《货币时间价值英语》PPT课件

TheTimeValueofMoney,WhatisTimeValue?,WesaythatmoneyhasatimevaluebecausethatmoneycanbeinvestedwiththeexpectationofearningapositiverateofreturnInotherwords,“adollarreceivedtodayisworthmorethanadollartobereceivedtomorrow”Thatisbecausetodaysdollarcanbeinvestedsothatwehavemorethanonedollartomorrow,TheTerminologyofTimeValue,PresentValue-Anamountofmoneytoday,orthecurrentvalueofafuturecashflowFutureValue-AnamountofmoneyatsomefuturetimeperiodPeriod-Alengthoftime(oftenayear,butcanbeamonth,week,day,hour,etc.)InterestRate-Thecompensationpaidtoalender(orsaver)fortheuseoffundsexpressedasapercentageforaperiod(normallyexpressedasanannualrate),Abbreviations,PV-PresentvalueFV-FuturevaluePmt-PerperiodpaymentamountN-Eitherthetotalnumberofcashflowsorthenumberofaspecificperiodi-Theinterestrateperperiod,Timelines,PV,FV,Today,AtimelineisagraphicaldeviceusedtoclarifythetimingofthecashflowsforaninvestmentEachtickrepresentsonetimeperiod,CalculatingtheFutureValue,Supposethatyouhaveanextra$100todaythatyouwishtoinvestforoneyear.Ifyoucanearn10%peryearonyourinvestment,howmuchwillyouhaveinoneyear?,-100,?,CalculatingtheFutureValue(cont.),Supposethatattheendofyear1youdecidetoextendtheinvestmentforasecondyear.Howmuchwillyouhaveaccumulatedattheendofyear2?,-110,?,GeneralizingtheFutureValue,Recognizingthepatternthatisdeveloping,wecangeneralizethefuturevaluecalculationsasfollows:,Ifyouextendedtheinvestmentforathirdyear,youwouldhave:,CompoundInterest,NotefromtheexamplethatthefuturevalueisincreasingatanincreasingrateInotherwords,theamountofinterestearnedeachyearisincreasingYear1:$10Year2:$11Year3:$12.10Thereasonfortheincreaseisthateachyearyouareearninginterestontheinterestthatwasearnedinpreviousyearsinadditiontotheinterestontheoriginalprincipleamount,CompoundInterestGraphically,TheMagicofCompounding,OnNov.25,1626PeterMinuit,aDutchman,reportedlypurchasedManhattanfromtheIndiansfor$24worthofbeadsandothertrinkets(珠子和其他饰品).WasthisagooddealfortheIndians?Thishappenedabout371yearsago,soiftheycouldearn5%peryeartheywouldnow(in1997)have:,Iftheycouldhaveearned10%peryear,theywouldnowhave:,Thatsabout54,563Trillion(万亿)dollars!,TheMagicofCompounding(cont.),TheWallStreetJournal(17Jan.92)saysthatallofNewYorkcityrealestateisworthabout$324billion.Ofthisamount,Manhattanisabout30%,whichis$97.2billionAt10%,thisis$54,562trillion!OurU.S.GNPisonlyaround$6trillionperyear.Sothisamountrepresentsabout9,094yearsworthofthetotaleconomicoutputoftheUSA!.,CalculatingthePresentValue,Sofar,wehaveseenhowtocalculatethefuturevalueofaninvestmentButwecanturnthisaroundtofindtheamountthatneedstobeinvestedtoachievesomedesiredfuturevalue:,PresentValue:AnExample,Supposethatyourfive-yearolddaughterhasjustannouncedherdesiretoattendcollege.Aftersomeresearch,youdeterminethatyouwillneedabout$100,000onher18thbirthdaytopayforfouryearsofcollege.Ifyoucanearn8%peryearonyourinvestments,howmuchdoyouneedtoinvesttodaytoachieveyourgoal?,Annuities,Anannuityisaseriesofnominallyequalpaymentsequallyspacedintime(等时间间隔)Annuitiesareverycommon:RentMortgagepaymentsCarpaymentPensionincomeThetimelineshowsanexampleofa5-year,$100annuity,100,100,100,100,100,ThePrincipleofValueAdditivity,Howdowefindthevalue(PVorFV)ofanannuity?First,youmustunderstandtheprincipleofvalueadditivity:ThevalueofanystreamofcashflowsisequaltothesumofthevaluesofthecomponentsInotherwords,ifwecanmovethecashflowstothesametimeperiodwecansimplyaddthemalltogethertogetthetotalvalue价值相加,PresentValueofanAnnuity,Wecanusetheprincipleofvalueadditivitytofindthepresentvalueofanannuity,bysimplysummingthepresentvaluesofeachofthecomponents:,PresentValueofanAnnuity(cont.),Usingtheexample,andassumingadiscountrateof10%peryear,wefindthatthepresentvalueis:,100,100,100,100,100,62.09,68.30,75.13,82.64,90.91,379.08,PresentValueofanAnnuity(cont.),Actually,thereisnoneedtotakethepresentvalueofeachcashflowseparatelyWecanuseaclosed-formofthePVAequationinstead:,PresentValueofanAnnuity(cont.),Wecanusethisequationtofindthepresentvalueofourexampleannuityasfollows:,Thisequationworksforallregularannuities,regardlessofthenumberofpayments,TheFutureValueofanAnnuity,Wecanalsousetheprincipleofvalueadditivitytofindthefuturevalueofanannuity,bysimplysummingthefuturevaluesofeachofthecomponents:,TheFutureValueofanAnnuity(cont.),Usingtheexample,andassumingadiscountrateof10%peryear,wefindthatthefuturevalueis:,100,100,100,100,100,146.41,133.10,121.00,110.00,=610.51atyear5,TheFutureValueofanAnnuity(cont.),JustaswedidforthePVAequation,wecouldinsteaduseaclosed-formoftheFVAequation:,Thisequationworksforallregularannuities,regardlessofthenumberofpayments,TheFutureValueofanAnnuity(cont.),Wecanusethisequationtofindthefuturevalueoftheexampleannuity:,AnnuitiesDue预付年金,Thusfar,theannuitiesthatwehavelookedatbegintheirpaymentsattheendofperiod1;thesearereferredtoasregularannuitiesAannuitydueisthesameasaregularannuity,exceptthatitscashflowsoccuratthebeginningoftheperiodratherthanattheend,100,100,100,100,100,100,100,100,100,100,5-periodAnnuityDue,5-periodRegularAnnuity,PresentValueofanAnnuityDue,Wecanfindthepresentvalueofanannuitydueinthesamewayaswedidforaregularannuity,withoneexceptionNotefromthetimelinethat,ifweignorethefirstcashflow,theannuityduelooksjustlikeafour-periodregularannuityTherefore,wecanvalueanannuityduewith:,PresentValueofanAnnuityDue(cont.),Therefore,thepresentvalueofourexampleannuitydueis:,NotethatthisishigherthanthePVofthe,otherwiseequivalent,regularannuity,FutureValueofanAnnuityDue,TocalculatetheFVofanannuitydue,wecantreatitasregularannuity,andthentakeitonemoreperiodforward:,Pmt,Pmt,Pmt,Pmt,Pmt,FutureValueofanAnnuityDue(cont.),Thefuturevalueofourexampleannuityis:,Notethatthisishigherthanthefuturevalueofthe,otherwiseequivalent,regularannuity,DeferredAnnuities递延年金,Adeferredannuityisthesameasanyotherannuity,exceptthatitspaymentsdonotbeginuntilsomelaterperiodThetimelineshowsafive-perioddeferredannuity,0,1,2,3,4,5,100,100,100,100,100,6,7,PVofaDeferredAnnuity,Wecanfindthepresentvalueofadeferredannuityinthesamewayasanyotherannuity,withanextrasteprequiredBeforewecandothishowever,thereisanimportantruletounderstand:WhenusingthePVAequation,theresultingPVisalwaysoneperiodbeforethefirstpaymentoccurs,PVofaDeferredAnnuity(cont.),TofindthePVofadeferredannuity,wefirstfindusethePVAequation,andthendiscountthatresultbacktoperiod0Hereweareusinga10%discountrate,0,1,2,3,4,5,0,0,100,100,100,100,100,6,7,PV2=379.08,PV0=313.29,PVofaDeferredAnnuity(cont.),Step1:,Step2:,FVofaDeferredAnnuity,ThefuturevalueofadeferredannuityiscalculatedinexactlythesamewayasanyotherannuityTherearenoextrastepsatall,UnevenCashFlows,VeryoftenaninvestmentoffersastreamofcashflowswhicharenoteitheralumpsumoranannuityWecanfindthepresentorfuturevalueofsuchastreambyusingtheprincipleofvalueadditivity,UnevenCashFlows:AnExample(1),Assumethataninvestmentoffersthefollowingcashflows.Ifyourrequiredreturnis7%,whatisthemaximumpricethatyouwouldpayforthisinvestment?,100,200,300,UnevenCashFlows:AnExample(2),Supposethatyouweretodepositthefollowingamountsinanaccountpaying5%peryear.Whatwouldthebalanceoftheaccountbeattheendofthethirdyear?,300,500,700,Non-annualCompounding,SofarwehaveassumedthatthetimeperiodisequaltoayearHowever,thereisnoreasonthatatimeperiodcantbeanyotherlengthoftimeWecouldassumethatinterestisearnedsemi-annually,quarterly,monthly,daily,oranyotherlengthoftimeTheonlychangethatmustbemadeistomakesurethattherateofinterestisadjustedtotheperiodlength,Non-annualCompounding(cont.),Supposethatyouhave$1,000availableforinvestment.Afterinvestigatingthelocalbanks,youhavecompiledthefollowingtableforcomparison.Inwhichbankshouldyoudeposityourfunds?,Non-annualCompounding(cont.),Tosolvethisproblem,youneedtodeterminewhichbankwillpayyouthemostinterestInotherwords,atwhichbankwillyouhavethehighestfuturevalue?Tofindout,letschangeourbasicFVequationslightly:,Inthisversionoftheequationmisthenumberofcompoundingperiodsperyear,Non-annualCompounding(cont.),WecanfindtheFVforeachbankasfollows:,FirstNationalBan