1. GlobAl
edITIon
•
Principles of
Managerial Finance
FoUrTeenTh edITIon
Lawrence J. Gitman • Chad J. Zutter

2. 558
Why This Chapter Matters to You
In your professional life
Accounting You need to understand how to calculate and analyze operating
and financial leverage and to be familiar with the tax and earnings effects of
various capital structures.
informAtion SYStemS You need to understand the types of capital and what
capital structure is because you will provide much of the information needed in
management’s determination of the best capital structure for the firm.
mAnAgement You need to understand leverage so that you can control risk
and magnify returns for the firm’s owners and to understand capital structure
theory so that you can make decisions about the firm’s optimal capital structure.
mArketing You need to understand breakeven analysis, which you will use in
pricing and product feasibility decisions.
operAtionS You need to understand the impact of fixed and variable
operating costs on the firm’s breakeven point and its operating leverage because
these costs will have a major effect on the firm’s risk and return.
In your personal life
Like corporations, you routinely incur debt,
using both credit cards for short-term needs
and negotiated long-term loans. When you borrow over the long term, you
experience the benefits and consequences of leverage. Also, the level of your
outstanding debt relative to net worth is conceptually the same as a firm’s capital
structure. it reflects your financial risk and affects the availability and cost of
borrowing.
Leverage and Capital
Structure
13
Learning Goals
LG 1 Discuss leverage, capital
structure, breakeven
analysis, the operating
breakeven point, and the
effect of changing costs
on the breakeven point.
LG 2 understand operating,
financial, and total
leverage and the
relationships among
them.
LG 3 Describe the types of
capital, external
assessment of capital
structure, the capital
structure of non–u.S.
firms, and capital
structure theory.
LG 4 explain the optimal
capital structure using a
graphical view of the
firm’s cost-of-capital
functions and a zero-
growth valuation model.
LG 5 Discuss the eBit–epS
approach to capital
structure.
LG 6 review the return and risk
of alternative capital
structures, their linkage to
market value, and other
important considerations
related to capital
structure.

3. 559
Lowe’s Builds Leverage
In April 2012, the home improvement chain
Lowe’s issued $2 billion worth of bonds with
maturities ranging from 5 to 30 years. The com-
pany’s chief financial officer, Robert Hull, ex-
plained in a conference call with investors that
Lowe’s planned to use the proceeds from the bond
sale, along with cash flow generated by the busi-
ness, to buy back up to $4.5 billion of its own
stock. That plan represented a significant shift in the firm’s capital structure (its mix of debt and eq-
uity financing), a move that would put more cash in the hands of shareholders and apply more
pressure on Lowe’s management to generate positive cash flow from the business to repay the
debt. With more of its financing coming from debt, Lowe’s was adding financial leverage to its
business, meaning that if the firm succeeded in selling its products, the returns to shareholders
would be magnified. However, if Lowe’s instead experienced a decline in its business, paying
back the debt might be difficult, and returns to shareholders would suffer as a result.
At first, Lowe’s financial strategy appeared to have backfired, as the company reported dis-
appointing revenues and profits from the spring and summer months of 2012, and its stock price fell
from around $31 in April to $24.50 in early August. Helped by a recovering economy and later
by Hurricane Sandy, however, Lowe’s business began to turn around. In the third quarter of 2012,
Lowe’s profits surged 76 percent, and investors sent its stock price up 7 percent in a single day. In
the 12 months starting August 1, 2012, Lowe’s stock price rose more than 70 percent, whereas the
Standard & Poor’s 500 Stock Composite Index managed to gain a little more than 20 percent.
Lowe’s experience after shifting its capital structure toward more debt illustrates the general
principle that as a company relies more heavily on debt, its profits become more sensitive to underly-
ing business conditions. Earnings rise rapidly in good times and fall more steeply in bad times, and
stock prices react accordingly. In this chapter, we’ll uncover the factors that influence a company’s
decisions about financing its operations with debt or equity.
Lowe’s

4. 560 PART 6 Long-Term Financial Decisions
13.1 Leverage
Leverage refers to the effects that fixed costs have on the returns that sharehold-
ers earn. By “fixed costs,” we mean costs that do not rise and fall with changes in
a firm’s sales. Firms have to pay these fixed costs whether business conditions are
good or bad. These fixed costs may be operating costs, such as the costs incurred
by purchasing and operating plant and equipment, or they may be financial costs,
such as the fixed costs of making debt payments. We say that a firm with higher
fixed costs has greater leverage. Generally, leverage magnifies both returns and
risks. A firm with more leverage may earn higher returns on average than a firm
with less leverage, but the returns on the more leveraged firm will also be more
volatile.
Many business risks are out of the control of managers, but not the risks
associated with leverage. Managers can either increase or decrease leverage by
adopting strategies that rely more heavily on fixed or variable costs. For exam-
ple, a choice that many firms confront is whether to make their own products
or to outsource manufacturing to another firm. A company that does its own
manufacturing may invest billions in factories around the world. These facto-
ries generate costs whether they are running or not so a firm that does its own
manufacturing will tend to have higher leverage. In contrast, a company that
outsources production can quickly reduce its costs when demand is low simply
by not placing orders. Therefore, such a firm will generally have lower leverage
compared to a firm that manufactures its own goods.
Managers also influence leverage by choosing a specific capital structure,
which is the mix of long-term debt and equity maintained by a firm. The more
debt a firm issues, the higher are its debt repayment costs, and those costs must
be paid regardless of how the firm’s products are selling. Because leverage can
have such a large impact on a firm, the financial manager must understand how
to measure and evaluate leverage, particularly when making capital structure
decisions.
Table 13.1 uses an income statement to highlight where different sources of
leverage come from.
LG 2
LG 1
leverage
Refers to the effects that fixed
costs have on the returns that
shareholders earn; higher
leverage generally results in
higher but more volatile
returns.
capital structure
The mix of long-term debt and
equity maintained by the firm.
TABLE 13.1 General Income Statement Format and Types of Leverage
Operating leverage
Sales revenue
Less: Cost of goods sold
Gross profits
Less: Operating expenses
Financial leverage
Earnings before interest and taxes (EBIT)
Less: Interest Total leverage
Net profits before taxes
Less: Taxes
Net profits after taxes
Less: Preferred stock dividends
Earnings available for common stockholders
Earnings per share (EPS)
¯˚˘˚˙
¯˚˚˚˘˚˚˚˙
¯
˚
˚
˚
˚
˚
˘
˚
˚
˚
˚
˚
˙

