Question
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Artie's Wrestling Stuff is considering building a new plant. This plant would require an initial cash...
Artie's Wrestling Stuff is considering building a new plant. This plant would require an initial cash outlay of $ 8 million and would generate annual free cash inflows of $ 1 million per year for 8 years. Calculate the project's MIRR given: a. A required rate of return of 9 percent b. A required rate of return of 12 percent c. A required rate of return of 15 percent
Solutions
Expert Solution
a
| Combination approach | |||||||||
| All negative cash flows are discounted back to the present and all positive cash flows are compounded out to the end of the project’s life | |||||||||
| Thus year 8 modified cash flow=(1.83)+(1.68)+(1.54)+(1.41)+(1.3)+(1.19)+(1.09)+(1) | |||||||||
| =11.04 | |||||||||
| Thus year 0 modified cash flow=-8 | |||||||||
| =-8 | |||||||||
| Discount rate | 9.000% | ||||||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Cash flow stream | -8.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
| Discount factor | 1.000 | 1.090 | 1.188 | 1.295 | 1.412 | 1.539 | 1.677 | 1.828 | 1.993 |
| Compound factor | 1.000 | 1.828 | 1.677 | 1.539 | 1.412 | 1.295 | 1.188 | 1.090 | 1.000 |
| Discounted cash flows | -8.000 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Compounded cash flows | -0.125 | 1.83 | 1.68 | 1.54 | 1.41 | 1.3 | 1.19 | 1.09 | 1 |
| Modified cash flow | -8.000 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 11.040 |
| Discounting factor (using MIRR) | 1.000 | 1.041 | 1.084 | 1.128 | 1.175 | 1.223 | 1.273 | 1.326 | 1.380 |
| Discounted cash flows | -8.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 7.999 |
| NPV = Sum of discounted cash flows | |||||||||
| NPV= | 0.00 | ||||||||
| MIRR is the rate at which NPV = 0 | |||||||||
| MIRR= | 4.11% | ||||||||
| Where | |||||||||
| Discounting factor = | (1 + discount rate)^(Corresponding period in years) | ||||||||
| Discounted Cashflow= | Cash flow stream/discounting factor | ||||||||
| Compounding factor = | (1 + reinvestment rate)^(time of last CF-Corresponding period in years) | ||||||||
| Compounded Cashflow= | Cash flow stream*compounding factor | ||||||||
b
| All negative cash flows are discounted back to the present and all positive cash flows are compounded out to the end of the project’s life | |||||||||
| Thus year 8 modified cash flow=(2.21)+(1.97)+(1.76)+(1.57)+(1.4)+(1.25)+(1.12)+(1) | |||||||||
| =12.28 | |||||||||
| Thus year 0 modified cash flow=-8 | |||||||||
| =-8 | |||||||||
| Discount rate | 12.000% | ||||||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Cash flow stream | -8.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
| Discount factor | 1.000 | 1.120 | 1.254 | 1.405 | 1.574 | 1.762 | 1.974 | 2.211 | 2.476 |
| Compound factor | 1.000 | 2.211 | 1.974 | 1.762 | 1.574 | 1.405 | 1.254 | 1.120 | 1.000 |
| Discounted cash flows | -8.000 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Compounded cash flows | -0.125 | 2.21 | 1.97 | 1.76 | 1.57 | 1.4 | 1.25 | 1.12 | 1 |
| Modified cash flow | -8.000 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12.280 |
| Discounting factor (using MIRR) | 1.000 | 1.055 | 1.113 | 1.174 | 1.239 | 1.307 | 1.379 | 1.455 | 1.535 |
| Discounted cash flows | -8.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 8.000 |
| NPV = Sum of discounted cash flows | |||||||||
| NPV= | 0.00 | ||||||||
| MIRR is the rate at which NPV = 0 | |||||||||
| MIRR= | 5.50% | ||||||||
| Where | |||||||||
| Discounting factor = | (1 + discount rate)^(Corresponding period in years) | ||||||||
| Discounted Cashflow= | Cash flow stream/discounting factor | ||||||||
| Compounding factor = | (1 + reinvestment rate)^(time of last CF-Corresponding period in years) | ||||||||
| Compounded Cashflow= | Cash flow stream*compounding factor | ||||||||
c
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