Cost-Volume-Profit and Break-Even Analysis
CVP and break-even analysis tests your ability to convert cost behaviour into contribution, break-even, target profit and margin of safety, and to explain operating leverage. Questions often combine a single-product calculation with a multi-product sales-mix extension.
Core rules
- Contribution per unit = selling price - variable cost per unit. Contribution-to-sales ratio = contribution / sales.
- Break-even units = fixed costs / contribution per unit. Break-even revenue = fixed costs / C/S ratio.
- Target profit units = (fixed costs + target profit) / contribution per unit.
- Margin of safety = budgeted sales - break-even sales. As a percentage, divide by budgeted sales.
- For multiple products, use weighted average contribution per unit or per sales mix; a change in mix changes break-even.
Worked example
A product sells for ₦50, variable cost is ₦30 and fixed costs are ₦100,000. Contribution is ₦20 per unit, so break-even is 100,000/20=5,000 units, or ₦250,000 revenue. At budgeted sales of 6,500 units, margin of safety is 1,500 units, or 1,500/6,500=23.08%. To earn ₦40,000 target profit, required units = (100,000+40,000)/20=7,000 units. The reasoning: each unit contributes ₦20 first to fixed costs, then to profit; the C/S ratio of 40% gives the same revenue break-even.
Traps
Using gross profit instead of contribution; deducting fixed costs per unit; applying a single-product break-even to a changing mix; using actual instead of budgeted sales for margin of safety; ignoring the relevant range.