PK06Word格式文档下载.docx
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PK06Word格式文档下载.docx
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I.ChapterOutline
6.1MultipleCashFlows
A.FutureValueofMultipleCashFlows
∙IncontrasttoChapter5,wenowconsidersituationsinwhichtherearemultiplecashflows.Solvingfuturevalueproblemswithmultiplecashflowsinvolvesasimpleprocess.
∙First,drawatimelinetomakesurethateachcashflowisplacedinthecorrecttimeperiod.
∙Second,calculatethefuturevalueofeachcashflowforitstimeperiod.
∙Third,addupthefuturevalues.
B.PresentValueofMultipleCashFlows
∙Manysituationsinbusinesscallforcomputingthepresentvalueofaseriesofexpectedfuturecashflows.Thiscouldbetodeterminethemarketvalueofasecurityorbusinessortodecidewhetheracapitalinvestmentshouldbemade.
∙Theprocessissimilartodeterminingthefuturevalueofmultiplecashflows.
∙First,prepareatimelinetoidentifythemagnitudeandtimingofthecashflows.
∙Next,calculatethepresentvalueofeachcashflowusingEquation5.4fromthepreviouschapter.
∙Finally,addupallthepresentvalues.
∙Thesumofthepresentvaluesofastreamoffuturecashflowsistheircurrentmarketprice,orvalue.
6.2LevelCashFlows:
AnnuitiesandPerpetuities
∙Therearemanysituationsinwhichbothbusinessesandindividualswouldbefacedwitheitherreceivingorpayingaconstantamountforalengthofperiod.
∙Whenafirmfacesastreamofconstantpaymentsonabankloanforaperiodoftime,wecallthatstreamofcashflowsanannuity.
▪Individualinvestorsmaymakeconstantpaymentsontheirhomeorcarloans,orinvestafixedamountyearafteryeartosavefortheirretirement.
▪Anyfinancialcontractthatcallsforequallyspacedandlevelcashflowsoverafinitenumberofperiodsiscalledanannuity.
∙Ifthecashflowpaymentscontinueforever,thecontractiscalledaperpetuity.
∙Constantcashflowsthatoccurattheendofeachperiodarecalledordinaryannuities.
A.PresentValueofanAnnuity
∙Wecancalculatethepresentvalueofanannuitythesamewayaswecalculatedthepresentvalueofmultiplecashflows.However,ifthenumberofpaymentsweretobeverylarge,thenthisprocesswillbetedious.
∙InsteadwecansimplifyEquation5.4toobtainanannuityfactor.ThisresultsinEquation6.1,whichcanbeusedtocalculatethepresentvalueofanannuity.
∙Inadditiontousingthisannuityequationtosolveforthepresentvalueofanannuity,financialcalculatorsandspreadsheetsmaybeused.PresentvalueandannuitytablescreatedwiththehelpofEquation6.1havelimiteduseoutsideofaclassroomsetting.
∙Oneproblemthatiswidelysolvedusingafinancialcalculatorisfindingthemonthlypaymentonacarloanorhomeloan.
B.PreparingaLoanAmortizationSchedule
∙Amortizationreferstothewaytheborrowedamount(principal)ispaiddownoverthelifeoftheloan.
∙Themonthlyloanpaymentisstructuredsothateachmonthaportionoftheprincipalispaidoffandatthetimetheloanmatures,theloanisentirelypaidoff.
∙Withanamortizedloan,eachloanpaymentcontainssomepaymentofprincipalandaninterestpayment.
∙Aloanamortizationscheduleisjustatablethatshowstheloanbalanceatthebeginningandendofeachperiod,thepaymentmadeduringthatperiod,andhowmuchofthatpaymentrepresentsinterestandhowmuchrepresentsrepaymentofprincipal.
∙Withanamortizedloan,abiggerproportionofeachmonth’spaymentgoestowardinterestintheearlyperiods.Astheloangetspaiddown,agreaterproportionofeachpaymentisusedtopaydowntheprincipal.
∙Amortizationschedulesarebestdoneonaspreadsheet(seeExhibit6.5).
C.FindingtheInterestRate
∙Theannuityequationcanalsobeusedtothefindtheinterestrateordiscountrateforanannuity.
∙Todeterminetherateofreturnfortheannuity,weneedtosolvetheequationfortheunknownvaluei.
∙Otherthanusingatrial-and-errorapproach,itiseasiertosolveusingthiswithafinancialcalculator.
D.FutureValueofanAnnuity
∙Futurevalueannuitycalculationsusuallyinvolvefindingwhatasavingsoraninvestmentactivityisworthatsomepointinthefuture.
∙Thiscouldbesavingperiodicallyforavacation,car,orhouse,orevenretirement.
