Break even analysis can be used by a business to calculate the revenue or number of sales units needed in order for the business to make zero profit. At this point the contribution margin (sometimes referred to as the gross margin) is equal to the fixed costs and the business is said to break even or be at its break even point.

## Break Even Sales Revenue

The break even point is the level of revenue needed to produce a net income of zero, and is given by the break even analysis formula as follows:

For example, if a business has operating expenses of 50,000 and a contribution margin percentage of 40%, then the revenue needed to reach break even is calculated as follows:

Break even revenue = Fixed costs / Contribution margin % Break even revenue = 50,000 / 40% Break even revenue = 125,000

At a revenue of 125,000, the contribution margin will be 50,000 (125000 x 40%), less the fixed costs of 50,000 gives a net income of zero.

## Break Even Formula in Units

Having calculated the break even revenue, and knowing the selling price per unit, then it is possible to calculate the number of units needed to reach break even.

Using the example above, if the selling price per unit is 12.50, then the number of units to reach break even is given as follows:

Break even units = Break even revenue / Selling price per unit Break even units = 125,000 / 12.50 Break even units = 10,000 units

The break even units is 10,000. At this level of sales, the revenue is 125,000 (10,000 x 12.50), and the contribution margin is 50,000 (125,000 x 40%), less the fixed costs of 50,000 gives a net income of zero. The break even units is sometimes referred to as the break even quantity or BEQ.

Units | 10,000 |
---|---|

Revenue (unit 12.50) | 125,000 |

Contribution margin (40%) | 50,000 |

Fixed costs | 50,000 |

Net income | 0 |

In a well managed business, the fixed costs and contribution margin should remain relatively stable. Providing the unit selling price remains the same, then the number of units needed to reach break even is a known figure which can be used on a day to day basis to manage the business. In the above example, the business needs to sell on average 28 units per day (10,000 / 365) to break even. Management now know that anything above that figure means they are profitable, anything below that figure and they will incur losses.

The break even unit formula (bep formula) can also be rewritten in terms of the unit selling price and unit cost price as follows:

In the example above the unit cost price is 7.50 (12.50 x 60%) and the break even units can be calculated as follows:

Break even units = Fixed costs / (Selling price - Variable cost) Break even units = 50,000 / (12.50 - 7.50) Break even units = 10,000 units

## Break Even Analysis and Target Profit

A variation of the break even analysis formula can be used to determine the revenue needed to achieve a target profit level.

Suppose the target profit level in the example above was 12,000, as before, the fixed costs are 50,000, and the contributions margin percentage is 40%, then the revenue needed to achieve the target profit is given as follows.

Revenue = (Fixed costs + Target profit) / Contribution margin % Revenue = (50,000 + 12,000) / 40% Revenue = 155,000

At this level of revenue, the contribution margin is 62,000 (155,000 x 40%), less the fixed costs of 50,000 leaves a net income of 12,000, which is the required target profit. The number of units to achieve the target profit is 12,400, calculated by dividing the break even revenue by the unit selling price (155,000/12.50).

Again, the break even units formula used above can be restated to include a target profit.

Units = (Fixed costs + Target profit) / (Selling price - Variable cost) Units = (50,000 + 12,000) / (12.50 - 7.50) Units = 12,400 units

Our break even analysis calculator is available to help calculate the break even revenue based on the current level of sales, contribution margin, and fixed costs.

## 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.