### Learning Outcomes

- Calculate break-even point

The **break-even point** is the number of units that must be sold to achieve an operating income of zero. At the break-even point, sales in dollars equal costs. The break-even calculation answers the question: How many units does the company have to sell to pay all its expenses for the month?

Let’s follow the BlankBooks example as we explore how to use the CVP analysis model in order to solve this business problem.

BlankBooks, Inc. purchases raw materials (paper and bindings) and converts those to finished goods (blank journals). The company uses a Just-In-Time (JIT) inventory management system for work-in-process and finished goods, so the only inventory on hand at the end of each month is raw materials.

Here is the data we have to work with from the month of July, 20XX:

Bindings | $5.00 | each |

Pages (preassembled, ready to bind) | $1.00 | each |

Labor per piece assembled | $2.00 | each |

Sales Salary | $2,000.00 | per month |

Commission | 3.00% | each |

Internet and web site | $200.00 | per month |

Production facility rent | $1,200.00 | per month |

Sales Price | $10.00 | each |

First, we sorted out the variable and fixed costs:

Description | Amount | Total | ||
---|---|---|---|---|

Variable Costs (per unit) | ||||

Bindings | $ 5.00 | |||

Pages (preassembled, ready to bind) | 1.00 | |||

Labor per piece assembled | 2.00 | |||

Subcategory, Commission |
||||

Sales price | $10.00 | |||

X rate | 3.00% | 0.30 | ||

Single Line$ 8.30Double line | ||||

Fixed Costs | ||||

Sales Salary | $ 2,000.00 | |||

Internet and web site | 200.00 | |||

Production facility rent | 1,200.00 | |||

Single Line$ 3,400.00Double line |

Then, we created a contribution margin statement from this data. In order to do this, we made an initial guess of 2,500 units that we could sell (and because we’re using a JIT inventory system, production will match sales).

Units | $/Unit | Total | |
---|---|---|---|

Sales | 2,500 | $ 10.00 | $ 25,000.00 |

Variable costs | 2,500 | $ 8.30 | 20,750.00 |

Contribution Margin | $ 1.70 | Single Line4,250.00 | |

Fixed costs | $ 3,400.00 | ||

Operating income | Single Line$ 850.00Double line | ||

CM ratio | 17.00% |

What is your best guess for the units of production that will result in a break-even point, where contribution margin just covers fixed costs with almost $0 profit?

Let’s try 1,400 units:

Units | $/Unit | Total | |
---|---|---|---|

Sales | 1,400 | $ 10.00 | $ 14,000.00 |

Variable costs | 1,400 | $ 8.30 | 11,620.00 |

Contribution Margin | $ 1.70 | Single Line2,380.00 | |

Fixed costs | 3,400.00 | ||

Operating income | Single Line$ (1,020.00)Double line | ||

CM ratio | 17.00% |

At the 1,400 units sales/production level, we lose money. We could continue to guess, rerunning the calculation until we came close to $0 profit, but there is an easier way.

We know each unit provides $1.70 in contribution margin. The contribution margin covers fixed costs and profit.

In this case, we want to know the point where profit is closest to $0, which means all we have to do is cover fixed costs of $3,400.

Divide fixed costs by contribution margin per unit:

$3,400 / $1.70/unit = 2000 units

We can enter that into our Contribution Margin statement to see if it works:

Units | $/Unit | Total | |
---|---|---|---|

Sales | 2,000 | $ 10.00 | $ 20,000.00 |

Variable costs | 2,000 | $ 8.30 | 16,600.00 |

Contribution Margin | $ 1.70 | Single Line3,400.00 | |

Fixed costs | 3,400.00 | ||

Operating income | Single Line$ 0.00Double line | ||

CM ratio | 17.00% |

You could also calculate the break-even point by dividing fixed costs by the contribution margin ratio, which will give you the break-even point in sales dollars:

$3,400 / 0.17 = $20,000.00

Since each unit sells for $10.00, the number of units we need to sell just to break-even would be:

$20,000.00 / $10.00/unit = 2,000 units

If the break-even point is greater than the actual production capacity, the company will operate at a loss. Likewise, if the break-even point is greater than the organization’s sales capacity, it will operate at a loss. We expect our student workers to make 25 books an hour, so to make 2,000 books per month, we’ll need 80 hours of labor, or approximately 20 hours per week. In addition, we’ll need the raw materials on hand or at least a steady supply during the month.

Here is a review of calculating break-even:

You can view the transcript for “Cost Volume Profit Analysis (CVP): calculating the Break Even Point” here (opens in new window).

Before we adapt this model to accommodate a target profit, let’s check your understanding of the break-even analysis.