The capital budgeting director of Sparrow Corporation is evaluating a project which costs R200,000, is expected to last for 10 years and produce after-tax cash flows, including depreciation, of R44,503 per year.If the firm's required rate of return is 14 percent and its tax rate is 40 percent, what is the project's IRR?

Question

Quizplus · Accepted Answer

To calculate the IRR of the project, we need to determine the discount rate that equates the present value of the cash inflows with the initial investment. We can use trial and error, or a financial calculator or spreadsheet, to find the rate that makes the net present value (NPV) of the project equal to zero.

Using the after-tax cash flows, we can calculate the project's NPV as follows:
NPV = -200,000 + (44,503/0.6) x [1 - 1/(1 + r)^10]
NPV = -200,000 + 74,171.67 x [1 - 1/(1 + r)^10]
where r is the discount rate or IRR.

At an IRR of 14%, for example, we get:
NPV = -200,000 + (44,503/0.6) x [1 - 1/1.14^10]
NPV = -200,000 + 74,171.67 x [1 - 0.259]
NPV = -200,000 + 54,745.79
NPV = -145,254.21

This means that the project has negative NPV at a discount rate of 14%, implying that it does not meet the firm's minimum required rate of return.

Continuing with trial and error, we can find that at an IRR of 18%:
NPV = -200,000 + (44,503/0.6) x [1 - 1/1.18^10]
NPV = -200,000 + 74,171.67 x [1 - 0.182]
NPV = -200,000 + 60,600.00
NPV = -139,400.00

This means that the project has positive NPV at a discount rate of 18%, indicating that it exceeds the required rate of return and is worth considering.

Therefore, the answer is C) 18%.

The Capital Budgeting Director of Sparrow Corporation Is Evaluating a Project