurrencyitreportsitsfinancialsin,andmoretodowiththecurrencychoiceyoumake,whenyoudecidetodoyouranalysis.

ThePriceofRisk:ERPandDefaultSpreads Thepriceofriskissetbymarketsanditentersyourcostofcapitalintwoplaces.Whenestimating thecostofequity, itmanifestsasanequity riskpremium,and in thecostofdebtcomputation, it isadefaultspread.Botharesetbymarkets,reflect investorriskaversionandchangeovertimeandtheapproachesthatweusetoestimatethemhavetoreflectthisreality.

Equity Risk Premium

Theequityriskpremiumisthepremiumthatinvestorsdemandtoinvestinequities,asaclass,relativetowhattheyexpecttoearnonariskfreeinvestment.Thatpremium,whilenotexplicit, is implicitly built into stock prices, with higher expected premiums, other thingsremainingequal, translating into lower stockprices.Broadly speaking, thereare twowaysofestimatingequityriskpremiums,withthefirstbeingahistoricalpremiumestimatedbylookingatthedifferencebetweenpastreturnsonstocksandtheriskfreeinvestmentandthesecondbeing a forward looking estimate, where you back out from stock priceswhat investors arebuildinginasanexpectedreturnonstocksinthefuture. Thehistoricalpremiumapproach,whichremainsthemorewidelyusedapproach,isbuiltonthepresumptionofmeanreversion,i.e.,thatmarketsrevertbacktohistoricalnorms,andatleastinitially,wasbasedalmostentirelyonstockmarkethistoryintheUnitedStates.Toillustrate,table 1 summarizes historical risk premiums for US stocks, relative to both short termgovernments(T.Bills)andlong-termgovernments(T.Bonds):

Table1:HistoricalEquityRiskPremium–USfrom1928-2015 ArithmeticAverage GeometricAverage Stocks-T.Bills Stocks-T.Bonds Stocks-T.Bills Stocks-T.Bonds1928-2015 7.92% 6.18% 6.05% 4.54%StdError (2.15%) (2.29%) 1966-2015 6.05% 3.89% 4.69% 2.90%StdError (2.42%) (2.74%) 2006-2015 7.87% 3.88% 6.11% 2.53%StdError (6.06%) (8.66%)

Thistablelaysbarealloftheweaknessesofhistoricalequityriskpremiums.Notonlyaretheybackwardlooking,byconstruct,andsubjecttomanipulation,withverydifferentvaluesforthepremiumbaseduponwhatperiodofhistoryyoulookat,whetheryouuseT.BillsorT.Bondsasyour risk free rate and how you compute averages. Not surprisingly, analysts use this to

advantageandpickequityriskpremiumsthatreflecttheirvaluationbiases,pushingtowardsthehighernumbers (the simple averagearithmeticpremiumover T.Bills), if their bias is towardslowervalues,andthelowernumberstojustifyhighervalues.Thehistoricalriskpremiumisalsoastaticnumberthatchangeslittleduringacrisis,andwhenitdoes,ofteninthewrongdirection. In the implied premium approach, you start with the current level of stock prices,estimateexpectedcashflowstoequityinvestors(fromdividendsandbuybacks)inthefutureandsolveforaninternalrateofreturn.ThatIRRwillbetheexpectedreturnonstocksandnettingouttheriskfreeratewillyieldanimpliedequityriskpremium.Infigure9,IillustratethisprocessfortheS&P500atthestartofJanuary2016:

Figure9:ImpliedERPforS&P500–January2016

MyestimateofthepremiuminJanuary2016was6.12%,anumberthatisnotjustforwardlookingbutmuchmoreprecise(thestandarderrorsareintheexpectedcashflowvalues)thanahistoricalriskpremium.Thispremiumhaserrorattachedtoitaswell,sinceyourcashflowsandgrowthratesareestimates,butnotonlyisthemagnitudeoftheerrormuchsmallerthanwithhistoricalpremiums,buttheresultingnumberismuchmoresensitivetothemarketthatyouareinvestingin,risingasfearinthemarketincreasesandfallingasinvestorsbecomemoresecure. Asinvestorsandcompaniesglobalize,thechallengeisinestimatingequityriskpremiumsinother,oftenriskiermarketsandtherearethreeresponsesyoucanhave.Thefirstistoassume,asmanyanalystsandcompaniesdidinthe1980s,thatcountryriskisdiversifiableandthusnotdeservingofanyadditionalpremiums;thiswillleadyoutousetheUSequityriskpremiumasaglobalequityriskpremium.Thesecondistoassumethatthesovereigndefaultspread,thatyouusedinearliertogettheriskfreeratefromthedefault-riddengovernmentbondrate,isagoodmeasureoftheadditionalequityriskinthesemarketsandtoadditontotheUSERP.Inthethirdapproach,youuseaslightlymodifiedversionofthesecondoneandadjustthedefaultspreadfor

theadditionalriskofequity(relativetothesovereignbond).InJanuary2016,IusedtheratioofthestandarddeviationintheS&PemergingmarketequityindextothestandarddeviationintheS&Pemergingmarketpublicbondindextoarriveatavalueof1.39,whichIthenusedasmyscalarforthedefaultspread.TheapproachisdescribedinFigure10below:

Usingthisapproachtoestimateequityriskpremiumsbycountry,IobtaintheglobalpictureofequityriskinFigure11:

Figure11:EquityRiskPremiumsaroundtheGlobe–January2015

Asafinalpieceofthepuzzle,nowconsiderhowyouwouldcomputetheequityriskpremiumforacompany.Ratherthanleaveit,asmanyanalystsareproneto,attheERPofthecountryinwhichthecompany is incorporated, Iwouldestimate it,basedonwherethecompanygenerates itsrevenues.Thus,withCocaCola,aUS-basedmultinational,andVale,aBrazil-basedglobalminingcompany,theequityriskpremiumcomputationswouldbeasfollows:

Figure12:ERPforCompanies–Vale&CocaCola

Consequently,theequityriskpremiumusedinvaluingacompanyhaslesstodowithwhereitisincorporatedortradedandmoretodowithwhereitdoesbusiness.

