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The Data Required
To graph a financing plan, we need to know at least two EBITâ€“EPS coordinates.
The approach for obtaining coordinates can be illustrated by an example.

The current capital structure of JSG Company, a soft-drink manufacturer, is as
EXAMPLE
shown in the following table. Note that JSGâ€™s capital structure currently contains
only common stock equity; the firm has no debt or preferred stock. If for conve-
nience we assume the firm has no current liabilities, its debt ratio (total
liabilities total assets) is currently 0% (\$0 \$500,000); it therefore has zero
financial leverage. Assume the firm is in the 40% tax bracket.

Current capital structure

Long-term debt \$ 0
Common stock equity (25,000 shares @ \$20) 500,000
Total capital (assets) \$500,000

EBITâ€“EPS coordinates for JSGâ€™s current capital structure can be found by
assuming two EBIT values and calculating the EPS associated with them.14
Because the EBITâ€“EPS graph is a straight line, any two EBIT values can be used
to find coordinates. Here we arbitrarily use values of \$100,000 and \$200,000.

EBIT (assumed) \$100,000 \$200,000
Interest (rate \$0 debt) 0 0
Net profits before taxes \$100,000 \$200,000
Taxes (T 0.40) 40,000 80,000
Net profits after taxes \$ 60,000 \$120,000

\$60,000 \$120,000
EPS \$2.40 \$4.80
25,000 sh. 25,000 sh.

14. A convenient method for finding one EBITâ€“EPS coordinate is to calculate the financial breakeven point, the level
of EBIT for which the firmâ€™s EPS just equals \$0. It is the level of EBIT needed just to cover all fixed financial costsâ€”
annual interest (I) and preferred stock dividends (PD). The equation for the financial breakeven point is
PD
Financial breakeven point I
1T
where T is the tax rate. It can be seen that when PD = \$0, the financial breakeven point is equal to I, the annual
interest payment.
445
CHAPTER 11 Leverage and Capital Structure

FIGURE 11.4 Graphic Presentation of a Financing Plan
JSG Companyâ€™s zero-leverage financing plan

10
9
8
7
\$4.80

EPS (\$)
6 Debt
(2)
= 0%
5 Ratio
4 \$2.40
(1)
3
2
1
0
50 100 150 200

EBIT (\$000)

The two EBITâ€“EPS coordinates resulting from these calculations are (1) \$100,000
EBIT and \$2.40 EPS and (2) \$200,000 EBIT and \$4.80 EPS.

Plotting the Data
The two EBITâ€“EPS coordinates developed for JSG Companyâ€™s current zero-lever-
age (debt ratio 0 percent) situation can be plotted on a set of EBITâ€“EPS axes, as
financial breakeven point
shown in Figure 11.4. The figure shows the level of EPS expected for each level of
The level of EBIT necessary to
EBIT. For levels of EBIT below the x-axis intercept, a loss (negative EPS) results.
just cover all fixed financial
Each of the x-axis intercepts is a financial breakeven point, the level of EBIT nec-
costs; the level of EBIT for which
essary to just cover all fixed financial costs (EPS \$0).
EPS \$0.

Comparing Alternative
Capital Structures
We can compare alternative capital structures by graphing financing plans, as
shown in Figure 11.4. The following example illustrates this procedure.

JSG Company, whose current zero-leverage capital structure was described in the
EXAMPLE
preceding example, is contemplating shifting its capital structure to either of two
leveraged positions. To maintain its \$500,000 of total capital, JSGâ€™s capital
structure will be shifted to greater leverage by issuing debt and using the pro-
ceeds to retire an equivalent amount of common stock. The two alternative capi-
tal structures result in debt ratios of 30% and 60%, respectively. The basic infor-
mation on the current and two alternative capital structures is summarized in
Table 11.9.
446 PART 4 Long-Term Financial Decisions

TABLE 11.9 Basic Information on JSG Companyâ€™s Current and
Alternative Capital Structures

Capital Shares of
structure Interest Annual common stock
debt Total Debt Equity rate on interest outstanding
assetsa debtb [(4) \$20]c
ratio [(1) (2)] [(2) (3)] [(3) (5)]
(1) (2) (3) (4) (5) (6) (7)

0% (current) \$500,000 \$ 0 \$500,000 0% \$ 0 25,000
30 500,000 150,000 350,000 10 15,000 17,500
60 500,000 300,000 200,000 16.5 49,500 10,000
aBecause for convenience the firm is assumed to have no current liabilities, total assets equals total capital of \$500,000.
bThe interest rate on all debt increases with increases in the debt ratio due to the greater leverage and risk associated with
higher debt ratios.
cThe \$20 value represents the book value of common stock equity.

Using the data in Table 11.9, we can calculate the coordinates needed to plot
the 30% and 60% debt capital structures. For convenience, using the same
\$100,000 and \$200,000 EBIT values used earlier to plot the current capital struc-
ture, we get the information in the following table.

