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L4: Break-Even (Formula Method)

Revision and practice on why businesses use break-even analysis, and how to calculate it using the formula method.

Key vocabulary: Fixed Costs, Variable Costs, Contribution, Break-Even Output

Key Concepts

What Is Break-Even Analysis?

Break-even analysis is a tool that helps businesses work out how many units they need to sell to cover all their costs. At the break-even point, total revenue equals total costs — the business is making neither a profit nor a loss.

Why businesses use break-even analysis:

  • To find out the minimum quantity (output) of sales needed before the business starts making a profit.
  • To help with pricing decisions — businesses can see how changing the price affects the break-even point.
  • To support business plans and loan applications, by showing banks and investors that the business understands its finances.
  • To assess the impact of changes in costs — for example, what happens to profitability if rent increases.

The Break-Even Formula

The break-even point can be calculated using a formula, built from three ideas: fixed costs, variable costs, and contribution.

  • Contribution per unit = Selling price per unit − Variable cost per unit.
  • Break-even output (units) = Fixed costs ÷ Contribution per unit.
  • Total contribution = Contribution per unit × number of units sold.
  • Margin of safety = Actual sales − Break-even output — the amount by which current sales exceed the break-even point, and a measure of how much sales could fall before the business starts making a loss.

Real-World Case Studies

Deliveroo — reaching break-even after a decade of losses

Deliveroo reached break-even across all its regions in the second half of 2022, after a series of cost-reduction measures, before going on to report its first full-year profit — £3 million — in 2024. It had taken the company 12 years since launch to get there. This shows break-even isn't a one-off calculation for a new product, but something a whole business can work towards over years, by growing revenue, controlling costs, or both.

Source: verified via search, September 2026 — RetailDetail EU and UKTN coverage of Deliveroo's path to profitability.

Peloton — moving the break-even point by cutting costs, not just chasing sales

Peloton posted operating income of $41.3 million in the quarter to September 2025 and $52.5 million in the quarter to March 2026 — its first sustained run of operating profit — even though its number of paying subscribers kept falling over the same period. It got there mainly by cutting costs rather than growing sales. This is a useful reminder that a business's break-even output isn't fixed: lowering fixed or variable costs moves the break-even point down, so a business can move towards profit even while selling less than before.

Source: verified via search, September 2026 — Peloton's own investor Q1 FY2026 and Q2 FY2026 results releases.

Quick Quiz

Pick an answer for instant feedback. Your score is just for you — it isn't saved anywhere.

1. A business sells a product for £20. Variable cost per unit is £8. What is the contribution per unit?

2. Fixed costs are £6,000 and contribution per unit is £15. What is the break-even output?

3. A business's break-even output is 500 units and it currently sells 650 units. What is its margin of safety?

4. At the break-even point, what is true of a business's total revenue and total costs?

5. Which of these would lower a business's break-even output?

Score: 0 / 0

Fill in the Blank

Tap the word or phrase that correctly completes each formula.

1. Contribution per unit = Selling price per unit − ____.

2. Break-even output = Fixed costs ÷ ____.

3. Margin of safety = Actual sales − ____.

4. Total contribution = Contribution per unit × ____.

Score: 0 / 0

Quick Knowledge Check

Short, snappy recall questions — tap to reveal the answer.

What is the break-even formula? (1 mark)

Fixed costs ÷ Contribution per unit.

How is contribution per unit calculated? (1 mark)

Selling price per unit − Variable cost per unit.

What is the margin of safety formula? (1 mark)

Actual sales − Break-even output.

Key Term Flashcards

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Tap a card to flip it, then rate yourself.

Break-even point
The point at which total revenue equals total costs — the business makes neither a profit nor a loss.
Contribution per unit
Selling price per unit minus variable cost per unit — the amount each sale contributes towards covering fixed costs.
Margin of safety
Actual sales minus break-even output — how far sales could fall before the business makes a loss.
Fixed costs
Costs that don't change with output, e.g. rent, salaries, marketing.
Variable costs
Costs that change directly with output, e.g. raw materials, packaging.

A*/A Stretch

Examiner's eye

In break-even calculation questions, always show your working line by line (contribution per unit, then the division), not just a final number — method marks are usually available even if the final answer is wrong due to a small slip.

Synoptic link

Connecting to sources of finance (L2, this unit): A lower break-even output makes a business less risky to lend to, since it needs fewer sales to cover its costs — this is exactly why banks and investors often ask to see break-even analysis as part of a loan application or business plan, linking this topic directly to sources of finance.

Try This With AI

Before using this: AI tools can get facts or mark scheme details wrong, and quality varies by tool. Always check anything factual against your notes or ask your teacher.

Give me three short break-even calculation problems of increasing difficulty, similar in style to an AQA A-Level Business exam, with the numbers hidden until I ask for the answer. After I attempt each one, mark my working and tell me whether I've shown the correct formula and method, not just the correct final number.