XXXX秋季在职研究生财务2(1).pptx
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XXXX秋季在职研究生财务2(1).pptx
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财务管理,江萍2010年秋季,Handout2,HandoutOutline,DiscountedCashFlowValuation贴现现金流估值NetPresentValueandOtherInvestmentCriteria净现值与其他投资标准Determiningtherelevantcashflows确定相关现金流,1.DiscountedCashFlowValuationOutline,IntroductiontoValuation:
TheTimeValueofMoneyFutureValueandCompounding(连续复利)PresentValueandDiscountingMoreonthefutureandpresentvaluesFutureandPresentValuesofMultiple(复杂,多重的)CashFlowsApplication(应用),I.IntroductiontoValuation:
TheTimeValueofMoney,BasicDefinitions(基本定义):
PresentValueearliermoneyonatimelineFutureValuelatermoneyonatimelineInterestrate“exchangerate”betweenearliermoneyandlatermoneyDiscountrate(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),A.FutureValueandCompoundingExample1,Supposeyouinvest$100foroneyearat5%peryear.Whatisthefuturevalueinoneyear?
Interest=$100*5%=$5Valueinoneyear=principal+interest=$100+$5=$105FutureValue(FV)=$100(1+5%)=$105Supposeyouleavethemoneyinforanotheryear.Howmuchwillyouhavetwoyearsfromnow?
FV=$100(1+5%)(1+5%)=$100(1+5%)2=$110.25,FutureValues:
GeneralFormula,FV=PV(1+r)tFV=futurevaluePV=presentvaluer=periodinterestrateT=numberofperiodsFuturevalueinterestfactor=(1+r)t,Futurevalueof$1,FVof$1=(1+r)t,FutureValuesExample2,Supposeyouinvestthe$100fromtheprevious(之前的)examplefor5years.Howmuchwouldyouhave?
FV=$100(1+5%)5=$127.63,EffectsofCompounding,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,EffectsofCompounding,Considertheexample1FVwithsimpleinterest=$100+5+5=$110FVwithcompoundinterest=$110.25Theextra$0.25comesfromtheinterestof$5*5%=$0.25earnedonthefirstinterestpaymentConsiderexample2FVwithsimpleinterest=$100+5*5=$125FVwithcompoundinterest=$127.63Theeffectofcompoundingissmallforasmallnumberofperiods,butincreasesasthenumberofperiodsincreases(from$0.25to$2.63).,Futurevalue,simpleinterestandcompoundinterest,Theeffectofcompoundingincreasesasthenumberofperiodsincreases.随着期限的增加复利对终值的影响逐渐增加。
FutureValuesExample3ThecaseofPeterMinuetandtheIndians,In1626,MinuetboughtallofManhattanIsland(曼哈顿岛)forabout$24ingoodsandtrinkets(珠宝饰物).Thissoundscheap,buttheIndiansmayhavegottenthebetterendofthedeal.Toseewhy,supposetheIndianshadsoldthegoodsandinvestedthe$24at10%.Howmuchwoulditbeworthtoday?
Thefuturevalueinterestfactorisapproximately:
1.13805,000,000,000,000,000TheFVof$24willbe$24*5quadrillion(千万亿)Howmuchisit?
Well,ifyouhadit,youcouldbuytheU.S.Allofit.Cash.Withmoneyleftover(剩下的)tobuyCanada,Mexico,andtherestoftheworld.,B.PresentValueandDiscounting,HowmuchdoIhavetoinvesttodaytohavesomeamountinthefuture?
FV=PV(1+r)tRearrangetosolveforPV=FV/(1+r)tPVinterestfactor=1/(1+r)tThepresentvalueisalwayslessthanthefuturevaluewhenwehavepositiveratesofinterest.,PresentValues,Whenwetalkaboutdiscounting,wemeanfindingthepresentvalueofsomefutureamount.Whenwetalkaboutthe“value”ofsomething,wearetalkingaboutthepresentvalueunlesswespecificallyindicatethatwewantthefuturevalue.(无特殊情况,我们提到价值即指现值),PVOne-PeriodExample,Supposeyouneed$10,000inoneyearforthedownpaymentonanewcar.Ifyoucanearn7%annually(每年),howmuchdoyouneedtoinvesttoday?
