Question

Question 3 (1 point) A firm is considering a potential investment project that would result in an immediate loss in free cash flow of $110 Million, but would generate positive free cash flow of $6 Million next year. The firm expects the free cash flow produced by the project to grow annually at 3% forever. The firm's weighted average cost of capital (WACC) is 6%. What is the NPV of the project? (Enter your answer in millions of dollars rounded to two decimal places. For example, if your answer is -1.23 Million, then enter just -1.23 in the answer box.] Your Answer:

Answer 1

Let the cash flow in Year n be CF_n

Growth in free cash flow = g = 3%

Given,
CF₀ = -110 m
CF₁ = 6 m
CF₂ = 6(1+0.03)
CF₃ = 6(1+0.03)²
.....

WACC = r = 6%

Net Present Value = -CF₀ + CF₁/(1+r) + CF₂/(1+r)² + CF₃/(1+r)³ + .......
= -110 + 6/(1+0.06) + 6(1+0.03)/(1+0.06)² + 6(1+0.03)²/(1+0.06)³ .....
= -110 + 1/(1+0.06) [ 6 + 6(1+0.03)/(1+0.06) + 6(1+0.03)²/(1+0.06)² .....]
= -110 + 1/(1+0.06) [ 6/(1 - (1+0.03)/(1+0.06))]
= $90 million

Here, we have used the sum of an infinite geometric progression a, ar, ar², .... = a/(1 - r)