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Unformatted text preview: Long-Term
© Yang Yu—FOTOLIA (http://www.fotolia.com/p/42518) Long-term financing decisions concern how the firm finances its assets over the
long-term (that is, for more than one year). At issue are the proper balance between
debt and equity financing, and the procedures associated with raising money from
the various long-term financing sources. Chapter 13 begins this section with an
introduction to capital structure theory, which examines the aspects of financing
with debt and financing with equity and how the blend affects the firm. Chapter
14 covers long-term debt financing and financing from sources that are similar to
long-term debt: preferred stock and leasing. Chapter 15 covers financing obtained
from the firm’s owners in the form of common stock ownership. Chapter 16 ends
the section with the study of what to do with the firm’s excess funds, examining
the factors that lead to either distributing the funds to stockholders in the form of
dividends or retaining it for growth. 381 CHAPTERS 13 Capital Structure Basics 14 Corporate Bonds, Preferred
Stock, and Leasing 15 Common Stock 16 Dividend Policy Capital Structure
“The Lord forbid that I should be out of debt,
as if, indeed, I could not be trusted.”
—François Rabelais A Popcorn Venture
Jason is a college student who wants to start his own business. Jason’s
business idea is to sell popcorn from a cart, just as he has seen done in the
downtown area of the city in which he lives. The downtown vendor sells
about 500 bags of popcorn a day, and Jason thinks he might be able to do
as well with a similar popcorn stand near the college in his town.
However, the wagon contains both a popcorn-making machine and
a storage room for supplies, so it isn’t cheap. Also, if Jason went into this
business, he would need an expensive business operator’s license from the
city. The downtown vendor charges only $1 for a bag of popcorn, so Jason
would have to sell a lot of popcorn to recoup the high price of the wagon
and the license, $8,000 and $4,000 respectively. His variable costs are
$0.04 per bag.
Is this a viable business idea or not? What are the risks and the potential
returns of this business? Is this a better path than taking a McJob, as many of
Jason’s friends have done? In this chapter we’ll look at some of these issues. Source: Jason’s popcorn venture is based on actual events. The entrepreneur’s name has been changed and approximate
numbers have been used, because data about this private company are confidential. 382 © Furtuna Dan Emanuel—FOTOLIA
(http://www.fotolia.com/p/63785”>Furtuna Dan Emanuel) Chapter Overview Learning Objectives In this chapter we investigate how fixed costs affect the volatility of a firm’s
operating and net income. We see how fixed operating costs create operating
leverage, which magnifies the effect of sales changes on operating income. We
also examine how fixed financial costs create financial leverage, which magnifies
the effect of changes in operating income on net income. Then we analyze the risk
and return of leveraged buyouts (LBOs). Finally, we see how changes in a firm’s
capital structure affect the firm’s overall value. After reading this chapter,
you should be able to: 1. Define capital structure. 2. Explain operating,
financial, and combined
leverage effects and the
resulting risks. 3. Find the breakeven level of
sales for a firm. Capital Structure
Capital structure is the mixture of funding sources (debt, preferred stock, or
common stock) that a firm uses to finance its assets. A central question in finance
is what blend of these financing sources is best for the firm. That is, how much of
a firm’s assets should be financed by borrowing? How much should be financed
by preferred stockholders? How much should be financed by the common
stockholders? The question is important because each of these financing sources
has a different cost, as you learned in Chapter 9, and each of them has a different
degree of risk. Therefore, the choice of financing directly affects a firm’s weighted
average cost of capital and the degree of riskiness in the firm.
The amount of debt that a firm uses to finance its assets creates leverage. A
firm with a lot of debt in its capital structure is said to be highly levered. A firm
with no debt is said to be unlevered. In physics, the term leverage describes how
a relatively small force input can be magnified to create a larger force output.
383 4. Describe the risks and
returns of a leveraged
buyout. 5. Explain how changes in
capital structure affect a
firm’s value. 384 Part IV Long-Term Financing Decisions For example, if a farmer wants to move a large boulder in a field, he can wedge a long
board (a lever) between the large boulder and a small rock (a fulcrum), which gives him
enough leverage to push down on the end of the long board and easily move the boulder.
The power of leverage can also be harnessed in a financial setting. Its magnifying
power can help or hurt a business. A firm that has leverage will earn or lose more than
it would without leverage. In the sections that follow, we investigate specific types of
leverage and the risks associated with each type. Operating Leverage
Operating leverage refers to the phenomenon whereby a small change in sales triggers
a relatively large change in operating income (or earnings before interest and taxes, also
known as EBIT). Operating leverage occurs because of fixed costs in the operations of
the firm. A firm with fixed costs in the production process will see its EBIT rise by a
larger percentage than sales when unit sales are increasing. If unit sales drop, however,
the firm’s EBIT will decrease by a greater percentage than its sales.
Table 13-1 illustrates the operating leverage effect for a firm in which all production
costs, a total of $5,000, are fixed. Observe how the presence of the fixed costs causes a
10 percent change in sales to produce a 20 percent change in operating income.
Calculating the Degree of Operating Leverage The degree of operating leverage, or
DOL, measures the magnitude of the operating leverage effect. The degree of operating
leverage is the percentage change in earnings before interest and taxes (%ΔEBIT)
divided by the percentage change in sales (%ΔSales):
Degree of Operating Leverage (DOL)
DOL = %∆ EBIT
%∆ Sales (13-1) where: %Δ EBIT = ercentage change in earnings before interest and taxes
P %Δ Sales = Percentage change in sales According to Equation 13-1, the DOL for the firm in Table 13-1 is
DOL = 20%
10% = 2.0 Table 13-1 The Operating Leverage Effect—Fixed Costs Only Period 1 Period 2 Percent Change Sales $ 10,000 $ 1,000 1 Fixed Costs – 5,000 – 5,000 Operating Income $ 5,000 $ 6,000 10%
20% Chapter 13 Capital Structure Basics We see that, for a firm with a 10 percent change in sales and a 20 percent change
in EBIT, the DOL is 2.0. A DOL greater than 1 shows that the firm has operating
leverage. That is, when sales change by some percentage, EBIT will change by a greater
The Effect of Fixed Costs on DOL Table 13-2 shows the projected base-year and
second-year income statement for Jason’s Popcorn Wagon. The income statement allows
us to analyze Jason’s operating leverage. (Note that Table 13-2 divides the operating
expenses into two categories, fixed and variable.) We see that sales and operating
expenses are likely to change in the second and subsequent years. We also see the
predicted impact on EBIT, given the sales forecast.
