CH07TimeValueofMoney(财务管理,英文版)

7-1Copyright©2001byHarcourt,Inc.Allrightsreserved.FuturevaluePresentvalueRatesofreturnAmortizationCHAPTER7TimeValueofMoney7-2Copyright©2001byHarcourt,Inc.Allrightsreserved.Timelinesshowtimingofcashflows.CF0CF1CF3CF20123i%Tickmarksatendsofperiods,soTime0istoday;Time1istheendofPeriod1;orthebeginningofPeriod2.7-3Copyright©2001byHarcourt,Inc.Allrightsreserved.Timelinefora$100lumpsumdueattheendofYear2.100012Yeari%7-4Copyright©2001byHarcourt,Inc.Allrightsreserved.Timelineforanordinaryannuityof$100for3years.1001001000123i%7-5Copyright©2001byHarcourt,Inc.Allrightsreserved.TimelineforunevenCFs-$50att=0and$100,$75,and$50attheendofYears1through3.10050750123i%-507-6Copyright©2001byHarcourt,Inc.Allrightsreserved.What’stheFVofaninitial$100after3yearsifi=10%?FV=?012310%100FindingFVsiscompounding.7-7Copyright©2001byHarcourt,Inc.Allrightsreserved.After1year:FV1=PV+INT1=PV+PV(i)=PV(1+i)=$100(1.10)=$110.00.After2years:FV2=PV(1+i)2=$100(1.10)2=$121.00.7-8Copyright©2001byHarcourt,Inc.Allrightsreserved.After3years:FV3=PV(1+i)3=100(1.10)3=$133.10.Ingeneral,FVn=PV(1+i)n.7-9Copyright©2001byHarcourt,Inc.Allrightsreserved.FourWaystoFindFVsSolvetheequationwitharegularcalculator.Usetables.Useafinancialcalculator.Useaspreadsheet.7-10Copyright©2001byHarcourt,Inc.Allrightsreserved.Financialcalculatorssolvethisequation:FVn=PV(1+i)n.Thereare4variables.If3areknown,thecalculatorwillsolveforthe4th.FinancialCalculatorSolution7-11Copyright©2001byHarcourt,Inc.Allrightsreserved.Here’sthesetuptofindFV:Clearingautomaticallysetseverythingto0,butforsafetyenterPMT=0.Set:P/YR=1,ENDINPUTSOUTPUT310-1000NI/YRPVPMTFV133.107-12Copyright©2001byHarcourt,Inc.Allrightsreserved.10%What’sthePVof$100duein3yearsifi=10%?FindingPVsisdiscounting,andit’sthereverseofcompounding.1000123PV=?7-13Copyright©2001byHarcourt,Inc.Allrightsreserved.SolveFVn=PV(1+i)nforPV:nnnni+11FV=i+1FV=PVPV=$10011.10=$100PVIF=$1000.7513=$75.13.i,n÷3.7-14Copyright©2001byHarcourt,Inc.Allrightsreserved.FinancialCalculatorSolution3100100NI/YRPVPMTFV-75.13EitherPVorFVmustbenegative.HerePV=-75.13.Putin$75.13today,takeout$100after3years.INPUTSOUTPUT7-15Copyright©2001byHarcourt,Inc.Allrightsreserved.Ifsalesgrowat20%peryear,howlongbeforesalesdouble?Solveforn:FVn=1(1+i)n;2=1(1.20)nUsecalculatortosolve,seenextslide.7-16Copyright©2001byHarcourt,Inc.Allrightsreserved.20-102NI/YRPVPMTFV3.8GraphicalIllustration:0123412FV3.8YearINPUTSOUTPUT7-17Copyright©2001byHarcourt,Inc.Allrightsreserved.OrdinaryAnnuityPMTPMTPMT0123i%PMTPMT0123i%PMTAnnuityDueWhat’sthedifferencebetweenanordinaryannuityandanannuitydue?7-18Copyright©2001byHarcourt,Inc.Allrightsreserved.What’stheFVofa3-yearordinaryannuityof$100at10%?100100100012310%110121FV=3317-19Copyright©2001byHarcourt,Inc.Allrightsreserved.3100-100331.00FinancialCalculatorSolutionHavepaymentsbutnolumpsumPV,soenter0forpresentvalue.INPUTSOUTPUTI/YRNPMTFVPV7-20Copyright©2001byHarcourt,Inc.Allrightsreserved.What’sthePVofthisordinaryannuity?100100100012310%90.9182.6475.13248.68=PV7-21Copyright©2001byHarcourt,Inc.Allrightsreserved.HavepaymentsbutnolumpsumFV,soenter0forfuturevalue.3101000-248.69INPUTSOUTPUTNI/YRPVPMTFV7-22Copyright©2001byHarcourt,Inc.Allrightsreserved.FindtheFVandPViftheannuitywereanannuitydue.100100012310%1007-23Copyright©2001byHarcourt,Inc.Allrightsreserved.3101000-273.55Switchfrom“End”to“Begin.”ThenentervariablestofindPVA3=$273.55.ThenenterPV=0andpressFVtofindFV=$364.10.INPUTSOUTPUTNI/YRPVPMTFV7-24Copyright©2001byHarcourt,Inc.Allrightsreserved.WhatisthePVofthisunevencashflowstream?010013002300310%-50490.91247.93225.39-34.15530.08=PV7-25Copyright©2001byHarcourt,Inc.Allrightsreserved.Inputin“CFLO”register:CF0=0CF1=100CF2=300CF3=300CF4=-50EnterI=10,thenpressNPVbuttontogetNPV=530.09.(HereNPV=PV.)7-26Copyright©2001byHarcourt,Inc.Allrightsreserved.Whatinterestratewouldcause$100togrowto$125.97in3years?3-1000125.978%$100(1+i)3=$125.97.INPUTSOUTPUTNI/YRPVPMTFV7-27Copyright©2001byHarcourt,Inc.Allrightsreserved.WilltheFVofalumpsumbelargerorsmallerifwecompoundmoreoften,holdingthestatedI%constant?Why?LARGER!Ifcompoundingismorefrequentthanonceayear--forexample,semiannually,quarterly,ordaily--interestisearnedoninterestmoreoften.7-28Copyright©2001byHarcourt,Inc.Allrightsreserved.012310%01235%456134.01100133.101230100Annually:FV3=100(1.10)3=133.10.Semiannually:FV6=100(1.05)6=134.01.7-29Copyright©2001byHarcourt,Inc.Allrightsreserved.Wewilldealwith3differentrates:iNom=nominal,orstated,orquoted,rateperyear.iPer=periodicrate.EAR=EFF%=.effectiveannualrate7-30Copyright©2001byHarcourt,Inc.Allrightsreserved.iNomisstatedincontracts.Periodsperyear(m)mustalsobegiven.Examples:8%;Quarterly8%,Dailyinterest(365days)7-31Copyright©2001byHarcourt,Inc.Allrightsreserved.Periodicrate=iPer=iNom/m,wheremisnumberofcompoundingperiodsperyear.m=4forquarterly,12formonthly,and360or365fordailycompounding.Examples:8%quarterly:iPer=8%/4=2%.8%daily(365):iPer=8%/365=0.021918%.7-32Copyright©2001byHarcourt,Inc.Allrightsreserved.EffectiveAnnualRate(EAR=EFF%):TheannualratethatcausesP