搜索
CORPORATEFINANCIALCORPORATEFINANCIALMANAGEMENTMANAGEMENTPARTIIDETERMINANTSOFVALUATION(chapter4-7)Chapter4Chapter4TheTimeValueofMoneyIntroductionIntroductionIntroductionIntroduction1.Interest2.FutureValueandPresentValue3.Annuity4.UnevenpaymentNotationNotationItodenotesimpleinterestitodenotetheinterestrateperperiodntodenotethenumberofperiodsPMTtodenotecashpaymentPVtodenotethepresentvaluedollaramountttodenotetimeTtodenotethetaxratePV0=principalamountattime0FVn=futurevaluentimeperiodsfromtime051.Interest1.InterestzSimpleInterest–InterestpaidontheprincipalsumonlyzCompoundInterest–InterestpaidontheprincipalandonpriorinterestthathasnotbeenpaidorwithdrawnzInFinance,CompoundInterestismoreimportantFigure4.1Simpleinterestandcompoundinterest(PMT=$1,000;i=6%)...continued...continued7...continued...continuedFigure4.2Growthofa$100InvestmentatVariousCompoundInterestRates82.Futurevalue2.Futurevaluez“Howmuchisadollarworthlater?”AttheendofyearnforasumcompoundedatinterestrateiisFVn=PV0(1+i)nFormulaInTableIinthetext,(FVIFi,n)showsthefuturevalueof$1investedfornyearsatinterestratei:FVIFi,n=(1+i)nTableIWhenusingthetable,FVn=PV0(FVIFi,n)......continuedcontinuedInterestfactors(IF)Timeperiods(n)Interestratesperperiod(i)Ifyouknowanytwo,youcansolvealgebraicallyforthethirdvariable.z“Howmuchisadollarinthefutureworthtoday?”PV0=FVn[]FormulaPVIFi,n=TableIIPV0=FVn(PVIFi,n)TableII1(1+i)n1(1+i)nPresentValuePresentValue11Figure4.3PresentValueof$100atVariousDiscountRates...continued...continued12......continuedcontinued•WhatisthePVof$100oneyearfromnowwith12percentinterestcompoundedmonthly?PV0=$100×1/(1+.12/12)(12×1)=$100×1/(1.126825)=$100×(.88744923)=$88.74PV0=FVn(PVIFi,n)=$100(.887)FromTableII=$88.70SpecialProblemsSpecialProblemszSolvingfortheinterestratezSolvingforthenumberofcompoundingperiodsInterestcompoundedInterestcompoundedmorefrequentlythanonceperyearmorefrequentlythanonceperyearm=#oftimesinterestiscompoundedn=#ofyearsnm=numberofperiodsFutureValuenmnom0nmi1PVFV)(+=PresentValue)nmminom(1+FVnPV0=EffectiveinterestrateEffectiveinterestratezEffectiveinterestrate:theactualrateofinterestsoitisthemosteconomicallyrelevantinterestratezNominalinterestrate:theperiodrateofinterestthatisstatedinaloanagreementorsecurity–Effectiveannualrateofinterestieff=(1+inom/m)m–1–Rateofinterestpercompoundingperiodim(annual/quarterly/monthly)thatwillyieldtheeffectiverateieffim=(1+ieff)1/m–116zAseriesofequaldollarCFsforaspecifiednumberofperiodszOrdinaryAnnuity(PVAN,FVAN)iswheretheCFsoccurattheendofeachperiod.Example:paycheck,interestpaymentszAnnuityDue(PVAND,FVAND)iswheretheCFsoccuratthebeginningofeachperiod.Examples:apartmentrent,insurancepremiums3.Annuity3.Annuity1)ordinaryannuity1)ordinaryannuity----------FVFVzFVIFAi,n==FormulaforIFzFVANn=PMT(FVIFAi,n)TableIIIzSinkingfundproblem:determinetheannuityamountthatmustbeinvestedeachyeartoproduceafuturevaluePMT=FVANn/(FVIFAi,n)TableIII(1+i)n–1i∑=−+ntti11)1(18Figure4.4TimelineoftheFutureValueofanOrdinaryAnnuity(PMT=$1,000;i=6%;n=3)zPVIFAi,n==FormulazPVAN0=PMT(PVIFAi,n)TableIVzCapitalrecoveryproblem:determinetheannuityamountnecessarytorecoversomeinitialinvestmentzLoanamortizationproblem:determinethepaymentsnecessarytopayofforamortizealoanPMT=PVAN0/(PVIFAi,n)TableIVi)i1(1n−+−1)ordinaryannuity1)ordinaryannuity----------PVPV∑=−+ntti1)1(Figure4.5TimelineofaPresentValueofanOrdinaryAnnuity(PMT=$1,000;i=6%;n=5)2)2)AnnuitydueAnnuityduezFutureValueofanAnnuityDueFVANDn=PMT(FVIFAi,n)(1+i)TableIII=PMT=PMT(FVIFAi,n+1-1)zPresentValueofanAnnuityDuePVAND0=PMT(PVIFAi,n)(1+i)TableIV=PMT=PMT(PVIFAi,n-1+1⎥⎦⎤⎢⎣⎡−−++11)1(1iin⎥⎦⎤⎢⎣⎡++−−−1)1(1)1(iin22Figure4.6TimelineoftheFutureValueofanAnnuityDue(PMT=$1,000;i=6%;n=3))Figure4.7TimelineofaPresentValueofanAnnuityDue(PMT=$1,000;i=6%;n=5)3)Deferredannuity3)DeferredannuityzDeferredannuity:anannuitybeginsmorethanoneyearinthefuturezPVAN0=PMT=PMT(PVIFAi,n)(PVIFi,m)Formulam=deferredperiodzPVAN0=PMT=PMT[(PVIFAi,m+n)(PVIFAi,m)]Formula⎥⎦⎤⎢⎣⎡+−−iin)1(1mi−+)1(⎥⎦⎤⎢⎣⎡+−−+−−+−iiiimnm)1(1)1(1)(25Figure4.8TimelineofaDeferredFour-YearAnnuity(i=12%)4)4)PerpetuityPerpetuityzPerpetuity:afinancialinstrumentthatpromisestopayanequalcashflowperperiodforever/aninfiniteseriesofannuityzPVPER0=PMT=PMTn,1+i-nPVPER0=FormulaExample:preferredstockdividendsiPMT∑=−+ntti1)1(⎥⎦⎤⎢⎣⎡+−−iin)1(144..UnevenpaymentUnevenpaymentzPVofanunevenpaymentstream(usefulincapitalbudgeting)–takeindividualpaymentpresentvaluesandaddthemupFigure4.9TimelineofaPresentValueofUnequalPayments(i=10%;n=5)Chapter6Chapter6Fixed-IncomeSecurities:CharacteristicsandValuationIntroductionIntroductionIntroductionIntroduction1.Characteristicsoflong-termdebt2.Valuationofassets3.Bondvaluation4.Characteristicsofpreferredstock5.Valuationofpreferredstock1.Characteristicsoflong-termdebtzTypesoflong-termdebt–Mortgagebondssecured–DebenturesunsecuredSubordinatedandunsubordinated–ConvertibleBond–WarrantBond–FloatingRateBond–Incomebonds......continuedcontinuedzU.S.governmentdebtsecurities–U.S.TreasurybillsS-TMaturitiesof3,6,and12monthsMinimumdenominationsof$10,000Soldatadiscountfromm