We see from Table 13-2 that Jason’s percentage change in sales is 10 percent, and
his percentage change in EBIT (or operating income) is 17.1 percent. We use Equation
13-1 to find Jason’s DOL, as follows:
DOL = %∆ EBIT
%∆ Sales = (19, 680 − 16,800) / 16,800
(33, 000 − 30, 000) / 30, 000 = .171
.10 = 1.71 Our DOL calculations indicate that if Jason’s Popcorn Wagon business sales increase
by 10 percent from the base year to the next year, EBIT will increase by 17.1 percent.
This larger percentage increase in EBIT is caused by the company’s fixed operating
costs. No matter how much popcorn Jason produces and sells, his wagon and license
costs stay the same. The fixed costs cause the EBIT to increase faster than sales. If sales
decrease, the fixed costs must still be paid. As a result, the fixed costs cause EBIT to
drop by a greater percentage than sales.
Jason’s Popcorn Wagon Projected Income Statement
(Fixed Costs Are $12,000, Variable Costs Are $0.04 per Unit,
and Price per Unit is $1.00) Base Year Year 2 Sales $30,000 $33,000
– VC – 1,200 – – FC – 12,000 = $16,800 = $19,680 33,000 − 30,000
= .10, or 10%
30,000 %∆ = 19,680 − 16,800
= .171, or 17.1%
16,800 – 12,000 = EBIT %∆ = 1,320 385 386 Part IV Long-Term Financing Decisions The Alternate Method of Calculating DOL Instead of using Equation 13-1, we may
also find the DOL by using only numbers found in the base-year income statement.
Subtract total variable costs from sales, divide that number by sales minus total variable
costs minus fixed costs, and solve for DOL. The formula for the alternate method of
finding DOL, Equation 13-2, follows:
Degree of Operating Leverage (DOL) (alternate)
DOL = Sales − VC
Sales − VC − FC (13-2) where: VC = Total variable costs FC = Total fixed costs From Table 13-2, we know that in the base year, Jason’s Popcorn Wagon has sales
of $30,000, variable costs of $1,200, and fixed costs of $12,000. Using the alternate
formula, we find that Jason has the following DOL:
DOL = Sales - VC
Sales − VC − FC = 30, 000 - 1, 200
30, 000 − 1, 200 − 12, 000 = 28,800
16,800 = 1.71 We find a DOL of 1.71, just as we did with Equation 13-1. How did this happen?
The alternate formula, Equation 13-2, uses only numbers from the base year income
statement, whereas Equation 13-1 requires information from the base year and year 2.1
Why use two different ways to calculate DOL when they both give the same answer?
The answer is that each method reveals different information about operating leverage.
The percentage change version of the DOL formula, Equation 13-1, shows the effect
of the leverage—sales change by a certain percentage, triggering a greater percentage
change in operating income if the DOL is greater than 1. The percentage change in
operating income, then, is the product of the percentage change in sales and this degree
of operating leverage.
The alternate DOL formula, Equation 13-2, shows that fixed costs cause the
leveraging effect. Whenever fixed costs are greater than 0, DOL is greater than 1, indicating
a leverage effect (the percentage change in EBIT is greater than the percentage change
in sales). The larger the amount of fixed costs, the greater the leveraging effect.
Taken together, the two formulas demonstrate that leverage has the effect of
triggering a greater percentage change in operating income when a percentage change
in sales occurs and that fixed costs cause operating leverage. Equation 13-3 shows how
changes in sales and DOL combine to determine the change in EBIT.
Percentage Change in EBIT %Δ EBIT = %Δ Sales × DOL Equations 13-1 and 13-2 give the same numeric result when sales price per unit, fixed costs, and variable costs per unit
are constant. 1 (13-3) Chapter 13 Capital Structure Basics where: Δ Sales = Percentage change in sales
% DOL = Degree of operating leverage The Risk of Operating Leverage As we know from Chapter 7, the risk associated with
operating leverage is business risk. Recall that business risk refers to the volatility of
operating income. The more uncertainty about what a company’s operating income will
be, the higher its business risk. Volatility of sales triggers business risk. The presence of
fixed costs, shown by the amount of DOL, magnifies business risk. The total degree of
business risk that a company faces is a function of both sales volatility and the degree
of operating leverage. Financial Leverage
Fluctuations in sales and the degree of operating leverage determine the fluctuations
in operating income (also known as EBIT). Now let’s turn our attention to financial
leverage. Financial leverage is the additional volatility of net income caused by the
presence of fixed-cost funds (such as fixed-rate debt) in the firm’s capital structure.
Interest on fixed-rate debt is a fixed cost because a firm must pay the same amount of
interest, no matter what the firm’s operating income.
Calculating the Degree of Financial Leverage (DFL) The degree of financial
leverage (DFL) is the percentage change in net income (%ΔNI) divided by the
percentage change in EBIT (%ΔEBIT). The formula for DFL follows:
Degree of Financial Leverage (DFL)
DFL = %∆ NI
%∆ EBIT (13-4) where: %Δ NI = Percentage change in net income %Δ EBIT = ercentage change in earnings before interest and taxes
P If net income changes by a greater percentage than EBIT changes, then the DFL
will have a value greater than 1, and this indicates a financial leverage effect.2
Table 13-3 shows the entire base-year income statement for Jason’s Popcorn Wagon
and the projections for year 2. Notice that the lower portion of the income statements
contains fixed interest expense, so we would expect the presence of financial leverage.
