7115 · 4.2

Costs, scale of production and break-even analysis — practice questions

Practice and worked examples for 7115 Costs, scale of production and break-even analysis. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

Nova Crafts sells handmade lamps for $48 each. Variable cost is $18 per lamp and fixed costs are $12 000 per month.

(a) Calculate the break-even output in units. (b) The business currently sells 450 lamps per month. Calculate the margin of safety in units and as a percentage.

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(a) Contribution per unit Contribution = $48 −$ 18 = $30 per lamp

Break-even output BE = $12 000 \div$ 30 = 400 units per month

(b) Margin of safety (units) MoS = 450 − 400 = 50 units

Margin of safety (%) MoS% = (50 ÷ 450) × 100 = 11.1% (to 1 d.p.)

The business can afford a fall of 50 units (11.1%) before reaching break-even.

Worked example 2

Using the same data (SP $48, VC$ 18, FC $12 000, contribution $30 per unit):

Calculate the output required to achieve a monthly profit of $3 000.$

Show solution outline

Output for target profit Required contribution = Fixed costs + Target profit = $12 000 +$ 3 000 = $15 000$

Output = $15 000 \div$ 30 = 500 units per month

Check: at 500 units, contribution = 500 × $30 =$ 15 000. After fixed costs ($12 000), profit = $3 000 ✓

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