The calculation of the break-even point in units and revenue, the contribution per unit and contribution to sales ratio, the margin of safety, target-profit output, and the construction and limitations of break-even charts.

What this dot point is asking

AQA wants you to calculate the break-even point in units and revenue, find the contribution and contribution to sales ratio, calculate the margin of safety and the output for a target profit, and construct and critique break-even charts. This is unit 3.2.3, a quantitative topic where a full multi-part calculation is a standard Paper 2 task.

Break-even and contribution

The intuition is that fixed costs are a fixed pot that must be filled before any profit is made. Each unit sold throws its contribution into that pot. Once enough units have been sold that total contribution equals fixed costs, the pot is full (break-even) and every further unit's contribution becomes profit. This is why break-even is simply fixed costs divided by contribution per unit, and why profit beyond break-even rises at the rate of the contribution per unit.

To find break-even in revenue rather than units, either multiply the break-even units by the selling price, or divide fixed costs by the contribution to sales ratio, $\dfrac{\text{contribution}}{\text{sales}}$. The contribution to sales ratio (also called the profit-volume ratio) is useful when a business sells many products and thinks in sales value rather than units.

Margin of safety and target profit

A large margin of safety means demand can fall a long way before the business makes a loss, so it is a measure of risk as well as performance. For a target profit, the target is added to fixed costs in the numerator because the pot to be filled by contribution is now fixed costs plus the profit the business wants on top.

Worked example

Limitations of break-even charts

Break-even analysis assumes selling price and variable cost per unit are constant, that costs split neatly into fixed and variable, and that everything produced is sold. In reality, bulk discounts lower the selling price at high volumes, variable cost per unit can fall with efficiency or rise with overtime, fixed costs are often stepped (a new machine or supervisor at higher output), and unsold output sits in inventory. A break-even chart is therefore a simplified planning tool, best used for a quick first pass and for sensitivity testing, not as the sole basis for a decision.

Try this

Q1. Fixed costs are $30{,}000$ and contribution per unit is $15$. Calculate the break-even output. [2 marks] $\dfrac{30{,}000}{15} = 2{,}000$ units.

Q2. State one limiting assumption of break-even analysis. [1 mark] For example that selling price and variable cost per unit stay constant.