Question

Compute the PI statistic for Project X and note whether the firm should accept or reject the project with the cash flows shown below if the appropriate cost of capital is 11 percent. Time: 0 1 2 3 4 5 Cash flow: -78 -78 0 113 88 63 51.00%, accept 29.71%, accept 38.09%, accept 11.00%, reject

Answer 1

Time	Cash Flow
0	-78
1	-78
2	0
3	113
4	88
5	63

NPV = ΣCFn/(1+r)ⁿ

Where, CF_n is the cash flow in time period n

r = cost of capital = 11%

=> NPV = -78 - 78/(1+0.11) + 0/(1+0.11)² + 113/(1+0.11)³ + 88/(1+0.11)⁴ + 63/(1+0.11)⁵ = $29.71

Profitability Index = PV of future cash flows / Present Value of Initial investment

Present Value of Initial Investment = 78

PV of future cash flows = NPV + Present Value of Initial investment = 29.71 + 78 = $107.71

=> Profitability Index = 107.71 / 78 = 1.3809

Since PI is greater than 1, the project should be accepted

PI statistics = 1.3809 - 1 = 0.3809 or 38.09%