∙Wecanderivethefuturevalueannuityequationfromthepresentvalueannuityequation(Equation6.1).ThisresultsinEquation6.2,asfollows.
∙Aswithpresentvalueannuitycalculations,futurevaluecalculationsaremadeeasierwhenfinancialcalculatorsorspreadsheetsareused,especiallywhenlengthyinvestmentperiodsareinvolved.
E.Perpetuities
∙Aperpetuityisaconstantstreamofcashflowsthatgoesonforaninfiniteperiod.
∙Inthestockmarkets,preferredstockissuesareconsideredtobeperpetuities,withtheissuerpayingaconstantdividendtoholders.
∙Theequationforthepresentvalueofaperpetuitycanbederivedfromthepresentvalueofanannuityequationwithntendingtoinfinity.
∙Onethingthatshouldbeemphasizedintherelationshipbetweenthepresentvalueofanannuityandaperpetuityisthatjustasaperpetuityequationwasderivedfromthepresentvalueannuityequation,wecouldalsoderivethepresentvalueofanannuityfromtheequationforaperpetuity.
F.AnnuityDue
∙Whenyouhaveanannuitywiththepaymentbeingincurredatthebeginningofeachperiodratherthanattheend,theannuityiscalledanannuitydue.
∙Rentorleasepaymentsaretypicallymadeatthebeginningofeachperiodratherthanattheendofeachperiod.
∙Theannuitytransformationmethod(Equation6.4)showstherelationshipbetweentheordinaryannuityandtheannuitydue.
∙Eachperiod’scashflowthusearnsanextraperiodofinterestcomparedtoanordinaryannuity.Thus,thepresentvalueorfuturevalueofanannuitydueisalwayshigherthanthatofordinaryannuity.
Annuitydue=Ordinaryannuityvalue(1+i)
6.3CashFlowsThatGrowataConstantRate
∙Inadditiontoconstantcashflowstreams,onemayhavetodealwithcashflowsthatgrowataconstantrateovertime.
∙Thesecashflowstreamsarecalledgrowingannuitiesorgrowingperpetuities.
A.GrowingAnnuity
∙Businessmayneedtocomputethevalueofmultiyearproductorservicecontractswithcashflowsthatincreaseeachyearataconstantrate.
∙Thesearecalledgrowingannuities.
∙Anexampleofagrowingannuitycouldbethevaluationofagrowingbusinesswhosecashflowsareincreasingeveryyearataconstantrate.
∙Thisequationtoevaluatethepresentvalueofagrowingannuity(Equation6.5)canbeusedwhenthegrowthrateislessthanthediscountrate.
B.GrowingPerpetuity
∙Whenthecashflowstreamfeaturesaconstantgrowingannuityforever,itiscalledagrowingperpetuity.
∙ThiscanbederivedfromEquation6.5whenntendstoinfinityandresultsinEquation6.6.
6.4TheEffectiveAnnualInterestRate
∙Interestratescanbequotedinthefinancialmarketsinavarietyofways.
∙Themostcommonquote,especiallyforaloan,istheannualpercentagerate(APR).
∙TheAPRisaratethatrepresentsthesimpleinterestaccruedonaloanoraninvestmentinasingleperiod.Thisisannualizedoverayearbymultiplyingitbytheappropriatenumberofperiodsinayear.
A.CalculatingtheEffectiveAnnualInterestRate(EAR)
∙Thecorrectwaytocomputeanannualizedrateistoreflectthecompoundingthatoccurs.Thisinvolvescalculatingtheeffectiveannualrate(EAR).
∙Theeffectiveannualinterestrate(EAR)isdefinedastheannualgrowthratethattakescompoundingintoaccount.
∙Equation6.7showshowtheEARiscomputed.
EAR=(1+Quotedrate/m)m–1,
where,misthenumberofcompoundingperiodsduringayear.
∙TheEARconversionformulaaccountsforthenumberofcompoundingperiodsand,thus,effectivelyadjuststheannualizedinterestrateforthetimevalueofmoney.
∙TheEARisthetruecostofborrowingandlending.
B.ConsumerProtectionActsandInterestRateDisclosure
∙CongresspassedtheTruth-in-LendingActin1968toensurethatthetruecostofcreditwasdisclosedtoconsumerssothattheycouldmakesoundfinancialdecisions.
∙Similarly,anotherpieceoflegislationcalledtheTruth-in-SavingsActwaspassedtoprovideconsumerswithanaccurateestimateofthereturntheywouldearnonaninvestment.
∙ThesetwopiecesoflegislationrequirebylawthattheAPRbedisclosedonallconsumerloansandsavingsplansandthatitbeprominentlydisplayedonadvertisingandcontractualdocuments.
∙ItisimportanttonotethattheEAR,nottheAPR,istheappropriateratetouseinpresentandfuturevaluecalculations.
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