Capital structure

30% Debt ratio 60% Debt ratio

EBIT (assumed) \$100,000 \$200,000 \$100,000 \$200,000
Interest (Table 11.9) 15,000 15,000 49,500 49,500
Net profits before taxes \$ 85,000 \$185,000 \$ 50,500 \$150,500
Taxes (T 0.40) 34,000 74,000 20,200 60,200
Net profits after taxes \$ 51,000
3 \$111,000 \$ 30,300 \$ 90,300

\$51,000 \$111,000 \$30,300 \$90,300
EPS \$2.91 \$6.34 \$3.03 \$9.03
17,500 sh. 17,500 sh. 10,000 sh. 10,000 sh.

The two sets of EBITâ€“EPS coordinates developed in the preceding table, along
with those developed for the current zero-leverage capital structure, are summa-
rized and plotted on the EBITâ€“EPS axes in Figure 11.5. This figure shows that
each capital structure is superior to the others in terms of maximizing EPS over
certain ranges of EBIT: The zero-leverage capital structure (debt ratio 0%) is
superior to either of the other capital structures for levels of EBIT between \$0 and
\$50,000. Between \$50,000 and \$95,500 of EBIT, the capital structure associated
with a debt ratio of 30% is preferred. And at a level of EBIT above \$95,500, the
60% debt ratio capital structure provides the highest earnings per share.15

15 An algebraic technique can be used to find the indifference points between the capital structure alternatives. Due
to its relative complexity, this technique is not presented. Instead, emphasis is given here to the visual estimation of
these points from the graph.
447
CHAPTER 11 Leverage and Capital Structure

FIGURE 11.5 EBITâ€“EPS Approach
A comparison of selected capital structures for JSG Company

10 Debt
= 60%
Ratio
9
8
Debt
7 = 30%
60% Ratio
6
Debt
5 = 0%
Ratio
4
EPS (\$) 3
30%
2
1 0%
0
30%
â€“1
â€“2 Financial
60%
â€“3 Breakeven
â€“4 Points

50 100 150 200
95.50
EBIT (\$000)

EBIT
\$100,000 \$200,000
Capital structure
debt ratio Earnings per share (EPS)
0% \$2.40 \$4.80
30 2.91 6.34
60 3.03 9.03

Considering Risk in EBITâ€“EPS Analysis
When interpreting EBITâ€“EPS analysis, it is important to consider the risk of each
capital structure alternative. Graphically, the risk of each capital structure can be
viewed in light of two measures: (1) the financial breakeven point (EBIT-axis
intercept) and (2) the degree of financial leverage reflected in the slope of the cap-
ital structure line: The higher the financial breakeven point and the steeper the
slope of the capital structure line, the greater the financial risk.
Further assessment of risk can be performed by using ratios. As financial
leverage (measured by the debt ratio) increases, we expect a corresponding
decline in the firmâ€™s ability to make scheduled interest payments (measured by the
times interest earned ratio).

Reviewing the three capital structures plotted for JSG Company in Figure 11.5,
EXAMPLE
we can see that as the debt ratio increases, so does the financial risk of each alter-
native. Both the financial breakeven point and the slope of the capital structure
lines increase with increasing debt ratios. If we use the \$100,000 EBIT value, for
448 PART 4 Long-Term Financial Decisions

example, the times interest earned ratio (EBIT interest) for the zero-leverage
capital structure is infinity (\$100,000 \$0); for the 30% debt case, it is 6.67
(\$100,000 \$15,000); and for the 60% debt case, it is 2.02 (\$100,000
\$49,500). Because lower times interest earned ratios reflect higher risk, these
ratios support the conclusion that the risk of the capital structures increases with
increasing financial leverage. The capital structure for a debt ratio of 60% is
riskier than that for a debt ratio of 30%, which in turn is riskier than the capital
structure for a debt ratio of 0%.

The Basic Shortcoming of EBITâ€“EPS Analysis
The most important point to recognize when using EBITâ€“EPS analysis is that this
technique tends to concentrate on maximizing earnings rather than maximizing
owner wealth. The use of an EPS-maximizing approach generally ignores risk. If
investors did not require risk premiums (additional returns) as the firm increased
the proportion of debt in its capital structure, a strategy involving maximizing
EPS would also maximize owner wealth. But because risk premiums increase
with increases in financial leverage, the maximization of EPS does not ensure
owner wealth maximization. To select the best capital structure, both return
(EPS) and risk (via the required return, ks) must be integrated into a valuation
framework consistent with the capital structure theory presented earlier.

Review Question

11â€“13 Explain the EBITâ€“EPS approach to capital structure. Include in your
explanation a graph indicating the financial breakeven point; label the
axes. Is this approach consistent with maximization of the ownersâ€™ wealth?

Choosing the Optimal Capital Structure
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A wealth maximization framework for use in making capital structure decisions
should include the two key factors of return and risk. This section describes the
procedures for linking to market value the return and risk associated with alter-
native capital structures.

To determine the firmâ€™s value under alternative capital structures, the firm must
find the level of return that must be earned to compensate owners for the risk
being incurred. Such a framework is consistent with the overall valuation frame-
work developed in Chapters 6 and 7 and applied to capital budgeting decisions in
Chapter 9.
The required return associated with a given level of financial risk can be esti-
mated in a number of ways. Theoretically, the preferred approach would be first
to estimate the beta associated with each alternative capital structure and then to
use the CAPM framework presented in Equation 5.7 to calculate the required
return, ks. A more operational approach involves linking the financial risk associ-
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CHAPTER 11 Leverage and Capital Structure

ated with each capital structure alternative directly to the required return. Such an
approach is similar to the CAPM-type approach demonstrated in Chapter 9 for
linking project risk and required return (RADR). Here it involves estimating the
required return associated with each level of financial risk, as measured by a sta-
tistic such as the coefficient of variation of EPS. Regardless of the approach used,
one would expect the required return to increase as the financial risk increases.