5. ChAPTER 13 Leverage and Capital Structure 561
• Operating leverage is concerned with the relationship between the firm’s sales
revenue and its earnings before interest and taxes (EBIT) or operating profits.
When costs of operations (such as cost of goods sold and operating expenses) are
largely fixed, small changes in revenue will lead to much larger changes in EBIT.
• Financial leverage is concerned with the relationship between the firm’s EBIT
and its common stock earnings per share (EPS). On the income statement, you
can see that the deductions taken from EBIT to get to EPS include interest,
taxes, and preferred dividends. Taxes are clearly variable, rising and falling
with the firm’s profits, but interest expense and preferred dividends are usu-
ally fixed. When these fixed items are large (that is, when the firm has a lot of
financial leverage), small changes in EBIT produce larger changes in EPS.
• Total leverage is the combined effect of operating and financial leverage. It is
concerned with the relationship between the firm’s sales revenue and EPS.
We will examine the three types of leverage concepts in detail. First, though,
we will look at breakeven analysis, which lays the foundation for leverage con-
cepts by demonstrating the effects of fixed costs on the firm’s operations.
BREAKEVEN ANALYSIS
Firms use breakeven analysis, also called cost-volume-profit analysis, (1) to
determine the level of operations necessary to cover all costs and (2) to evaluate
the profitability associated with various levels of sales. The firm’s operating
breakeven point is the level of sales necessary to cover all operating costs. At that
point, earnings before interest and taxes (EBIT) equals $0.1
The first step in finding the operating breakeven point is to divide the cost of
goods sold and operating expenses into fixed and variable operating costs. Fixed
costs are costs that the firm must pay in a given period regardless of the sales
volume achieved during that period. These costs are typically contractual; rent,
for example, is a fixed cost. Because fixed costs do not vary with sales, we typi-
cally measure them relative to time. For example, we would typically measure
rent as the amount due per month. Variable costs vary directly with sales volume.
Shipping costs, for example, are a variable cost.2
We typically measure variable
costs in dollars per unit sold.
Algebraic Approach
Using the following variables, we can recast the operating portion of the firm’s
income statement given in Table 13.1 into the algebraic representation shown in
Table 13.2, where
P = sale price per unit
Q = sales quantity in units
FC = fixed operating cost per period
VC = variable operating cost per unit
breakeven analysis
Used to indicate the level of
operations necessary to cover
all costs and to evaluate the
profitability associated with
various levels of sales; also
called cost-volume-profit
analysis.
operating breakeven point
The level of sales necessary to
cover all operating costs; the
point at which EBIT 5 $0.
1. Quite often, the breakeven point is calculated so that it represents the point at which all costs—both operating
and financial—are covered. For now, we focus on the operating breakeven point as a way to introduce the concept
of operating leverage. We will discuss financial leverage later.
2. Some costs, commonly called semifixed or semivariable, are partly fixed and partly variable. An example is sales
commissions that are fixed for a certain volume of sales and then increase to higher levels for higher volumes. For
convenience and clarity, we assume that all costs can be classified as either fixed or variable.

