第三章融资的利息因素(房地产金融与投资-武汉理工大学.ppt

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1、Chapter 3 The Interest Factor in Financing融资的利息因素q3.1 复利 compound interest复利有四个基本组成部分1.本金,即投资的现值present value2.利息率interest rate3.期限time4.未来某特定时期的价值future value2021/9/1813.2 Future Value终值q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q一般公式2021/9/182计息期间对复利的影响q一般公式q按月计息 m=12q按天计息m=3652021/9/183名义年利率与

2、实际年收益率q实际年收益率EAY(effective annual yield)q按年计息q按月计息2021/9/184复利因子IF(interest factors)q对公式q对按月计算公式为年复利因子为月复利因子2021/9/185复利表compound interest tableq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%11.0050001.00667021.0100251.01337831.0150751.02013441.0201511.02693551.0252511.03378161.0303781.04067371.0355291.04761

3、02021/9/1863.3 Present Value现值q现值即未来收益的折现(Discounting),它反映了货币的时间价值(time value),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)。q折现过程是计算复利的逆过程,如2021/9/187折现因子discounting factors1元现值表（年折现因子）年数6%15%10.9433960.86956520.8899960.75614430.8396190.65751640.7920940.57175350.7472580.49717760.70496

4、10.4323282021/9/188Question 1qHow much should an investor pay today for a real estate investment that will return 20000 yuan at the end of three years,assuming the investor desires an annual return of 15 percent interest on the amount invested?2021/9/189Question 2qHow much should an investor pay to

5、receive 12000 yuan three years(36 months)from now,assuming that the investor desires an annual return of 9 percent compounded monthly?qSolution2021/9/18103.5 年金的终值FVAFuture Value of an Annuityq每隔等长时间收入或支付的等额系列款项叫年金。q年末存款的年金公式q或2021/9/1811年金复利因子FVIFAq月末投入q年末投入2021/9/1812Question 3qAn investor pays 20

6、0yuan per month into a real estate investment that promises to pay an annual rate of interest of 8 percent compounded monthly.If the investor makes consecutive monthly payments for five years,what is the future value at the end of five years?qSolution2021/9/18133.5 年金的现值PVAPresent Value of an Annuit

7、yq基本思路：将投资者定期收入的等额款项（R）折为现值。2021/9/1814q月末收入q年末收入年金现值因子PVIFA2021/9/1815例2021/9/1816Question 4qAn investor has an opportunity to invest in a rental property that will provide net cash returns of 400 yuan per year.The investor believes that an annual return of 10 percent should be earned on this inves

8、tment,how much should the investor pay for the rental property?qSolution2021/9/1817Question 5qA real estate partnership predicts that it will pay$300 at the end of each month to its partners over the next six months.Assuming the partners desire an 8 percent return compounded monthly on their investm

9、ent.how much should they pay?qSolution2021/9/1818总计终值的累积Accumulation of a Future SumqFor example,assume we have a debt of$20000 that must be repaid in one lump sum at the end of five years.We would like to make a series of equal annual payments at the end of each of the five years,so that we will ha

10、ve$20000 at the end of the fifth year from the accumulated deposits plus interest.Assuming that we can earn 10 percent interest per year on those deposits,how much should each annual deposit be?2021/9/1819qSolutionq0.163797被称为偿债基金因子SFF（sinking-fund factor）,或一般形式:2021/9/18203.7 投资收益率或内部收益率的计算q3.7.1 具

11、有单一收入来源的投资An investor has an opportunity today to buy an unimproved one-acre lot for$5639,the lot is expected to appreciate in value and to be worth$15000 after seven years.What rate of interest(or investment yield)would be earned on the investment?v15%即为该投资的投资收益率或内部收益率IRR(internal rate of return)20

12、21/9/18213.7.2 年金投资的收益率Yields on Investment AnnuitiesqSuppose an investor has an opportunity to make an investment in real estate costing$3170 that would provide him with cash income of$1000 at the end of each year for four years.What investment yield,or internal rate of return,would the investor ea

13、rn on$3170?2021/9/1822qSolve for investment yield2021/9/1823内部收益率与现金收入情况表1234Investment(balance)$3170$2487$1736$910IRR at 10%317249*174*90*Cash received$1000$1000$1000$1000 Less:Cash yield at 10%31724917490Recovery of investment$683$751$826$910Investment(beginning of year)$3170$2487$1736$910 Less:Re

14、covery of investment683751826910Investment(end of year)$2487$1736$9100*Rounded(近似值)2021/9/1824按月年金的投资收益率Monthly Annuities:Investment YieldsqSuppose an investor makes an investment of$51593 to receive$400 at the end of each month for the next 20 years(240 months).What annual rate of return,compound m

15、onthly,would be earned on$51593?2021/9/18253.7.3 实际年收益率Effective Annual YieldsqEANR(equivalent nominal annual rate)-等值名义年利率q一般形式2021/9/18262021/9/1827qAn investment is made in the amount of$8000 and the contract calls for investment returns to be reported as compounded annually.Monthly cash flows of$500 are received for 17 months.What is the annual return on the investment?qSolution2021/9/18282021/9/18292021/9/18302021/9/18312021/9/1832