# Contribution Margin

Contribution margin (CM) is the amount by which a product's sales exceeds its variable costs. It is the net amount available to cover the fixed costs and target profit. It is expressed either as total contribution margin, contribution margin per unit or contribution margin ratio.

Variable costs are costs which vary directly with sales. For example, if sales double, variable costs double too, and vice versa. Variable cost may be direct as well as indirect. Direct variable costs include direct material cost and direct labor cost. Indirect variable costs include certain variable overheads.

Contribution margin income statement, the output of the variable costing is useful in making cost-volume-profit decisions. It is an important input in calculation of breakeven point, i.e. the sales level (in units and/or dollars) at which a company makes zero profit. Breakeven point (in units) equals total fixed costs divided by contribution margin per unit and breakeven point (in dollars) equals total fixed costs divided by contribution margin ratio.

## Formula

Total contribution margin (TCM) is calculated by subtracting total variable costs from total sales.

Total Contribution Margin = Sales - Total Variable Costs

Contribution margin per unit equals sales price per unit P minus variable costs per unit V. It can be calculated by dividing total contribution margin CM by total units sold Q.

$$\text{Contribution Margin per Unit}\ =\ \frac{\text{Total Contribution Margin}}{\text{Quantity}}=\text{P}\ -\ \text{V}$$

When the sales price is higher than the variable cost per unit, the contribution margin per unit is positive and increasing sales would result in increase in profit but if the sales price is less than the variable cost per unit, the contribution margin per unit is negative, and additional sales would result in reduction in profit.

Contribution margin ratio equals contribution margin per unit as a percentage of price or total contribution margin TCM expressed as a percentage of sales S.

$$\text{Contribution Margin Ratio}\ =\frac{\text{Contribution Margin per Unit}}{\text{Price}}=\frac{\text{TCM}}{\text{S}}$$

Weighted average contribution margin per unit equals the sum of contribution margins of all products divided by total units. Weighted average contribution margin ratio equals the sum of contribution margins of all products divided by total sales.

## Example: contribution margin and break-even point

Jump, Inc. is a sports footwear startup which currently sells just one shoe brand, A. The sales price is $80, variable costs per unit is$50 and fixed costs are $2,400,000 per annum (25% of the which are manufacturing overhead costs) . During financial year 2015, the company sold 200,000 units. Calculate the company’s contribution margin for the period and calculate its breakeven point in both units and dollars. ### Solution Contribution margin per unit = Sales price – Variable cost per unit =$80 – $50 =$30

Total contribution margin
= Total sales – Total variable costs
= Units sold × Sales price – Units sold × Variable cost per unit
= Units sold × (Sales price – Variable cost per unit)
= $80 × 200,000 -$50 × 200,000
= 200,000 × ($80 -$50)
= $6,000,000 Total contribution margin can also be calculated as follows: Total contribution margin = Contribution margin per unit × Unit sales =$30 × 200,000 = $6,000,000 Breakeven point in units = Fixed costs/Contribution margin per unit =$2,400,000/$30 = 80,000 units Breakeven point in dollars = Breakeven point in units × Sales price = 80,000 ×$80 = $6,400,000 ## Example: contribution margin and target profit You work as a management accountant at Swish, Inc., a company which manufactures three types of sports shoes: Tennis, Football and Baseball. Your CFO has asked you to find out the increase in total revenue if total units sold for each type increases by 10,000 units. You have the following data: • Tennis: sales price is$200, and it costs $130 to produce one unit. • Football: the contribution margin ratio of Football shoes is 40% and its sales price is$250.
• Baseball: Total sales of baseball shoes are $20 million, total associated variable costs are$11 million and total units sold are 75,000.

### Solution

You need to work out the contribution margin per unit, the increase in profit if there is a one unit increase in sales.

The contribution margin for Tennis shoes is easiest to calculate: it equals $70, i.e. the difference between sales price ($200) and variable cost per unit ($130). We need to use the contribution margin ratio formula to work out contribution per unit for Football shoes: Contribution Margin per Unit (Football) = Contribution Margin Ratio × Sales Price = 40% ×$250
= $100 Contribution Margin per Unit (Baseball) = Total Contribution Margin ÷ Total Units = ($20 million − $11 million) ÷ 75,000 =$120

Knowing the contribution margin per unit for each product, we can determine total increase in profit if there is a 10,000 increase in sales of each type of shoes:

Increase in Profit
= 10,000 × ($70 +$100 + $120) =$2.9 million