6. 562 PART 6 Long-Term Financial Decisions
Rewriting the algebraic calculations in Table 13.2 as a formula for earnings be-
fore interest and taxes yields Equation 13.1:
EBIT = (P * Q) - FC - (VC * Q) (13.1)
Q =
FC
P - VC
(13.3)
Operating Leverage, Costs, and Breakeven Analysis
Item Algebraic
representation
Sales revenue (P 3 Q)
Operating leverage Less: Fixed operating costs 2 FC
Less: Variable operating costs 2 (VC 3 Q)
Earnings before interest and taxes EBIT
TABLE 13.2
Simplifying Equation 13.1 yields
where Q is the firm’s operating breakeven point.3
Assume that Cheryl’s Posters, a small poster retailer, has fixed operating costs of
$2,500. Its sale price is $10 per poster, and its variable operating cost is $5 per
poster. Applying Equation 13.3 to these data yields
Q =
$2,500
$10 - $5
=
$2,500
$5
= 500 units
At sales of 500 units, the firm’s EBIT should just equal $0. The firm will have
positive EBIT for sales greater than 500 units and negative EBIT, or a loss, for sales
less than 500 units. We can confirm this conclusion by substituting values above
and below 500 units, along with the other values given, into Equation 13.1.
Example 13.1 ▶
3. Because the firm is assumed to be a single-product firm, its operating breakeven point is found in terms of unit
sales, Q. For multiproduct firms, the operating breakeven point is generally found in terms of dollar sales, S. We can
find S by substituting the contribution margin, which is 100 percent minus total variable operating costs as a per-
centage of total sales, denoted VC%, into the denominator of Equation 13.3. The result is Equation 13.3a
S =
FC
1 - VC,
(13.3a)
This multiproduct-firm breakeven point assumes that the firm’s product mix remains the same at all levels of sales.
¯
˘
˙
EBIT = Q * (P - VC) - FC (13.2)
As noted above, the operating breakeven point is the level of sales at which all
fixed and variable operating costs are covered, that is, the level at which EBIT
equals $0. Setting EBIT equal to $0 and solving Equation 13.2 for Q yields
MyFinancelab Solution
Video

7. ChAPTER 13 Leverage and Capital Structure 563
Graphical Approach
Figure 13.1 presents in graphical form the breakeven analysis of the data in the
preceding example. The firm’s operating breakeven point is the point at which its
total operating cost—the sum of its fixed and variable operating costs—equals
sales revenue. At this point, EBIT equals $0. The figure shows that for sales be-
low 500 units, total operating cost exceeds sales revenue, and EBIT is less than $0
(a loss). For sales above the breakeven point of 500 units, sales revenue exceeds
total operating cost, and EBIT is greater than $0.
Changing Costs and the Operating Breakeven Point
A firm’s operating breakeven point is sensitive to a number of variables: the fixed
operating cost (FC), the sale price per unit (P), and the variable operating cost per
unit (VC). Refer to Equation 13.3 to see how increases or decreases in these vari-
ables affect the breakeven point. The sensitivity of the breakeven sales volume
(Q) to an increase in each of these variables is summarized in Table 13.3. As
FIGuRE 13.1
Breakeven Analysis
Graphical operating
breakeven analysis
Sales
Revenue
Total
Operating
Cost
Operating
Breakeven
Point
E
B
I
T
Fixed
Operating
Cost
500
0 1,000 1,500 2,000 2,500 3,000
Loss
12,000
10,000
8,000
6,000
4,000
2,000
Costs/Revenues
($)
Sales (units)
TABLE 13.3
Sensitivity of Operating Breakeven Point
to Increases in Key Breakeven Variables
Increase in variable
Effect on operating
breakeven point
Fixed operating cost (FC) Increase
Sale price per unit (P) Decrease
Variable operating cost per unit (VC) Increase
Note: Decreases in each of the variables shown would have the opposite
effect on the operating breakeven point.

8. 564 PART 6 Long-Term Financial Decisions
might be expected, an increase in cost (FC or VC) tends to increase the operating
breakeven point, whereas an increase in the sale price per unit (P) decreases the
operating breakeven point.
Assume that Cheryl’s Posters wishes to evaluate the impact of several options:
(1) increasing fixed operating costs to $3,000, (2) increasing the sale price per
unit to $12.50, (3) increasing the variable operating cost per unit to $7.50, and
(4) simultaneously implementing all three of these changes. Substituting the ap-
propriate data into Equation 13.3 yields
(1) Operating breakeven point =
$3,000
$10 - $5
= 600 units
(2) Operating breakeven point =
$2,500
$12.50 - $5
= 3331
3units
(3) Operating breakeven point =
$2,500
$10 - $7.50
= 1,000 units
(4) Operating breakeven point =
$3,000
$12.50 - $7.50
= 600 units
Comparing the resulting operating breakeven points to the initial value of 500
units, we can see that the cost increases (actions 1 and 3) raise the breakeven
point, whereas the revenue increase (action 2) lowers the breakeven point. The
combined effect of increasing all three variables (action 4) also results in an in-
creased operating breakeven point.
Rick Polo is considering having a new fuel-saving device in-
stalled in his car. The installed cost of the device is $240 paid
up front plus a monthly fee of $15. He can terminate use of the device any time
without penalty. Rick estimates that the device will reduce his average monthly
gas consumption by 20%, which, assuming no change in his monthly mileage,
translates into a savings of about $28 per month. He is planning to keep the car
for 2 more years and wishes to determine whether he should have the device in-
stalled in his car.
To assess the financial feasibility of purchasing the device, Rick calculates the
number of months it will take for him to break even. Letting the installed cost of
$240 represent the fixed cost (FC), the monthly savings of $28 represent the ben-
efit (P), and the monthly fee of $15 represent the variable cost (VC), and substi-
tuting these values into the breakeven point equation, Equation 13.3, we get
Breakeven point (in months) = $240 , ($28 - $15) = $240 , $13
5 18.5 months
Because the fuel-saving device pays itself back in 18.5 months, which is less than
the 24 months that Rick is planning to continue owning the car, he should have
the fuel-saving device installed in his car.
Example 13.2 ▶
Personal Finance Example 13.3 ▶

