 # Break-Even Calculations

As they say, a picture is worth a thousand words, and that is certainly true for the CVP graphic just presented. However, everyone is not an artist, and you may find it more precise to do a little algebra to calculate the break-even point. Consider that:

Break-even results when: Sales = Total Variable Costs + Total Fixed Costs

For Leyland, the math turns out this way:

(Units X \$2,000) = (Units X \$800) + \$1,200,000

Solving:

Step a: (Units X \$2,000) = (Units X \$800) + \$1,200,000 Step b: (Units X \$1,200) = \$1,200,000

Step c: Units = 1,000

Now, it is possible to "jump to step b" above by dividing the fixed costs by the contribution margin per unit. Thus, a break-even short cut is:

Break-Even Point in Units = Total Fixed Costs / Contribution Margin Per Unit 1,000 Units = \$1,200,000 / \$1,200

Sometimes, you may want to know the break-even point in dollars of sales (rather than units). This approach is especially useful for companies with more than one product, where those products all have a similar contribution margin ratio:

Break-Even Point in Sales = Total Fixed Costs / Contribution Margin Ratio \$2,000,000 = \$1,200,000 / 0.60

# Target Income Calculations

Breaking even is not a bad thing, but hardly a satisfactory outcome for most businesses. Instead, a manager may be more interested in learning the necessary sales level to achieve a targeted profit. The approach to solving this problem is to treat the "target income" like an added increment of fixed costs. In other words, the margin must cover the fixed costs and the desired profit:

Target Income results when:

Sales = Total Variable Costs + Total Fixed Costs + Target Income

Assume Leyland wants to know the level of sales to reach a \$600,000 income:

(Units X \$2,000) = (Units X \$800) + \$1,200,000 + \$600,000

Solving:

Step a: (Units X \$2,000) = (Units X \$800) + \$1,200,000 + \$600,000

Step b: (Units X \$1,200) = \$1,800,000

Step c: Units = 1,500

Again, it is possible to "jump to step b" by dividing the fixed costs and target income by the per unit contribution margin:

Units to Achieve a Target Income

(Total Fixed Costs + Target Income) / Contribution Margin Per Unit 1,500 Units = \$1,800,000 / \$1,200

If you want to know the dollar level of sales to achieve a target net income:

Sales to Achieve a Target Income

(Total Fixed Costs + Target Income) / Contribution Margin Ratio \$3,000,000 = \$1,800,000 / 0.60

CVP is more than just a mathematical tool to calculate values like the break-even point. It can be used for critical evaluations about business viability.

For instance, a manager should be aware of the "margin of safety." The margin of safety is the degree to which sales exceed the break-even point. For Leyland, the degree to which sales exceed \$2,000,000 (its break-even point) is the margin of safety. This will give a manager valuable information as they plan for inevitable business cycles.

A manager should also understand the scalability of the business. This refers to the ability to grow profits with increases in volume. Compare the income analysis for Leaping Lemming Corporation and Leaping Leopard Corporation: Both companies "broke even" in 20X1. Which company would you rather own? If you knew that each company was growing rapidly and expected to double sales each year (without any change in cost structure), which company would you prefer? With the added information, you would expect the following outcomes for 20X2: This analysis reveals that Leopard has a more scalable business model. Its contribution margin is high and once it clears its fixed cost hurdle, it will turn very profitable. Lemming is fighting a never ending battle; sales increases are met with significant increases in variable costs. Be aware that scalability can be a double-edged sword. Pull backs in volume can be devastating to companies like Leopard because the fixed cost burden can be consuming. Whatever the situation, managers need to be fully cognizant of the effects of changes in scale on the bottom-line performance.