A project costs $500,000 today and is expected to return 10% before corporate income taxes. The appropriate after-tax cost of capital is 12%, and the firm pays taxes at the marginal rate of
30%. What is this project's NPV? Round your answer to the nearest dollar.

Question

Quizplus · Accepted Answer

First, we need to calculate the before-tax cash flows:
Year 1: $500,000 x 10% = $50,000
Year 2: $500,000 x 10% = $50,000
Year 3: $500,000 x 10% = $50,000
Year 4: $500,000 x 10% = $50,000
Year 5: $500,000 x 10% = $50,000
The before-tax cash flows total $250,000.
Next, we need to calculate the after-tax cash flows:
Year 1: $50,000 x (1 - 0.3) = $35,000
Year 2: $50,000 x (1 - 0.3) = $35,000
Year 3: $50,000 x (1 - 0.3) = $35,000
Year 4: $50,000 x (1 - 0.3) = $35,000
Year 5: $50,000 x (1 - 0.3) = $35,000
The after-tax cash flows total $175,000.
To calculate NPV, we discount the after-tax cash flows using the after-tax cost of capital:
NPV = -$500,000 + ($35,000/1.12) + ($35,000/1.12^2) + ($35,000/1.12^3) + ($35,000/1.12^4) + ($35,000/1.12^5)
NPV = -$22,321 (rounded to the nearest dollar). Therefore, the best choice is B as it has the closest number to our answer.

A Project Costs $500,000 Today and Is Expected to Return