$(20$ points$)$ The Ajax Corporation has an overhead crane that has an estimated remaining

life of $8$ years. The crane can be sold now for $$5,000.$ If the crane is kept in service, it

must be overhauled immediately at a cost of $$4,000.$ Operating and maintenance costs

will be $$2,500$ per year after the crane is overhauled. The overhauled crane will have zero

MV at the end of the $7-$year study period. A new crane will cost $$16,000,$ will last for $7$

years, and will have a $$3,200$ MV at that time. Operating and maintenance costs are$

$1,200$ per year for the new crane. The company uses a before$-$tax interest rate of $15\%$ per

year in evaluating investment alternatives. Should the company replace the old crane?