Break-even quantity and revenue
At break-even, contributions cover fixed costs exactly. The formula is short, and so is the classic mistake: dividing by the price instead of the contribution.
Worked example
A product sells for £104.50; variable costs are £63.00 per unit and fixed costs £112,050.00. At what quantity are all costs covered (break-even point)? What is the revenue there?
Worked solution
- 1.Unit contribution = £104.50 − £63.00 = £41.50
- 2.Break-even quantity = fixed costs / unit contribution = £112,050.00 / £41.50 = 2,700 units
- 3.Revenue = 2,700 × £104.50 = £282,150.00
Typical mistake: Dividing fixed costs by the price instead of the unit contribution.
Your turn
Three problems of exactly this type, each time with new numbers. Amounts with or without thousands separators.
Task
A product sells for £123.00; variable costs are £80.00 per unit and fixed costs £109,650.00. At what quantity are all costs covered (break-even point)? What is the revenue there?
Break-even quantity in units
Break-even revenue in £
Amounts like 12,500 or 12500.50; percentages as a number (12.5). Round to the penny or 2 decimal places.
Formulas for this topic
- Break-even quantity = fixed costs / unit contribution
- Break-even revenue = quantity × price
- Quantity for a target profit = (fixed costs + profit) / unit contribution
- Margin of safety = planned sales − break-even quantity
Typical mistake: Dividing fixed costs by the price instead of the unit contribution.
Frequently asked questions
What is the typical mistake in "Break-even quantity and revenue"?
Dividing fixed costs by the price instead of the unit contribution.
Why divide by contribution and not by price?
Each unit first covers its own variable cost; only the rest, the contribution, is left for fixed costs.