A firm is evaluating two mutually exclusive projects, A and B, with initial investments and end-of-year cash flows as shown in the table. The firm has a required payback period of two years. Determine which project(s) should be accepted or rejected.

1. Problem Description

A firm is evaluating two mutually exclusive projects, A and B, with initial investments and end-of-year cash flows as shown in the table. The firm has a required payback period of two years. Determine which project(s) should be accepted or rejected.

2. Solution Steps

First, calculate the cumulative cash flows for each project year by year, until the initial investment is recovered.

Project A:

Year 1 cash flow: $20,000$

Cumulative cash flow after year 1: $20,000$

Year 2 cash flow: $20,000$

Cumulative cash flow after year 2: $20,000 + 20,000 = 40,000$

The initial investment of $40,000$ is recovered within 2 years. So, the payback period is 2 years for Project A.

Project B:

Year 1 cash flow: $40,000$

Cumulative cash flow after year 1: $40,000$

Year 2 cash flow: $40,000$

Cumulative cash flow after year 2: $40,000 + 40,000 = 80,000$

The initial investment is $90,000$.

Since the cumulative cash flow after 2 years is $80,000$, it is less than $90,000$. So the payback period is more than 2 years.

The firm has a required payback period of two years. Project A has a payback period of two years, so it is acceptable. Project B has a payback period exceeding two years, so it is not acceptable.

Therefore, the firm should accept Project A and reject Project B.

3. Final Answer

a. Accept Project A and reject Project B