第02章 货币的时间价值.ppt

1、1,公司金融,武汉大学经济与管理学院,2,第二章 货币的时间价值,一、时间与价值 二、单利与复利 三、资金等值计算,3,Which would you prefer - $100,000 today or $100,000 in 5 years?,Obviously, $100,000 today.,You already recognize that there is TIME VALUE of MONEY!,Obviously, $100,000 today.,You already recognize that there is TIME VALUE of MONEY!,Obviousl

2、y, $100,000 today.,4,Should you get your master degree？ How should you arrange your plans for good dreams? (town house, BMW, spacewalk),5,一、时间与价值,Why is TIME such an important element in your decision? TIME allows you the opportunity to postpone consumption and earn INTEREST.,6,What Would Represent

3、the Time Value of Money?,No risk, no inflation. Interest rate of T-bills (one-year) (in America) 一年期基准存款利率（in China),7,Interest Rates In China ( ),8,Compound Interest Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent).,Simple Interest Interest paid (e

4、arned) on only the original amount, or principal borrowed (lent).,二、单利与复利,9,单利法与复利法,单利法：只以本金作为计算利息的基数 复利法：以本金和累计利息之和作为计算利息的基数,10,单利法计算利息结果,11,复利法计算利息结果,12,The Effect of Compounding,13,The Effect of Compounding,1626年印地安人以24美元把纽约曼哈顿岛卖给英国移民，几乎所有人都认为卖得太便宜了！但若印地安人能把24美元投资年报酬率7%的股票或定存连续到2004年(378年后)则可得7,4

5、41,204,377,345 美元(74.4兆美元)，超过2004年纽约曼哈顿房地产的总市值2.5兆美元！,14,连续复利,What is the EAR if the quoted rate is r% and the compounding is: annual semi-annual quarterly monthly weekly daily every hour, minute, second Continuous compounding : EAR = er-1 where e is 2.718.,15,10%简单年利率下计息次数与EAR之间的关系,16,简单年利率与有效年利率,当

6、计算利息的周期小于一年时，将用计息周期表示的利率按单利法和复利法转换为年利率，其结果是不同的（一年内计息次数为m)。 按单利法转换的年利率为简单年利率（APR） 按复利法转换的年利率为有效年利率（EAR）,17,连续复利的计算,计算利息的周期趋近于无穷小，一年内计算利息的次数趋近于无穷大，这种计算利息的方法称为连续复利。 连续复利所得的复利价值最大 常用于数学模型进行经济问题分析,18,小心成为卡奴！,信用卡可以让人债台高筑。 例，招商银行，日复利万分之五（0.05%)，其简单年利率为0.05%36518.25%，有效年利率为（10.05%)365-1=20%. (我国一年期存款利率为4.14

7、，13年期贷款基准利率为7.74%.) 以循环利率20，每月只还最低应缴金额3来计算，欠200,000卡债，全部还清得十四年九个月，总共要花359,789元。欠500,000的要还二十年三个月！,19,三、资金等值计算,现值与终值 年金的现值与终值 资金回收 偿债基金 其他问题,20,现值与终值的概念,基本公式:,上式中， PV 为现值， FV 为终值， r 为利率（复利）， t 为期数。,21,图示,二维坐标系表示现金流量发生的时间与大小 三要素： 时间轴；箭头方向；箭头长短。,22,一次支付现值的计算,PV=FV1/（1+r)t=FV(P/F, r, t) (P/F, r, t)称为一次支

8、付现值系数 现在存多少钱，在利率为r的情况下，经过t个周期后等于一元钱？,23,复利现值系数表（一次支付现值系数， 查附表）,PV2=1000（P/F,i,t) =1000（ P/F,7%,2) =10000.873=873,查表计算：一次支付现值的计算,24,Application to Personal Finance: An Example,Suppose it is January 1st 2007, you just turned 25 and expecting to retire at the age of 65 on January 1st 2047. Your biggest

9、 dream is to go on a 1-month yacht tour in the Mediterranean that will cost you $65,000 in 2047 when you retire. To be able to pay for this yacht tour in 2047, how much should you put in a savings account that has an interest rate of 1% per quarter compounded quarterly?,25,一次支付的终值计算,FV=PV （1+r)t=PV(

10、F/P, r, t) (F/P, r, t)称为一次支付终值系数 现在的一元钱在利率为r的情况下，经过t个周期后值多少钱？,26,复利终值系数表（一次支付终值系数，查附表）,FV2=1000（F/P,i,t) =1000（ F/P,7%,2) =10001.1449=1144.9,查表计算：一次支付的终值计算,27,年金的现值与终值,普通年金 增长年金 永久年金,28,普通年金,A constant stream of cash flows with a fixed maturity.(年金是指稳定有规律、持续一段时间的现金流),29,普通年金的现值计算,年金的现值(查附表）,30,年金的现值