9. ChAPTER 13 Leverage and Capital Structure 565
OPERATING LEVERAGE
Operating leverage results from the existence of fixed costs that the firm must pay
to operate. Using the structure presented in Table 13.2, we can define operating
leverage as the use of fixed operating costs to magnify the effects of changes in
sales on the firm’s earnings before interest and taxes.
Using the data for Cheryl’s Posters (sale price, P = $10 per unit; variable operat-
ing cost, VC = $5 per unit; fixed operating cost, FC = $2,500), Figure 13.2
presents the operating breakeven graph originally shown in Figure 13.1. The ad-
ditional notations on the graph indicate that as the firm’s sales increase from
1,000 to 1,500 units (Q1 to Q2), its EBIT increases from $2,500 to $5,000 (EBIT1
to EBIT2). In other words, a 50% increase in sales (1,000 to 1,500 units) results
in a 100% increase in EBIT ($2,500 to $5,000). Table 13.4 includes the data for
Figure 13.2 as well as relevant data for a 500-unit sales level. We can illustrate
two cases using the 1,000-unit sales level as a reference point:
Case 1 A 50% increase in sales (from 1,000 to 1,500 units) results in a 100%
increase in earnings before interest and taxes (from $2,500 to $5,000).
Case 2 A 50% decrease in sales (from 1,000 to 500 units) results in a 100%
decrease in earnings before interest and taxes (from $2,500 to $0).
From the preceding example, we see that operating leverage works in both
directions. When a firm has fixed operating costs, operating leverage is present.
Example 13.4 ▶
operating leverage
The use of fixed operating costs
to magnify the effects of changes
in sales on the firm’s earnings
before interest and taxes.
FIGuRE 13.2
Operating Leverage
Breakeven analysis and
operating leverage
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
500
0 1,000 1,500 2,000 2,500 3,000
Q1 Q2
Sales (units)
Costs/Revenues
($)
EBIT1
$2,500
EBIT2
$5,000
Loss
EBIT
Fixed
Operating
Cost
Total
Operating
Cost
Sales
Revenue

10. 566 PART 6 Long-Term Financial Decisions
An increase in sales results in a more-than-proportional increase in EBIT; a
decrease in sales results in a more-than-proportional decrease in EBIT.
Measuring the degree of Operating Leverage (dOL)
The degree of operating leverage (DOL) is a numerical measure of the firm’s op-
erating leverage. It can be derived using the equation4
TABLE 13.4 The EBIT for Various Sales Levels
Case 2 Case 1
250% 150%
Sales (in units) 500 1,000 1,500
Sales revenuea
$5,000 $10,000 $15,000
Less: Variable operating costsb
2,500 5,000 7,500
Less: Fixed operating costs 2,500 2,500 2,500
Earnings before interest and taxes (EBIT) $ 0 $ 2,500 $ 5,000
2100% 1100%
a
Sales revenue = $10/unit * sales in units.
b
Variable operating costs = $5/unit * sales in units.
4. The degree of operating leverage also depends on the base level of sales used as a point of reference. The closer the
base sales level used is to the operating breakeven point, the greater the operating leverage. Comparison of the de-
gree of operating leverage of two firms is valid only when the same base level of sales is used for both firms.
degree of operating
leverage (DOL)
The numerical measure of the
firm’s operating leverage.
DOL =
Percentage change in EBIT
Percentage change in sales
(13.4)
Whenever the percentage change in EBIT resulting from a given percentage
change in sales is greater than the percentage change in sales, operating lever-
age exists. In other words, as long as DOL is greater than 1, there is operating
leverage.
Applying Equation 13.4 to cases 1 and 2 in Table 13.4 yields the following results:
Case 1
+100,
+50,
= 2.0
Case 2
-100,
-50,
= 2.0
These calculations show that Cheryl’s Posters’ EBIT changes twice as much (on a
percentage basis) as its sales. For a given base level of sales, the higher the value
resulting from applying Equation 13.4, the greater the degree of operating leverage.
Example 13.5 ▶
MyFinancelab Solution
Video

