Question
In: Finance
1. An expansion project being considered by your firm has an initial cost of $8,000,000 and...
1. An expansion project being considered by your firm has an initial cost of $8,000,000 and expected net cash flows of $1,500,000 per year for the first 2 years, 1,800,000 for the third and fourth years, and $1,900,000 per year for the fifth and sixth years. All cash flows will occur at the end of each year. Assume that the project will be terminated at the end of the sixth year. Your firm’s cost of capital is 11%. Calculate the Net Present Value (NPV), the Modified Internal Rate of Return (MIRR), the Discounted Payback Period, and the Equivalent Annual Annuity for this project. Should the project be accepted? Why or why not? Give an interpretation for each of the four methods and indicate how they are used.
Solutions
Expert Solution
1. NPV = -$785,979.65
NPV Calculation:
| Formula | Year (n) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Initial investment | -80,00,000 | |||||||
| Cash flow | 15,00,000 | 15,00,000 | 18,00,000 | 18,00,000 | 19,00,000 | 19,00,000 | ||
| (Initial investment + cash flow) | Net cash flow | -80,00,000 | 15,00,000 | 15,00,000 | 18,00,000 | 18,00,000 | 19,00,000 | 19,00,000 |
| 1/(1+d)^n | Discount factor @ 11% | 1.000 | 0.901 | 0.812 | 0.731 | 0.659 | 0.593 | 0.535 |
| (Net cash flow*Discount factor) | Discount cash flow | -80,00,000.00 | 13,51,351.35 | 12,17,433.65 | 13,16,144.49 | 11,85,715.75 | 11,27,557.52 | 10,15,817.59 |
| Sum of all discounted cash flows | NPV | -7,85,979.65 |
2. MIRR = 9.10%
MIRR Calculation:
| Formula | Year (n) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Net cash flow | -80,00,000 | 15,00,000 | 15,00,000 | 18,00,000 | 18,00,000 | 19,00,000 | 19,00,000 | |
| 1/(1+d)^n where d = 11% | Discount factor @11% | 1.000 | ||||||
| Present value of cash outflow | -80,00,000.00 | |||||||
| (1+c)^n where c = 11% | Compounding factor @11% | 1.685 | 1.518 | 1.368 | 1.232 | 1.110 | 1.000 | |
| Future value of cash in flows | 25,27,587.23 | 22,77,105.62 | 24,61,735.80 | 22,17,780.00 | 21,09,000.00 | 19,00,000.00 | ||
| Total FV of cash inflows | 1,34,93,208.65 |
Now, in order to find MIRR,
PV of cash outflow = PV of FV of cash inflow
800,000 = 13,493,208.65 /(1+MIRR)^6
(1+MIRR)^6 = 1.6867
MIRR = (1.867)^(1/6) - 1
MIRR = 9.10%
3. Discounted Payback Period is more then the life of the project ie. beyond 6 years.
| Formula | Year (n) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Discount cash flow | -80,00,000.00 | 13,51,351.35 | 12,17,433.65 | 13,16,144.49 | 11,85,715.75 | 11,27,557.52 | 10,15,817.59 | |
| Cumulative cash flow | -80,00,000.00 | -66,48,648.65 | -54,31,215.00 | -41,15,070.51 | -29,29,354.76 | -18,01,797.24 | -7,85,979.65 |
As can be seen, the cumulative cash flow never becomes positive during the life of the project.
4. Equivalent Annual Annuity C = r*NPV/[(1 - (1+r)^-n]
However, given that the NPV is negative, C will also be negative.
EAA is useful when deciding between projects with differing lives. In this case, since only one project is being evaluated, it is not of much use.
This project should not be accepted because it has a negative NPV, its MIRR is less than the cost of capital and the discounted payback period exceeds the life of the project.
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