Expanding the JSG Company example presented earlier, we assume that the firm
EXAMPLE
is attempting to choose the best of seven alternative capital structuresâ€”debt
ratios of 0%, 10%, 20%, 30%, 40%, 50%, and 60%. For each of these struc-
tures the firm estimated the (1) EPS, (2) coefficient of variation of EPS, and (3)
required return, ks. These values are shown in columns 1 through 3 of Table
11.10. Note that EPS (in column 1) is maximized at a 50% debt ratio though the
risk of EPS measured by its coefficient of variation (in column 2) is constantly
increasing. As expected, the estimated required return of owners, ks (in col-
umn 3), increases with increasing risk, as measured by the coefficient of variation
of EPS (in column 2). Simply stated, for higher degrees of financial leverageâ€”
debt ratiosâ€”owners require higher rates of return.

Estimating Value
The value of the firm associated with alternative capital structures can be esti-
mated by using one of the standard valuation models. If, for simplicity, we
assume that all earnings are paid out as dividends, we can use a zero-growth val-
uation model such as that developed in Chapter 7. The model, originally stated in
Equation 7.2, is restated here with EPS substituted for dividends (because in each
year the dividends would equal EPS):
EPS
P0 (11.12)
ks
By substituting the expected level of EPS and the associated required return, ks,
into Equation 11.12, we can estimate the per-share value of the firm, P0.

TABLE 11.10 Calculation of Share Value Estimates
Associated with Alternative Capital Structures
for JSG Company

Estimated Estimated
Capital coefficient Estimated share value
structure Expected EPS of variation of EPS required return, ks [(1) Ă· (3)]
debt ratio (1) (2) (3) (4)

0% \$2.40 0.71 .115 \$20.87
10 2.55 0.74 .117 21.79
20 2.72 0.78 .121 22.48
30 2.91 0.83 .125 23.28
40 3.12 0.91 .140 22.29
50 3.18 1.07 .165 19.27
60 3.03 1.40 .190 15.95
450 PART 4 Long-Term Financial Decisions

We can now estimate the value of JSG Companyâ€™s stock under each of the alter-
EXAMPLE
native capital structures. Substituting the expected EPS (column 1 of Table
11.10) and the required returns, ks (column 3 of Table 11.10), into Equation
11.12 for each of the capital structures, we obtain the share values given in col-
umn 4 of Table 11.10. Plotting the resulting share values against the associated
debt ratios, as shown in Figure 11.6, clearly illustrates that the maximum share
value occurs at the capital structure associated with a debt ratio of 30%.

Maximizing Value versus Maximizing EPS
Throughout this text, the goal of the financial manager has been specified as max-
imizing owner wealth, not profit. Although there is some relationship between
expected profit and value, there is no reason to believe that profit-maximizing
strategies necessarily result in wealth maximization. It is therefore the wealth of
the owners as reflected in the estimated share value that should serve as the crite-
rion for selecting the best capital structure. A final look at JSG Company will
highlight this point.

Further analysis of Figure 11.6 clearly shows that although the firmâ€™s profits
EXAMPLE
(EPS) are maximized at a debt ratio of 50%, share value is maximized at a 30%
debt ratio. Therefore, the preferred capital structure would be the 30% debt
ratio. The two approaches provide different conclusions because EPS maximiza-
tion does not consider risk.

FIGURE 11.6
Estimating Value
Estimated Share Value (\$)

25.00
Estimated share value and Maximum Share Value = \$23.28
EPS for alternative capital
structures for JSG Company

20.00

Estimated
Share Value
15.00

Maximum EPS = \$3.18
3.50
EPS (\$)

EPS
3.00
2.50
2.00

0 10 20 30 40 50 60 70
Maximum Maximum
Share Value EPS
Debt Ratio (%)
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CHAPTER 11 Leverage and Capital Structure

Some Other Important Considerations
Because there is really no practical way to calculate the optimal capital structure,
any quantitative analysis of capital structure must be tempered with other impor-
tant considerations. Some of the more important additional factors involved in
capital structure decisions are summarized in Table 11.11.

