财务管理基础课件：Valuation and Rates of Return

ValuationandRatesofReturn

ChapterOutlineValuationofassets,basedonthepresentvalueoffuturecashflowsTherequiredrateofreturninvaluinganassetbasedontheriskinvolvedBondvaluationanddeterminationofpresentvalueofinterestandmaturitypaymentsPreferredstockvaluationbasedondividendpaidStockvaluationanddeterminationofpresentvalueoffuturebenefitsValuationofFinancialAssetsHelpsinevaluatingfinancialcommitmentafirmneedstomaketo:StockholdersandbondholdersAttractinvestmentCostofcorporatefinancing(capital)isusedinanalyzingthefeasibilityofaninvestmentonanensuingprojectTherelationshipbetweentimevalueofmoney,requiredreturn,costoffinancing,andinvestmentdecisionsisshowninthefollowingdiagram:ValuationConceptsValuationofafinancialassetisbasedondeterminingthepresentvalueoffuturecashflowsRequiredrateofreturn(thediscountrate)Dependsonthemarket’sperceivedlevelofriskassociatedwiththeindividualsecurityItisalsocompetitivelydeterminedamongcompaniesseekingfinancialcapitalImplyingthatinvestorsarewillingtoacceptlowreturnforlowriskandviceversaEfficientuseofcapitalinthepastresultsinalowerrequiredrateofreturnforinvestorsValuationofBondsAbondprovidesanannuitystreamofinterestpaymentsandaprincipalpaymentatmaturityCashflowsarediscountedatY(yieldtomaturity)ValueofYisdeterminedinthebondmarketThepriceofthebondisequalto:ThepresentvalueofregularinterestpaymentsdiscountedatYAddedtothepresentvalueoftheprincipal(alsodiscountedatY)ValuationofBonds(cont’d)Where:=Priceofthebond;=Interestpayments;=Principalpaymentatmaturity;t=Numbercorrespondingtoaperiod(runningfrom1ton);n=Numberofperiods;Y=Yieldtomaturity(orrequiredrateofreturn)Assuminginterestpayments()=$100;principalpaymentsatmaturity()=$1,000;yieldtomaturity(Y)=10%andtotalnumberofperiods(n)=20.Thus,thepriceofbonds();PresentValueofInterestPaymentsTodeterminethepresentvalueofa$100annuityfor20years,withadiscountrateof10%Wehave:PresentValueofPrincipalPayment(ParValue)atMaturityPrincipalpaymentatmaturityisusedinterchangeablywithparvalueorfacevalueofthebondDiscounting$1,000backtothepresentat10%,wehave:Thecurrentpriceofthebond,basedonthepresentvalueofinterestpaymentsandthepresentvalueoftheprincipalpaymentatmaturity:Here,thepriceofthebondisessentiallythesameasitspar,orstatedvaluetobereceivedatmaturityof$1,000ConceptofYieldtoMaturityTheyieldtomaturityorthediscountrateistherequiredrateofreturnrequiredbybondholdersThreefactorsinfluencetherequiredrateofreturn:RequiredrealrateofreturnDemandedbytheinvestoragainstcurrentuseofthefundsonanon-adjustedbasisInflationpremiumCompensationtowardsthenegativeeffectofinflationonthevalueofadollarRiskfreerateofreturncompensatesfortheuseoffundsandlossduetoinflationRiskpremiumTowardsspecialrisksofaninvestmentConceptofYieldtoMaturity(cont’d)BusinessRisk:inabilityofthefirmtoretainitscompetitivepositionandstabilityandgrowthFinancialrisk:inabilityofthefirmtomeetitsdebtobligationsasandwhendueAssuming:Therealrateofreturn3%,inflationpremium4%andriskpremiumis3%,anoverallrequiredrateofreturnof10%canbecomputed;PriceofaBondwithIncreaseinInflationPremiumAssumeInflationpremiumgoesupfrom4to6%,witheverythingelsebeingconstantPresentvalueofinterestpayments:$100annuityfor20yearsatadiscountrateof12%;PriceofaBondwithIncreaseinInflationPremium(cont’d)Presentvalueofprincipalpaymentatmaturity:Presentvalueof$1,000after20yearsatadiscountrateof12%;Totalpresentvalue:Assumingthatincreasedinflationincreasesrequiredrateofreturnanddecreasesthebondpriceby$150approximatelyPriceofaBondwithDecreaseinInflationPremiumAssumingthattheinflationpremiumdeclines:Therequiredrateofreturndecreaseto8%,wherethe20yearbondwitha10%interestratewouldnowsellfor;PresentvalueofinterestpaymentsPresentvalueofprincipalpaymentatmaturityTotalpresentvalueBondPriceTableThefurthertheyieldtomaturityonabondchangesfromthestatedinterestrateonthebond,thegreaterthepricechangeeffectwillbe.Thefollowingtableillustratestheimpactofdifferencesbetweenyieldtomaturityandcouponratesonbondprices.TimetoMaturityInfluencestheimpactofachangeinyieldtomaturityonvaluationLongerthematurity,thegreatertheimpactofchangesinyieldImpactofTimetoMaturityonBondPricesTheamount(premium)aboveparvalueisreducedasthenumberofyearstomaturitybecomessmallerandsmallerTheamount(discount)belowparvalueisreducedwithprogressivelyfeweryearstomaturityThefollowingtableshowsthecriticaleffectoftimetomaturityonbondpricesensitivityRelationshipBetweenTimetoMaturityandBondPriceDeterminingYieldtoMaturityfromtheBondPriceTheyieldtomaturity(Y),thatwillequatetheinterestpayments()andtheprincipalpayments()tothepriceofthebond()DeterminingYieldtoMaturityfromtheBondPrice(cont’d)Assumingthata15yearbondpays$110peryear(11%)ininterestand$1,000after15yearsinprincipalrepaymentChoosing13%asaninitialdiscountrate,wehave:Presentvalueofinterestpayments:PresentvalueofprincipalpaymentatmaturityTotalpresentvalueDeterminingYieldtoMaturityfromtheBondPrice(cont’d)Presentvalueofinterestpaymentsat12%PresentvalueofprincipalpaymentatmaturityTotalpresentvalueFormulaforBondYieldWeightedaverageisusedtogettheaverageinvestmentover15yearholdingperiod,principal

