金融学·课件梳理8 货币的时间价值1


2017-2018 学年度第二学期期末考试复习材料 金融学·课件梳理

2017-2018 学年度第二学期期末考试复习材料

金融学· 课件梳理

Lesson8The Time Value of Money1 第 8 课货币的时间价值 1 Today’s Agenda
? The Time Value of Money

1、Intuition Behind Present Value 现值背后的直觉
(1)There are three reasons why a dollar tomorrow is worth less than a dollar today ? Individuals prefer present consumption to future consumption. To induce people to give up present consumption you have to offer them more in the future. 个人喜欢现在的消费而不是将来的消费。为了诱使人们放弃现在的消费,你必须在 将来给他们更多的东西。 ? When there is monetary inflation, the value of currency decreases over time. The greater the inflation, the greater the difference in value between a dollar today and a dollar tomorrow. 当货币通货膨胀时,货币的价值随着时间的推移而减少。通货膨胀越大,今天的美 元和明天的美元之间的价值差距就越大。 ? If there is any uncertainty (risk) associated with the cash flow in the future, the less that cash flow will be valued. 如果未来现金流有任何不确定性(风险) ,那么现金流将被低估。 (2)Other things remaining equal, the value of cash flows in future time periods will decrease as 其他情况不变,未来时间期间现金流量的价值将减少。 ? The preference for current consumption increases. 对当前消费增长的偏好。 ? Expected inflation increases. 预期通货膨胀增加。 ? The uncertainty in the cash flow increases. 现金流量的不确定性增加。

2、Discounting and Compounding 贴现和复合

2017-2018 学年度第二学期期末考试复习材料 金融学·课件梳理

? How to factoring in these elements? We need the discount rate.Discount rate is a rate at which present and future cash flows are traded off. It incorporates 如何分解这些元素?我们需要贴现率。贴现率是指当前和未来现金流被交易的比率。 它集成了…… ? Preference for current consumption (Greater… Higher discoun t rate) ? Expected inflation (Higher inflation … Higher discount rate) ? Uncertainty in the future cash flows (Higher risk … Higher discount rate) ? A higher discount rate is also opportunity cost, since it captures the returns that an individual would have made on the next best opportunity. 较高的折现率也是机会成本,因为它捕获了个人在下一个最佳机会下的回报。

3、Effects of Compounding 复合效应
? Simpleinterest: interestearnedonlyontheoriginal investment, not on interest. 简单利息:只在原始投资中赚取利息,而非利息。 ? Compoundinterest: interestearnedonboth 复利:原投资和利息所得利息。 ? Suppose you invest $1000 for two years at 5% per year. What is the future value in two years? original investment and interest.

4、Comparison: Future Value of $100 at 10Percent


5、Present value principle 现值原则
? Cashflowsatdifferentpoints intimecannotbe compared and aggregated. 不同时间点的现金流无法比较和汇总。 ? All cash flows have to be brought to the same point in time, before comparisons and aggregations are made. 在进行比较和聚合之前,所有现金流都必须按时送到相同的时间点。 ? That p oint of time can be today (present value) or a point in time in the future (future

2017-2018 学年度第二学期期末考试复习材料 金融学·课件梳理

value). 这个时间点可以是今天(现值) ,也可以是将来的某个时间点(未来值) 。

6、Cash flow types and discountingmechanics 现金流类型和贴现机制
? There are five types of cash flows ? Simple cash flows ? Annuities 年金 ? Growing annuities ? Perpetuities 永续年金 ? Growingperpetuities ? Most assets represent combinations of these cash flows. Thus, a bond is a combination of an annuity (coupons) and a simple cash flow (face value at maturity) 大多数资产代表这些现金流的组合。因此,债券是年金(息票)和简单现金流(到 期时面值)的组合。 ? A stock maybe a combination of a growing annuity and a growing perpetuity. 股票也许结合越来越多的年金和永续增长。

7、Time lines 年表

? Show the timing of cash flows. ? Tick marks occur at the end of periods, so Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period.时间 1 是第一阶段(年、月等)的结束或第二阶段的开始。 8、Drawing time lines
$100 lump sum due in 2 years2 年付清 100 美元


2017-2018 学年度第二学期期末考试复习材料 金融学·课件梳理

3 year $100 ordinary annuity3 年普通年金 100 美元

Uneven cash flow stream 现金流不均衡

9、FV of Lump Sum 总金额终值 ? What is the future value (FV) of an initial $100 after 3 years, if I/YR = 10%? ? FV can be solved by using the formula andfinancial calculator methods.
FV 可以用公式和财务计算器的方法来解决。

10、Future Values: General Formula 未来价值:一般公式

11、Solving for FV:The formula methods
? After 1 year: FV1 = PV (1 + I) = $100 (1.10)= $110.00
2 2 ? After 2 years:FV 2 = PV (1 + I) = $100 (1.10) =$121.00 N ? After N years (general case):FVN = PV (1 + I)

12、Financial Calculator
? Basic setup for Texas Instruments BA -II Plus ? Set decimal places to 4

2017-2018 学年度第二学期期末考试复习材料 金融学·课件梳理

? Press [2nd] [Format] [4] [Enter] ? Set payments per Year (P/Y) to one ? Press [2nd] [1] [Enter]

? FV=future value ? PV=present value ? I/Y=period interest rate ? N=number of periods ? Sign convention (PV and FV have the opposite sign) oryou will receive an error when solving for r or t. 13、Solving for FV:The calculator method
? Solves the general FV equation. ? Requires 4 inputs into calculator, and will solve for the fifth. (Set to P/YR = 1 and END mode.)

14、PV of Lump Sum ? What is the present value (PV) of $100 due in 3 years, if I/YR = 10%? ? The PVshows the value of cash flows in terms of today’s purchasing power.

