How to approach it
- Get units and cost per unit for each product from the current results.
- Project next year product by product: new price, new volume (including units made with freed hours), new unit costs.
- Total contribution ÷ total sales = weighted C/S ratio; break-even sales = fixed costs ÷ C/S ratio.
- Margin of safety % = (budgeted sales − break-even sales) ÷ budgeted sales.
Key rules to apply
- Multi-product break-even assumes a constant sales mix.
- Labour hours freed from one product can be used for another only if the question says so; convert hours into units with hours per unit.
Common mistakes
Drawn from the examiners' comments for this sitting (summarised in our words) and from typical errors on this topic.
- Changing prices but forgetting the volume changes, or the knock-on effect on variable costs (examiners' point).
- Margin of safety computed as break-even ÷ budget.
Similar question with worked solution
Written by us with our own numbers; it tests the same skills as Q4 without copying it.
Original practice question
Break-even after a price change
Product P: 10,000 units at Rs 80, variable cost Rs 50, 2 hours per unit. Product Q: 8,000 units at Rs 100, variable cost Rs 70, 2 hours per unit. Fixed costs Rs 400,000.
Next year Q's price rises 10% and its volume falls 5%; the hours freed are used to make more P. Costs are unchanged.
Required: Calculate next year's break-even sales and margin of safety.
Worked solution
| Product | Units | Sales (Rs) | Contribution (Rs) |
|---|---|---|---|
| Q: 7,600 × 110 / × 40 | 7,600 | 836,000 | 304,000 |
| P: 10,000 + 800 h ÷ 2 = 10,400 | 10,400 | 832,000 | 312,000 |
| Total | 1,668,000 | 616,000 |
C/S ratio = 616,000 ÷ 1,668,000 = 36.93%. Break-even = 400,000 ÷ 0.3693 = Rs 1,083,117.
Answer: Break-even ≈ Rs 1.08m; margin of safety = (1,668,000 − 1,083,117) ÷ 1,668,000 ≈ 35.1%.