CVP for Multiple Products
When a company sells more than one product, there is no single break-even number until you fix the sales mix. You blend the products into one weighted average contribution margin, find total break-even units, then split them back out by the mix.
What you will learn
- Why break-even with several products depends on the sales mix
- How to calculate the weighted average contribution margin per unit
- How to find total break-even units and split them by product
- How the package or composite unit method gives the same answer
The formulas
- mix weightᵢ
- product i's share of total units sold
- CMᵢ
- contribution margin per unit of product i
- FC
- total fixed costs for the whole company
- WACM
- weighted average contribution margin per unit
Worked example
A firm sells Product A (price $20, variable cost $12) and Product B (price $30, variable cost $15) in a 3:2 unit mix. Fixed costs are $54,000. What is the break-even point for each product?
- Contribution margins: A = $20 − $12 = $8; B = $30 − $15 = $15.
- Mix weights: A = 3 ÷ 5 = 60%; B = 2 ÷ 5 = 40%.
- WACM = 0.6 × $8 + 0.4 × $15 = $10.80.
- Total break-even units = $54,000 ÷ $10.80 = 5,000 units.
- Split by mix: A = 5,000 × 60% = 3,000; B = 5,000 × 40% = 2,000.
- Check: 3,000 × $8 + 2,000 × $15 = $54,000, exactly covering fixed costs.
Answer: Break-even is 3,000 units of A and 2,000 units of B (5,000 in total).
Common questions
How do you calculate break-even for multiple products?
Find each product's contribution margin, weight them by the sales mix to get a weighted average contribution margin, then divide total fixed costs by it. That gives total break-even units, which you split between products using the same mix.
What is sales mix in break-even analysis?
Sales mix is the proportion in which a company sells its products, such as 3 units of A for every 2 units of B. Break-even for several products only works once you assume a mix, because each product contributes a different margin.
What happens to break-even if the sales mix changes?
If the mix shifts toward products with higher contribution margins, break-even units fall. If it shifts toward lower-margin products, break-even rises, even if prices and costs stay the same.
Can you use dollars instead of units for multi-product break-even?
Yes. Use a weighted average contribution margin ratio based on the sales dollar mix, then divide fixed costs by that ratio to get total break-even sales dollars. This is handy when a company sells many products or only knows its sales mix in dollars.