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Unformatted text preview: CHAPTER 3 ANSWERS 31 The opportunity cost rate 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 k in the TVM equations, and it is shown on the top of a cash flow 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 2). 32 True. The second series is an uneven payment 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. 33 True, because of compounding effects—that is, growth on growth. The following example demonstrates the point. The annual growth rate is i in the following equation: $1(1 + k) 10 = $2. The term (1 + k) 10 is the interest factor for k percent, 10 years. We can find i in one of three ways: 1. Using a financial calculator input N = 10, PV = 1, PMT = 0, FV = 2, and I = ?. Solving for I you obtain 7.18%. 2. Solve directly for k using the following method: FV n = PV(1 + k) n $2 = $1(1 + k) 10 (1 + k) 10 = $2/$1 = 2.0 k = (2.0) 1/10 1 = 1.07177  1 = 0.07177 = 7.18% 3. Use the “Rate” function on a spreadsheet, which can be set up as follows, the solution is: 55 6% ( 29 26 . 747 ) 74726 . ( 000 , 1 06 . 1 1 000 , 1 PV 5 = = = Viewed another way, if earnings had grown at the rate of 10 percent per year for 10 years, then EPS would have increased from $1.00 to $2.59, found as follows: FV 10 = PV(1.10) 10 = $1(2.5937) = $2.59. Using a financial calculator, input N = 10, I = 10, PV = 1, PMT = 0, and FV = ?. Solving for FV you obtain $2.59. This formulation recognizes the "interest on interest" phenomenon. The annual growth actually would be 10 percent per year only if the interest earned each year was not reinvested, thus compounded growth would not be possible. If the investor invested $1 at the beginning of each year at 10 percent, he or she would earn $0.10 each year. If the $.010 interest earned each year was taken out of the investment at the end of the year and “deposited” in a coffee can, then, at the end of 10 years, the investor would have $1 in the coffee can. The total value of the original $1 investment then would be $2 ($1 principal plus $1 interest in the coffee can). 34 For the same stated rate, more compounding is better. You would earn more “interest on interest.” Computing the effective annual rate for each alternative shows this to be true: EAR semiannual = (1 + 0.05/2) 2  1 = 5.0625% EAR daily = (1 + 0.05/365) 365 1 = 5.1267% 35 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 stream of cash flows.the other individual cash flows to determine the present value of the stream of cash flows....
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This note was uploaded on 06/19/2009 for the course FIN 5FMA taught by Professor Dusa during the Three '09 term at La Trobe University.
 Three '09
 DUSA
 Finance, Interest

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