IB DP Business Management: Break-even analysis – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – the IB holds copyright in its own papers. Use these alongside the official past papers available through your school or the IB store.

These questions cover section 5.5 (Break-even analysis) of the IB Business management guide, first assessment 2024, for SL and HL. The section is in Unit 5 (Operations management) and none of it is marked HL only. The guide does not supply formulas here, so the answers use the usual textbook forms. Learn the method from the 5.5 study guide and the 5.5 revision notes. Also see the IB Business Management hub, the printable checklist and the free diagnostics. All businesses and figures are invented, and money is in dollars.

Questions

Questions 2 to 10 use Pellindor Honey, which sells jars of honey at a price of 8 per jar. Variable cost is 3 per jar and fixed costs are 15,000 per year. Output and sales are 4,200 jars per year unless a question says otherwise.

1. Define the term break-even point. [2]

2. Using the Pellindor Honey data:

(a) Calculate the contribution per unit. [1] (b) Calculate the total contribution at 4,200 jars. [1] (c) Calculate the profit at 4,200 jars. [2]

3. Using the Pellindor Honey data:

(a) Calculate the break-even quantity. [2] (b) Calculate the margin of safety in jars. [1] (c) Give the margin of safety as a percentage of the output actually sold, to one decimal place. [1]

4. Pellindor Honey wants a profit of 10,000. Calculate the output needed. [3]

5. Pellindor Honey expects to sell 4,000 jars and wants a profit of 9,000. Calculate the price it must charge. [4]

6. Pellindor Honey’s break-even chart is being drawn.

(a) Complete the table for total costs and total revenue. [3]

Output (jars)	Total costs	Total revenue
0	15,000	0
2,000	?	?
3,000	?	?
6,000	?	?

(b) State the break-even quantity shown by the table. [1]

7. Pellindor Honey considers cutting its price to 7 per jar, with costs unchanged and sales of 4,200 jars.

(a) Calculate the new break-even quantity. [2] (b) Calculate the new margin of safety in jars. [1] (c) Calculate the new profit. [2] (d) Explain how the price cut would change the break-even chart. [2]

8. Distinguish between total contribution and contribution per unit. [3]

9. Fixed costs at Pellindor Honey rise to 18,000, with the price at 8 and sales at 4,200 jars. Analyse the effect on the break-even quantity, the profit and the margin of safety. [5]

10. Explain two limitations of using break-even analysis as a decision-making tool. [4]

11. Larkspar Print sells boxed art prints at 20 each. Variable cost is 8 per box and fixed costs are 24,000 per year. It sells 2,500 boxes now, and capacity is 3,500 boxes. The owner proposes a price of 17 per box. The sales forecast at that price is 3,300 boxes.

(a) Calculate the current break-even quantity and the current margin of safety in boxes. [3] (b) Calculate the break-even quantity and the profit at the proposed price. [3] (c) Evaluate whether Larkspar Print should adopt the proposal. [6]

Answers

1. The output (or sales) at which total revenue equals total costs [1], so the business breaks even, with no profit and no loss [1]. [2] Examiner insight: A definition that names only “no profit” can gain less credit than one that also says revenue equals total cost, because the second part shows how the point arises.

2. (a) 8 − 3 = 5 per jar [1] (b) 4,200 × 5 = 21,000 [1] (c) Profit = 21,000 − 15,000 [1] = 6,000 [1] Examiner insight: A correct final figure with no working leaves the marker nothing to credit if it is wrong, so write the subtraction of fixed costs on its own line.

3. (a) 15,000 / 5 [1] = 3,000 jars [1] (b) 4,200 − 3,000 = 1,200 jars [1] (c) 1,200 / 4,200 × 100 = 28.6% [1] Examiner insight: Margin of safety is measured from actual output. Dividing by capacity or by the break-even quantity gives a different figure, so state your base.

4. Target profit output = (fixed costs + target profit) / contribution per unit [1]; (15,000 + 10,000) / 5 [1] = 5,000 jars [1] [3] Examiner insight: Dividing only fixed costs by contribution gives the break-even quantity, which answers a different question. Show the target profit inside the numerator.

5. Variable costs = 4,000 × 3 = 12,000 [1]; revenue needed = 15,000 + 12,000 + 9,000 = 36,000 [1]; price = 36,000 / 4,000 [1] = 9 per jar [1] [4] Examiner insight: Target price needs total variable costs at that output, not variable cost per jar. Check by working forward to the profit.

6. (a) 2,000 jars: total costs 15,000 + 6,000 = 21,000 and revenue 16,000 [1]; 3,000 jars: costs 24,000 and revenue 24,000 [1]; 6,000 jars: costs 33,000 and revenue 48,000 [1] (b) 3,000 jars (where costs equal revenue) [1] Examiner insight: The total cost line starts at the fixed cost level, not zero. Costs of 15,000 at zero output is the cue to build each value as fixed costs plus 3 per jar.

