上海交通大学：《金融学原理》课程教学资源（练习与答案）Chapter Four Allocating Resources Over Time

Chapter Four Allocating Resources Over Time Multiple Choice 1 is the process of going from present value to future value,whereas is finding the present value of some future amount. (a)Discounting;compounding (b)Compounding;annualizing (c)Compounding;discounting (d)Discounting;leasing Answer:(c) 2.The difference between an immediate annuity and an ordinary annuity is (a)the number of periods (b)the amount of the payments (c)the interest rate (d)the timing of the payments Answer:(d) 3.The preferred stock of Tavistock Realty offers a cash dividend of $2.28 per year and it is selling at a price of $110 per share.What is the yield of Tavistock Realty preferred stock? (a)2.07% (b)2.12% (c)2.28% (d)48.25% Answer:(a) 4.Consider the situation where you have won a $10 million lottery to be received in 25 annual equal payments of $400,000.What will happen to the present value of these winnings if the interest rate increases during the next 25 years? (a)it will not change (b)it will be worth more (c)it will be worth less (d)it cannot be determined Answer:(c) 4-1

4-1 Chapter Four Allocating Resources Over Time Multiple Choice 1. ________ is the process of going from present value to future value, whereas ________ is finding the present value of some future amount. (a) Discounting; compounding (b) Compounding; annualizing (c) Compounding; discounting (d) Discounting; leasing Answer: (c) 2. The difference between an immediate annuity and an ordinary annuity is ________. (a) the number of periods (b) the amount of the payments (c) the interest rate (d) the timing of the payments Answer: (d) 3. The preferred stock of Tavistock Realty offers a cash dividend of $2.28 per year and it is selling at a price of $110 per share. What is the yield of Tavistock Realty preferred stock? (a) 2.07% (b) 2.12% (c) 2.28% (d) 48.25% Answer: (a) 4. Consider the situation where you have won a $10 million lottery to be received in 25 annual equal payments of $400,000. What will happen to the present value of these winnings if the interest rate increases during the next 25 years? (a) it will not change (b) it will be worth more (c) it will be worth less (d) it cannot be determined Answer: (c)

5.What is the effective annual rate on a bank account that has APR of 8 percent with interest compounded quarterly? (a)6.12% (b)8.24% (c)8.48% (d)17.17% Answer:(b) 6.If you purchase a $12,000 certificate of deposit today with an APR of 14%,with quarterly compounding,what will the CD be worth when it matures in 5 years? (a)$20,846.99 (b)$20,865.60 (c)$23,104.97 (d)$23,877.47 Answer:(d) 7.The CFO of CyberChain Inc.plans to unleash a media campaign that is expected to cost $15 million four years from today.How much cash should she set aside to pay for this if the current interest rate is 13%? (a）$9.2 million (b)$13.3 million (c)$14.4 million (d)$16.9 million Answer:(a) 8.The NPV is a measure of how much your wealth changes as a result of your choice and if the NPV is it does not pay to undertake that choice. (a)future;negative (b)current:negative (c)current;positive (d)future;positive Answer:(b) 4-2

4-2 5. What is the effective annual rate on a bank account that has APR of 8 percent with interest compounded quarterly? (a) 6.12% (b) 8.24% (c) 8.48% (d) 17.17% Answer: (b) 6. If you purchase a $12,000 certificate of deposit today with an APR of 14%, with quarterly compounding, what will the CD be worth when it matures in 5 years? (a) $20,846.99 (b) $20,865.60 (c) $23,104.97 (d) $23,877.47 Answer: (d) 7. The CFO of CyberChain Inc. plans to unleash a media campaign that is expected to cost $15 million four years from today. How much cash should she set aside to pay for this if the current interest rate is 13%? (a) $9.2 million (b) $13.3 million (c) $14.4 million (d) $16.9 million Answer: (a) 8. The NPV is a measure of how much your ________ wealth changes as a result of your choice and if the NPV is ________it does not pay to undertake that choice. (a) future; negative (b) current; negative (c) current; positive (d) future; positive Answer: (b)

