Question

Sunland Auto has 200 auto-maintenance service outlets nationwide. It provides two main lines of service: oil changes and brake repair. Oil changes and related services represent 70% of its sales and provide a contribution margin ratio of 20%. Brake repair represents 30% of its sales and provides a 60% contribution margin ratio. The company's fixed costs are $15,600,000 (that is, $78,000 per service outlet). Calculate the dollar amount of each type of service that the company must provide in order to break even.

Answer 1

To break even, Sunland Auto must achieve $34,125,000 in sales from oil changes and $14,625,000 from brake repairs, given the different contribution margin ratios and total fixed costs of $15,600,000.

Step-by-step explanation:

Break-Even Analysis for Sunland Auto

To calculate the dollar amount of each type of service required to break even, we need to consider the contribution margin ratio of each service and the company's fixed costs. Break-even point in dollars (BEP) can be calculated using the formula: BEP = Fixed Costs / Overall Contribution Margin Ratio. The overall contribution margin ratio is the weighted average of the contribution margin ratios of oil changes and brake repairs, based on their sales mix.

Firstly, we find the weighted contribution margin ratio for Sunland Auto:

• Oil Changes Contribution Margin = 70% of sales × 20% = 14%
• Brake Repair Contribution Margin = 30% of sales × 60% = 18%

The overall contribution margin ratio is therefore 14% + 18% = 32%.

Then we calculate the dollar amounts necessary for each service to reach the break-even point:

1. Total break-even sales = $15,600,000 / 0.32 = $48,750,000
2. Break-even for Oil Changes = 70% of $48,750,000 = $34,125,000
3. Break-even for Brake Repairs = 30% of $48,750,000 = $14,625,000

Sunland Auto needs to achieve $34,125,000 in sales from oil changes and $14,625,000 from brake repairs to break even.