PV=$10,000/(1.07)1=$9,345.79,PresentValuesExample2,Youwanttobeginsavingforyourdaughterscollegeeducationandyouestimatethatshewillneed$150,000in17years.Ifyoufeelconfident(有信心)thatyoucanearn8%peryear,howmuchdoyouneedtoinvesttoday?
PV=$150,000/(1.08)17=$40,540.34,PVImportantRelationshipI,Foragiveninterestratethelongerthetimeperiod,thelowerthepresentvalue(ceterisparibus:
allelseequal其他条件不变)Whatisthepresentvalueof$500tobereceivedin5years?
10years?
Thediscountrateis10%5years:
PV=$500/(1.1)5=$310.4610years:
PV=$500/(1.1)10=$192.77,PVImportantRelationshipII,Foragiventimeperiodthehighertheinterestrate,thesmallerthepresentvalue(ceterisparibus)Whatisthepresentvalueof$500receivedin5yearsiftheinterestrateis10%?
15%?
Rate=10%:
PV=$500/(1.1)5=$310.46Rate=15%;PV=$500/(1.15)5=$248.59,PresentValueof$1,PVof$1=1/(1+r)t,C.MoreonPresentandFutureValues,TheBasicPVEquation-RefresherPV=FV/(1+r)tTherearefourpartstothisequationPV,FV,r,andtIfweknowanythree,wecansolvefor(求解)thefourth,DiscountRate,Often,wewillwanttoknowwhattheimpliedinterestrateisinaninvestment.Rearrange(颠倒,转换)thebasicPVequationandsolveforrFV=PV(1+r)tr=(FV/PV)1/t1,FindingtheNumberofPeriods,StartwithbasicequationandsolvefortFV=PV(1+r)tt=ln(FV/PV)/ln(1+r)lnisthenaturallogarithm(自然对数)andcanbefoundonthecalculator.,Theruleof72,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?
Example:
SpreadsheetStrategies,AnotherTVMformulathatcanbefoundinaspreadsheet(电子表格)isthepaymentformulaPMT(rate,nper,pv,fv)NPER(rate,pmt,pv,fv)Rate(nper,pmt,pv,fv)Thesamesignconvention(惯例,公约)holdsasforthePVandFVformulasClickontheExcelicon(图标)foranexamplerate贷款利率nper该项贷款的付款总数pv现值fv为未来值type数字0或1pmt贷款的每期支付额,II.FutureandPresentValuesofMultipleCashFlows,FVandPVcalculationwhentherearemultiple(复合的,不同的)cashflows.不同于multipleperiods,ie,一个cashflow,贴现到N年前的case.,TwoWaystoCalculateFVforMultipleCFs,
(1)compoundtheaccumulatedbalanceforwardoneyearatatimeor计算出每年的现金流余额再求终值
(2)calculatethefuturevalueofeachcashflowfirstandthenaddtheseup.计算出每个现金流的终值再相加。
Bothgivethesameanswer,soyoucandoiteitherway.,MultipleCashFlowsFVExample,Supposeyouplantodeposit$100intoanaccount(账户)inoneyearand$300intotheaccountinthreeyears.Howmuchwillbeintheaccountinfiveyearsiftheinterestrateis8%?
FV=$100(1.08)4+$300(1.08)2=$136.05+$349.92=$485.97,ExampleTimeLine,$100,0,1,2,3,4,5,$300,$136.05,$349.92,$485.97,MultipleCashFlowsPV,ItissimilarforPVcalculationExample:
Youareofferedaninvestmentthatwillpayyou$200inoneyear,$400thenextyear,$600thenextyearand$800attheendofthenextyear.Youcanearn12percentonverysimilarinvestments.Whatisthemostyoushouldpayforthisone?
(Or“Howmuchisthisinvestmentworth?
