Calculating the the number of units which need to be sold for the business to reach break even is relatively straight forward when a business sells only one product.

As an example, suppose a business with operating expenses (fixed overhead) of 4,500, has only one product which has a unit selling price of 10.00, and a unit cost price of 4.00.

The break even units formula is used as follows:

Unit contribution margin = Selling price - Cost price Unit contribution margin = 10.00 - 4.00 = 6.00 Break even units = Operating expenses / Unit contribution margin Break even units = 4,500 / 6.00 Break even units = 750 units

This can be summarized as follows:

Unit | Total | |
---|---|---|

Units | 750 | |

Revenue | 10.00 | 7,500 |

Cost of sales | 4.00 | 3,000 |

Contribution margin | 6.00 | 4,500 |

Operating expenses | 4,500 | |

Net income | 0 |

However, most businesses sell more than one product, and the calculation of the break even units needs to be amended to reflect this.

## Break Even Analysis for Multiple Products

In order to carry out a break even analysis for multiple product lines. Suppose for example, our business has the same operating expenses of 4,500, but this time is has two product lines. Product A is our low margin product with a selling price of 5.00 and a cost price of 4.00, and product B is our high margin product with a selling price of 20.00 and a cost price of 7.00. In addition, our financial projections show that our unit sales mix is 90% / 10%, meaning that 90% of our unit sales will be product A, and 10% will be product B.

The break even analysis for multiple products is carried out using the following steps:

### Step 1: Calculate the Weighted Average Contribution Margin

In the single product example we used the contribution margin of the product to work out the break even units. Because we now have two products, we need to find the average contribution margin of both products, however, because the products are not sold in equal numbers of units, we need to weight the contribution margin by the sales mix as follows:

Product A unit contribution margin = 5.00 - 4.00 = 1.00 Product B unit contribution margin = 20.00 - 7.00 = 13.00

As the unit sales mix is 90% product A to 10% product B, the weighted average contribution margin (WACM) per unit is calculated using the sales mix formula as follows:

WACM = Product A contribution x Product A sales mix % + Product B contribution x Product B sales mix % WACM = 1.00 x 90% + 13.00 x 10% = 2.20

For these products, with a sales mix of 90%/10%, the weighted average contribution for every unit sold is 2.20 as shown in the diagram below.

### Step 2: Calculate the Break Even Units

The break even units are calculated as before except this time we use the weighted average contribution margin.

Weighted average contribution margin = 2.20 Break even units = Operating expenses / Unit contribution margin Break even units = 4,500 / 2.20 Break even units = 2,046 units

### Step 3: Analyse the Break Even Units by Product

The break even units can now be split between the two products using the unit sales mix percentages as follows:

Break even units = 2,046 units Unit sales mix = 90% A / 10% B Units of product A = 2,046 x 90% = 1,842 Units of product B = 2,046 x 10% = 205

It should be noted that as the business can’t sell a part of a product, the number of units is always rounded up.

This can be summarized as follows:

Unit A | A | Unit B | B | Total | |
---|---|---|---|---|---|

Units | 1,842 | 205 | 2047 | ||

Revenue | 5.00 | 9,210 | 20.00 | 4,100 | 13,310 |

Cost of sales | 4.00 | 7,368 | 7.00 | 1,435 | 8,803 |

Contribution margin | 1.00 | 1,842 | 13.00 | 2,665 | 4,507 |

Operating expenses | 4,500 | ||||

Net income | 7 |

The business breaks even when it sells 1,842 units of product A, and 205 units of product B. The small net income of 7 is due to rounding up to the nearest unit during the calculations.

## Multi Product Break Even Analysis

While this example uses a two product business, the calculations can be carried out for any number of products, the only change to the calculation is in step 1, where the weighted average contribution margin is calculated.

So for example, if the business had five products with contribution margins and sales mix percentages as follows:

Product | Margin | Mix % |
---|---|---|

A | 2.20 | 30% |

B | 4.90 | 10% |

C | 13.00 | 25% |

D | 22.00 | 15% |

E | 16.00 | 20% |

The weighted average contribution margin is then calculated using the sales mix formula

as:

WACM = Product A contribution x Product A sales mix % + Product B contribution x Product B sales mix % ......... WACM = 2.20 x 30% + 4.90 x 10% + 13.00 x 25% + 22.00 x 15% + 16.00 x 20% WACM = 10.90

The weighted average contribution margin can now be used as before in steps 2 and 3 above.

It should be noted that this method of break even analysis for multiple products only works when the product sales mix remains constant. When preparing financial projections an estimate of the sales mix will be used and a break even position can be calculated. If as time passes the actual results reveal a different sales mix, then the financial projections would be revised and a new break even position must be determined using a revised sales mix calculation.

## About the Author

Chartered accountant Michael Brown is the founder and CEO of Plan Projections. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a BSc from Loughborough University.