# Break Even Point

## Definition

Break-Even Point is the level of sales that results in a state of no profit and no loss for the business.

## Formula

Break-Even Point (Units) | = | Total Fixed Costs |

Contribution Margin per unit |

## Explanation

Break-Even Point is the number of sales units that cause the business to break even. Sale of 1 unit more than the break-even point will result in a profit whereas sales of 1 unit lower than the break-even Point will result in a loss for the business.

**How is the Breakeven Point Formula derived?**

A business breaks even when its total revenue equals its total cost. We can restate the equation to formulate the break-even point formula as follows:

Total Revenue | = | Total Cost |

Total Revenue | = | Total Fixed Cost + Total Variable Cost |

Total Revenue - Total Variable Cost | = | Total Fixed Cost |

(Selling Price per Unit x Unit Sales) - (Variable Cost per Unit x Unit Sales) | = | Total Fixed Cost |

Unit Sales x (Selling Price per Unit - Variable Cost per Unit) | = | Total Fixed Cost |

Unit Sales x (Contribution Margin per unit) | = | Total Fixed Cost |

Unit Sales ^{Break-Even Point} | = | Total Fixed Costs |

Contribution Margin per unit |

### Example

Sara who is the owner of a car showroom wants to know the minimum number of cars that she needs to sell in order to avoid making a loss in her first year of business.

She has provided you with the following cost and revenue estimates.

Scenario 1 | Scenario 2 | |

Sales | 50 units | 100 units |

Revenue | $50,000 | $100,000 |

Expenses | ||

Rent | $10,000 | $10,000 |

Salaries and wages | $20,000 | $30,000 |

Depreciation | $10,000 | $10,000 |

Transportation | $5,000 | $10,000 |

Overheads | $10,000 | $12,000 |

Calculate the breakeven point for Sara.

**Step 1 Identify Fixed Costs**

Rent and depreciation are fixed costs as they do not change with a change in sales quantity.

**Step 2 Identify Semi-Variable Costs**

Transportation costs are completely variable as they increase proportionate to the increase in sales quantity (i.e. transportation costs double when the sales double).

Salaries and overhead costs are semi-variable because they do not increase proportionately to the increase in sales.

**Step 3 Calculate fixed cost element of semi-variable costs**

Fixed cost portion of salaries and overheads can be found by using the high low method.

Salaries | Overheads | ||

Total Cost - 1000 units | A | $30,000 | $12,000 |

Total Cost - 500 units | B | $20,000 | $10,000 |

Variable Cost/unit | C = (A - B) /(100 units - 50 units) | $200 | $40 |

Fixed Cost | A - C × 1000 | $10,000 | $8,000 |

**Step 4 Calculate the total fixed costs**

Fixed Cost $ | |

Rent | 10,000 |

Salaries and wages | 10,000 |

Depreciation | 10,000 |

Overheads | 8,000 |

Total Fixed Cost | 38,000 |

**Step 5 Calculate sales revenue per unit**

Sales revenue per unit | = | Total sales revenue / unit sales |

= | $100,000 / 100 | |

= | $1,000 |

**Step 6 Calculate variable cost per unit**

Variable Cost per unit $ | ||

Salaries | From Step 3 | 200 |

Overheads | From Step 3 | 40 |

Transportation | $5000 / 50 units | 100 |

Total | 340 |

**Step 7 Calculate Contribution Margin Per Unit**

Contribution margin per unit | = | Sales revenue - variable cost |

= | $1000 - $124 | |

= | $660 |

**Step 8 Calculate the break-even point**

Break-Even Point | = | Total Fixed Costs |

Contribution Margin per unit | ||

= | $38,000 (Step 4) | |

$660(Step 7) | ||

= | 58 units |

Sara needs to sell at least 58 units to avoid making a loss in the first year.

## Importance

Break-Even Point is important to know on a basic business level because it tells how many units a business needs to sell in order to avoid a loss which can inform business decisions. Break-Even Point Analysis helps to analyze the risk of running into a loss by assessing the margin of safety. Such information can help users to make informed decisions involving for example forming minimum sales targets, feasibility analysis, shutdown decisions and risk analysis.