9.The is the rate that one can earn somewhere else if one did not invest in the project under evaluation. (a)opportunity cost of capital (b)cost of debt (c)cost of equity (d)weighted average cost of capital Answer:(a) 10.You are trying to decide whether or not to buy a bond for $990 that will make one payment for $1,050 four years from today.What is the internal rate of return on the bond's cash flows? (a)1.06% (b)1.48% (c)10.6% (d)14.8% Answer:(b) 11.After each payment of an amortized loan,the outstanding balance is reduced by the amount of principal repaid.Therefore,the portion of the payment that goes toward the payment of interest is than the previous period's interest payment and the portion going toward repayment of principal is than the previous period's. (a)greater;lower (b)lower:lower (c)greater;greater (d)lower;greater Answer:(d) 12.The earnings of BGB Computers have grown from $3.20 to $6.90 in 6 years.Determine the annual compound rate (a)1.14% (b)13.7% (c)15.6% (d)115.6% Answer:(b) 13.In five years you intend to go to graduate school.For each of your four years in graduate school,you need to have a fund that will provide $25,000 per year at the beginning of each year.If the interest rate is 9%throughout,how much must you put in the fund today? 4-3

4-3 9. The ________ is the rate that one can earn somewhere else if one did not invest in the project under evaluation. (a) opportunity cost of capital (b) cost of debt (c) cost of equity (d) weighted average cost of capital Answer: (a) 10. You are trying to decide whether or not to buy a bond for $990 that will make one payment for $1,050 four years from today. What is the internal rate of return on the bond’s cash flows? (a) 1.06% (b) 1.48% (c) 10.6% (d) 14.8% Answer: (b) 11. After each payment of an amortized loan, the outstanding balance is reduced by the amount of principal repaid. Therefore, the portion of the payment that goes toward the payment of interest is ________ than the previous period’s interest payment and the portion going toward repayment of principal is ________ than the previous period’s. (a) greater; lower (b) lower; lower (c) greater; greater (d) lower; greater Answer: (d) 12. The earnings of BGB Computers have grown from $3.20 to $6.90 in 6 years. Determine the annual compound rate. (a) 1.14% (b) 13.7% (c) 15.6% (d) 115.6% Answer: (b) 13. In five years you intend to go to graduate school. For each of your four years in graduate school, you need to have a fund that will provide $25,000 per year at the beginning of each year. If the interest rate is 9% throughout, how much must you put in the fund today?

(a)$64,996 (b)$57,379 (c)$50,184 (d)$16,249 Answer:(b) 14.A rule of thumb with using the internal rate of return is to invest in a project if the IRR is the opportunity cost of capital. (a)greater than (b)less than (c)less than or equal to (d)one-half of Answer:(a) 15.The NPV is the difference between the value of all cash inflows minus the value of all current and future cash outflows (a)future;present;present (b)present;future;present (c)present;present;future (d)present;future;future Answer:(b) 16.If you purchased a $10,000 certificate of deposit today with an APR of 12%,with monthly compounding,what would be the CD worth when it matures in 6 years? (a)$56,340 (b)$20,468 (c)$19,738 (d)$5,066 Answer:(b) 17.The real interest rate is 3.2%,the nominal interest rate is 8.36%and the rate of inflation is 5%. We are interested in determining the future value of $200 in 35 years time.What is the future price level? a)2.91 b)3.012 c)5.516 d)16.61 Answer:(c) 4-4

4-4 (a) $64,996 (b) $57,379 (c) $50,184 (d) $16,249 Answer: (b) 14. A rule of thumb with using the internal rate of return is to invest in a project if the IRR is ________ the opportunity cost of capital. (a) greater than (b) less than (c) less than or equal to (d) one-half of Answer: (a) 15. The NPV is the difference between the ________ value of all ________ cash inflows minus the ________ value of all current and future cash outflows. (a) future; present; present (b) present; future; present (c) present; present; future (d) present; future; future Answer: (b) 16. If you purchased a $10,000 certificate of deposit today with an APR of 12%, with monthly compounding, what would be the CD worth when it matures in 6 years? (a) $56,340 (b) $20,468 (c) $19,738 (d) $5,066 Answer: (b) 17. The real interest rate is 3.2%, the nominal interest rate is 8.36% and the rate of inflation is 5%. We are interested in determining the future value of $200 in 35 years time. What is the future price level? a) 2.91 b) 3.012 c) 5.516 d) 16.61 Answer: (c)

18.If the real rate is 4%and the rate of inflation is 6%,what is the nominal rate? a)8.16% b)10.16% c)10.24% d)10.36% Answer:(c) 19.You have an investment opportunity with a nominal rate of 6%compounded daily.If you want to have $100.000 in your investment account in 15 years,how much should you deposit today,to the nearest dollar? a.$43,233 b.$41,727 C. $40,930 d.$40,660 Answer:(d) 20.You have determined the present value of an expected cash inflow stream.Which of the following would cause the stream to have a higher present value? a)The discount rate increases. b)The cash flows are paid over a shorter period of time. c)The discount rate decreases. d)Statements(b)and(c)are both correct. Answer:(d) 4-5

