Final answer:
The payback period for the investment is 4 years, and the project will be accepted.
Step-by-step explanation:
The payback period is the amount of time it takes for an investment to recoup its initial cost. To calculate the payback period, we add up the cash flows until they equal or exceed the initial investment. In this case, the cash flows are $14,000, $10,000, $12,000, $13,000, and $14,000 for the next five years.
Year 1: $14,000
Year 2: $10,000 + $12,000 = $22,000
Year 3: $22,000 + $13,000 = $35,000
Year 4: $35,000 + $14,000 = $49,000
Since the cash flows exceed the initial investment of $45,000 in year 4, the payback period is 4 years.
The project will be accepted because the payback period is 4 years or less.