🔢 Break-even output formula
The Formula: Break-even output = Fixed costs ÷ Contribution per unit
Where contribution per unit = selling price − variable cost per unit
Worked example
A business has fixed costs of $20 000. It sells each product for $50 and the variable cost per unit is $30.
- Contribution per unit = $50 − $30 = $20
- Break-even output = $20 000 ÷ $20 = 1000 units
- The business must sell 1000 units to cover all its costs
Always show your working! Even if you get the final number wrong, you can still earn method marks. ✍️
🛡️ Margin of safety
The Formula: Margin of safety = Actual (or estimated) sales − Break-even output
The margin of safety tells you how far sales can drop before the business starts making a loss. A bigger margin = more safety!
Worked example
- Break-even output = 1000 units
- Actual sales = 1500 units
- Margin of safety = 1500 − 1000 = 500 units
- Sales could drop by 500 units before the business makes a loss
A small margin of safety is risky — a small drop in sales could push the business into a loss. A large margin of safety means the business has a comfortable buffer.
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💵 Calculating profit and loss
The Formula: Profit (or loss) = Total revenue − Total costs
OR: Profit = Total contribution − Fixed costs
Worked example
A business sells 1500 units at $50 each. Variable cost per unit is $30. Fixed costs are $20 000.
- Total revenue = 1500 × $50 = $75 000
- Total variable costs = 1500 × $30 = $45 000
- Total costs = $45 000 + $20 000 = $65 000
- Profit = $75 000 − $65 000 = $10 000
Shortcut method: Contribution per unit ($20) × units sold (1500) = $30 000 total contribution. Minus fixed costs ($20 000) = $10 000 profit. Same answer, fewer steps!
🎯 Target profit and target price
Finding output needed for a target profit
The Formula: Output for target profit = (Fixed costs + Target profit) ÷ Contribution per unit
- Fixed costs = $20 000, target profit = $10 000, contribution = $20
- Output needed = ($20 000 + $10 000) ÷ $20 = 1500 units
Finding the price needed for a target profit
Sometimes a business knows how many units it expects to sell and wants to know what price to charge to reach a certain profit.
- Total costs + target profit = required total revenue
- Required price = required total revenue ÷ number of units
- This type of question tests your ability to work backwards from a profit target
Exam tip: Target price questions are tricky — read carefully, identify what you know and what you need to find, then work step by step.