ACCA PM: C/S ratio for single and multi-product CVP
The contribution to sales (C/S) ratio shows how much of each $1 of sales revenue is left to cover fixed costs and then create profit. The examiner likes it because one ratio gives break-even revenue, profit and margin of safety quickly, and because candidates often mix it up with the variable cost ratio.
The rule
C/S ratio = contribution ÷ sales revenue, which for one product is also contribution per unit ÷ selling price. Break-even revenue = fixed costs ÷ C/S ratio. For several products, use the combined C/S ratio = total contribution ÷ total sales revenue, calculated at the expected sales mix. If the mix shifts towards products with a lower C/S ratio, the combined ratio falls, break-even revenue rises and profit falls, even when total revenue is unchanged.
Worked example
A firm sells two products with a budgeted mix of sales revenue.
X: sales $60,000, variable costs $30,000, contribution $30,000 (C/S 50%)
Y: sales $40,000, variable costs $30,000, contribution $10,000 (C/S 25%)
Fixed costs: $24,000
Combined C/S ratio = $40,000 ÷ $100,000 = 40%
Break-even revenue = $24,000 ÷ 0.40 = $60,000
Profit = ($100,000 × 0.40) − $24,000 = $16,000
Now the mix moves to $40,000 of X and $60,000 of Y. Contribution = $20,000 + $15,000 = $35,000, so the combined C/S ratio = 35%.
Break-even revenue = $24,000 ÷ 0.35 = $68,571
Profit = $35,000 − $24,000 = $11,000
Total sales are the same, but profit has fallen by $5,000.
Remember: the C/S ratio is contribution ÷ sales, not variable cost ÷ sales, and a change in sales mix changes the combined ratio even when total revenue is on budget.
Where candidates lose marks
Using the variable cost ratio as the C/S ratio, for example 15/25 = 60% instead of 10/25 = 40%.
Multiplying fixed costs by the C/S ratio instead of dividing, or dividing fixed costs by the selling price and getting units instead of revenue.
Assuming profit depends only on total revenue and ignoring that a shift to a lower C/S product reduces contribution.
Try it: 4 questions
Fit4All Co sells a membership pack at $50 per unit. Its break-even sales revenue is $400,000 and fixed costs are $140,000. Which TWO of the following statements are correct?
Select the two that apply (each shows on its own).
Answer: B, E. Break-even revenue = fixed costs ÷ C/S ratio, so C/S ratio = $140,000 ÷ $400,000 = 35%. Contribution per unit = 35% × $50 = $17.50, and variable cost per unit = $50 − $17.50 = $32.50. So the variable cost is 65% of selling price. The other options are wrong: 65% is the variable cost ratio, not the C/S ratio. 2,800 units comes from dividing fixed costs by the selling price, while break-even units are $400,000 ÷ $50 = 8,000. $17.50 is the contribution per unit, not the variable cost, so treating 35% as the variable cost ratio is the error.
Alpine Dairy Co-op sells two products. Budgeted sales are $700,000 at a combined C/S ratio of 35%, and fixed costs are $140,000. Actual sales revenue was exactly $700,000 and fixed costs were as budgeted, but the sales mix moved towards the lower C/S product, giving an actual combined C/S ratio of 32%. Which of the following is the correct interpretation?
Answer: A. Budget: break-even revenue = $140,000 / 0.35 = $400,000; profit = $700,000 x 0.35 - $140,000 = $245,000 - $140,000 = $105,000. Actual: break-even revenue = $140,000 / 0.32 = $437,500; profit = $700,000 x 0.32 - $140,000 = $224,000 - $140,000 = $84,000. The same revenue produces less contribution because more of it comes from the product with the lower C/S ratio. Each $1 of sales contributes less towards fixed costs, so more sales are needed to break even and the margin of safety falls from $300,000 to $262,500. Why the others are wrong: Option B and Option C assume profit depends only on revenue, ignoring the mix. Option D keeps break-even at $400,000, but break-even revenue depends on the C/S ratio, so it must rise when the ratio falls.
A trainee accountant at Harbour Craft Co, a boat builder, prepared this working for a fitting with a selling price of $25 and a variable cost of $15. Fixed costs are $80,000. Working: 'C/S ratio = 15/25 = 60%. Break-even revenue = $80,000 / 0.60 = $133,333.' Which of the following correctly identifies the error and gives the correct break-even sales revenue?
Answer: A. The C/S ratio = contribution / sales = ($25 - $15) / $25 = 10/25 = 40%. The trainee divided the variable cost ($15) by the price, which gives the variable cost ratio of 60%. Break-even revenue = $80,000 / 0.40 = $200,000. Why the others are wrong: Option B finds the right ratio but gives the answer in units (80,000 / $10 = 8,000 units), whereas the C/S method gives revenue. Option C accepts the 60% as the C/S ratio. Option D multiplies fixed costs by the C/S ratio ($80,000 x 0.40) instead of dividing.
Pixel Forge Co, a mobile game studio, sells one in-game bundle. The bundle has a contribution to sales (C/S) ratio of 30%, fixed costs are $90,000 and current sales revenue is $400,000. Management proposes cutting the selling price by 10%. Variable cost per unit and total fixed costs would not change. Which of the following correctly shows the new C/S ratio and the new break-even sales revenue?
Answer: A. Break-even revenue = fixed costs / C/S ratio. Take an original price of $100: variable cost is $70 and contribution is $30. After a 10% price cut the price is $90, variable cost is still $70, and contribution falls to $20. New C/S = 20/90 = 22.2%. New break-even revenue = $90,000 / 0.2222 = $405,000 (up from $90,000 / 0.30 = $300,000). Because the whole price cut comes out of contribution, the C/S ratio falls by much more than 10%. Why the others are wrong: Option B treats the C/S ratio as falling by 10 percentage points to 20%, which ignores that the lower price also shrinks the denominator. Option C reduces 30% by 10% proportionally (30% x 0.9), which is not how the ratio is built. Option D keeps the contribution per unit at $30, but the price cut reduces it to $20, and the 33.3% result would be a rise in C/S, not a fall.
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Divide contribution by sales revenue, using either totals or per-unit figures. For example, a $25 price with a $15 variable cost gives $10 ÷ $25 = 40%.
How do you find break-even revenue using the C/S ratio?
Divide fixed costs by the C/S ratio. With fixed costs of $80,000 and a 40% ratio, break-even revenue is $80,000 ÷ 0.40 = $200,000.
How do you calculate the C/S ratio for a multi-product business?
Add up total contribution from all products and divide by total sales revenue at the given sales mix. This is the combined (weighted average) C/S ratio, and it changes whenever the mix changes.