As shown in Table 13-3, the percentage change in EBIT from the base year to year
2 is 17.1 percent, and the percentage change in net income from the base year to year 2
is 18 percent. Jason’s degree of financial leverage according to Equation 13-4 follows:
= %∆ NI
.171 = 1.05
Note that the degree of financial leverage calculated using Equation 13-4 will be faced by preferred stockholders and common
stockholders together. If you were interested in finding the degree of financial leverage faced by common stockholders only, you
would modify Equation 13-4 by subtracting preferred dividends from net income. 2 387 388 Part IV Long-Term Financing Decisions Table 13-3 Jason’s Popcorn Wagon Projected Income Statements Base Year Year 2 Sales $30,000 $33,000 % ∆ = 33,000 − 30,000 = .10, or 10%
– VC – – FC – 12,000 – 12,000 = EBIT = $16,800 = $19,800 % ∆ = – Int – – 1,200 800 – 1,320 800 = EBT = 16,000 = 18,880 (
– Tax 15%) – – = NI = 13,600 19,680 − 16,800
= .171, or 17.1%
16,800 2,400 2,832 = 16,048 % ∆ = 16,048 − 13,600 = .18, or 18%
13,600 Our calculations show that Jason’s Popcorn Wagon business has a degree of financial
leverage of 1.05.
Another Method of Calculating Financial Leverage Just as with DOL, there are two
ways to compute DFL. Instead of using Equation 13-4, the percentage change in NI
divided by the percentage change in EBIT, we could instead calculate the DFL using
only numbers found in the base-year income statement. By dividing EBIT by EBIT
minus interest expense (Int), we can find DFL. The equation looks like this:
Degree of Financial Leverage (DFL) (alternate)
DFL = EBIT
EBIT − Int (13-5) where: EBIT = Earnings before interest and taxes Int = Interest expense The base-year income statement numbers in Table 13-3 show that Jason’s EBIT is
$16,800 and his interest expense is $800. To find the degree of financial leverage, we
apply Equation 13-5 as follows:
DFL = EBIT
EBIT − Int = 16,800
16,800 − 800 = 16,800
16, 000 = 1.05 Chapter 13 Capital Structure Basics Equation 13-5 yields the same DFL for Jason’s business as Equation 13-4.3 Both
formulas are important because they give us different but equally important insights
about financial leverage. Equation 13-4 shows the effect of financial leverage—net
income (NI) will vary by a larger percentage than operating income (EBIT). Equation
13-5 pinpoints the source of financial leverage—fixed interest expense. The degree of
financial leverage, DFL, will be greater than 1 if interest expense (I) is greater than 0.
In sum, interest expense magnifies the volatility of NI as operating income changes.
How Interest Expense Affects Financial Leverage To illustrate the financial leverage
effect, suppose that to help start his business, Jason borrowed $10,000 from a bank at an
annual interest rate of 8 percent. This 8 percent annual interest rate means that Jason will
have to pay $800 ($10,000 × .08) in interest each year on the loan. The interest payments
must be made, no matter how much operating income Jason’s business generates. In
addition to Jason’s fixed operating costs, he also has fixed financial costs (the interest
payments on the loan) of $800.
The fixed financial costs magnify the effect of a change in operating income on net
income. For instance, even if Jason’s business does well, the bank interest payments do
not increase, even though he could afford to pay more. If Jason’s business does poorly,
however, he cannot force the bank to accept less interest simply because he cannot
afford the payments.
The Risk of Financial Leverage The presence of debt in a company’s capital structure
and the accompanying interest cost create extra risk for a firm. As we know from Chapter
7, the extra volatility in NI caused by fixed interest expense is financial risk. The financial
risk of the firm compounds the effect of business risk and magnifies the volatility of net
income. Just as fixed operating expenses increase the volatility of operating income and
business risk, so too fixed financial expenses increase the volatility of NI and increase
financial risk. This is shown in Equation 13-6.
Percentage Change in Net Income %Δ NI = %Δ EBIT × DFL (13-6) where: %Δ EBIT = ercentage change in earnings before interest and taxes
P DFL = Degree of financial leverage Now we explore the combined effect of operating and financial leverage next. Combined Leverage
The combined effect of operating leverage and financial leverage is known as combined
leverage. Combined leverage occurs when net income changes by a larger percentage
than sales, which occurs if there are any fixed operating or financial costs. The following
combined leverage formula solves for the net income change due to sales changes that
occur when fixed operating and financial costs are present. Equations 13-4 and 13-5 give the same DFL value only if the fixed financial costs (interest expense) and the tax rate
are constant. 3 389 390 Part IV Long-Term Financing Decisions The degree of combined leverage (DCL) is the percentage change in net
income (%Δ NI) divided by the percentage change in sales (%Δ Sales), as shown in
Degree of Combined Leverage (DCL) DCL = where: %∆ NI
%∆ Sales (13-7) %Δ NI = Percentage change in net income
%Δ Sales = Percentage change in sales The alternate DCL formula follows:
Degree of Combined Leverage (DCL) (alternate 1) DCL = Sales − VC
Sales − VC − FC − Int where: VC = Total variable costs FC = Total fixed costs (13-8) Int = Interest expense We can also calculate the degree of combined leverage (DCL) a third way:
multiplying the degree of operating leverage (DOL) by the degree of financial leverage
(DFL). The third DCL formula is shown in Equation 13-9.
Degree of Combined Leverage (DCL) (alternate 2) DCL = DOL × DFL where: DOL = Degree of operating leverage (13-9) DFL = Degree of financial leverage Equation 13-10 shows the combined effect of DOL and DFL on net income (NI).
Percentage Change in Net Income (NI) %Δ NI = %Δ Sales × DOL × DFL (13-10) where: %Δ Sales = Percentage change in sales DOL = Degree of operating leverage DFL = Degree of financial leverage Equation 13-10 shows how the change in net income is determined by the change
in sales and the compounding effects of operating and financial leverage.
Fixed Costs and Combined Leverage Fixed operating costs create operating leverage,
fixed financial costs create financial leverage, and these two types of leverage together
form combined leverage. If fixed operating costs (FC) and fixed interest costs (Int) were Chapter 13 Capital Structure Basics both zero, there would be no leverage effect. The percentage change in net income (NI)
would be the same as the percentage change in sales. If either, or both, fixed operating
costs and fixed financial costs exceed zero, a leverage effect will occur (DCL > 1).
