Question

Aldo Redondo drives his own car on company business. His employer reimburses him for such travel at the rate of 36 cents per mile. Aldo estimates that his fixed costs per year such as taxes, insurance, and depreciation are $2,052. The direct or variable costs such as gas, oil, and maintenance average about 14.4 cents per mile. How many miles must he drive to break even?

Answer 1

Solution and Explanation:

Step 1

Consider the given information:

Reimbursement = 36 cents per mile

Fixed cost per year = $2,052 minus 205200 cents

Direct variable cost = 14.4 cents per mile

Step 2

At the break-even point, total cost becomes equal to the total revenue.

Suppose it takes Q miles for ARto reach break-even.

Step1: Calculate the total cost of AR when the car cover Q miles, as shown below:

Total Cost = Fixed cost + Variable Cost

                 = 205,200 + 14.4 Q

Step 2 Calculate the total revenue (reimbursement) of AR when the car covers Q miles, as shown below:

Total Revenue = Reimbursement multiply with Total miles

                       = 36Q

Step 3: Calculate the break-even miles for the car, as shown below:

At break-even,  Total cost = Total revenue

205,200 plus 14.4Q = 36Q

      36Q minus 14.4Q = 205,200

            21.6Q = 205,200

   Q = 205,200 divide by 21.6

    Q = 9,500 miles

Hence, AR should drive 9,500 miles to break-even.