ICAEW BIP · Chapter 11
Cost-volume-profit analysis and limiting factors MCQs with Answers
10 multiple-choice questions on Cost-volume-profit analysis and limiting factors for ICAEW BIP Business Insight and Performance. Try each one before revealing the answer and explanation.
Practise this chapter interactivelyQuestion 1
A company's fixed costs are £288,000 a year and the contribution per unit of its only product is £24. What is the breakeven point in units?
- A) 1,000 units
- B) 15,000 units
- C) 12,000 units
- D) 8,000 units
Show answer & explanation
Answer: C) 12,000 units
Breakeven point = fixed costs / contribution per unit = £288,000 / £24 = 12,000 units. At this volume total contribution exactly covers fixed costs, so profit is nil.
Question 2
A product sells for £40 and has a variable cost of £26 per unit. Fixed costs are £189,000. What is the breakeven revenue?
- A) £290,769
- B) £540,000
- C) £13,500
- D) £255,150
Show answer & explanation
Answer: B) £540,000
Contribution per unit = £40 - £26 = £14. C/S ratio = £14 / £40 = 35%. Breakeven revenue = fixed costs / C/S ratio = £189,000 / 0.35 = £540,000. 13,500 would be the breakeven point in units, not £.
Question 3
Budgeted sales are 15,000 units and the breakeven point is 12,000 units. What is the margin of safety as a percentage of budgeted sales?
- A) 10%
- B) 25%
- C) 80%
- D) 20%
Show answer & explanation
Answer: D) 20%
Margin of safety = budgeted sales - breakeven sales = 15,000 - 12,000 = 3,000 units. As a percentage of budgeted sales: 3,000 / 15,000 = 20%. This shows how far sales could fall below budget before a loss is made.
Question 4
A company's fixed costs are £288,000 and its contribution per unit is £24. It wants to make a profit of £96,000. How many units must it sell?
- A) 16,000 units
- B) 4,000 units
- C) 12,000 units
- D) 8,000 units
Show answer & explanation
Answer: A) 16,000 units
Required units = (fixed costs + target profit) / contribution per unit = (£288,000 + £96,000) / £24 = £384,000 / £24 = 16,000 units.
Question 5
A company sells products X and Y in the fixed ratio 3:2 by units. Product X earns a contribution of £10 per unit and product Y earns £15 per unit. Fixed costs are £180,000. How many units of product Y must be sold to break even?
- A) 12,000 units
- B) 9,000 units
- C) 6,000 units
- D) 15,000 units
Show answer & explanation
Answer: C) 6,000 units
Contribution from one 'batch' of 3 X and 2 Y = (3 x £10) + (2 x £15) = £60. Breakeven batches = £180,000 / £60 = 3,000. Units of Y = 3,000 x 2 = 6,000 (with 9,000 units of X, 15,000 units in total).
Question 6
On a profit-volume (P/V) chart for a single product, what does the slope (gradient) of the profit line represent?
- A) Contribution per unit
- B) Fixed costs
- C) Selling price per unit
- D) Variable cost per unit
Show answer & explanation
Answer: A) Contribution per unit
A P/V chart plots profit against sales volume. The line starts at a loss equal to fixed costs at zero sales, and profit rises by the contribution earned on each extra unit, so the gradient is contribution per unit. If sales are measured in £ revenue, the gradient is the C/S ratio. The line crosses the horizontal axis at the breakeven point.
Question 7
Which of the following is an assumption of basic cost-volume-profit analysis?
- A) Inventory levels change significantly during the period
- B) Selling price and variable cost per unit stay constant at all levels of activity
- C) The sales mix changes as total volume increases
- D) Fixed costs rise in steps as output increases
Show answer & explanation
Answer: B) Selling price and variable cost per unit stay constant at all levels of activity
CVP analysis assumes linear relationships: a constant selling price and variable cost per unit, fixed costs that stay the same within the relevant range, a constant sales mix where there is more than one product, and production equal to sales, so there is no change in inventory. These assumptions are also its main limitations.
Question 8
A company sells 20,000 units a year of a product priced at £50. The variable cost is £30 per unit and fixed costs are £150,000. The company plans to cut the price by 10%. How many units must it sell at the new price to earn the same profit as now (to the nearest unit)?
- A) 16,667 units
- B) 22,000 units
- C) 10,000 units
- D) 26,667 units
Show answer & explanation
Answer: D) 26,667 units
Current profit = 20,000 x (£50 - £30) - £150,000 = £250,000. New price = £50 x 0.9 = £45, so the new contribution is £15 per unit. Required units = (£250,000 + £150,000) / £15 = 26,666.67, so 26,667 units must be sold. A 10% price cut needs a 33% increase in volume just to keep profit the same.
Question 9
A company makes three products. Labour is limited to 9,000 hours in the coming period. Product A: contribution £36 per unit, 3 labour hours per unit, maximum demand 1,200 units Product B: contribution £30 per unit, 2 labour hours per unit, maximum demand 2,000 units Product C: contribution £44 per unit, 4 labour hours per unit, maximum demand 1,500 units What is the maximum total contribution the company can earn?
- A) £118,600
- B) £169,200
- C) £115,000
- D) £102,000
Show answer & explanation
Answer: A) £118,600
Contribution per labour hour: A £12; B £15; C £11. Ranking is B, A, C. Production plan: B 2,000 units; A 1,200 units; C 350 units (B uses 4,000 hours, A uses 3,600 hours, leaving 1,400 hours for 350 units of C). Total contribution = £60,000 + £43,200 + £15,400 = £118,600. Ranking by contribution per unit gives only £102,000 because it ignores the scarce resource.
Question 10
A company has demand for 5,000 units of its only product. Each unit needs 2 kg of material and 3 labour hours. Next period 9,000 kg of material and 16,000 labour hours are available. Which of the following is correct?
- A) Both material and labour are limiting factors
- B) Material is a limiting factor, but labour is not
- C) Neither material nor labour is a limiting factor; sales demand is the only limit
- D) Labour is a limiting factor, but material is not
Show answer & explanation
Answer: B) Material is a limiting factor, but labour is not
Material needed = 5,000 x 2 kg = 10,000 kg, but only 9,000 kg are available, so material is a limiting factor (it allows only 4,500 units). Labour needed = 5,000 x 3 = 15,000 hours, which is within the 16,000 hours available. Labour is not a limiting factor.