4) (40 points) John just inherited $200,000 and is considering the following two

Question

4) (40 points) John just inherited $200,000 and is considering the following two investment opportunities. Project A requires an initial investment of $200,000 and promises to return an annual amount of $47,480 for 5 years. Project B requires an initial investment of $180,000 and is expected to return $42,300 every year for 5 years. If John's MARR is 5% per year compounded annually, which project should John choose, if any. Solve using the internal rate of return approach. (Note: You must solve for IRR rounded to the nearest whole %.)

Explanation / Answer

Find the IRR on first investment such that NPV is 0

-200,000 + 47,480(P/A, i%, 5) = 0

(P/A, i%, 5) = 200,000/47,480

(P/A, i%, 5) = 4.2123

From compound interest tables we find that (P/A, 6%, 5) = 4.212. Hence the first investment has IRR = 6%.

Find the IRR on second investment such that NPV is 0

-180,000 + 42,300(P/A, i%, 5) = 0

(P/A, i%, 5) = 180,000/42,300

(P/A, i%, 5) = 4.2553

From compound interest tables we find that (P/A, 5%, 5) = 4.329. This implies that the IRR for the second investment lies between 5% and 6%. Interpolation gives an IRR = 5.628% or 6% in the nearest whole number.Hence the first investment that has a higher IRR at 6% should be selected as IRR(1) > IRR(2)

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