Break-Even: The Effect of Changes in Price, Costs and Output
Break-even output changes whenever selling price, variable cost per unit, or fixed costs change, because each of these is part of the break-even formula: break-even output = fixed costs / contribution per unit, where contribution per unit = selling price - variable cost per unit.
Method
- Note the original selling price, variable cost per unit and fixed costs, and calculate, or note, the original break-even output.
- Identify exactly what has changed, the selling price, the variable cost per unit, or the fixed costs, and recalculate the contribution per unit if the price or variable cost has changed.
- Recalculate break-even output using the formula with the new figures: break-even output = fixed costs / new contribution per unit.
- Compare the new break-even output with the original, and state whether it has risen or fallen.
- Explain the direction of the change: a higher contribution per unit lowers break-even output; higher fixed costs raise break-even output.
- For an evaluate-style question, weigh the benefit of the change, e.g. a lower break-even point after a price rise, against a possible drawback, e.g. higher prices might reduce the number of units actually sold.
Worked example
A business has fixed costs of 8,000 pounds, a selling price of 20 pounds and a variable cost of 12 pounds per unit. It is considering raising its selling price to 25 pounds, with the variable cost staying at 12 pounds per unit. Calculate the original break-even output and the new break-even output after the price rise, and state the effect of the price rise on the break-even output.
- Calculate the original contribution per unit: 20 - 12 = 8 pounds.
- Calculate the original break-even output: 8,000 / 8 = 1,000 units.
- Calculate the new contribution per unit after the price rise: 25 - 12 = 13 pounds.
- Calculate the new break-even output: 8,000 / 13 = approximately 615.4, rounded up to 616 units.
- State the effect: the break-even output falls from 1,000 units to 616 units, so the price rise means the business needs to sell fewer units to break even.
Practice questions
Try each question, then tap to reveal the answer.
Q1If fixed costs rise but the contribution per unit stays the same, what happens to the break-even output?Show answer
Answer: It rises - a business needs to sell more units to cover the higher fixed costs before it starts making a profit.
Q2If a business successfully cuts its variable cost per unit while keeping its selling price the same, what happens to its break-even output?Show answer
Answer: It falls - a lower variable cost per unit increases the contribution per unit, so fewer units need to be sold to cover the fixed costs.
Q3A business's contribution per unit is 10 pounds and its fixed costs are 5,000 pounds. Calculate its break-even output.Show answer
Answer: 5,000 / 10 = 500 units.
Q4The same business's fixed costs rise to 6,500 pounds, with the contribution per unit unchanged. Calculate the new break-even output.Show answer
Answer: 6,500 / 10 = 650 units.
Q5Give one possible drawback of raising the selling price to lower the break-even output.Show answer
Answer: A higher price may put off some customers, reducing the number of units actually sold, so the business might not benefit from the lower break-even point if demand falls.
Q6A business's selling price is 15 pounds and variable cost per unit is 9 pounds. Calculate the contribution per unit.Show answer
Answer: 15 - 9 = 6 pounds.
Q7Using your answer above, if fixed costs are 3,600 pounds, calculate the break-even output.Show answer
Answer: 3,600 / 6 = 600 units.
Exam-style questions
Written in the style of a GCSE Business exam paper, with a full mark scheme.
A business currently has fixed costs of 15,000 pounds, a selling price of 50 pounds per unit and a variable cost of 30 pounds per unit. A new supplier offers cheaper materials, which would cut the variable cost per unit to 25 pounds, but the supplier requires a new storage contract that would raise fixed costs to 17,000 pounds. (a) Calculate the current break-even output. (2 marks) (b) Calculate the new contribution per unit if the business switches supplier. (2 marks) (c) Calculate the new break-even output after switching supplier, using the new fixed costs. (2 marks) (d) State whether the business should switch supplier on break-even grounds alone, using your figures to support your answer. (2 marks)
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Explain two ways in which a rise in a business's fixed costs could affect its break-even output and its overall profitability.
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See real GCSE Business past-paper questions, with official mark schemes →
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