Break-even with several products
The classic break-even formula, fixed costs ÷ contribution margin per unit, assumes a single product. Most businesses sell several, each with its own price and margin. The solution is to use a weighted average contribution margin, based on the sales mix: the share of each product in units sold.
The formulas
- Contribution margin of product i: price − variable cost.
- Weighted margin = Σ (mix share × contribution margin).
- Break-even units = fixed costs ÷ weighted margin, split between products according to the mix.
- Break-even revenue = break-even units × weighted average price, or fixed costs ÷ weighted contribution margin ratio.
Example
Fixed costs of $30,000 a month and three products:
| Product | Price | Variable cost | Margin | Mix |
|---|---|---|---|---|
| 1 | $40 | $22 | $18 | 50% |
| 2 | $60 | $30 | $30 | 30% |
| 3 | $100 | $45 | $55 | 20% |
- weighted margin: 0.5 × 18 + 0.3 × 30 + 0.2 × 55 = $29 per unit;
- break-even: 30,000 ÷ 29 ≈ 1,035 units: about 518, 311 and 207 of each product;
- weighted average price: $58, so a contribution margin ratio of 50%;
- break-even revenue: $60,000 a month.
Why the mix matters
The break-even point is valid only for the assumed mix. Shift sales toward the low-margin product and break-even rises; shift them toward the high-margin one and it falls. If product 1 rose to 70% of units, with 15% each for the others, the weighted margin would drop to $25.35 and break-even would climb to about 1,184 units. This is why companies push high-margin products and track the mix as closely as volume.
Using the result
- Pricing and promotion: a discount on a high-margin product can be worth more than a bigger one on a low-margin product.
- Product decisions: a product with a low margin may still be worth keeping if it drives sales of others.
- Margin of safety: compare expected sales with break-even to see how far sales can fall before a loss.
Limits
- Fixed costs are assumed constant over the range considered, and variable costs strictly proportional.
- Fixed costs specific to one product, such as a dedicated machine, are better analyzed product by product.
- Mix shares are in units. If you know the mix in revenue, convert it to units first.