4-5 18. If the real rate is 4% and the rate of inflation is 6%, what is the nominal rate? a) 8.16% b) 10.16% c) 10.24% d) 10.36% Answer: (c) 19. You have an investment opportunity with a nominal rate of 6% compounded daily. If you want to have $100,000 in your investment account in 15 years, how much should you deposit today, to the nearest dollar? a. $43,233 b. $41,727 c. $40,930 d. $40,660 Answer: (d) 20. You have determined the present value of an expected cash inflow stream. Which of the following would cause the stream to have a higher present value? a) The discount rate increases. b) The cash flows are paid over a shorter period of time. c) The discount rate decreases. d) Statements (b) and (c) are both correct. Answer: (d)

Short Problems 1.GeorgiaSun Inc.has preferred stock that pays an annual dividend of $10.50.If the security has no maturity (an "infinite"life),what is its value to an investor who wishes to obtain an 8.5 percent rate ofreturn? Answer. PV of a level Perpetuity $10.50/0.085 =$123.53 2.Let us suppose you have a choice between investing in a bank savings account that pays 9% compounded annually (Bank Yearly)and one that pays 8.5%compounded daily (Bank Daily). (Assume this is based on 365 days).Using only effective annual rates,which bank would you prefer? Answer: Effective annual rate:Bank Yearly =9% Effective annual rate:Bank Daily =[1+0.085/3651365-1 =8.87% You would prefer Bank Yearly because you will earn more money. 3.The manufacturing manager of CyberNow Inc.estimates that she can save the company $20,000 cash per year over the next 5 years by implementing a recycling plan.What is the value of the savings today if the appropriate interest rate for the firm is 8%.Assume that cash flows occur at the end of the year. Answer: PV=$79,854.20 4. Stroll Inc.has been offered a $2,000,000 jet under a 10 year loan agreement.The loan requires Stroll Inc.to make equal,annual,end-of-year payments that include both principal and interest on the outstanding balance.The interest rate on the loan is 11%.Calculate the amount of these annual payments. Answer. PMT=S339,602.85 5.Herb Flint decides to put $2,000 a year into an IRA fund over his 35 year working life and then retire.Assume the deposits are made at the end of the year.If the account earns 11% compounded annually,what will Herb have in the account when he retires? Answer: FV=S683,179.11 4-6

4-6 Short Problems 1. GeorgiaSun Inc. has preferred stock that pays an annual dividend of $10.50. If the security has no maturity (an “infinite” life), what is its value to an investor who wishes to obtain an 8.5 percent rate of return? Answer: PV of a level Perpetuity = $10.50/0.085 = $123.53 2.Let us suppose you have a choice between investing in a bank savings account that pays 9% compounded annually (Bank Yearly) and one that pays 8.5% compounded daily (Bank Daily). (Assume this is based on 365 days). Using only effective annual rates, which bank would you prefer? Answer: Effective annual rate: Bank Yearly = 9% Effective annual rate: Bank Daily = [1 + 0.085/365]365 – 1 = 8.87% You would prefer Bank Yearly because you will earn more money. 3. The manufacturing manager of CyberNow Inc. estimates that she can save the company $20,000 cash per year over the next 5 years by implementing a recycling plan. What is the value of the savings today if the appropriate interest rate for the firm is 8%. Assume that cash flows occur at the end of the year. Answer: PV = $79,854.20 4. Stroll Inc. has been offered a $2,000,000 jet under a 10 year loan agreement. The loan requires Stroll Inc. to make equal, annual, end-of-year payments that include both principal and interest on the outstanding balance. The interest rate on the loan is 11%. Calculate the amount of these annual payments. Answer: PMT = $339,602.85 5. Herb Flint decides to put $2,000 a year into an IRA fund over his 35 year working life and then retire. Assume the deposits are made at the end of the year. If the account earns 11% compounded annually, what will Herb have in the account when he retires? Answer: FV = $683,179.11

6.What is the real rate of interest if the nominal rate is 11.5%per year and the rate of inflation is 7%per year? Answer: Real interest rate Nominal interest rate-rate of inflation 1 rate of inflation =0.115-0.07 1.07 =0.04206 Real interest rate 4.21% 7.I have $200 today and am interested in finding out what its equivalent real future value will be in 40 years.What are the two ways I have available to me in computing the real future value? Answer: Compute the future value using the real rate of interest. 2 Compute the nominal future value using the nominal rate,and then deflate it to find the real future value. 8.You have decided to buy a car that costs $35,000.The dealer offers you a 5 year loan with monthly payments of $814 per month.What is the annual interest rate on the loan? Answer: i=1.165 The annual nominal interest rate 1.165 12 =13.98%per year 4-7

