Break-even analysis

What break-even analysis shows

Break-even analysis finds the level of output where total revenue equals total costs, so the business makes neither a profit nor a loss. It is one of the business management toolkit tools and is often tested with calculations in Paper 2.

Key formulas

• Contribution per unit = selling price − variable cost per unit
• Break-even quantity = fixed costs ÷ contribution per unit
• Margin of safety = actual (or planned) sales − break-even quantity
• Profit = (contribution per unit × quantity sold) − fixed costs
• Output needed for a target profit = (fixed costs + target profit) ÷ contribution per unit

Worked example

A bakery has fixed costs of $12,000 a month. A cake sells for $20 and its variable cost is $8.

• Contribution per cake = $20 − $8 = $12
• Break-even quantity = $12,000 ÷ $12 = 1,000 cakes
• If it sells 1,500 cakes, the margin of safety is 1,500 − 1,000 = 500 cakes
• Profit at 1,500 cakes = (1,500 × $12) − $12,000 = $6,000
• To make a target profit of $9,000: ($12,000 + $9,000) ÷ $12 = 1,750 cakes

Drawing the break-even chart

Plot fixed costs as a horizontal line, total costs starting from the fixed cost line, and total revenue starting from zero. Where total revenue crosses total costs is the break-even point. Label the profit and loss areas and the margin of safety.

Evaluating break-even

Break-even is simple and helps with pricing and planning, but:

• prices may need to fall to sell more, changing contribution;
• variable costs per unit may fall with bulk buying;
• it assumes all output is sold;
• most businesses sell more than one product.

In an exam answer, link these points to the business in the case: is its market competitive, are its costs stable, and how reliable are its sales forecasts?

Common mistakes

• Dividing fixed costs by the selling price instead of the contribution.
• Rounding the break-even quantity down. You cannot sell part of a unit, so round up.
• Calculating without commenting. Paper 2 often asks you to explain what the result means.