The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is $65,000. The variable cost of recapping a tire is $7.5. The company charges$25 to recap a tire. a. For an annual volume of 15, 000 tire, determine the total cost, total revenue, and profit. b. Determine the annual break-even volume for the Retread Tire Company operation.

Accepted Solution

Part a) Total CostTotal Cost for recapping the tires is the sum of fixed cost and the variable cost. i.e.The total cost is ( $65,000 fixed) + (15,000 x $7.5)=$65,000+$112,500=$177,500  Part b) Total RevenueRevenue from 1 tire = $25Total tires recapped = 15000So, Total revenue = 15000 tires x $25/tireTotal Revenue =$375,000  Part c) Total ProfitTotal Profit = Revenue - CostUsing the above values, we get:Profit = $375,000 - $177,500Profit = $197,500  Part d) Break-even PointBreak-even point point occurs where the cost and the revenue of the company are equal. Let the break-even point occurs at x-tires. We can write:For break-even pointCost of recapping x tires = Revenue from x tires65,000 + 7.5 x = 25x 65,000 = 17.5 xx = 3714 tiresThus, on recapping 3714 tires, the cost will be equal to the revenue generating 0 profit. This is the break-even point.