公司金融第9次课(19-20学时) 贴现现金流量估价

1、Chapter 6贴现现金流量估价多期现金流量1多期现金流量的终值假定今天你在一个8%利率的账户中存入100美元，1年后你再存入100美元，那么2年后你将有多少钱？（224.64美元）画出现金流量图。2多期现金流量的终值例6-1（P93）如果你在接下来的3年的每一年的年末，在一个利率为8%的银行账户中存入4000美元。目前你在该账户中有7000美元。3年后你将拥有多少钱？4年后呢？（21803.58美元，23547.87美元）3多期现金流量的终值计算多期现金流量的终值的两种方法：（1）将累积余额每次向前复利1年；（2）先计算每笔现金流量的终值，然后再把它们加起来。4多期现金流量的终值例6-2（

2、P95）如果你在1年后存入100美元，2年后存入200美元，3年后存入300美元，那么，第3年年末你将拥有多少钱？其中多少是利息？如果你不再存入额外金额，5年后你将拥有多少钱？假定贴现率始终都是7%。（628.49美元，719.56美元）5Example 1Suppose that you want to buy a computer in 3 years time. With this objective in mind you decide to put some money in the bank in the beginning of each year, starting now.

3、So today you will do a deposit of 1,200, next year 1,400 and 2 years from now you will deposit 1,000. Knowing that the bank is paying an interest rate of 4% how much money will you have in the bank by year 3?6多期现金流量的现值假定你1年后需要1000美元，2年后需要2000美元。如果你的钱可以赚取9%的报酬，那么，你现在应该存入多少，才能正好达到未来所需的这些金额呢？（2600.79美元

4、）7Multiple cash flowsSo far weve only considered a single cash flow. Most real-world investments will involve a stream of cash flows.The present value of a stream of cash flows equals the sum of the present value of each of the cash flows.8年金普通年金：在某段固定期间内，发生在每期期末的一系列固定现金流量。年金的具体情形：消费贷款和住房贷款9年金的现值假定我

5、们正在考察一项资产，该资产承诺在接下来的3年的每年年末支付500美元。如果我们想要赚取10%的报酬率，我们应该对这笔年金出价多少呢？ （1243.43美元）如何计算？10年金的现值11年金的现值年金现值系数12年金的现值例6-5（P98）你已经确定你能负担每月支付632美元来购买一辆新跑车。你打电话给当地银行，查出当前48个月期的月利率是1%。你可以借到多少钱呢？（24000美元）13年金的现值年金现值系数表（P486-487）求付款额C（P99）求付款期t（例6-6 P99 ）求贴现率r（P100）14Finding the annuitySometimes instead of findi

6、ng the present value of a series of payments we may need to know what is the series of payments which will lead to a certain present value.15年金的现值假定你希望创业，经营目前所流行的健康食品冻椰奶。要生产和销售你的产品，你需要借100 000美元。你希望用5年的时间偿还这笔借款，如果利率是18%，每期必须付多少呢？假设每期还的金额是相同的。（31977美元）16Example 2Bill Gates had his wealth estimated in

7、 yearly 2002 at about $52 billion. How much could Mr Gates spend yearly in 40 more years of luxury and excitement if he were to devote his entire money to those purposes? Assume that his money is invested at 9% interest.17Example 3Suppose that a house costs 125,000, and that the buyer puts down 20%

8、of the purchase price, in cash, borrowing the remaining from a mortgage lender. What is the appropriate monthly mortgage payment knowing that the interest rate is 1% per month? (Assume that the mortgage is paid in 30 years).Draw a table showing how much the loan is diminishing and how much interest

9、is being paid in the first 5 months.18Example 3 (table of amortisation of loan)19Mortgage amortisation抵押贷款分期偿还20年金的现值例6-6（P99） 你在春假期间因为手头紧张，从信用卡中透支了1000美元，每个月你最多只付得起20美元的最低付款额。假定信用卡的利率是每月1.5%，你需要多长时间才能还清这笔1000美元的借款呢？（93个月或7.75年）21年金的现值假定你的一位亲戚想向你借3000美元，并将在接下来的4年中每年还你1000美元。他所付给你的利率是多少呢？（12.59%）22Fu

10、ture value of an annuity年金的终值Example 4 Imagine that you deposit in a bank 3000 at the end of every year in order to buy a car. If your savings earn interest of 8% a year, how much will you have in the bank at the end of 4 years?23How to calculate the future value of an annuityCalculate the future va

