第三章融资的利息因素房地产金融与投资武汉理工大学

第三章融资的利息因素(房地产金融与投资武汉理工大学2023/12/28第三章融资的利息因素(房地产金融与投资武汉理工大学3.2FutureValue

终值常用符号PV:现值,即本金principali:利息率I:利息额FV:n年后的本息和,即终值一般公式第三章融资的利息因素(房地产金融与投资武汉理工大学计息期间对复利的影响一般公式按月计息m=12按天计息m=365第三章融资的利息因素(房地产金融与投资武汉理工大学名义年利率与实际年收益率实际年收益率EAY(effectiveannualyield)按年计息按月计息第三章融资的利息因素(房地产金融与投资武汉理工大学复利因子IF(interestfactors)对公式对按月计算公式为年复利因子为月复利因子第三章融资的利息因素(房地产金融与投资武汉理工大学复利表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%11.0050001.00667021.0100251.01337831.0150751.02013441.0201511.02693551.0252511.03378161.0303781.04067371.0355291.047610第三章融资的利息因素(房地产金融与投资武汉理工大学3.3PresentValue

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,如第三章融资的利息因素(房地产金融与投资武汉理工大学折现因子discountingfactors1元现值表（年折现因子）年数6%15%10.9433960.86956520.8899960.75614430.8396190.65751640.7920940.57175350.7472580.49717760.7049610.432328第三章融资的利息因素(房地产金融与投资武汉理工大学Question1Howmuchshouldaninvestorpaytodayforarealestateinvestmentthatwillreturn20000yuanattheendofthreeyears,assumingtheinvestordesiresanannualreturnof15percentinterestontheamountinvested?第三章融资的利息因素(房地产金融与投资武汉理工大学Question2Howmuchshouldaninvestorpaytoreceive12000yuanthreeyears(36months)fromnow,assumingthattheinvestordesiresanannualreturnof9percentcompoundedmonthly?Solution第三章融资的利息因素(房地产金融与投资武汉理工大学3.5年金的终值FVA

FutureValueofanAnnuity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或第三章融资的利息因素(房地产金融与投资武汉理工大学年金复利因子FVIFA月末投入年末投入第三章融资的利息因素(房地产金融与投资武汉理工大学Question3Aninvestorpays200yuanpermonthintoarealestateinvestmentthatpromisestopayanannualrateofinterestof8percentcompoundedmonthly.Iftheinvestormakesconsecutivemonthlypaymentsforfiveyears,whatisthefuturevalueattheendoffiveyears?Solution第三章融资的利息因素(房地产金融与投资武汉理工大学3.5年金的现值PVA

PresentValueofanAnnuity基本思路：将投资者定期收入的等额款项（R）折为现值。第三章融资的利息因素(房地产金融与投资武汉理工大学月末收入年末收入年金现值因子PVIFA第三章融资的利息因素(房地产金融与投资武汉理工大学例第三章融资的利息因素(房地产金融与投资武汉理工大学Question4Aninvestorhasanopportunitytoinvestinarentalpropertythatwillprovidenetcashreturnsof400yuanperyear.Theinvestorbelievesthatanannualreturnof10percentshouldbeearnedonthisinvestment,howmuchshouldtheinvestorpayfortherentalproperty?Solution第三章融资的利息因素(房地产金融与投资武汉理工大学Question5Arealestatepartnershippredictsthatitwillpay$300attheendofeachmonthtoitspartnersoverthenextsixmonths.Assumingthepartnersdesirean8percentreturncompoundedmonthlyontheirinvestment.howmuchshouldtheypay?Solution第三章融资的利息因素(房地产金融与投资武汉理工大学总计终值的累积

AccumulationofaFutureSumForexample,assumewehaveadebtof$20000thatmustberepaidinonelumpsumattheendoffiveyears.Wewouldliketomakeaseriesofequalannualpaymentsattheendofeachofthefiveyears,sothatwewillhave$20000attheendofthefifthyearfromtheaccumulateddepositsplusinterest.Assumingthatwecanearn10percentinterestperyearonthosedeposits,howmuchshouldeachannualdepositbe?第三章融资的利息因素(房地产金融与投资武汉理工大学Solution0.163797被称为偿债基金因子SFF（sinking-fundfactor）,或一般形式:第三章融资的利息因素(房地产金融与投资武汉理工大学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?15%即为该投资的投资收益率或内部收益率IRR(internalrateofreturn)第三章融资的利息因素(房地产金融与投资武汉理工大学3.7.2年金投资的收益率

YieldsonInvestmentAnnuitiesSupposeaninvestorhasanopportunitytomakeaninvestmentinrealestatecosting$3170thatwouldprovidehimwithcashincomeof$1000attheendofeachyearforfouryears.Whatinvestmentyield,orinternalrateofreturn,wouldtheinvestorearnon$3170?第三章融资的利息因素(房地产金融与投资武汉理工大学Solveforinvestmentyield第三章融资的利息因素(房地产金融与投资武汉理工大学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)第三章融资的利息因素(房地产金融与投资武汉理工大学按月年金的投资收益率

MonthlyAnnuities:InvestmentYieldsSupposeaninvestormakesaninvestmentof$51593toreceive$400attheendofeachmonthforthenext20years(240months).Whatannualrateofreturn,compoundmonthly,wouldbeearnedon$51593?第三章融资的利息因素(房地产金融与投资武汉理工大学3.7.3实际年收益率

EffectiveAnnualYieldsEANR(equivalentnominalannualrate)--等值名义年利率一般形式第三章融资的利息因素(房地产金融与投资武汉理工大学第三章融资的利息因素(房地产金融与投资武汉理工大学Aninvestmentismadeintheamountof$8000andthecontractcallsforinvestmentreturnstobereportedascompoundedannually.Monthlycashflowsof$