Final answer:
The payback period for the project is between four and five years, based on the given annual expected cash flows cumulatively offsetting the initial cost of $29,250.
Step-by-step explanation:
The payback period is a capital budgeting metric used to determine the timeframe in which an investment will recoup the initial outlay of capital. In this case, we're calculating the time it will take a project with an initial cost of $29,250 to generate enough expected cash flows to cover this cost.
The cash flows over five years are expected to be $5,100, $7,200, $8,350, $7,250, and $5,900, respectively. To find out the payback period, we cumulatively add these cash flows year over year until the total reaches the initial cost:
- Year 1: $5,100
- Year 2: $5,100 + $7,200 = $12,300
- Year 3: $12,300 + $8,350 = $20,650
- Year 4: $20,650 + $7,250 = $27,900 (close to initial investment)
After four years, the project has almost generated enough cash to cover the initial cost. Proceeding to Year 5, the project would achieve and surpass the initial investment early in the year. Thus, the payback period is somewhere between 4 and 5 years. To pinpoint the exact moment within the fifth year when payback occurs would require further calculation, prorating the cash flows of Year 5 over each period (monthly or daily depending on precision required).