Contribution margin analysis

Definitions

Contribution margin

The amount by which sales revenue exceeds variable costs. It represents the portion of revenue available to cover fixed costs and generate profit. This margin is calculated on both a per-unit and total basis, providing insight into the profitability of each unit sold and the overall profitability of operations.

Contribution margin is widely used in different types of analyses:

1. Break-even analysis: Determine the sales volume required to cover all fixed costs.
2. Profit planning: Estimate how changes in sales, costs, or prices affect operating income.
3. Decision-making: Evaluate the profitability of products, services, or business segments by focusing on the incremental contribution each makes toward covering fixed costs.
4. Cost-volume-profit (CVP) analysis: Assess the impact of cost structures and sales volumes on profitability.

Unit contribution margin (CM)

The formula for the CM per unit is as follows:

$$\text{CM per unit}=\text{Sales price per unit}-\text{Variable costs per unit}$$

Variable costs per unit include all costs that vary with volume: variable manufacturing costs (direct materials, direct labor, variable overhead) and variable selling and administrative costs such as sales commissions and shipping. This is different from gross margin, which subtracts cost of goods sold (including fixed manufacturing overhead) and ignores selling costs.

Example: GreenLine Furniture

GreenLine budgets sales of 5,000 units at a sales price of $200 per unit.

Variable costs per unit: $48.50, composed of:

• Direct materials: $12
• Direct labor: $30
• Variable overhead: $1.50
• Variable selling costs (sales commission): $5

Item	Per unit amount
Sales price	$200
Variable costs	$48.50
CM per unit	$151.50

Answer: CM per unit = $200 − $48.50 = $151.50

This CM per unit for GreenLine means that every unit sold adds $151.50 toward covering fixed costs. Once fixed costs are fully covered, the same $151.50 per unit contributes directly to profit.

Watch out: Only variable costs are subtracted to find CM per unit. Fixed costs are never part of the CM per unit formula - they’re covered by the contribution margin dollars generated, not deducted from them.

Total contribution margin (CM)

Calculated in two ways, either by multiplying the unit contribution margin by total units sold or by subtracting total variable costs from total sales.

Method 1

$$\text{Total CM}=\text{Total units sold}\times \text{Unit CM}$$

Item	Total amount
Units sold (from sales budget)	5,000
CM per unit	$151.50
Total contribution margin (CM)	$757,500

Method 2

$$\text{Total CM}=\text{Total sales}-\text{Total variable costs}$$

Item	Per unit amount	Units sold	Total amount
Sales revenue	$200	5,000	$1,000,000
Variable costs	$48.50	5,000	($242,500)
Contribution margin (CM)	$151.50		$757,500

The $757,500 represents the pool of funds generated by GreenLine’s sales that can be applied to covering fixed costs and then contributing to profit:

• If total fixed costs are less than $757,500, the excess becomes operating profit.
• If total fixed costs are greater than $757,500, the company would report a loss equal to the difference.

Contribution margin (CM) ratio

The CM ratio expresses contribution margin as a percentage of sales rather than as a dollar amount, which makes it easy to apply to any sales forecast without recalculating unit-level figures. It’s calculated as follows:

$$\text{CM ratio}=\frac{\text{Total CM}}{\text{Total sales}}$$

The CM ratio for GreenLine is $757,500 ÷ $1,000,000 = 75.75%. That means 75.75 cents of every sales dollar goes toward covering fixed costs and generating profit.

Because the CM ratio ties sales directly to profit, it’s also useful for projecting operating income straight from a sales forecast:

$$\text{Operating income}=(\text{Total sales}\times \text{CM ratio})-\text{Total fixed costs}$$

For example, if GreenLine expects total fixed costs of $600,000, its projected operating income is ($1,000,000 × 75.75%) − $600,000 = $757,500 − $600,000 = $157,500.

Allocating resources when they’re scarce

Contribution margin also guides resource allocation decisions when a resource such as machine hours or labor hours is limited. In that situation, rank products by CM per unit of the scarce resource, not by CM per unit alone - the product with the highest contribution margin per unit isn’t always the best use of limited capacity.

Example: Ranking products under a labor hour constraint

Product A has a CM of $60 per unit and requires 3 labor hours per unit, for a CM of $20 per labor hour.

Product B has a CM of $40 per unit and requires 1 labor hour per unit, for a CM of $40 per labor hour.

Answer: Even though Product A has the higher CM per unit, Product B is the better use of a limited number of labor hours, since it generates more contribution margin for each hour consumed.

Applying contribution margin to profit planning

Break-even and other CVP tools build directly on CM (break-even units = total fixed costs ÷ CM per unit) and are covered in depth in CMA Part 2, Section C.