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1、5TimevalueofmoneyCompindingfuturevalueFVDiscountingpresentvaluePVInterestrateexchangeratebetweenearlierandlatermoneyvFV=PV(1+r)tvPV=FV/(1+r)t§r=periodinterestrate,expressedasadecimal§t=numberofperiods§Futurevalueinterestfactor=(1+r)t复利终值系数§1/(1+r)tpresentvaluef
2、actor现值系数§Foragiveninterestrate–thelongerthetimeperiod,thelowerthepresentvalue§Foragiventimeperiod–thehighertheinterestrate,thesmallerthepresentvaluevr=(FV/PV)1/t–1vt=ln(FV/PV)/ln(1+r)6DiscountedCashFlowValuationvFutureandPresentValuesofMultipleCashFlowsYouthin
3、kyouwillbeabletodeposit$4,000attheendofeachofthenextthreeyearsinabankaccountpaying8percentinterest.Youcurrentlyhave$7,000intheaccount.Howmuchwillyouhaveinthreeyears?Infouryears?Today(year0CF):3N;8I/Y;-7,000PV;CPTFV=8,817.98FV=7000(1.08)3=8,817.98Year1CF:2N;8I/Y
4、;-4000PV;CPTFV=4,665.60FV=4,000(1.08)2=4,665.60Year2CF:1N;8I/Y;-4000PV;CPTFV=4,320FV=4,000(1.08)=4,320Year3CF:value=4,000Totalvaluein3years=8817.98+4665.60+4320+4000=21,803.58Valueatyear4:1N;8I/Y;-21803.58PV;CPTFV=23,547.87Youareofferedaninvestmentthatwillpayyo
5、u$200inoneyear,$400thenextyear,$600thenextyearand$800attheendofthenextyear.Youcanearn12percentonverysimilarinvestments.Whatisthemostyoushouldpayforthisone?Pointoutthatthequestioncouldalsobephrasedas“Howmuchisthisinvestmentworth?”Calculator:Year1CF:N=1;I/Y=12;FV
6、=200;CPTPV=-178.57Year2CF:N=2;I/Y=12;FV=400;CPTPV=-318.88Year3CF:N=3;I/Y=12;FV=600;CPTPV=-427.07Year4CF:N=4;I/Y=12;FV=800;CPTPV=-508.41TotalPV=178.57+318.88+427.07+508.41=1,432.93现金流都发生在年末e/g后付变先付相当于原来的数据*（1+r）vValuingLevelCashFlows:AnnuitiesandPerpetuitiesuAnn
7、uity年金连续相同的现金流–finiteseriesofequalpaymentsthatoccuratregularintervalsvIfthefirstpaymentoccursattheendoftheperiod,itiscalledanordinaryannuity普通年金vIfthefirstpaymentoccursatthebeginningoftheperiod,itiscalledanannuitydue先付年金uPerpetuity–infiniteseriesofequalpayments
8、永续年金只有现值没有终值期数无限vPerpetuity:PV=C/rvAnnuities优先股有永续年金的特征杠杆：自由资金撬动借有资产美国杠杆高借贷方便FVDN先付FVIFA普通GrowingPerpetuity增长年金Agrowingstreamofcashflowswithafixedmaturity增长率一定Agrowingstream
