11 23 a project a using a financial calculator enter

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11-23 a. Project A: Using a financial calculator, enter the following data: CF 0 = -30; CF 1 = 5; CF 2 = 10; CF 3 = 15; CF 4 = 20; I/YR = 10; and solve for NPV A = $7.74; IRR A = 19.19%. Calculate MIRR A at WACC = 10%: Step 1: Calculate the NPV of the uneven cash flow stream, so its FV can then be calculated. With a financial calculator, enter the cash flow stream into the cash flow registers, then enter I/YR = 10, and solve for NPV = $37.739. Step 2: Calculate the FV of the cash flow stream as follows: Enter N = 4, I/YR = 10, PV = -37.739, and PMT = 0 to solve for FV = $55.255. Step 3: Calculate MIRR A as follows: Enter N = 4, PV = -30, PMT = 0, and FV = 55.255 to solve for I/YR = 16.50%. Payback A (cash flows in millions): Annual Period Cash Flows Cumulative 0 ($30) ($30) 1 5 (25) 2 10 (15) 3 15 0 4 20 20 Payback A = 3 years. Discounted Payback A (cash flows in millions): Annual Discounted @10% Cumulative Period Cash Flows Cash Flows Cash Flows 0 ($30) ($30.00) ($30.00) 1 5 4.55 (25.45) 2 10 8.26 (17.19) 3 15 11.27 (5.92) 4 20 13.66 7.74 Discounted Payback A = 3 + $5.92/$13.66 = 3.43 years.
284 Comprehensive/Spreadsheet Problem Chapter 11: The Basics of Capital Budgeting Project B: Using a financial calculator, enter the following data: CF 0 = -30; CF 1 = 20; CF 2 = 10; CF 3 = 8; CF 4 = 6; I/YR = 10; and solve for NPV B = $6.55; IRR B = 22.52%. Calculate MIRR B at WACC = 10%: Step 1: Calculate the NPV of the uneven cash flow stream, so its FV can then be calculated. With a financial calculator, enter the cash flow stream into the cash flow registers, then enter I/YR = 10, and solve for NPV = $36.55. Step 2: Calculate the FV of the cash flow stream as follows: Enter N = 4, I/YR = 10, PV = -36.55, and PMT = 0 to solve for FV = $53.52. Step 3: Calculate MIRR B as follows: Enter N = 4, PV = -30, PMT = 0, and FV = 53.52 to solve for I/YR = 15.57%. Payback B (cash flows in millions): Annual Period Cash Flows Cumulative 0 ($30) ($30) 1 20 (10) 2 10 0 3 8 8 4 6 14 Payback B = 2 years. Discounted Payback B (cash flows in millions): Annual Discounted @10% Cumulative Period Cash Flows Cash Flows Cash Flows 0 ($30) ($30.00) ($30.00) 1 20 18.18 (11.82) 2 10 8.26 (3.56) 3 8 6.01 (2.45) 4 6 4.10 6.55 Discounted Payback B = 2 + $3.56/$6.01 = 2.59 years. Summary: Project A Project B NPV $7.74 $6.55 IRR 19.19% 22.52% MIRR 16.50% 15.57% Payback 3 years 2 years Discounted Payback 3.43 years 2.59 years b. If the two projects are independent, both projects will be accepted because their NPVs are greater than zero. c. If the two projects are mutually exclusive, at WACC = 10% Project A should be chosen since NPV A > NPV B .
Chapter 11: The Basics of Capital Budgeting Comprehensive/Spreadsheet Problem 285 d. WACC NPV A NPV B 0% $20.00 $14.00 5 13.24 9.96 10 7.74 6.55 15 3.21 3.64 19.19 0 1.52 20 (0.56) 1.13 22.52 (2.23) 0 -5 0 5 10 15 20 25 0% 5% 10% 15% 20% 25% WACC (%) NPV ($) Project A Project B e. At WACC = 5% and the two projects are mutually exclusive, NPV A > NPV B so choose Project A. This doesn’t change our recommendation. At WACC = 15% and the two projects are mutually exclusive, NPV B > NPV A so choose Project B. This does change our recommendation. Both of these decisions can be made from looking at the NPV profile in part d. f. The crossover rate is the cost of capital at which the NPV profiles of two projects cross and, thus, at which the projects’ NPVs are equal. At a cost of capital less than the crossover rate there is a conflict between NPV and IRR but at a cost of capital greater than the crossover rate there is no conflict between NPV and IRR.

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