11. ChAPTER 13 Leverage and Capital Structure 567
Substituting Q = 1,000, P = $10, VC = $5, and FC = $2,500 into Equation
13.5 gives us
DOL at 1,000 units =
1,000 * ($10 - $5)
1,000 * ($10 - $5) - $2,500
=
$5,000
$2,500
= 2.0
As before, the DOL value of 2.0 means that at Cheryl’s Posters a change in sales
volume results in an EBIT change that is twice as large in percentage terms.6
See the Focus on Practice box for a discussion of operating leverage at soft-
ware maker Adobe.
Example 13.6 ▶
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 5
total revenue in dollars at a base level of sales and TVC = total variable operating costs in dollars, can be used:
DOL at base dollar sales TR =
TR - TVC
TR - TVC - FC
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, TR = Q * P and TVC = Q * VC, substitution of these values into Equation 13.5
results in the equation given here.
A more direct formula for calculating the degree of operating leverage at a
base sales level, Q, is5
DOL at base sales level Q =
Q * (P - VC)
Q * (P - VC) - FC
(13.5)
Adobe Systems, one of
the largest PC software
company in the United States, domi-
nates the graphic design, imaging, dy-
namic media, and authoring-tool soft-
ware markets. Website designers favor
its Photoshop and Illustrator software ap-
plications, and Adobe’s Acrobat soft-
ware has become a standard for shar-
ing documents online.
Adobe’s ability to manage discre-
tionary expenses helps keep its bottom
line strong. Adobe has an additional ad-
vantage: operating leverage, the use of
fixed operating costs to magnify the ef-
fect of changes in sales on earnings be-
fore 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 development
focus on PRACTICE
Adobe’s Leverage
decrease in EBIT in 2009. A 22.6 per-
cent increase in 2007 sales resulted in
EBIT growth of 39.7 percent, but in
2009 as the economy endured a severe
recession, Adobe revenues plunged
17.7 percent. The effect of operating le-
verage was that EBIT declined even
faster, posting a 35.3 percent drop.
▶ Summarize the pros and cons of
operating leverage.
and initial marketing stages. The up-front
development costs are fixed, and subse-
quent production costs are practically
zero. The economies of scale are huge:
Once a company sells enough copies to
cover its fixed costs, incremental dollars
go primarily to profit.
As demonstrated in the following
table, operating leverage magnified
Adobe’s increase in EBIT in 2007,
2010, and 2012 while magnifying the
Source: Adobe Systems Inc., “2009 and 2012 Annual Reports,” http://www.adobe.com/investor-relations/financial-documents.html.
in practice
Item FY2007 FY2008 FY2009 FY2010 FY2011 FY2012
Sales revenue (millions) $3,158 $3,580 $2,946 $3,800 $4,216 $4,404
EBIT (millions) $947 $1,089 $705 $1,000 $1,102 $1,186
(1) Percent change in sales 22.6% 13.4% –17.7% 29.0% 11.0% 4.4%
(2) Percent change in EBIT 39.7% 15.0% –35.3% 41.9% 10.2% 7.6%
DOL [(2) ÷ (1)] 1.8 1.1 2.0 1.4 0.9 1.7

12. 568 PART 6 Long-Term Financial Decisions
Fixed Costs and Operating Leverage
Changes in fixed operating costs affect operating leverage significantly. Firms
sometimes can alter the mix of fixed and variable costs in their operations.
For example, a firm could make fixed-dollar lease payments rather than pay-
ments equal to a specified percentage of sales. or it could compensate sales rep-
resentatives with a fixed salary and bonus rather than on a pure percent-of-sales
commission basis. The effects of changes in fixed operating costs on operating
leverage can best be illustrated by continuing our example.
Assume that Cheryl’s Posters eliminates sales commissions and increases salaries.
This exchange results in a reduction in the variable cost per unit from $5 to $4.50
and an increase in the fixed costs from $2,500 to $3,000. Table 13.5 presents an
analysis like that in Table 13.4, but using the new costs. Although the EBIT of
$2,500 at the 1,000-unit sales level is the same as before the shift in cost struc-
ture, Table 13.5 shows that the firm has increased its operating leverage by in-
creasing fixed costs and lowering variable costs.
With the substitution of the appropriate values into Equation 13.5, the de-
gree of operating leverage at the 1,000-unit base level of sales becomes
DOL at 1,000 units =
1,000 * ($10 - $4.50)
1,000 * ($10 - $4.50) - $3,000
=
$5,500
$2,500
= 2.2
Comparing this value to the DOL of 2.0 before the shift to more fixed costs makes
it clear that the higher the firm’s fixed operating costs relative to variable operat-
ing costs, the greater the degree of operating leverage. Under the new cost struc-
ture, a 50% change in sales would lead to a 110% (50% 3 2.2) change in EBIT.
FINANCIAL LEVERAGE
Financial leverage results from the presence of fixed financial costs that the firm
must pay. Using the framework in Table 13.1, we can define financial leverage
as the use of fixed financial costs to magnify the effects of changes in earnings
Example 13.7 ▶
Operating Leverage and Increased Fixed Costs
Case 2 Case 1
250% 150%
Sales (in units) 500 1,000 1,500
Sales revenuea
$5,000 $10,000 $15,000
Less: Variable operating costsb
2,250 4,500 6,750
Less: Fixed operating costs 3,000 3,000 3,000
Earnings before interest and taxes (EBIT) 2$ 250 $ 2,500 $ 5,250
2110% 1110%
a
Sales revenue was calculated as indicated in Table 13.4.
b
Variable operating costs 5 $4.50/unit 3 sales in units.
TABLE 13.5
financial leverage
The use of fixed financial costs
to magnify the effects of
changes in earnings before
interest and taxes on the firm’s
earnings per share.

