The break even point is the level of revenue needed to generate sufficient gross margin to cover the operating expenses of running a business

The break even point formula is as follows:

Break even revenue = Operating expenses / Gross margin %

By knowing the break even revenue and the product unit selling price, it is possible to calculate the number of units which need to be sold for the business to break even.

## Break Even Units Example

If a business sells a product for 130.00 a unit, and it costs 58.50 to produce, then the gross margin percentage for the product is calculated as follows:

Gross margin = Selling price - Cost Gross margin = 130.00 - 58.50 Gross margin = 71.50 and Gross margin % = Gross margin / Selling price Gross margin % = 71.50 / 130.00 Gross margin % = 0.55 or 55%

If the business has operating expenses of 60,500, then the break even formula above allows us to calculate the break even revenue.

Break even revenue = Operating expenses / Gross margin % Break even revenue = 60,500 / 55% Break even revenue = 110,000

The business will break even when it reaches a revenue of 110,000. Using the selling price of 130.00 per unit, we can now calculate the break even units as follows:

Break even units = Break even revenue / Selling price per unit Break even units = 110,000 / 130.00 Break even units = 846.15 units Break even units = 847 units

The business must sell 847 units before it will break even. To demonstrate this the income statements at 846 and 847 units are shown below.

Units | 847 | 846 |
---|---|---|

Revenue (unit 130.00) | 110,110 | 109,980 |

Cost of sales (unit 58.50) | 49,550 | 49,491 |

Gross margin | 60,560 | 60.489 |

Operating expenses | 60,500 | 60,500 |

Net income | 60 | -11 |

At 847 units the business makes a profit of 60, whereas at 846 units the business makes a small loss of 11.

## Alternative Breakeven Units Formula

It should be noted that the break even units formula given above can also be rearranged to give the break even units in terms of the fixed costs, selling price and variable cost per unit.

Breakeven units = Break even revenue / Selling price Breakeven units = Fixed costs / (Selling price – Variable cost) Breakeven units = 60,500 / (130.00 – 58.50) = 847 units

## Using the Break Even Units to Manage

The gross margins and operating expenses of a well managed business should stabilize over time. Providing the selling price of the product remains constant, then if the break even units figure is known management can tell whether the business is making a profit on a day to day basis by monitoring actual units sold against break even units.

In the above example, the break even point is 847 units, if this figure is say for one week, then assuming a five day week, management know they must sell at least 170 units a day to break even. Suppose they sell 180 units, they know they have broken even and as the operating costs have now been covered, then any unit sold above break even must result in a profit for the business. The profit for the day can be estimated as follows:

Profit = Units above break even x Profit per unit Profit = (180 - 170) x (130.00 - 58.50) Profit = 715

These are only ‘back of the envelope’ calculations and assume that the operating expenses will accrue evenly throughout the year. However, the break even unit calculations do provide a useful tool for business owners to monitor the day to day performance of their business allowing corrections to be made at the earliest opportunity.

Our breakeven units calculator will calculate the break even units for up to four different scenarios by inserting values for unit selling price, cost price, and operating expenses.

## 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.