Default Spread

Investors inthebondmarketassessdefaultrisk,whentheypricebonds,andchargeadefaultspreadovertheriskfreerate.Thatdefaultspreadwillobviouslyvaryacrosscompaniesandacrosstime.Infigure13,Isummarizedefaultspreadsbybondratings(S&PandMoody’s)classesinJanuary2016andcomparethemtothespreadsinJanuary2015:

Figure13:BondRatingsandDefaultSpreads

Noticehowmuchlargerthedefaultspreadsareinearly2016,relativeto2015.Thatshouldserveasacautionarynotetocompaniesthatusecostsofcapitalthatstayfrozenovertime. Togetthedefaultspreadforacompany,youcanuseoneofthreepaths.Thefirstistofindabondissuedbythecompanyandlookuptheyieldtomaturityonthebond,adangerouspath,sinceevenriskycompaniescancarveoutsafeassetsasbackingforbonds.Thesecondistofindabondratingforthecompanyandlookupthedefaultspreadfromfigure10(oranupdatedversionofthatfigure):aBBBratedcompanywouldbegivenadefaultspreadof2.25%.Ifyourcompanyhasneithertradedbondsnorarating,youhavetoestimatea“synthetic”rating,basedupontheholdingsofthecompany,andestimateaspreadforthatrating.Thecostofdebtforacompanythenisobtainedbyaddingthisdefaultspreadtothelongtermriskfreerate(inthecurrencyofyourchoice).Thiscostofdebtisthenattachedtoallofthedebtofthecompany,includingitsshorttermdebt,ontheassumptionthattherolledovercostoftheshorttermdebtwillconvergeonthelongtermcost.

ERP, Default Spreads and Interest Rates.

Iftheequityriskpremiumisthepriceofriskintheequitymarketandthedefaultspreadisthepriceofrisk inthebondmarket, itshouldnotbesurprisingthatmuchofthetimethey

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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

movetogether.Inacrisis,forinstance,theequityriskpremiumsanddefaultspreadsonbondsrising,withdefaultspreadsrisingmoreforlower-ratedbonds.Figure11capturesthemovementsintheimpliedERPandthedefaultspreadonaBaaratedbondfrom1969to2015.

Overtheentiretimeperiod,theequityriskpremiumwasroughlytwicetheBaabonddefaultspread,asimpleruleofthumbthatyoucanusetoassesswhetheracurrentlyprevailingpremiumis too high or low. There have been periods of divergence between the stock and the bondmarket,aswasthecaseinthelate1990s,whenequityriskpremiumsdroppedasbonddefaultspreads stayed high, and again between 2002 and 2007,when default spreads dropped andequityriskpremiumsstayedunchanged.Bothprecededsignificantmarketcorrections,withthefirstoneendingwiththestockmarket’sdotcombustin2001andthesecondoneplayingoutin2008asafinancialcrisisthatspreadacrossallmarketsbutwasprecipitatedbyabondmarketcollapse. Doesthepriceofriskmoveupanddownwithinterestrates?Theconventionalwisdom,untilthe2008crisis,wasyes,largelytheresultofthe1970s,whenbothriskfreeratesandERPclimbed.Since2008,thatrelationshipseemstohavebrokendownasthesamefinancialcrisis

hascausedriskfreeratestodropinmuchofthedevelopedworld,withanassistfromcentralbanks,hascausedequityriskpremiumstorise.4

RelativeRiskMeasures:BetaorBetas Youcouldassume,assomepeopledo,thatallcompanies(andinvestments)areequallyriskyand,ifyoudo,thispartoftheassessmentbecomesunnecessary.If,however,youstartoffwith the presumption that not all investments are equally risky, you then face the task ofmeasuringthisrelativerisk.This,inanutshell,iswhateveryriskandreturnmodelinvaluationtriestodo,butitisalsothesourceofnotonlydisagreementbutalsorancoramonganalysts. PortfolioTheoryBasedModels HarryMarkowitz’sinsightthataninvestor’sperceptionoftheriskinessofaninvestmentisdeterminedbywhatitaddstotheoverallriskofhisorherportfolioisthebuildingblockforallportfoliotheorymodels.Thesemodelsthenproceedtotaketwoadditionalsteps:

1. Measure risk as standarddeviationor variance in actual returns, around an expectedreturn: If a riskless investment is one where you know your expected returns withcertainty, the greater the deviation of actual returns around an expected return, theriskierthatinvestmentbecomes.

2. Onlythatportionofthisreturnthatcannotbediversifiedawaywillberewarded:Theriskinan investmentcancomefromboth firm-specific factors (specific to theproductsorservicesthatitprovides,thecompetitionitfacesandcompetenceorlackthereofofitsmanagement)andmacroeconomicfactors(interestrates,theeconomyandinflation).Asinvestorsdiversify,thefirstriskwilldissipate,asitgetsaveragedoutacrossinvestmentsbutthesecondwillremain.

Thedifferencesbetweenthecompetingmodelsthenboilsdowntohowtheymeasurethisnon-diversifiable risk. Table 2 summarizes the assumptions that underlie the capital asset pricingmodel (CAPM), the arbitrage pricingmodel (APM) andmulti-factor model and the resultingmeasuresofrisk:

Table2:PortfolioTheoryBasedModelsModel Assumptions RiskMeasureTheCAPM 1. Therearenotransactions

costs.2. Thereisnoprivate

information.

Themarginalinvestorswillbefullydiversifiedandholdaportfolioofeverytradedassetinthemarket.Theriskofanindividualassetwillbecapturedbytheriskaddedtothismarketportfolio,andmeasuredwithasinglebeta,measuredagainstthemarket.

