Answer:
The payback period is a measure of the length of time it takes to recoup the initial investment in a project or asset. It is calculated by dividing the initial investment by the annual cash flows generated by the asset.
Step-by-step explanation:
In this case, the initial investment is $21,000, and the annual cash flow generated by the machine is $2,000 - $1,500 = $500 (income minus depreciation).
Therefore, the payback period for the new machine would be:
$21,000 / $500 = 42
So it will take 42 years to recoup the initial investment.
Please note that the payback period is a simple measure of profitability, but it doesn't take into account the time value of money. It may be useful as a rule of thumb but is not a good measure of profitability when trying to compare projects with different lifetimes or cash flows. It is also not considering the potential future income after the payback period.