Firms that have high operating leverage need to be careful about how much debt they
pile onto their balance sheets, and the accompanying interest costs they incur, because
of combined leverage effects. Remember that for Jason’s Popcorn Wagon, the degree
of operating leverage (DOL) was 1.71 and the degree of financial leverage was 1.05.
The degree of combined leverage for Jason’s business according to Equation 13‑8 is
1.80 (1.71 × 1.05 = 1.80 rounded to two decimal places). Jason is quite confident that
his sales will be high enough so that this high leverage will not be a problem. If the
sales outlook were questionable, though, the combined leverage effect could magnify
poor sales results.
Leverage is helpful when sales increase (positive percentage changes). Magnifying
this positive change benefits the firm. However, leverage is harmful when sales decrease
because it magnifies the negative change. Because future sales for most companies are
uncertain, most companies view leverage with mixed feelings. Breakeven Analysis and Leverage
Investments in projects may change a firm’s fixed operating and financing costs, thereby
affecting firm value. Fixed costs may affect firm value because of leverage effects and
the resulting risk from those leverage effects.
To understand a firm’s potential for risk and return, then, financial managers must
understand two types of leverage effects: operating leverage and financial leverage.
Breakeven analysis is a key to understanding operating leverage. In breakeven
analysis we examine fixed and variable operating costs. Fixed costs are those costs that
do not vary with the company’s level of production. Variable costs are those costs that
change as the company’s production levels change.
In breakeven analysis, the sales breakeven point is the level of sales that a firm
must reach to cover its operating costs. Put another way, it is the point at which the
operating income (earnings before interest and taxes) equals zero.
A company with high fixed operating costs must generate high sales revenue to
reach the sales breakeven point. A company with low fixed operating costs requires
relatively low sales revenue to reach its sales breakeven point.
We usually observe a high/low trade-off in breakeven analysis. Firms with high
fixed operating costs tend to have low variable costs, and vice versa. A company that
automates a factory, for instance, commits to significant fixed costs—the expensive
equipment. But the company’s variable labor costs are likely to be low at a highly
automated plant that operates with relatively few employees. In contrast, a company that
produces handmade pottery with little overhead and hires hourly workers as needed, is
likely to have low fixed costs but high variable costs.4
To demonstrate the high/low trade-off, we gather data for a sales breakeven chart
for two firms. The first firm has high fixed and low variable costs. The second firm has
low fixed and high variable costs.
Labor costs can be either fixed or variable. If workers are guaranteed pay for a certain minimum number of hours per week, as
might be called for in a union contract, the labor costs associated with this minimum guaranteed pay would be fixed costs. The
costs associated with hourly worker pay with no guaranteed minimum are variable. 4 391 Interactive Module
Go to www.textbookmedia.
com and find the free
companion material for
this book. Follow the
instructions there. Observe
how fixed operating costs
and fixed financial costs
lead to operating leverage
and financial leverage,
respectively. 392 Part IV Long-Term Financing Decisions Constructing a Sales Breakeven Chart
A breakeven chart shows graphically how fixed costs, variable costs, and sales revenue
interact. Analysts construct the chart by plotting sales revenue and costs at various unit
sales levels on a graph. To illustrate, let’s construct the breakeven chart for Jason’s
Popcorn Wagon, featured in the opening of the chapter.
The first step in constructing the breakeven chart is to find the breakeven point
for the business. Let’s look at some of the numbers for Jason’s business and calculate
the level of sales Jason must achieve to break even. Recall that at the breakeven point,
operating income equals zero. If sales are below the breakeven point, Jason suffers an
operating loss. If sales are above the breakeven point, Jason enjoys an operating profit.
(Interest and taxes, subtracted after finding operating income, will be discussed in the
last section of the chapter.)
Jason wants to know that his business venture has the potential for a positive
operating profit, so he is keenly interested in finding his breakeven point. To find this
point, we need to know how many bags of popcorn he must sell before the sales revenue
contributed by each bag sold just covers his fixed and variable operating costs. The
relevant sales breakeven figures for Jason’s proposed business are shown in Table 13‑4.
The numbers in Table 13-4 show that Jason’s fixed costs are high compared with
his sales price of $1 per bag of popcorn. The fixed costs include the $8,000 annual
rental fee for the wagon and the $4,000 annual license fee. Jason must pay these costs
no matter how much popcorn he produces and sells.
In contrast to the high fixed operating costs, Jason’s variable operating costs per
unit are a tiny fraction of his sales price of $1 per unit. The bag, oil, salt, and popcorn
that help produce one bag of popcorn cost a total of $0.04. Each bag of popcorn that
is sold, then, contributes $0.96 to cover the fixed costs, and ultimately the profit of the
business ($1.00 – $0.04 = $0.96). The sales price per unit minus the variable cost per
unit, $.96 in this case, is the contribution margin.
From the numbers presented in Table 13-4, we can calculate the breakeven level
of sales for Jason’s business. We find the level of sales needed to reach the operating
income breakeven point by applying the following formula: Table 13-4 Jason’s Relevant Figures for Breakeven Analysis Fixed Costs: Wagon (annual rental) $ 8,000 City License (annual fee) $ 4,000 Total $ 2,000
1 Variable Costs per Unit: One Paper Bag $ 0.020 Oil $ 0.005 Salt $ 0.003 Popcorn $ 0.012 Total $ 0.040 $ 1.00 Sales Price per Unit: Chapter 13 Capital Structure Basics The Breakeven Point in Unit Sales, Qb.e.
Q b.e. = FC
p − vc (13-11) where: Qb.e. = Quantity unit sales breakeven level FC = Total fixed costs p = Sales price per unit vc = Variable cost per unit For Jason’s business, the total fixed costs are $12,000, the price per unit is $1, and
the variable cost per unit is $.04. According to Equation 13-11, Jason’s popcorn business
has the following sales breakeven point:
Q b.e. =
= $12, 000
$1.00 − $.04
$.96 = 12, 500 We find that Jason’s sales breakeven point with $12,000 in fixed costs, $.04 per
unit in variable costs, and a $1 per bag sales price, is 12,500 units. At $1 per bag, this
is $12,500 in sales to reach the breakeven point.