15、Solving for PV:The formula method ? Solve the general FV equation for PV: N ? PV = FV N / (1 + I) 3 3 ? PV = FV 3 / (1 + I) = $100 / (1.10) = $75.13

16、Solving for PV:The calculator method ? Exactly like solving for FV, except we have different input information and are solving for a different variable.


2017-2018 学年度第二学期期末考试复习材料 金融学·课件梳理

17、Solving for I: ? What interest rate would cause $100 to grow to$125.97 in 3 years? ? Solves the general FV equation for I.

18、Solving for N: ? If sales grow at 20% per year, how long before sales double? ? Hard to solve without a financial calculator or spreadsheet.

Next: Multiple Cash Flows 19、Solving for FV:3-year ordinary annuity of $100 at 10% ? $100 payments occur at the end of each period, but there is no PV.

20、Solving for PV:3-year ordinary annuity of $100 at 10% ? $100 payments still occur at the end of each period, but now there is no FV.

21、Solving for FV:3-year annuity due of $100 at 10% ? Now, $100 payments occur at the beginning of each period. ? Set calculator to “BEGIN” mode and solve for the FV of the annuity:


2017-2018 学年度第二学期期末考试复习材料 金融学·课件梳理

? Again, $100 payments occur at the beginning of each period. ? Set calculator to “BEGIN” mode and solve for the PV of the annuity:

22、Multiple cash flows-Future valueexample ? Suppose you invest $500 in a mutual fund today and $600 in one year. If the fund pays 9% annually, how much will you have in two years?

23、Multiple cash flows-Future valueexample continued ? How much will you have in 5 year s if you make no further deposits?

24、Another Way…. ? Another way is to use the cash flow keys ? Texas Instruments BA -II Plus ? Press CF and enter the cash flows beginning with year 0. You have to press the “Enter” key for each cash flow Use the down arrow key to move to the next cash flow ? The “F” is the number of times a given cash flow occurs in consecutive years ? Use the NPV key to compute the present value byentering the ? interest rate for I, pressing the down arrow and then compute ? Clear th e cash flow keys by pressing CF and then CLR Work

25、PV of Uneven Cash Flow Stream


2017-2018 学年度第二学期期末考试复习材料 金融学·课件梳理

26、Solving for PV:Uneven cash flow stream ? Input cash flows in the calculator’s “CFLO” register: ? CF0 = 0 ? CF1 = 100 ? CF2 = 300 ? CF3 = 300 ? CF4 =-50 ? Enter I/YR = 10, press NPV button to get NPV =$530.087. 27、Practice ? Your broker calls you and tells you that he has this great investment opportunity. If you invest$100 today, you will receive $40 in one year and$75 in two years. If you require a 15% return on investments of this risk, should you take the investment? 28、Special cases for multiple cash flows ? Perpetuities 永续年金 ? Annuity ? Annuity due期初应付年金 29、PV of Perpetuity

(Here NPV = PV.)

What is the present value of a$100 perpetuity at 10%? Question: FV of perpetuity? PV = PMT / I = $100/0.1 = $1,000. The first payment starts one period from now! ? Preferred stock is an important example of a perpetuity ? A fixed cash dividend every period forever. ? Suppose the Fellini Co. wants to sell preferred stock at$100 per share. A very similar issue of preferred stock already outstanding has a price of $40 per share and offers a dividend of $1 every quarter starting from next quarter. What dividend will Fellini have to offer starting from next quarter if the preferred stock is going to sell.

2017-2018 学年度第二学期期末考试复习材料 金融学·课件梳理

30、Practice ? If an investment pays $1000 per year forever starting in 3 years (i.e., 3 years from now) and you could make 11% return per year on similar investments, how much would you pay today to make the investment? 31、Annuities ? Annuity: Finite series of equal payments that occurs at regular intervals (examples: car loans and home mortgages)
年金:定期支付的有限系列的等额付款(例如:汽车贷款和住房抵押贷款) 。

33、The Power of Compound Interest 复利 A 20-year-old student wants to save $3 a day for her retirement. Every day she places $3 in a drawer. At the end of the year, she invests the accumulated savings ($1,095) in a brokerage account with an expected annual return of 12%. How much money will she have when she is 65 years old? 34、Solving for FV:Savings problem ? If she begins saving today, and sticks to her plan, she will have$1,487,261.89 when she is 65.

35、If you wait until you are 40 years old tostart saving the same amount, how much money will you have at age 65? 1. $107,690 2. $146,001 3. $787,201 4. $1,487,262 36、Solving for FV:Savings problem ? If a 40 -year-old investor begins saving today, and sticks to the plan, he or she will have $146,000.59 at age 65.This is $1.3 million less than if starting at age 20. ? Lesson:It pays to start saving early.


2017-2018 学年度第二学期期末考试复习材料 金融学·课件梳理

37、Solving for PMT: How much must the 40-year old deposit annually to catch the 20-year old? ? To find the required annual contribution, enter the number of years until retirement and the final goal of$1,487,261.89, and solve for PMT.

38、Annuity Due ? An annuity due: the first payment occurs today (or at the beginning of each period).
年金到期:第一笔付款发生在今天(或每一期开始) 。

39、What is the difference between an ordinary annuity and an annuity due?

40、Annuity Due and the Calculator ? Ordinary annuity vers us annuity due ? You can switch your calculator between the twotypes by using the 2nd BGN 2nd Set on the TI BA-II Plus ? Annuity Due: You are saving for a new house and you put $10,000 per year in an account paying 8%. The first payment is made today. How much will you have in 3 years? ? FV=35061.12 41、Ordinary Annuity and Annuity Due ? What is the relation between ordinary annuity and annuity due?



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