Auto Repair Shop

The dealership incurs a fixed annual cost of $500,000, which covers tools, rent, employee benefits, service managers, and other overhead expenses. It employs 10 mechanics, each earning an average hourly wage of $50. All mechanics are available to work 8 hours a day for 250 days per year, excluding weekends, vacations, and holidays.

The dealership charges $100 per hour for vehicle repairs, which is comparable to rates at other dealerships and independent service shops.

Calculate the following: 

1. Breakeven hours of service per year

2. Breakeven hours of service per year if the fixed cost is reduced by 15%

3. Breakeven hours of service per year if the variable cost is reduced by 15%

4. Breakeven hours of service per year if the price is increased by 15%

5. Breakeven hours of service per year if everything, including fixed cost, variable cost, and the price, is increased by 15%. 

Solution

Total labor capacity

1. Breakeven Hours of Service

Assume that the cost will break even at X hours of service per year. Therefore, the total cost to provide X hours of service per year is:

Total Revenue

At breakeven, total revenue equals total cost. Therefore, 

2. Reduction of Fixed Costs

Assume that the dealership was able to reduce the fixed cost by 15%. The total number of breakeven hours required can then be calculated as:

Therefore, the percentage change in breakeven service hours

3. Reduction of Variable Costs

Therefore, the percentage change in breakeven service hours

4. Increase in Price 

Therefore, the percentage change in breakeven service hours

It is worth noting that increasing the hourly charges has a significant effect on the breakeven demand.

5. The Most Likely Situation

Both fixed costs and variable costs usually increase over time. Therefore, the price (in this case, the hourly service charge) tends to rise to compensate for these increasing costs. Assume that both fixed costs and variable costs increase by 15%. Calculate the required percentage increase in the hourly service rate needed to offset the cost increase while maintaining the same breakeven level of 10,000 service hours.

• Therefore, the increase in the hourly charge rate will be 15%, as expected (calculated as (1.15-1) * 100%).

• While a flat rate of 15% for all changes is very unlikely, similar calculation procedures can be used to account for percentage changes as they occur.

6. Increase in Utilization

Instead of operating at 50% capacity just to break even, the shop can increase its utilization to 75%—equivalent to 15,000 service hours per year—and generate an annual profit of $250,000, as shown in the following calculations.

• Revenue = 15,000 hours × $100/hour = $1,500,000

• Total Cost= Fixed Costs ($500,000) + Variable Costs (15,000 × $50/hour) = $1,250,000

• Profit = $1,500,000 – $1,250,000 = $250,000 per year

6. Increase in Utilization

Instead of operating at 50% capacity just to break even, the shop can increase its utilization to 75%—equivalent to 15,000 service hours per year—and generate an annual profit of $250,000, as shown in the following calculations.

• Revenue = 15,000 hours × $100/hour = $1,500,000

• Total Cost= Fixed Costs ($500,000) + Variable Costs (15,000 × $50/hour) = $1,250,000

• Profit = $1,500,000 – $1,250,000 = $250,000 per year

Solution Using MS Excel 

The solution using Excel in Figure 2-14 provides detailed insights into varying service hours, ranging from 0 hours to the maximum capacity of 20,000 hours. 

• While the manual solution using calculus provides a single optimum point for price, demand, cost, revenue, and profit, solving the problem using Microsoft Excel offers even deeper insights, including how cost, revenue, and profit change over a wide range of demand values.

• For example, the maximum profit the shop can earn would occur at 100% capacity utilization—an extremely unlikely scenario. Nevertheless, evaluating the full range of possible outcomes helps support better decision-making.