# Break Even Units

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

The break even point formula is as follows:

Obviously by knowing the break even revenue and the product unit selling price, it is possible to calculate the number of units to sell for the business to break even.

## Break Even Units Example

To illustrate suppose a business sells a product for 130.00 a unit, and it costs 58.50 to produce. In this case the calculation of the gross margin percentage for the product is 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%
```

Furthermore suppose the business has operating expenses of 60,500. In this case 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. Additionally 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 illustrate this we have set out below the income statements at 846 and 847 units respectively.

Income statements near break even
Units847846
Revenue (unit 130.00)110,110109,980
Cost of sales (unit 58.50)49,55049,491
Gross margin60,56060.489
Operating expenses60,50060,500
Net income60-11

As can be seen at 847 units the business makes a profit of 60. In contrast 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 breakeven units.

In the above example, the breakeven 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 breakeven. 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. Consequently we can estimate the profit for the day as follows:

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

It is important to realize that 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 corrective action at the earliest opportunity.

Additionally 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.