XXXX秋季在职研究生财务2(1)

1-0财务管理江萍2010年秋季Handout21-1HandoutOutline1.DiscountedCashFlowValuation贴现现金流估值2.NetPresentValueandOtherInvestmentCriteria净现值与其他投资标准3.Determiningtherelevantcashflows确定相关现金流1-21.DiscountedCashFlowValuationOutlineI.IntroductiontoValuation:TheTimeValueofMoneyFutureValueandCompounding(连续复利)PresentValueandDiscountingMoreonthefutureandpresentvaluesII.FutureandPresentValuesofMultiple(复杂，多重的)CashFlowsIII.Application(应用)1-3I.IntroductiontoValuation:TheTimeValueofMoneyBasicDefinitions(基本定义)：•PresentValue–earliermoneyonatimeline•FutureValue–latermoneyonatimeline•Interestrate–“exchangerate”betweenearliermoneyandlatermoneyDiscountrate(贴现率)Costofcapital(资本成本)Opportunitycostofcapital(资本的机会成本)Requiredreturn(必要收益率或内部收益率)1-4A.FutureValueandCompoundingExample1•Supposeyouinvest$100foroneyearat5%peryear.Whatisthefuturevalueinoneyear?Interest=$100*5%=$5Valueinoneyear=principal+interest=$100+$5=$105FutureValue(FV)=$100(1+5%)=$105•Supposeyouleavethemoneyinforanotheryear.Howmuchwillyouhavetwoyearsfromnow?FV=$100(1+5%)(1+5%)=$100(1+5%)2=$110.251-5FutureValues:GeneralFormula•FV=PV(1+r)tFV=futurevaluePV=presentvaluer=periodinterestrateT=numberofperiods•Futurevalueinterestfactor=(1+r)t1-6Futurevalueof$1FVof$1=(1+r)t1-7FutureValues–Example2•Supposeyouinvestthe$100fromtheprevious(之前的)examplefor5years.Howmuchwouldyouhave?FV=$100(1+5%)5=$127.631-8EffectsofCompounding•Simpleinterest(interestisearnedonlyontheoriginalprincipal)单利：只对原始本金支付利息•Compoundinterest(interestisearnedonprincipalandoninterestreceived)复利：计息的基础为原始本金，也包括已经获得的利息1-9EffectsofCompounding•Considertheexample1FVwithsimpleinterest=$100+5+5=$110FVwithcompoundinterest=$110.25Theextra$0.25comesfromtheinterestof$5*5%=$0.25earnedonthefirstinterestpayment•Considerexample2FVwithsimpleinterest=$100+5*5=$125FVwithcompoundinterest=$127.63Theeffectofcompoundingissmallforasmallnumberofperiods,butincreasesasthenumberofperiodsincreases(from$0.25to$2.63).1-10Futurevalue,simpleinterestandcompoundinterestTheeffectofcompoundingincreasesasthenumberofperiodsincreases.随着期限的增加复利对终值的影响逐渐增加。1-11FutureValues–Example3ThecaseofPeterMinuetandtheIndians•In1626,MinuetboughtallofManhattanIsland(曼哈顿岛)forabout$24ingoodsandtrinkets(珠宝饰物).Thissoundscheap,buttheIndiansmayhavegottenthebetterendofthedeal.Toseewhy,supposetheIndianshadsoldthegoodsandinvestedthe$24at10%.Howmuchwoulditbeworthtoday?Thefuturevalueinterestfactorisapproximately:1.1380≈5，000，000，000，000，000TheFVof$24willbe$24*5quadrillion(千万亿）Howmuchisit?Well,ifyouhadit,youcouldbuytheU.S.Allofit.Cash.Withmoneyleftover(剩下的)tobuyCanada,Mexico,andtherestoftheworld.1-12B.PresentValueandDiscounting•HowmuchdoIhavetoinvesttodaytohavesomeamountinthefuture?FV=PV(1+r)tRearrangetosolveforPV=FV/(1+r)tPVinterestfactor=1/(1+r)t•Thepresentvalueisalwayslessthanthefuturevaluewhenwehavepositiveratesofinterest.1-13PresentValues•Whenwetalkaboutdiscounting,wemeanfindingthepresentvalueofsomefutureamount.•Whenwetalkaboutthe“value”ofsomething,wearetalkingaboutthepresentvalueunlesswespecificallyindicatethatwewantthefuturevalue.(无特殊情况，我们提到价值即指现值)1-14PV–One-PeriodExample•Supposeyouneed$10,000inoneyearforthedownpaymentonanewcar.Ifyoucanearn7%annually(每年),howmuchdoyouneedtoinvesttoday?PV=$10,000/(1.07)1=$9,345.791-15PresentValues–Example2•Youwanttobeginsavingforyourdaughter’scollegeeducationandyouestimatethatshewillneed$150,000in17years.Ifyoufeelconfident(有信心)thatyoucanearn8%peryear,howmuchdoyouneedtoinvesttoday?PV=$150,000/(1.08)17=$40,540.341-16PV–ImportantRelationshipI•Foragiveninterestrate–thelongerthetimeperiod,thelowerthepresentvalue(ceterisparibus:allelseequal其他条件不变)Whatisthepresentvalueof$500tobereceivedin5years?10years?Thediscountrateis10%5years:PV=$500/(1.1)5=$310.4610years:PV=$500/(1.1)10=$192.771-17PV–ImportantRelationshipII•Foragiventimeperiod–thehighertheinterestrate,thesmallerthepresentvalue(ceterisparibus)Whatisthepresentvalueof$500receivedin5yearsiftheinterestrateis10%?15%?Rate=10%:PV=$500/(1.1)5=$310.46Rate=15%;PV=$500/(1.15)5=$248.591-18PresentValueof$1PVof$1=1/(1+r)t1-19C.MoreonPresentandFutureValues•TheBasicPVEquation-RefresherPV=FV/(1+r)t•TherearefourpartstothisequationPV,FV,r,andtIfweknowanythree,wecansolvefor(求解)thefourth1-20DiscountRate•Often,wewillwanttoknowwhattheimpliedinterestrateisinaninvestment.•Rearrange(颠倒，转换)thebasicPVequationandsolveforrFV=PV(1+r)tr=(FV/PV)1/t–11-21FindingtheNumberofPeriods•StartwithbasicequationandsolvefortFV=PV(1+r)tt=ln(FV/PV)/ln(1+r)lnisthenaturallogarithm(自然对数)andcanbefoundonthecalculator.1-22Theruleof72•Theruleof72isaquickwaytoestimatehowlongitwilltaketodoubleyourmoney.#yearstodouble=72/rwhererisapercent,notadecimal.72/r年后,投资可以翻倍,其中r为百分数.•Ifyouwanttobuyacarwhichcosts￥200,000.Youcurrentlyhave￥100,000.Supposeyouareabletoearn24%eachyear.Howlongwillitbebeforeyouhaveenoughmoneytopaycashforthecar?1-23Example:SpreadsheetStrategies•AnotherTVMformulathatcanbefoundinaspreadsheet(电子表格)isthepaymentformulaPMT(rate,nper,pv,fv)NPER(rate,pmt,pv,fv)Rate(nper,pmt,pv,fv)Thesamesignconvention(惯例，公约)holdsasfortheP