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chap006

# Solve each of these factors for the r that would

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Unformatted text preview: se factors for the r that would cause the factor to equal zero. The resulting rates are the two IRRs for project A. They are either r = 0% or r = 100%. Note: By inspection you should have known that one of the IRRs of project A is zero. Notice that the sum of the un-discounted cash flows for project A is zero. Thus, not discounting the cash flows would yield a zero NPV. The discount rate which is tantamount to not discounting is zero. Here are some of the interactions used to find the IRR by trial and error. Sophisticated calculators can compute this rate without all of the tedium involved in the trial-and-error method. NPV = -\$150 + \$50 / 1.3 + \$100 / 1.32 + \$150 / 1.33 = \$15.91 NPV = -\$150 + \$50 / 1.4 + \$100 / 1.42 + \$150 / 1.43 = -\$8.60 NPV = -\$150 + \$50 / 1.37 + \$100 / 1.372 + \$150 / 1.373 = -\$1.89 NPV = -\$150 + \$50 / 1.36 + \$100 / 1.36 2 + \$150 / 1.363 = \$0.46 NPV = -\$150 + \$50 / 1.36194 + \$100 / 1.361942 + \$150 / 1.361943 = \$0.0010 NPV = -\$150 + \$50 / 1.36195 + \$100 / 1.361952 + \$150 / 1.361953 = -\$0.0013 NPV = -\$150 + \$50 / 1.361944 + \$100 / 1.3619442 + \$150 / 1.3619443 = \$0.0000906 Thus, the IRR is approximately 36.1944%. 6.10 a. Solve r in the equation: \$5,000 - \$2,500 / (1 + r) - \$2,000 / (1 + r)2 - \$1,000 / (1 + r)3 - \$1,000 / (1 + r)4 = 0 By trial and error, IRR = r = 13.99% Since this problem is the case of financing, accept the project if the IRR is less than the required rate of return. IRR = 13.99% > 10% Reject the offer. IRR = 13.99% < 20% Accept the offer. When r = 10%: NPV = \$5,000 - \$2,500 / 1.1 - \$2,000 / 1.12 - \$1,000 / 1.13 - \$1,000 / 1.14 = -\$359.95 When r = 20%: NPV = \$5,000 - \$2,500 / 1.2 - \$2,000 / 1.22 - \$1,000 / 1.23 - \$1,000 / 1.24 = \$466.82 Yes, they are consistent with the choices of the IRR rule since the signs of the cash flows change only once. b. c. d. B-66 Answers to End-of-Chapter Problems 6.11 a. b. c. d. e. Project A: NPV = -\$5,000 + \$3,500 / (1 + r) + \$3,500 / (1 + r)2 = 0 IRR = r = 25.69% Project B: NPV = -\$100,000 + \$65,000 / (1 + r) + \$65,000 / (1 + r)2 = 0 IRR = r = 19.43% Choose project A because it has a higher IRR. The difference in...
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