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Unformatted text preview: Answers to End-of-Chapter Questions 5-1 The opportunity cost is the rate of interest one could earn on an alternative investment with a risk equal to the risk of the investment in question. This is the value of I in the TVM equations, and it is shown on the top of a time line, between the first and second tick marks. It is not a single rate—the opportunity cost rate varies depending on the riskiness and maturity of an investment, and it also varies from year to year depending on inflationary expectations (see Chapter 6). 5-2 True. The second series is an uneven cash flow stream, but it contains an annuity of $400 for 8 years. The series could also be thought of as a $100 annuity for 10 years plus an additional payment of $100 in Year 2, plus additional payments of $300 in Years 3 through 10. 5-3 True, because of compounding effects—growth on growth. The following example demonstrates the point. The annual growth rate is I in the following equation: $1(1 + I) 10 = $2. We can find I in the equation above as follows: Using a financial calculator input N = 10, PV = -1, PMT = 0, FV = 2, and I/YR = ? Solving for I/YR you obtain 7.18%. Viewed another way, if earnings had grown at the rate of 10% per year for 10 years, then EPS would have increased from $1.00 to $2.59, found as follows: Using a financial calculator, input N = 10, I/YR = 10, PV = -1, PMT = 0, and FV = ?. Solving for FV you obtain $2.59. This formulation recognizes the “interest on interest” phenomenon. 5-4 For the same stated rate, daily compounding is best. You would earn more “interest on interest.” 5-5 False. One can find the present value of an embedded annuity and add this PV to the PVs of the other individual cash flows to determine the present value of the cash flow stream. 5-6 The concept of a perpetuity implies that payments will be received forever. FV (Perpetuity) = PV (Perpetuity)(1 + I) ∞ = ∞ . 5-7 The annual percentage rate (APR) is the periodic rate times the number of periods per year. It is also called the nominal, or stated, rate. With the “Truth in Lending” law, Congress required that financial institutions disclose the APR so the rate charged would be more “transparent” to consumers. The APR is equal to the effective annual rate only when compounding occurs annually. If more frequent compounding occurs, the effective rate is always greater than the annual percentage rate. Nominal rates can be compared with one another, but only if the instruments Chapter 5: Time Value of Money Answers and Solutions 1 being compared use the same number of compounding periods per year. If this is not the case, being compared use the same number of compounding periods per year....
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