Break-even analysis

Contribution is what each unit sold contributes towards covering fixed costs, and then towards profit once they are covered:

It is not profit. A product with a contribution of $8 a unit can still be loss-making overall if too few are sold to cover the rent — which is exactly the question break-even answers.

The logic: every unit contributes a fixed amount; fixed costs are a fixed total; the number of units needed to cover them is one divided by the other. Anything that raises contribution per unit — a higher price, a lower variable cost — lowers break-even output; anything that raises fixed costs raises it.

The chart draws three lines against output on the horizontal axis and costs and revenue on the vertical:

• Fixed costs — horizontal, at the fixed-cost total, because it does not change with output.
• Total cost — starts at the fixed-cost total and rises at the variable cost per unit.
• Total revenue — starts at zero and rises at the selling price per unit.

Break-even is where total revenue crosses total cost. To the left, the gap between the lines is the loss at that output; to the right, the profit. Exam questions on the chart ask you to read those off, to mark the margin of safety, or to say how a line moves when a price or cost changes — a price rise steepens total revenue and moves break-even left; a rent rise lifts both fixed and total cost and moves it right.

The margin of safety is how far sales can fall before the business starts losing money — and is therefore the number a manager actually looks at. It can be expressed in units, in revenue, or as a percentage of current output; state which.

• Paper 2, 3-mark calculate — break-even output, contribution or margin of safety from case figures. Formula, working, units.
• Paper 1, 2-mark define / 3-mark explain — “define margin of safety”; “explain one limitation of break-even analysis”.
• 8-mark analyse — “analyse how break-even analysis could help the owner decide whether to…”: two chains, from the numbers to the decision.
• 12-mark evaluate — how useful break-even is to a specific decision in the case. This is where the limitations below become the evaluation, and where the top band needs them applied tothis business’s numbers.

See the 12-mark structure for how the evaluation is built and banded.

Break-even is simple because it assumes things that are rarely true. Each assumption is an evaluative point when it is tied to the case:

• Costs and revenue are linear. In practice, buying in bulk lowers variable cost per unit and selling more may need discounts — both bend the lines.
• Everything produced is sold. Output and sales are treated as the same; unsold stock has costs and no revenue.
• One product, one price. A business with a range needs an average contribution that changes with the sales mix.
• Fixed costs stay fixed. Beyond current capacity a new machine or a second site steps them up.
• The data are estimates. For a new product the variable cost and the price are forecasts, so the break-even figure inherits their error.

A Level 3 evaluation does not list these. It picks the one or two that bite for the business in the case — a start-up whose costs are guesses, a multi-product retailer — and judges how much they reduce the usefulness of the number for the decision being made.

1. 1.Dividing fixed costs by price instead of contribution

   The commonest error, and it gives an answer that is too low. Subtract variable cost first: it is the contribution that covers fixed costs.

2. 2.No units on the answer

   “400” is ambiguous — boards or dollars? Write “400 boards” or “$168 000 revenue”. The final mark is often for the correct unit.

3. 3.Margin of safety as a number with no comparison

   Fifty boards means little alone. As 11% of current output it becomes the point: a small dip in demand puts the business at break-even.

4. 4.Not recalculating after a change

   When a cost or price changes, contribution changes, so break-even changes. Recompute from the new contribution; do not adjust the old answer by feel.

5. 5.Treating contribution as profit

   Contribution covers fixed costs first. Profit is what is left after they are covered: total contribution − fixed costs.