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当前位置:首页 > 商业/管理/HR > 企业财务 > 财务管理(英文第十三版)ch 3_sheena
TimeValueofMoneyTheInterestRateSimpleInterestCompoundInterestCompoundingMoreThanOnceperYearAmortizingaLoanPresentValueValuetodayofafuturecashflow.FutureValueAmounttowhichaninvestmentwillgrowafterearninginterestDiscountRateInterestrateusedtocomputepresentvaluesoffuturecashflows.DiscountFactorPresentvalueofa$1futurepayment.Obviously,$10,000today.ThereasonisthatthereisTIMEVALUEOFMONEY!!Whichwouldyouprefer--$10,000todayor$10,000in5years?TIMEallowsyoutheopportunitytopostponeconsumptionandearnINTEREST.WhyisTIMEsuchanimportantelementinyourdecision?CompoundInterest•Interestpaid(earned)onanypreviousinterestearned,aswellasontheprincipalborrowed(lent).•InterestonInterestSimpleInterestInterestpaid(earned)ononlytheoriginalamount,orprincipal,borrowed(lent).FormulaSI=P0(i)(n)SI:SimpleInterestP0:Deposittoday(t=0)i:InterestRateperPeriodn:NumberofTimePeriodsSI=P0(i)(n)=$1,000(.07)(2)=$140Assumethatyoudeposit$1,000inanaccountearning7%simpleinterestfor2years.Whatistheaccumulatedinterestattheendofthe2ndyear?FV=P0+SI=$1,000+$140=$1,140FutureValueisthevalueatsomefuturetimeofapresentamountofmoney,oraseriesofpayments,evaluatedatagiveninterestrate.WhatistheFutureValue(FV)ofthedeposit?ThePresentValueissimplythe$1,000youoriginallydeposited.Thatisthevaluetoday!P0=FV-SIPresentValueisthecurrentvalueofafutureamountofmoney,oraseriesofpayments,evaluatedatagiveninterestrate.WhatisthePresentValue(PV)ofthepreviousproblem?050001000015000200001stYear10thYear20thYear30thYearFutureValueofaSingle$1,000Deposit10%SimpleInterest7%CompoundInterest10%CompoundInterestFutureValue(U.S.Dollars)Assumethatyoudeposit$1,000atacompoundinterestrateof7%for2years.012$1,000FV27%FV1=P0(1+i)1=$1,000(1.07)=$1,070CompoundInterestYouearned$70interestonyour$1,000depositoverthefirstyear.Thisisthesameamountofinterestyouwouldearnundersimpleinterest.FV1=P0(1+i)1FV2=P0(1+i)2GeneralFutureValueFormula:FVn=P0(1+i)norFVn=P0(FVIFi,n)SeeTableIFVIFi,nisonTableIattheendofthebookPeriod6%7%8%11.0601.0701.08021.1241.1451.16631.1911.2251.26041.2621.3111.36051.3381.4031.469JulieMillerwantstoknowhowlargeherdepositof$10,000todaywillbecomeatacompoundannualinterestrateof10%for5years.012345$10,000FV510%CalculationbasedonTableI:FV5=$10,000(FVIF10%,5)=$10,000(1.611)=$16,110[DuetoRounding]Calculationbasedongeneralformula:FVn=P0(1+i)nFV5=$10,000(1+0.10)5=$16,105.10Wewillusethe“Rule-of-72”Quick!Howlongdoesittaketodouble$5,000atacompoundrateof12%peryear(approx.)?a)72/12%=6Yearsorb)72/6years=12%Assumethatyouneed$1,000in2years.Let’sexaminetheprocesstodeterminehowmuchyouneedtodeposittodayatadiscountrateof7%compoundedannually.012$1,0007%PV1PV0GeneralFutureValueFormula:FVn=PV0(1+i)nFVn=PV0(FVIFi,n)GeneralPresentValueFormula:PV0=FVn/(1+i)norPV0=FVn(PVIFi,n)--SeeTable2PVIFi,nisonTableIIattheendofthebookPeriod6%7%8%1.943.935.9262.890.873.8573.840.816.7944.792.763.7355.747.713.681JulieMillerwantstoknowhowlargeofadeposittomakesothatthemoneywillgrowto$10,000in5yearsatadiscountrateof10%.012345$10,00010%Calculationbasedongeneralformula:PV0=FVn/(1+i)nPV0=$10,000/(1+0.10)5=$6,209.21CalculationbasedonTable2:PV0=$10,000(PVIF10%,5)=$10,000(.621)=$6,210.00[DuetoRounding]Ifyouinvest$1,000today,youwillreceive$3,000inexactly8years.Whatisthecompoundinterestrateimplicitinthissituation?FVn=PV0(FVIFi,n)(FVIFi,8)=FV8/PV0=3,000/1,000=3i=14.68%Howlongwouldittakeforaninvestmentof$1,000togrowto$1,900ifweinvesteditatacompoundannualinterestrateof10percent?FVn=PV0(FVIFi,n)(FVIF10%,n)=FVn/PV0=1,900/1,000=1.9n=6.72yearsWhatisthefuturevalueof$1millioninvestedat10percentfor25years?◦FVn=PV0(FVIFi,n)◦FV25=PV0(FVIF10%,25)=$1,000,000*10.835=$10,835,000Youneed$30,000incashtobuyahouse4yearsfromtoday.Youexpecttoearn5percentonyoursavings.Howmuchdoyouneedtodeposittodayifthisistheonlymoneyyousaveforthispurpose?◦PV0=FVn(PVIFi,n)◦PV0=FV4(PVIF5%,4)=$30,000*0.823=$246,900Yourfirmhasbeentoldthatitneeds$74,300todaytofunda$120,000expense6yearsfromnow.Whatrateofinterestwasusedinthecomputation?◦FVn=PV0(FVIFi,n)◦(FVIFi,6)=FV6/PV0=120,000/74,300=1.615i=8.3%OrdinaryAnnuity:Paymentsorreceiptsoccurattheendofeachperiod.AnnuityDue:Paymentsorreceiptsoccuratthebeginningofeachperiod.AnAnnuityrepresentsaseriesofequalpayments(orreceipts)occurringoveraspecifiednumberofequaldistantperiods.StudentLoanPaymentsCarLoanPaymentsInsurancePremiumsMortgagePaymentsRetirementSavings0123$100$100$100EndofPeriod1EndofPeriod2TodayEqualCashFlowsEach1PeriodApartEndofPeriod30123$100$100$100BeginningofPeriod1BeginningofPeriod2TodayEqualCashFlowsEach1PeriodApartBeginningofPeriod3Itisanordinaryannuitywhosepaymentsorreceiptscontinueforever.PVA∞=R/ITheABSCo.wantstoofferpreferredstockforsaleatapriceof$60ashare.Ifthecompanywantstheirinvestorstoearnatleasta7.5percentrateofreturn,whatistheminimumannualdividendtheywillneedtopaypershare?◦R=PVA∞*i=60*7.5%=$4.5FVAn=R(FVIFAi,n)PVAn=R(PVIFAi,n)FVADn=R(FVIFAi,n)(1+i)PVADn=(1+i)(R)(PVIFAi,n)RistheperiodreceiptWhatisthefuturevalueofannualpaymentsof$6,500foreightyearsat12percent?FVAn=R(FVIFAi,n)FVA8=$6,500*(FVIFA12%,8
本文标题:财务管理(英文第十三版)ch 3_sheena
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