The capital budgeting director of Sparrow Corporation is evaluating a project which costs $200,000, is expected to last for 10 years and produce after-tax cash flows, including depreciation, of $44,503 per year. If the firm's cost of capital is 14 percent and its tax rate is 40 percent, what is the project's IRR?

Question

Quizplus · Accepted Answer

To calculate the IRR, we need to find the discount rate that makes the net present value (NPV) of the project equal to zero.

NPV = -initial investment + PV of cash flows

NPV = -$200,000 + $44,503 * [(1 - 0.4) / 0.14 - 10 / (1 + 0.14) ^ 10]

NPV = -$200,000 + $44,503 * (0.6 / 0.14 - 3.433)

NPV = -$200,000 + $22,116

NPV = -$177,884

To find the IRR, we need to solve for the discount rate that makes NPV = 0.

At a discount rate of 18%, NPV is about -$27, which is too high.

At a discount rate of 12%, NPV is about -$107, which is still too high.

Therefore, the IRR must be between 14% and 18%. By trial and error, we can find that the IRR is about 16.3%, which is closest to choice C.

The Capital Budgeting Director of Sparrow Corporation Is Evaluating a Project