Topic1ValuationofFutureCashFlows(未来现金流定

ValuationofFutureCashFlowsEC50002GlobalFinancialMarketsTopic1Reading1−2•Bodie,MertonandCleeton,FinancialEconomics–Chapter4Outline1−3•RateofReturn•FutureValueandPresentValue–CompoundInterest–Ruleof72•Perpetuities–Valuesofconsolsandstocks•Annuities–LoanAmortisationRateofReturn1−4•Percentagechangeinthevalueoftheinvestmentoveraperiodoftime𝑅𝑅𝑅𝑅𝑜𝑜𝑅𝑅𝑅𝑅𝑅𝑅=𝑃𝑅𝑜𝑜𝑃𝑅𝑃𝐼𝑅𝐼𝑅𝑃𝑅𝐼𝑅𝑅𝑅×100%𝑅𝑅𝑅𝑅𝑜𝑜𝑅𝑅𝑅𝑅𝑅𝑅=𝑅𝑡𝐼𝑅𝐼𝑅𝑃𝑅𝐼𝑅𝑅𝑅=𝐶0𝑃𝑅𝑜𝑜𝑃𝑅𝑃=𝐶𝑡−𝐶0+𝐼𝑅𝑅𝑅𝑅𝑃𝐼𝑐𝑅𝑃𝑐𝑜𝑓𝑜𝑓𝑃RateofReturn1−5•Rateofreturnonholdingashare𝑅𝑡=𝑃𝑡−𝑃0+𝐷𝑃𝐼0,𝑡𝑃0×100%012tPtP2P1P0timeDividendRateofReturn1−6•Rateofreturnonholdingabond𝑅𝑡=𝑃𝑡−𝑃0+𝐶𝑜𝑅𝐶𝑜𝑅0,𝑡𝑃0×100%012tPtP2P1P0timeInterest/CouponRateofReturn1−7Example1Youboughtasharefor£100.After5months,youreceivedadividendof£5andsoldthesharefor£110.Whatisyourrateofreturnfortheholdingperiod?𝑅𝑡=£110−£100+£5£100×100%=£110−£100£100+£5£100×100%CapitalGainDividendYieldRateofReturn1−8•Decompositionofrateofreturn–TimevalueofmoneyApoundinhandtodayisworthmorethanapoundpromisedatsometimeinthefuture.Risk-freeinterestrate–Compensationforrisk–AdjustmentforinflationFutureValue1−9•Futurevalue(FV)referstotheamountofmoneyaninvestmentwillgrowtooversomeperiodoftimeatsomegiveninterestrate.Example2Supposeyouput£1,000intoanaccountearninganinterestrateof10%peryear.(1)WhatistheFVofyourinvestmentafteroneyear?𝐹𝐹1=£1,000×1+10%=£1,100(2)WhatistheFVofyourinvestmentafterfiveyears?FutureValue1−10•SimpleInterestInterestonlyearnedontheoriginalprincipal(theamountborrowedorlent)Example2-continuedSupposeyouput£1,000intoanaccountearninganinterestrateof10%peryear.(1)WhatistheFVofyourinvestmentafteroneyear?𝐹𝐹1=£1,000×1+10%=£1,100(2)WhatistheFVofyourinvestmentafterfiveyears?𝐹𝐹5=£1,000×1+10%×5=£1,500FutureValue1−11•CompoundInterestInterestearnedonboththeoriginalprincipalandinterestalreadypaidExample2-continuedSupposeyouput£1,000intoanaccountearninganinterestrateof10%peryear.(1)WhatistheFVofyourinvestmentafteroneyear?𝐹𝐹1=£1,000×1+10%=£1,100(2)WhatistheFVofyourinvestmentafterfiveyears?𝐹𝐹5=£1,000×1+10%5=£1,610.51FutureValue1−12•Ruleof72Thenumberofperiodsittakesforasumofmoneytodoubleinvalueisapproximatelyequalto72dividedbytheinterestrateexpressedinpercentperperiod.Example3Ataninterestrateof3%permonth,howlongwillittakeyoutodoubleyourmoney?D𝑜𝑅𝑜𝑓𝑃𝑅𝑜𝑇𝑃𝐼𝑅=72𝐼𝐼𝑡𝐼𝐼𝐼𝐼𝑡𝑅𝑅𝑡𝐼=723=24𝐼𝑜𝑅𝑅𝑐𝑃FutureValue1−13•Ruleof72–Thenumberofperiodsittakesforasumofmoneytodoubleinvalueisapproximatelyequalto72dividedbytheinterestrateexpressedinpercentperperiod.