2. What is the contribution margin ratio? How is it related to the variable cost ratio?
3. If a product’s variable cost per unit increases while the selling price and fi xed cost decrease, what will happen to the contribution margin per unit?
4. How can a company increase a product’s contribution margin?
G U I D E D U N I T P R E P A R A T I O N
Once you understand cost behavior, you can begin to use that knowledge in making business decisions. One of the basic tools for making such decisions is the contribution margin. In this unit you will learn how to calculate the contri- bution margin and how to construct a contribution format income statement to support business decision making.
Contribution Margin
If an organization wants to make a profi t, it must generate more sales revenue than the expenses it incurs. This relation can be expressed using the following profi t equation:
Operating income=Sales revenue–Total expenses or
Operating income= Sales revenue–Total variable expenses–Total fixed expenses
Operating income=1Sales price per unit3# of units sold221Variable cost per unit3# of units sold2 2 Fixed expenses
Operating income=31Sales price per unit–Variable cost per unit23# of units sold4–Fixed expenses
Contribution margin per unit=Sales price per unit–Variable cost per unit or
Contribution margin =Sales revenue –Total variable expenses
Operating income=3Contribution margin per unit 3 # of units sold4–Fixed expenses Let’s expand this profi t equation based on our knowledge of cost behavior.
Since variable cost per unit remains constant, we can express total variable expense as a function of the number of units sold. Likewise, we can express total sales revenue as a function of the number of units sold, resulting in the following expanded profi t equation.
Applying some basic algebra to this equation, we can express operating income in the following way:
The above equation highlights the contribution margin, an important relation- ship between sales and variable cost. The contribution margin is the difference between sales revenue and variable expenses. In other words, it is the amount that remains to cover fi xed expenses and provide a profi t. The contribution margin can be expressed in unit terms, as the sales price per unit minus the variable cost per unit, or as a total:
Using the defi nition of contribution margin, we can rewrite the profi t equation as
This version of the profi t equation should help you understand an important relation between contribution margin and profi t. As the number of units sold in- creases, total contribution margin increases, but fi xed expenses remain the same.
Thus, as the number of units sold rises, profi t increases by the additional contri- bution margin per unit.
Suppose Universal Sports Exchange pays C&C Sports $14.80 for each base- ball jersey and sells the jerseys to customers for $20. Let’s assume the only other
You will notice that sometimes we refer to variable and fi xed costs and at other times to vari- able and fi xed expenses. A cost is the cash or other value given up to obtain goods or services in the expectation that they will generate future benefi ts. A cost can be capitalized as an asset on the balance sheet, as in the purchase of inventory for resale.
Once the future benefi ts have been received, however, the cost becomes an expense on the income statement. So an expense is an expired, or used up, cost.
In the inventory example, when inventory is sold, the future benefi t—sales revenue—
has been realized, so the original capitalized cost is expensed on the income statement as the cost of goods sold. At the same time, the inventory asset on the balance sheet is reduced.
Some costs, such as salaries and wages, are expensed in the same period in which they are incurred and are never re- ported on the balance sheet.
WATCH OUT!
Unit 2.3 Contribution Margin Analysis 63 variable expense Universal incurs is the 6% sales commission it pays each sales-
person ($20 3 6% 5 $1.20 per jersey). Therefore, the jersey has a $4 contribution margin ($20 2 $14.80 2 $1.20). For each jersey sold, Universal earns $4 to cover its total fi xed expenses and provide some profi t.
In assessing business opportunities, the contribution margin ratio is some- times a useful tool. The contribution margin ratio is the ratio of the contribution margin to sales.
Technological advances have made vital information more readily available to restaurant managers than it was in the past. Before restaurants had “back-offi ce” computer systems to provide vital operating information, managers would look at a recipe, develop a best-guess estimate of the cost to prepare the item, and then increase it by 300 to 400% to arrive at the menu price. With today’s systems, however, guessing is no longer necessary. Based on a recipe and the prices of its ingredients, these systems can calculate the contribution margin of a menu item. Armed with this information, restaurant owners can quickly perform menu engineering and identify dishes that aren’t selling or aren’t making money.
