Calculate a Break-Even Point in Units and Dollars
Calculate a Break-Even Point in Units and Dollars
Basics of the Break-Even Point
Figure 3.3 Break-Even Point.
The basic theory illustrated in Figure 3.3 is that, because of the existence of fixed costs in most production processes, in the first stages of production and subsequent sale of the products, the company will realize a loss. For example, assume that in an extreme case the company has fixed costs of $20,000, a sales price of $400 per unit and variable costs of $250 per unit, and it sells no units. It would realize a loss of $20,000 (the fixed costs) since it recognized no revenue or variable costs. This loss explains why the company's cost graph recognized costs (in this example, $20,000) even though there were no sales. If it subsequently sells units, the loss would be reduced by $150 (the contribution margin) for each unit sold. This relationship will be continued until we reach the break-even point, where total revenue equals total costs. Once we reach the break-even point for each unit sold the company will realize an increase in profits of $150.
For each additional unit sold, the loss typically is lessened until it reaches the break-even point. At this stage, the company is theoretically realizing neither a profit nor a loss. After the next sale beyond the break-even point, the company will begin to make a profit, and the profit will continue to increase as more units are sold. While there are exceptions and complications that could be incorporated, these are the general guidelines for break-even analysis.
As you can imagine, the concept of the break-even point applies to every business endeavor – manufacturing, retail, and service. Because of its universal applicability, it is a critical concept to managers, business owners, and accountants. When a company first starts out, it is important for the owners to know when their sales will be sufficient to cover all of their fixed costs and begin to generate a profit for the business. Larger companies may look at the break-even point when investing in new machinery, plants, or equipment in order to predict how long it will take for their sales volume to cover new or additional fixed costs. Since the break-even point represents that point where the company is neither losing nor making money, managers need to make decisions that will help the company reach and exceed this point as quickly as possible. No business can operate for very long below break-even. Eventually the company will suffer losses so great that they are forced to close their doors.
ETHICAL CONSIDERATIONS
Break-Even Analysis and Profitability
The first step in determining the viability of the business decision to sell a product or provide a service is analyzing the true cost of the product or service and the timeline of payment for the product or service. Ethical managers need an estimate of a product or service's cost and related revenue streams to evaluate the chance of reaching the break-even point.
Determining an accurate price for a product or service requires a detailed analysis of both the cost and how the cost changes as the volume increases. This analysis includes the timing of both costs and receipts for payment, as well as how these costs will be financed. An example is an IT service contract for a corporation where the costs will be frontloaded. When costs or activities are frontloaded, a greater proportion of the costs or activities occur in an earlier stage of the project. An IT service contract is typically employee cost intensive and requires an estimate of at least 120 days of employee costs before a payment will be received for the costs incurred. An IT service contract for $100,000 in monthly services with a 30% profit margin will require 4 months of upfront financing of $280,000 balanced over the four months before a single payment is received.
The overall profit at a specific point in time requires a careful determination of all of the costs associated with creating and selling the product or providing the service. An ethical managerial accountant will provide a realistic cost estimate, regardless of management's desire to sell a product or provide a service. What might be a lucrative product on its face needs additional analysis provided by the managerial accountant.
To illustrate the concept of break-even, we will return to Hicks Manufacturing and look at the Blue Jay birdbath they manufacture and sell.
Sales Where Operating Income Is $0
Hicks Manufacturing is interested in finding out the point at which they break even selling their Blue Jay Model birdbath. They will break even when the operating income is $0. The operating income is determined by subtracting the total variable and fixed costs from the sales revenue generated by an enterprise. In other words, the managers at Hicks want to know how many Blue Jay birdbaths they will need to sell in order to cover their fixed expenses and break even. Information on this product is:|
Hick's Manufacturing Blue Jay Model For Year Ended December 31, 2019 |
|
| Sales Price per Unit | $100 |
| Variable Cost per Unit | 20 |
| Contribution Margin per Unit | 80 |
| Total Fixed Cost per Month | $18,000 |
In order to find their break-even point, we will use the contribution margin for the Blue Jay and determine how many contribution margins we need in order to cover the fixed expenses, as shown in the formula in Figure 3.4.
Figure 3.4 Break-Even Point in Units.