TABLE 11.11 Important Factors to Consider in Making Capital Structure
Decisions

Concern Factor Description

Business risk Revenue stability Firms that have stable and predictable revenues can more safely
undertake highly leveraged capital structures than can firms with
volatile patterns of sales revenue. Firms with growing sales tend to
benefit from added debt because they can reap the positive benefits
of financial leverage, which magnifies the effect of these increases.
Cash flow When considering a new capital structure, the firm must focus on its
ability to generate the cash flows necessary to meet obligations. Cash
forecasts reflecting an ability to service debts (and preferred stock)
must support any shift in capital structure.
Agency costs Contractual obligations A firm may be contractually constrained with respect to the type of
funds that it can raise. For example, a firm might be prohibited from
selling additional debt except when the claims of holders of such
debt are made subordinate to the existing debt. Contractual con-
straints on the sale of additional stock, as well as on the ability to
distribute dividends on stock, might also exist.
Management preferences Occasionally, a firm will impose an internal constraint on the use of
debt to limit its risk exposure to a level deemed acceptable to man-
agement. In other words, because of risk aversion, the firmâ€™s man-
agement constrains the firmâ€™s capital structure at a level that may or
may not be the true optimum.
Control A management concerned about control may prefer to issue debt
rather than (voting) common stock. Under favorable market condi-
tions, a firm that wanted to sell equity could make a preemptive
offering or issue nonvoting shares (see Chapter 7), allowing each
shareholder to maintain proportionate ownership. Generally, only in
closely held firms or firms threatened by takeover does control
become a major concern in the capital structure decision.
Asymmetric information External risk assessment The firmâ€™s ability to raise funds quickly and at favorable rates
depends on the external risk assessments of lenders and bond raters.
The firm must therefore consider the impact of capital structure
decisions both on share value and on published financial statements
from which lenders and raters assess the firmâ€™s risk.
Timing At times when the general level of interest rates is low, debt financ-
ing might be more attractive; when interest rates are high, the sale of
stock may be more appealing. Sometimes both debt and equity capi-
tal become unavailable at what would be viewed as reasonable
terms. General economic conditionsâ€”especially those of the capital
marketâ€”can thus significantly affect capital structure decisions.
452 PART 4 Long-Term Financial Decisions

Review Questions

11â€“14 Why do maximizing EPS and maximizing value not necessarily lead to
the same conclusion about the optimal capital structure?
11â€“15 What important factors in addition to quantitative factors should a firm
consider when it is making a capital structure decision?

SUMMARY
FOCUS ON VALUE
The amount of leverage (fixed-cost assets or funds) employed by a firm directly affects its
risk, return, and share value. Generally, higher leverage raises, and lower leverage reduces,
risk and return. Operating leverage is concerned with the level of fixed operating costs;
financial leverage focuses on fixed financial costs, particularly interest on debt and any pre-
ferred stock dividends. The firmâ€™s financial leverage is determined by its capital structureâ€”
its mix of long-term debt and equity financing. Because of its fixed interest payments, the
more debt a firm employs relative to its equity, the greater its financial leverage. The value
of the firm is clearly affected by its degree of operating leverage and by the composition of
its capital structure.
The financial manager must carefully consider the types of operating and financial costs
the firm incurs, recognizing that with greater fixed costs comes higher risk. Major decisions
with regard to both operating cost structure and capital structure must therefore focus on
their impact on the firmâ€™s value. Only those leverage and capital structure decisions that are
consistent with the firmâ€™s goal of maximizing its stock price should be implemented.

REVIEW OF LEARNING GOALS
costs by the firm to magnify the effects of changes
Discuss the role of breakeven analysis, the oper-
LG1
in sales on EBIT. The higher the fixed operating
ating breakeven point, and the effect of chang-
costs, the greater the operating leverage. Financial
ing costs on it. Breakeven analysis measures the
leverage is the use of fixed financial costs by the
level of sales necessary to cover total operating
firm to magnify the effects of changes in EBIT on
costs. The operating breakeven point may be calcu-
EPS. The higher the fixed financial costsâ€”typically,
lated algebraically, by dividing fixed operating costs
interest on debt and preferred stock dividendsâ€”the
by the difference between the sale price per unit and
greater the financial leverage. The total leverage of
variable operating cost per unit, or it may be deter-
the firm is the use of fixed costsâ€”both operating
mined graphically. The operating breakeven point
and financialâ€”to magnify the effects of changes in
increases with increased fixed and variable operat-
sales on EPS. Total leverage reflects the combined
ing costs and decreases with an increase in sale
effect of operating and financial leverage.
price, and vice versa.

Describe the types of capital, external assess-
Understand operating, financial, and total
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ment of capital structure, the capital structure
leverage and the relationships among them.
of non-U.S. firms, and capital structure theory. Two
Operating leverage is the use of fixed operating
453
CHAPTER 11 Leverage and Capital Structure