What’s the bottom-line result? Using such a system, Chip Motley, the owner of four res- taurants in the Washington, DC area, was able to identify a rib-eye steak special that was selling well but wasn’t making much money. He decided to raise the price and increase the contribution margin. Because the increased price did little to change the sales volume, the result was a bottom-line improvement from the increased contribution margin.
An estimated 30% of all new restaurants fail within their fi rst year of business. Perhaps if more restaurant owners understood the concept of the contribution margin, the failure rate would be lower.
Sources: “Back-Offi ce Bonanza,” Nation’s Restaurant News, October 27, 2003, 8–12; John Nessell, “Is Your Menu Working For or Against You?” Restaurant Resource Group, http://www.rrgconsulting.com/menu_engineering.htm (accessed March 12, 2008); “Restaurant Management Tips: Sell the Big Contributors,” Chef2Chef Culinary Portal, http://foodservice.chef2chef.net/restaurant-management/chapters/tip01.shtml (accessed March 12, 2008); Chana R. Schoenberger, “A Burger with a Side of Losses,” Forbes, December 9, 2002, 168, available online at http://www.
forbes.com/free_forbes/2002/1209/168.html (accessed March 12, 2008).
An estimated 30% of all new restaurants fail within their
fi rst year of business.
REALITY CHECK —The contribution margin recipe
© pidjoe/iStockphoto
Contribution margin ratio= Contribution margin
Sales revenue = Contribution margin per unit Sales price per unit
Contribution margin ratio= $4
$20 =20%
The contribution margin ratio for Universal’s baseball jersey is 20%:
The contribution margin ratio can be used to determine the increase in profi ts from a given dollar increase in sales revenue. With a 20% contribution margin ratio, each dollar in baseball jersey sales generates $0.20 ($1.00 3 20%) in contribution margin for Universal. So an additional $100 in jersey sales will generate $20 in additional contribution margin.
Contribution Format Income Statement
Recall from the chapter opener that Universal missed its target sales goal by 10% and Martin Keck, vice president for sales, was trying to understand how the lower sales volume affected income. Exhibit 2-9 presents Universal Sports Exchange’s income statement that raised Martin’s questions.3
EXHIBIT 2-9 Universal Sports Exchange’s functional income statement.
UNIVERSAL SPORTS EXCHANGE Income Statement
52 Weeks Ended February 1, 2014
Sales $1,039,500
Cost of goods sold 769,230
Gross profi t 270,270
Selling and administrative expense 230,370
Operating income 39,900
Tax expense (30%) 11,970
Net income $ 27,930
This format, which is consistent with GAAP, does not help managers predict the fi nancial results of their decisions. This shortcoming is due to the format of GAAP statements, which is based on cost function (product, sales, administra- tion) rather than on cost behavior.
What Martin needs to answer his questions is an income statement that classifi es expenses by behavior. Such a statement will allow him to easily assess the impact of sales volume on operating income. This type of income statement is called a contri- bution format income statement, and it presents expenses by behavior, as follows:
For the purposes of illustration, let’s assume that Universal sells only one prod- uct, baseball jerseys. Universal buys each jersey from C&C for $14.80 and sells it for $20. That means that both the sales revenue and cost of goods sold vary with the number of jerseys sold. Selling and administrative expenses are made up of $178,870 in selling expenses and $51,500 in administrative expenses. The selling expenses include a 6% sales commission paid to the sales staff. That is, for every dol- lar of sales made by a sales representative, Universal pays a $0.06 commission. Since sales revenue varies with activity, total sales commissions also vary with activity. The rest of the selling expenses are fi xed, as are all the administrative expenses.