13. ChAPTER 13 Leverage and Capital Structure 569
before interest and taxes on the firm’s earnings per share. The two most com-
mon fixed financial costs are (1) interest on debt and (2) preferred stock divi-
dends. These charges must be paid regardless of the amount of EBIT available
to pay them.7
Chen Foods, a small Asian food company, expects EBIT of $10,000 in the cur-
rent year. It has a $20,000 bond with a 10% (annual) coupon rate of interest and
an issue of 600 shares of $4 (annual dividend per share) preferred stock outstand-
ing. It also has 1,000 shares of common stock outstanding. The annual interest
on the bond issue is $2,000 (0.10 3 $20,000). The annual dividends on the pre-
ferred stock are $2,400 ($4.00/share 3 600 shares). Table 13.6 presents the earn-
ings per share (EPS) corresponding to levels of EBIT of $6,000, $10,000, and
$14,000, assuming that the firm is in the 40% tax bracket. The table illustrates
two situations:
Case 1 A 40% increase in EBIT (from $10,000 to $14,000) results in a
100% increase in earnings per share (from $2.40 to $4.80).
Case 2 A 40% decrease in EBIT (from $10,000 to $6,000) results in a 100%
decrease in earnings per share (from $2.40 to $0).
Example 13.8 ▶
7. Although a firm’s board of directors can elect to stop paying preferred stock dividends, the firm typically cannot
pay dividends on common stock until the preferred shareholders receive all the dividends that they are owed. Al-
though failure to pay preferred dividends cannot force the firm into bankruptcy, it increases the common stockhold-
ers’ risk because they cannot receive dividends until the claims of preferred stockholders are satisfied.
TABLE 13.6 The EPS for Various EBIT Levelsa
Case 2 Case 1
240% 140%
EBIT $6,000 $10,000 $14,000
Less: Interest (I) 2,000 2,000 2,000
Net profits before taxes $4,000 $ 8,000 $12,000
Less: Taxes (T = 0.40) 1,600 3,200 4,800
Net profits after taxes $2,400 $ 4,800 $ 7,200
Less: Preferred stock dividends (PD) 2,400 2,400 2,400
Earnings available for common (EAC) $ 0 $ 2,400 $ 4,800
Earnings per share (EPS) $0
1,000
5 $0
$2,400
1,000
5 $2.40
$4,800
1,000
5 $4.80
2100% 1100%
a
As noted in Chapter 2, for accounting and tax purposes, interest is a tax-deductible expense, whereas
dividends must be paid from after-tax cash flows.
The effect of financial leverage is such that an increase in the firm’s EBIT
results in a more-than-proportional increase in the firm’s earnings per share,
whereas a decrease in the firm’s EBIT results in a more-than-proportional
decrease in EPS.

14. 570 PART 6 Long-Term Financial Decisions
Measuring the degree of Financial Leverage (dFL)
The degree of financial leverage (DFL) is a numerical measure of the firm’s finan-
cial leverage. Computing it is much like computing the degree of operating lever-
age. One approach for obtaining the DFL is8
8. This approach is valid only when the same base level of EBIT is used to calculate and compare these values. In
other words, the base level of EBIT must be held constant to compare the financial leverage associated with different
levels of fixed financial costs.
degree of financial leverage
(DFL)
The numerical measure of the
firm’s financial leverage.
DFL =
Percentage change in EPS
Percentage change in EBIT
(13.6)
Whenever the percentage change in EPS resulting from a given percentage change
in EBIT is greater than the percentage change in EBIT, financial leverage exists. In
other words, whenever DFL is greater than 1, there is financial leverage.
Applying Equation 13.6 to cases 1 and 2 in Table 13.6 yields the following two
cases:
Case 1
+100,
+40,
= 2.5
Case 2
-100,
-40,
= 2.5
These calculations show that when Chen Foods’ EBIT changes, its EPS changes
2.5 times as fast on a percentage basis due to the firm’s financial leverage. The
higher this value is, the greater the degree of financial leverage.
Shanta and Ravi Shandra wish to assess the impact effect of
additional long-term borrowing on their degree of financial
leverage (DFL). The Shandras currently have $4,200 available after meeting all
their monthly living (operating) expenses, before making monthly loan pay-
ments. They currently have monthly loan payment obligations of $1,700 and
are considering the purchase of a new car, which would result in a $500 per
month increase (to $2,200) in their total monthly loan payments. Because a
large portion of Ravi’s monthly income represents commissions, the Shandras
believe that the $4,200 per month currently available for making loan pay-
ments could vary by 20% above or below that amount.
To assess the potential impact of the additional borrowing on their financial
leverage, the Shandras calculate their DFL for both their current ($1,700) and
proposed ($2,200) loan payments as shown on the next page using the currently
available $4,200 as a base and a 20% change.
Based on their calculations, the amount the Shandras will have available
after loan payments with their current debt changes by 1.68% for every 1%
change in the amount they will have available for making the loan payments.
Example 13.9 ▶
Personal Finance Example 13.10 ▶

15. ChAPTER 13 Leverage and Capital Structure 571
This change is considerably less responsive—and therefore less risky—than the
2.10% change in the amount available after loan payments for each 1% change
in the amount available for making loan payments with the proposed addi-
tional $500 in monthly debt payments. Although it appears that the Shandras
can afford the additional loan payments, they must decide if, given the variabil-
ity of Ravi’s income, they are comfortable with the increased financial leverage
and risk.
A more direct formula for calculating the degree of financial leverage at a
base level of EBIT is given by Equation 13.7, where the notation from Table 13.6
is used.9
Note that in the denominator the term 1/(1 2 T) converts the after-tax
preferred stock dividend to a before-tax amount for consistency with the other
terms in the equation.
Current DFL Proposed DFL
Available for making
loan payments $4,200 (120%) $5,040 $4,200 (120%) $5,040
Less: Loan payments 1,700 1,700 2,200 2,200
Available after loan
payments $2,500 (133.6%) $3,340 $2,000 (142%) $2,840
DFL =
+33.6,
+20,
= 1.68 DFL =
+42,
+20,
= 2.10
9. By using the formula for DFL in Equation 13.7, it is possible to get a negative value for the DFL if the EPS for the
base level of EBIT is negative. Rather than show absolute value signs in the equation, we instead assume that the
base-level EPS is positive.
DFL at base level EBIT =
EBIT
EBIT - I - aPD *
1
1 - T
b
(13.7)
Entering EBIT = $10,000, I = $2,000, PD = $2,400, and the tax rate
(T = 0.40) from Table 6 into Equation 13.7 yields
DFL at $10,000 EBIT =
$10,000
$10,000 - $2,000 - a$2,400 *
1
1 - 0.40
b
=
$10,000
$4,000
= 2.5
Note that the formula given in Equation 13.7 provides a more direct method
for calculating the degree of financial leverage than the approach illustrated using
Table 13.6 and Equation 13.6.
Example 13.11 ▶