Now that we know Jason’s sales breakeven point, we need revenue and cost
information to construct the breakeven chart.
Revenue Data At any given level of unit sales, Jason’s total sales revenue can be found
using Equation 13-12:
Total Revenue (TR) TR = p × Q (13-12)
where: p = Sales price per unit Q = Unit sales (Quantity sold)
Table 13-5 shows how to calculate Jason’s sales revenues at different sales levels.
For instance, we see that if Jason sells 5,000 bags of popcorn at the price of $1 per bag,
his total revenue will be 5,000 × $1.00 = $5,000. If Jason sells 10,000 bags, his total
revenue will be $10,000.
Cost Data By definition, Jason’s fixed costs will remain $12,000, regardless of the
level of unit production and sales. His variable costs, however, increase by $0.04 for
each unit sold. Jason’s total costs for any given level of unit production and sales can
be found using Equation 13-13 as follows:
Total Costs (TC) TC = FC + (vc × Q) (13-13) 393 394 Part IV Long-Term Financing Decisions Table 13-5 Sales Revenues at Different Unit Sales Levels
Unit Sales (Q) x Price (P) = 0 x $1 = Total Revenue (TR) 5,000 x $1 = $ 5,000 10,000 x $1 = $ 0,000
1 $ 0 15,000 x $1 = $ 5,000
1 20,000 x $1 = $ 0,000
2 25,000 x $1 = $ 5,000
2 30,000 x $1 = $ 0,000
3 where: FC = Fixed costs vc = Variable costs per unit Q = Units produced Table 13-6 demonstrates how we use Equation 13-13 to calculate Jason’s total costs
for different production and sales levels. For instance, we see that if Jason sells 5,000
bags of popcorn at a variable cost of $0.04 per bag and fixed costs of $12,000, his total
cost will be $12,200. At 10,000 bags, his total cost will be $12,400. We assume the
number of units produced equals the number of units sold.
Plotting Data on the Breakeven Chart Jason’s breakeven chart is shown in Figure
13-1. The chart is constructed with units produced and sold (Q) on the horizontal axis
and cost and revenue dollars on the vertical axis. Total revenues from Table 13-5 are
shown on the TR line, and total costs from Table 13-6 are shown on the TC line.
We see from the chart that to break even, Jason has to sell $12,500 worth of popcorn
at $1 per bag—a quantity of 12,500 bags. Table 13-6 Jason’s Total Costs for Different Sales Levels
Fixed Costs (FC) + $12,000 + $12,000 $12,000 (Variable Cost/Unit (vc) x Units Produced (Q) = Total
Cost (TC) ($.04 x 0) = $12,000 + ($.04 x 5,000) = $12,200 + ($.04 x 10,000) = $12,400 $12,000 + ($.04 x 15,000) = $12,600 $12,000 + ($.04 x 20,000) = $12,800 $12,000 + ($.04 x 25,000) = $13,000 $12,000 + ($.04 x 30,000) = $13,200 Chapter 13 Capital Structure Basics 395 $30,000 $30,000
Total Costs Revenues and Costs $25,000 $25,000 $20,000 $20,000 $15,000 $15,000
$12,000 $12,200 $10,000 $12,400 $13,000 $13,200 $10,000
$0 $12,800 $12,600 0 Break even at12,500
5,000 10,000 15,000 20,000 25,000 30,000 Units Produced and Sold Applying Breakeven Analysis
Although 12,500 bags of popcorn may seem like a lot of sales just to break even, Jason
has watched another vendor downtown sell on average 500 bags of popcorn a day.
Jason plans to sell for three months during the summer, four weeks a month, five days
a week. He estimates that he could sell 30,000 bags of popcorn (500 bags × 3 months ×
4 weeks × 5 days) during the summer. At this sales level, Jason expects $30,000 in gross
sales revenue at $1 per bag and $16,800 in operating income [$30,000 total revenue –
$12,000 fixed costs – ($30,000 × .04 variable costs) = $16,800 operating income]. Not
a bad summer job income.
How is it possible to make so much money selling popcorn? Note how once Jason
passes the breakeven point in sales, each additional $1 bag of popcorn he sells generates
$0.96 of operating profit. The $0.04 in variable costs incurred in the production of that
bag of popcorn represents a small part of the $1 in revenue generated. Operating profit
rises rapidly as sales climb above the breakeven point of 12,500 units, as shown by
Figure 13-1. Were Jason’s sales potential not so promising, however, his risk of loss
(negative operating income) would be a greater concern. The red area of the graph in
Figure 13-1 shows Jason’s loss potential.
The breakeven chart allows Jason to see the different sales scenarios to understand
his profit and loss potential. Because the total revenue line in Figure 13-1 is much
steeper than the total cost line (because the sales price per unit is much greater than
the variable cost per unit) the profit potential is great. Because of the high fixed costs,
however, the loss potential is great, too. What happens depends on how much popcorn
Jason can sell. Figure 13-1 Breakeven
Chart for Jason’s Popcorn
Wagon 396 Part IV Long-Term Financing Decisions To illustrate what happens with a low breakeven business, let’s construct a breakeven
chart for Carey, another college student, who wants to sell hotplate mini-cookbooks
(only five pages long) to college students.5
Because Carey plans to operate from her apartment and use her own recipes for
the mini-cookbook, her only fixed cost would be a $1,000 printer’s design fee. Her
variable costs consist of her paper printing costs at $0.60 per unit. Carey plans to sell
her cookbook for $1 per unit.
This is a low-risk business. The design fee is modest and there are no other fixed
costs. The contribution margin is $0.40 ($1.00 sales price – $0.60 variable cost per unit).
We can find Carey’s breakeven point using Equation 13-11:
Q b.e. = FC
p − vc = $1, 000
$1 − $.60 = $1, 000
$.40 = 2, 500 We find that Carey’s breakeven point is 2,500 units. Carey figures she can sell to
friends in the dorm. Beyond that, however, the sales potential is uncertain. She may or
may not reach the breakeven point.
To find Carey’s breakeven point, we find her total revenue and total costs at different
sales levels and plot them on a breakeven chart (see Figure 13-2).
