In: Finance
Year Cash Flow 0 –$ 15,900 1 7,930 2 9,490 3 8,970 4 7,210 5 – 3,580 Required: The company uses an interest rate of 12 percent on all of its projects. Calculate the MIRR of the project using all three methods. (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) MIRR Discounting approach % Reinvestment approach % Combination approach %
Discounting Approach | ||||||
All negative cash flows are discounted back to the present at the required return and added to the initial cost | ||||||
Thus year 0 modified cash flow=-15900-2031.39 | ||||||
=-17931.39 | ||||||
Year | 0 | 1 | 2 | 3 | 4 | 5 |
Cash flow stream | -15900.000 | 7930.000 | 9490.000 | 8970.000 | 7210.000 | -3580.000 |
Discounting factor (Using discount rate) | 1.000 | 1.120 | 1.254 | 1.405 | 1.574 | 1.762 |
Discounted cash flows | -15900.000 | 7080.357 | 7565.370 | 6384.669 | 4582.085 | -2031.388 |
Modified cash flow | -17931.388 | 7930.000 | 9490.000 | 8970.000 | 7210.000 | 0.000 |
Discounting factor (using MIRR) | 1.000 | 1.313 | 1.724 | 2.264 | 2.973 | 3.903 |
Discounted cash flows | -17931.388 | 6039.348 | 5504.272 | 3962.260 | 2425.508 | 0.000 |
NPV = Sum of discounted cash flows | ||||||
NPV Reinvestment rate = | 0.00 | |||||
MIRR is the rate at which NPV = 0 | ||||||
MIRR= | 31.31% | |||||
Where | ||||||
Discounting factor = | (1 + discount rate)^(Corresponding period in years) | |||||
Discounted Cashflow= | Cash flow stream/discounting factor | |||||
Reinvestment Approach | ||||||
All cash flows except the first are compounded to the last time period and IRR is calculated | ||||||
Thus year 5 modified cash flow=(12478.01)+(13332.77)+(11251.97)+(8075.2)+(-3580) | ||||||
=41557.95 | ||||||
Discount rate | 12.000% | |||||
Year | 0 | 1 | 2 | 3 | 4 | 5 |
Cash flow stream | -15900.000 | 7930.000 | 9490.000 | 8970.000 | 7210.000 | -3580.000 |
Compound factor | 1.000 | 1.574 | 1.405 | 1.254 | 1.120 | 1.000 |
Compounded cash flows | -15900.000 | 12478.01 | 13332.77 | 11251.97 | 8075.2 | -3580 |
Modified cash flow | -15900.000 | 0 | 0 | 0 | 0 | 41557.950 |
Discounting factor (using MIRR) | 1.000 | 1.212 | 1.469 | 1.780 | 2.157 | 2.614 |
Discounted cash flows | -15900.000 | 0.000 | 0.000 | 0.000 | 0.000 | 15900.001 |
NPV = Sum of discounted cash flows | ||||||
NPV Discount rate = | 0.00 | |||||
MIRR is the rate at which NPV = 0 | ||||||
MIRR= | 21.19% | |||||
Where | ||||||
Compounding factor = | (1 + reinvestment rate)^(time of last CF-Corresponding period in years) | |||||
compounded Cashflow= | Cash flow stream*compounding factor | |||||
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 5 modified cash flow=(12478.01)+(13332.77)+(11251.97)+(8075.2) | ||||||
=45137.95 | ||||||
Thus year 0 modified cash flow=-15900-2031.39 | ||||||
=-17931.39 | ||||||
Discount rate | 12.000% | |||||
Year | 0 | 1 | 2 | 3 | 4 | 5 |
Cash flow stream | -15900.000 | 7930.000 | 9490.000 | 8970.000 | 7210.000 | -3580.000 |
Discount factor | 1.000 | 1.120 | 1.254 | 1.405 | 1.574 | 1.762 |
Compound factor | 1.000 | 1.574 | 1.405 | 1.254 | 1.120 | 1.000 |
Discounted cash flows | -15900.000 | 0 | 0 | 0 | 0 | -2031.39 |
Compounded cash flows | 0.000 | 12478.01 | 13332.77 | 11251.97 | 8075.2 | 0 |
Modified cash flow | -17931.390 | 0 | 0 | 0 | 0 | 45137.950 |
Discounting factor (using MIRR) | 1.000 | 1.203 | 1.447 | 1.740 | 2.093 | 2.517 |
Discounted cash flows | -17931.390 | 0.000 | 0.000 | 0.000 | 0.000 | 17931.390 |
NPV = Sum of discounted cash flows | ||||||
NPV= | 0.00 | |||||
MIRR is the rate at which NPV = 0 | ||||||
MIRR= | 20.28% | |||||
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 |