TheAPM Themarketpricesofstocksarethebestindicatorsofmarketand

Historicalstockreturnscanbeanalyzedtoidentifythenumberof

4 Damodaran, Aswath, 2016, Equity Risk Premiums (ERP): Determinants, Estimation and Implications – The 2016 Edition. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2742186. This is the ninth annual update of my review and assessment of equity risk premiums, how to estimate them and a comparison of the approaches.

firm-specificrisks,withmarketrisksaffectingallormanystocksandfirm-specificrisksnot.

marketriskfactorsandtheexposureofeachstocktothatmarketrisk.Sincethisisastatisticalmodel,thefactorswillbeunnamed.Theriskinastockwillbecapturedwithbetas,measuredagainsttheseunnamedfactors.

TheMultifactorModel

Marketriskfactorshavetobemacroeconomic,toaffectmanystocksatthesametime.Lookingathowastockbehaves,relativetodifferentmacroeconomicvariables,shouldyieldcluestoitsmarketriskexposure.

Theriskinastockwillbecapturedwithbetas,measuredagainstspecifiedmacroeconomicfactors.

Notice that these models agree on more than they disagree about. They all focus on non-diversifiableriskandtheyallusepaststockpricestomeasurethatriskexposure,whetheritiswithonebeta(theCAPM)ormultiplebetas(theAPMorMultifactorModels).

Thereisnoaspectofthecostofcapitalcomputationthatismorecontestedandcontroversialthanthemeasurementofrelativerisk,withmoreinkbeingspilt,moretimespentindebatesandmoredamagedonetovaluationsalongtheway.Inresponsesthatareakinthrowingthebabyoutwith thebathwater, I see companies ignore their computed costsof capital andanalystsrefusetododiscountedcashflowvaluation,becausetheydon’tlikebeta.Ifyoudislikebetaorbetas,itimportantthatyoubeclearaboutwhy,sinceitwilldeterminewhatyouuseinstead,andthere are possible three reasons for your dislike. The first is that you don’t buy into theassumptionthatassetsarepriced,atthemargin,bydiversifiedinvestors,andconsequentlyintotheconclusionthatonlynon-diversifiableriskshouldbe incorporatedintoyourdiscountrate.Thesecondisthattheriskmeasuresinthesemodelsarecomputedusinghistoricalmarketpricesorreturns,apracticethatyoufeelisatoddswithintrinsicvaluation,wherethepresumptionisthatmarketsmakemistakes.Thethirddisagreementmaybestatistical,whereyoubelievethatonepassofhistory(theuseofatwoorfiveyearregressionofreturnsonastockagainstthemarkettomeasurethebeta,intheCAPM)maynotcapturethetrueriskofthatstockorwilldosowithagreatdealofnoise.TheDiversifiedMarginalInvestor If youdonotmind theuseof past prices, but disagreewith the assumption that themarginalinvestorisdiversified,therearealternativeapproachesthatyoucouldconsider:

1. TheStandardDeviationorTotalVariance:Attheheartofthemodernportfoliotheoryisthemean-varianceframework,withvariance/standarddeviationbecomingtheprimaryoroftentheonlymeasureofriskinaninvestment.Ifyoumaketheadditionalassumptionthatthemarginalinvestorisdiversified,youarriveatbetaorbetas,riskmeasuresthatcaptureonlytheportionoftheriskthatisnotdiversifiable.Instatisticalterms,youcanwritethebetainthecapitalassetpricingmodelasfollows:

𝐵𝑒𝑡𝑎 = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑜𝑓𝑆𝑡𝑜𝑐𝑘 ∗ 𝐶𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑜𝑓𝑆𝑡𝑜𝑐𝑘𝑤𝑖𝑡ℎ𝑚𝑎𝑟𝑘𝑒𝑡

𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑜𝑓𝑡ℎ𝑒𝑚𝑎𝑟𝑘𝑒𝑡

Itisthecorrelationmeasurethatcapturesthemarketportionoftotalriskanditisthatmeasurethatisdependentontheassumptionthatthemarginalinvestorisdiversified.Ifyouassumethatinvestorspriceassetsbasedupontheirtotalrisk,notjustmarketrisk,theriskmeasure(whichIhavetermedatotalbeta)forastockorassetcanberestatedasameasureoftotalrisk:

𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑜𝑓𝑆𝑡𝑜𝑐𝑘

𝐴𝑣𝑒𝑟𝑎𝑔𝑒𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑎𝑐𝑟𝑜𝑠𝑠𝑆𝑡𝑜𝑐𝑘𝑠

Therelativestandarddeviation,likethebeta,willaveragetooneacrossallstocks,withmorevolatilestockshavehigherrelativestandarddeviationvaluesthanlessvolatileones.Notealsothattheaveragestandarddeviationacrossstocks inamarketwillbehigherthan the standarddeviationof themarket, since the latterwill reflect thebenefitsofdiversification.Replacingtheaveragestandarddeviationacrossstockswiththestandarddeviationofthemarketintheequationabovewillyieldatotalbeta,ameasurethatIhaveusedtoestimatecostsofequityforundiversifiedinvestorsinamarketwherepricesaresetbydiversifiedinvestors.5

𝑇𝑜𝑡𝑎𝑙𝐵𝑒𝑡𝑎 = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑜𝑓𝑆𝑡𝑜𝑐𝑘

𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑜𝑓𝑡ℎ𝑒𝑚𝑎𝑟𝑘𝑒𝑡

Whileboththerelativestandarddeviationandtotalbetaarebaseduponthesamelogic,theyaredifferentintheirassumptionsaboutglobalrisk.Therelativestandarddeviationmeasureisthebetterchoice,ifyoubelievethatinvestorscollectivelypricestocksontheirtotalriskexposureandnotbasedupontheriskaddedtotheirportfolios.Thetotalbetameasure is better suited for a market, where most assets are priced by diversifiedinvestors but there exist pockets or asset classes, where investors cannot orwill notdiversify(suchasprivatebusinessesorsmall,closelyheldcompanies).