7. (a) Contribution = 7 − 3 = 4 [1]; 15,000 / 4 = 3,750 jars [1] (b) 4,200 − 3,750 = 450 jars [1] (c) 4,200 × 4 = 16,800, then 16,800 − 15,000 = 1,800 [1][1] (d) The total revenue line becomes less steep [1], so it crosses the total cost line further right and break-even output rises [1] Examiner insight: Strong answers say which line moves and in which direction. Saying only “break-even goes up” gives less detail about the chart than the question asks for.

8. Contribution per unit is the selling price minus the variable cost of one unit [1]; total contribution is contribution per unit multiplied by the number of units sold [1]. The first measures what one sale adds towards fixed costs and profit, the second shows what all sales add, and profit is total contribution minus fixed costs [1] [3] Examiner insight: A “distinguish” answer needs both items and a point of difference. Defining each in isolation without saying how they differ can leave a mark unearned.

9. Break-even quantity: 18,000 / 5 = 3,600 jars, up from 3,000 [1]; profit: 21,000 − 18,000 = 3,000, down from 6,000 [1]; margin of safety: 4,200 − 3,600 = 600 jars, down from 1,200 [1]. On the chart the total cost line shifts up by 3,000 with the same slope [1], so the business needs to sell 600 more jars to break even and has less protection against a fall in demand [1] [5] Examiner insight: An “analyse” answer does more than list three new figures. Comparing each figure with its original and saying what the change means is what separates a developed answer from a restatement.

10. Any two limitations, each identified and explained. For example, straight lines: the model assumes a constant price and constant variable cost per jar [1], but discounts for bulk buying or price cuts to sell stock make the real lines bend, so the break-even point may be wrong [1]. Forecast data: costs, price and demand are estimates [1], and an error in any of them moves the break-even point, so a decision could be based on a figure that does not hold [1] [4] Examiner insight: A limitation named without an explanation is a list item, not an answer. Give the reason the limitation weakens the result.

11. (a) Contribution = 20 − 8 = 12 [1]; 24,000 / 12 = 2,000 boxes [1]; margin of safety = 2,500 − 2,000 = 500 boxes [1] (b) Contribution = 17 − 8 = 9 [1]; break-even = 24,000 / 9 = 2,666.7, so 2,667 boxes [1]; profit = 3,300 × 9 − 24,000 = 29,700 − 24,000 = 5,700 [1] (c) Current profit is 2,500 × 12 − 24,000 = 6,000, so the proposal lowers profit by 300 [1]. Break-even rises from 2,000 to 2,667 boxes [1]. Margin of safety is 3,300 − 2,667 = 633 boxes, larger than 500 in units, but as a percentage of actual output it is 19.2% against 20.0%, so the cushion is not much stronger [1]. To match 6,000 profit it needs (24,000 + 6,000) / 9 = 3,333.3, so 3,334 boxes [1], only 166 below capacity, which leaves little room for forecast error [1]. The calculations assume the 3,300 forecast is right and ignore competitor response. Judgement: Larkspar Print should not adopt the price cut on these figures, because profit is lower and risk is higher, unless it values market share or has strong evidence for the forecast [1] [12] Examiner insight: For “evaluate”, use the numbers on both sides, then finish with a judgement, and state what it depends on. A calculation without a conclusion tends to stop short of the command word.

Where marks are usually lost

• Using the selling price, not the contribution on each unit, as the divisor for fixed costs.
• Using the total cost line through the origin instead of starting at the fixed cost level.
• Leaving out fixed costs when asked for profit, giving total contribution instead.
• Mixing up target profit output (the output) and target profit (the profit).
• Giving margin of safety as a percentage with no stated base.
• Forgetting to round a break-even quantity up to a whole unit.
• Naming a limitation without explaining why it weakens the result.
• Answering “evaluate” with numbers alone and no reasoned judgement.

Next steps

• Read the 5.5 revision notes for condensed formulas.
• Review the 5.5 study guide for worked examples.
• Check the IB Business Management hub and the printable checklist.
• Try all free 10-minute diagnostics.
• Book a free trial class: trial classes.

Frequently asked questions

What do these break-even practice questions cover? They cover section 5.5 of the IB DP Business Management guide (first assessment 2024): contribution, break-even charts and quantity, profit or loss, margin of safety, target profit output, target profit, target price, the effects of changes and limitations.

What is the difference between target profit output and target profit? Target profit output is the number of units needed to reach a chosen profit. Target profit is the profit made at a chosen output. Mixing the two up is a common error.

Should you round a break-even quantity? Yes. Round up to the next whole unit, because a business cannot sell part of a unit and still break even.

How should you answer an evaluate question on break-even? Do not rely on numbers alone. Tie one or two limitations to the case, explain why they weaken the result, and give a reasoned judgement on whether the tool is still useful.

Official syllabus

International Baccalaureate Organization, Business management guide, first assessment 2024, section 5.5 Break-even analysis.