The Break-Even Point
A company breaks even for a given period when sales revenue and costs incurred during that period are equal. Thus the break-even point is that level of operations at which a company realizes no net income or loss.
A company may express a break-even point in dollars of sales revenue or number of units produced or sold. No matter how a company expresses its break-even point, it is still the point of zero income or loss. To illustrate the calculation of a break-even point, Video Productions produces videotapes selling for USD 20 per unit. Fixed costs per period total USD 40,000, while variable cost is USD 12 per unit.
Contribution Margin
Before we turn to the calculation of the break-even point, it’s important to understand contribution margin. Contribution margin is the portion of revenue that is not consumed by variable cost. In a simple example, if you were to buy a candy bar for 50 cents and resell it for $1 then the contribution margin would be 50 cents— the amount not consumed by cost.
Of course, in business this is generally more complicated. It requires you to understand the variable costs for an item, or those costs that are directly tied to creating a new unit. When selling lemonade from a stand, the costs of the water, lemon juice, sweetener, ice, and serving glass are all variable costs that will recur with each item sold. The cost of the stand is a fixed cost. The labor required to make and serve the lemonade is also generally a fixed cost as it doesn’t vary based on the number of glasses sold. Let’s look at this in numeric terms, as follows:
Inputs | Cost | Category |
Lemons, sweetener, ice, and water | 20 cents per glass | Variable |
Glasses | 5 cents each | Variable |
Labor | $100 per day per employee | Fixed |
Lemonade stand rental | $2,000 per month | Fixed |
If we know that the stand sells 1,000 glasses of lemonade each day at $3 per glass, and that one employee can make and serve 1,000 glasses, then we can calculate the contribution margin.
The cost of raw materials is 25 cents (20 for ingredients + 5 for glasses). If the lemonade is sold for $3 per glass, then the contribution margin is $2.75 per glass.
It’s important to know the contribution margin in order to calculate what portion of the revenue from a product is consumed by the variable costs and what portion can be used to cover, or contribute to, fixed costs.
Break-Even in Units
We compute the break-even point in units by dividing total fixed costs by the contribution margin per unit. The contribution margin per unit is USD 8 (USD 20 selling price per unit – USD 12 variable cost per unit). In the following break-even equation, BE refers to the break-even point:
[latex]\text{BE units} = \frac{\text{Fix costs}}{\text{Contribution margin per unit}} [/latex]
[latex]\text{BE units} = \frac{\text{USD 40,000}}{\text{USD 8 per unit}} [/latex]
[latex]\text{BE units} = \text{5,000 units} [/latex]
The result tells us that Video Productions breaks even at a volume of 5,000 units per month. We can prove that to be true by computing the revenue and total costs at a volume of 5,000 units. Revenue = 5,000 units X USD 20 sales price per unit = USD 100,000. Total costs = USD 100,000 = USD 40,000 fixed costs + USD 60,000 variable costs (USD 60,000 = USD 12 per unit X 5,000 units).
Note that the revenue and total cost lines cross at 5,000 units—the break-even point. Video Productions has net income at volumes greater than 5,000, but it has losses at volumes less than 5,000 units.
Break-Even in Sales Dollars
Companies frequently think of volume in sales dollars instead of units. For a company such as GM that makes Cadillacs and certain small components, it makes no sense to think of a break-even point in units. GM breaks even in sales dollars.
The formula to compute the break-even point in sales dollars looks a lot like the formula to compute the break-even in units, except we divide fixed costs by the contribution margin ratio instead of the contribution margin per unit.
[latex]\text{BE units} = \frac{\text{Fix costs}}{\text{Contribution margin ratio}} [/latex]
A Broader Perspective: Even Colleges Use CVP
The dean of the Business School at a particular university was considering whether to offer a seminar for executives. The tuition would be USD 650 per person. Variable costs, including meals, parking, and materials, would be USD 80 per person. Certain costs of offering the seminar, including advertising, instructors’ fees, room rent, and audiovisual equipment rent, would not be affected by the number of people attending (within a “relevant range”). Such costs, which could be thought of as fixed costs, amounted to USD 8,000 for the seminar.
In addition to these costs, a number of staff, including the dean, would work on the program. Although the salaries paid to these staff were not affected by offering the seminar, working on it took these people away from other duties, thus creating an opportunity cost, estimated to be USD 7,000 for this seminar.
Given this information, the school estimated the break-even point to be (USD 8,000 + USD 7,000)/(USD 650 – USD 80) = 26.3 students. If the school wanted at least to break even on this program, it should offer the program only if it expected at least 27 students to attend.
Based on the authors’ research.
The contribution margin ratio expresses the contribution margin as a percentage of sales. To calculate this ratio, divide the contribution margin per unit by the selling price per unit, or total contribution margin by total revenues. Video Production’s contribution margin ratio is:
[latex]\text{Contribution margin ratio} = \frac{\text{Contribution margin per unit}}{\text{Selling price per unit}} [/latex]
[latex]\frac{\text{USD 20}-\text{USD 12}}{\text{USD 20}} = \frac{\text{USD 8}}{\text{USD 20}} = 0.40 [/latex]
Or, referring to the income statement in which Video Productions had a total contribution margin of USD 48,000 on revenues of USD 120,000, we compute the contribution margin ratio as follows:
[latex]\text{Contribution margin ratio} = \frac{\text{Total contribution margin}}{\text{Total revenues}} [/latex]
[latex]\frac{\text{USD 48,000}}{\text{USD 120,000}} = 0.40 [/latex]
That is, for each dollar of sales, there is a USD 0.40 contribution to covering fixed costs and generating net income.
