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Ross4eChap05sm

# Ross4eChap05sm - Chapter 5 The Time Value of Money 5.1 a b...

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Chapter 5: The Time Value of Money 5.1 a. \$1,000 × 1.05 10 = \$1,628.89 b. \$1,000 × 1.07 10 = \$1,967.15 c. \$1,000 × 1.05 20 = \$2,653.30 d. Interest compounds on the interest already earned. Therefore, the interest earned in part c, \$2653.30, is more than double the amount earned in part a, \$628.89. 5.2 a.\$1,000 / 1.1 7 = \$513.16 b.\$2,000 / 1.1 = \$1,818.18 c.\$500 / 1.1 8 = \$233.25 5.3 You can make your decision by computing either the present value of the \$2,000 that you can receive in ten years, or the future value of the \$1,000 that you can receive now. Present value: \$2,000 / 1.08 10 = \$926.39 is less than \$1000 today; Future value: \$1,000 × 1.08 10 = \$2,158.92 is greater than \$2000 in 10 years. Either calculation indicates you should take the \$1,000 now. 5.4 Since this bond has no interim coupon payments, its present value is simply the present value of the \$1,000 that will be received in 25 years. Note: As will be discussed in the next chapter, the present value of the payments associated with a bond is the price of that bond. PV = \$1,000 /1.1 25 = \$ 92.30 5.5 PV = \$1,500,000 / 1.04 27 = \$520,224.86 5.6 a. At a discount rate of zero, the future value and present value are always the same. Remember, FV = PV (1 + r) t . If r = 0, then the formula reduces to FV = PV. Therefore, the values of the alternatives are \$10,000,000 and \$20,000, 000, respectively. You should choose the second option. b. Option one: \$10,000,000 / 1.1 = \$9,090,909 Option two: \$20,000,000 / 1.1 5 = \$12,418,426 Choose the second option. c. Option one: \$10,000,000 / 1.2 = \$8,333,333 Option two: \$20,000,000 / 1.2 5 = \$ 8,037,551 Choose the first option. d. You are indifferent at the rate that equates the PVs of the two alternatives. You know that rate must fall between 10% and 20% because the option you would choose differs at these rates. Let r be the discount rate that makes you indifferent between the options. \$10,000,000 / (1 + r) = \$20,000,000 / (1 + r) 5 (1 + r) 4 = \$20,000,000 / \$10,000,000 = 2 1 + r = 1.189207115 r = 0.189207115 = 18.92% 5.7 PV of Joneses’ offer = \$150,000 / (1.1) 3 = \$ 112,697.22 Answers to End-of-Chapter Problems B-21

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Since the PV of Joneses’ offer is less than Smiths’ offer of \$115,000, you should choose Smiths’ offer. 5.8 a. P 0 = \$1,000 / 1.08 20 = \$214.55 b. P 10 = P 0 (1.08) 10 = \$463.19 c. P 15 = P 0 (1.08) 15 = \$680.58 5.9 PV = \$5,000,000 / 1.12 10 = \$1,609,866.18 5.10 a. The cost of investment is \$900,000. PV of cash inflows = \$120,000 / 1.12 + \$250,000 / 1.12 2 + \$800,000 / 1.12 3 = \$875,865.53. Since the PV of cash inflows is less than the cost of investment, you should not make the investment. b. NPV = -\$900,000 + \$875,865.53 = -\$24,134.47 c. NPV = -\$900,000 + \$120,000 / 1.11 + \$250,000 / 1.11 2 + \$800,000 / 1.11 3 = -\$4,033.18 Since the NPV is negative, so you should not make the investment. 5.11
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Ross4eChap05sm - Chapter 5 The Time Value of Money 5.1 a b...

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