Question

Suppose a company had an initial investment of $45,000. The cash flow for the next five years are $13,000, $11,000, $10,000, $13,000, and $13,000, respectively.

What is the payback period? (Enter your answer rounded to 2 DECIMAL PLACES)
If the firm accepts projects with payback periods 3 years or less, will this project be accepted?

Answer 1

The payback period for the investment is 3.75 years. The project would be accepted.

Step-by-step explanation:

The payback period is the time it takes for an investment to generate enough cash flow to recover the initial investment cost. To calculate the payback period, we add up the cash flows until we reach or exceed the initial investment. In this case, the cash flows are $13,000, $11,000, $10,000, $13,000, and $13,000 for the next five years, respectively. Adding up these cash flows, we get:

• $13,000 + $11,000 + $10,000 + $13,000 + $13,000 = $60,000

Since the sum of the cash flows exceeds the initial investment of $45,000, the payback period is less than 5 years. We can calculate the payback period by determining when the cumulative cash flow reaches $45,000:

• Cumulative cash flow after year 1: $13,000
• Cumulative cash flow after year 2: $13,000 + $11,000 = $24,000
• Cumulative cash flow after year 3: $24,000 + $10,000 = $34,000
• Cumulative cash flow after year 4: $34,000 + $13,000 = $47,000

The cumulative cash flow exceeds $45,000 in year 4. Therefore, the payback period is between 3 and 4 years. Rounding to 2 decimal places, the payback period is 3.75 years.

Since the payback period is less than 3 years, this project would be accepted based on the firm's payback period criteria.