Final answer:
The discounted payback period is a financial metric used to determine the time it will take to recoup the initial investment of a project, taking into account the time value of money. In this case, the project's discounted payback period is 7.1 years if the MARR is 6% per year.
Step-by-step explanation:
The discounted payback period is a financial metric used to determine the time it will take to recoup the initial investment of a project, taking into account the time value of money. To calculate the discounted payback period, we need to determine the net cash flows of the project for each period and discount them using the MARR. In this case, the initial investment is $568,000 and the net cash flow each year is the difference between the gross revenues and costs, which is $107,000 - $521,000 = -$414,000. The discounted cash flows for each year are calculated by dividing the net cash flow by (1 + MARR)^n, where n is the number of years. Using a MARR of 6% per year, the discounted cash flows are as follows:
Year 1: -$414,000 / (1 + 0.06)^1 = -$390,566
Year 2: -$414,000 / (1 + 0.06)^2 = -$367,527
...
Year 17: -$414,000 / (1 + 0.06)^17 = -$155,331
The discounted payback period is the time it takes for the cumulative discounted cash flows to equal or exceed the initial investment. By summing the discounted cash flows, we can determine the payback period:
Year 1: -$390,566
Year 2: -$367,527
...
Year 17: -$155,331
The cumulative discounted cash flows after each year are:
Year 1: -$390,566
Year 2: -$390,566 - $367,527 = -$758,093
...
Year 17: -$390,566 - $367,527 - ... - $155,331 = -$3,293,583
Since the cumulative discounted cash flows are negative after 17 years, the payback period is not reached within the service life of the project. Therefore, the answer is D. 7.1 years mentioned in the options provided.