ACCA Applied Skills · Performance Management

Cost-volume-profit analysis (CVP): formula sheet

Full chapter guide

Key formulas

Contribution per unit: Contribution per unit = Selling price per unit − Variable cost per unit; Variable cost must include all variable costs, such as variable selling costs and variable overheads.
C/S (P/V) ratio: C/S ratio = Contribution ÷ Sales revenue = Contribution per unit ÷ Selling price per unit; Same as the contribution margin ratio and profit-volume ratio. Usually shown as a percentage.
Break-even point in units: Break-even units = Total fixed costs ÷ Contribution per unit; Round up to the next whole unit if the answer is not whole, as you cannot sell part of a unit and still break even.
Break-even point in sales revenue: Break-even revenue = Total fixed costs ÷ C/S ratio = Break-even units × Selling price; Both routes give the same answer.
Equation approach: Sales − Variable costs − Fixed costs = Profit; set Profit = 0 and solve for units; Useful when the question gives costs in a mixed form.
Units for a target profit: Required units = (Fixed costs + Target profit) ÷ Contribution per unit; Same logic as break-even, with target profit added to the fixed costs.
Contribution per unit: Selling price per unit − variable cost per unit; Use all variable costs, including variable selling costs.
C/S ratio (contribution to sales ratio): Contribution ÷ Sales revenue; Also called the PV ratio. Can use unit figures or totals.
Break-even point: Fixed costs ÷ contribution per unit (units); Fixed costs ÷ C/S ratio (revenue); Round units up to a whole unit if the question needs whole units.
Margin of safety: Budgeted sales − break-even sales; Works in units or revenue. Keep the same measure for both figures.
Margin of safety percentage: (Budgeted sales − break-even sales) ÷ budgeted sales × 100%; The denominator is budgeted sales, not break-even sales.
Sales for target profit: (Fixed costs + target profit) ÷ contribution per unit (units); (Fixed costs + target profit) ÷ C/S ratio (revenue); Target profit must be before tax.
Pre-tax profit from after-tax target: After-tax profit ÷ (1 − tax rate); Assumes tax is a flat rate on profit.
Contribution per unit: Selling price per unit − variable cost per unit; This is the gradient of the PV chart line when volume is in units.
Break-even point (units): Fixed costs ÷ contribution per unit; Where total revenue equals total cost, and where the PV line crosses zero.
C/S ratio: Contribution ÷ sales revenue; Gradient of the PV chart when the horizontal axis is sales value.
Break-even point (sales value): Fixed costs ÷ C/S ratio; Use when volume is measured in sales value.
Margin of safety (units): Budgeted sales units − break-even sales units; The horizontal distance between budget and break-even on the chart.
Margin of safety (%): (Budgeted sales − break-even sales) ÷ budgeted sales × 100; Express as a percentage of budgeted sales.
Profit at any volume: Units × contribution per unit − fixed costs; Read from the PV chart as the vertical distance from the axis to the line.
PV chart intercept: Vertical axis intercept = −fixed costs; At zero volume the loss equals fixed costs.
Package contribution: Σ (units of each product in the mix × contribution per unit); Use the mix ratio as the number of units of each product in one package.
Weighted average contribution per unit: Package contribution ÷ total units in the package; Equivalent to weighting each product's unit contribution by its share of total units.
Break-even packages: Fixed costs ÷ package contribution; Multiply by each product's units per package to get break-even units by product.
Break-even units (total): Fixed costs ÷ weighted average contribution per unit; Split between products using the mix ratio.
Weighted average C/S ratio: Package contribution ÷ package sales revenue; Break-even revenue = fixed costs ÷ weighted average C/S ratio.
Target profit: (Fixed costs + target profit) ÷ package contribution = packages required; Same method as break-even with the target added to fixed costs.
Contribution per unit: Selling price per unit − variable cost per unit; Constant per unit under the CVP assumptions.
Break-even point (units): Total fixed costs ÷ contribution per unit; Valid only within the relevant range and with constant price and variable cost.
Margin of safety (%): (Budgeted sales − break-even sales) ÷ budgeted sales × 100; Shows how far sales can fall before a loss occurs.
Sensitivity of an input (%): Price: profit ÷ total sales revenue × 100. Variable cost: profit ÷ total variable cost × 100. Volume: profit ÷ total contribution × 100. Fixed costs: profit ÷ total fixed costs × 100.; Each form gives the % adverse change in that input that would reduce profit to zero. Use contribution, not sales revenue, for volume. A smaller % means a more sensitive input.
Weighted average contribution per unit: Σ (contribution per unit × mix proportion); Used for multi-product break-even. Break-even changes if the mix changes.

