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Chapter 13
Leverage and Capital Structure
Instructor’s Resources
Overview
This chapter introduces the student to the concepts of operating and financial leverage and the associated business
and financial risks. As a prerequisite to operating leverage, breakeven analysis is presented through graphic and
algebraic methods. The limitations of breakeven analysis are also discussed. Financial leverage is presented
graphically by comparing financial plans on a set of earnings before interest and tables-earnings per share
(EBIT-EPS) axes. The degree of operating, financial, and total leverage are presented to provide tools to measure
the relative differences in risk of differing operating and financial structures within the firm. Capital structure is
discussed with regard to a firm’s optimal mix of debt and equity, and the EBIT-EPS and valuation model
approaches to evaluate capital structure, as well as important qualitative factors, are presented. Chapter 13 explains
how such concepts as breakeven analysis, leverage, and risk arising from borrowing will impact the student’s
professional life and personal life.
Suggested Answer to Opener-in-Review Question
a. Now that the company has decided to use the proceeds from a bond issue to repurchase shares, what
would you expect the effect of that decision to be on Lowe's degree of total leverage?
A company’s degree of total leverage is influenced both by its operating leverage and financial leverage. In
Lowe’s case, the operating leverage is unaffected by the decision to use the proceeds from the bond issue to
b. Calculate the percentage change in revenues and in EPS from 2011 to 2012 (before Lowe’s altered its
capital structure). What was Lowe’s degree of total leverage at this time?
c. Calculate the percentage changes in revenues and EPS from 2012 to 2013 (after Lowe’s altered its
capital structure). What was Lowe’s degree of total leverage at this time?
© 2015 Pearson Education, Inc.
d. Do your findings in questions b and c align with your expectations from question a?
e. What do you think happened to the beta of Lowe’s common stock from 2011 to 2013?
Answers to Review Questions
1. Leverage is the use of fixed-cost assets or funds to magnify the returns to owners. Leverage is closely related
to the risk of being unable to meet operating and financial obligations when due. Operating leverage refers to
2. The firm’s operating breakeven point is the level of sales at which all fixed and variable operating costs are
3. Operating leverage is the ability to use fixed operating costs to magnify the effects of changes in sales on
( )
DOL at base sales level ( )
Q P VC
QQ P VC FC
´ -
=´ - -
where:
Q quantity of units
P sales price per unit
VC variable costs per unit
FC fixed costs per period
4. Financial leverage is the use of fixed financial costs to magnify the effects of changes in EBIT on EPS. Financial
a.
=% change in EPS
DFL % change in EBIT
b.
[ ]
=- - ´ ¸ -
EBIT
DFL at base level EBIT EBIT (1 (1 ))I PD T
where:
EPS earnings per share
5. The total leverage of the firm is the combined effect of fixed costs, both operating and financial, and is
their effects are not additive but rather they are multiplicative. This means that the overall effect of the
6. A firm’s capital structure is the mix of long-term debt and equity it utilizes. The key differences between debt
and equity capital are summarized in the table below.
Key Differences between Debt and Equity Capital:
Characteristic
Type of Capital
Debt Equity
*In default, debt holders and preferred stockholders may receive a voice in management;
otherwise, only common stockholders have voting rights.
The ratios used to determine the degree of financial leverage in the firm’s capital structure are the debt ratio
7. The capital structure of non-U.S. companies can be quite different from that of U.S. corporations. These firms
tend to have more debt than domestic companies. Several reasons contribute to this fact. U.S. capital markets
Similarities exist between non-U.S. and U.S. firms with regard to capital structure. Debt ratios within industry
groupings generally follow similar patterns, as they do in the United States, and large multinational companies
8. The tax deductibility of interest is the major benefit of debt financing. In effect, the government subsidizes
9. Business risk is the risk that the firm will be unable to cover its operating costs. Three factors affecting business
risk are the use of fixed operating costs (operating leverage), revenue stability, and cost stability. Revenue
Financial risk is the risk that the firm will be unable to meet required financial obligations. The more
10. The agency problem occurs because lenders provide funds to a firm based on their expectations for the firm’s
current and future capital expenditures and capital structure, which determine the firm’s business and
financial risk. Firm managers, as agents of the owners, have an incentive to “take advantage” of lenders.
