## Break Even

### 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: - 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). - 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:

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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:

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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:

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