A delivery service feels they could increase their profits by purchasing a new truck for $$50,500.$ This should lead to increased profits of $$16,000$ in the $1$st year, $$13,000$ in the $2$nd year, and $$10,500$ in the $3$rd year. It could sell the truck at the end of $3$ years for $$11,000.$

a$.$ If the company's required rate of return is $6\mathrm{.}5\%$ compounded annually, what is the Discounted Cash Flow $($DCF$)$ of the net returns?

b$.$ Is this a worthwhile investment?

a$.$ Yes

b$.$ No