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Dizzyland Enterprises has been presented with an investment opportunity which will yield end -of-year cash flows of $30,000 per year in Years 1 through 4, $35,000 per year in Years 5 through 9, and $40,000 in Year 10
Dizzyland Enterprises has been presented with an investment opportunity which will yield end -of-year cash flows of $30,000 per year in Years 1 through 4, $35,000 per year in Years 5 through 9, and $40,000 in Year 10. This investment will cost the firm $150,000 today, and the firm's cost of capital is 10%. What is the profitability index for this investment?
|
0.87 |
||
|
1.85 |
||
|
0.21 |
||
|
1.34 |
Expert Solution
Given the following information,
| Years | Cashflows |
| 1 | 30000 |
| 2 | 30000 |
| 3 | 30000 |
| 4 | 30000 |
| 5 | 35000 |
| 6 | 35000 |
| 7 | 35000 |
| 8 | 35000 |
| 9 | 35000 |
| 10 | 40000 |
Cost of capital = r = 10% = 0.10
We know that profitability index is given by the following formula,
Profitability index = Present value of future cashflows/Initial investment required
Where,
Present value of future cashflows = ∑ CFi/(1+r)^i
CFi = Cashflow in year i
| Years(i) | Cashflows(CFi) | (1+r)^i = (1+0.1)^i | Cashflows/(1+r)^i |
| 1 | 30000 | 1.1000 | 27272.73 |
| 2 | 30000 | 1.2100 | 24793.39 |
| 3 | 30000 | 1.3310 | 22539.44 |
| 4 | 30000 | 1.4641 | 20490.40 |
| 5 | 35000 | 1.6105 | 21732.25 |
| 6 | 35000 | 1.7716 | 19756.59 |
| 7 | 35000 | 1.9487 | 17960.53 |
| 8 | 35000 | 2.1436 | 16327.76 |
| 9 | 35000 | 2.3579 | 14843.42 |
| 10 | 40000 | 2.5937 | 15421.73 |
| ∑ CFi/(1+r)^i = | 201138.24 |
∑ CFi/(1+r)^i = 27272.73 + 24793.39 + 22539.44 + 20490.40 + 21732.25 + 19756.59 + 17960.53 + 16327.76 + 14843.42 + 15421.73
∑ CFi/(1+r)^i = 201138.24
Initial investment required = 150,000 (given)
Substituting these in the above equation, we get
Profitability index = 201138.24/150,000
Profitability index = 1.34
Therefore, the profitability index for this investment is 1.34
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