公司理财chap4

CH4:DiscountedCashFlowValuationKeyConceptsandSkillsBeabletocomputethefuturevalueandpresentvalueofasinglecashfloworseriesofcashflowsUnderstandNPVofaninvestmentKnowAPRandEARUnderstandannuitiesandperpetuitiesChapterOutline4.1Valuation:TheOne-PeriodCase4.2TheMultiperiodCase4.3CompoundingPeriods4.4Simplifications4.5WhatIsaFirmWorth?DonistryingtosellapieceoflandinAlaska.Yesterday,hewasoffered$10,000fortheproperty.Hewasaboutreadytoaccepttheofferwhenanotherindividualofferedhim$11,424.However,thesecondofferwastobepaidayearfromnow.Donhassatisfiedhimselfthatbothbuyersarehonestandfinanciallysolvent,sohehasnofearthattheofferheselectswillfallthrough.WhichoffershouldDonchoose?Mike,Don’sfinancialadvisor,pointsoutthatifDontakesthefirstoffer,hecouldinvestthe$10,000inthebankataninsuredrateof12percent.4.1TheOne-PeriodCaseIfyouweretoinvest$10,000at5-percentinterestforoneyear,yourinvestmentwouldgrowto$10,500.$500wouldbeinterest($10,000×.05)$10,000istheprincipalrepayment($10,000×1)$10,500isthetotaldue.Itcanbecalculatedas:$10,500=$10,000×(1.05)ThetotalamountdueattheendoftheinvestmentiscalledtheFutureValue(FV).FutureValueIntheone-periodcase,theformulaforFVcanbewrittenas:FV=C0×(1+r)WhereC0iscashflowtoday(timezero),andristheappropriateinterestrate.PresentValueIfyouweretobepromised$10,000dueinoneyearwheninterestratesare5-percent,yourinvestmentwouldbeworth$9,523.81intoday’sdollars.05.1000,10$81.523,9$Notethat$10,000=$9,523.81×(1.05)Theamountthataborrowerwouldneedtosetasidetodaytobeabletomeetthepromisedpaymentof$10,000inoneyeariscalledthePresentValue(PV).Intheone-periodcase,theformulaforPVcanbewrittenas:rCPV11WhereC1iscashflowatdate1,andristheappropriateinterestrate.NetPresentValueTheNetPresentValue(NPV)ofaninvestmentisthepresentvalueoftheexpectedcashflows,lessthecostoftheinvestment.Supposeaninvestmentthatpromisestopay$10,000inoneyearisofferedforsalefor$9,500.Yourinterestrateis5%.Shouldyoubuy?81.23$81.523,9$500,9$05.1000,10$500,9$NPVNPVNPVThepresentvalueofthecashinflowisgreaterthanthecost.Inotherwords,theNetPresentValueispositive,sotheinvestmentshouldbepurchased.Intheone-periodcase,theformulaforNPVcanbewrittenas:NPV=–Cost+PVSupposeyouhasput$500inasavingsaccountatthebank.Theaccountearns7%,compoundedannually.Howmuchwillyouhaveattheendof3years?Howmuchwillyouhaveattheendof3yearsifsimpleinterestisused?500+500×7%×3=605500×(1+7%)3=612.524.2TheMultiperiodCaseThegeneralformulaforthefuturevalueofaninvestmentovermanyperiodscanbewrittenas:FV=C0×(1+r)TWhereC0iscashflowatdate0,ristheappropriateinterestrate,andTisthenumberofperiodsoverwhichthecashisinvested.TrTFVIFr,,)1(简写为称为复利终值系数FutureValueandCompoundingPresentValueandDiscountingHowmuchwouldaninvestorhavetosetasidetodayinordertohave$20,000fiveyearsfromnowifthecurrentrateis15%?012345$20,000PV5)15.1(000,20$53.943,9$Inthemultiperiodcase,theformulaforthepresentcanbewrittenas:TrTTTTTPVIFrrCrCPV,,)1(1)1(1)1(简写为叫做复利现值系数HowLongistheWait?Ifwedeposit$5,000todayinanaccountpaying10%,howlongdoesittaketogrowto$10,000?TrCFV)1(0T)10.1(000,5$000,10$2000,5$000,10$)10.1(T)2ln()10.1ln(Tyears27.70953.06931.0)10.1ln()2ln(TWhatRateIsEnough?Assumethetotalcostofacollegeeducationwillbe$50,000whenachildenterscollegein12years.His/Herparentshave$5,000toinvesttoday.Whatrateofinterestmusthis/herparentsearnontheirinvestmenttocoverthecostofthechild’seducation?TrCFV)1(012)1(000,5$000,50$r10000,5$000,50$)1(12r12110)1(r2115.12115.1110121rAbout21.15%At9percentinterest,howlongdoesittaketodoubleyourmoney?Toquadrupleit?Haveatry!!!MultipleCashFlowsConsideraninvestmentthatpays$200oneyearfromnow,withcashflowsincreasingby$200peryearthroughyear4.Iftheinterestrateis12%,whatisthepresentvalueofthisstreamofcashflows?Iftheissueroffersthisinvestmentfor$1,500,shouldyoupurchaseit?01234200400600800178.57318.88427.07508.411,432.93PresentValueCost→DoNotPurchaseThepresentvalueofthefollowingcashflowstreamis$6,453whendiscountedat10percentannually.Whatisthevalueofthemissingcashflow?Year1Cashflow$1,200Year2Cashflow?Year3Cashflow$2,400Year4Cashflow$2,600Haveatry!!!4.3CompoundingPeriodsCompoundinganinvestmentmtimesayearforTyearsprovidesforfuturevalueofwealth:TmmrCFV10Forexample,ifyouinvest$50for3yearsat12%compoundedsemi-annually,yourinvestmentwillgrowto6%,663250$93.70$)06.1(50$212.150$FVIFFVEffectiveAnnualRatesofInterestAreasonablequestiontoaskintheaboveexampleis“whatistheeffectiveannualrateofinterestonthatinvestment?”TheEffectiveAnnualRate(EAR)ofinterestistheannualratethatwouldgiveusthesameend-of-investmentwealthafter3years:93.70$)1(50$3EAR1236.150$93.70$31EARSo,investingat12.36%compoundedannuallyisthesameasinvestingat12%compoundedsemi-annually.FindtheEffectiveAnnualRate(EAR)ofan18%APRloanthatiscompoundedmonthly.Whatwehaveisaloanwithamonthlyinterestrateof1.5%.Thisisequivalenttoaloanwithanannualinterestrateof19.56%.1956.01)015.1(11218.11212EARAPRandEAR11mmrEAR11mmAPREAR4.4SimplificationsAnnuity(年金)Astreamofconstantcashflow