11. Asymmetric information results when a firm’s managers have more information about operations and future
prospects than do investors. This additional information will generally cause financial managers to raise funds
Because of management’s access to asymmetric information, the firm’s financing decisions can give signals
to investors reflecting management’s view of the stock value. The use of debt sends a positive signal that
12. As financial leverage increases, both the cost of debt and the cost of equity increase, with equity rising at a
faster rate. The overall cost of capital—with the addition of debt—first begins to decrease, reaches a
13. The EBIT-EPS approach is based upon the assumption that the firm, by attempting to maximize EPS, will
also maximize the owners’ wealth. The theoretical approach to identifying the optimal capital structure
evaluates capital structure based upon the minimization of the overall cost of capital and maximizing value;
14. It is very unlikely that the two objectives of maximizing value and maximizing EPS would lead to the same
15. Basically, the firm should find the optimal capital structure that balances risk and return factors to maximize
share value. This requires estimates of required rates of return under different levels of risk: the estimate of
Suggested Answer to Focus on Practice Box: Adobe’s Leverage
Summarize the pros and cons of operating leverage.
Operating leverage exists when a firm uses fixed operating costs to magnify the effects of changes in sales on
EBIT. When a firm has fixed operating costs, an increase in sales results in a greater-than-proportional increase in
Suggested Answer to Focus on Ethics Box: Repo 105
Assume that Lehman’s Repo 105 transactions fall within the limits allowed by Generally Accepted
Accounting Principles as Lehman’s management has argued. What are the ethical implications of
undertaking transactions expressly to temporarily hide how much money a firm has borrowed?
Lehman’s actions were aimed at misrepresenting the firm’s indebtedness to outsiders. In effect, investors were not
Answers to Warm-Up Exercises
E13-1. Breakeven analysis
Answer: The operating breakeven point is the level of sales at which all fixed and variable operating costs are
E13-2. Changing costs and the operating breakeven point
Answer: Calculate the breakeven point for the current process and the breakeven point for the new process, and
compare the two.
E13-3. Risk-adjusted discount rates
Answer: Use Equation 13.5 to find the DOL at 15,000 units.
15,000
$20
$12
$30,000
Q
P
VC
FC
=
=
=
=
15,000 ($20 $12) $120,000
DOL at 15,000 units 1.33
15,000 ($20 $12) $30,000 $90,000
´ -
= = =
´ - -
E13-4. DFL
Answer: Substitute EBIT $20,000, I $3,000, PD $4,000, and the tax rate (T 0.38) into
( )
$12,350 1,300
($24.95 $15.45)
FC
QP VC
Q
=-
= =
-
P13-2. Breakeven comparisons—algebraic
LG 1; Basic
a.
( )
FC
QP VC
=-
Firm F:
( )
$45,000 4,000 units
$18.00 $6.75
Q= =
-
Firm G:
( )
$30,000 4,000 units
$21.00 $13.50
Q= =
-
Firm H:
( )
$90,000 5,000 units
$30.00 $12.00
Q= =
-
b. From least risky to most risky: F and G are of equal risk, then H. It is important to recognize that
operating leverage is only one measure of risk.
P13-3. Breakeven point—algebraic and graphical
LG 1; Intermediate
a. Q FC (P VC)
b.
P13-4. Breakeven analysis
LG 1; Intermediate
a.
( )
= =
-
$73,500 21,000 CDs
$13.98 $10.48
Q
d. EBIT (P Q) FC (VC Q)
P13-5. Personal finance: Breakeven analysis
LG 1; Easy
