The payback period is the time it takes for the initial investment to be recovered through the net cash flows generated by the project. In this case, we will track the cumulative cash flows for each year and determine when the total equals or exceeds the initial investment.

Given:

• Initial Investment: $50,000
• Year 1 cash flow: $20,320
• Year 2 cash flow: $25,180
• Year 3 cash flow: $23,350

Let's calculate the cumulative cash flows year by year.

1. After Year 1: $\text{Cumulative Cash Flow} = 20,320$ At this point, the investment has not been recovered yet.

2. After Year 2: $\text{Cumulative Cash Flow} = 20,320 + 25,180 = 45,500$ The investment still has not been fully recovered.

3. After Year 3: $\text{Cumulative Cash Flow} = 45,500 + 23,350 = 68,850$ Now, the investment has been fully recovered between Year 2 and Year 3.

Payback Period Calculation:

The total amount after Year 2 is $45,500, and the remaining amount to recover is: $50,000 - 45,500 = 4,500$ The cash flow in Year 3 is $23,350, so the fraction of Year 3 required to recover the remaining $4,500 is: $\frac{4,500}{23,350} \approx 0.193$ Thus, the payback period is 2 full years plus 0.193 of the 3rd year.

$\text{Payback Period} = 2 + 0.193 \approx 2.19 \text{ years}$

Conclusion:

The payback period for the project is approximately 2.19 years.

Would you like more details on any specific part or have any further questions?

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Here are 5 related questions to explore:

1. What is the significance of the payback period in project evaluation?
2. How does the payback period differ from other investment appraisal techniques like NPV or IRR?
3. What factors can affect the cash flows over the years and, hence, the payback period?
4. How is the payback period used in decision-making for multiple projects?
5. Can the payback period method account for the time value of money?

Tip: While the payback period is easy to calculate, it ignores cash flows after the break-even point and the time value of money, so it’s often used alongside other methods like NPV.