22 4.2 Cost-Volume-Profit Analysis for Single-Product Companies
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Last updated
- Dec 28, 2020
Learning Objectives
- Perform cost-volume-profit analysis for single-product companies.
Question: The profit equation1 shows that profit equals total revenues minus total variable costs and total fixed costs. This profit equation is used extensively in cost-volume-profit (CVP) analysis, and the information in the profit equation is typically presented in the form of a contribution margin income statement (first introduced in Chapter 3). What is the relationship between the profit equation and the contribution margin income statement?
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Break-Even and Target Profit
Question: Companies such as Snowboard Company often want to know the sales required to break even, which is called the break-even point. What is meant by the term break-even point?
Break- Even Point in Units
Question: How is the break-even point in units calculated, and what is the break-even point for Snowboard Company?
Question: Although it is helpful for companies to know the break-even point, most organizations are more interested in determining the sales required to make a targeted amount of profit. How does finding the target profit in units help companies like Snowboard Company?
Question: Let’s formalize this discussion by using the profit equation. How is the profit equation used to find a target profit amount in units?
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Shortcut Formula
Question: Although using the profit equation to solve for the break-even point or target profit in units tends to be the easiest approach, we can also use a shortcut formula derived from this equation. What is the shortcut formula, and how is it used to find the target profit in units for Snowboard Company?
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Break-Even Point in Sales Dollars
Question: Finding the break-even point in units works well for companies that have products easily measured in units, such as snowboard or bike manufacturers, but not so well for companies that have a variety of products not easily measured in units, such as law firms and restaurants. How do companies find the break-even point if they cannot easily measure sales in units?
The contribution margin per unit6 is the amount each unit sold contributes to (1) covering fixed costs and (2) increasing profit. We calculate it by subtracting variable costs per unit (V) from the selling price per unit (S).
Contribution margin per unit = S – V (4.2.7)
For Snowboard Company the contribution margin is $100:
Contribution margin per unit = S – V
Thus each unit sold contributes $100 to covering fixed costs and increasing profit.
Contribution Margin Ratio
The contribution margin ratio7 (often called contribution margin percent) is the contribution margin as a percentage of sales. It measures the amount each sales dollar contributes to (1) covering fixed costs and (2) increasing profit. The contribution margin ratio is the contribution margin per unit divided by the selling price per unit. (Note that the contribution margin ratio can also be calculated using the total contribution margin and total sales; the result is the same.
For Snowboard Company the contribution margin ratio is 40 percent:
Thus each dollar in sales contributes 40 cents ($0.40) to covering fixed costs and increasing profit.
Question: With an understanding of the contribution margin and contribution margin ratio, we can now calculate the break-even point in sales dollars. How do we calculate the break-even point in sales dollars for Snowboard Company?
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Contribution Margin Target Profit in Sales Dollars
Question: Finding a target profit in sales dollar8 simply means that a company would like to know total sales measured in dollars required to achieve a certain profit. Finding the target profit in sales dollars is similar to finding the break-even point in sales dollars except that “target profit” is no longer set to zero. Instead, target profit is set to the profit the company would like to achieve. Recall that management of Snowboard Company asked the following question: What is the amount of total sales dollars required to earn a target profit of $30,000?
Business in Action 4.1: Measuring the Break-Even Point for Airlines
(Unsplah License; Nick Herasimenka via Unsplash)
During the month of September 2001, United Airlines was losing $15 million per day. With $2.7 billion in cash, United had six months to return to profitability before facing a significant cash shortage. Many analysts believed United’s troubles resulted in part from a relatively high break-even point.
Airlines measure break-even points, also called load factors, in terms of the percentage of seats filled. At the end of 2001, one firm estimated that United had to fill 96 percent of its seats just to break even. This is well above the figure for other major airlines, as you can see in the list that follows:
- American Airlines: 85 percent
- Delta Airlines: 85 percent
- Southwest Airlines: 65 percent
- Alaska Airlines: 75 percent
United Airlines filed for bankruptcy at the end of 2002 and emerged from bankruptcy in 2006 after reducing costs by $7 billion a year. Other airlines continue to work on reducing their break-even points and maximizing the percentage of seats filled.
Source: Lisa DiCarlo, “Can This Airline Be Saved?” Forbes magazine’s Web site (http://www.forbes.com), November 2001; “United Airlines Emerges from Bankruptcy,” Reuters (http://www.foxnews.com), February 1, 2005.
CVP Graph
Question: The relationship of costs, volume, and profit can be displayed in the form of a graph. What does this graph look like for Snowboard Company, and how does it help management evaluate financial information related to the production of snowboards?
Margin of Safety
Question: Managers often like to know how close projected sales are to the break-even point. How is this information calculated and used by management?
Key Takeaway
Cost-volume-profit analysis involves finding the break-even and target profit point in units and in sales dollars. The key formulas for an organization with a single product are summarized in the following list. Set the target profit to $0 for break-even calculations, or to the appropriate profit dollar amount for target profit calculations. The margin of safety formula is also shown:
- Break-even or target profit point measured in units:
Total fixed costs + Target profit (4.2.13)
Selling price per unit −Variable cost per unit(The denominator is also called “contribution margin per unit.”)
- Break-even or target profit point measured in sales dollars:
Total fixed costs + Target profit (4.2.14)
Contribution margin ratio -
Margin of safety in units or sales dollars:Projected sales − Break-even sales (4.2.15)
Review problem 4.1
Star Symphony would like to perform for a neighboring city. Fixed costs for the performance total $5,000. Tickets will sell for $15 per person, and an outside organization responsible for processing ticket orders charges the symphony a fee of $2 per ticket. Star Symphony expects to sell 500 tickets.
- How many tickets must Star Symphony sell to break even?
- How many tickets must the symphony sell to earn a profit of $7,000?
- How much must Star Symphony have in sales dollars to break even?
- How much must Star Symphony have in sales dollars to earn a profit of $7,000?
- What is the symphony’s margin of safety in units and in sales dollars?
Definitions
3. The number of units that must be sold to achieve zero profit.
4. The total sales measured in dollars required to achieve zero profit.
5. The number of units that must be sold to achieve a certain profit.
6. The amount each unit sold contributes to (1) covering fixed costs and (2) increasing profit.
7. The contribution margin as a percentage of sales; it measures the amount each sales dollar contributes to (1) covering fixed costs and (2) increasing profit; also called contribution margin percent.
8. The total sales measured in dollars required to achieve a certain profit.
9. The excess of expected sales over the break-even point, measured in units and in sales dollars.
