CVP and breakeven analysis, worked through a coffee roastery
Cost-volume-profit analysis finds the exact sales level where a business stops losing money and starts making it. Here it is worked through Alma Roasters, from contribution per bag to the margin of safety, with every figure reconciled.
Cost-volume-profit (CVP) analysis answers one question a business owner actually loses sleep over: how much do I need to sell before I stop making a loss? The sales level where total revenue exactly covers total cost is the breakeven point, and everything else in CVP, the margin of safety, the target-profit calculation, the profit at any volume, is built on the same single idea. That idea is contribution, and once it clicks the whole topic becomes arithmetic rather than memory.
CVP is one of the most reliably examined areas of the ACCA MA exam, and it rewards students who can work the numbers quickly and explain what they mean. The cleanest way to see it is through a business with real figures, so meet Mateo Reyes at Alma Roasters again.
Alma Roasters: the figures
Mateo sells bags of roasted coffee. Here is the cost and price information for a typical month:
| Item | Amount |
|---|---|
| Selling price | £9.00 per bag |
| Direct materials (green beans) | £2.40 per bag |
| Direct labour | £1.20 per bag |
| Variable production overhead | £0.90 per bag |
| Fixed costs (rent, insurance, the roaster lease) | £3,000 for the month |
The variable cost of one bag is £2.40 + £1.20 + £0.90 = £4.50. That is the cost that goes up with every extra bag Mateo makes and sells. The £3,000 of fixed cost does not move with volume: it is the same whether he sells one bag or ten thousand. Splitting costs into fixed and variable like this is the groundwork CVP depends on, and where a cost is a mix of the two you separate it first, often with the high-low method.
Contribution: the one idea CVP is built on
Contribution is what one sale adds once its own variable cost is paid, before any fixed cost is considered. For Mateo:
Contribution per bag = selling price − variable cost = £9.00 − £4.50 = £4.50.
Every bag sold throws £4.50 into a pot. That pot first has to fill the £3,000 hole of fixed cost; once it does, every further £4.50 is profit. That is the whole model. It is also worth knowing the contribution as a fraction of the selling price, called the contribution to sales (or C/S) ratio, because it lets you work in pounds of revenue rather than units:
C/S ratio = contribution ÷ selling price = £4.50 ÷ £9.00 = 0.5, or 50%.
The breakeven point
Breakeven is the volume where total contribution exactly equals fixed cost, so profit is zero. In units:
Breakeven (units) = fixed cost ÷ contribution per unit = £3,000 ÷ £4.50 = 666.7 bags.
You cannot sell seven tenths of a bag, and 666 bags leaves £1.50 of fixed cost uncovered, so you always round a breakeven point up to the next whole unit: 667 bags. To get breakeven as a revenue figure, the C/S ratio is quicker than converting units:
Breakeven (revenue) = fixed cost ÷ C/S ratio = £3,000 ÷ 0.5 = £6,000.
Profit at any volume
Once you have contribution and fixed cost, the profit at any sales level is a single line: total contribution minus fixed cost. Here is Mateo's month at several volumes, including the one where he actually sold 1,600 bags:
| Bags sold | Contribution (× £4.50) | Less fixed cost | Profit / (loss) |
|---|---|---|---|
| 0 | £0 | (£3,000) | (£3,000) |
| 667 (breakeven) | £3,002 | (£3,000) | £0 |
| 1,000 | £4,500 | (£3,000) | £1,500 |
| 1,600 | £7,200 | (£3,000) | £4,200 |
| 2,000 | £9,000 | (£3,000) | £6,000 |
The £4,200 profit at 1,600 bags is worth pausing on: it is exactly the profit Alma Roasters reports under marginal costing in the same month, because marginal costing and CVP are the same contribution-based view of the business wearing different hats.
Target profit
Breakeven is just the special case of a target profit of zero. To hit any profit target, add it to the fixed cost the pot has to fill:
Units for target profit = (fixed cost + target profit) ÷ contribution per unit.
Say Mateo wants to make £6,000 in a month. He needs (£3,000 + £6,000) ÷ £4.50 = £9,000 ÷ £4.50 = 2,000 bags, which at £9.00 each is £18,000 of revenue. That gives him a concrete sales goal rather than a vague hope, which is exactly the point of the technique.
Margin of safety
The margin of safety says how far sales can fall before the business drops into a loss. It is the gap between planned sales and the breakeven point. Using the month Mateo sold 1,600 bags against a breakeven of 667:
Margin of safety (units) = 1,600 − 667 = 933 bags.
Margin of safety (%) = 933 ÷ 1,600 = 58%.
In plain terms, sales could fall by more than half before Alma Roasters stopped making a profit. A high margin of safety is comfort; a thin one is a warning that a small dip in demand tips the business into a loss, which is a genuinely useful thing for Mateo to know before he signs a bigger lease.
The assumptions CVP rests on
CVP is a model, and the exam likes to test whether you know where the model stops being reliable. It assumes selling price per unit is constant at every volume, variable cost per unit is constant, fixed costs stay fixed across the range you are looking at (the relevant range), and that everything produced is sold so inventory does not muddy the picture. For a business selling more than one product it also assumes the sales mix stays constant. In the real world a big customer negotiates a discount, or a supplier raises bean prices, and the straight lines bend. Knowing that is the difference between using CVP well and trusting it blindly.
Frequently asked questions
What is CVP analysis in ACCA MA?
Cost-volume-profit analysis studies how profit changes as sales volume changes, by separating costs into fixed and variable and focusing on contribution (selling price minus variable cost per unit). It is used to find the breakeven point, the sales needed for a target profit, and the margin of safety.
How do you calculate the breakeven point?
Divide total fixed costs by the contribution per unit to get breakeven in units, and always round up to the next whole unit. To get breakeven in revenue, divide fixed costs by the contribution to sales (C/S) ratio instead.
What is the margin of safety?
The margin of safety is the amount by which planned or actual sales exceed the breakeven point, shown in units, in revenue, or as a percentage of sales. It measures how far sales can fall before the business makes a loss.
What is the contribution to sales (C/S) ratio?
The C/S ratio is contribution divided by selling price, expressed as a percentage. It tells you how much of every pound of sales becomes contribution, and it lets you calculate breakeven and target-profit figures directly in revenue rather than in units.