公司理财培训课件(PPT 38页)

CH4:DiscountedCashFlowValuation,KeyConceptsandSkills,BeabletocomputethefuturevalueandpresentvalueofasinglecashfloworseriesofcashflowsUnderstandNPVofaninvestmentKnowAPRandEARUnderstandannuitiesandperpetuities,ChapterOutline,4.1Valuation:TheOne-PeriodCase4.2TheMultiperiodCase4.3CompoundingPeriods4.4Simplifications4.5WhatIsaFirmWorth?,DonistryingtosellapieceoflandinAlaska.Yesterday,hewasoffered$10,000fortheproperty.Hewasaboutreadytoaccepttheofferwhenanotherindividualofferedhim$11,424.However,thesecondofferwastobepaidayearfromnow.Donhassatisfiedhimselfthatbothbuyersarehonestandfinanciallysolvent,sohehasnofearthattheofferheselectswillfallthrough.WhichoffershouldDonchoose?Mike,Donsfinancialadvisor,pointsoutthatifDontakesthefirstoffer,hecouldinvestthe$10,000inthebankataninsuredrateof12percent.,4.1TheOne-PeriodCase,Ifyouweretoinvest$10,000at5-percentinterestforoneyear,yourinvestmentwouldgrowto$10,500.$500wouldbeinterest($10,000.05)$10,000istheprincipalrepayment($10,0001)$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$9,523.81intodaysdollars.,Notethat$10,000=$9,523.81(1.05),Theamountthataborrowerwouldneedtosetasidetodaytobeabletomeetthepromisedpaymentof$10,000inoneyeariscalledthePresentValue(PV).,Intheone-periodcase,theformulaforPVcanbewrittenas:,WhereC1iscashflowatdate1,andristheappropriateinterestrate.,NetPresentValue,TheNetPresentValue(NPV)ofaninvestmentisthepresentvalueoftheexpectedcashflows,lessthecostoftheinvestment.Supposeaninvestmentthatpromisestopay$10,000inoneyearisofferedforsalefor$9,500.Yourinterestrateis5%.Shouldyoubuy?,Thepresentvalueofthecashinflowisgreaterthanthecost.Inotherwords,theNetPresentValueispositive,sotheinvestmentshouldbepurchased.,Intheone-periodcase,theformulaforNPVcanbewrittenas:NPV=Cost+PV,Supposeyouhasput$500inasavingsaccountatthebank.Theaccountearns7%,compoundedannually.Howmuchwillyouhaveattheendof3years?,Howmuchwillyouhaveattheendof3yearsifsimpleinterestisused?,500+5007%3=605,500(1+7%)3=612.52,4.2TheMultiperiodCase,Thegeneralformulaforthefuturevalueofaninvestmentovermanyperiodscanbewrittenas:FV=C0(1+r)TWhereC0iscashflowatdate0,ristheappropriateinterestrate,andTisthenumberofperiodsoverwhichthecashisinvested.,FutureValueandCompounding,PresentValueandDiscounting,Howmuchwouldaninvestorhavetosetasidetodayinordertohave$20,000fiveyearsfromnowifthecurrentrateis15%?,$20,000,PV,Inthemultiperiodcase,theformulaforthepresentcanbewrittenas:,HowLongistheWait?,Ifwedeposit$5,000todayinanaccountpaying10%,howlongdoesittaketogrowto$10,000?,WhatRateIsEnough?,Assumethetotalcostofacollegeeducationwillbe$50,000whenachildenterscollegein12years.His/Herparentshave$5,000toinvesttoday.Whatrateofinterestmusthis/herparentsearnontheirinvestmenttocoverthecostofthechildseducation?,About21.15%,At9percentinterest,howlongdoesittaketodoubleyourmoney?Toquadrupleit?,Haveatry!,MultipleCashFlows,Consideraninvestmentthatpays$200oneyearfromnow,withcashflowsincreasingby$200peryearthroughyear4.Iftheinterestrateis12%,whatisthepresentvalueofthisstreamofcashflows?Iftheissueroffersthisinvestmentfor$1,500,shouldyoupurchaseit?,PresentValueCostDoNotPurchase,Thepresentvalueofthefollowingcashflowstreamis$6,453whendiscountedat10percentannually.Whatisthevalueofthemissingcashflow?Year1Cashflow$1,200Year2Cashflow?Year3Cashflow$2,400Year4Cashflow$2,600,Haveatry!,4.3CompoundingPeriods,CompoundinganinvestmentmtimesayearforTyearsprovidesforfuturevalueofwealth:,Forexample,ifyouinvest$50for3yearsat12%compoundedsemi-annually,yourinvestmentwillgrowto,EffectiveAnnualRatesofInterest,Areasonablequestiontoaskintheaboveexampleis“whatistheeffectiveannualrateofinterestonthatinvestment?”,TheEffectiveAnnualRate(EAR)ofinterestistheannualratethatwouldgiveusthesameend-of-investmentwealthafter3years:,So,investingat12.36%compoundedannuallyisthesameasinvestingat12%compoundedsemi-annually.,FindtheEffectiveAnnualRate(EAR)ofan18%APRloanthatiscompoundedmonthly.Whatwehaveisaloanwithamonthlyinterestrateof1.5%.Thisisequivalenttoaloanwithanannualinterestrateof19.56%.,APRandEAR,4.4Simplifications,Annuity(年金)AstreamofconstantcashflowsthatlastsforafixednumberofperiodsGrowingannuity(增长年金)AstreamofcashflowsthatgrowsataconstantrateforafixednumberofperiodsPerpetuity(永续年金)AconstantstreamofcashflowsthatlastsforeverGrowingperpetuity(永续增长年金)Astreamofcashflowsthatgrowsataconstantrateforever,Annuity,Aconstantstreamofcashflowswithafixedmaturity,Annuity:Example,Ifyoucanafforda$400monthlycarpayment,howmuchcarcanyouaffordifinterestratesare7%on36-monthloans?,Whatisthepresentvalueofafour-yearannuityof$100peryearthatmakesitsfirstpaymenttwoyearsfromtodayifthediscountrateis9%?,012345,$100$100$100$100,$323.97,$297.22,Whatisthepresentandfuturevalueofafour-yearannuityof$100peryearifthefirstpaymentoccursimmediately?(thediscountrateis9%),Haveatry!,GrowingAnnuity,Agrowingstreamofcashflowswithafixedmaturity,GrowingAnnuity:Example,Adefined-benefitretirementplanofferstopay$20,000peryearfor40yearsandincreasetheannualpaymentby3%eachyear.Whatisthepresentvalueatretirementifthediscountrateis10%?,Youareevaluatinganincomegeneratingproperty.Netrentisreceivedattheendofeachyear.Thefirstyearsrentisexpectedtobe$8,500,andrentisexpectedtoincrease7%eachyear.Whatisthepresentvalueoftheestimatedincomestreamoverthefirst5yearsifthediscountrateis12%?,$34,706.28,Perpetuity,Aconstantstreamofcashflowsthatlastsforever,Perpetuity:Exam