A more direct formula for calculating the degree of operating leverage at a
base sales level, Q, is shown in Equation 13.5.5
(13.5)
Substituting , and into Equation
13.5 yields the following result:
The use of the formula results in the same value for DOL (2.0) as that found by
using Table 13.4 and Equation 13.4.6
See the Focus on Practice box for a discussion of operating leverage at software
maker Adobe.
DOL at 1,000 units =1,000 *($10 –$5)
1,000 *($10 –$5) –$2,500 =$5,000
$2,500 =2.0
FC =$2,500Q=1,000, P=$10, VC =$5
Example 13.6 3
DOL at base sales level Q =Q*(P–VC)
Q*(P–VC)–FC
CHAPTER 13 Leverage and Capital Structure 515
5. Technically, the formula for DOL given in Equation 13.5 should include absolute value signs because it is possible
to get a negative DOL when the EBIT for the base sales level is negative. Because we assume that the EBIT for the
base level of sales is positive, we do not use the absolute value signs.
6. When total revenue in dollars from sales—instead of unit sales—is available, the following equation, in which
TR total revenue in dollars at a base level of sales and TVC total variable operating costs in dollars, can be used:
This formula is especially useful for finding the DOL for multiproduct firms. It should be clear that because in the
case of a single-product firm, , substitution of these values into Equation 13.5
results in the equation given here.
TR =Q*P and TVC =Q*VC
DOL at base dollar sales TR =TR –TVC
TR –TVC –FC
==
focus on PRACTICE
Adobe’s Leverage
2009. A 22.6 percent increase in
2007 sales resulted in EBIT growth of
39.7 percent. In 2008, EBIT increased
just a little faster than sales did, but in
2009 as the economy endured a severe
recession, Adobe revenues plunged
17.7 percent. The effect of operating
leverage was that EBIT declined even
faster, posting a 35.3 percent drop.
3
Summarize the pros and cons of
operating leverage.
development and initial marketing stages.
The up-front development costs are fixed,
and subsequent production costs are
practically zero. The economies of scale
are huge: Once a company sells enough
copies to cover its fixed costs, incremen-
tal dollars go primarily to profit.
As demonstrated in the following
table, operating leverage magnified
Adobe’s
increase
in EBIT in 2007 while
magnifying the
decrease
in EBIT in
Adobe Systems, the
second largest PC soft-
ware company in the United States,
dominates the graphic design, imag-
ing, dynamic media, and authoring-tool
software markets. Website designers
favor its Photoshop and Illustrator soft-
ware applications, and Adobe’s
Acrobat software has become a stan-
dard for sharing documents online.
Adobe’s ability to manage discre-
tionary expenses helps keep its bottom
line strong. Adobe has an additional
advantage:
operating leverage,
the use
of fixed operating costs to magnify the
effect of changes in sales on earnings
before interest and taxes (EBIT). Adobe
and its peers in the software industry
incur the bulk of their costs early in a
product’s life cycle, in the research and
in practice
Item FY2007 FY2008 FY2009
Sales revenue (millions) $3,158 $3,580 $2,946
EBIT (millions) $947 $1,089 $705
(1) Percent change in sales 22.6% 13.4% ⫺17.7%
(2) Percent change in EBIT 39.7% 15.0% ⫺35.3%
DOL [(2)⫼(1)] 1.8 1.1 2.0
Source:
Adobe Systems Inc., “2009 Annual Report,” http.//www.adobe.com/aboutadobe/invrelations/pdfs/fy09_10k.pdf.