Question

Gold Mining, Inc. is using the profitability index (PI) when evaluating projects. Gold Mining’s cost of capital is 11.35 percent. What is the PI of a project if the initial costs are $2,118,606 and the project life is estimated as 5 years? The project will produce the same after-tax cash inflows of $479,544 per year at the end of the year.

Answer 1

Profitability Index = Present value of future Cash flows/Initial Investment

Let the cash flow in Year n be CF_n

Given,
CF₀ = -2118606
CF₁ = 479544
CF₂ = 479544
CF₃ = 479544
CF₄ = 479544
CF₅ = 479544

Cost of capital = r = 11.35%

Present Value of future cash flows = CF₁/(1+r) + CF₂/(1+r)² + CF₃/(1+r)³ + CF₄/(1+r)⁴ + CF₅/(1+r)⁵
= 479544/(1+0.1135) + 479544/(1+0.1135)² + 479544/(1+0.1135)³ + 479544/(1+0.1135)⁴ + 479544/(1+0.1135)⁵
= -$1756850.76

Profitability Index = Present value of future Cash flows/Initial Investment

= 1756850.76/2118606

= 0.83