basic types of capitalâ€”debt capital and equity capi- capital (WACC). The optimal capital structure is
talâ€”make up a firmâ€™s capital structure. They differ the one that minimizes the WACC. Graphically,
with respect to voice in management, claims on in- although both debt and equity costs rise with
come and assets, maturity, and tax treatment. Capi- increasing financial leverage, the lower cost of debt
tal structure can be externally assessed by using fi- causes the WACC to decline and then rise with
nancial ratiosâ€”debt ratio, times interest earned increasing financial leverage. As a result, the firmâ€™s
ratio, and fixed-payment coverage ratio. Non-U.S. WACC exhibits a U-shape, whose minimum value
companies tend to have much higher degrees of in- defines the optimal capital structure that maximizes
debtedness than do their U.S. counterparts, primar- owner wealth.
ily because U.S. capital markets are much more de-
veloped. Similarities between U.S. corporations and Discuss the EBITâ€“EPS approach to capital
LG5
those of other countries include industry patterns of structure. The EBITâ€“EPS approach evaluates
capital structure, large multinational company capi- capital structures in light of the returns they provide
tal structures, and the trend toward greater reliance the firmâ€™s owners and their degree of financial risk.
on securities issuance and less reliance on banks for Under the EBITâ€“EPS approach, the preferred capital
financing. structure is the one that is expected to provide max-
Research suggests that there is an optimal capital imum EPS over the firmâ€™s expected range of EBIT.
structure that balances the firmâ€™s benefits and costs of Graphically, this approach reflects risk in terms of
debt financing. The major benefit of debt financing is the financial breakeven point and the slope of the
the tax shield. The costs of debt financing include the capital structure line. The major shortcoming of
probability of bankruptcy, caused by business and EBITâ€“EPS analysis is that it concentrates on maxi-
financial risk; agency costs imposed by lenders; and mizing earnings rather than ownersâ€™ wealth.
asymmetric information, which typically causes
firms to raise funds in a pecking order of retained Review the return and risk of alternative capi-
LG6
earnings, then debt, and finally external equity tal structures, their linkage to market value,
financing, in order to send positive signals to the mar- and other important considerations related to capi-
ket and thereby enhance the wealth of shareholders. tal structure. The best capital structure can be se-
lected by using a valuation model to link return
Explain the optimal capital structure using a and risk factors. The preferred capital structure is
LG4
graphical view of the firmâ€™s cost-of-capital the one that results in the highest estimated share
functions and a zero-growth valuation model. The value, not the highest EPS. Other important non-
zero-growth valuation model can be used to define quantitative factors, such as revenue stability, cash
the firmâ€™s value as its after-tax EBIT divided by its flow, contractual obligations, management prefer-
weighted average cost of capital. Assuming that ences, control, external risk assessment, and timing,
EBIT is constant, the value of the firm is maxi- must also be considered when making capital struc-
mized by minimizing its weighted average cost of ture decisions.

SELF-TEST PROBLEMS (Solutions in Appendix B)
ST 11â€“1 Breakeven point and all forms of leverage TOR most recently sold 100,000
LG1 LG2
units at \$7.50 each; its variable operating costs are \$3.00 per unit, and its fixed
operating costs are \$250,000. Annual interest charges total \$80,000, and the
firm has 8,000 shares of \$5 (annual dividend) preferred stock outstanding. It
currently has 20,000 shares of common stock outstanding. Assume that the firm
has a 40% tax rate.
a. At what level of sales (in units) would the firm break even on operations (that
is, EBIT \$0)?
454 PART 4 Long-Term Financial Decisions

b. Calculate the firmâ€™s earnings per share (EPS) in tabular form at (1) the cur-
rent level of sales and (2) a 120,000-unit sales level.
c. Using the current \$750,000 level of sales as a base, calculate the firmâ€™s degree
of operating leverage (DOL).
d. Using the EBIT associated with the \$750,000 level of sales as a base, calcu-
late the firmâ€™s degree of financial leverage (DFL).
e. Use the degree of total leverage (DTL) concept to determine the effect (in per-
centage terms) of a 50% increase in TORâ€™s sales from the \$750,000 base
level on its earnings per share.

ST 11â€“2 EBITâ€“EPS analysis Newlin Electronics is considering additional financing of
LG5
\$10,000. It currently has \$50,000 of 12% (annual interest) bonds and 10,000
shares of common stock outstanding. The firm can obtain the financing through
a 12% (annual interest) bond issue or through the sale of 1,000 shares of com-
mon stock. The firm has a 40% tax rate.
a. Calculate two EBITâ€“EPS coordinates for each plan by selecting any two EBIT
values and finding their associated EPS values.
b. Plot the two financing plans on a set of EBITâ€“EPS axes.
c. On the basis of your graph in part b, at what level of EBIT does the bond
plan become superior to the stock plan?

ST 11â€“3 Optimal capital structure Hawaiian Macadamia Nut Company has collected
LG3 LG6
the following data with respect to its capital structure, expected earnings per
share, and required return.

Capital structure Expected earnings Required
debt ratio per share return, ks

0% \$3.12 13%
10 3.90 15
20 4.80 16
30 5.44 17
40 5.51 19
50 5.00 20
60 4.40 22

a. Compute the estimated share value associated with each of the capital struc-
tures, using the simplified method described in this chapter (see Equation
11.12).
b. Determine the optimal capital structure on the basis of (1) maximization of
expected earnings per share and (2) maximization of share value.
c. Which capital structure do you recommend? Why?

PROBLEMS
11â€“1 Breakeven pointâ€”Algebraic Kate Rowland wishes to estimate the number of
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flower arrangements she must sell at \$24.95 to break even. She has estimated
455
CHAPTER 11 Leverage and Capital Structure

fixed operating costs of \$12,350 per year and variable operating costs of \$15.45
per arrangement. How many flower arrangements must Kate sell to break even
on operating costs?

11â€“2 Breakeven comparisonsâ€”Algebraic Given the price and cost data shown in the
LG1
accompanying table for each of the three firms, F, G, and H, answer the follow-
ing questions.

