# Flows come in from these projects the firm will

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flows come in from these projects, the firm will either pay them out to investors, or use them as a substitute for outside capital which costs 10 percent. Thus, since these cash flows are expected to save the firm 10 percent, this is their opportunity cost reinvestment rate. The IRR method assumes reinvestment at the internal rate of return itself, which is an incorrect assumption, given a constant expected future cost of capital, and ready access to capital markets. Answers and Solutions: 1 0 1 - 18 N P V ( M i l l i o n s o f D o l l a r s ) C r o s s o v e r R a t e = 1 1 . 7 % I R R A = 1 5 . 0 3 % I R R B = 2 2 . 2 6 % A B C o s t o f C a p i t a l ( % ) 1 2 5 I R R = 1 1 . 7 % 1 0 1 0 0 7 5 1 5 5 0 2 0 2 5 2 5 - 2 5 3 0 - 5 0 5
1 0 1 -16 Plane A: Expected life = 5 years; Cost = \$100 million; NCF = \$30 million; COC = 12%. Plane B: Expected life = 10 years; Cost = \$132 million; NCF = \$25 million; COC = 12%. 0 1 2 3 4 5 6 7 8 9 10 A: | | | | | | | | | | | -100 30 30 30 30 30 30 30 30 30 30 -100 -70 Enter these values into the cash flow register: CF 0 = -100; CF 1-4 = 30; CF 5 = -70; CF 6- 10 = 30. Then enter I = 12, and press the NPV key to get NPV A = 12.764 \$12.76 million. 0 1 2 3 4 5 6 7 8 9 10 B: | | | | | | | | | | | -132 25 25 25 25 25 25 25 25 25 25 Enter these cash flows into the cash flow register, along with the interest rate, and press the NPV key to get NPV B = 9.256 ≈ \$9.26 million. Project A is the better project and will increase the company's value by \$12.76 million. The EAA of plane A is found by first finding the PV: N = 5, I/YR = 12, PMT = 30, FV = 0; solve for PV = −108.143. The NPV is \$108.143 − \$100 = \$8.143 million. We convert this to an equivalent annual annuity by inputting: N = 5, I/YR = 12, PV = −8.143, FV = 0, and solve for PMT = EAA = 2.259 ≈ \$2.26 million. For plane B, we already found the NPV of 9.256. We convert this to an equivalent annual annuity by inputting: N = 10, I/YR = 12, PV = −9.256, FV = 0, and solve for PMT = EAA = 1.638 ≈ \$1.64 million. Answers and Solutions: 1 0 1 - 19
1 0 1 -17 0 1 2 3 4 5 6 7 8 A: | | | | | | | | | -10 4 4 4 4 4 4 4 4 -10 -6 Machine A's simple NPV is calculated as follows: Enter CF 0 = -10 and CF 1-4 = 4. Then enter I = 10, and press the NPV key to get NPV A = \$2.679 million. However, this does not consider the fact that the project can be repeated again. Enter these values into the cash flow register: CF 0 = -10; CF 1-3 = 4; CF 4 = -6; CF 5-8 = 4. Then enter I /YR = 10, and press the NPV key to get Extended NPV A = \$4.5096 ≈ \$4.51 million. 0 1 2 3 4 5 6 7 8 B: | | | | | | | | | -15 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 Enter these cash flows into the cash flow register, along with the interest rate, and press the NPV key to get NPV B = \$3.672 ≈ \$3.67 million. Machine A is the better project and will increase the company's value by \$4.51 million. The EAA of machine A is found by first finding the PV: N = 4, I/YR = 10, PMT = 4, FV = 0; solve for PV = −12.679. The NPV is \$12.679 − \$10 = \$2.679 million. We convert this to an equivalent annual annuity by inputting: N = 4, I/YR = 10, PV = −2.679, FV = 0, and solve for PMT = EAA = 0.845 ≈ \$0.85 million. For machine B, we already found the NPV of 3.672. We convert this to an equivalent annual annuity by inputting: N = 8, I/YR = 10, PV = −3.672, FV = 0, and solve for PMT = EAA = 0.688 ≈ \$0.69 million. 1 0 1 -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