4-7 6. What is the real rate of interest if the nominal rate is 11.5% per year and the rate of inflation is 7% per year? Answer: Real interest rate = Nominal interest rate – rate of inflation 1 + rate of inflation = 0.115 – 0.07 1.07 = 0.04206 Real interest rate = 4.21% 7. I have $200 today and am interested in finding out what its equivalent real future value will be in 40 years. What are the two ways I have available to me in computing the real future value? Answer: 1. Compute the future value using the real rate of interest. 2. Compute the nominal future value using the nominal rate, and then deflate it to find the real future value. 8. You have decided to buy a car that costs $35,000. The dealer offers you a 5 year loan with monthly payments of $814 per month. What is the annual interest rate on the loan? Answer: i = 1.165 The annual nominal interest rate = 1.165 * 12 = 13.98% per year

Longer Problems 1.Heathcliff is currently 25 years old and expects to retire at age 65.Suppose that Heathcliff takes a job immediately and can earn $35,000 for the remainder of his working life.What is the present value of his future earnings? Answer: n i PV FV PMT Result 40 0 S35,000 PV=S600,568 2.In order to finance your dream home,you are considering borrowing $120,000.The annual percentage rate is 9%and payments are made annually over 5 years.Construct the loan- amortization schedule for the annual payments Answer: 双 i PV FV PMT Result 5 9 -S120.000 0 PT=S30.856 Loan Amortization Schedule is as follows: Year Beginning Annual Interest Paid Principal Remaining Balance Payment Paid Balance 1 S120.000 S30.856 S10.800 S20.056 S99.944 2 S99.944 S30,856 88.995 S21,861 S78.083 3 S78,083 S30,856 S7,027 S23,829 S54,254 4 S54,254 S30,856 S4,883 S25,973 S28,281 5 S28,281 S30,856 S2,545 S28,311 Totals S154,280 S34,250 S-120,000 4-8

4-8 Longer Problems 1. Heathcliff is currently 25 years old and expects to retire at age 65. Suppose that Heathcliff takes a job immediately and can earn $35,000 for the remainder of his working life. What is the present value of his future earnings? Answer: n i PV FV PMT Result 40 5 ? 0 $35,000 PV = $600,568 2.In order to finance your dream home, you are considering borrowing $120,000. The annual percentage rate is 9% and payments are made annually over 5 years. Construct the loan￾amortization schedule for the annual payments Answer: n i PV FV PMT Result 5 9 –$120,000 0 ? PMT = $30,856 Loan Amortization Schedule is as follows: Year Beginning Balance Annual Payment Interest Paid Principal Paid Remaining Balance 1 $120,000 $30,856 $10,800 $20,056 $99,944 2 $99,944 $30,856 $ 8,995 $21,861 $78,083 3 $78,083 $30,856 $ 7,027 $23,829 $54,254 4 $54,254 $30,856 $ 4,883 $25,973 $28,281 5 $28,281 $30,856 $ 2,545 $28,311 - Totals $154,280 $34,250 $~120,000

3You are 60 years old and are considering whether it pays to buy an annuity from an insurance company.For a cost of $25,000,the insurance company will pay you $3,000 per year for the rest of your life.If you can earn 8%per year on your money in a bank account and expect to live until age 80,is it worth buying the annuity?What implied interest rate is the insurance company paying you? Answer. First compute the present value of the annuity. n PV FV PMT Result 20 8 0 3,000 PV=S29.454.44 Now compute the NPV of the investment of the annuity: NPV=S29,454.44-S25,000 =S4.454.44 So the annuity looks worth buying. To compute the implied interest rate on the annuity,we need to find the discount rate that makes the NPV zero.On a financial calculator,we find the answer to be 10.32%per year. 4-9

4-9 3You are 60 years old and are considering whether it pays to buy an annuity from an insurance company. For a cost of $25,000, the insurance company will pay you $3,000 per year for the rest of your life. If you can earn 8% per year on your money in a bank account and expect to live until age 80, is it worth buying the annuity? What implied interest rate is the insurance company paying you? Answer: First compute the present value of the annuity. n i PV FV PMT Result 20 8 ? 0 $3,000 PV = $29,454.44 Now compute the NPV of the investment of the annuity: NPV = $29,454.44 - $25,000 = $4,454.44 So the annuity looks worth buying. To compute the implied interest rate on the annuity, we need to find the discount rate that makes the NPV zero. On a financial calculator, we find the answer to be 10.32% per year