Homework Answers
| 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=-28100-5784,96 | ||||||
| =-33884,96 | ||||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
| Cash flow stream | -28100,000 | 10300,000 | 13000,000 | 14900,000 | 12000,000 | -8500,000 |
| Discounting factor (Using discount rate) | 1,000 | 1,080 | 1,166 | 1,260 | 1,360 | 1,469 |
| Discounted cash flows | -28100,000 | 9537,037 | 11145,405 | 11828,100 | 8820,358 | -5784,957 |
| Modified cash flow | -33884,957 | 10300,000 | 13000,000 | 14900,000 | 12000,000 | 0,000 |
| Discounting factor (using MIRR) | 1,000 | 1,172 | 1,373 | 1,609 | 1,885 | 2,209 |
| Discounted cash flows | -33884,957 | 8790,187 | 9468,150 | 9261,235 | 6365,386 | 0,000 |
| NPV = Sum of discounted cash flows | ||||||
| NPV Reinvestment rate = | 0,00 | |||||
| MIRR is the rate at which NPV = 0 | ||||||
| MIRR= | 17,18% | |||||
| 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=(14013,04)+(16376,26)+(17379,36)+(12960)+(-8500) | ||||||
| =52228,66 | ||||||
| Discount rate | 8,000% | |||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
| Cash flow stream | -28100,000 | 10300,000 | 13000,000 | 14900,000 | 12000,000 | -8500,000 |
| Compound factor | 1,000 | 1,360 | 1,260 | 1,166 | 1,080 | 1,000 |
| Compounded cash flows | -28100,000 | 14013,04 | 16376,26 | 17379,36 | 12960 | -8500 |
| Modified cash flow | -28100,000 | 0 | 0 | 0 | 0 | 52228,660 |
| Discounting factor (using MIRR) | 1,000 | 1,132 | 1,281 | 1,451 | 1,642 | 1,859 |
| Discounted cash flows | -28100,000 | 0,000 | 0,000 | 0,000 | 0,000 | 28100,000 |
| NPV = Sum of discounted cash flows | ||||||
| NPV Discount rate = | 0,00 | |||||
| MIRR is the rate at which NPV = 0 | ||||||
| MIRR= | 13,20% | |||||
| 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=(14013,04)+(16376,26)+(17379,36)+(12960) | ||||||
| =60728,66 | ||||||
| Thus year 0 modified cash flow=-28100-5784,96 | ||||||
| =-33884,96 | ||||||
| Discount rate | 8,000% | |||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
| Cash flow stream | -28100,000 | 10300,000 | 13000,000 | 14900,000 | 12000,000 | -8500,000 |
| Discount factor | 1,000 | 1,080 | 1,166 | 1,260 | 1,360 | 1,469 |
| Compound factor | 1,000 | 1,360 | 1,260 | 1,166 | 1,080 | 1,000 |
| Discounted cash flows | -28100,000 | 0 | 0 | 0 | 0 | -5784,96 |
| Compounded cash flows | 0,000 | 14013,04 | 16376,26 | 17379,36 | 12960 | 0 |
| Modified cash flow | -33884,960 | 0 | 0 | 0 | 0 | 60728,660 |
| Discounting factor (using MIRR) | 1,000 | 1,124 | 1,263 | 1,419 | 1,595 | 1,792 |
| Discounted cash flows | -33884,960 | 0,000 | 0,000 | 0,000 | 0,000 | 33884,960 |
| NPV = Sum of discounted cash flows | ||||||
| NPV= | 0,00 |
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