Note how small the loss potential is for Carey’s business, as shown in the red area
in Figure 13-2, compared with Jason’s loss potential, shown in the red area in Figure
13-1. Carey’s loss potential is small because her breakeven level of sales ($0 operating
income) is 2,500 units, compared with Jason’s 12,500 unit breakeven point. Even if
she sold nothing, Carey would lose only the $1,000 in fixed costs that she had to pay
(compared with Jason’s $12,000). Table 13-7 shows the profit and loss potential for
Jason and Carey.
The risk of Jason’s business is also evident when we look at sales of 15,000 units
for each business. Jason has a profit of only $2,400, whereas Carey would earn a profit
of $5,000; at 30,000 units sold, however, Jason earns a profit of $16,800 and Carey
earns only $11,000, as shown in Table 13-7. Jason’s profits are much more dependent
on selling a large number of units than Carey’s.
Now compare the profit potential for the two proposed businesses. Jason has the
potential to make much more profit (operating income) than Carey. At a sales level
of 30,000, Table 13-7 shows Jason makes $16,800, whereas Carey would make only
$11,000. Even though Jason’s business has more risk—he stands to lose much more if
sales don’t go well—he has the potential for greater returns.
Whether the high fixed cost and low variable cost per unit business (like Jason’s)
is better than the low fixed cost and high variable cost per unit business (like Carey’s)
depends on two factors: how many units you think you can sell and how much tolerance Believe it or not, Carey’s business is also inspired by a true story. Oliver Stone would be proud. 5 Chapter 13 Capital Structure Basics 397 $30,000 $30,000
Total Costs Revenues and Costs $25,000 $25,000 $20,000 $20,000 Break even
$13,000 $10,000 $10,000 $4,000 $1,000
$0 $7,000 $5,000 $5,000 $10,000 0 5,000 10,000 15,000 20,000 25,000 30,000 Units Produced and Sold Figure 13-2 Breakeven
Chart for Carey’s MiniCookbooks Table 13-7 Jason’s and Carey’s Profit and Loss Potential Units P roduced $Total a nd Sold Costs Jason $Total $Operating Revenue Income $Total Costs Carey
Revenue Income 0 12,000 0 –12,000 1,000 0 –1,000 5,000 12,200 5,000 –7,200 4,000 5,000 1,000 10,000 12,400 10,000 –2,400 7,000 10,000 3,000 15,000 12,600 15,000 2,400 10,000 15,000 5,000 20,000 12,800 20,000 7,200 13,000 20,000 7,000 25,000 13,000 25,000 12,000 16,000 25,000 9,000 30,000
13,200 30,000 16,800 19,000 30,000 11,000 35,000 13,400 35,000 21,600 22,000 35,000 13,000 40,000 13,600 40,000 26,400 25,000 40,000 15,000 you have for risk. High fixed costs and low variable costs per unit mean high profit
potential and high loss potential, as in the case of Jason’s proposed business. Conversely,
low fixed costs and high variable costs per unit mean low profit potential and low loss
potential, as in the case of Carey’s proposed business. Take Note
and cable companies are
examples of firms with
high fixed costs and low
variable costs per unit. A
consulting firm would be
an example of a firm with
low fixed costs and high
variable costs. 398 Part IV Long-Term Financing Decisions LBOs
Many publicly owned corporations have been bought out by a small group of investors,
including top management of the firm, using a large amount of borrowed money.
Such a purchase is called a leveraged buyout, or LBO. The leverage referred to is
In an LBO, investment banking firms work to identify attractive target companies.
These investment banking firms solicit investors to acquire the target. To take over the
target, the purchasing group raises cash, mostly borrowed, to purchase the common stock
shares from the general public. The stock purchase converts the publicly owned corporation
to a privately owned one. The investment banking firm would collect fees for its advice
and for underwriting the bond issue that helped raise the additional debt capital.
Because of the dramatic increase in financial leverage, some LBOs have worked
out well for investors and others have been disasters. For instance, Kohlberg, Kravis, &
Roberts made a 50 percent annual rate of return on its $1.34 billion investment after the
Beatrice Company LBO. In contrast, the 1986 $1.4 billion LBO of Revco Drug Stores
didn’t fare as well. Two years later the company filed for bankruptcy when it was unable
to generate enough cash flow to pay the interest and principal due on its bonds. Other
companies purchased through LBOs include Toys R Us, Neiman Marcus, Borg-Warner,
Montgomery Ward, Safeway, Southland, and RJR Nabisco. Bain Capital, Blackstone
Group, Carlyle Group and Kohlberg Kravis Roberts & Co. were reported in May of
2006 to have joined forces with Grupo Televisa SA to launch an LBO of Univision
Communications Inc, the Spanish language television company. This target company
is known for its soccer announcer who yells “goooooooooooooooooooal” after a score.
When a company with a normal debt load goes through an LBO, investors holding
the company’s bonds issued before the LBO are often hurt. The surge in the company’s
debt results in more financial risk. With higher risk, the market requires a higher rate of
return, so the bonds issued before the LBO will see their market interest rates rise—and
their market prices fall—after the company announces an LBO.
To illustrate the effects on bondholders, consider the 2005 LBO of SunGard Data
Systems. Table 13-8 shows how holders of SunGard’s bonds suddenly had a claim on
a much riskier company.
The risk of an LBO is large because of financial leverage effects. As the Beatrice
and Revlon examples indicate, potential returns from an LBO may be large positive or
negative values because of financial leverage effects. Bondholders may suddenly see
the value of their bonds drop precipitously after an LBO announcement. In Chapter 14,
we discuss how bondholders can protect themselves against this risk.