Quick revision

Contribution per unit = selling price − variable cost per unit.
Break-even units = fixed costs ÷ contribution per unit.
Break-even sales value = fixed costs ÷ C/S ratio.
C/S ratio = contribution ÷ sales, which equals contribution per unit ÷ selling price.
Target profit units = (fixed costs + target profit) ÷ contribution per unit.
Margin of safety = budgeted sales − break-even sales, in units, value or as a percentage of budget.
Profit = total contribution − fixed costs.
On a profit-volume chart the line cuts the vertical axis at the fixed cost loss, and crosses the horizontal axis at break-even.
For several products, use a weighted average contribution based on the expected sales mix.
The break-even point for a multi-product firm changes if the sales mix changes.
CVP assumes a single relevant range, constant selling price and variable cost per unit, and fixed costs that stay fixed.
Check whether the question asks for units, sales value or percentage before you answer.

Common mistakes

Leaving out variable selling or packaging costs when calculating contribution. Fix: Read every cost line. Any cost that moves with units sold is variable, wherever it appears.
Including depreciation or allocated overheads in variable cost. Fix: Fixed overhead is never in contribution. Take fixed costs as a total and use them only as the numerator.
Dividing the margin of safety by break-even sales to get the percentage. Fix: Always divide by budgeted (or actual) sales. The percentage shows how far sales can fall from the budget.
Using after-tax profit directly as the target profit. Fix: Check for the word 'after tax'. If present, divide by (1 − tax rate) first.
Starting the total cost line at the origin Fix: Always start total cost at the fixed cost level on the vertical axis. Only the variable cost line (in a contribution chart) starts at the origin.
Starting the PV line at zero instead of −fixed costs Fix: The PV line starts below the axis at the loss equal to fixed costs. It crosses zero at break-even.
Using a simple average of the products' contributions instead of a weighted average. Fix: Always weight by the units in the mix. A mix of 3:2 means weights of 3 and 2, not 1 and 1.
Treating the mix ratio as a ratio of sales revenue when the question gives units, or the reverse. Fix: Check the wording. If the mix is in units, build the package in units. If it is in revenue, use the C/S ratio approach instead.
Listing assumptions without applying them to the scenario. Fix: For each point, add one sentence linking it to the business in the question and its effect on break-even.
Changing price and treating variable cost as changed too. Fix: Change one input at a time and write the new contribution per unit before anything else.

Exam tips

In Section A and OT cases, break-even questions are all or nothing, so check that your units match what is asked: units or revenue.
Read cost lists slowly and mark each as variable or fixed before any arithmetic.
In Section C, show contribution per unit and the formula on separate lines, so you can earn method marks even if a figure is wrong.
Do the check line (units × contribution = fixed costs). It takes seconds and catches most errors.
Expect break-even to be a stepping stone: later parts often ask for margin of safety, target profit or the effect of a price or cost change.
In Section A and OT cases, read for 'after tax', 'units' versus 'revenue', and 'percentage'. Many wrong answers come from missing one of these words.
Choose the right base for the percentage: the margin of safety is a percentage of budgeted sales.
In Section C, show each step: contribution, fixed costs plus target, then the answer. Method marks are available even if arithmetic slips.