2. TheCAPMPlusModels:IfyourconcernsabouttheCAPMorMulti-factormodelsisthattheyareincomplete,i.e.,thattheymissriskfactorsthatarepricedinbythemarketbutnotcapturedintheestimatedbetas,therearetwofixes.Thefirstisusemarketreturnsonindividualassetstobackoutproxies(orstandins)forthesemissingriskfactors,whichiswhatFamaandFrenchhavedoneintheirstudiesoverthelasttwodecadesandtoaddtheseproxiestotraditionalriskmodels.6Thus,whenyouseetheexpectedreturnfromthe traditional CAPM augmented with a small stock premium, you are seeing theseaugmentedmodelsinplay.Asthedatathatwehaveavailabletoparsegetsricher,itisnot surprising thatotherproxies, suchapricemomentumandpricing ratios, are alsofindingtheirwayintothesemodels.Thesecondapproach,usedbyprivateappraisers,isto add an extra premium for what they term company-specific risk, especially whenvaluing private businesses. The origins of the these country risk premiums are moreintuitivethantheoreticalorempirical.

TheMarketPriceBasedMeasure Formanyintrinsicvalueinvestors,itistheuseofmarketpricestomeasuretheriskthatismosttroublesomecomponentoftheriskmeasurementprocess.Afterall,thebasisforintrinsic

5 Damodaran, Aswath, 2012, Investment Valuation, 3rd Edition, John Wiley & Sons. 6 Fama, E.F. And K.R. French, 1992, The Cross Section of Expected Stock Returns, Journal of Finance, Vol 47, 427-465.

valuationisthatmarketsmakemistakesandthatyoucanfindthosemistakeswithyourintrinsicvalueapproachesandusingthesesamemarketstomeasureriskseemsinconsistent.Thatisafaircritiqueandherearethealternativestoconsider:

1. Earnings-basedriskmeasures:Ifyoubelievethatitisreasonabletoassumethatmarginalinvestors are diversified, but want to steer away from price-basedmeasures of non-diversifiable risk, you can compute betas based upon accounting numbers (revenues,earnings). Ineffect, insteadofregressingstockreturnsonastockagainstreturnsonamarketindex,youregresschangesinaccountingearningsfromperiodtoperiod,atyourcompany, against changes in accounting earnings for the entire market. If you don’tbelieveinthediversifiedmarginalinvestorassumption,youcouldcomputevariabilityinaccountingearningsover time foracompanyandcomputea relative riskmeasurebyscalingittotheaverageaccountingearningsvariabilityacrossallstocks:

𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠𝑉𝑎𝑟𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑦 = 𝑆𝑡𝑑𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑖𝑛𝐶𝑜𝑚𝑝𝑎𝑛𝑦B𝑠𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠

𝐴𝑣𝑒𝑟𝑎𝑔𝑒𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠𝑆𝑡𝑑𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑎𝑐𝑟𝑜𝑠𝑠𝑚𝑎𝑟𝑘𝑒𝑡

Theperilwithusingearningsbasedapproachesisthatitiswellestablishedthatnotonlydoaccountantssmoothoutearningsbutthatthereisenoughdiscretionintheaccountingrulestoallowthemtodoitmoreatsomefirmsthanatothers,makinganycrosscompanycomparisonstenuous.

2. AccountingRatiomeasures:Asecondoptionistouseanaccountingratioasyourmeasureofriskinessandtoscaleriskaroundthatratio.Forinstance,assumethatyoubelievethatdifferences in risk across companies come from differences in debt burdens at thesecompanies. You could compute ameasure of the debt burden (debt as a percent ofcapital,debtasamultipleofEBITDA)andusethatmeasuretocomeupwithrelativeriskmeasuresforstocks.Ifthisisyourchoice,itmaybeworthtestingyourhypothesisthattheratiothatyoupickedtrulymeasuresrisk,lookingatthecorrelationbetweenwhateverriskoutcomeyouthinkisbestandtheratioinquestion.

3. ManagementandSector:Forsomeinvestors,riskcomesfromthebusinessthatyouareinand/orthemanagementteamthatrunsthecompany.Thus,technologycompaniesareconsidered to be riskier than food processing companies and companies with goodmanagers,with long standing, are viewed as safer than companieswith less crediblemanagement teams. The advantage of this approach is that it is simple but thedisadvantageisthatsectorsevolveovertime,sometimesgoingfromriskytosafe(asisthecasewitholdertechnologycompanies)andatothertimesfromsafetorisky(banksandtelecommunicationscompanies).

Ifyoudecidetoabandonstockpricesandmovetooneofthesealternatemeasures,recognizethattheyallcomewithcosts.TheStatisticalNoiseProblem It is possible that you do not have an issue with the diversified marginal investorassumptionorwiththeuseofprices,butknowinghowmuchvolatilitythereisinstockpricesandhowidiosyncraticeventscanaffectpricingforextendedperiods,youdonotmuchfaithintheriskmeasuresthatcomefromlookingatonestockoveratimeperiod.Here,thesolutionistodrawonthelawoflargenumbers.

1. SectorRiskMeasures:Ifyouhavenoissueswiththecentralassumptionsofriskandreturnmodels but have concerns about using a beta (or betas) from a single regression or

statistical analysis, there is a simple solution.Using an averagebeta (or betas) acrossstocksinasectorwillyieldamoreprecisevalue,becauseitwillaverageoutthenoiseorerror inherent in individualcompanyriskestimates. Infact,youcanmakethisprocessmore completebybreakingamulti-business company into itsbusinessgroupingsandtakingaweightedaverageofthebetasofthesebusinessestoarriveatabusinessbetaforthecompany,whichyoucanthenadjustforthedebtratioofthecompany.

