Ch 3 time value of money

8-1FuturevaluePresentvalueAnnuitiesRatesofreturnAmortizationCHAPTER3TimeValueofMoney8-2Timelinesshowtimingofcashflows.CF0CF1CF3CF20123i%Tickmarksatendsofperiods,soTime0istoday;Time1istheendofPeriod1;orthebeginningofPeriod2.8-3Timelinefora$100lumpsumdueattheendofYear2.100012Yeari%8-4Timelineforanordinaryannuityof$100for3years.1001001000123i%8-5TimelineforunevenCFs:-$50att=0and$100,$75,and$50attheendofYears1through3.10050750123i%-508-6SELF-TESTQUESTIONIP.958-7Whichwouldyouprefer--$10,000todayor$10,000in5years?YoualreadyrecognizethatthereisTIMEVALUETOMONEY!!TheInterestRate8-8TypesofInterestCompoundInterestInterestpaid(earned)onanypreviousinterestearned,aswellasontheprincipalborrowed(lent).SimpleInterestInterestpaid(earned)ononlytheoriginalamount,orprincipal,borrowed(lent).8-9SimpleInterestFormulaSI=SI:SimpleInterestP0:Deposittoday(t=0)i:InterestRateperPeriodn:NumberofTimePeriodsP0(1+ixn).8-10SimpleInterestExampleAssumethatyoudeposit$1,000inanaccountearning7%simpleinterestfor2years.Whatistheaccumulatedinterestattheendofthe2ndyear?8-11FutureValueisthevalueatsomefuturetimeofapresentamountofmoney,oraseriesofpayments,evaluatedatagiveninterestrate.SimpleInterest(FV)WhatistheFutureValue(FV，终值)ofthedeposit?FVn=PV0x(1+ixn)8-12CompoundInterest(FV)What’stheFVofaninitial$100after3yearsifi=10%?FV=?012310%Theprocessofgoingfromtoday’svalues,orpresentvalues,tofutureValuesiscalledcompounding.1008-13After1year:FV1=PV+INT1=PV+PV(i)=PV(1+i)=$100(1.10)=$110.00.After2years:FV2=PV(1+i)2=$100(1.10)2=$121.00.8-14After3years:FV3=PV(1+i)3=$100(1.10)3=$133.10.Ingeneral,FVn=PV(1+i)n.8-15ThreeWaystoFindFVsSolvetheequationwitharegularcalculator.Useafinancialcalculator.Useaspreadsheet.8-16Financialcalculatorssolvethisequation:Thereare4variables.If3areknown,thecalculatorwillsolveforthe4th.FVPVinn1.FinancialCalculatorSolution8-17310-1000NI/YRPVPMTFV133.10Here’sthesetuptofindFV:Clearingautomaticallysetseverythingto0,butforsafetyenterPMT=0.Set:P/YR=1,END.INPUTSOUTPUT8-18JulieMillerwantstoknowhowlargeherdepositof$10,000todaywillbecomeatacompoundannualinterestrateof10%for5years.StoryProblemExample012345$10,000FV510%8-1910%What’sthePVof$100duein3yearsifi=10%?FindingPVsisdiscounting,andit’sthereverseofcompounding.1000123PV=?8-20SolveFVn=PV(1+i)nforPV:PV=FV1+i=FV11+innnnPV=$10011.10=$1000.7513=$75.13.38-21Assumethatyouneed$1,000in2years.Let’sexaminetheprocesstodeterminehowmuchyouneedtodeposittodayatadiscountrateof7%compoundedannually.012$1,0007%PV1PV0PresentValueSingleDeposit(Graphic)8-22PV0=PresentValueSingleDeposit(Formula)012$1,0007%PV08-23JulieMillerwantstoknowhowlargeofadeposittomakesothatthemoneywillgrowto$10,000in5yearsatadiscountrateof10%.StoryProblemExample012345$10,000PV010%8-24PowerofcompoundinterestSupposeoneofyourmorefrugalancestorshadinvested$5foryouata6percentinterestrate200yearsago.Howmuchwouldyouhavetoday?8-25FinancialCalculatorSolution3100100NI/YRPVPMTFV-75.13EitherPVorFVmustbenegative.HerePV=-75.13.Putin$75.13today,takeout$100after3years.INPUTSOUTPUT8-26FindingtheTimetoDouble20%2012?-1FV=PV(1+i)n$2=$1(1+0.20)n(1.2)n=$2/$1=2nLN(1.2)=LN(2)n=LN(2)/LN(1.2)n=0.693/0.182=3.8.8-2720-102NI/YRPVPMTFV3.8INPUTSOUTPUTFinancialCalculator8-28SELF-TESTQUESTIONIIP.103SELF-TESTQUESTIONIIP.1048-29TypesofAnnuities(年金）OrdinaryAnnuity（普通年金）:Paymentsorreceiptsoccurattheendofeachperiod.AnnuityDue（即付年金）:Paymentsorreceiptsoccuratthebeginningofeachperiod.AnAnnuityrepresentsaseriesofequalpayments(orreceipts)occurringoveraspecifiednumberofequidistantperiods.8-30PartsofanAnnuity0123$100$100$100(OrdinaryAnnuity)EndofPeriod1EndofPeriod2TodayEqualCashFlowsEach1PeriodApartEndofPeriod38-31PartsofanAnnuity0123$100$100$100(AnnuityDue)BeginningofPeriod1BeginningofPeriod2TodayEqualCashFlowsEach1PeriodApartBeginningofPeriod38-32OrdinaryAnnuityPMTPMTPMT0123i%PMTPMT0123i%PMTAnnuityDueWhat’sthedifferencebetweenanordinaryannuityandanannuitydue?PVFV8-33ExamplesofAnnuitiesStudentLoanPaymentsCarLoanPaymentsInsurancePremiumsMortgagePaymentsRetirementSavings8-34FVAn=OverviewofanOrdinaryAnnuity--FVARRR012nn+1R=PeriodicCashFlowCashflowsoccurattheendoftheperiodi%...8-35What’stheFVofa3-yearordinaryannuityof$100at10%?100100100012310%110121FV=3318-36PVAn=OverviewofanOrdinaryAnnuity--PVARRR012nn+1PVAnR=PeriodicCashFlowi%...Cashflowsoccurattheendoftheperiod8-37PVA3=ExampleofanOrdinaryAnnuity--PVA$1,000$1,000$1,00001234$=PVA37%$934.58$873.44$816.30Cashflowsoccurattheendoftheperiod8-38PresentValueInterestFactorforanAnnuity(PVIFAi,n):Thepresentvalueinterestfactorforanannuityofnperiodsdiscountedatipercent.GeneralPresentValueFormula:PVAn=Ax(P/A,i,n)orPVAn=PMT(PVIFAi,n年金现值系数)--SeeTableA-2ExampleofanOrdinaryAnnuity--PVA8-39What’sthePVofthisordinaryannuity?100100100012310%90.9182.6475.13248.69=PV8-40FindtheFVandPViftheannuitywereanannuitydue.100100012310%1008-41FVADn=OverviewViewofanAnnuityDue--FVADRRRRR0123n-1nFVADni%...Cashflowsoccuratthebeginningoftheperiod8-42FVAD3=ExampleofanAnnuityDue--FVAD$1,000$1,000$1,000$1,07001234$=FVAD