Figure 14-8.Present value of an Annuity of $1 in Arrears

-Refer to Figure 14-8. Sawyer Company is considering a project with an initial investment of $226,000 that will yield annual net cash flows of $40,000, and will be depreciated at $22,600 per year over its ten year life. What is the internal rate of return?

Question

Figure 14-8.Present value of an Annuity of $1 in Arrears
 
-Refer to Figure 14-8. Sawyer Company is considering a project with an initial investment of $226,000 that will yield annual net cash flows of $40,000, and will be depreciated at $22,600 per year over its ten year life. What is the internal rate of return?

Quizplus · Accepted Answer

To calculate the internal rate of return (IRR), we need to find the discount rate that will make the present value of cash inflows equal to the initial investment of $226,000.

Using the formula for calculating the present value of an annuity in arrears, we can find the present value of annual net cash flows of $40,000 over ten years at a discount rate of x%:

PV = $40,000 x [(1 - (1 / (1+x)^10)) / x] = $276,423.11

Then, we need to find the discount rate that will make the present value of cash inflows equal to the initial investment:

$226,000 = $22,600 + $276,423.11 / (1 + IRR)^1 + $22,600 + $276,423.11 / (1 + IRR)^2 + ... + $22,600 + $276,423.11 / (1 + IRR)^10

Using trial and error or an Excel function, we can find that the IRR is approximately 12%. Therefore, the best choice is D.