Final answer:
The discounted payback period is a measure used to determine the length of time it takes for the cash inflows from a project to recover the initial cost, taking into account the time value of money. For this project, the discounted payback period is 2.55 years.
Step-by-step explanation:
The discounted payback period is a measure used to determine the length of time it takes for the cash inflows from a project to recover the initial cost, taking into account the time value of money. To calculate the discounted payback period, we need to discount the cash inflows using the required rate of return. In this case, the initial cost is $14,500 and the cash inflows are $4,600, $6,100, and $8,500 over the next three years, respectively. We will discount these cash inflows at a rate of 15%.
Year 1: $4,600 / (1 + 0.15) = $4,000
Year 2: $6,100 / (1 + 0.15)^2 = $4,582.63
Year 3: $8,500 / (1 + 0.15)^3 = $5,950.68
Now, we sum up the discounted cash inflows to find the discounted payback period:
$4,000 + $4,582.63 + $5,950.68 = $14,533.31
The discounted payback period is the time it takes for the discounted cash inflows to equal or exceed the initial cost. In this case, it takes just over 2 years for the discounted cash inflows to reach $14,533.31, which exceeds the initial cost of $14,500.
Therefore, the discounted payback period is 2.55 years.