question archive Task 3: The firm is considering the purchase of a new device that costs €7,000
Task 3: The firm is considering the purchase of a new device that costs €7,000
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Task 3: The firm is considering the purchase of a new device that costs €7,000. Assume a required rate of retum of 8% and the following cash flow schedule: Year 1 €3,000 Year 2 2,500 Year 3 2,000 1) Calculate the profitability index of the project. 2) Should the firm accept this project?
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Initial outflow = 7,000
Rate of return = r = 8%
| Year | Cashflows |
| 1 | 3000 |
| 2 | 2500 |
| 3 | 2000 |
1)
| Year | Cashflows | PV Factor | Cashflows * PV Factor | |||
| 1 | 3000 | 1/(1+r)^1 | 1/(1+8%)^1 | 1/(1.08)^1 | 0.925925926 | 2777.7778 |
| 2 | 2500 | 1/(1+r)^2 | 1/(1+8%)^2 | 1/(1.08)^2 | 0.85733882 | 2143.3471 |
| 3 | 2000 | 1/(1+r)^3 | 1/(1+8%)^3 | 1/(1.08)^3 | 0.793832241 | 1587.6645 |
Sum of Present value of cash inflows = 
Cashflows * PV Factor
Sum of Present value of cash inflows = 2,777.7778 + 2143.3471 + 1587.6645
Sum of Present value of cash inflows = 6508.7894
Profitability index = Sum of Present value of cash inflows / Initial outflow
Profitability index = 6508.7894 / 7000
Profitability index = 0.9298
2)
No, the firm should not accept the project due to the fact that the profitability index of the project at 8% rate of return is 0.9298 which is less than 1, this means at 8% rate of return the project will not be profitable for the investors.
Therefore, the project should not be accepted.