16. 572 PART 6 Long-Term Financial Decisions
TOTAL LEVERAGE
We also can assess the combined effect of operating and financial leverage on the
firm’s risk by using a framework similar to that used to develop the individual
concepts of leverage. This combined effect, or total leverage, can be defined as the
use of fixed costs, both operating and financial, to magnify the effects of changes
in sales on the firm’s earnings per share. Total leverage can therefore be viewed as
the total impact of the fixed costs in the firm’s operating and financial structure.
Cables, Inc., a computer cable manufacturer, expects sales of 20,000 units at $5 per
unit in the coming year and must meet the following obligations: variable operating
costs of $2 per unit, fixed operating costs of $10,000, interest of $20,000, and pre-
ferred stock dividends of $12,000. The firm is in the 40% tax bracket and has 5,000
shares of common stock outstanding. Table 13.7 presents the levels of earnings per
share associated with the expected sales of 20,000 units and with sales of 30,000 units.
Table 13.7 illustrates that as a result of a 50% increase in sales (from 20,000
to 30,000 units), the firm would experience a 300% increase in earnings per share
(from $1.20 to $4.80). Although it is not shown in the table, a 50% decrease in
sales would, conversely, result in a 300% decrease in earnings per share. The linear
nature of the leverage relationship accounts for the fact that sales changes of equal
magnitude in opposite directions result in EPS changes of equal magnitude in the
corresponding direction. At this point, it should be clear that whenever a firm has
fixed costs—operating or financial—in its structure, total leverage will exist.
Example 13.12 ▶
total leverage
The use of fixed costs, both
operating and financial, to
magnify the effects of changes
in sales on the firm’s earnings
per share.
The Total Leverage Effect
150%
Sales (in units) 20,000 30,000
Sales revenuea
$100,000 $150,000
Less: Variable operating costsb
40,000 60,000
DOL =
+60,
+50,
= 1.2
Less: Fixed operating costs 10,000 10,000
Earnings before interest
and taxes (EBIT) $ 50,000 $ 80,000
160%
DTL =
+300,
+50,
= 6.0
Less: Interest 20,000 20,000
Net profits before taxes $ 30,000 $ 60,000
Less: Taxes (T 5 0.40) 12,000 24,000
Net profits after taxes $ 18,000 $ 36,000
Less: Preferred stock dividends 12,000 12,000
DFL =
+300,
+60,
= 5.0
Earnings available for
common stockholders $ 6,000 $ 24,000
Earnings per share (EPS)
$6,000
5,000
= $1.20
$24,000
5,000
= $4.80
1300%
a
Sales revenue 5 $5/unit 3 sales in units.
b
Variable operating costs 5 $2/unit 3 sales in units.
TABLE 13.7
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˚
˚
˙
¯
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˘
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˙

17. ChAPTER 13 Leverage and Capital Structure 573
Measuring the degree of Total Leverage (dTL)
The degree of total leverage (DTL) is a numerical measure of the firm’s total le-
verage. It can be computed much like operating and financial leverage are com-
puted. One approach for measuring DTL is10
degree of total leverage (DTL)
The numerical measure of the
firm’s total leverage.
10. This approach is valid only when the same base level of sales is used to calculate and compare these values. In
other words, the base level of sales must be held constant if we are to compare the total leverage associated with
different levels of fixed costs.
11. By using the formula for DTL in Equation 13.9, it is possible to get a negative value for the DTL if the EPS for
the base level of sales is negative. For our purposes, rather than show absolute value signs in the equation, we in-
stead assume that the base-level EPS is positive.
DTL =
Percentage change in EPS
Percentage change in sales
(13.8)
Whenever the percentage change in EPS resulting from a given percentage change
in sales is greater than the percentage change in sales, total leverage exists. In
other words, as long as the DTL is greater than 1, there is total leverage.
Applying Equation 13.8 to the data in Table 13.7 yields
DTL =
+300,
+50,
= 6.0
Because this result is greater than 1, total leverage exists. The higher the value is,
the greater the degree of total leverage.
A more direct formula for calculating the degree of total leverage at a given base
level of sales, Q, is given by the following equation,11
which uses the same nota-
tion that was presented earlier:
Example 13.13 ▶
DTL at base sales level Q =
Q * (P - VC)
Q * (P - VC) - FC - I - aPD *
1
1 - T
b
(13.9)
Substituting Q 5 20,000, P 5 $5, VC 5 $2, FC 5$10,000, I 5 $20,000, PD 5
$12,000, and the tax rate (T 5 0.40) into Equation 13.9 yields
DTL at 20,000 units
=
20,000 * ($5 - $2)
20,000 * ($5 - $2) - $10,000 - $20,000 - a$12,000 *
1
1 - 0.40
b
=
$60,000
$10,000
= 6.0
Clearly, the formula used in Equation 13.9 provides a more direct method for
calculating the degree of total leverage than the approach illustrated using Table
13.7 and Equation 13.8.
Example 13.14 ▶

