1.6.2 Break-Even Analysis — Practice Questions

Seven original multiple-choice questions on break-even analysis: contribution, finding the break-even point, the margin of safety, what moves the break-even point and the limits of the method.

7 questions Edexcel B A-Level Multiple choice Model answers included

Not read the notes yet? Start with the 1.6.2 Break-Even Analysis revision notes.

1. 1. A food truck sells loaded fries at £7.50 a portion. Each portion uses £2.70 of potatoes, toppings and packaging, and the truck's pitch fee and insurance come to £1,800 a month. The £4.80 left from each portion's price is the truck's

   Definition in context

   Select one answer

   A Average cost per portion.

   B Contribution per portion.

   C Margin of safety per portion.

   D Profit per portion.
   Show model answer

   Answer: B (Contribution per portion.). Contribution per unit = selling price − variable cost per unit = £7.50 − £2.70 = £4.80.
   It is what each portion leaves over once its own costs are paid. It goes towards the £1,800 of fixed costs first, and only once those are covered does it become profit.

   Why the other options are wrong

   • A — Average cost is total costs divided by output, so it would include a share of the £1,800 of fixed costs. £4.80 is not a cost at all; it is what is left after the variable cost is paid.
   • C — The margin of safety is how far sales are above the break-even point, in units or as a percentage of sales. It is not an amount per portion.
   • D — £4.80 is not profit yet, because the £1,800 of fixed costs still has to be paid. Until the truck sells 1,800 ÷ 4.80 = 375 portions in a month, it is making a loss.

2. 2. A cider maker sells kegs to pubs at £42 each. Each keg costs £18 in apples, the keg itself and delivery, and the firm's fixed costs are £5,000 a month. The smallest whole number of kegs it must sell each month to cover all its costs is

   Calculation

   Select one answer

   A 120

   B 208

   C 209

   D 278
   Show model answer

   Answer: C (209). Contribution per keg = £42 − £18 = £24.
   Break-even output = fixed costs ÷ contribution per unit = £5,000 ÷ £24 = 208.33.
   Round up to 209 kegs. A firm cannot sell a third of a keg, and at 208 its total contribution is 208 × £24 = £4,992, just short of the £5,000 of fixed costs.

   Why the other options are wrong

   • A — This divides fixed costs by the selling price: £5,000 ÷ £42 = 119.05, rounded up to 120. It ignores the £18 each keg costs, so it understates break-even.
   • B — The division is right, but 208.33 has been rounded down. At 208 kegs the firm is £8 short of covering its fixed costs, so it has not yet broken even.
   • D — This divides fixed costs by the variable cost per keg: £5,000 ÷ £18 = 277.8, rounded up to 278. The divisor should be contribution, the price minus the variable cost.

3. 3. A phone-repair shop charges £60 a repair. Parts for each repair cost £20 on average, and its fixed costs are £6,000 a month. It carries out 210 repairs a month. To one decimal place, its margin of safety as a percentage of actual sales is

   Calculation

   Select one answer

   A 28.6%

   B 40.0%

   C 52.4%

   D 71.4%
   Show model answer

   Answer: A (28.6%). Contribution per repair = £60 − £20 = £40.
   Break-even output = £6,000 ÷ £40 = 150 repairs.
   Margin of safety = 210 − 150 = 60 repairs.
   As a percentage of actual sales: 60 ÷ 210 × 100 = 28.6%.
   Sales could fall by just over a quarter before the shop made a loss.

   Why the other options are wrong

   • B — This divides the margin of safety by break-even output: 60 ÷ 150 × 100. The question asks for it as a percentage of actual sales, so the divisor is 210.
   • C — This finds break-even by dividing fixed costs by the price: £6,000 ÷ £60 = 100, which gives a margin of 110 repairs and 110 ÷ 210 × 100 = 52.4%. Break-even uses contribution, £40, not the price.
   • D — This is break-even output as a percentage of actual sales: 150 ÷ 210 × 100. The margin of safety is the part of sales above break-even, which is the remaining 28.6%.

4. 4. A maker of yoga mats is choosing between four plans for next year. Table 1 shows the selling price, the variable cost of each mat and the annual fixed costs under each plan.
   Using Table 1, the plan with the lowest break-even output is

   Data interpretation

   Table 1: Four plans for a yoga mat maker

   	Selling price per mat	Variable cost per mat	Fixed costs per year
   Plan 1	£25	£14	£12,000
   Plan 2	£28	£15	£13,500
   Plan 3	£27	£15	£12,000
   Plan 4	£25	£15	£10,500

   Select one answer

   A Plan 1.

   B Plan 2.

   C Plan 3.

