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Payback, NPV, and MIRR

Your division is considering two investment projects, each of which requires an up-front expenditure of $22 million. You estimate that the cost of capital is 12% and that the investments will produce the following after-tax cash flows (in millions of dollars):

Year Project A Project B
1 5 20
2 10 10
3 15 8
4 20 6

What is the regular payback period for each of the projects? Round your answers to two decimal places.
Project A: years
Project B: years

1 Answer

3 votes

Final answer:

The payback period for Project A is approximately 2.47 years, while for Project B it is approximately 1.1 years.

Step-by-step explanation:

The payback period for an investment project is the time it takes for the cash flows from the investment to repay the initial investment cost. To calculate the payback period for Projects A and B, we simply sum the cash flows year by year until they equal or exceed the initial investment of $22 million.

For Project A:

Year 1: $5 million

Year 2: $5 million + $10 million = $15 million

Year 3: $15 million + $15 million = $30 million

Project A's payback occurs during Year 3.

For Project B:

Year 1: $20 million

Year 2: $20 million + $10 million = $30 million

Project B's payback occurs during Year 1.

To determine the exact payback period, we need to interpolate between the cumulative cash flows to find the fraction of the year when the payback occurs. For Project A, $15 million is recovered by the end of Year 2 and the payback is completed in Year 3. Assuming linear cash flows for simplicity, ($22 million - $15 million) / $15 million = 0.47, so the payback period for Project A is 2 years plus 0.47 years, which rounds to 2.47 years.

For Project B, the payback happens during the first year itself, specifically, $22 million / $20 million = 1.1, which signifies the project pays back just after Year 1, equating to a payback period of approximately 1.1 years.

Therefore, the mentioned correct option in final answer for the payback period is 2.47 years for Project A and 1.1 years for Project B, rounded to two decimal places as requested.

User Guilherme Meireles
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