Final answer:
The payback period for the capital budgeting project is approximately 2.43 years, which is calculated using the Payback Method by adding up the cash flows until they offset the initial investment.
Step-by-step explanation:
The student is asking how to calculate the payback period for a capital budgeting project using the Payback Method. The payback period is the amount of time it takes for a project to generate enough cash flow to cover the initial investment. The initial investment here is -$1,000, and the future cash flows are $400 at t = 1, $500 at t = 2, $233 at t = 3, and $206 at t = 4.
To calculate the payback period, we sum the cash flows until the initial investment is recovered. Here's how the calculation would work:
Cumulative cash flow at t = 1: -$1,000 + $400 = -$600
Cumulative cash flow at t = 2: -$600 + $500 = -$100
Cumulative cash flow at t = 3: -$100 + $233 = $133
The payback period occurs in year 3 since by then the cumulative cash flow has turned positive. But to find the exact payback period to two decimal places, we would need to interpolate between year 2 and year 3. Since $233 covers the outstanding $100 and provides an additional $133 in year 3, we use the proportion of the year 3 cash flow that would be needed to cover the remaining $100 at the end of year 2. This proportion is $100/$233, which gives approximately 0.43 of a year. Added to the two full years, the payback period is 2 + 0.43, or approximately 2.43 years.