Now that we have analyzed how fixed operating and financial costs can create
leverage effects and risk, we will consider the optimal capital structure for a firm. Capital Structure Theory
Every time a company borrows, it increases its financial leverage and financial risk. New
equity financing decreases financial leverage and risk. Changes in financial leverage,
we have seen, bring the potential for good and bad results. How then do financial
managers decide on the right balance of debt and equity? Financial managers analyze
many factors, including the tax effects of interest payments and how the comparative
costs of debt and equity affect firm value. Chapter 13 Capital Structure Basics Table 13-8 Effect of a Leveraged Buyout on SunGard Data Systems Before the Buyout After the Buyout (2004) (2005) Total Assets $5,195 $14,587 554 7,429 3,252 3,572 Debt to Assets Ratio 11% 51% Total Debt Stockholder’s Equity Price of Company’s
Bonds Maturing in 2014 $980 $840 S&P Bond Rating BBB+ B+ Source: SunGard Data Systems SEC Form 10-K filed March 13, 2006, and “LBOs May Spoil The Corporate-Bond Party” by Mark Whitehouse, Staff Reporter of The Wall Street Journal, August 1, 2005 (accessed online at .wsj.com, June 14, 2006) Tax Deductibility of Interest
Debt in a firm’s capital structure can be beneficial. First, debt creates the potential
for leveraged increases in net income (NI) when operating income (EBIT) is rising.
Second, debt gives the company a tax deduction for the interest that is paid on the debt.
In contrast to debt, an issue of common stock to raise equity funds results in no tax
break. In short, interest paid on business debt is tax deductible, but dividends paid to
common stockholders are not. The tax laws, therefore, give companies an incentive to
use debt in their capital structures.
Although the tax deductibility of interest payments on debt is a benefit, debt has
costs, too. We know that the financial risk of the firm increases as debt increases. As
financial risk increases, including an increasing risk of bankruptcy, a company will incur
costs to deal with this risk. For example, suppliers may refuse to extend trade credit to
the company, and lawyers’ fees may drain funds that could go to either bondholders or
common stock investors.
Modigliani and Miller
How does a company balance the costs and benefits of debt? In 1958, Franco Modigliani
and Merton Miller wrote a seminal paper that has influenced capital structure discussion
ever since. Modigliani and Miller (known in economics and finance circles as M&M)
concluded that when interest payments are tax deductible to a firm, a capital structure
of all debt is optimal.
In reaching this conclusion, M&M assumed the following: 1. here were no transaction costs.
T 2. urchasers of a company’s bonds or common stock paid no income tax.
P 3. orporations and investors can borrow at the same rate of interest.
C 4. nvestors and management have the same information about the firm.
I 5. ebt the firm issues is riskless.
D 6. perating income is not affected by the use of debt.
O 399 400 Part IV Long-Term Financing Decisions In such an environment, M&M showed that the tax benefits to the firm from issuing
debt were so beneficial that the benefits allowed the company to increase its value by
issuing more and more debt. Given the assumptions, a 100 percent debt capital structure
The assumptions, of course, do not exist in the real world. Companies don’t seek
a 100 percent debt capital structure, suggesting that capital structure is not optimal. In
the real world, capital structures vary widely. Toward an Optimal Capital Structure
Firms seek to balance the costs and benefits of debt to reach an optimal mix that
maximizes the value of the firm. Figure 13-3 shows the component costs and weighted
cost of capital according to the view of most financial managers. Given the way suppliers
of capital react in the real world, many financial managers believe this view is more
realistic than the M&M model.
Figure 13-3 illustrates what many believe happens to the cost of debt, equity, and
the weighted average cost of capital (WACC) as the capital structure of the firm changes.
First, the graph shows that debt is cheaper than equity capital. Second, it shows that the
weighted average cost of capital equals the cost of equity when the firm has no debt.
Third, it shows that at point Z firms minimize the weighted average cost of capital, so
at that point the capital structure maximizes the value of the firm. The cost advantage
that debt has over equity dominates the increasing risk up to point Z. At this point, the
greater risk begins to dominate and causes the weighted average cost of capital to begin
to turn upward.
We learned in Chapter 9 how to estimate the costs of debt and equity and weighted
average figures. Here we study how capital structure changes may affect the firm’s cost
of capital and its value.
The Lower Cost of Debt Figure 13-3 shows that debt capital has a lower cost than
equity capital. Debt is cheaper than equity for two reasons. As mentioned earlier, interest
payments made by a firm are tax deductible and dividend payments made to common
stockholders are not. Even without the tax break, however, debt funds are cheaper than
equity funds. The required rate of return on a bond is lower than the required rate of
return on common stock for a given company because its debt is less risky than its
equity to investors. Debt is less risky because bondholders have a claim superior to that
of common stockholders on the earnings and assets of the firm.
How Capital Costs Change as Debt Is Added If we examine the WACC line in Figure
13-3, we see that the weighted average cost of capital equals the cost of equity when the
firm has no debt. Then, as debt is added, the cost advantage (to the issuing company) of
debt over equity makes the weighted average cost of capital decrease, up to a point, as
more of the cheaper debt funds and less of the more expensive equity funds are used.
The effect of adding debt to capital structure is shown in Figure 13-3 as we move along
the horizontal axis from the origin.
The Effect of Risk What causes the WACC to increase, as shown in Figure 13-3, beyond
point Z? As the firm moves to a capital structure with higher debt (moves to the right
along the horizontal axis of Figure 13-3), the risk of the firm increases. As financial risk
rises with additional debt, the required return of both debt and equity investors increases. 401 Costs of Capital Chapter 13 Capital Structure Basics
2% Cost of Cost of Equity
Weighted Average Cost of Capital
Cost of Debt Z 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Debt to Firm Value Ratio Notice that the cost of equity curve starts to climb sooner than the cost of debt curve.
This is because common stockholders get paid after bondholders.
As both the cost of debt and the cost of equity curves turn upward, the curve depicting
the weighted average of the cost of debt and the cost of equity eventually turns upward,
too. According to the capital structure view depicted in Figure 13-3, if a firm has less
debt than the amount at Z, the WACC is higher than it needs to be. Likewise, if a firm
has more debt than the amount at Z, the WACC is higher than it needs to be. Only at
the capital structure at point Z do firms minimize the weighted average cost of capital.
This is the capital structure, then, that maximizes the value of the firm.
Establishing the Optimal Capital Structure in Practice In the real world, it is
unlikely that financial managers can determine an exact point for Z where the WACC is
minimized. Many financial managers try instead to estimate Z and set a capital structure
close to it. Unfortunately, no formula can help estimate point Z. The optimal capital
structure for a firm depends on the future prospects of that firm.
