Michael Scott Paper, Inc. is considering a new machine that requires an initial investment of $$650,000,$ including installation costs, and has a useful life of ten years. The expected annual after$-$tax cash flows for the machine are $$90,000$ during the first two years, $$115,000$ during years three through six, and $$85,000$ during the remaining years of its useful life. What is the net present value $($NPV$)$ when the discount rate is $8\%?$

Group of answer choices

$-$$$12,751\mathrm{.}67$

$$17,846\mathrm{.}39$

$$12,387\mathrm{.}99$

$-$$$13,899\mathrm{.}32$