# Contribution Margin Ratio

Contribution margin ratio is the ratio of contribution margin to sales. It is calculated by dividing the excess of sales over variable costs with sales. CM ratio is used to calculate break-even point.

Contribution margin (CM) ratio is an important input in calculation of break-even point, which is the level of sales (in units or dollars) at which a business is neither making profit nor incurring loss. It is the point at which a company breaks even, i.e. its total costs equal total sales.

Breakeven point in dollars equals total fixed costs divided by contribution margin ratio and breakeven point in units of sales equals total fixed costs by contribution margin per unit.

## Formula

Contribution margin ratio can be worked out using either of the following formula:

$$ \text{Contribution Margin Ratio}\ =\ \frac{\text{Contribution Margin}}{\text{Sales}} $$

$$ \text{Contribution Margin Ratio}\ =\ \frac{\text{Sales}\ -\ \text{Total Variable Cost}}{\text{Sales}} $$

Contribution margin ratio can also be calculated using per-unit figures:

$$ \text{Contribution Margin Ratio}\ =\ \frac{\text{Sales Price}\ -\ \text{Variable Cost per Unit}}{\text{Sales Price}} $$

If a company has more than one product, contribution margin ratio depends on the its sales mix:

$$ \text{Contribution Margin Ratio}\ =\ \frac{{\rm \text{CM}} _ \text{1}\ +\ {\rm \text{CM}} _ \text{2}\ +\text{...}+{\rm \text{CM}} _ \text{n}}{\text{Total Sales}} $$

## Example

Jump, Inc. is a footwear company which has three main products: one for cricket players, one for football players and one for tennis players. Following table shows the sales price, variable cost per unit and units sold of each product:

Cricket | Football | Tennis | |
---|---|---|---|

Price per unit | $80 | $100 | $150 |

Variable cost per unit | $40 | $75 | $95 |

Units sold | 200,000 | 50,000 | 5,000 |

*Calculate the separate contribution margin ratio for each product and the weighted-average contribution margin ratio of the company as a whole. If the company’s fixed costs are $2,200,000 per annum, calculate the breakeven distribution of products.*

**Solution**

Contribution margin ratio = (sales price – variable cost per unit)/sales price

Contribution margin ratio (cricket) = ($80 - $40)/$80 = 50%

Contribution margin ratio (football) = ($100 - $75)/$100 = 25%

Contribution margin ratio (tennis) = ($150 - $95)/$150 = 37%

In order to calculate weighted-average contribution margin ratio, we need some intermediate figures worked out in the following table, such as total sales and proportion of each product in the sales mix:

Units sold | Sales Price | Total Sales | Variable Cost per Unit | Contribution Margin per Unit | Total Contribution Margin | |
---|---|---|---|---|---|---|

Cricket | 200,000 | 80 | 16,000,000 | 40 | 40 | 8,000,000 |

Football | 50,000 | 100 | 5,000,000 | 75 | 25 | 1,250,000 |

Tennis | 5,000 | 150 | 750,000 | 95 | 55 | 275,000 |

255,000 | 21,750,000 | 9,525,000 |

$$ \text{Weighted average CM ratio}\\= \frac{\text{Total Contribution Margin}}{\text{Total Sales}}\\=\frac{\text{\$9,525,000}}{\text{\$21,750,000}}\\=\text{43.8%} $$

The weighted-average contribution margin can be used to calculate the composite break-even point:

$$ \text{Breakeven Point}=\frac{\text{FC}}{\text{CM Ratio}}=\frac{\text{\$2,200,000}}{\text{43.8%}}=\text{\$5,023,622} $$

Breakeven sales required for each product depends on the proportion of each product in the sales mix:

Sales | % in Sales | Breakeven Sales | Breakeven Units | |
---|---|---|---|---|

Cricket | 16,000,000 | 73.56% | 3,695,538 | 46,194 |

Football | 5,000,000 | 22.99% | 1,154,856 | 11,549 |

Tennis | 750,000 | 3.45% | 173,228 | 1,155 |

21,750,000 | 5,023,622 | 58,898 |

Proportion in sales of each product is worked by dividing the product sales by total sales, i.e. $16,000,000 divided by $21,750,000 equals 73.56%.

Breakeven sales level (in dollars) for each product is calculated by multiplying total breakeven sales with the proportion (weight) of each product in total sales, i.e. 73.56% of $5,023,622 equals $3,695,538, etc.

Breakeven sales level (in units) for each product equals the product breakeven sales divided by its price, i.e. $3,695,538 divided by $80 works out to 46,194 units of cricket shoes.

Total breakeven units can also be calculated by dividing total fixed costs by weighted average contribution margin per unit, which is calculated as follows:

% in units | Contribution Margin per Unit | |
---|---|---|

Cricket | 78% | 40 |

Football | 20% | 25 |

Tennis | 2% | 55 |

Weighted average contribution margin per unit

= 78% × $40 + 20% × $25 + 2% × $55

= $37.35

Weighted average breakeven units

= $2,200,000/$37.35

= 58,898

Please note that the breakeven units calculated under both the methods are the same. The breakeven analysis can be complemented by margin of safety analysis.

by Obaidullah Jan, ACA, CFA and last modified on

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