What this tells us is that Hicks must sell 225 Blue Jay Model birdbaths in order to cover their fixed expenses. In other words, they will not begin to show a profit until they sell the 226th unit. This is illustrated in their contribution margin income statement.
| Hick's Manufacturing Blue Jay Model For Year Ended December 31, 2019 |
|
| Sales(225 units at $100 per return | $22,500 |
| Variable Cost (225 units at $20 per return) | 4,500
|
| Contribution Margin | 18,000 |
| Fixed Costs | 18,000 |
| Operating Income | $ 0 |
The break-even point for Hicks Manufacturing at a sales volume of $22,500 (225 units) is shown graphically in Figure 3.5.
Figure 3.5 Hicks Manufacturing Break-Even Point for 225 Units.
As you can see, when Hicks sells 225 Blue Jay Model birdbaths, they will make no profit, but will not suffer a loss because all of their fixed expenses are covered. However, what happens when they do not sell 225 units? If that happens, their operating income is negative.Sales Where Operating Income Is Negative
In a recent month, local flooding caused Hicks to close for several days, reducing the number of units they could ship and sell from 225 units to 175 units. The information in Figure 3.6 reflects this drop in sales.| HICKS MANUFACTURING Contribution Margin Income Statement For Year Ended December 31, 2019 |
|
| Sales (175 units at $20 per unit) | $17,500 |
| Variable Cost (175 units at $20 per unit) | 3,500
|
| Contribution Margin | 14,000 |
| Fixed Costs | 18,000 |
| Operating Income | $ (4,000) |
Figure 3.6 Hicks Manufacturing Contribution Margin Income Statement.
At 175 units ($17,500 in sales), Hicks does not generate enough sales revenue to cover their fixed expenses and they suffer a loss of $4,000. They did not reach the break-even point of 225 units.
Figure 3.7 Hicks Manufacturing Break-Even Point for 175 Units.
Sales Where Operating Income Is Positive
What happens when Hicks has a busy month and sells 300 Blue Jay birdbaths? We have already established that the contribution margin from 225 units will put them at break-even. When sales exceed the break-even point the unit contribution margin from the additional units will go toward profit. This is reflected on their income statement.| HICKS MANUFACTURING Contribution Margin Income Statement For Year Ended December 31, 2019 |
|
| Sales (300 units at $100 per unit) | $30,000 |
| Variable Cost (300 units at $20 per unit) | 6,000
|
| Contribution Margin | 24,000 |
| Fixed Costs | 18,000 |
| Operating Income | $ 6,000 |
Again, looking at the graph for break-even (Figure 3.8), you will see that their sales have moved them beyond the point where total revenue is equal to total cost and into the profit area of the graph.
Figure 3.8 Hicks Manufacturing Break-Even Point for 300 Units.
However, using the contribution margin per unit is not the only way to determine a break-even point. Recall that we were able to determine a contribution margin expressed in dollars by finding the contribution margin ratio. We can apply that contribution margin ratio to the break-even analysis to determine the break-even point in dollars. For example, we know that Hicks had $18,000 in fixed costs and a contribution margin ratio of 80% for the Blue Jay model. We will use this ratio (Figure 3.9) to calculate the break-even point in dollars.
Figure 3.9 Break-Even Point in Dollars.
Hicks Manufacturing will have to generate $22,500 in monthly sales in order to cover all of their fixed costs. In order for us to verify that Hicks' break-even point is $22,500 (or 225 units) we will look again at the contribution margin income statement at break-even:
| HICKS MANUFACTURING Contribution Margin Income Statement For Year Ended December 31, 2019 |
|
| Sales (225 units at $100 per unit) | $22,500 |
| Variable Cost (225 units at $20 per unit) | 4,500
|
| Contribution Margin | 18,000 |
| Fixed Costs | 18,000 |
| Operating Income | $ 0 |
By knowing at what level sales are sufficient to cover fixed expenses is critical, but companies want to be able to make a profit and can use this break-even analysis to help them.
THINK IT THROUGH
The Cost of a Haircut
You are the manager of a hair salon and want to know how many ladies' haircuts your salon needs to sell in a month in order to cover the fixed costs of running the salon. You have determined that, at the current price of $35 per haircut, you have $20 in variable costs associated with each cut. These variable costs include stylist wages, hair product, and shop supplies. Your fixed costs are $3,000 per month. You perform a break-even analysis on a per-unit basis and discover the following:
| Sales price per service | $ 35 |
| Variable cost per service | 20 |
| Contribution margin per service | 15 |
| Break-even (in services) | 200 |
You have 4 stylists plus yourself working in the salon and are open 6 days per week. Considering the break-even point and the number of available stylists, will the salon ever break even? If it does, what will need to happen? What can be done to achieve the break-even point?