Allied, Inc. is considering Project A and Project B, which are two mutually exclusive projects with unequal lives

Question

Project A is an eight-year project that has an initial outlay or cost of $180,000. Its future cash inflows for years 1 through 8 are $38,000. Project B is a six-year project that has an initial outlay or cost of $160,000. Its future cash inflows for years 1 through 6 are the same at $36,000. Allied uses the equivalent annual annuity (EAA) method and has a discount rate of 11.50%. Will Allied accept the project?
A) Allied accepts Project B because it has a more positive EAA.
B) Allied rejects both projects because both have a negative NPV (and thus negative EAA).
C) Allied accepts Project A because its EAA is about $2,396 and Project B's EAA is only about $1,097.
D) Allied accepts Project A because its NPV (and thus EAA) is positive and Project B's NPV (and thus EAA) is negative.

Answer 1

Answer: D
Explanation: D) We will compute the EAA for both projects and choose the one with the greater positive EAA. If both EAAs are negative, then we will reject both projects. If one Project has a negative NPV (and thus negative EAA), then we will choose the project with the positive NPV (and thus positive EAA).
For Project A, the NPV = -CF0 + . Inserting the given values, we have: NPV = -$180,000 + = -$180,000 + ($38,000 × 5.055637)
= -$180,000 + $192,114.20 = $12,114.20. The EAA is the NPV divided by the PVIFA.
We have: EAA (Project A) = = $2,396.18.
For Project B, the NPV = -CF0 +
= -$160,000 + = -$160,000 + ($36,000 × 4.170294)
= -$160,000 + $150,130.59 = -$9,869.41. The EAA is the NPV divided by the PVIFA. We have: EAA (Project B) = = -$2,366.60. Allied will take Project A, not only because its EAA is positive and superior to Project B's, but because the NPV for Project B is negative. Thus, we can really only consider one project, and that is Project A.