Eat at State is considering buying a new food truck. It will cost $$65,000$ but is expected to generate $$20,000$ in annual sales over the next $4$ years. At the end of the $4$th year, the truck will be sold to Eat Like a Wolverine in Ann Arbor for $$5,000($after taxes$).$ It will require $$15,000$ in additional Net Working capital that will not be recovered when the truck is sold. The Dean of Food Services will only authorize the purchase if it is cash positive by the end of the $4$th year. Using the discounted payback period method, should the truck be purchased, and why?