Final answer:
The discounted payback period is a financial metric used to determine the time it takes for an investment project to recoup its initial cost, taking into account the time value of money. The discounted payback period can be calculated by discounting the cash flows using the given discount rate and summing them up until they cover the initial cost. The discounted payback period differs depending on the discount rate used.
Step-by-step explanation:
The discounted payback period is a financial metric used to determine the time it takes for an investment project to recoup its initial cost, taking into account the time value of money. To calculate the discounted payback period, we need to discount the cash flows of the project using the given discount rate and then sum them up until they cover the initial cost.
a. If the discount rate is 0 percent, the cash flows are not discounted, and the payback period would be the time it takes for the cumulative cash flows to equal or exceed the initial cost. In this case, the discounted payback period would be 4 years (13,300 / 3,400 = 3.91, rounded to 4).
b. If the discount rate is 5 percent, we need to discount the cash flows using this rate. The discounted payback period would be the time it takes for the cumulative discounted cash flows to equal or exceed the initial cost. In this case, the discounted payback period would be 5 years (13,300 - 3,400*0.05 = 12,865, 12,865/3,400 = 3.78, rounded to 5).
c. If the discount rate is 22 percent, the discounted payback period would be 6 years (the entire duration of the cash flows) since the project would not generate enough discounted cash flows to cover the initial cost within the given time frame.