18. 574 PART 6 Long-Term Financial Decisions
Relationship of Operating, Financial, and Total Leverage
Total leverage reflects the combined impact of operating and financial leverage
on the firm. High operating leverage and high financial leverage will cause total
leverage to be high. The opposite will also be true. The relationship between op-
erating leverage and financial leverage is multiplicative rather than additive. The
relationship between the degree of total leverage (DTL) and the degrees of oper-
ating leverage (DOL) and financial leverage (DFL) is given by
DTL = DOL * DFL (13.10)
Substituting the values calculated for DOL and DFL, shown on the right-hand
side of Table 13.7, into Equation 13.10 yields
DTL = 1.2 * 5.0 = 6.0
The resulting degree of total leverage is the same value that we calculated directly
in the preceding examples.
The Focus on Ethics box considers some ethical issues relating to the topic of
leverage.
Example 13.15 ▶
Lehman Brothers’ fall
was perhaps the most
stunning development of the financial
crisis. Dating back to the mid-1800s,
the firm had survived the Great Depres-
sion and numerous recessions to be-
come a major player on Wall Street
and around the world. Lehman’s busi-
ness included investment banking,
sales, research and trading, investment
management, private equity, and pri-
vate banking. Lehman was also a major
player in the subprime mortgage indus-
try, which would ultimately lead to the
firm’s undoing.
In the years before the subprime
mortgage crisis, financial firms bor-
rowed heavily, and Lehman was no
exception. By early 2008, Lehman had
$32 in debt for each $1 in equity. That
much leverage implied that a small
drop in the value of Lehman’s assets
could wipe out the firm.
Lehman’s exposure to the sub-
prime mortgage industry left it vulnera-
ble during the crisis. As its financial
health deteriorated, Lehman used off–
balance sheet transactions to hide the
extent of its indebtednesses. The trans-
actions, known within Lehman as
Repo 105s, were executed near the
end of each quarter, just before
Lehman filed its quarterly financial
reports. In these repos, Lehman sold
some of its assets with an agreement
to buy them back (with interest) a few
days later. Lehman used the cash from
the asset sale to pay down other lia-
bilities. The Repo 105 transactions
enabled Lehman to reduce both total
liabilities and total assets and allowed
the firm to report lower leverage
ratios. With the start of a new quarter,
Lehman would unwind the transactions
and restore the liabilities to their bal-
ance sheet.
The effects of Lehman’s Repo 105
transactions were sizable, allowing the
firm to briefly remove as much as $50
billion in debt from its balance sheet.
Because Lehman did not detail the Repo
105 transactions in its financial state-
ments, outsiders were unaware of the
transactions. Within Lehman, concerns
were raised over the Repo 105 pro-
gram. The firm’s global financial control-
ler warned of the reputational risk to
Lehman if the public became aware of
the firm’s reliance on such transactions.
▶ Assume that Lehman’s Repo 105
transactions fall within the limits al-
lowed by generally accepted account-
ing principles as Lehman’s manage-
ment has argued. What are the
ethical implications of undertaking
transactions expressly to temporarily
hide how much money a firm has
borrowed?
focus on EThICS
Repo 105
in practice

19. ChAPTER 13 Leverage and Capital Structure 575
LG 4
LG 3
➔ REVIEW QuESTIONS
13–1 What is meant by the term leverage? How are operating leverage, finan-
cial leverage, and total leverage related to the income statement?
13–2 What is the operating breakeven point? How do changes in fixed oper-
ating costs, the sale price per unit, and the variable operating cost per
unit affect it?
13–3 What is operating leverage? What causes it? How is the degree of oper-
ating leverage (DOL) measured?
13–4 What is financial leverage? What causes it? How is the degree of finan-
cial leverage (DFL) measured?
13–5 What is the general relationship among operating leverage, financial le-
verage, and the total leverage of the firm? Do these types of leverage
complement one another? Why or why not?
13.2 The Firm’s Capital Structure
Capital structure is one of the most complex areas of financial decision making
because of its interrelationship with other financial decision variables. Poor capi-
tal structure decisions can result in a high cost of capital, thereby lowering the
NPVs of projects and making more of them unacceptable. Effective capital struc-
ture decisions can lower the cost of capital, resulting in higher NPVs and more
acceptable projects and thereby increasing the value of the firm.
TYPES OF CAPITAL
All the items on the right-hand side of the firm’s balance sheet, excluding current liabil-
ities, are sources of capital. The following simplified balance sheet illustrates the basic
breakdown of total capital into its two components, debt capital and equity capital:
Balance Sheet
Long-term debt
Assets Stockholders’ equity
Preferred stock
Common stock equity
Common stock
Retained earnings
Current liabilities
Equity
capital
Debt
capital
Total
capital
The cost of debt is lower than the cost of other forms of financing. Lenders de-
mand relatively lower returns because they take the least risk of any contributors of
long-term capital. Lenders have a higher priority of claim against any earnings or
assets available for payment, and they can exert far greater legal pressure against the
company to make payment than can owners of preferred or common stock. The tax
deductibility of interest payments also lowers the debt cost to the firm substantially.
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