Skip to main content

19.3 Apply Cost-Volume-Profit Analysis for Multiple-Product and Service Companies

Sales Mix​

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 Margin​

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: €25 price, €10 variable cost, 40% of sales
  • Lunch Special: €15 price, €6 variable cost, 35% of sales
  • Light Meal: €12 price, €5 variable cost, 25% of sales

Contribution Margins:

  • Signature Dish: €25 - €10 = €15
  • Lunch Special: €15 - €6 = €9
  • Light Meal: €12 - €5 = €7

Weighted Average Contribution Margin:

  • Signature Dish: €15 Γ— 40% = €6.00
  • Lunch Special: €9 Γ— 35% = €3.15
  • Light Meal: €7 Γ— 25% = €1.75
  • Total: €10.90

Break-Even with Multiple Products​

Break-Even Point (Units) = Total Fixed Costs Γ· Weighted Average Contribution Margin

Example: Fixed costs: €8,000 per month Weighted average contribution margin: €10.90

Break-Even Point (Units) = €8,000 Γ· €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 Dollars​

Weighted Average Contribution Margin Ratio: Weighted Average CM Ratio = Weighted Average CM Γ· Weighted Average Selling Price

Weighted Average Selling Price:

  • Signature Dish: €25 Γ— 40% = €10.00
  • Lunch Special: €15 Γ— 35% = €5.25
  • Light Meal: €12 Γ— 25% = €3.00
  • Total: €18.25

Weighted Average CM Ratio: €10.90 Γ· €18.25 = 0.597 or 59.7%

Break-Even (Dollars) = €8,000 Γ· 0.597 = €13,400

Changes in Sales Mix​

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: (€15 Γ— 50%) + (€9 Γ— 30%) + (€7 Γ— 20%) = €11.60
  • New break-even: €8,000 Γ· €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 Companies​

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: €15,000 per month (office rent, salaries)
  • Variable costs: €50 per hour (materials, travel)
  • Billing rate: €150 per hour
  • Contribution margin per hour: €150 - €50 = €100

Break-Even (Hours) = €15,000 Γ· €100 = 150 hours per month

Luxembourg Compliance Note​

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 Through​

Why is sales mix important in CVP analysis? How can a business use CVP analysis to make decisions about which products to emphasize?