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This lesson covers break-even analysis in depth — a core quantitative technique in AQA A-Level Business topic 3.5.2. You will learn how to calculate break-even output, contribution per unit, total contribution, and margin of safety. You will also learn how to construct and interpret break-even charts and evaluate the usefulness of break-even analysis.
Key Definition: The break-even point is the level of output (or sales) at which total revenue equals total costs. At this point, the business makes neither a profit nor a loss.
At break-even: Total Revenue = Total Costs (and therefore Profit = £0).
Understanding contribution is essential before calculating break-even.
Key Definition: Contribution per unit is the selling price per unit minus the variable cost per unit. It represents the amount each unit sold contributes towards covering fixed costs and, once fixed costs are covered, towards profit.
Formula: Contribution per unit = Selling price per unit - Variable cost per unit
Formula: Total contribution = Contribution per unit x Number of units sold
Alternatively: Total contribution = Total revenue - Total variable costs
A business sells handmade candles at £12 each. The variable cost per candle (wax, wick, packaging, labour) is £4.50.
Contribution per unit = £12.00 - £4.50 = £7.50
If the business sells 2,000 candles:
Total contribution = £7.50 x 2,000 = £15,000
If fixed costs are £10,000, then:
Profit = Total contribution - Fixed costs = £15,000 - £10,000 = £5,000
Formula: Break-even output = Fixed costs / Contribution per unit
This formula tells you how many units a business must sell to cover all its costs.
Using the candle business from above:
Break-even output = £10,000 / £7.50 = 1,333.33 units
Since you cannot sell a fraction of a candle, break-even output is 1,334 candles (always round up to the next whole unit).
Key Definition: The margin of safety is the difference between the actual (or forecast) level of output and the break-even level of output. It shows how much output can fall before the business starts making a loss.
Formula: Margin of safety = Actual (or forecast) output - Break-even output
If the candle business expects to sell 2,000 candles per month:
Margin of safety = 2,000 - 1,334 = 666 candles
This means sales could fall by up to 666 candles before the business would start making a loss.
The margin of safety can also be expressed as a percentage:
Margin of safety (%) = (Margin of safety / Actual output) x 100 = (666 / 2,000) x 100 = 33.3%
A higher margin of safety indicates lower risk.
A break-even chart is a graphical representation of break-even analysis. It plots total revenue, total costs, and fixed costs against output.
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