Break-Even Calculations
Break-even is the point where total revenue equals total costs—no profit, no loss. These questions appear in numerical reasoning tests for business and finance roles. Here's how to solve them.
Basic Formula
Break-even units = Fixed costs ÷ Contribution margin per unit
Where Contribution margin per unit = Selling price − Variable cost per unit
The contribution margin is how much each unit sold contributes toward covering fixed costs and then profit.
Break-Even in Revenue
Break-even revenue = Fixed costs ÷ Contribution margin ratio
Where Contribution margin ratio = (Selling price − Variable cost) ÷ Selling price
Or: Contribution margin ratio = Contribution margin per unit ÷ Selling price.
Example: Price £10, variable cost £6. Contribution = £4. Ratio = 4 ÷ 10 = 0.4 (40%). If fixed costs are £20,000, break-even revenue = 20,000 ÷ 0.4 = £50,000.
Break-Even Units from Revenue
Break-even units = Break-even revenue ÷ Selling price
Or use the first formula directly: Break-even units = Fixed costs ÷ (Price − Variable cost per unit).
Common Question Types
- "How many units must be sold to break even?" – Fixed costs ÷ (Price − Variable cost).
- "What is the break-even revenue?" – Fixed costs ÷ Contribution margin ratio.
- "If fixed costs increase by 10%, how many more units to break even?" – New fixed = Old × 1.10. New break-even = New fixed ÷ Contribution per unit. Difference = New − Old.
- "What is the contribution margin?" – Price − Variable cost per unit.
Pitfalls
- Fixed vs variable – Fixed costs (rent, salaries) don't change with output. Variable costs (materials, commissions) do. Classify correctly.
- Per unit – Ensure variable cost is per unit, not total. If total variable cost is given for X units, divide by X to get per unit.
Practice with numerical reasoning questions and the numerical reasoning test.
Frequently Asked Questions
What if there are multiple products?
Break-even is trickier with a product mix. Tests often assume a single product or give a weighted average contribution. If the question gives a mix ratio (e.g. 2:1), calculate weighted contribution first.
How do I find variable cost per unit when only total cost is given?
You need to separate fixed and variable. Sometimes the question gives both. Or: at two output levels, the difference in total cost = variable cost of the extra units. (Total cost 2 − Total cost 1) ÷ (Units 2 − Units 1) = variable cost per unit.
What is margin of safety?
Margin of safety = Actual sales − Break-even sales. It shows how far sales can fall before the company makes a loss. Sometimes asked as a percentage: (Actual − Break-even) ÷ Actual × 100.