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Business calculations: revenue, costs and profit

Method

Identify the fixed costs (costs that do not change with output, e.g. rent) and the variable cost per unit (cost that changes directly with each unit made, e.g. materials).
Calculate the contribution per unit: selling price per unit minus variable cost per unit.
Apply the formula: break-even output = fixed costs / contribution per unit.
If asked for the margin of safety, subtract the break-even output from the actual or budgeted output.
On a break-even chart, plot fixed costs as a horizontal line, total costs as a line starting at the fixed cost level and rising with output, and total revenue as a line starting at zero and rising more steeply; the break-even point is where total cost and total revenue lines cross.
Always state units in the final answer, e.g. 500 units, and check the answer is a sensible whole number of units where the context requires one.

Worked example

A business makes a single product. Its fixed costs are 9,000 pounds per month. Each unit sells for 25 pounds and costs 10 pounds in materials and labour to make. Calculate the contribution per unit and the break-even output per month. If the business currently sells 800 units per month, calculate its margin of safety.

Calculate the contribution per unit: selling price - variable cost per unit = 25 - 10 = 15 pounds.
Apply the break-even formula: break-even output = fixed costs / contribution per unit = 9,000 / 15.
Calculate: 9,000 / 15 = 600 units.
Calculate the margin of safety: actual output - break-even output = 800 - 600 = 200 units.
State the answers: the break-even output is 600 units per month, and the margin of safety at 800 units of sales is 200 units.

Practice questions

Try each question, then tap to reveal the answer.

Q1What does 'break-even' mean?Show answer

Answer: The level of output at which total revenue equals total costs, so the business makes neither a profit nor a loss.

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Q2State the formula for contribution per unit.Show answer

Answer: Contribution per unit = selling price per unit - variable cost per unit.

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Q3State the formula for break-even output.Show answer

Answer: Break-even output = fixed costs / contribution per unit.

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Q4A product sells for 40 pounds and has a variable cost of 15 pounds per unit. Fixed costs are 5,000 pounds. Calculate the break-even output.Show answer

Answer: Contribution per unit = 40 - 15 = 25 pounds. Break-even output = 5,000 / 25 = 200 units.

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Q5What does the margin of safety measure?Show answer

Answer: How much actual (or budgeted) sales can fall before the business reaches its break-even point and stops making a profit.

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Q6On a break-even chart, what does the point where the total cost and total revenue lines cross represent?Show answer

Answer: The break-even point, the output at which total revenue equals total costs.

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Q7A business has a break-even output of 300 units and currently sells 450 units. Calculate its margin of safety.Show answer

Answer: 450 - 300 = 150 units.

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Exam-style questions

Written in the style of a GCSE Business exam paper, with a full mark scheme.

Q1[8 marks]

A business is planning to launch a new product. Fixed costs are 12,000 pounds per month. Each unit will sell for 30 pounds, and the variable cost per unit is 18 pounds. (a) Calculate the contribution per unit. (2 marks) (b) Calculate the break-even output per month. (2 marks) (c) The business plans to sell 1,200 units per month. Calculate the margin of safety. (2 marks) (d) State one reason the business should be cautious even though it has a positive margin of safety. (2 marks)

Show mark scheme

Tick each line you got. Your score builds from the marks on the scheme.

subtracts the variable cost per unit from the selling price (30 - 18).1 mark
correct answer for part (a) of 12 pounds.1 mark
divides fixed costs by the contribution per unit (12,000 / 12).1 mark
correct answer for part (b) of 1,000 units.1 mark
subtracts the break-even output from the planned output (1,200 - 1,000).1 mark
correct answer for part (c) of 200 units.1 mark
identifies a valid reason for caution, for example that the sales forecast of 1,200 units may not be achieved, especially for a new product with no sales history.1 mark
final answer stated clearly: (a) 12 pounds; (b) 1,000 units; (c) 200 units; (d) demand forecasts for new products are uncertain, so if sales fall below 1,000 units the business will make a loss.1 mark

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Q2[6 marks]

Assess the extent to which break-even analysis is useful for a new business deciding whether to launch a product.

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Tick each line you got. Your score builds from the marks on the scheme.

basic, undeveloped points are made about break-even analysis with little or no application.2 marks
points are explained with some development and applied to a new business, for example that it shows the minimum output needed to avoid a loss, helping decide if a sales target is realistic, but that it relies on cost and price estimates that may be inaccurate for a brand new, untested product.2 marks
a balanced answer weighs the usefulness of break-even analysis against its limitations with developed reasoning and reaches a supported judgement, for example concluding it is a useful first check but should not be the only tool used, since it assumes all units are sold at a single fixed price and ignores factors such as competitor reactions and changing costs.1 mark
Specific content that earns credit: break-even analysis is useful because it quickly shows the output level needed to cover fixed and variable costs, helps set sales targets and supports decisions on pricing and finance needs; its limitations include that it assumes costs and the selling price stay constant regardless of output, it assumes every unit made is sold, and it relies on estimated figures that may be unreliable for a genuinely new product with no sales history, so it should be used alongside other forms of market research.1 mark

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See real GCSE Business past-paper questions, with official mark schemes →

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Break-Even: The Effect of Changes in Price, Costs and Output Cash-flow forecasting

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Break-even analysis

Before you start

Method

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Practice questions

Exam-style questions

Free printable worksheet

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