You are considering two mutually exclusive projects. Project A has cash flows of −$72,000, $21,400, $22,900, and $56,300 for Years 0 to 3, respectively. Project B has cash flows of −$81,000, $20,100, $22,200, and $74,800 for Years 0 to 3, respectively. Both projects have a required 2.5-year payback period. Should you accept or reject these projects based on payback analysis?Single choice
A
A. Accept both Projects A and B
B
B. Reject both Projects A and B
C
C. Accept Project A and reject Project B
D
D. Reject Project A and accept Project B

Question

You are considering two mutually exclusive projects. Project A has cash flows of −$72,000, $21,400, $22,900, and $56,300 for Years 0 to 3, respectively. Project B has cash flows of −$81,000, $20,100, $22,200, and $74,800 for Years 0 to 3, respectively. Both projects have a required 2.5-year payback period. Should you accept or reject these projects based on payback analysis?Single choice

A

A. Accept both Projects A and B

B

B. Reject both Projects A and B

C

C. Accept Project A and reject Project B

D

D. Reject Project A and accept Project B

BlackTom AI · Accepted Answer

Payback period measures how long it takes cumulative cash inflows to recover the initial cash outlay; compare each project’s payback to the required 2.5-year cutoff.

Project A:
- Year 0: cumulative = −72,000.
- After Year 1: cumulative = −72,000 + 21,400 = −50,600.
- After Year 2: cumulative = −50,600 + 22,900 = −27,700.
- After Year 3: cumulative = −27,700 + 56,300 = 28,600 (recovered during Year 3).
Amount remaining to recover at end of Year 2 = 27,700. Year 3 cash inflow = 56,300.
Fraction of Year 3 required = 27,700 / 56,300 ≈ 0.4922 years.
Payback(A) = 2 + 0.4922 = 2.4922 years ≈ 2.49 years.
Since 2.49 years < required 2.5 years, Project A meets the payback criterion (accept).

Project B:
- Year 0: cumulative = −81,000.
- After Year 1: cumulative = −81,000 + 20,100 = −60,900.
- After Year 2: cumulative = −60,900 + 22,200 = −38,700.
- After Year 3: cumulative = −38,700 + 74,800 = 36,100 (recovered during Year 3).
Amount remaining to recover at end of Year 2 = 38,700. Year 3 cash inflow = 74,800.
Fraction of Year 3 required = 38,700 / 74,800 ≈ 0.5174 years.
Payback(B) = 2 + 0.5174 = 2.5174 years ≈ 2.52 years.
Since 2.52 years > required 2.5 years, Project B fails the payback criterion (reject).

Why other choices are incorrect:
- A (accept both): incorrect because B’s payback exceeds 2.5 years.
- B (reject both): incorrect because A’s payback meets the 2.5-year requirement.
- D (reject A, accept B): incorrect because A qualifies and B does not.