   D Plan 4.
   Show model answer

   Answer: C (Plan 3.). Break-even output = fixed costs ÷ (price − variable cost per unit).
   Plan 1: £12,000 ÷ £11 = 1,090.9, so 1,091 mats.
   Plan 2: £13,500 ÷ £13 = 1,038.5, so 1,039 mats.
   Plan 3: £12,000 ÷ £12 = 1,000 mats.
   Plan 4: £10,500 ÷ £10 = 1,050 mats.
   Plan 3 breaks even soonest. No single column tells you this: contribution has to be worked out and divided into fixed costs for every plan.

   Why the other options are wrong

   • A — Plan 1 has the lowest variable cost per mat, but its price is joint lowest, so its contribution is only £11 and it needs 1,091 mats, the most of the four.
   • B — Plan 2 has the biggest contribution per mat, £13, but its fixed costs are also the highest. It needs 1,039 mats, 39 more than Plan 3.
   • D — Plan 4 has the lowest fixed costs, but also the smallest contribution, £10 a mat, so it needs 1,050 mats. Dividing fixed costs by the price instead of by contribution would wrongly make Plan 4 the lowest.

5. 5. A pizza takeaway works out its break-even point using fixed costs of £4,000 a month. To make more than 2,500 pizzas a month, it would have to rent a second oven and hire another salaried manager. The assumption of break-even analysis that this most clearly breaks is that

   Applied reasoning

   Select one answer

   A Every unit that is made is sold.

   B Each unit sells at the same price.

   C Variable cost per unit stays the same.

   D Fixed costs stay fixed at all outputs.
   Show model answer

   Answer: D (Fixed costs stay fixed at all outputs.). Break-even analysis draws fixed costs as a flat line at every output. Here they are only fixed up to 2,500 pizzas: beyond that, the rent on a second oven and another salary make them jump to a higher level. A break-even point above 2,500 pizzas worked out with £4,000 of fixed costs would be too low.

   Why the other options are wrong

   • A — Nothing in the stem says pizzas go unsold or are wasted. The problem is a cost that changes once output passes 2,500.
   • B — Nothing in the stem mentions discounts or different prices. The figure that changes is a fixed cost.
   • C — Oven rent and a manager's salary do not rise with each pizza made; they are fixed costs that step up once. Nothing is said about the cost of dough or toppings per pizza.

6. 6. A kayak-hire firm charges £35 a hire, and each hire costs it £10 in cleaning and repairs. Its break-even point is 600 hires a season, and it expects 840 hires this season. Its expected profit for the season is

   Calculation

   Select one answer

   A £6,000

   B £8,400

   C £15,000

   D £21,000
   Show model answer

   Answer: A (£6,000). Contribution per hire = £35 − £10 = £25.
   The first 600 hires cover the fixed costs exactly; every hire after that adds its contribution to profit.
   Margin of safety = 840 − 600 = 240 hires.
   Profit = 240 × £25 = £6,000.
   Check: fixed costs = 600 × £25 = £15,000. Total contribution = 840 × £25 = £21,000. Profit = £21,000 − £15,000 = £6,000.

   Why the other options are wrong

   • B — This multiplies the 240 hires beyond break-even by the price, £35. Each of those hires still costs £10, so it adds only £25 to profit.
   • C — This is the firm's fixed costs, 600 × £25: the contribution from the first 600 hires, all of which goes on covering them.
   • D — This is total contribution, 840 × £25: what is left before the fixed costs are paid. Take off the £15,000 of fixed costs to get profit.

7. 7. Café X and Café Y each sell 5,000 drinks a month. Café X breaks even at 2,500 drinks a month and Café Y at 4,500. Roadworks then cut sales at both cafés by 20%, with prices and costs unchanged. The result is that

   Applied reasoning

   Select one answer

   A Both cafés make a loss.

   B Both cafés stay in profit.

   C Only Café X makes a loss.

   D Only Café Y makes a loss.
   Show model answer

   Answer: D (Only Café Y makes a loss.). A 20% fall takes each café from 5,000 drinks to 4,000.
   Café X: 4,000 is still above its break-even of 2,500, so it stays in profit. Its margin of safety was 2,500 drinks, 50% of sales.
   Café Y: 4,000 is below its break-even of 4,500, so it now makes a loss. Its margin of safety was only 500 drinks, 10% of sales.
   A 20% fall is bigger than Café Y's margin of safety but smaller than Café X's.

   Why the other options are wrong

   • A — Café X could lose half its sales before making a loss. At 4,000 drinks it is still 1,500 above break-even.
   • B — Café Y's margin of safety is only 500 drinks, 10% of its sales. A 20% fall takes it 500 drinks below break-even.
   • C — This mixes the two up. Café X has the lower break-even point, so it has the bigger margin of safety and is the safer of the two.