第三章融资的利息因素(房地产金融与投资-武汉理工大学

Chapter3TheInterestFactorinFinancing融资的利息因素3.1复利compoundinterest复利有四个基本组成部分1.本金,即投资的现值presentvalue2.利息率interestrate3.期限time4.未来某特定时期的价值futurevalue3.2FutureValue终值常用符号PV:现值,即本金principali:利息率I:利息额FV:n年后的本息和,即终值一般公式niPVFV1计息期间对复利的影响一般公式mnmiPVFV1按月计息m=12按天计息m=365061678.1100001206.0110000121FV061831.11000036506.01100003651FV名义年利率与实际年收益率实际年收益率EAY(effectiveannualyield)PVPVFVEAY按年计息按月计息%1678.6100001000078.10616EAY%6100001000010600EAY复利因子IF(interestfactors)对公式对按月计算公式niPVFV1),,(1年niFVIFin为年复利因子mnmiPVFV1),,(1月mniFVIFmimn为月复利因子复利表compoundinteresttable复利表中列出了不同名义年利率和期限下的复利因子,如下为月复利表月数6%8%11.0050001.00667021.0100251.01337831.0150751.02013441.0201511.02693551.0252511.03378161.0303781.04067371.0355291.0476103.3PresentValue现值现值即未来收益的折现(Discounting),它反映了货币的时间价值(timevalue),是计算抵押还款额、确定抵押贷款的实际成本和计算收益性房地产价值等一系列的房地产融资活动的基石(cornerstone)。折现过程是计算复利的逆过程,如年niPVIFFViFVPVn,,11折现因子discountingfactors1元现值表（年折现因子）年数6%15%10.9433960.86956520.8899960.75614430.8396190.65751640.7920940.57175350.7472580.49717760.7049610.432328Question1Howmuchshouldaninvestorpaytodayforarealestateinvestmentthatwillreturn20000yuanattheendofthreeyears,assumingtheinvestordesiresanannualreturnof15percentinterestontheamountinvested?315.0112000PV年3%,15,2000PVIF32.13150657516.02000Question2Howmuchshouldaninvestorpaytoreceive12000yuanthreeyears(36months)fromnow,assumingthattheinvestordesiresanannualreturnof9percentcompoundedmonthly?SolutionmosMPVIFPV36%,9,1200079.9169764149.0120003.5年金的终值FVAFutureValueofanAnnuity每隔等长时间收入或支付的等额系列款项叫年金。年末存款的年金公式PiPiPFVAnn2111或iiPiPFVAnntt11110年金复利因子FVIFA月末投入年末投入iinyrsiFVIFAn11),,(121121),,(iimiMFVIFAm月Question3Aninvestorpays200yuanpermonthintoarealestateinvestmentthatpromisestopayanannualrateofinterestof8percentcompoundedmonthly.Iftheinvestormakesconsecutivemonthlypaymentsforfiveyears,whatisthefuturevalueattheendoffiveyears?SolutionmosMFVIFAFVA60%,8,20037.14695476856.732003.5年金的现值PVAPresentValueofanAnnuity基本思路：将投资者定期收入的等额款项（R）折为现值。niRiRiRPVA11111121nnnttiiiRiR111111月末收入年末收入iiiiinyrsiPVIFAnnn11111),,(121211),,(iimiMPVIFAm月年金现值因子PVIFA例486852.21.01.0113%,10,3年PVIFA862452.51208.01208.0116%,8,6月年MPVIFAQuestion4Aninvestorhasanopportunitytoinvestinarentalpropertythatwillprovidenetcashreturnsof400yuanperyear.Theinvestorbelievesthatanannualreturnof10percentshouldbeearnedonthisinvestment,howmuchshouldtheinvestorpayfortherentalproperty?SolutionyrsPVIFAFVA3%,10,40074.994486852.2400Question5Arealestatepartnershippredictsthatitwillpay$300attheendofeachmonthtoitspartnersoverthenextsixmonths.Assumingthepartnersdesirean8percentreturncompoundedmonthlyontheirinvestment.howmuchshouldtheypay?Solution个月6%,8,300MPVIFAFVA74.1758862452.5300总计终值的累积AccumulationofaFutureSumForexample,assumewehaveadebtof$20000thatmustberepaidinonelumpsumattheendoffiveyears.Wewouldliketomakeaseriesofequalannualpaymentsattheendofeachofthefiveyears,sothatwewillhave$20000attheendofthefifthyearfromtheaccumulateddepositsplusinterest.Assumingthatwecanearn10percentinterestperyearonthosedeposits,howmuchshouldeachannualdepositbe?Solution200005%,10,yrsFVIFAP20000105100.6P105100.620000P95.3275163797.0200000.163797被称为偿债基金因子SFF（sinking-fundfactor）,或一般形式:11),(niiniSFF年3.7投资收益率或内部收益率的计算3.7.1具有单一收入来源的投资Aninvestorhasanopportunitytodaytobuyanunimprovedone-acrelotfor$5639,thelotisexpectedtoappreciateinvalueandtobeworth$15000aftersevenyears.Whatrateofinterest(orinvestmentyield)wouldbeearnedontheinvestment?711150005639i%15i15%即为该投资的投资收益率或内部收益率IRR(internalrateofreturn)3.7.2年金投资的收益率YieldsonInvestmentAnnuitiesSupposeaninvestorhasanopportunitytomakeaninvestmentinrealestatecosting$3170thatwouldprovidehimwithcashincomeof$1000attheendofeachyearforfouryears.Whatinvestmentyield,orinternalrateofreturn,wouldtheinvestorearnon$3170?yrsPVIFA4%,?,1000$3170$Solveforinvestmentyieldntti1111000$3170$ii4111000$3170$%10i内部收益率与现金收入情况表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)按月年金的投资收益率MonthlyAnnuities:InvestmentYieldsSupposeaninvestormakesaninvestmentof$51593toreceive$400attheendofeachmonthforthenext20years(240months).Whatannualrateofreturn,compoundmonthly,wouldbeearnedon$51593?PVAyrsMPVIFAR20%,?,51593121211400240ii%5833.0)(mi%712%5833.0)(yi3.7.3实际年收益率EffectiveAnnualYieldsEANR(equivalentnominalannualrate)--等值名义年利率EAYENAR112112121112/1EAYENARmEAYENARm11/1一般形式1216.0112/1ENAR%84106.5121004868.1%6EAY112%7112EAY%2286.71%5833.0112Aninvestmentismadeintheamountof$8000andthecontractcallsforinvestmentreturnstober