a$.$ The manager of Automated Products is contemplating the purchase of a new machine that will cost $$300,000$ and has a useful life of five years. The machine will yield $($year$-$end$)$ cost reductions to Automated Products of $$50,000$ in year $1,$$$60,000$ in year $2,$$$75,000$ in year $3,$ and $$90,000$ in years $4$ and $5.$ What is the present value of the cost savings of the machine if the interest rate is $8$ percent? Should the manager purchase the machine?