Using this information, we can prepare an income statement in the contribution format, as shown in Exhibit 2-10. Notice that we arrived at the same operating income as in the original income statement in Exhibit 2-9. Changing from a traditional func- tional income statement to a contribution format income statement does not change the amount of income. Rather, it just rearranges the individual components. If you notice that operating income has changed after you convert from one format of the in- come statement to the other, you have made an error; you should recheck your work.
Sales revenue 2 Variable expenses
⫽ Contribution margin 2 Fixed expenses
⫽ Operating income
Unit 2.3 Contribution Margin Analysis 65 We are not quite ready to predict how much income Universal lost by failing
to meet its sales targets because we don’t have the information in “constant” form.
(Recall from the WATCH OUT! box on page 49 that you should always put your information in constant form before you begin to estimate the results of a change in activity.) So what do we need to do? Fixed expenses are in the correct format because they are in their “constant” form—that is, in total. Variable expenses, however, need to be converted to a per unit basis, as shown in Exhibit 2-11.
EXHIBIT 2-10
Universal Sports Exchange’s contribution format income statement.
UNIVERSAL SPORTS EXCHANGE Income Statement
52 Weeks Ended February 1, 2014
EXHIBIT 2-11
Universal Sports Exchange’s contribution format income statement with unit data.
UNIVERSAL SPORTS EXCHANGE Income Statement
52 Weeks Ended February 1, 2014
Per Unit Ratio
Sales $1,039,500 $20.00 100%
Less: variable expenses
Cost of goods sold $769,230 14.80 74%
Sales commissions 62,370 1.20 6%
Total variable expenses 831,600 16.00 80%
Contribution margin 207,900 $ 4.00 20%
Less: fi xed expenses
Selling 116,500
Administrative 51,500
Total fi xed expenses 168,000
Operating income $ 39,900
Notice that in the “Ratio” column, variable amounts are shown as a percentage of sales. The contribution margin ratio is 20%; the variable cost ratio is 80%, or 1 minus the contribution margin ratio.
Remember that Universal sold 10% fewer jerseys than it expected, so how many jerseys had it planned to sell? First, we need to know the current sales volume, and we can calculate that amount by dividing total sales dollars by sales price per unit:
Shirts sold= $1,039,500
$20.00 =51,975 jerseys
Sales $1,039,500
Less: variable expenses
Cost of goods sold $769,230
Sales commissions (0.06 3 $1,039,500) 62,370
Total variable expenses 831,600
Contribution margin 207,900
Less: fi xed expenses
Selling ($178,870 2 $62,370) 116,500
Administrative 51,500
Total fi xed expenses 168,000
Operating income $ 39,900
Based on actual sales of 51,975 jerseys, Universal’s original sales projection was 57,750 jerseys (51,975/0.9). Therefore, Universal would need to sell 5,775 ad- ditional jerseys to reach that goal. So how much more income would these 5,775 additional jerseys generate? Each jersey generates $4 in contribution margin, so the total increase in operating income would be $23,100 ($4 3 5,775). Net in- come would increase by $16,170 after taxes ($23,100 3 (1 2 0.30)). We could have obtained the same result using the contribution margin ratio:
Additional sales revenue3 Contribution margin ratio= Additional contribution margin 1$2035,775 jerseys230.20=$23,100
Exhibit 2-12 shows how the contribution format income statement would have looked had the expected level of sales been achieved. Notice that the variable items—sales, variable expenses, and contribution margin—would have varied in total, whereas the fi xed expenses would have remained fi xed.
If the managers at Universal Sports Exchange had decided to lower the sales prices of jerseys to increase sales volume and total sales revenue, what would have been the effect on the following?
• Cost of goods sold per unit
• Commission per jersey sold
• Contribution margin per unit
If the strategy had worked as planned, what would have been the change in the following?
• Total sales revenue
• Total cost of goods sold
• Total commissions paid
• Total contribution margin