财务管理基础斯坦利布洛克Chapter(8)

FINANCIALMANAGEMENTChapter9TimeValueofMoneyInstructor:Dr.Renee,RenGuTheSchoolofEconomicsandCommerceSCUT,Guangzhou2013/11/21Today’sContentsSECTIONONEBASICCONCEPTS1.1WHATISTIMEVALUE?1.2WHATISPRESENTVALUE?1.3WHATISFUTUREVALUE?1.4CASHFLOWTIMELINE1.1WhatIsTimeValue?Moneyhasatimevalueassociatedwithitandthereforeadollarreceivedtodayisworthmorethanadollarreceivedinthefuture.•Theinvestordemandsthatfinancialrent,thereturnonaninvestment,bepaidonhisorherfunds.•Understandingtheeffectiverateonabusinessloan,etc.,isdependentonusingthetimevalueofmoney.Theinvestor/lenderThetimevalueofmoneyisthevalueofmoneyfiguringinagivenamountofinterestearnedoveragivenamountoftime1.2Whatispresentvalue(PV)?Howmuchtheamountthatyouwillreceiveinthefutureareworthnow?(Itisthevalueonagivendateofafuturepayment.)DISCOUNTINGItiswidelytoprovideameanstocomparecashflowsatdifferenttimesonameaningfulliketolikebasis.1.3Whatisfuturevalue(FV)?Howmuchwhatyoureceivenowgrowstowhencompoundedatagivenrate?Futurevalueisthevalueofanassetataspecificdate.Thefuturevalueandpresentvalueofadollarisbasedonthenumberofperiodsinvolvedandthegoinginterestrate.CAPITALIZATION1.4Analytictool–cashflowtimelineDefinitionLinedepictingtheoperatingactivitiesandcashflowsforafirmoveraparticularperiod.01234-1005%500CashFlowTimelineofFV01234-100010%1100（$1,000×1.10）1,210（×1.10）1,331（×1.10）1,464（×1.10）?CashFlowTimelineofPV1,464÷1.1time01234?10%÷1.1÷1.1÷1.11,000SECTIONTWOSINGLEAMOUNTVSANNUITY1.FutureValueofASingleAmount2.PresentValueofASingleAmount3.FutureValueofAnAnnuity4.PresentValueofAnAnnuity5.DeterminingtheAnnuityValue6.DeterminingtheYieldonanInvestmentTomeasurethevalueofanamountthatisallowedtogrowatagiveinterestrateoveraperiodoftime.1.FutureValue-SingleAmountAssumeaninvestorhas$1000andwishestoknowitsworthafterfouryearsifitgrowsat10%peryear.1styear$1,000×1.10=$1,1002ndyear$1,100×1.10=$1,2103rdyear$1,210×1.10=$1,3314thyear$1,331×1.10=$1,464CashFlowTimelinetime01234-100010%11001,2101,3311,464（$1,000×1.10）（×1.10）（×1.10）（×1.10）?)i+PV(1=FVnFV=FutureValuePV=PresentValuei=theinterestrateperperiodn=thenumberofcompoundingperiodsSimpleFormula:Inthiscase,PV=$1,000,i=10%,n=4,soFV=?FV=$1,000×(1.1)4=$1,464Quickerprocess：AppendixATheformulamayberestatedas:FVxPV=FVIFTherelationshipmaybeexpressedbythefollowingformula:theinterestfactorTheFVIFtermisfoundinTable9-1QuickerProcess–aninterestratetableperiods1%2%4%6%8%10%11.0101.0201.0401.0601.0801.10021.0201.0401.0821.1241.1661.21031.0301.0611.1251.1911.2601.33141.0411.0821.1701.2621.3601.46451.0511.1041.2171.3381.4691.611101.1051.2191.4801.7912.1592.594201.2201.4862.1913.2074.6616.727FutureValueof$1(Table9-1)2.PresentValue--SingleAmount•Thepresentvalueofafuturesumistheamountinvestedtoday,atagiveninterestrate,thatwillequalthefuturesumataspecifiedpointintime.discountrateCashFlowTimeLine1,464÷1.1time01234?10%÷1.1÷1.1÷1.11,000RelationshipofPVandFV•Therelationshipmaybeexpressedinthefollowingformula:)i+(11FV=PVn•Theformulamayberestatedas:PVxFV=PVIFThePVIFtermisfoundinTable9-2Quickerprocess：AppendixBDiscountFactorPresentValueDiscountFactor=DF=PVof$1DiscountFactorscanbeusedtocomputethepresentvalueofanycashflow.DFrt=+11()PresentValueof$1(Table9-2)periods1%2%4%6%8%10%10.9900.9800.9620.9430.9260.90920.9800.9610.9250.8900.8570.82630.9710.9420.8890.8400.7940.75140.9610.9240.8550.7920.7350.68350.9510.9060.8220.7470.6810.621100.9050.8200.6760.5580.4630.386200.8200.6730.4560.3120.2150.149ValuinganOfficeBuildingStep1:ForecastcashflowsCostofbuilding=C0=350SalepriceinYear1=C1=400Step2:EstimateopportunitycostofcapitalIfequallyriskyinvestmentsinthecapitalmarketofferareturnof7%,thenCostofcapital=r=7%ValuinganOfficeBuildingStep3:DiscountfuturecashflowsStep4:GoaheadifPVofpayoffexceedsinvestment374)07.1(400)1(1===++rCPV24374350=+−=NPVNetPresentValuerC++1C=NPVinvestmentrequired-PV=NPV103.FutureValue--Annuity3.1DefinitionAnannuityrepresentsconsecutivepaymentsorreceiptsofequalamount.Note:Theannuityvalueisnormallyassumedtotakeplaceattheendoftheperiod.(OrdinaryAnnuity)Thefuturevalueofanannuityrepresentsthesumofthefuturevalueoftheindividualflows.3.2ordinaryannuityIfweinvest$1,000attheendofeachyearforfouryearsandourfundsgrowat10%,whatisthefuturevalueofthisannuity?Thefuturevaluefortheannuityis4,641.Pleasetrytodrawthetimeline.Compoundingprocessforannuity01234$1,000$1,000×1.100=1,100$1,000×1.210=1,210$1,000×1.331=1,331Thefuturevaluefortheannuityis4,641.1,0001,0001,00010%Theformulaforthefuturevalueforanannuityis:FVA=A×FVIFAProofprocess:1210(1)(1)(1)(1)nnAFVAiAiAiAi−−=+++++++(1)1nIFAiAAFVi+−==×Ifawealthyrelativeofferedtosetaside$2,500ayearforyouforthenext20years,howmuchwouldyouhaveinyouraccountafter20yearsifthefundsgrewat8%?Theanswerisasfollows:FVA=A×FVIFA(n=20,I=8%)TheFVIFAtermisfoundinTable9-3.(P231)3.3AnnuityDue•Ifweinvest$1,000attheBEGINNINGofeachyearforfouryearsandourfundsgrowat10%,whatisthefuturevalueofthisannuity?01234$1,0001,0001,0001,00010%$1,000×1.12=1,210$1,000×1.13=1,331$1,000×1.14=1464$1,000×1.1=1,1006105Equation:(1)1()(1)(1)nIFAiFVdueAiAFVii+−=×+=×+Summary:FVxPV=FVIF