Final answer:
The discounted payback period is the time taken for an investment's cash flows to cover its initial cost when factoring in the time value of money. It is shorter when the discount rate is lower and longer when the discount rate is higher, requiring present value calculations for accurate determination.
Step-by-step explanation:
The question at hand involves calculating the discounted payback period for a given investment project, which is within the realm of finance and business. The discounted payback period is the time it takes for the initial investment to be recovered through discounted cash flows, which takes into account the time value of money.
For part a, with a discount rate of zero percent, the discounted cash flows are simply the actual cash flows. Thus, the $12,200 investment would be recovered in $3,200 annual increments, resulting in a payback period of 3.81 years (which is $12,200 / $3,200).
For part b, at a discount rate of 5 percent, the annual cash flows need to be discounted to their present value. The discounted payback period would be the amount of time it takes for the sum of these discounted cash flows to equal the initial investment of $12,200. A present value table or financial calculator would be used to determine the specific year when the cumulative discounted cash flows match the initial investment.
For part c, when the discount rate is 19 percent, the annual cash flows are discounted even more steeply. Hence, it would take longer for the discounted cash flows to accumulate to the point of covering the initial investment. As with the 5 percent discount rate, calculating the exact period would require a present value calculation for each period until the initial investment is recovered.