# Contribution Margin Ratio

Contribution margin ratio equals contribution margin expressed as a percentage of total sales. Contribution margin is the amount by which sales revenue exceeds total variable costs. It calculates what percentage of sales revenue is available to cover the fixed costs of a business and yield a profit.

Contribution margin (CM) ratio is an important input in calculation of breakeven point, which is the level of sales (in units or dollars) needed to cover all the costs of a business (fixed costs and variable costs). It is the point at which a company breaks even, i.e. neither makes profit nor loss. Breakeven amount of sales equals total fixed costs divided by contribution margin ratio while breakeven units of sales can be calculated by dividing total fixed costs by contribution margin per unit.

## Formula

Contribution margin ratio can be calculated from total contribution margin or from contribution margin per unit using any of the following two formulas:

Contribution Margin Ratio = | Total Contribution Margin |

Total Sales |

Contribution Margin Ratio = | Contribution Margin per Unit |

Sales Price |

Since contribution margin per unit equals sales price minus variable cost per unit, contribution margin ratio formula can also be expressed as:

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

Sales Price |

If there is a sales mix of two or more products, we calculate the weighted average contribution margin ratio as shown below:

Weighted Average CM Ratio = | Sum of Contribution of the Products |

Sum of Sales of the Products |

## Example: Breakeven Point Calculation Using CM Ratio

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 |

CM ratio (cricket) = ($80 – $40) ÷ $80 = 50%

CM ratio (football) = ($100 – $75) ÷ $100 = 25%

CM 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 CM | |
---|---|---|---|---|---|---|

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 |

Weight Average CM Ratio = | Total Contribution Margin | = | $9,525,000 | = 43.8% |

Total Sales | $21,750,000 |

Weighted Average Break-even in $ = | Fixed Costs | = | $2,200,000 | $5,023,622 |

Weighted Average CM Ratio | 43.8% |

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 | CM 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.

Written by Obaidullah Jan, ACA, CFAhire me at