Ch. 5 Cost Components and Cost-Volume-Profit
5.4 Contribution Margin and Break-Even
Learning Objectives
After finishing this section, students will be able to:
- Distinguish between fixed and variable cost.
- Calculate contribution margin.
- Calculate break-even point.
- Calculate how to make a profit.
If you are not controlling costs, you will not make a profit or even break-even. Knowing your costs help you manage your business. Managing your business helps board room meetings not be so tense!
Contribution Margin
Contribution margin is the amount by which a product’s selling price exceeds its total variable cost per unit. This difference between the sales price and the per unit variable cost is called the contribution margin because it is the per unit contribution toward covering the fixed costs.
Unit Contribution Margin = Unit Sales Price – Unit Variable Cost
Let’s look deeper into fixed and variable costs.
Fixed Cost
A fixed cost is an unavoidable operating expense that does not change in total over the short term, even if a business experiences variation in its level of activity. Fixed costs do not change in total as the level of activity changes, but what about fixed costs on a per-unit basis? Let’s examine Tony’s screen-printing company to illustrate how costs can remain fixed in total but change on a per-unit basis.
Tony operates a screen-printing company, specializing in custom T-shirts. One of his fixed costs is his monthly rent of $1,000. Regardless of whether he produces and sells any T-shirts, he is obligated under his lease to pay $1,000 per month. However, he can consider this fixed cost on a per-unit basis.
| Monthly Rent | # of T-shirts Manufactured | Average Rent Cost per T-shirt |
|---|---|---|
| $1,000 | 200 | $5.00 |
| 1,000 | 400 | 2.50 |
| 1,000 | 600 | 1.67 |
Tony’s information illustrates that, despite the unchanging fixed cost of rent, as the level of activity increases, the per-unit fixed cost falls. In other words, fixed costs remain fixed in total but can increase or decrease on a per-unit basis.
Variable Cost
In addition to understanding fixed costs, it is critical to understand variable costs, the second fundamental cost classification. A variable cost is one that varies in direct proportion to the level of activity within the business. Typical costs that are classified as variable costs are the cost of raw materials used to produce a product, labor applied directly to the production of the product, and overhead expenses that change based upon activity.
Unlike fixed costs that remain fixed in total but change on a per-unit basis, variable costs remain the same per unit, but change in total relative to the level of activity in the business. Revisiting Tony’s T-Shirts shows how the variable cost of ink behaves as the level of activity changes.
| Cost of Ink per T-shirt | # of T-shirts Manufactured | Total Variable Cost of Ink |
|---|---|---|
| $0.15 | 200 | $30 |
| $0.15 | 400 | 60 |
| $0.15 | 600 | 90 |
| Cost of T-shirt | # of T-shirts Manufactured | Total Variable Cost of Ink |
|---|---|---|
| $5.00 | 200 | $30 |
| $5.00 | 400 | 60 |
| $5.00 | 600 | 90 |
In our example, the sales revenue from one shirt is $15 and the variable cost of one shirt is $5.15, so the individual contribution margin is $9.85. This $9.85 contribution margin is assumed to first cover fixed costs first and then realized as profit.
Break-even Point
The break-even point is the dollar amount (total sales dollars) or production level (total units produced) at which the company has recovered all variable and fixed costs. In other words, no profit or loss occurs at break-even because Total Cost = Total Revenue.
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.
Break-Even in Units = Total Fixed Cost / Contribution Margin per Unit
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.
| Product Information | Total Variable Cost of Ink |
|---|---|
| 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. Applying this to Hicks calculates as: Break-even in units (225 units) = Total Fixed Costs ($18,000) / Contribution Margin per Unit ($80). 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.
Make a Profit of $16,000
Companies typically do not want to simply break even, as they are in business to make a profit. Break-even analysis also can help companies determine the level of sales (in dollars or in units) that is needed to make a desired profit. The process for factoring a desired level of profit into a break-even analysis is to add the desired level of profit to the fixed costs and then calculate a new break-even point.
Target Units = (Total Fixed Cost + Desired Profit) / Contribution Margin per Unit
We know that Hicks Manufacturing breaks even at 225 Blue Jay birdbaths, but what if they have a target profit for the month of July? They can simply add that target to their fixed costs. By calculating a target profit, they will produce and (hopefully) sell enough bird baths to cover both fixed costs and the target profit. If Hicks wants to earn $16,000 in profit in the month of May, we can calculate their new break-even point as follows: Target Units (425 units) = (Total Fixed Cost ($18,000) + Desired Profit ($16,000)) / Contribution Margin per Unit ($80). If we sell 425 units at a sales price of $100, we will make a profit of $42,500.
We can now understand that managers set sales goals based on desired profits. If a company does not have sales goals, desired profits will not be reached.
5.4a Example
RJ is a manufacture of blue LED lights. The business produces 3,000 LED lights per month, which are sold to independent retailers for $50, who then sell the LED lights to customers for $90. Variable costs are $20 per LED light and fixed costs are $70,000 per month.
Instructions:
- How much is the contribution margin per LED light?
- What is the company’s profit when 3,000 LED lights are sold?
- If the economy had a downturn, how many LED lights would need to be sold for the company to break-even?
5.4a Practice
Unagi Enterprises teaches 30-minute self-defense classes to elementary-aged students. Each 30-minute class costs the student $25. The teacher is paid $10 per student attending the class. Unagi’s fixed costs are $20,000. The company wants to make $10,000 profit each month.
Instructions:
- How many classes need to be taught each month to break even and make the desired profit?
- If only 10 students can attend classes at a time, how many classes must be offered each month?
- Assuming each month has four weeks, how many hours a week will the studio be used?
- If the studio has ten teachers, how many sessions a week must each teacher teach?
- Based on your answer in #4 and assuming each class is at capacity, how much will each teacher earn a week?
- How much is the teacher earning an hour?
- Based on the calculations above, what would you change about this business?
Check Figures:
- Hours a week studio will be used, 25 hours
- Solution (Excel file will download)
5.4a Homework
ABC Computer makes and sells gaming computers. The selling price of each computer is $1,000. The variable cost for each computer is $400. Total fixed costs for ABC Computer are $90,000.
Instructions:
- What is the contribution margin per computer?
- How many computers must ABC Computer sell to reach the breakeven point?
- What is ABC Computer’s total profit when 200 computers are sold?
- How many computers must ABC Computer sell to yield a profit of $60,000?
- Do to the recent economic changes, the variable costs of each computer will increase to $600. Fixed costs will remain the same. With this change, how many computers will ABC Computer need to sell to reach the breakeven point?
- Using the changes in #5, how many computers must ABC Computer sell to yield a profit of $60,000?
Licensing and Attribution:
Content on this page is adapted from the following openly licensed resource(s):
Principles of Accounting, Volume 2: Managerial Accounting by Mitchell Franklin, Patty Graybeal, and Dixon Cooper licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License
is an unavoidable operating expense that does not change in total over the short term, even if a business experiences variation in its level of activity.
is one that varies in direct proportion to the level of activity within the business.
is the dollar amount (total sales dollars) or production level (total units produced) at which the company has recovered all variable and fixed costs.
