2. If a product’s variable cost per unit increases while the selling price and fi xed costs remain constant, what will happen to the breakeven point?
3. How do you calculate the breakeven point in units? In dollars?
4. What actions can a company take to reduce its breakeven point?
5. What is the margin of safety? How is it calculated?
G U I D E D U N I T P R E P A R A T I O N
Unit 3.1 Breakeven Analysis 83 In Step (1) we put everything into “constant” form—sales price per unit, variable
cost per unit, and total fi xed expenses. We set the number of jerseys equal to x because that is what we want to know—the number of jerseys that must be sold to break even. Step (2) shows that we could have started the calculation with the
$4 contribution margin per unit, skipping Step (1). Step (3) reveals an essential relationship: At the breakeven point, the total contribution margin equals total fi xed expenses. In Step (4), we solved the breakeven question: 42,000 jerseys must be sold to break even.
We can use our defi nition of the contribution margin as a shortcut to fi nding the breakeven point. Since the contribution margin is the amount that is avail- able to cover fi xed expenses and provide a profi t ($0 in the breakeven case), we can use the following formula to calculate the breakeven point in units:
UNIVERSAL SPORTS EXCHANGE Contribution Format Income Statement for the 52 Weeks Ending 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 Fixed expenses:
Selling expenses 116,500 Administrative expenses 51,500
Total fi xed expenses 168,000
Operating income $ 39,900
EXHIBIT 3-1
Universal Sports Exchange’s contribution format income statement.
(1) $20x 2 $16x 2 $168,000 5 $0 (2) $4x 2 $168,000 5 $0 (3) $4x 5 $168,000
(4) x 5 42,000 jerseys
Total fixed expenses
Contribution margin per unit = Breakeven point in units
$168,000
$4.00 =42,000 jerseys
Notice that this formula is just a restatement of the mathematical operations made between Steps (3) and (4).
Sometimes it is useful to know the breakeven point in terms of sales dollars rather than units. If we know the breakeven point in units, we can simply mul- tiply it by the sales price per unit: $20 3 42,000 5 $840,000. Alternatively, we
Break even calculations will not always yield a breakeven point that is in whole units.
Since you can’t sell a fractional unit of a product, always round breakeven points up to the next whole unit.
WATCH OUT!
could use the contribution margin ratio and the profi t relationships examined on the previous page, as in the following formula:
Breakeven Graphs
While calculating a breakeven point is useful, managers are also interested in the profi ts generated at other sales levels. A breakeven graph illustrates this relationship between sales revenue and expenses, allowing managers to view a
Total fixed expenses
Contribution margin ratio = Breakeven point in sales dollars
$168,000
0.20 =$840,000 in sales dollars to break even Retail establishments and manufacturers have an obvious interest in breakeven analysis. But do service organizations such as airlines and art galleries ever use the concept? Absolutely.
Airlines calculate a “breakeven load factor” which is the average percent of seats on an average fl ight that must be occupied by a customer paying an average fare before the fl ight generates a profi t. Analysts estimated in early 2012 that “network” carriers such as American, Delta, United, and US Airways break even when they achieve an 86.6% load factor. But at that time, these carriers fi lled only 86% of their seats on average. “Value” carriers such as JetBlue and Southwest should break even if they fi ll 79.3% of their seats, and these carriers achieved an average load factor of 83% in that period. Increasing breakeven load factors have plagued the industry since 2000, and airlines have reduced operating costs, increased fares, and implemented extra fees for checked baggage and other services to lower the breakeven load factor to acceptable levels. While these actions may have helped to some degree, US Airways reported in June 2012 that a hypothetical fl ight of 100 passengers paying an average domestic fare of $146 and $18 in fees had a breakeven load factor of almost 99%.
Before the Bellagio Gallery of Fine Art, housed in the Bellagio Casino in Las Vegas, opened a show of 21 Monets on loan from the Museum of Fine Arts in Boston, Marc Glimcher estimated that 400 people a day, paying between $12 and $15 each, needed to view the exhibit to achieve the breakeven point. Since shows of works by Andy Warhol and Fabergé had drawn over 150,000 visitors, this level of attendance did not appear to be out of reach. The show averaged 1,000 visitors each day, far exceeding the projected breakeven attendance. The show generated approximately $6 million in ticket sales, with more than
$1 million going back to Boston’s Museum of Fine Arts. Following the show’s success, the gallery staged another show of Impressionist paintings from the museum, and other muse- ums are expressing interest in showing their works at the Bellagio.
