Problem 10-9-NPVs and IRRs for Mutually Exclusive Projects Davis Industries must
ID: 2715124 • Letter: P
Question
Problem 10-9-NPVs and IRRs for Mutually Exclusive Projects
Davis Industries must choose between a gas-powered and an electric powered forklift truck for moving materials in its factory. Because both forklifts perform the same function, the firm will choose only one. (They are mutually exclusive investments). The electric powered truck will cost more, but will be less expensive to operate, it will cost $22,000 whereas the gas powered truck will cost $17,500. The cost of capital that applies to both investments is 12%. The life for both types of truck is estimated to be 6 years, during which time the net cash flows for the electric powered truck will be $6, 290 per year and those for the gas powered truck will be $5,000 per year. Annual net cash flows include depreciation expenses. Calculate the NPV and IRR for each type of truck and decide which is recommended.
The Answer is: NPVe = $3,861; IRRe = 18%
NPVg = $3,057; IRRg = 18%
SHOW ALL WORK AND FORMULAS TO SUPPORT ANSWERS
Explanation / Answer
At IRR ,Present value of cash flow should be equal to Initial invetment
IRR : for electric - Present value at 18% , PVAF@18%, 6 *cash flow
= 3.49760 * 6290
= $ 21999.9 (approx 22000)
For gas truck ,present value at 18 % - 3.49760 * 5000
= 17488
Present value at 17% - 3.58918 * 5000
= 17945.92
IRR = LDR + [(Present value at LDR -initial investment)(HDR -LDR)]/[present value at LDR -Present value at HDR) ]
= 17 + [17945.92 - 17500 ) (18-17) ] /[17945.92 - 17488]
= 17 + [445.92* 1 / 457.92]
= 17 + .97
= 17.97 % (approx 18%)
Electric truck Gas truck Intial Investment (A) 22000 17500 present value of cash flow (B) PVAF@12%,6* cash flow PVAF@12%,6* cash flow 4.11141 * 6290 4.11141 * 5000 = 25860.75 20557.05 NPV = present value -Initial investment (B-A) $ 3860.75 (approx 3861) $ 3057.05