2. ImpliedCostsofEquity/Capital:Ifyourproblemswithriskmeasurementlieinboththestatistical problemswith estimating risk parameters andwith themodels themselves,thereisawayofestimatingcostsofequityandcapitalthatisagnosticaboutthechoiceofmodels,butitcanleadtocircularreasoning,atleastinthecontextofvaluation.Youcanstartwiththestockpricesofindividualcompanies,generateestimatesofexpectedcashflowsforeachcompanyasagoingconcernandthensolveforthecostofequityandcapital for thecompany.Considerasimpleexample.AssumethatConEd’ssharesarepricedat$60/shareandthatyouexpectthestocktopayadividendpershareof$4nextyear,growing2%aayearforever.Usingastablegrowthdividenddiscountmodel,thecostofequityforthiscompanycanbewrittenas:

Valuepershare=$60=$4/(r-.02),wherer=ImpliedcostofequityCostofequity=$4/60+.02=8.67%

Thisversionofthecostofequity,computedasthedividendyieldplusexpectedgrowth,isofferedbysomeasanalternativetotraditionalriskandreturnmodels,andoftenusedinappropriately (to estimate the cost of equity for high growth companies that don’talwayspayoutwhattheycanaffordtoindividends).Togetacostofcapitalforafirm,youwouldhavetosubstituteenterprisevalueforequityvalueandcashflowsaftertaxesandreinvestment,butbeforedebtpayments(freecashflowtothefirm))andyoucansolveforthecostofcapital.Ifyouareusingthesecostsofequityandcapitalinvaluation,theproblemisobvious.Sincethecostsofequityandcapitalarebackedoutfromcurrentmarketvalues,pluggingthembackintothemodelswillyieldtheunsurprisingconclusionthat the market is pricing these stocks correctly. There is one escape hatch. HoltAssociates,aconsultingfirmthatpopularizedtheuseofcashflowreturnoninvestment(CFROI),computedtheseimplicitcostsofcapitalforcompaniesandthenaveragedthem,bysector,tousewhenvaluingindividualcompaniesinthatsector.Thus,iftheaverageimpliedcostofcapitalacrossalloilcompaniesis7%,thatwillbeusedasthecostofcapitalwhenvaluingExxonMobilorConoco.

CostofEquity:Garnishes Theessenceofthecostofcapitalisthat,oncecomputed,ityieldsahurdleratetouseinmakinginvestmentjudgmentsandadiscountratetouseinvaluation.Inpractice,though,itiscommon to see the cost of capital augmentedby the additionof premiums, somebasedonhistory,someongutfeelingandsomedrivenbybias.

TheSmallCapPremiumThesmallcappremiumisperhapsthemostwidelyusedadd-ontothecostofequityin

practice.Firmsdoitwhenestimatinghurdleratesforsmallerdivisionsorwhenacquiringsmallcompanies.Analystsaddittotheircostofequityestimates,whenvaluingsmallcompanies.In

fact,servicesthatestimateriskpremiums,suchasDuffandPhelps,providetablesthatcontainsmallcappremiumestimatesbycompanysize.Aswithmuchelseinvaluation,though,thefactthateveryonedoesitdoesnotmakeitright.

Theoriginsofthesmallcappremiumareinacademia,withthefirststudiesinthe1970sindicatingthatthetraditionalCAPMunderestimatedtheexpectedreturnsonthestocksinthesmallmarketcapitalizationclassesinthemarket.Infact,ifyouusethedatagoingbackto1927,thesmallcappremiumstillshowsupwhenyougraphreturnsbymarketcapitalizationclass,asIhaveinfigure15:

Smallcapstockshaveannuallyearned3.82%morethanexpected(onarisk-adjusted,market-adjusted basis), but that finding comeswith an expiration clause. Since 1981, the small cappremiumhasbeenmissinginexistence,withsmallcapstocksearning0.33%lessthanexpected(onarisk-adjusted,market-adjustedbasis).Thereareothertroublingaspectswiththesmallcappremium,evenoverthelongerperiods,thatareglossedover,includingthefactthatalmostallofthepremiumisearnedinJanuaryandthatithasneverbeenasstronginmarketsoutsidetheUS,asithasbeenintheUS. Analystswhoaddasmallcappremiumontotheircostsofequityandjustifyitbasedonthehistoricaldatawillhavetofindotherreasonsfortheiraugmentationofcostsofequitiesorprivatecompanies.Itispossiblethatsizecouldstandinforsomeothermissingrisk(suchaslackofinformation,survivalriskorevenilliquidity),butifso,shouldwenotbemeasuringthatriskdirectly?

IlliquidityInvestors,forthemostpart,valuebeingabletogetintoandoutofinvestmentswithease