Firm F G H

Sale price per unit \$ 18.00 \$ 21.00 \$ 30.00
Variable operating cost per unit 6.75 13.50 12.00
Fixed operating cost 45,000 30,000 90,000

a. What is the operating breakeven point in units for each firm?
b. How would you rank these firms in terms of their risk?

11â€“3 Breakeven pointâ€”Algebraic and graphical Fine Leather Enterprises sells its
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single product for \$129.00 per unit. The firmâ€™s fixed operating costs are
\$473,000 annually, and its variable operating costs are \$86.00 per unit.
a. Find the firmâ€™s operating breakeven point in units.
b. Label the x axis â€śSales (units)â€ť and the y axis â€śCosts/Revenues (\$),â€ť and
then graph the firmâ€™s sales revenue, total operating cost, and fixed operating
cost functions on these axes. In addition, label the operating breakeven point
and the areas of loss and profit (EBIT).

11â€“4 Breakeven analysis Barry Carter is considering opening a record store. He
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wants to estimate the number of CDs he must sell to break even. The CDs will
be sold for \$13.98 each, variable operating costs are \$10.48 per CD, and annual
fixed operating costs are \$73,500.
a. Find the operating breakeven point in number of CDs.
b. Calculate the total operating costs at the breakeven volume found in
part a.
c. If Barry estimates that at a minimum he can sell 2,000 CDs per month,
should he go into the record business?
d. How much EBIT will Barry realize if he sells the minimum 2,000 CDs per
month noted in part c?

11â€“5 Breakeven pointâ€”Changing costs/revenues JWG Company publishes Creative
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Crosswords. Last year the book of puzzles sold for \$10 with variable operating
cost per book of \$8 and fixed operating costs of \$40,000. How many books
must JWG sell this year to achieve the breakeven point for the stated operating
costs, given the following different circumstances?
a. All figures remain the same as last year.
b. Fixed operating costs increase to \$44,000; all other figures remain the same.
c. The selling price increases to \$10.50; all costs remain the same as last year.
d. Variable operating cost per book increases to \$8.50; all other figures remain
the same.
456 PART 4 Long-Term Financial Decisions

e. What conclusions about the operating breakeven point can be drawn from

11â€“6 EBIT sensitivity Stewart Industries sells its finished product for \$9 per unit. Its
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fixed operating costs are \$20,000, and the variable operating cost per unit is \$5.
a. Calculate the firmâ€™s earnings before interest and taxes (EBIT) for sales of
10,000 units.
b. Calculate the firmâ€™s EBIT for sales of 8,000 and 12,000 units, respectively.
c. Calculate the percentage changes in sales (from the 10,000-unit base level)
and associated percentage changes in EBIT for the shifts in sales indicated
in part b.
d. On the basis of your findings in part c, comment on the sensitivity of changes
in EBIT in response to changes in sales.

11â€“7 Degree of operating leverage Grey Products has fixed operating costs of
LG2
\$380,000, variable operating costs of \$16 per unit, and a selling price of \$63.50
per unit.
a. Calculate the operating breakeven point in units.
b. Calculate the firmâ€™s EBIT at 9,000, 10,000, and 11,000 units, respectively.
c. With 10,000 units as a base, what are the percentage changes in units sold
and EBIT as sales move from the base to the other sales levels used in part b?
d. Use the percentages computed in part c to determine the degree of operating
leverage (DOL).
e. Use the formula for degree of operating leverage to determine the DOL at
10,000 units.

11â€“8 Degree of operating leverageâ€”Graphical Levin Corporation has fixed operat-
LG2
ing costs of \$72,000, variable operating costs of \$6.75 per unit, and a selling
price of \$9.75 per unit.
a. Calculate the operating breakeven point in units.
b. Compute the degree of operating leverage (DOL) for the following unit sales
levels: 25,000, 30,000, 40,000. Use the formula given in the chapter.
c. Graph the DOL figures that you computed in part b (on the y axis) against
sales levels (on the x axis).
d. Compute the degree of operating leverage at 24,000 units; add this point to
e. What principle do your graph and figures illustrate?

11â€“9 EPS calculations Southland Industries has \$60,000 of 16% (annual interest)
LG2
bonds outstanding, 1,500 shares of preferred stock paying an annual dividend of
\$5 per share, and 4,000 shares of common stock outstanding. Assuming that the
firm has a 40% tax rate, compute earnings per share (EPS) for the following lev-
els of EBIT:
a. \$24,600
b. \$30,600
c. \$35,000

LG2 11â€“10 Degree of financial leverage Northwestern Savings and Loan has a current cap-
ital structure consisting of \$250,000 of 16% (annual interest) debt and 2,000
shares of common stock. The firm pays taxes at the rate of 40%.
457
CHAPTER 11 Leverage and Capital Structure

a. Using EBIT values of \$80,000 and \$120,000, determine the associated earn-
ings per share (EPS).
b. Using \$80,000 of EBIT as a base, calculate the degree of financial leverage
(DFL).
c. Rework parts a and b assuming that the firm has \$100,000 of 16% (annual
interest) debt and 3,000 shares of common stock.

