# Contribution Margin per Unit

Contribution margin per unit is the net amount that each additional unit sold contributes towards a company’s fixed costs and profit. It equals the difference between the product’s sales price and variable cost per unit.

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 per unit is an important intermediate input in cost-volume-profit (CVP) analysis. Break-even point in units is calculated by dividing total fixed costs with contribution margin per unit. Similarly, contribution margin ratio is calculated by dividing the contribution margin per unit with sales price. Total contribution margin equals the product of contribution margin per unit and total units. Contribution margin per unit also features in standard costing and variance analysis where it is used to find out sales mix variances.

While total contribution margin changes with change in output, contribution margin per unit remains constant. It is because one of the assumptions of (CVP) analysis is that the price and variable cost per unit remains constant.

## Formula

Contribution margin per unit can be calculated by subtracting the variable cost per unit from sales price:

Contribution Margin per Unit = Sales Price – Variable Cost per Unit

The cost-volume-profit relationship can be expressed in terms of contribution margin per unit using the following equation:

Operating Profit = Contribution Margin per Unit × Total Units – Fixed Costs

## Example

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