Question

determine the payback period in years for a project that costs $120,000 and would yield after-tax cash flows of $24,000 the first year, $26,000 the second year, $29,000 the third year, $31,000 the fourth year, $35,000 the fifth year, and $41,000 the sixth year.

Answer 1

The project's payback period is just over 4 years, specifically between the fourth and fifth year, roughly translating to 4 years and 3.5 months.

Step-by-step explanation:

The payback period for the project is calculated by adding up the after-tax cash flows year by year until the initial investment is recovered.

The first year's cash flow is $24,000, the second year's $26,000, the third year's $29,000, the fourth year's $31,000, the fifth year's $35,000, and the sixth year's $41,000. By the end of the third year, the total cash flow is $79,000 ($24,000+$26,000+$29,000), by the end of the fourth year it's $110,000, and by the end of the fifth year, it's $145,000. Since the cost is $120,000, it gets fully recovered between the fourth and fifth years.

To find the exact payback period, we see that by the end of the fourth year, $110,000 is recovered, leaving a balance of $10,000 to be paid back. If we divide $10,000 by the fifth year's cash flow, which is $35,000, we get approximately 0.29. Therefore, the payback period is 4 years plus approximately 0.29 of a year (roughly one-third of a year), which could translate to around 4 years and 3.5 months.