Break-even level of output

Break-even level of output is the number of units a business must sell for its total revenue to equal its total costs. At that output the business makes neither a profit nor a loss — profit is zero.

To find it in units, use:

Break-even point in units = fixed costs ÷ (selling price − variable cost per unit)

The bracket (selling price − variable cost per unit) is the money each sale contributes towards covering fixed costs. For example, a bike repair shop has fixed costs of £5,400 a month, charges £30 per repair and has variable costs of £12 per repair. Each repair adds £30 − £12 = £18 towards those fixed costs. Break-even = £5,400 ÷ £18 = 300 repairs.

To express break-even as revenue:

Break-even point in costs or revenue = break-even point in units × selling price

For the repair shop: 300 × £30 = £9,000. You can check this: at 300 repairs, total costs are £5,400 + (300 × £12) = £9,000, exactly the same as revenue.

Below break-even, total costs are greater than total revenue, so the business makes a loss. At 240 repairs, revenue is £7,200 but total costs are £8,280, so the loss is £1,080. Above break-even, revenue is greater than total costs, so the business makes a profit.

You need to learn the break-even formulae, along with the formulae for revenue, total costs, margin of safety and interest, because they are not given in the exam.