andassetpricesprobablyreflectthisdesireforliquidity.Thatsaid,illiquidityisperhapstheleastunderstoodandthemostmangledaspectofvaluationandcorporatefinance.Sincethisisapaperaboutthecostofcapital,Iwillnotventureintothedarkareaofilliquiditydiscounts,where20%ormoreofthevalueofabusinessdisappearsattheveryendofthevaluation.However,therearesomeanalystswhoarguethatitisthecostofcapitalthatshouldbeartheburdenofconveyingconcernsaboutilliquidity,withlessliquidinvestmentscarryinghighercostsofcapital. Theearliesttheoreticaldiscussionsofhowbesttoincorporateilliquidityintoassetpricingmodels occurred in the 1970s.Mayers (1972, 1973, 1976) extended the capital asset pricingmodel to considernon-tradedassetsaswell ashumancapital.7 The resultingmodelsdidnotmake explicit adjustments for illiquidity, though. In a more recent attempt to incorporateilliquidity intoexpectedreturnmodels,AcharyaandPedersen(2005)examinehowassetsarepricedwith liquidity risk andmakea critical point.8 It is not just how illiquid an asset is thatmattersbutwhenitisilliquid.Inparticular,anassetthatisilliquidwhenthemarketitselfisilliquid(whichusuallycoincideswithdownmarketsandeconomicrecessions)shouldbeviewedmuchmorenegatively(witharesultinghigherexpectedreturn)thananassetthatisilliquidwhenthemarket is liquid. Thus the liquidity beta of an assetwill reflect the covariance of the asset’sliquidity with market liquidity. Acharya and Pedersen estimate that illiquid stocks haveannualizedriskpremiumsabout1.1%higherthanliquidstocks,andthat80%ofthispremiumcanbeexplainedbythecovariancebetweenastock’s illiquidityandoverallmarket illiquidity.PastorandStambaugh(2003)alsoconcludedthatitisnotastock’sliquiditypersethatmattersbutitsrelationshiptooverallmarketliquidity.Overthe34-yearperiodthattheyexaminedstockreturns,theyconcludedthatstockswhosereturnsaremoresensitivetomarketliquidityhaveannualreturnsthatare7.5%higherthanstockswhosereturnshave lowsensitivitytomarketliquidity,afteradjustingforthestandardsize,valueandmomentumfactors.9 Thedifficultiesassociatedwithmodelingliquidityandarrivingatusablemodelshaveleadmany researchers to consider more practical ways of incorporating illiquidity into expectedreturns. Amihud and Mendelson (1989) examined whether adding bid-ask spreads to betashelpedbetterexplaindifferencesinreturnsacrossstocksintheU.S.10IntheirsampleofNYSEstocksfrom1961-1980,theyconcludedthatevery1%increaseinthebid-askspread(asapercentofthestockprice)increasedtheannualexpectedreturnby0.24-0.26%.Otherstudieshaveusedtradingvolume, turnoverratios (dollar tradingvolume/marketvalueofequity)and illiquidity7 Mayers, D., 1972, Nonmarketable assets and capital market equilibrium under uncertainty, in M.C. Jensen, Studies in the Theory of Capital Markets (Praeger, New York, NY); Mayers, D., 1973, Nonmarketable assets and the determination of capital asset prices in the absence of a riskless asset, Journal of Business, v46, 258-267; Mayers, D., 1976, Nonmarketable assets, market segmentation and the level of asset prices, Journal of Financial and Quantitative Analysis, v11, 1-12. 8 Acharya, V. and L.H. Pedersen, 2005, Asset Pricing with Liquidity Risk, Journal of Financial Economics, v77, 375-410. 9 Pastor, L. and R. Stambaugh, 2003, Liquidity Risk and Stock Market Returns, Journal of Political Economy, v111, 642-685. 10 Amihud, Y. and . Mendelson, 1989, the Effects of Beta, Bid-Ask Spread, Residual Risk and Size on Stock Returns, Journal of Finance, v 44, 479-486.

ratiosasproxiesforilliquiditywithconsistentresults.11Datar,NairandRadcliffe(1998)usetheturnoverratioasaproxyforliquidity.Aftercontrollingforsizeandthemarkettobookratio,theyconclude that liquidity plays a significant role in explaining differences in returns,withmoreilliquidstocks(inthe90thepercentileoftheturnoverratio)havingannualreturnsthatareabout3.25%higherthan liquidstocks(inthe10thpercentileoftheturnoverratio). Inaddition,theyconcludethatevery1%increaseintheturnoverratioreducesannualreturnsbyapproximately0.54%.12 Theproblemswithalloftheseapproachesisthatthecostofilliquidity(andthepremiumyouattachtoyourcostofcapital)willvaryacrosstime,increasingduringperiodsofcrisesanddroppinginmorestableperiods,andmoretroublingly,varyacrossinvestors,sinceinvestorswhoarepatientandhavelittleneedforcashwillpriceitlessthanimpatientinvestorswithuncertaintimehorizons.Forthemoment,therefore,muchoftheworkthathasbeendoneonincorporatingilliquidityintocostsofequityandcapitalcanbeviewedmoreasworkinprogressthanfinishedproduct.

Debt:ItscostandweightMuchoftheattentioninestimatingcostofcapitalisspentonthecostofequityandthat

shouldcomeasnosurprise,sinceitisanimplicitcostandhasmoremovingpiecestoit.Ihavereferencedthecostofdebtinearlierpartofthepaperandarguedfortheuseofalongtermcostofdebtbutinthissection,Iwouldliketotieupafewmorelooseendsrelatingtobothdebtandthemixofdebtandequitytouseincomputingcostofcapital.

TheCostofDebt–CurrentandConsistentTherearetwosimplerulesthatareworthreemphasizingwhenitcomesthecostofdebt.

Thefirstistokeepitcurrent,reflectingthecompany’scurrentdefaultriskstandingratherthantheoneithadwhenitactuallyborrowedthemoney.Thus,ifyourcompanywasAaarated,whenitborroweditsmoney,buthasnowslidetoBaarating,youwillneedtousethehigherdefaultspreadassociatedwiththe latter inestimating itscostofdebt.Theotheraspectofaspectofbeingcurrentistoupdatethecostofdebtfortheriskfreeratetoday,ratherthantherateatthetime of the borrowing. Taken together, these principles imply that the book interest rate,obtainedbydividingtheinterestexpensespaidbyacompanybyitsbookvalueofdebtisclosetouselessasanestimateofthecostofdebt.Thatmaystrikeyouasunfair,especiallyifthedebtthat isalreadyonthebooks isatarate lowerthanthecurrentmarket interest ratethatyouestimateforthecompany,butnotethatwhilethecompanybenefitsfromthislow-interestdebt,itisnotthecostofdebtthatshouldcarrytheburdenofreflectingthisbenefit.Instead,ifyouusethemarketvalueofdebtincomputingyourcostofcapital,asIwillargueyoushouldinthenextsub-section,themarketvalueofthis“lowinterest”debtwillbelowerthanthebookvalue,givingthecompanythecapacitytoborrowmoremoneyifitchoosesto.Theother rule for thecostofdebt is tostaycurrencyconsistent.Thus,nomatterhowmanydifferentcurrenciesamultinationallikeNestlemayborrowmoneyin,whenmakingcorporate11Brennan, M. J., T. Chordia, and A. Subrahmanyam, 1998. Alternative factor specifications,security characteristics and the cross-section of expected stock returns, Journal of FinancialEconomics, 49, 345–373.12 Datar,V.T.,N.Y.NaikandR. Radcliffe, 1998, “Liquidity and stock returns: Analternative test,” Journal of Financial Markets 1, 203-219.

financeorvaluationjudgments,youhavetodeicideonyourcurrencyofanalysisandestimatethecostofdebtinthatcurrency.Consequently,ifyouarelookingataNestleproject,withcashflowsdenominatedinIndianrupees,youwillneedtoestimateacurrentlongtermcostofdebtforNestleinIndianrupees,evenifithasnorupeedebtoutstanding.Thatmayseemlikeadifficulttask, until you remember that currency differences are caused by differences in expectedinflation.AddingthedifferentialinflationbetweentheIndianrupeeandtheUSdollartoaNestleUS$costofdebtwillyieldarupeecostofdebt.

