公司理财04净现值.ppt

1 CorporateFinance 第4章金融市场和净现值 4 1单期投资情形4 2多期投资情形4 3复利计息期数4 4简化公式4 5如何确定公司价值4 6小结 2 CorporateFinance 4 1单期投资情形TheOne PeriodCase FutureValue 一 终值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 ThetotalamountdueattheendoftheinvestmentiscalltheFutureValue FV 3 CorporateFinance Intheone periodcase theformulaforFVcanbewrittenas FV C1 1 r WhereC1iscashflowatdate1andristheappropriateinterestrate 4 CorporateFinance 二 现值Ifyouweretobepromised 10 000dueinoneyearwheninterestratesareat5 percent yourinvestmentbeworth 9 523 81intoday sdollars Theamountthataborrowerwouldneedtosetasidetodaytotoabletomeetthepromisedpaymentof 10 000inoneyeariscallthePresentValue PV of 10 000 Notethat 10 000 9 523 81 1 05 5 CorporateFinance Intheone periodcase theformulaforPVcanbewrittenas WhereC1iscashflowatdate1andristheappropriateinterestrate 6 CorporateFinance 三 净现值TheNetPresentValue NPV ofaninvestmentisthepresentvalueoftheexpectedcashflows lessthecostoftheinvestment Supposeaninvestmentthatpromisestopay 10 000inoneyearisofferedforsalefor 9 500 Yourinterestrateis5 Shouldyoubuy 结论 Yes 7 CorporateFinance Intheone periodcase theformulaforNPVcanbewrittenas IfwehadnotundertakenthepositiveNPVprojectconsideredonthelastslide andinsteadinvestedour 9 500elsewhereat5 percent ourFVwouldbelessthanthe 10 000theinvestmentpromisedandwewouldbeunambiguouslyworseoffinFVtermsaswell 9 500 1 05 9 975 10 000 8 CorporateFinance 4 2多期投资情形TheMultiperiodCase FutureValue 一 终值和复利Thegeneralformulaforthefuturevalueofaninvestmentovermanyperiodscanbewrittenas FV C0 1 r TWhereC0iscashflowatdate0 ristheappropriateinterestrate andTisthenumberofperiodsoverwhichthecashisinvested 9 CorporateFinance SupposethatJayRitterinvestedintheinitialpublicofferingoftheModiglianicompany Modiglianipaysacurrentdividendof 1 10 whichisexpectedtogrowat40 percentperyearforthenextfiveyears Whatwillthedividendbeinfiveyears FV C0 1 r T 5 92 1 10 1 40 5 10 CorporateFinance Noticethatthedividendinyearfive 5 92 isconsiderablyhigherthanthesumoftheoriginaldividendplusfiveincreasesof40 percentontheoriginal 1 10dividend 5 92 1 10 5 1 10 40 3 30Thisisduetocompounding 11 CorporateFinance 0 1 2 3 4 5 10 1 12 CorporateFinance 二 复利的威力1 从华尔街上的一块石碑谈起 1996年 24美元 370年 300亿美元1626年 荷兰人用24美元的饰物买下了整个曼哈顿 而20世纪90年代 曼哈顿价值300亿美元 2 谁更聪明 荷兰有一种永久性的证券 年息为8 24 1 0 08 371 60万亿 13 CorporateFinance 3 复利的威力 投入1万元 那么 盈利10年后 万 20年后 万 10 2 596 7320 6 192835 20 10404100 1024 001048576 14 CorporateFinance 三 现值和复利Howmuchwouldaninvestorhavetosetasidetodayinordertohave 20 000fiveyearsfromnowifthecurrentrateis15 0 1 2 3 4 5 20 000 PV 15 CorporateFinance 四 期数的计算Ifwedeposit 5 000todayinanaccountpaying10 howlongdoesittaketogrowto 10 000 16 CorporateFinance 五 利率的计算Assumethetotalcostofacollegeeducationwillbe 50 000whenyourchildenterscollegein12years Youhave 5 000toinvesttoday Whatrateofinterestmustyouearnonyourinvestmenttocoverthecostofyourchild seducation About21 15 17 CorporateFinance 4 3复利计息期数CompoundingPeriods 一 名义利率与实际利率 Forexample ifyouinvest 50for3yearsat12 compoundedsemi annually yourinvestmentwillgrowto FV 18 CorporateFinance Areasonablequestiontoaskintheaboveexampleiswhatistheeffectiveannualrateofinterestonthatinvestment TheEffectiveAnnualInterestRate EAR istheannualratethatwouldgiveusthesameend of investmentwealthafter3years 19 CorporateFinance So investingat12 36 compoundedannuallyisthesameasinvestingat12 compoundedsemiannually 20 CorporateFinance 实际利率与名义利率的关系 假设名义利率为r 每年复利m次 则实际利率为 21 CorporateFinance 二 多年期复利计息的终值 22 CorporateFinance 三 连续复利Thegeneralformulaforthefuturevalueofaninvestmentcompoundedcontinuouslyovermanyperiodscanbewrittenas FV C0 erTWhereC0iscashflowatdate0 risthestatedannualinterestrate Tisthenumberofperiodsoverwhichthecashisinvested andeisatranscendentalnumber 超越数 approximatelyequalto2 718 exisakeyonyourcalculator 23 CorporateFinance 4 4简化公式Simplifications 永续年金PerpetuityAconstantstreamofcashflowsthatlastsforever 永续增长年金GrowingperpetuityAstreamofcashflowsthatgrowsataconstantrateforever 年金AnnuityAstreamofconstantcashflowsthatlastsforafixednumberofperiods 增长年金GrowingannuityAstreamofcashflowsthatgrowsataconstantrateforafixednumberofperiods 24 CorporateFinance 4 4 1永续年金Perpetuity Aconstantstreamofcashflowsthatlastsforever Theformulaforthepresentvalueofaperpetuityis 25 CorporateFinance 举例 WhatisthevalueofaBritishconsolthatpromisestopay 15eachyear everyyearuntilthesunturnsintoaredgiantandburnstheplanettoacrisp Theinterestrateis10 percent 26 CorporateFinance 4 4 2永续增长年金GrowingPerpetuity Agrowingstreamofcashflowsthatlastsforever Theformulaforthepresentvalueofagrowingperpetuityis 27 CorporateFinance 例 Theexpecteddividendnextyearis 1 30anddividendsareexpectedtogrowat5 forever Ifthediscountrateis10 whatisthevalueofthispromiseddividendstream 28 CorporateFinance 4 4 3年金Annuity Aconstantstreamofcashflowswithafixedmaturity Theformulaforthepresentvalueofanannuityis 29 CorporateFinance 例 Ifyoucanafforda 400monthlycarpayment howmuchcarcanyouaffordifinterestratesare7 on36 monthloans 30 CorporateFinance 4 4 4增长年金GrowingAnnuity Agrowingstreamofcashflowswithafixedmaturity Theformulaforthepresentvalueofagrowingannuity 31 CorporateFinance 例 Adefined benefitretirementplanofferstopay 20 000peryearfor40yearsandincreasetheannualpaymentby3 percenteachyear Whatisthepresentvalueatretirementifthediscountrateis10 percent 32 CorporateFinance 4 5如何确定公司的价值WhatIsaFirmWorth 理论上计 公司的价值就是其未来现金流的现值 Conceptually afirmshouldbeworththepresentvalueofthefirm scashflows 问题是如何确定这些现金流的数量 时间及风险 Thetrickypartisdeterminingthesi