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chap006

# Chap006

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Unformatted text preview: Chapter 6: Some Alternative Investment Rules 6.1 a. b. Payback period of Project A = 1 + (\$7,500 - \$4,000) / \$3,500 = 2 years Payback period of Project B = 2 + (\$5,000 - \$2,500 -\$1,200) / \$3,000 = 2.43 years Project A should be chosen. NPVA = -\$7,500 + \$4,000 / 1.15 + \$3,500 / 1.152 + \$1,500 / 1.153 = -\$388.96 NPVB = -\$5,000 + \$2,500 / 1.15 + \$1,200 / 1.152 + \$3,000 / 1.153 = \$53.83 Project B should be chosen. Payback period = 6 + {\$1,000,000 - (\$150,000 6)} / \$150,000 = 6.67 years Yes, the project should be adopted. 11 \$150,000 0.10 = \$974,259 The discounted payback period = 11 + (\$1,000,000 - \$974,259) / (\$150,000 / 1.112) = 11.54 years NPV = -\$1,000,000 + \$150,000 / 0.10 = \$500,000 Average Investment: (\$16,000 + \$12,000 + \$8,000 + \$4,000 + 0) / 5 = \$8,000 Average accounting return: \$4,500 / \$8,000 = 0.5625 = 56.25% 1. AAR does not consider the timing of the cash flows, hence it does not consider the time value of money. 2. AAR uses an arbitrary firm standard as the decision rule. 3. AAR uses accounting data rather than net cash flows. 6.2 a. b. c. 6.3 a. b. 6.4 Average Investment = (\$2,000,000 + 0) / 2 = \$1,000,000 Average net income = [\$100,000 {(1 + g)5 - 1} / g] / 5 = {\$100,000A (1.075 - 1} / 0.07} / 5 = \$115,014.78 AAR = \$115,014.78 / \$1,000,000 = 11.50% No, since the machine's AAR is less than the firm's cutoff AAR. a PI = \$40,000 0.15 / \$160,000 = 1.04 Since the PI exceeds one accept the project. 7 6.5 6.6 6.7 The IRR is the discount rate at which the NPV = 0. -\$3,000 + \$2,500 / (1 + IRRA) + \$1,000 / (1 + IRRA)2 = 0 By trial and error, IRRA = 12.87% Since project B's cash flows are two times of those of project A, the IRRB = IRRA = 12.87% a. b. Solve x by trial and error: -\$4,000 + \$2,000 / (1 + x) + \$1,500 / (1 + x)2 + \$1,000 / (1 + x)3 = 0 x = 6.93% No, since the IRR (6.93%) is less than the discount rate of 8%. 6.8 Answers to End-of-Chapter Problems B-65 6.9 Find the IRRs of project A analytically. Since the IRR is the discount rate that makes the NPV equal to zero, the following equation must hold. -\$200 + \$200 / (1 + r) + \$800 / (1 + r)2 - \$800 / (1 + r)3 = 0 \$200 [-1 + 1 / (1 + r)] - {\$800 / (1 + r)2}[-1 + 1 / (1 + r)] = 0 [-1 + 1 / (1 + r)] [\$200 - \$800 / (1 + r)2] = 0 For this equation to hold, either [-1 + 1 / (1 + r)] = 0 or [\$200 - \$800 / (1 + r)2] = 0. Solve each of the...
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