《金融学》答案第四章 货币的时间价值与现金流贴现分析.docx

1、金融学答案第四章 货币的时间价值与现金流贴现分析CHAPTER 4THE TIME VALUE OF MONEY AND DISCOUNTED CASH FLOW ANALYSISObjectivesTo explain the concepts of compounding and discounting, future value and present value.To show how these concepts are applied to making financial decisions.Outline4.1 Compounding4.2 The Frequency of C

2、ompounding4.3 Present Value and Discounting4.4 Alternative Discounted Cash Flow Decision Rules4.5 Multiple Cash Flows4.6 Annuities4.7 Perpetual Annuities4.8 Loan Amortization4.9 Exchange Rates and Time Value of Money4.10 Inflation and Discounted Cash Flow Analysis4.11 Taxes and Investment DecisionsS

3、ummaryCompounding is the process of going from present value (PV) to future value (FV). The future value of $1 earning interest at rate i per period for n periods is (1+i)n.Discounting is finding the present value of some future amount. The present value of $1 discounted at rate i per period for n p

4、eriods is 1/(1+i)n.One can make financial decisions by comparing the present values of streams of expected future cash flows resulting from alternative courses of action. The present value of cash inflows less the present value of cash outflows is called net present value (NPV). If a course of actio

5、n has a positive NPV, it is worth undertaking.In any time value of money calculation, the cash flows and the interest rate must be denominated in the same currency.Never use a nominal interest rate when discounting real cash flows or a real interest rate when discounting nominal cash flows. How to D

6、o TVM Calculations in MS ExcelAssume you have the following cash flows set up in a spreadsheet:AB1tCF20-1003150426053706NPV7IRRMove the cursor to cell B6 in the spreadsheet. Click the function wizard fx in the tool bar and when a menu appears, select financial and then NPV. Then follow the instructi

7、ons for inputting the discount rate and cash flows. You can input the column of cash flows by selecting and moving it with your mouse. Ultimately cell B6 should contain the following: =NPV(0.1,B3:B5)+B2The first variable in parenthesis is the discount rate. Make sure to input the discount rate as a

8、decimal fraction (i.e., 10% is .1). Note that the NPV function in Excel treats the cash flows as occurring at the end of each period, and therefore the initial cash flow of 100 in cell B2 is added after the closing parenthesis. When you hit the ENTER key, the result should be $47.63.Now move the cur

9、sor to cell B7 to compute IRR. This time select IRR from the list of financial functions appearing in the menu. Ultimately cell B7 should contain the following: =IRR(B2:B5)When you hit the ENTER key, the result should be 34%. Your spreadsheet should look like this when you have finished:AB1tCF20-100

10、3150426053706NPV47.637IRR34% Solutions to Problems at End of Chapter1. If you invest $1000 today at an interest rate of 10% per year, how much will you have 20 years from now, assuming no withdrawals in the interim?SOLUTION:niPVFVPMTResult20101000?0FV =6,727.50 2. a. If you invest $100 every year fo

11、r the next 20 years, starting one year from today and you earn interest of 10% per year, how much will you have at the end of the 20 years? b. How much must you invest each year if you want to have $50,000 at the end of the 20 years?SOLUTION:niPVFVPMTResulta. 20100?100FV = 5,727.50b. 2010050,000?PMT

12、 = 872.983. What is the present value of the following cash flows at an interest rate of 10% per year?a. $100 received five years from now.b. $100 received 60 years from now.c. $100 received each year beginning one year from now and ending 10 years from now.d. $100 received each year for 10 years be

13、ginning now.e. $100 each year beginning one year from now and continuing forever. SOLUTION:niPVFVPMTResulta. 5 10?1000 PV = $62.09b. 6010?1000PV = $.3284c. 1010?0100 ordinaryPV = $614.46d. 1010?0 100 immediate PV = $675.90e. Perpetuity10?0100 ordinarySee below e. PV = $100 = $1,000 .104. You want to

14、 establish a “wasting” fund which will provide you with $1000 per year for four years, at which time the fund will be exhausted. How much must you put in the fund now if you can earn 10% interest per year?SOLUTION:niPVFVPMTResult410?01,000PV =$3,169.87 5. You take a one-year installment loan of $100

15、0 at an interest rate of 12% per year (1% per month) to be repaid in 12 equal monthly payments.a. What is the monthly payment?b. What is the total amount of interest paid over the 12-month term of the loan?SOLUTION:niPVFVPMTResult1211,0000?PMT = $88.85a. PMT = $88.85b. 12 x $88.85 - $1,000 = $66.206