Using this ratio, we calculate Video Production’s break-even point in sales dollars as:
[latex]\text{BE dollars} = \frac{\text{Fix costs}}{\text{Contribution margin rate}} [/latex]
[latex]\text{BE dollars} = \frac{\text{USD 40,000}}{0.40} =\text{USD 100,000} [/latex]
The break-even volume of sales is USD 100,000 (5,000 units at USD 20 per unit). At this level of sales, fixed costs plus variable costs equal sales revenue, as shown here:
Revenue | $120,000 |
Less: variable costs | 72,000 |
Contribution margin | $ 48,000 |
Less: Fixed costs | 40,000 |
Net income | $ 8,000 |
The cost-volume-profit chart above shows that in a period of complete idleness, Video Productions would lose USD 40,000 (the amount of fixed costs). However, when Video Productions has an output of 10,000 units, the company has net income of USD 40,000. Other points on the graph show that sales of 7,500 units results in USD 150,000 of revenue. At that point, Video Production’s total costs amount to USD 130,000, leaving net income of USD 20,000.
Although you are likely to use cost-volume-profit analysis for a single product, you will more frequently use it in multi-product situations. The easiest way to use cost-volume-profit analysis for a multi-product company is to use dollars of sales as the volume measure. For CVP purposes, a multi-product company must assume a given product mix. Product mix refers to the proportion of the company’s total sales attributable to each type of product sold.
To illustrate the computation of the break-even point for Wonderfood, a multi-product company that makes three types of cereal, assume the following historical data:
Product | ||||||||
1 | 2 | 3 | Total | |||||
Amount | Per cent | Amount | Per cent | Amount | Per cent | Amount | Per cent | |
Sales | $60,000 | 100% | $30,000 | 100% | $10,000 | 100% | $100,000 | 100% |
Less: | ||||||||
Variable costs | 40,000 | 67% | 16,000 | 53% | 4,000 | 40% | 60,000 | 60% |
Contribution margin | $20,000 | 33% | $14,000 | 47% | $ 6,000 | 60% | $ 40,000 | 40% |
We use the data in the total columns to compute the break-even point. The contribution margin ratio is 40 per cent or (USD 40,000/USD 100,000). Assuming the product mix remains constant and fixed costs for the company are USD 50,000, break-even sales are USD 125,000, computed as follows:
[latex]\text{BE dollars} = \frac{\text{Fix costs}}{\text{Contribution margin ratio}} [/latex]
[latex]\text{BE dollars} = \frac{\text{USD 50,000}}{0.40} = \text{USD 125,000} [/latex]
[To check our answer: (USD 125,000 X 0.40) – USD 50,000 = USD 0.]
To find the three product sales totals, we multiply total sales dollars by the per cent of product mix for each of the three products. The product mix for products 1, 2, and 3 is 60:30:10, respectively. That is, out of the USD 100,000 total sales, there were sales of USD 60,000 for product 1, USD 30,000 for product 2, and USD 10,000 for product 3. Therefore, the company has to sell USD 75,000 of product 1 (0.6 X USD 125,000), USD 37,500 of product 2 (0.3 X USD 125,000), and USD 12,500 of product 3 (0.1 X USD 125,000) to break even.
An Accounting Perspective: Business Insight
The founder of Domino’s Pizza, Inc. nearly went bankrupt several times before he finally made Domino’s a financial success. One early problem was that the company was providing small pizzas that cost almost as much to make and just as much to deliver as larger pizzas. Because they were small, the company could not charge enough to cover its costs. At one point, the company’s founder was so busy producing small pizzas that he did not have time to determine that the company was losing money on them.
If a company’s current sales are more than its break-even point, it has a margin of safety equal to current sales minus break-even sales. The margin of safety is the amount by which sales can decrease before the company incurs a loss. For example, assume Video Productions currently has sales of USD 120,000 and its break-even sales are USD 100,000. The margin of safety is USD 20,000, computed as follows:
Margin safety = Current sales – Break-even sales
= USD 120,000 – USD 100,000
= USD 20,000
Sometimes people express the margin of safety as a percentage, called the margin of safety rate. The margin of safety rate is equal to [latex]\frac{\text{(Current sales} - \text{Break-even sales)}}{\text{Current sales}} [/latex]. Using the data just presented, we compute the margin of safety rate as follows:
Margin of safety rate = [latex]\frac{\text{(Current sales} - \text{Break-even sales)}}{\text{Current sales}} [/latex]
[latex]\frac{\text{(USD 120,000} - \text{USD 100,000)}}{\text{USD 120,000}} = 16.67 \text{per cent} [/latex]
This means that sales volume could drop by 16.67 per cent before the company would incur a loss.
Check Your Understanding
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