Final answer:
The discounted payback period is calculated by determining the time needed to recover an investment through its discounted cash flows. At 0%, it takes 4.6875 years to recover the investment cost. For discount rates of 6% and 20%, the period is extended and needs to be calculated based on the present value of future cash flows.
Step-by-step explanation:
The question involves calculating the discounted payback period for an investment, which represents the time needed to recover the investment through its cash flows when considering the time value of money. This concept falls under the subject of finance, specifically in the valuation and capital budgeting section. To solve the problem, one must understand the present value of cash flows and the cumulative effect of discounting those cash flows at a given rate.
a. With a discount rate of 0%, the annual cash flows do not need to be discounted, so the discounted payback period is the time it takes for the cash flows to cover the initial investment, which in this case is $15,000 / $3,200 = 4.6875 years.
b. When the discount rate is 6%, the cash flows are discounted at this rate for each year, and one must calculate when the sum of these discounted cash flows equals or exceeds the investment of $15,000.
c. Similarly, with a 20% discount rate, the cash flows are discounted more heavily, thus extending the period it takes for the cash flows to total $15,000.