11、计算,例：某公司员工每年的房屋补贴是9600元，假设年利率为3%，那么十年的房屋补贴的现值为多少元？,根据现值的计算公式： 其中A=9600，r=3%，t=10 查表计算：PV=81888元,31,普通年金的终值,经济含义：从第一年年末到第t年年末，每年存入银行1元钱，在利率为r的情况下，在第t年年末能取出多少钱？,32,年金的终值计算,年金的终值(查附表）,年金的终值计算,例：某工程计划投资10亿元，施工期5年，假定每年分担投资2亿元，如果全部投资由银行贷款，贷款利率为7%，问工程建成时，实际欠款多少？ 由公式： 其中： A=2，t=5，r=7% 查表计算：FV=11.5亿元,33,34,增

12、长年金,A growing stream of cash flows with a fixed maturity.,The formula for the present value of a growing annuity:,35,计算：增长年金的现值,A defined-benefit retirement plan offers to pay $20,000 per year for 40 years and increase the annual payment by three-percent each year. What is the present value at retir

13、ement if the discount rate is 10 percent?,例：小王年收入10万元，预计收入增长率为5%，收入的30%用于储蓄，小王打算5年后购房，存款利息为8%，5年后储蓄积累的资金为多少？,增长年金的终值,五年后的储蓄积累为：,36,37,永久年金,A constant stream of cash flows that lasts forever.,永久年金的现值计算：,38,Perpetuity: Example,What is the value of a British consol that promises to pay 15 each year, ev

14、ery year until the sun turns into a red giant and burns the planet to a crisp? The interest rate is 10-percent.,39,永久增长年金,A growing stream of cash flows that lasts forever.,The formula for the present value of a growing perpetuity is:,40,稳定增长股利模型,41,Growing Perpetuity: Example,The expected dividend

15、next year is $1.30 and dividends are expected to grow at 5% forever. If the discount rate is 10%, what is the value of this promised dividend stream?,42,资金回收,年金的资金回收系数：已知现值求年金，是年金现值系数的倒数运算。,年金的资金回收计算,例：某人现借款10万元，年利率为6%，若要求5年内等额偿还，求每年末要偿还的金额。,根据公式： 其中PV=10，r=6%，t=5,查表计算：A=2.374万元,43,一个月后欠银行的贷款为：,等额本息

16、法的推导过程： 设贷款总额为A，银行月利率为r，总月数为n，月 还款额为b，可得：,等额本息法,两个月后欠银行的贷款为：,三个月后欠银行的贷款为：,依此类推，n个月后欠银行的贷款为： n个月还完贷款，所以 那么：,44,45,偿债基金,年金的偿债基金系数：已知终值求年金，是年金终值运算的倒数运算。,年金的偿债基金计算,例：企业准备10年内每年末存入银行一笔钱，以便在第10年末归还一笔到期100万元的债务。如果存款的年利率为10%，请问每年末至少应存入银行多少资金？,已知 =100，r=10%，t=10，求A,根据公式：,查表计算：A=6.27万元,还款100万,46,47,其他问题,注意事项

17、三对倒数关系 多重现金流问题,48,资金等值计算中的注意事项,一定要画现金流量图 注意时间概念 “现在”是指项目的第一年年初； 本年末即下年初； 通常每一时点代表当期期末。 当问题涉及FV和A的计算时，FV是年金中最后一个年金对应年份的等值。 当问题涉及PV和A的计算时，PV是年金中第一个年金前一年的等值。,49,例题,某企业购买一大型设备，若货款现在一次付清需100万元；也可采用分期付款，从第二年年末到第四年年末每年付款40万元。假设资金利率为10%，问该企业应选择何种付款方式？,50,方法一：选择“0”时点,分期付款好于一次付款,51,方法二：选择“1”时点,52,方法三：选择“4”时点,

18、53,方法四：比较“A”,54,三对倒数关系,55,Multiple Cash Flows,So far we have assumed a single cash flow, but we will be dealing with investments that generate multiple cash flows over their life times. Fortunately, the cash flows are additive as long as they are evaluated at the same point in time , i.e.,56,Multiple Cash Flows : Should you get your master degree?,Two years of work experience after college, you have to decide whether to get a master degree or not. Suppose you are earning ￥80,000/year before entering a business school and assume that the tuition costs are ￥ 20,000/year. Expected