”),ExampleTimeLine,Example:
SpreadsheetStrategies,YoucanusethePVorFVfunctionsinExceltofindthepresentvalueorfuturevalueofasetofcashflowsSettingthedataup(构建数组)ishalfthebattleifitissetupproperly,thenyoucanjustcopytheformulasClickontheExceliconforanexample,III.Application,ValuingAnnuitiesandPerpetuities年金和永续年金的估值LoanTypesandLoanAmortization贷款种类和按揭抵押贷款ValuationofBondandStock债券和股票估值,A.Annuities,DefinitionThecashflowsfromthisassetareintheformofathree-year,$500ordinaryannuityAnnuity(年金)finiteseriesofequalpaymentsthatoccuratregularintervalsIfthefirstpaymentoccursattheendoftheperiod,itiscalledanordinaryannuity(普通年金)Ifthefirstpaymentoccursatthebeginningoftheperiod,itiscalledanannuitydue(先付年金),OrdinaryAnnuitiesPV,OrdinaryAnnuities:
AnnuityPVExampleBuyingaHouse,Youarereadytobuyahouseandyouhave$20,000foradownpayment(首付)andclosingcosts(买方过户费用).Closingcostsareestimatedtobe4%oftheloanvalue.Youhaveanannualsalaryof$36,000andthebankiswillingtoallowyourmonthlymortgagepayment(每月按揭还款)tobeequalto28%ofyourmonthlyincome.Theinterestrateontheloanis6%peryearwithmonthlycompounding(.5%permonth)fora30-yearfixedrateloan.Howmuchmoneywillthebankloanyou?
Howmuchcanyouofferforthehouse?
BuyingaHouse-Continued,BankloanMonthlyincome=$36,000/12=$3,000Maximumpayment=.28($3,000)=$840PV=$84011/1.005360/.005=$140,105TotalPriceClosingcosts=.04($140,105)=$5,604Downpayment=$20,0005,604=$14,396TotalPrice=$140,105+14,396=$154,501,OrdinaryAnnuitiesFV,OrdinaryAnnuities:
AnnuitiesFVExample,Supposeyoubeginsavingforyourretirement(退休)bydepositing(存款)$2,000peryear(attheyearend)inaretirementaccount.Iftheinterestrateis7.5%,howmuchwillyouhavein40years?
FV=$2,000(1.075401)/.075=$454,513.04,SpreadsheetStrategiesAnnuityPV/FVExample,ThepresentvalueandfuturevalueformulasinaspreadsheetincludeaplaceforannuitypaymentsClickontheExcelicontoseeanexample,FindingthePayment,Supposeyouwanttoborrow$20,000foranewcar.Youcanborrowat8%peryear,compoundedmonthly(8/12=.666666667%permonth).Ifyoutakea4-yearloan,whatisyourmonthlypayment?
$20,000=C11/1.006666748/.0066667C=$488.26,FindingtheNumberofPayments,Youranalittleshortonyournewyearvacation,soyouput$1,000onyourcreditcard.Youcanonlyaffordtomaketheminimumpaymentof$20permonth.Theinterestrateonthecreditcardis1.5percentpermonth.Howlongwillyouneedtopayoffthe$1,000.,FindingtheNumberofPayments,Startwiththeequationandrememberyourlogs.$1,000=$20(11/1.015t)/.015.75=11/1.015t1/1.015t=.251/.25=1.015tt=ln(1/.25)/ln(1.015)=93.111months=7.75yearAndthisisonlytrueifyoudontchargeanythingmoreonthecard!
SpreadsheetStrategiesAnnuityPaymentExample,AnotherTVMformulathatcanbefoundinaspreadsheetisthepaymentformulaPMT(rate,nper,pv,fv)NPER(rate,pmt,pv,fv)Rate(nper,pmt,pv,fv)ThesamesignconventionholdsasforthePVandFVformulasClickontheExceliconforanexample,Perpetuities(永续年金),Perpetuity:
anannuityinwhichthecashflowscontinueforever.Pe
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