Question

Consider the two mutually exclusive investment projects given in the table below. Click the icon to view the cash flows for the projects. (a) To use the IRR criterion, what assumption must be made in comparing a set of mutually exclusive investments with unequal service lives? Select all that apply. A. Project A1 can be repeated at the same cost in the future. B. The required service period is 3 years. OC. Project A2 can be repeated at the same cost in the future. D. The required service period is infinity. (b) With the assumption made in part (a), determine the range of MARRs which will indicate that project A1 should be selected. Select the correct choice below an in the answer box to complete your choice. (Round to one decimal place.) - X OA. MARR More Info % OB. MARR = % O C. MARR> % 3 n Net Cash Flow Project A1 Project A2 - $10,000 - $15,000 5,000 20,000 5,000 5,000 1 2 3 Click to select and enter your answer(s). Print Done

Answer 1

a) A set of mutually exclusive projects imply that choosing any one project will imply that the other project can't be chosen. So, if we compare two such projects with unequal service life. There are specific assumptions which are taken into consideration. It assumes that each project can be repeated as many times necessary in order to reach a common life span. We also assume that the project's cost and annual cash inflows will not change, if we repeat the service life. It also says that the IRR of one project is the same as the IRR of two projects, if they the same project is repeated twice. So, as the service life of project A1 = 3 and projcet A2 = 1, we take the lowest common factor = 3 years, so the required service period = 3 years. Also, project A2 needs to be repeated thrice at the same cost in the future. So, statements C and B are those apply.

b) So, when project A2 is repeated thrice, the cash flow of year 1 = 20,000 - 15,000 = 5000, year 2 = 20,000-15,000 = 5000, year 3 = 20,000 -15000 = 5,000.

So, the NPV of project A2= -15,000+5000(P/A,i%,3)

NPV of project A1 = -10,000 +5000(P/A,i%,3)

So, the project A1 will be selected only if the NPV of A1> NPV of A2,

Also, we see that:

The project A1 needs to be selected for a MARR that makes its PW >0

0 = -10,000 + 5000(P/A, i%,3)

10,000/5000 = 2 = (P/A,i%,3)

So, i = MARR =  20% , as P/A factor = 2.106 for 3 years and i =20%.At this i = 20%, PW =530>0.

So, for i = 20%

NPV or PW of project A2 :

= -15,000+5000(P/A,i%,3) ,

= -15,000 + 5000 * 2.106

= -15,000 + 10,530 = -4470 <0,

so at a MARR of 20% and less, the project A1 will be selected as lower the MARR , higher is the PW , and thus, will yield a higher NPV of project A1. So, option A, MARR <20%.