How to Calculate Break-Even Output and Margin of Safety
Learn to calculate break-even output from fixed costs and contribution per unit, then find margin of safety from sales using a clear, step-by-step worked example.
To calculate break-even output, divide fixed costs by contribution per unit. To calculate the margin of safety, subtract break-even output from actual or forecast output. Use forecast output if actual sales are not given.
Break-even output
Fixed costs stay the same as output changes, such as rent. Variable costs change with each unit produced. Contribution per unit is the selling price minus the variable cost per unit: it is the amount each sale contributes towards fixed costs and, after those are covered, profit.
Contribution per unit=Selling price per unit−Variable cost per unit\text{Contribution per unit} = \text{Selling price per unit} - \text{Variable cost per unit}Contribution per unit=Selling price per unit−Variable cost per unit Break-even output=Fixed costsContribution per unit\text{Break-even output} = \frac{\text{Fixed costs}}{\text{Contribution per unit}}Break-even output=Contribution per unitFixed costsBreak-even is the output at which total revenue equals total costs, so the business makes neither a profit nor a loss. If the calculation gives part of a unit, round up to the next whole unit to find the minimum output needed to break even.
Margin of safety
Margin of safety=Actual or forecast output−Break-even output\text{Margin of safety} = \text{Actual or forecast output} - \text{Break-even output}Margin of safety=Actual or forecast output−Break-even outputThis shows how far sales could fall before the business reaches break-even. A larger margin gives more room for sales to fall, although it does not guarantee future sales.
The two calculations must use the same time period and the same unit of output. For instance, compare monthly fixed costs with monthly output, rather than mixing monthly costs with annual sales. If the question gives sales revenue instead of units sold, you cannot subtract it directly from break-even output in units; first convert revenue into units using the selling price per unit, assuming one product with a constant price. State whether your margin of safety uses actual or forecast sales.
For example, suppose fixed costs are £12,000\pounds 12{,}000£12,000, the selling price is £20\pounds 20£20 per unit and variable cost is £8\pounds 8£8 per unit. Contribution is £20−£8=£12\pounds 20-\pounds 8=\pounds 12£20−£8=£12 per unit, so break-even output is 12,000÷12=1,00012{,}000\div12=1{,}00012,000÷12=1,000 units. If actual output is 1,4001{,}4001,400 units, the margin of safety is 1,400−1,000=4001{,}400-1{,}000=4001,400−1,000=400 units.
Common mistake: Do not divide fixed costs by selling price. Each sale must also cover its variable cost, so use contribution per unit in the break-even calculation.
