Formula and method
Contribution per unit c = p − v; contribution margin ratio = c/p; fractional break-even q = F/c; whole units N = ceil(q); break-even revenue = pq; whole-unit profit = Nc − F. Requires c > 0.
Worked example
Fixed costs 10,000, price 50 and unit variable cost 30 give contribution 20, break-even quantity 500 and break-even revenue 25,000.
Assumptions and limits
- Price and unit costs must be nonnegative, and contribution must be positive. Zero or negative contribution cannot recover positive fixed costs through more sales; no finite break-even quantity is reported.
- Whole units are rounded upward and avoid a loss only within this constant-cost model. Fractional quantities may suit divisible services; use whole units for indivisible products. Inputs are not rounded to currency minor units. Displayed fractional quantities may be rounded; the whole-unit ceiling uses the decimal input values.
- Capacity, demand, tiered discounts, taxes, time value of money and multi-product sales mix are not modeled. Include relevant known costs and recalculate when business conditions change.
Frequently asked questions
What happens when fixed costs are zero?
With positive contribution, both break-even quantities are 0; any positive sales contribute profit in the model. If contribution is also 0, every quantity has zero profit and there is no unique positive break-even point.
Why can whole-unit profit be greater than zero?
The fractional break-even point may lie between whole units. Rounding up adds contribution, so the smallest integer covering costs may already earn a small profit.