11â€“11 DFL and graphical display of financing plans Wells and Associates has EBIT of
LG2 LG5
\$67,500. Interest costs are \$22,500, and the firm has 15,000 shares of common
stock outstanding. Assume a 40% tax rate.
a. Use the degree of financial leverage (DFL) formula to calculate the DFL for
the firm.
b. Using a set of EBITâ€“EPS axes, plot Wells and Associatesâ€™ financing
plan.
c. If the firm also has 1,000 shares of preferred stock paying a \$6.00 annual
dividend per share, what is the DFL?
d. Plot the financing plan, including the 1,000 shares of \$6.00 preferred stock,
on the axes used in part b.
e. Briefly discuss the graph of the two financing plans.

11â€“12 Integrativeâ€”Multiple leverage measures Play-More Toys produces inflatable
LG1 LG2
beach balls, selling 400,000 balls a year. Each ball produced has a variable oper-
ating cost of \$0.84 and sells for \$1.00. Fixed operating costs are \$28,000. The
firm has annual interest charges of \$6,000, preferred dividends of \$2,000, and a
40% tax rate.
a. Calculate the operating breakeven point in units.
b. Use the degree of operating leverage (DOL) formula to calculate DOL.
c. Use the degree of financial leverage (DFL) formula to calculate DFL.
d. Use the degree of total leverage (DTL) formula to calculate DTL. Compare
this to the product of DOL and DFL calculated in parts b and c.

11â€“13 Integrativeâ€”Leverage and risk Firm R has sales of 100,000 units at \$2.00 per
LG2
unit, variable operating costs of \$1.70 per unit, and fixed operating costs of
\$6,000. Interest is \$10,000 per year. Firm W has sales of 100,000 units at \$2.50
per unit, variable operating costs of \$1.00 per unit, and fixed operating costs of
\$62,500. Interest is \$17,500 per year. Assume that both firms are in the 40%
tax bracket.
a. Compute the degree of operating, financial, and total leverage for
firm R.
b. Compute the degree of operating, financial, and total leverage for
firm W.
c. Compare the relative risks of the two firms.

11â€“14 Various capital structures Charter Enterprises currently has \$1 million in total
LG1 LG2
assets and is totally equity-financed. It is contemplating a change in capital struc-
ture. Compute the amount of debt and equity that would be outstanding if the
firm were to shift to each of the following debt ratios: 10, 20, 30, 40, 50, 60,
and 90%. (Note: The amount of total assets would not change.) Is there a limit
to the debt ratioâ€™s value?
458 PART 4 Long-Term Financial Decisions

11â€“15 EBITâ€“EPS and capital structure Data-Check is considering two capital struc-
LG5
tures. The key information is shown in the following table. Assume a 40%
tax rate.

Source of capital Structure A Structure B

Long-term debt \$100,000 at 16% coupon rate \$200,000 at 17% coupon rate
Common stock 4,000 shares 2,000 shares

a. Calculate two EBITâ€“EPS coordinates for each of the structures by selecting
any two EBIT values and finding their associated EPS values.
b. Plot the two capital structures on a set of EBITâ€“EPS axes.
c. Indicate over what EBIT range, if any, each structure is preferred.
d. Discuss the leverage and risk aspects of each structure.
e. If the firm is fairly certain that its EBIT will exceed \$75,000, which structure
would you recommend? Why?

11â€“16 EBITâ€“EPS and preferred stock Litho-Print is considering two possible capital
LG6
structures, A and B, shown in the following table. Assume a 40% tax rate.

Source of capital Structure A Structure B

Long-term debt \$75,000 at 16% coupon rate \$50,000 at 15% coupon rate
Preferred stock \$10,000 with an 18% annual \$15,000 with an 18% annual
dividend dividend
Common stock 8,000 shares 10,000 shares

a. Calculate two EBITâ€“EPS coordinates for each of the structures by selecting
any two EBIT values and finding their associated EPS values.
b. Graph the two capital structures on the same set of EBITâ€“EPS axes.
c. Discuss the leverage and risk associated with each of the structures.
d. Over what range of EBIT is each structure preferred?
e. Which structure do you recommend if the firm expects its EBIT to be
\$35,000? Explain.

11â€“17 Optimal capital structure Nelson Corporation has collected the following data
LG6
associated with four possible capital structures.

Capital Estimated
structure Expected coefficient of variation
debt ratio EPS of EPS

0% \$1.92 .4743
20 2.25 .5060
40 2.72 .5581
60 3.54 .6432

The firmâ€™s research indicates that the marketplace assigns the following required
returns to risky earnings per share.
459
CHAPTER 11 Leverage and Capital Structure

Coefficient of variation Estimated required
of EPS return, ks

.43 15%
.47 16
.51 17
.56 18
.60 22
.64 24

a. Find the required return associated with each of the four capital structures.
b. Compute the estimated share value associated with each of the four capital
structures using the simplified method described in this chapter (see Equa-
tion 11.12).
c. Determine the optimal capital structure based on (1) maximization of
expected EPS and (2) maximization of share value.
d. Construct a graph (similar to Figure 11.6) showing the relationships in part c.
e. Which capital structure do you recommend? Why?