payment$1,000,withannualinterestpayment$110andpriceoftheBondis$932.21

*

*ThisformulaisdevelopedbyGabrielA.HawawiniandAshokVora,“YieldApproximations:AHistoricalPerspective,”JournalofFinance37(March1982),pp.145–56.SemiannualInterestandBondPricesA10%interestratemaybepaidas$50twiceayearinthecaseofsemiannualpaymentsTomaketheconversion:DividetheannualinterestratebytwoMultiplythenumberofyearsbytwoDividetheannualyieldtomaturitybytwoAssuminga10%,$1,000parvaluebondhasamaturityof20years,theannualyieldat12%10%/2=5%semiannualinterestrate;hence5%×$1,000=$50semiannualinterest20×2=40periodstomaturity12%/2=6%yieldtomaturity,expressedonasemiannualbasisSemiannualInterestandBondPrices(cont’d)Atapresentvalueofa$50annuityforthe40periods,atdiscountrateof6%:PresentvalueofinterestpaymentsPresentvalueofprincipalpaymentatmaturityTotalpresentvalueValuationandPreferredStockPreferredstockrepresentsaperpetuity,havingnomaturitydateIthasafixeddividendpaymentIthasnobindingcontractualobligationofinterestondebtBeingahybridsecurity,itdoesnothave:TheownershipprivilegeofacommonstockThelegalprovisionsthatcouldbeenforcedondebtPerpetuityofaPreferredStockWhere,=thepriceofthepreferredstock;=theannualdividendforthepreferredstock(constant);=requiredrateofreturn(discountrate)appliedtopreferredstockdividendsAmoreusableformulais:Assuming,theannualdividendis$10,andthestockholderrequiresa10%rateofreturn,thepriceofthepreferredstockwouldbe:PerpetuityofaPreferredStock(cont’d)Iftherateofreturnrequiredbysecurityholderschange,thevalueofthepreferredstockalsochangesThelongertheperiodofaninvestment,thegreatertheimpactofachangeintherequirerateofreturnWithperpetualsecurity,theimpactisatamaximumAssumingthattherequiredrateofreturnhasincreasedto12%.Thevalueofthepreferredstockwouldbe:Ifitwerereducedto8%,thevalueofthepreferredstockwouldbe:DeterminingtheRateofReturn(Yield)fromtheMarketPriceAssumingtheannualpreferreddividend()is$10andthepriceofthepreferredstock()is$100,therequiredrateofreturn(yield):Ahighermarketpriceprovidesquiteadeclineintheyield:ValuationofCommonStockInterpretedbytheshareholderasthepresentvalueofanexpectedstreamoffuturedividendsTheultimatevalueofanyholdinglieswith:ThedistributionofearningsintheformofdividendpaymentsTheearningsmustbetranslatedintocashflowforthestockholderDividendValuationModelWhere,=Priceofstocktoday;D=Dividendforeachyear;=therequiredrateofreturnforcommonstock(discountrate)Thisformula,withmodificationsisgenerallyappliedtothreedifferentsituations:NogrowthindividendsConstantgrowthindividendsVariablegrowthindividendsNoGrowthinDividendsThecommonstockpaysaconstantdividendasinthecaseofapreferredstockThisisnotaverypopularoption Where, =Priceofthecommonstock;=Currentannualcommonstockdividend(constant);=RequiredrateofreturnforcommonstockAssuming=$1.86and=12%,thepriceofthestockwouldbe:ConstantGrowthinDividendsThegeneralvaluationprocessisshown:Where,=Priceofcommonstocktoday=Dividendinyear1,=Dividendinyear2,,andsoong=Constantgrowthrateindividends=Requiredrateofreturnforcommonstock(discountrate)ConstantGrowthinDividends(cont’d)Assuming:=Last12month’sdividend(assume$1.87)=Firstyear,$2.00(growthrate,7%)=Secondyear,$2.14(growthrate,7%)=Thirdyear,$2.29(growthrate,7%)etc=Requiredrateofreturn(discountrate),12%ConstantGrowthDividendValuationModelTheformulashowncanbemodifiedtoasimpleformif:Thefirmmusthaveaconstantdividendgrowthrate(g)Thediscountrate(Ke)mustexceedthegrowthrate(g)Where: P0 =Priceofthestocktoday D1 =Dividendattheendofthefirstyear Ke =Requiredrateofreturn(discountrate)

g

=ConstantgrowthrateindividendsBasedonthecurrentexample;D1=$2.00;Ke=.12;g=.07.P0iscomputedas:StockValuationBasedonFutureStockValueAssumption:ToknowthepresentvalueofaninvestmentStockisheldonforthreeyearsandthensoldAddingthepresentvalueofthreeyearsofdividends,andthepresentvalueofthestockpriceafterthreeyearsgivesthepresentvalueofthebenefitsTheappropriateformulatobeusedis:DeterminingtheRequiredRateofReturnfromtheMarketPriceDeterminingtherequiredrateofreturn,knowingthefirstyear’sdividend,thestockprice,andthegrowthrate(g):Assuming;=Requiredrateofreturn(tobesolved)=Dividendattheendofthefirstyear,$2.00=Priceofthestocktoday,$40g=Constantgrowthrate7%,wehave:

=$2.00+7%=5%+7%=12%$40DeterminingtheRequiredRateofReturnfromMarketPrice(cont’d)ThestockholderisreceivingacurrentdividendplusanticipatedgrowthinthefutureIfthedividendyieldislow,thegrowthratemustbehightoprovidethenecessaryreturnIfthegrowthrateislow,ahighdividendyieldwillbeexpectedThefirsttermrepresentthedividendyieldthestockholderwillreceiveThesecondrepresentstheanticipatedgrowthindividends,earnings,andstockpricePrice-EarningsRatioConceptand