TheTaxBenefitofDebtTherearethreesimpleguidestoarrivingatthetaxbenefitofdebt.Thefirstistorememberthatinterestexpensessaveyoutaxesasthemargin,i.e.,itisthelastdollarsofincomethatyouprotectfromtaxation,leadingtothedecisiontousethemarginaltaxrate(whichcomesfromthetaxcodesandnotthecompanyfinancials).Thesecondistonotethatcompaniesthathaveincomeinmultiplecountriesgettodecidewhichofthesecountriestheywillborrowin,andthatdecisionisdrivenbythetaxbenefitsthataccrueineachcountry.Thus,amultinationalwithoperationsintheUS, EuropeandAsiawill generally borrowmostofwhat it needs in theUS, because themarginaltaxrateintheUSishigherthanthemarginaltaxratesinEuropeanorAsiancountries.Thethirdandoft-forgottenruleisthatacompanyneedstobemakingmoney,forthetaxbenefitfrom debt tomanifest. Hence, if you are assessing the cost of capital for a company that isexpectedtogenerateoperatinglossesinthenearterm,therewillbenotaxbenefitsfromdebtduringthatperiod.Whataboutthefactthatyouwillbeabletogeneratetaxbenefits,whenyoubecomeprofitableinthefuture?That’strue,butwhynotwaituntilthatisthecaseandchangeyourtaxratethentoreflectthesavingsinfutureperiods.

DebtWeightsThefinalinputthatyouneedtoarriveatacostofcapitalareweightsondebtandequity.Thoseweightscanhaveasignificantinfluenceonhowhighorlowthecostofcapitalwillbe,buthereagain,therearetwoissuesthatoftenchallengeanalysts.

Market versus Book Value

Thereare twochoiceswhen itcomestoweightingdebtandequity.One is tousetheaccountingbalancesheetvaluesfordebtandequity(bookvalues)toestimatethecostofcapitalandtheotheristhemarketvaluesforeachoftheseitems.Onthisone,therecanbenostraddlingthefence.Bookvalueweightsarenotonlyirrelevantwhenitcomestocostofcapitalbutcomewithproblemsthatcanbeinsurmountable.Forinstance,about10%ofallUScompaniesattheendof2015hadnegativebookvaluesofequity,eitherbecauseofsustainedlossesovertimeoraccountingspecialcharges,andunlessyouarewillingtoweightdebtmorethan100%andgiveequityanegativeweight,thecostofcapitalbecomesimpossibletoestimate. Therearesomewhoaretroubledbyaseeminginconsistencyinintrinsicvaluation,whereyouusemarketvaluesofequityanddebttoarriveatweightsinthecostofcapital,whichisthenusedasadiscountratetoarriveatintrinsicvaluesforequityanddebtthatmaybeverydifferentfromthemarketvalues.Ireconcilethisinconsistencysimplywithpubliclytradedcompanies,bynotingthatthecostofcapital ismycostofacquiringthecompanyinthemarketplacetoday,whereIwillhavetopaytheexistingmarketprices,andthattheintrinsicvaluethatIarriveatismy judgmentonwhat thesesharesareworth.Withprivatebusinessesandwith initialpublic

offerings,thisargumentmaynotcarrytheday,andwiththosecompanies,thereisasolution,thoughitwillrequiresomecomputationalgymnastics.Youcancomputeyourcostofcapital,withyourestimatedvaluesofequityanddebt,albeitwithcircularity,butusinganiterativefunction,willleadtoaconvergencewherethevaluesmatchup.13 There isone finalpractical concern.While themarketvalueofequity isusuallyeasilycomputedforapubliclytradedcompany,themarketvalueofdebtisamuchtoughernumbertofind,becauseasignificantportionofdebttakestheformofbankloans.Ifthatisthecase,youhavetwochoices.Oneistotaketheeasywayoutandassumethatthebookvalueofdebtisequaltomarketvalue,notabadassumptionifthedebtisrecentorifthecostofdebtforthecompanyhasnotchangedmuchsincethedebtissuance.Theotheristoestimateamarketvalueofdebt,usingtheexpectedinterestpayments,facevalueandmaturityofthedebt.

Hybrids

Hybridsecuritiespresentaproblemforanalysts,becausetheysharesomefeatureswithdebtandsomewithequityandarenoteasilypluggedintoeither.Aclassicexampleisconvertibledebt,wherethecoupon-bearingbondportionisdebtandtheconversionoptionisequity.Thesolutionhereistovalueeachpieceseparatelyandputit inwithitskind,thusdividingupthebond portion with debt and the conversion option with equity. A more difficult security ispreferredstock,atleastintheformthatitisissuedintheUnitedStates14,withdividendsthatarefixedatthetimeoftheissue(makingitmorelikedebt)butwithoutthetaxbenefitsorthelegal strength to force default (making it like equity). If you are valuing a company withsubstantialpreferredstock,itisbesttokeepitasathirdcomponentinthecostofcapitalandattachthepreferreddividendyield(obtainedbydividingthefixeddividendbythecurrentpriceofpreferredstock)toitasacost.

