# 3672 fv 0 and solve for pmt eaa 0688 069 a using a

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3.672, FV = 0, and solve for PMT = EAA = 0.688 \$0.69 million. 10-18 a. Using a financial calculator, input the following: CF 0 = -190000, CF 1 = 87000, N j = 3, and I = 14 to solve for NPV 190-3 = \$11,981.99 \$11,982 (for 3 years). Adjusted NPV 190-3 = \$11,982 + \$11,982/(1.14) 3 = \$20,070. Using a financial calculator, input the following: CF 0 = -360000, CF 1 = 98300, N j = 6, and I = 14 to solve for NPV 360-6 = \$22,256.02 \$22,256 (for 6 years). Both new machines have positive NPVs, hence the old machine should be replaced. Further, since its adjusted NPV is greater, choose Model 360-6. The EAA of machine 190-3 is found by converting its NPV to an equivalent annual annuity by inputting: N = 3, I/YR = 14, PV = 11,981.99, FV = 0, and solve for PMT = EAA = 5,161.019 \$5,161.02. The EAA of machine 360-6 is found by converting its NPV to an equivalent annual annuity by inputting: N = 6, I/YR = 14, PV = 22,256.02, FV = 0, and solve for PMT = EAA = 5,723.302 \$5,723.30.
Answers and Solutions: 10 - 20 10-19 a. The project's expected cash flows are as follows (in millions of dollars): Time Net Cash Flow 0 (\$ 4.4) 1 27.7 2 (25.0) We can construct the following NPV profile: Discount Rate NPV 0% (\$1,700,000) 9 (29,156) 10 120,661 50 2,955,556 100 3,200,000 200 2,055,556 300 962,500 400 140,000 410 70,204 420 2,367 430 (63,581) NPV (Mi l l i ons of Dol l ars) Maxi mum NPV at 80. 5% Di scount Rat e (%) I RR 1 = 9.2% I RR 2 = 420% NPV approaches -\$4. 0 as t he cost of capit al approaches 3 2 - 4 1 - 2 1 0 - 3 - 1 - 4 . 4 2 0 8 0 . 5 4 2 0
Answers and Solutions: 10- 21 The table above was constructed using a financial calculator with the following inputs: CF 0 = -4400000, CF 1 = 27700000, CF 2 = -25000000, and I = discount rate to solve for the NPV. b. If r = 8%, reject the project since NPV < 0. But if r = 14%, accept the project because NPV > 0. c. Other possible projects with multiple rates of return could be nuclear power plants where disposal of radioactive wastes is required at the end of the project's life, or leveraged leases where the borrowed funds are repaid at the end of the lease life. (See Chapter 20 for more information on leases.) d. Here is the MIRR for the project when r = 8%: PV costs = \$4,400,000 + \$25,000,000/(1.08) 2 = \$25,833,470.51. TV inflows = \$27,700,000(1.08) 1 = \$29,916,000.00. Now, MIRR is that discount rate which forces the PV of the TV of \$29,916,000 over 2 years to equal \$25,833,470.51: \$25,833,470.51 = \$29,916,000(PVIF r,2 ). Inputs 2 -25833470.51 0 29916000 Output = 7.61 MIRR = 7.61%. At r = 14%, Inputs 2 -23636688.21 0 31578000 Output = 15.58 MIRR = 15.58%. PV costs = \$4,400,000 + \$25,000,000/(1.14) 2 = \$23,636,688.21. TV inflows = \$27,700,000(1.14) 1 = \$31,578,000. N I/YR FV PMT PV N I/YR FV PMT PV
Answers and Solutions: 10 - 22 Now, MIRR is that discount rate which forces the PV of the TV of \$31,578,000 over 2 years to equal \$23,636,688.21: \$23,636,688.21 = \$31,578,000(PVIF r,2 ). Yes. The MIRR method leads to the same conclusion as the NPV method. Reject the project if r = 8%, which is greater than the corresponding MIRR of 7.61%, and accept the project if r = 14%, which is less than the corresponding MIRR of 15.58%. 10-20 a. The IRRs of the two alternatives are undefined. To calculate an IRR, the cash flow stream must include both cash inflows and outflows. b. The PV of costs for the conveyor system is (\$911,067), while the PV of costs for the forklift system is (\$838,834). Thus, the forklift system is expected to be (\$838,834) - (\$911,067) = \$72,233 less costly than the conveyor system, and hence the forklift trucks should be used. Financial calculator solution: Input: CF 0 = -500000, CF 1 = -120000, N j = 4, CF 2 = -20000, I/YR = 8, NPV C = ? NPV C = -911,067. Input: CF 0 = -200000, CF 1 = -160000, N 1 = 5, I/YR = 8, NPV F = ? NPV F = - 838,834. 10-21 a. Payback A (cash flows in thousands): Annual Period Cash Flows Cumulative 0 (\$25,000) (\$25,000) 1 5,000 (20,000) 2 10,000 (10,000) 3 15,000 5,000 4 20,000 25,000 Payback A = 2 + \$10,000/\$15,000 = 2.67 years.