Break-even point
At the break-even point revenue covers all costs exactly. Below it the firm makes a loss, above it a profit.
Formulas
- 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
Your turn
Three problems on this topic. Amounts with or without thousands separators, a point for pence.
Task
A product sells for £132.00; variable costs are £98.00 per unit and fixed costs £100,300.00. 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.
Worked example
A product sells for £86.50; variable costs are £41.00 per unit and fixed costs £161,525.00. At what quantity are all costs covered (break-even point)? What is the revenue there?
Worked solution
- 1.Unit contribution = £86.50 − £41.00 = £45.50
- 2.Break-even quantity = fixed costs / unit contribution = £161,525.00 / £45.50 = 3,550 units
- 3.Revenue = 3,550 × £86.50 = £307,075.00
Typical mistake: Dividing fixed costs by the price instead of the unit contribution.
Price £75.00, variable cost £31.00 per unit, fixed costs £129,800.00. Planned sales are 3,300 units. What is the margin of safety?
Worked solution
- 1.Break-even = £129,800.00 / (£75.00 − £31.00) = 2,950 units
- 2.Margin of safety = 3,300 − 2,950 = 350 units
- 3.in % = 350 / 3,300 × 100 = 10.61%
Typical mistake: Relating the margin of safety to the break-even quantity instead of planned sales.
Frequently asked questions
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.