Sources: Fred A. Bernstein, “A Loan That Keeps on Paying,” The New York Times, March 30, 2005; Kristen Peterson,
“Casino Handed Artistic Legacy,” Las Vegas Sun, February 8, 2008, http://www.lasvegassun.com/news/2008/feb/08/
casino-handed-artistic-legacy/ (accessed March 5, 2008); Steve Friess and Peter Plagens, “Show Me the Monet,” News- week, January 26, 2004, 60; Scott McCartney, “Airlines That Fill 86% of Seats and Still Lose Money on Domestic Flights,”
The Wall Street Journal, February 8, 2012; Scott McCartney, “How Airlines Spend Your Airfare,” The Wall Street Journal, June 7, 2010; U.S. Department of Transportation, “Rising Breakeven Load Factors Threaten Airline Finances,” October 2003, http://www.bts.gov/publications/special_reports_and_issue_briefs/issue_briefs/number_08/pdf/entire.pdf (ac- cessed September 7, 2012); Ken White, “Making an Impression,” Las Vegas Review-Journal Neon, June 10, 2005, http://www.reviewjournal.com/lvrj_home/2005/Jun-10-Fri-2005/weekly/2000819.html (accessed March 5, 2008).
US Airways reported in June 2012 that a hypothetical fl ight of 100 passengers had a breakeven
load factor of almost 99%.
REALITY CHECK —Who really uses breakeven analysis?
© izusek/iStockphoto
Unit 3.1 Breakeven Analysis 85 range of results at a single glance. Exhibit 3-2 shows Universal’s breakeven graph
based on the company’s sales and expense information. Notice that the total sales revenue line intersects the y-axis at $0 and has a slope of $20: for every jersey sold, Universal takes in $20 of revenue. The fi xed expense line intersects the y-axis at $168,000 and remains constant across all sales volumes. Even if no jerseys were sold, the company would incur fi xed expenses of $168,000. The total cost line represents the sum of fi xed and variable expenses, so it intersects the y-axis at $168,000 and increases at a rate (slope) of $16 per jersey. The point at which the total sales revenue line and the total expense line intersect is the breakeven point. Any level of sales to the left of the breakeven point represents an operating loss. Any level of sales to the right of the breakeven point represents operating income.
One of the activities managers like to engage in is called “what-if” analy- sis, or sensitivity analysis. “What if I could reduce fi xed expenses—how would profi ts change?” Before we get into this type of analysis, let’s use Universal’s breakeven graph to think conceptually about these questions. What if fi xed ex- penses decrease—how would the graph change? The fi xed expense line would shift downward, as would the total expense line. The revenue line would remain unchanged, so the breakeven point would shift to the left, indicating that fewer jerseys would need to be sold to break even. And since neither sales nor variable costs changes, the contribution margin doesn’t change either. The end result:
when expenses go down, operating profi t goes up.
Margin of Safety
A company’s margin of safety is the difference between current sales and break- even sales. It represents the volume of sales that can be lost before the company begins to lose money and can be measured in units or sales dollars.
EXHIBIT 3-2 Breakeven graph for Universal Sports Exchange.
10,000
Operating loss
Fixed expenses Total Sales Revenue Total Expenses
Breakeven point 42,000 jerseys
Operating profit
20,000 30,000 40,000 50,000 60,000 70,000 Jerseys Sold
$1,400,000
$1,200,000
$1,000,000
$800,000
$600,000
Breakeven point
$840,000 in sales
$400,000
$200,000
$0
Margin of safety 5 Current sales 2 Breakeven sales
Let’s calculate Universal’s margin of safety. From Exhibit 3-1 we can calculate Universal’s current unit sales: $1,039,500 4 $20 sales price per jersey 5 51,975 jerseys sold.
Universal is in good shape—it would have to lose 19.2% ($199,500 4 $1,039,500) of its sales before it started losing money.
Margin of safety in units=51,975 jerseys–42,000 jerseys=9,975 jerseys Margin of safety in sales dollars=$1,039,500–$840,000=$199,500
U N I T 3 . 1 R E V I E W
KEY TERMS
Breakeven graph p. 84 Breakeven point p. 82 Margin of safety p. 85
1. LO 1 At the breakeven point, sales revenue and total contribution margin are equal. True or False?
2. LO 1 Reese Manufacturing has a current breakeven point of 475,642 units. To reduce the breakeven point, Reese Manufacturing should
a. reduce the contribution margin.
b. increase fi xed expenses.
c. reduce the sales price per unit.
d. increase the contribution margin.
3. LO 1 Jordan Graft Images sells framed prints of various college landmarks. Jordan purchases the prints from his supplier for $30 and sells them through his website for $65. Jordan’s fi xed expenses are $89,250. What is Jordan’s breakeven point in units?
a. 940 b. 1,373 c. 2,550 d. 2,975
PRACTICE QUESTIONS
Fill in the rest of the table
WHAT IF . . . * EFFECT ON
Sales Revenue
Total Expenses
Contribution Margin per Unit
Breakeven Point
Operating Profi t fi xed expenses
decrease
no effect variable cost
per unit increases sales price increases
*Assume that sales volume remains constant.