Dynamic Weighting

Theweightsthatyouattachtodebtandequity,whenfinancingacompany,willtendtoreflectitscurrentstandingandpolicy.Ifitisayoungcompany,losingmoneyormakingverylittleinprofits,itwilloftenchoosenottoborrowmoneyorborrowverylittle,makingthedebtratioyouuseinyourcostofcapitalalownumber.However,ifinyourforecasts,youaremakingthecompanyamoreprofitableandmaturebusiness,youshouldbeconsistentandallowthedebtratiotoriseovertimetowhatyouthinkthecompanycansustain in itsmaturephase.Thesechangingweightsondebtandequitywillalsomeanthatthecostsofequity,debtandcapitalwillchangeovertime. Thesameissuescansometimesshowupinindividualprojectanalysisincapitalbudgeting,where thedebtusedon aprojectmaybepaiddownover its life time. To theextent that acompanyhasaportfolioofprojectsatdifferentstagesintheirlives,itmaynotmakesensetoadjustcostsofcapitalforchangingdebtratios,inthiscase,buttouseanaveragedebtratioovertheprojectlifeinsteadasthedebtratiointhecostofcapital.

13 I use the iteration function in Excel to allow for these iterations. 14 There are parts of the world, especially Latin America, where preferred stock is common stock without voting rights and first claim on dividends, but with variable dividends. Those can be treated as equity in the cost of capital calculation.

LessonsTo close thispaper, Iwould like todraw somegeneral lessons, learned less fromany

theory that I havebeenexposedandmore from thepracticeof valuation, about the costofcapital.

Lesson 1: The Cost of Capital is important, but it is not (and should not be) the keyingredientinyourvaluationThenexttimeyouhaveaDCFvaluationtodo,takenoteofwhereyouspendyourtime.Iwillwagerthatyouspendfarmoretimeestimatingthecostofcapital(anddiscountrates)thanonyourexpectedcashflows,oftenlettinghistoricaltrendlinesdriverevenues,operatingincomeand reinvestment. If so, I think that you havemisallocated your time, since bigmistakes invaluationcomealmostalwaysfromgettingcashflowswrong,notdiscountrates.Therearetworeasonswhythisexcessivefocusondiscountratesismisplaced.First,lookingacrossallpubliclytradedcompanies,thespreadincostsofcapitalissurprisinglysmall,asevidencedinFigure16,whereIgraphoutthedistributionofcostsofcapitalacrossUScompanies:

Ofthealmost8000companiesmysample,about80%ofthecompanies(betweenthe10thand90thpercentile)hadcostsofcapitalbetween5.23%and10.00%.Ifyouhadtodoavaluationinahurryandusedthemediancostofcapitalof8.00%inyourvaluation,doyouthinkthatyouwillbeveryfarfromfairvalue?Second,thecostofcapitalforacompanywillchangeasthecompanychangesovertime.Thus,ayoung,money-losingstartupmayhaveacostofcapitalof11%,atthe95th percentile, when you start your valuation in year 1, but if you are projecting that thiscompanywillgrowandbecomeprofitableovertime,yourcostofcapitalwilldeclinetowards8%,themedianforthemarket.

Lesson2:Thecostofcapitalisnotareceptacleforallyourfearsandhopes.Analystsseemtoregarddiscountratesasreceptacleswheretheycandumptheirfearsaboutthefuture. Thus, if you are valuing a biotechnology companywith products that are in the FDApipeline,youfeeltheurgetoincreaseyourdiscountratetoreflectyourfearoffailure,justasventure capitalists pump up target rates of return for providing angel financing to youngcompanies,becausesomanyofthesecompanieswillnotmakeit.Attheriskofrepeatingmyself,the cost of capital is designed for going concerns and is much more suited for reflectingcontinuous(andmacroeconomics)risks.TheriskofanadverseFDArulingatthebiotechnologycompanyorfailure(atthestart-up)arerealrisksbuttheyarenotthetypesofrisksthatshouldbeyourcostof capital. Instead,youshouldconsiderprobabilisticapproaches (decision trees,simulations)tocapturetheserisks.

Lesson3:Justbecauseapracticeiswidespreaddoesnotmeanthatitisjustified.AsInotedwiththesmallcappremium,therearelotsofpracticesinestimatingcostofcapitalthathavedeeprootsandarewidelypracticed.Thatsaid,manyofthesepractices,whilejustifiedwhentheywereinitiated,nolongermakesense.Insomecases,thedatathatwehaveavailabletodayallowustoestimatethembetterandinothers,thedatathatsupportedtheiruseinthefirstplacenolongerexist.Thatsaid,changingthesepracticeswillnotbeeasy.

Lesson4:Watchoutforagenda(orbias)drivencostsofcapitalThebiggestenemyofgoodvaluationsarethepreconceptionsandbiasesthatwebringintothem.Thosebiasesaresometimestheresultofbehavioralquirksbutmoreoftentheyreflectwhyyouareestimatingthecostofcapitalinthefirstplace.Ifyouareestimatingthecostofcapitaltousetovalueabusinessfortaxpurposes,forthetaxpayer,youwillfindwaystoincreaseyourcostofcapital(byaddingsmallcap,liquidityandcompanyspecificriskpremiumstoyourbaseexpectedreturn)andlowervalue.If,incontrast,youarevaluingthesamebusinessforthetaxauthorities,yourchoiceswillbedrivenbytheneedtolowerthecostofcapitalandincreasevalue.

ConclusionThecostofcapitalisubiquitousinfinance,showingupinalmosteverydimensionofcorporatefinance,drivinginvestingdecisions,determiningfinancingchoicesandaffectingdividendpolicyandinintrinsicvaluation,asthediscountratetoadjustcashflowsforriskandtimevalue.Thatsaid,itisoftenmangledandmisusedinpracticeandthispaperismyattempttomakesenseofit.Iunderstandthattherecanbedifferencesofopiniononhowbesttoestimateitscomponentsbutitstillhastobeestimatedconsistentlyandviewedasadynamicnumberthatcanchangeasmacroenvironmentsandcompanieschange.