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CHAPTER 6 TIME VALUE OF MONEY True-False (Difficulty: E = Easy, M = Medium, and T = Tough) PV versus FV 1 If the discount (or interest) rate is positive, the present value of an expected series of payments will always exceed the future value of the same series. a. True b. False 2 Disregarding risk, if money has time value, it is impossible for the present value of a given sum to be greater than its future value. a. True b. False 3 Disregarding risk, if money has time value, the future value of some amount of money will always be more than the amount originally invested, and the present value of some amount to be received in the future is always less than that future amount to be received. a. True b. False Discounting process 4 The process of discounting or finding the present value of a cash flow to be received in the future is really the reverse of compounding. a. True b. False Loan amortization 5 The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The later we are in the loan's life, the larger the principal portion of the payment. a. True b. False Effective annual rate 6 If a bank uses quarterly compounding for savings accounts, the nominal rate (APR) will be greater than the effective annual rate. a. True b. False Opportunity cost rate 7 The opportunity cost rate is only applicable if you as an investor actually have an alternative investment to compare. If you are making a decision about a single investment, the opportunity rate concept does not apply. a. True b. False PV of a sum 8 The present value of a future sum decreases as either the discount rate or the number of discount periods per year increases. a. True b. False Periodic and nominal rates 9 If we calculate a periodic interest rate, say a monthly rate, in order to get the nominal annual rate (APR), we can multiply the periodic rate by the number of periods within a year. a. True b. False Interest factors 10 For all positive interest rates, FVIFk,n 1.0 and PVIFAk,n n. a. True b. False Tabular and calculator methods 11 Financial calculator and tabular methods use different mathematical formulas to solve time value of money problems, and that is why they always lead to different results. a. True b. False Multiple Choice: Conceptual PV of a sum 12 Given some amount to be received several years in the future, if the interest rate increases, the present value of the future amount will be a. Higher. b. Lower. c. Stay the same. d. Cannot tell. e. Variable. PV and discount rate 13 You have determined the profitability of a planned project by finding the present value of all the cash flows from that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows? a. The discount rate decreases. b. The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same. c. The discount rate increases. d. Answers b and c above. e. Answers a and b above. Multiple Choice: Problems Time for a sum to double 14 A recent advertisement in the financial section of a magazine carried the following claim: "Invest your money with us at 14 percent, compounded annually, and we guarantee to double your money sooner than you imagine." Ignoring taxes, how long would it take to double your money at a nominal rate of 14 percent, compounded annually? a. Approximately 3.5 years b. Approximately 5 years c. Exactly 7 years d. Approximately 10 years e. Exactly 14 years FV of an annuity 15 What is the future value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate? a. $ 670.44 b. $ 842.91 c. $1,169.56 d. $1,522.64 e. $1,348.48 PV of an annuity 16 What is the present value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate? a. $ 670.43 b. $ 842.91 c. $1,169.56 d. $1,348.48 e. $1,522.64 Annuity payments 17 If a 5-year regular annuity has a present value of $1,000, and if the interest rate is 10 percent, what is the amount of each annuity payment? a. $240.42 b. $263.80 c. $300.20 d. $315.38 e. $346.87 PV of an uneven CF stream 18 Assume that you will receive $2,000 a year in Years 1 through 5, $3,000 a year in Years 6 through 8, and $4,000 in Year 9, with all cash flows to be received at the end of the year. If you require a 14 percent rate of return, what is the present value of these cash flows? a. $ 9,851 b. $13,250 c. $11,714 d. $15,129 e. $17,353 Finding PMT 19 Suppose the present value of a 2-year ordinary annuity is $100. If the discount rate is 10 percent, what must be the annual cash flow? a. $65.45 b. $82.64 c. $57.62 d. $53.78 e. $79.22 Quarterly compounding 20 If $100 is placed in an account that earns a nominal 4 percent, compounded quarterly, what will it be worth in 5 years? a. $122.02 b. $105.10 c. $135.41 d. $120.90 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20