11â€“18 Integrativeâ€”Optimal capital structure Triple D Corporation wishes to analyze
LG5 LG6
five possible capital structuresâ€”0%, 15%, 30%, 45%, and 60% debt ratios.
The firmâ€™s total assets of \$1 million are assumed to be constant. Its common
stock has a book value of \$25 per share, and the firm is in the 40% tax bracket.
The following additional data have been gathered for use in analyzing the five
capital structures under consideration.

Capital
structure Interest rate Required
debt ratio on debt, kd Expected EPS return, ks

0% 0.0% \$3.60 10.0%
15 8.0 4.03 10.5
30 10.0 4.50 11.6
45 13.0 4.95 14.0
60 17.0 5.18 20.0

a. Calculate the amount of debt, the amount of equity, and the number of
shares of common stock outstanding for each of the capital structures being
considered.
b. Calculate the annual interest on the debt under each of the capital structures
being considered. (Note: The interest rate given is applicable to all debt asso-
ciated with the corresponding debt ratio.)
c. Calculate the EPS associated with \$150,000 and \$250,000 of EBIT for each
of the five capital structures being considered.
d. Using the EBITâ€“EPS data developed in part c, plot the capital structures on
the same set of EBITâ€“EPS axes, and discuss the ranges over which each is
preferred. What is the major problem with the use of this approach?
e. Using the valuation model given in Equation 11.12 and the appropriate
data, estimate the share value for each of the capital structures being
considered.
460 PART 4 Long-Term Financial Decisions

f. Construct a graph similar to Figure 11.6 showing the relationships between
the debt ratio (x axis) and expected EPS (y axis) and share value (y axis).
g. Referring to the graph in part f: Which structure is preferred if the goal is to
maximize EPS? Which structure is preferred if the goal is to maximize share
value? Which capital structure do you recommend? Explain.

CHAPTER 11 CASE Evaluating McGraw Industriesâ€™ Capital Structure

M cGraw Industries, an established producer of printing equipment, expects
its sales to remain flat for the next 3 to 5 years because of both a weak
economic outlook and an expectation of little new printing technology develop-
ment over that period. On the basis of this scenario, the firmâ€™s management has
been instructed by its board to institute programs that will allow it to operate
more efficiently, earn higher profits, and, most important, maximize share value.
In this regard, the firmâ€™s chief financial officer (CFO), Ron Lewis, has been
charged with evaluating the firmâ€™s capital structure. Lewis believes that the cur-
rent capital structure, which contains 10% debt and 90% equity, may lack ade-
quate financial leverage. To evaluate the firmâ€™s capital structure, Lewis has gath-
ered the data summarized in the following table on the current capital structure
(10% debt ratio) and two alternative capital structuresâ€”A (30% debt ratio) and
B (50% debt ratio)â€”that he would like to consider.

Capital structurea
Current A B
Source of capital (10% debt) (30% debt) (50% debt)

Long-term debt \$1,000,000 \$3,000,000 \$5,000,000
Coupon interest rateb 9% 10% 12%
Common stock 100,000 shares 70,000 shares 40,000 shares
ksc
Required return on equity, 12% 13% 18%
aThesestructures are based on maintaining the firmâ€™s current level of \$10,000,000 of total financing.
bInterest
rate applicable to all debt.
cMarket-based return for the given level of risk.

Lewis expects the firmâ€™s earnings before interest and taxes (EBIT) to remain at
its current level of \$1,200,000. The firm has a 40% tax rate.

Required
a. Use the current level of EBIT to calculate the times interest earned ratio for
each capital structure. Evaluate the current and two alternative capital struc-
tures using the times interest earned and debt ratios.
b. Prepare a single EBITâ€“EPS graph showing the current and two alternative
capital structures.
c. On the basis of the graph in part b, which capital structure will maximize
McGrawâ€™s EPS at its expected level of EBIT of \$1,200,000? Why might this
not be the best capital structure?
461
CHAPTER 11 Leverage and Capital Structure

d. Using the zero-growth valuation model given in Equation 11.12, find the
market value of McGrawâ€™s equity under each of the three capital structures at
the \$1,200,000 level of expected EBIT.
e. On the basis of your findings in parts c and d, which capital structure would
you recommend? Why?

WEB EXERCISE Go to the Web site www.smartmoney.com. In the column on the right under
WW Quotes & Research enter the symbol DIS; click on Stock Snapshot; and then click
W
on Go.
1. What is the name of the company? Click on Financials.
2. What are the 5-year high and the 5-year low for the companyâ€™s debt/equity
ratio (the ratio of long-term debt to stockholdersâ€™ equity)?
At the bottom of this page under Stock Search, enter the next stock symbol from
the list below and then click on Submit. Enter the name of the company in the
matrix below and then click on Financials. Enter the 5-year high and low for the
debt/equity ratio in the matrix for each of the stock symbols.

Debt/equity ratio
Symbol Company name 5-yr. low 5-yr. high

DIS
AIT
MRK
LG
LUV
IBM
GE
BUD
PFE
INTC

3. Which of the companies have high debt/equity ratios?
4. Which of the companies have low debt/equity ratios?
5. Why do the companies that have a low debt/equity ratio use more equity
even though it is more expensive than debt?

Remember to check the bookâ€™s Web site at
www.aw.com/gitman