Time Value of Money

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Time Value of Money Practice Problems − Solutions
Dr. Stanley D. Longhofer 1) Jim makes a deposit of $12,000 in a bank account. The deposit is to earn interest annually at the rate of 9 percent for seven years. a) How much will Jim have on deposit at the end of seven years? P/Y = 1, N = 7, I = 9, PV = 12,000, PMT = 0 ⇒ FV = $21,936.47 b) Assuming the deposit earned a 9 percent rate of interest compounded quarterly, how much would he have at the end of seven years? P/Y = 4, N = 7 × 4 = 28 ⇒ FV = $22,374.54 c) In comparing parts (a) and (b), what are the respective effective annual yields? Which alternative is better? Because interest in compounded annual in part (a), the effective annual rate is the same as the nominal rate: EARA = 9%. In part (b), EARB = (1 + i/m)m – 1 = 1.02254 – 1 = 9.31%. This can be also solved using the TI BAII+ using the Interest Conversion worksheet. Simply press [2nd] [I Conv] (the second function of the 2 key) to bring up this worksheet. When the screen says NOM = press [9] and [Enter]. Then arrow up and make sure that [C/Y] reads 4 compounding periods per year; if not, press [4] and [Enter]. Finally arrow up to the EFF screen and press [CPT] to compute the effective annual rate. Alternative (b) is preferred because it compounds your interest more frequently. Thus you get to earn “interest on your interest” sooner. 2) John is considering the purchase of a lot. He can buy the lot today and expects the price to rise to $15,000 at the end of 10 years. He believes that he should earn an investment yield of 10 percent annually on this investment. The asking price for the lot is $7,000. Should he buy it? What is the annual yield (internal rate of return) of the investment if John purchases the property for $7,000 and is able to sell it 10 years later for $15,000? P/Y = 1, N = 10, I = 10, PMT = 0, FV = 15,000 ⇒ PV = − $5,783.15. Because the present value of this investment is less than the $7,000 asking price for the lot, John should not buy it. To solve for the internal rate of return enter PV = − 7,000 and compute I = 7.92%. 3) An investor can make an investment in a real estate development and receive an expected cash return of $45,000 after six years. Based on a careful study of other investment alternatives, she believes that an 18 percent annual return compounded quarterly is a reasonable return to earn on this investment. How much should she pay for it today? P/Y = 4, N = 6 × 4 = 24, I = 18, PMT = 0, FV = 45,000 ⇒ PV = − $15,646.66. 1

4) Suppose you have the opportunity to make an investment in a real estate venture that expects to pay investors $750 at the end of each month for the next eight years. You believe that a reasonable return on your investment should be 17 percent compounded monthly. a) How much should you pay for the investment? P/Y = 12, N = 8 × 12 = 96, I = 17, PMT = 750, FV = 0 ⇒ − $39,222.96. b) What will be the total sum of cash you will receive over the next eight years? This can be solved by setting I = 0, PV = 0, and computing FV = − $72,000. Notice that the sign of this solution is negative because the payments have been entered as positive values. c) Why is there such a large difference between (a) and (b)? The difference between the answers in parts (a) and (b) represents the foregone interest that results from receiving the payments in the future, rather than today. 5) Walt is evaluating an investment that will provide the following returns at the end of each of the following years: year 1, $12,500; year 2, $10,000; year 3, $7,500; year 4, $5,000; year 5, $2,500; year 6, $0; and year 7, $12,500. Walt believes that he should earn an annual rate of 9 percent on this investment. How much should he pay for this investment? This can be solved using the irregular cash flow worksheet: CF0 = 0 C01 = 12,500 C02 = 10,000 C03 = 7,500 C04 = 5,000 C05 = 2,500 C06 = 0 C07 = 12,500 Set I = 9 and solve for NPV = $37,681. 6) A loan of $50,000 is due 10 years from today. The borrower...
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