第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)2023/12/28第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)3.2FutureValue

終值常用符號PV:現(xiàn)值,即本金principali:利息率I:利息額FV:n年后的本息和,即終值一般公式第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)計息期間對復(fù)利的影響一般公式按月計息m=12按天計息m=365第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)名義年利率與實際年收益率實際年收益率EAY(effectiveannualyield)按年計息按月計息第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)復(fù)利因子IF(interestfactors)對公式對按月計算公式為年復(fù)利因子為月復(fù)利因子第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)復(fù)利表compoundinteresttable復(fù)利表中列出了不同名義年利率和期限下的復(fù)利因子,如下為月復(fù)利表月數(shù)6%8%11.0050001.00667021.0100251.01337831.0150751.02013441.0201511.02693551.0252511.03378161.0303781.04067371.0355291.047610第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)3.3PresentValue

現(xiàn)值現(xiàn)值即未來收益的折現(xiàn)(Discounting),它反映了貨幣的時間價值(timevalue),是計算抵押還款額、確定抵押貸款的實際成本和計算收益性房地產(chǎn)價值等一系列的房地產(chǎn)融資活動的基石(cornerstone)。折現(xiàn)過程是計算復(fù)利的逆過程,如第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)折現(xiàn)因子discountingfactors1元現(xiàn)值表（年折現(xiàn)因子）年數(shù)6%15%10.9433960.86956520.8899960.75614430.8396190.65751640.7920940.57175350.7472580.49717760.7049610.432328第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)Question1Howmuchshouldaninvestorpaytodayforarealestateinvestmentthatwillreturn20000yuanattheendofthreeyears,assumingtheinvestordesiresanannualreturnof15percentinterestontheamountinvested?第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)Question2Howmuchshouldaninvestorpaytoreceive12000yuanthreeyears(36months)fromnow,assumingthattheinvestordesiresanannualreturnof9percentcompoundedmonthly?Solution第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)3.5年金的終值FVA

FutureValueofanAnnuity每隔等長時間收入或支付的等額系列款項叫年金。年末存款的年金公式或第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)年金復(fù)利因子FVIFA月末投入年末投入第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)Question3Aninvestorpays200yuanpermonthintoarealestateinvestmentthatpromisestopayanannualrateofinterestof8percentcompoundedmonthly.Iftheinvestormakesconsecutivemonthlypaymentsforfiveyears,whatisthefuturevalueattheendoffiveyears?Solution第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)3.5年金的現(xiàn)值PVA

PresentValueofanAnnuity基本思路：將投資者定期收入的等額款項（R）折為現(xiàn)值。第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)月末收入年末收入年金現(xiàn)值因子PVIFA第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)例第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)Question4Aninvestorhasanopportunitytoinvestinarentalpropertythatwillprovidenetcashreturnsof400yuanperyear.Theinvestorbelievesthatanannualreturnof10percentshouldbeearnedonthisinvestment,howmuchshouldtheinvestorpayfortherentalproperty?Solution第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)Question5Arealestatepartnershippredictsthatitwillpay$300attheendofeachmonthtoitspartnersoverthenextsixmonths.Assumingthepartnersdesirean8percentreturncompoundedmonthlyontheirinvestment.howmuchshouldtheypay?Solution第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)總計終值的累積

AccumulationofaFutureSumForexample,assumewehaveadebtof$20000thatmustberepaidinonelumpsumattheendoffiveyears.Wewouldliketomakeaseriesofequalannualpaymentsattheendofeachofthefiveyears,sothatwewillhave$20000attheendofthefifthyearfromtheaccumulateddepositsplusinterest.Assumingthatwecanearn10percentinterestperyearonthosedeposits,howmuchshouldeachannualdepositbe?第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)Solution0.163797被稱為償債基金因子SFF（sinking-fundfactor）,或一般形式:第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)3.7投資收益率或內(nèi)部收益率的計算3.7.1具有單一收入來源的投資Aninvestorhasanopportunitytodaytobuyanunimprovedone-acrelotfor$5639,thelotisexpectedtoappreciateinvalueandtobeworth$15000aftersevenyears.Whatrateofinterest(orinvestmentyield)wouldbeearnedontheinvestment?15%即為該投資的投資收益率或內(nèi)部收益率IRR(internalrateofreturn)第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)3.7.2年金投資的收益率

YieldsonInvestmentAnnuitiesSupposeaninvestorhasanopportunitytomakeaninvestmentinrealestatecosting$3170thatwouldprovidehimwithcashincomeof$1000attheendofeachyearforfouryears.Whatinvestmentyield,orinternalrateofreturn,wouldtheinvestorearnon$3170?第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)Solveforinvestmentyield第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)內(nèi)部收益率與現(xiàn)金收入情況表1234Investment(balance)$3170$2487$1736$910IRRat10%317249*174*90*Cashreceived$1000$1000$1000$1000Less:Cashyieldat10%31724917490Recoveryofinvestment$683$751$826$910Investment(beginningofyear)$3170$2487$1736$910Less:Recoveryofinvestment683751826910Investment(endofyear)$2487$1736$9100*Rounded(近似值)第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)按月年金的投資收益率

MonthlyAnnuities:InvestmentYieldsSupposeaninvestormakesaninvestmentof$51593toreceive$400attheendofeachmonthforthenext20years(240months).Whatannualrateofreturn,compoundmonthly,wouldbeearnedon$51593?第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)3.7.3實際年收益率

EffectiveAnnualYieldsEANR(equivalentnominalannualrate)--等值名義年利率一般形式第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)第三章融資的利息因素(房地產(chǎn)金融與投資武漢理工大學(xué)Aninvestmentismadeintheamountof$8000andthecontractcallsforinvestmentreturnstobereportedascompoundedannually.Monthlycashflowsof$