11、lue of each cash flow and sum them.Calculate the present value of the stream of cash flows (using the Pv of an annuity formula), which results in:24Example 5In 50 years time you will retire. Suppose you believe that you need to accumulate 500,000 by your retirement date. How much must you deposit (i

12、n a bank) each year between now and your retirement to meet that future goal? Assume that the interest rate is 4%.25期初年金期初年金：现金流发生在每期期初的年金。期初年金的情形：房租，水电费26Annuity dueAnnuity due: level stream of cash flows which start immediately.27Relation between the Present values of an annuity and an annuity due

13、28Future value of an annuity dueExample 6 What would be the value of the annuity of example 5 if the deposit was done in the beginning of each period?29Level cash flows: perpetuities andannuitiesAnnuity: equally spaced level stream of cash flows, with a finite maturity.Perpetuity: Stream of cash flo

14、ws which last for ever.30Perpetuities永续年金Example 7 Suppose that you could invest 100 in a bank forever. Considering an interest rate of 5%, how much interest will you receive (forever) every year (assuming that you withdraw the interest every year)?31PerpetuitiesThe perpetuity formula gives us the v

15、alue of a regular stream of payments starting 1 period from now.32How to value annuitiesThere are 2 ways to value an annuity: Value each cash flow separately. Value two perpetuities and calculate the differenceExample 8 What is the present value of a stream of annual payments of 1 for 3 years. (Inte

16、rest rate r)33How to value annuities34How to value annuities35AnnuityThe perpetuity and annuity formulas assume that the payments are done at the end of the period36Effective annual interest rates实际年利率Effective annual interest rate: interest rate that is annualised using compound interest.Example 9:

17、 What is the effective annual interest rate which corresponds to a monthly interest rate of 1%?37EAR38利率报价例6-9（P104）如果你想从某笔放款中赚18%，而且你想以每月复利一次来公布利率。那么你公布的利率应该是多少呢？（16.68%）39Annual percentage rateAnnual percentage rate (APR): interest rate that is annualised using simple interest.APRs do not recognis

18、e the effect of compound interest.Example 10: What is the annual percentage rate which corresponds to a monthly interest rate of 1%?40Annual percentage rate or effective annual interest rateWhen comparing interest rates, it is best to use effective annual rates!Example 11: A car loan requiring quart

19、erly payments carries an APR of 8%. What is the effective annual rate of interest?41连续复利42贷款种类与分期偿还贷款纯折价贷款：到期还本付息纯利息贷款：定期付息，到期还本分期偿还贷款：定期还本付息（本金平均到每期偿还或每期支付固定金额）43分期偿还贷款某公司借款5000美元，期限为5年，利率为9%。借款合约中要求借款人每年支付借款余额的利息，而且每年偿还1000美元的借款余额。44分期偿还贷款45练习6.1 多期现金流量的现值 一位在第一轮选拔赛中选出的四分卫签了一项3年期、2 500万美元的合约。该合约当即

20、给他200万美元的奖金；然后，第1年年末，他将收到500万美元的工资；第2年年末，收回800万美元；最后1年年末，收回1 000万美元。假定贴现率是15%，这份合约值2 500万美元吗？这份合约应该值多少钱？46练习6.2 多期现金流量的终值 你计划在一个付息账户上做一系列的存款。你将在今天存入1 000美元，2年后存入2 000美元，5年后存入2 000美元；你在3年后取出1 500美元，7年后取出1 000美元。假设取款没有罚金，利率为7%。请问，8年后你有多少钱？这些现金流量的现值是多少？47练习6.3 年金现值 你正在思量一项可以在接下来10年中每年付给你12 000美元的投资。如果你

21、要求15%的报酬率，那么，你最多愿意为这项投资支付多少钱？6.4 APR和EAR 现行学生贷款利率是以8%APR报价的，贷款条件为按月支付。这种学生贷款的实际年利率（EAR）是多少？6.5 起作用的是本金 假定你借了10 000美元，将以5年的等额款还清，年利率是14%。请编制这项贷款的分期偿还贷款时间表。在贷款期间你共付了多少利息？48练习6.6 每个月只要一点点 最近你刚在Darnit学院拿到MBA学位。你自然必须马上买一辆全新的宝马（BMW）。汽车的价钱大约是21 000美元。对于10%头款的72个月贷款，银行的报价利率是15%APR。你计划2年后要把这辆车卖出去，再换辆新车。请问你每个月要付多少钱？这项贷款的EAR是多少？当你要换车时，贷款余额是多少？49练习29. 单利和