# 10 6 generally the failure to employ common life

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10-6 Generally, the failure to employ common life analysis in such situations will bias the NPV against the shorter project because it "gets no credit" for profits beyond its initial life, even though it could possibly be "renewed" and thus provide additional NPV. Answers and Solutions: 10 - 3
SOLUTIONS TO END-OF-CHAPTER PROBLEMS 10-1 a. \$52,125/\$12,000 = 4.3438, so the payback is about 4 years. b. Project K's discounted payback period is calculated as follows: Annual Discounted @12% Period Cash Flows Cash Flows Cumulative 0 (\$52,125) (\$52,125.00) (\$52,125.00) 1 12,000 10,714.80 (41,410.20) 2 12,000 9,566.40 (31,843.80) 3 12,000 8,541.60 (23,302.20) 4 12,000 7,626.00 (15,676.20) 5 12,000 6,808.80 (8,867.40) 6 12,000 6,079.20 (2,788.20) 7 12,000 5,427.60 2,639.40 8 12,000 4,846.80 7,486.20 The discounted payback period is 6 + 60 . 427 , 5 \$ 20 . 788 , 2 \$ years, or 6.51 years. Alternatively, since the annual cash flows are the same, one can divide \$12,000 by 1.12 (the discount rate = 12%) to arrive at CF 1 and then continue to divide by 1.12 seven more times to obtain the discounted cash flows (Column 3 values). The remainder of the analysis would be the same. c. NPV = -\$52,125 + \$12,000[(1/i)-(1/(i*(1+i) n )] = -\$52,125 + \$12,000[(1/0.12)-(1/(0.12*(1+0.12) 8 )] = -\$52,125 + \$12,000(4.9676) = \$7,486.20. Financial calculator: Input the appropriate cash flows into the cash flow register, input I = 12, and then solve for NPV = \$7,486.68. d. Financial calculator: Input the appropriate cash flows into the cash flow register and then solve for IRR = 16%. Answers and Solutions: 10 - 4
e. MIRR: PV Costs = \$52,125. FV Inflows: PV FV 0 1 2 3 4 5 6 7 8 | | | | | | | | | 12,000 12,000 12,000 12,000 12,000 12,000 12,000 12,000 13,440 15,053 16,859 18,882 21,148 23,686 26,528 52,125 MIRR = 13.89% 147,596 Financial calculator: Obtain the FVA by inputting N = 8, I = 12, PV = 0, PMT = 12000, and then solve for FV = \$147,596. The MIRR can be obtained by inputting N = 8, PV = -52125, PMT = 0, FV = 147596, and then solving for I = 13.89%. 10-2 Project A: Using a financial calculator, enter the following: CF 0 = -15000000 CF 1 = 5000000 CF 2 = 10000000 Answers and Solutions: 10 - 5 12%
Answers and Solutions: 10 - 6
Financial calculator: Input the appropriate cash flows into the cash flow register, input I = 14, and then solve for NPV = \$409. Financial calculator: Input the appropriate cash flows into the cash flow register and then solve for IRR = 14.99% ≈ 15%. MIRR: PV Costs = \$17,100. FV Inflows: PV FV 0 1 2 3 4 5 | | | | | | 5,100 5,100 5,100 5,100 5,100 5,814 6,628 7,556 8,614 17,100 MIRR = 14.54% (Accept) 33,712 Financial calculator: Obtain the FVA by inputting N = 5, I = 14, PV = 0, PMT = 5100, and then solve for FV = \$33,712. The MIRR can be obtained by inputting N = 5, PV = -17100, PMT = 0, FV = 33712, and then solving for I = 14.54%. Pulley: NPV = -\$22,430 + \$7,500(3.4331) = -\$22,430 + \$25,748 = \$3,318. (Accept) Financial calculator: Input the appropriate cash flows into the cash flow register, input I = 14, and then solve for NPV = \$3,318. Financial calculator: Input the appropriate cash flows into the cash flow register and then solve for IRR = 20%. MIRR: PV Costs = \$22,430. Answers and Solutions: 10 - 7 14%
FV Inflows: PV FV 0 1 2 3 4 5 | | | | | | 7,500 7,500 7,500 7,500 7,500 8,550 9,747 11,112 12,667 22,430 MIRR = 17.19% (Accept) 49,576 Financial calculator: Obtain the FVA by inputting N = 5, I = 14, PV = 0, PMT = 7500, and then solve for FV = \$49,576. The MIRR can be obtained by inputting N = 5, PV = -22430, PMT = 0, FV = 49576, and then solving for I = 17.19%.