16、. You are taking out a $100,000 mortgage loan to be repaid over 25 years in 300 monthly payments. a.If the interest rate is 16% per year what is the amount of the monthly payment? b.If you can only afford to pay $1000 per month, how large a loan could you take? c.If you can afford to pay $1500 per m

17、onth and need to borrow $100,000, how many months would it take to pay off the mortgage?d.If you can pay $1500 per month, need to borrow $100,000, and want a 25 year mortgage, what is the highest interest rate you can pay?SOLUTION:niPVFVPMTResulta. 30016/12100,0000?PMT =$1358.89b. 30016/12?01,000PV

18、= $73,590c. ? 16/12100,00001,500n = 166 d. 300?100,00001,500i = 1.482% per montha.Note: Do not round off the interest rate when computing the monthly rate or you will not get the same answer reported here. Divide 16 by 12 and then press the i key.b.Note: You must input PMT and PV with opposite signs

19、.c.Note: You must input PMT and PV with opposite signs.7. In 1626 Peter Minuit purchased Manhattan Island from the Native Americans for about $24 worth of trinkets. If the tribe had taken cash instead and invested it to earn 6% per year compounded annually, how much would the Indians have had in 198

20、6, 360 years later?SOLUTION:niPVFVPMTResult360624?0FV = 3.09 1010FV = 30,925,930,0008. You win a $1 million lottery which pays you $50,000 per year for 20 years, beginning one year from now. How much is your prize really worth assuming an interest rate of 8% per year?SOLUTION:niPVFVPMTResult208?050,

21、000PV = $490,9079. Your great-aunt left you $20,000 when she died. You can invest the money to earn 12% per year. If you spend $3,540 per year out of this inheritance, how long will the money last?SOLUTION:niPVFVPMTResult?1220,00003,540n = 10 years 10. You borrow $100,000 from a bank for 30 years at

22、 an APR of 10.5%. What is the monthly payment? If you must pay two points up front, meaning that you only get $98,000 from the bank, what is the true APR on the mortgage loan? SOLUTION:niPVFVPMTResult360.875100,0000?PMT = $914.74 If you must pay 2 points up front, the bank is in effect lending you o

23、nly $98,000. Keying in 98000 as PV and computing i, we get:niPVFVPMTResult360?98,0000914.74 i = .89575 i =.89575% per month; APR = 12 .89575 10.75%11. Suppose that the mortgage loan described in question 10 is a one-year adjustable rate mortgage (ARM), which means that the 10.5% interest applies for

24、 only the first year. If the interest rate goes up to 12% in the second year of the loan, what will your new monthly payment be?SOLUTION:Step 1 is to compute the remaining balance after the first 12 payments:niPVFVPMTResult348.875?0914.74PV = $ 99499.57 Step 2 is to compute the new monthly payment a

25、t an interest rate of 1% per month:niPVFVPMTResult348199499.570?PMT = $1,027.19 12. You just received a gift of $500 from your grandmother and you are thinking about saving this money for graduation which is four years away. You have your choice between Bank A which is paying 7% for one-year deposit

26、s and Bank B which is paying 6% on one-year deposits. Each bank compounds interest annually. What is the future value of your savings one year from today if you save your money in Bank A? Bank B? Which is the better decision? What savings decision will most individuals make? What likely reaction wil

27、l Bank B have?SOLUTION:Future Value in Bank A:niPVFVPMT17- $500Solve0$535Formula:$500 x (1.07) = $535Future Value in Bank B:niPVFVPMT16- $500Solve $530Formula:$500 x (1.06) = $530a.You will decide to save your money in Bank A because you will have more money at the end of the year. You made an extra

28、 $5 because of your savings decision. That is an increase in value of 1%. Because interest compounded only once per year and your money was left in the account for only one year, the increase in value is strictly due to the 1% difference in interest rates.b.Most individuals will make the same decisi

29、on and eventually Bank B will have to raise its rates. However, it is also possible that Bank A is paying a high rate just to attract depositors even though this rate is not profitable for the bank. Eventually Bank A will have to lower its rate to Bank Bs rate in order to make money.13.Sue Consultan

30、t has just been given a bonus of $2,500 by her employer. She is thinking about using the money to start saving for the future. She can invest to earn an annual rate of interest of 10%.a.According to the Rule of 72, approximately how long will it take for Sue to increase her wealth to $5,000? b.Exactly ho