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.