PROBLEM $3$ DCF$,$ accrual accounting rate of return, working capital, evaluationof performanceCentury Lab plans to purchase a new centrifuge machine for its New Hampshire facility.The machine costs $$137,500$ and is expected to have a useful life of $8$ years with a terminal disposal value of $$37,500.$ Saving in cash operating costs are expected to be $$31,500$ per year. However, additional working capital is needed to keep the machine running efficiently. The working capital must continually be replaced, so an investment of $$10,000$ needs to be maintained at all times, but this investment is fully recoverable $($will be cash$-$in$)$ at the end of the useful life. Century Lab's required rate of return is $14\%.$ Ignore income tax in your analysis. Assume all cash flows occurs at year$-$endexcept for initial investment amounts at the beginning of the year. Century lab usesstraight line depreciation for its machine.