–Theexactformulais(1+𝑅)𝑡=1+100%→𝑅=ln(1+100%)ln(1+𝑅)FutureValue1−14•Differentwaysofquotinginterestrates–Annualpercentagerate(APR)𝑅𝐶𝑅𝑅𝐶𝑅𝑅𝑃𝑜𝑝=𝐴𝑃𝑅𝐼𝐼=𝑅𝑅𝐼𝑜𝑅𝑅𝑜𝑜𝑐𝑜𝑅𝐼𝐶𝑜𝑅𝑅𝑝𝑃𝑅𝑜𝐶𝑅𝑅𝑃𝑜𝑝𝑃𝐶𝑅𝑅𝑦𝑅𝑅𝑅–Annualeffectiverate(AER):theequivalentinterestrateifcompoundingwasonceperyear𝐴𝐴𝑅=1+𝐴𝑃𝑅𝐼𝑚−1Withcontinuouscompounding(𝐼→∞),1+𝐴𝐴𝑅𝑚𝑚→𝑅𝐴𝐴𝑅FutureValue1−15iiiiiiivvPeriodsInterestValueperperAPRafterAERyearperiod(i×ii)oneyear16%6%1.066.000%2361.032=1.06096.09041.561.0154=1.061366.13612.561.00512=1.061686.16852.115461.00115452=1.061806.180365.016461.000164365=1.061836.183FutureValue1−16Example4Supposeyouareoffereda$80,000automobileloanatanAPRof6%withmonthlypayments.WhatistheAER?Andwhatwillbeyourtotalrepaymentoftheloan?FutureValue1−17Example4−continuedSupposeyouareoffereda$80,000automobileloanatanAPRof6%withmonthlypayments.WhatistheAER?Andwhatwillbeyourtotalrepaymentoftheloan?𝐴𝐴𝑅=1+𝐴𝑃𝑅𝐼𝑚−1=1+0.061212−1=6.1678%𝐿𝑜𝑅𝑅𝑃𝑅𝑦𝐼𝑅𝑅𝑅=$80,000×(1+𝐴𝐴𝑅)=$84,934.22PresentValue1−18•Presentvalue(PV)referstothecurrentvalueoffuturecashflowsdiscountedattheappropriatediscountrate(opportunitycostofcapital).Example5Supposeyouwishtohave£1,000oneyearfromnowandcanearn10%interestperyear.TheamountyoumustinvestnowisthePVof£1,000.𝑃𝐹1=£1,0001+10%=£909.09FVandPV1−19•Ingeneral,𝐹𝑅𝑅𝑅𝑅𝑅𝐼𝑅𝑓𝑅𝑅𝑜𝑅𝑐𝑅𝑜𝑅=1+𝑅𝑡𝑃𝑅𝑅𝑃𝑅𝑅𝑅𝐼𝑅𝑓𝑅𝑅𝑜𝑅𝑐𝑅𝑜𝑅=11+𝑅𝑡𝐹𝐹=𝑃𝐹1+𝑅𝑡𝐹𝐹=𝑃𝐹𝑅𝐼𝑡FVandPV1−20•MultiplecashflowsIftheinterestrateisconstantovertime,then𝐹𝐹=𝐶1×1+𝑅𝑇−1+𝐶2×1+𝑅𝑇−2+⋯+𝐶𝑇𝑃𝐹=𝐶11+𝑅1+𝐶21+𝑅2+⋯+𝐶𝑇1+𝑅𝑇1Ct=02C3C2C1234TCTFVandPV1−21•Netpresentvalue(NPV)methodincapitalbudgeting–AccepttheprojectisNPV0Example6Assumethatthecashflowsfromtheconstructionandsaleofanofficebuildingisasfollows.Givena5%requiredrateofreturn,shouldyougoaheadwiththeproject?000,320000,100000,1702Year1Year0Year+−−FVandPV1−22Example6–continuedAssumethatthecashflowsfromtheconstructionandsaleofanofficebuildingisasfollows.Givena5%requiredrateofreturn,shouldyougoaheadwiththeproject?()011,25£249,290000,320907.2238,95000,100952.1000,170000,1700.10ValuePresentFlowCashFactorDiscountPeriod205.1105.11==++=−−=−−TotalNPVFVandPV1−23Example6–continuedAssumethatthecashflowsfromtheconstructionandsaleofanofficebuildingisasfollows.Givena5%requiredrateofreturn,shouldyougoaheadwiththeproject?PresentValueYear0-170,000-100,000/1.05320,000/1.052Total=NPV-£170,000=-£170,000=-£95,238=£290,249=£25,011-£100,000+£320,000Year012Per