A delivery service feels they could increase their profits by purchasing a new truck for $$56,000.$ This should lead to increased profits of $$16,500$ in the $1$st year, $$14,000$ in the $2$nd year, and $$14,500$ 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 $7\mathrm{.}5\%$ compounded annually, what is the Discounted Cash Flow $($DCF$)$ of the net returns? b$.$ Is this a worthwhile investment?