A firm is evaluating a potential investment that is expected to generate cash flows of $100 in years 1 through 4 and $400 in years 5 through 7. The initial investment is $750. What is the payback for this investment?
A) 4.88 years
B) 4.48 years
C) 5.88 years
D) 5.48 years

Question

Quizplus · Accepted Answer

The payback period is the time it takes for the investment to generate cash flows to recover the initial investment cost. Here, the investment generates $100 annually for the first 4 years, totaling $400, and then $400 annually for the next 3 years. By the end of year 4, the investment has recovered $400 of the initial $750. In year 5, it generates another $400, fully recovering the initial investment and providing an excess. To find the exact payback period, calculate how much of year 5's cash flow is needed to reach $750. Since $400 in year 5 covers the remaining $350 needed ($750 - $400 from years 1-4), the payback period is 4 years plus the fraction of year 5 needed to recover the full investment. This fraction is $350 (the remaining amount to be recovered by the end of year 4) divided by $400 (the cash flow in year 5), which equals 0.875 (or 7/8) of a year. Therefore, the total payback period is 4 years + 0.875 years = 4.875 years, or approximately 4.88 years when rounded.

A Firm Is Evaluating a Potential Investment That Is Expected