19.3 Apply Cost-Volume-Profit Analysis for Multiple-Product and Service Companies
Sales Mixβ
Sales mix (also called product mix) is the relative proportion of different products or services sold. When a company sells multiple products, CVP analysis becomes more complex because different products have different contribution margins.
Weighted Average Contribution Marginβ
For multiple products, we calculate a weighted average contribution margin based on the sales mix.
Formula: Weighted Average Contribution Margin = Ξ£ (Contribution Margin per Unit Γ Sales Mix Percentage)
Example: Marie's restaurant sells three types of meals:
- Signature Dish: β¬25 price, β¬10 variable cost, 40% of sales
- Lunch Special: β¬15 price, β¬6 variable cost, 35% of sales
- Light Meal: β¬12 price, β¬5 variable cost, 25% of sales
Contribution Margins:
- Signature Dish: β¬25 - β¬10 = β¬15
- Lunch Special: β¬15 - β¬6 = β¬9
- Light Meal: β¬12 - β¬5 = β¬7
Weighted Average Contribution Margin:
- Signature Dish: β¬15 Γ 40% = β¬6.00
- Lunch Special: β¬9 Γ 35% = β¬3.15
- Light Meal: β¬7 Γ 25% = β¬1.75
- Total: β¬10.90
Break-Even with Multiple Productsβ
Break-Even Point (Units) = Total Fixed Costs Γ· Weighted Average Contribution Margin
Example: Fixed costs: β¬8,000 per month Weighted average contribution margin: β¬10.90
Break-Even Point (Units) = β¬8,000 Γ· β¬10.90 = 734 total meals
Break-Even by Product (based on sales mix):
- Signature Dish: 734 Γ 40% = 294 meals
- Lunch Special: 734 Γ 35% = 257 meals
- Light Meal: 734 Γ 25% = 184 meals
Break-Even in Sales Dollarsβ
Weighted Average Contribution Margin Ratio: Weighted Average CM Ratio = Weighted Average CM Γ· Weighted Average Selling Price
Weighted Average Selling Price:
- Signature Dish: β¬25 Γ 40% = β¬10.00
- Lunch Special: β¬15 Γ 35% = β¬5.25
- Light Meal: β¬12 Γ 25% = β¬3.00
- Total: β¬18.25
Weighted Average CM Ratio: β¬10.90 Γ· β¬18.25 = 0.597 or 59.7%
Break-Even (Dollars) = β¬8,000 Γ· 0.597 = β¬13,400
Changes in Sales Mixβ
If the sales mix changes, the break-even point changes.
Example: If sales mix shifts to more Signature Dishes (higher contribution margin):
- New mix: Signature 50%, Lunch 30%, Light 20%
- New weighted average CM: (β¬15 Γ 50%) + (β¬9 Γ 30%) + (β¬7 Γ 20%) = β¬11.60
- New break-even: β¬8,000 Γ· β¬11.60 = 690 meals (down from 734)
Impact:
- Favorable sales mix change (more high-margin products) reduces break-even
- Unfavorable sales mix change (more low-margin products) increases break-even
Service Companiesβ
Service companies can also use CVP analysis, but they typically have:
- No inventory (services are consumed as provided)
- Different cost structures (often more labor-intensive)
- Different revenue recognition (as services are performed)
Example: A Luxembourg consulting firm:
- Fixed costs: β¬15,000 per month (office rent, salaries)
- Variable costs: β¬50 per hour (materials, travel)
- Billing rate: β¬150 per hour
- Contribution margin per hour: β¬150 - β¬50 = β¬100
Break-Even (Hours) = β¬15,000 Γ· β¬100 = 150 hours per month
Luxembourg Compliance Noteβ
For Luxembourg SMEs with multiple products/services:
- Different VAT rates may apply (3%, 8%, 14%, 17%)
- CVP analysis should consider VAT impact on pricing
- Sales mix affects overall VAT liability
- Cost structure may vary by product/service type
- Consider Luxembourg-specific costs in analysis
Think It Throughβ
Why is sales mix important in CVP analysis? How can a business use CVP analysis to make decisions about which products to emphasize?