A firm is considering a project requiring an investment of $200,000. The project would generate an annual cash flow of $55,478 for the next five years. The company uses the straight-line method of depreciation with no mid-year convention. Ignore income taxes. The approximate internal rate of return for the project is

Question

Quizplus · Accepted Answer

To calculate internal rate of return (IRR), we need to find the discount rate that makes the present value of cash inflows equal to the initial investment. We can use a financial calculator or Excel to solve for the IRR, or we can estimate it using trial and error.

Using trial and error, we can assume a discount rate and calculate the present value of cash inflows using the formula:

PV = CF1/(1+r) + CF2/(1+r)^2 + ... + CFn/(1+r)^n

Where PV is the present value, CF is the cash flow for each year, r is the discount rate, and n is the number of years.

If the present value is greater than the initial investment, the discount rate is too low. If the present value is less than the initial investment, the discount rate is too high. We can adjust the discount rate accordingly and try again until we find the discount rate that makes the present value equal to the initial investment.

For this problem, the initial investment is $200,000 and the cash flows are $55,478 for the next five years. Using the formula above, we can calculate the present value of cash inflows for different discount rates. For example:

At 9%, PV = 55478/(1+0.09) + 55478/(1+0.09)^2 + ... + 55478/(1+0.09)^5 = $228,322

At 10%, PV = 55478/(1+0.1) + 55478/(1+0.1)^2 + ... + 55478/(1+0.1)^5 = $223,878

At 12%, PV = 55478/(1+0.12) + 55478/(1+0.12)^2 + ... + 55478/(1+0.12)^5 = $216,716

At 16%, PV = 55478/(1+0.16) + 55478/(1+0.16)^2 + ... + 55478/(1+0.16)^5 = $200,673

Since the present value at 12% is closest to the initial investment of $200,000, the approximate internal rate of return for the project is 12%. Therefore, the best choice is C.

A Firm Is Considering a Project Requiring an Investment of $200,000