By Yuriy Smirnov Ph.D.

The contribution margin (CM) is an accounting concept used in cost-volume-profit analysis to estimate the profitability of a specific product or service. It can be defined as per unit amount, total amount, ratio, or percentage.

This concept is very useful in various management decisions.

- When it is necessary to decide whether or not to sell additional products at a lower price.
- It helps to evaluate profitability at various level of business activity.
- The concept can be used to select the most profitable products. If a business is able to produce a variety of products but does not have enough resources to produce them all, products with a higher contribution margin are preferable.

The per unit amount is the difference between the sales price of a unit and the variable cost per unit.

Contribution Margin per Unit = Price per Unit - Variable Cost per Unit

The total contribution margin is the difference between sales and total variable costs.

Total Contribution Margin = Sales - Variable Costs

In other words, it is an amount by which sales exceed the total variable costs of a business.

The contribution margin ratio can be calculated by using either of the two formulas below.

Contribution Margin Ratio = | Sales - Variable Costs |

Sales |

or

Contribution Margin Ratio = | Price per Unit - Variable Costs per Unit |

Price per Unit |

The formulas above can be written as follows:

Contribution Margin Ratio = | Total Contribution Margin |

Sales |

or

Contribution Margin Ratio = | Contribution Margin per Unit |

Price per Unit |

Please note that the contribution margin ratio can also be expressed as a percentage.

The relationship between total contribution margin and sales level is shown in the graph below.

As far as sales revenue and total variable costs are in direct proportion with the level of business activity, the value of the total contribution margin is rising as sales increase.

In contrast, the contribution margin per unit remains constant at any level of business activity until any change in sales price and/or variable cost per unit. Its behavior is shown in the graph below.

However, the contribution margin can also have a negative value in some special situations, which means that sales revenue generated by a specific product does not even cover the variable costs incurred to manufacture it. If the special situation continues, a business should stop manufacuring and selling such a product.

Xander Fashion LLC is a clothing store with four main products. The data for sales price, variable cost per unit, and number of units sold in the last quarter are shown in the table below.

Let’s perform a contribution margin analysis using the formulas mentioned above.

CM per Unit _{Jeans} = $85 - $50 = $35

CM per Unit _{Pants} = $50 - $25 = $25

CM per Unit _{T-Shirts} = $45 - $30 = $15

CM per Unit _{Sweaters} = $90 - $60 = $30

Sales _{Jeans} = $85 × 2,500 = $212,500

Sales _{Pants} = $50 × 1,700 = $85,000

Sales _{T-Shirts} = $45 × 3,250 = $146,250

Sales _{Sweaters} = $90 × 1,300 = $117,000

Total Variable Costs _{Jeans} = $50 × 2,500 = $125,000

Total Variable Costs _{Pants} = $25 × 1,700 = $42,500

Total Variable Costs _{T-Shirts} = $30 × 3,250 = $97,500

Total Variable Costs _{Sweaters} = $60 × 1,300 = $78,000

Total CM _{Jeans} = $212,500 - $125,000 = $87,500

Total CM _{Pants} = $85,000 - $42,500 = $42,500

Total CM _{T-Shirts} = $146,250 - $97,500 = $48,750

Total CM _{Sweaters} = $117,000 - $78,000 = $39,000

CM Ratio _{Jeans} = $87,500 ÷ $212,500 = 0.412 or 41.2%

CM Ratio _{Pants} = $42,500 ÷ $85,000 = 0.500 or 50.0%

CM Ratio _{T-Shirts} = $48,750 ÷ $146,250 = 0.333 or 33.3%

CM Ratio _{Sweaters} = $39,000 ÷ $117,000 = 0.333 or 33.3%

The results of contribution margin analysis are summarized in the table below.

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