For example, say a company has a product in great demand that is protected by a
patent with many years to expiration. The company will find that bond and common
stock investors are comfortable with a large amount of debt. This firm’s Z value will
be high. But a firm in a competitive industry, with some quality control problems and
soft demand for its product, is in a different position. It will find that bond and common
stock investors get nervous (and demand higher returns) when the debt to total value6
ratio is above even a moderate level. This firm’s Z value will be much lower than that
of the first firm.
6 Total value here refers to the total market value of the firm’s outstanding debt and equity. Figure 13-3 Cost
of Capital and Capital
Structure 402 Part IV Long-Term Financing Decisions So the answer to the question, “What is the optimal capital structure for a firm?”
is, “It depends.” With no formula to use to estimate the firm’s Z value, management
examines the capital structure of similar companies and the future prospects of the firm.
Financial managers must balance the costs and benefits of debt and use expertise and
experience to develop the capital structure they deem optimal. What’s Next
In this chapter, we examined breakeven analysis, leverage effects, leveraged buyouts, and
the effects of changes in a firm’s capital structure. In Chapter 14, we look at corporate
bonds, preferred stock, and leasing. Summary
1. efine capital structure.
Capital structure is the mixture of funding sources (debt, preferred stock, or common
stock) that a firm uses to finance its assets. A central question in finance is what blend of
these financing sources is best for the firm. That is, how much of a firm’s assets should
be financed by borrowing? How much should be financed by preferred stockholders?
How much should be financed by the common stockholders? The question is important
because each of these financing sources has a different cost, and each of them has a
different degree of risk. Therefore, the choice of financing directly affects a firm’s
weighted average cost of capital and the degree of riskiness in the firm.
2. xplain operating, financial, and combined leverage effects and the resulting
business and financial risks.
Firms with high fixed costs have high operating leverage—that is, a small change in
sales triggers a relatively large change in operating income. Firms with low fixed costs
have less operating leverage. The effect of low operating leverage is that small changes
in sales do not cause large changes in operating income.
Business risk refers to the volatility of a company’s operating income. Business risk
is triggered by sales volatility and magnified by fixed operating costs.
If a company uses fixed-cost funds (such as fixed interest rate bonds) to raise capital,
financial leverage results. With financial leverage, fixed interest costs cause net income
to change by a greater percentage than a given percentage change in EBIT.
The presence of financial leverage creates financial risk for a firm—the risk that the
firm will not be able to make its interest payments if operating income drops. Financial
risk compounds the business risk already present.
The total effect of operating leverage and financial leverage is called combined
leverage. The value of the degree of financial leverage is multiplied by the value of
the degree of operating leverage to give the degree of combined leverage (DCL). The
DCL gives the percentage change in net income for a given percentage change in sales.
3. ind the breakeven level of sales for a firm.
The costs of operating a business can be categorized as fixed or variable. Operating costs
that do not vary with the level of production are fixed; operating costs that do vary with
the level of production are variable. High fixed costs are usually tied to low variable
costs per unit, and low fixed costs are usually tied to high variable costs per unit. Chapter 13 Capital Structure Basics The breakeven point is the level of sales that results in an operating income of zero.
At sales levels above the breakeven point, a firm begins to make a profit. A company
with high fixed operating costs must generate high sales revenue to cover its fixed costs
(and its variable costs) before reaching the sales breakeven point. Conversely, a firm with
low fixed operating costs will break even with a relatively low level of sales revenue.
4. escribe the risks and returns of a leveraged buyout.
LBOs, or leveraged buyouts, occur when publicly owned corporations are bought out
by a small group of investors using mostly borrowed funds. The purchase is leveraged
because the investors finance it with a large amount of borrowed money. Consequently,
when a firm is purchased in an LBO, it is saddled with a large amount of debt in its
capital structure and a large amount of financial leverage and financial risk.
5. xplain how changes in capital structure affect a firm’s value.
Capital structure theory deals with the mixture of debt, preferred stock, and equity a
firm utilizes. Because interest on business loans is a tax-deductible expense, and because
lenders demand a lower rate of return than stockholders for a given company (because
lending money is not as risky as owning shares), debt capital is cheaper than equity
capital. However, the more a company borrows, the more it increases its financial leverage
and financial risk. The additional risk causes lenders and stockholders to demand a higher
rate of return. Financial managers use capital structure theory to help determine the mix
of debt and equity at which the weighted average cost of capital is lowest. Equations Introduced in This Chapter
Degree of Operating Leverage (DOL):
DOL = %∆ EBIT
%∆ Sales where: Δ EBIT = Percentage change in earnings before interest and taxes
% %Δ Sales = Percentage change in sales Equation 13-2.
Degree of Operating Leverage (DOL) (alternate):
DOL = Sales − VC
Sales − VC − FC where: VC = Total variable costs FC = Total fixed costs Equation 13-3.
Percentage Change in EBIT:
%Δ EBIT = %Δ Sales × DOL where: %Δ Sales = Percentage change in sales DOL = Degree of operating leverage 403 404 Part IV Long-Term Financing Decisions Equation 13-4.
Degree of Financial Leverage (DFL):
DFL = %∆ NI
%∆ EBIT where: %Δ NI = Percentage change in net income %Δ EBIT = Percentage change in earnings before interest and taxes Equation 13-5.
Degree of Financial Leverage (DFL) (alternate):
DFL = where: EBIT
EBIT − Int EBIT = Earnings before interest and taxes
Int = Interest expense Equation 13-6.
Percentage Change in Net Income:
%Δ NI = %Δ EBIT × DFL where: Δ EBIT = Percentage change in earnings before interest and taxes
% DFL = Degree of financial leverage Equation 13-7.
Degree of Combined Leverage (DCL):
DCL = %∆ NI
%∆ Sales where: %Δ NI = Percentage change in net income %Δ Sales = Percentage change in sales Equation 13-8.
Degree of Combined Leverage (DCL) (alternate 1):
DCL = Sales − VC
Sales − VC − FC − Int where: VC = Total variable costs FC = Total fixed costs Int = Interest expense Chapter 13 Capital Structure Basics Equation 13-9.
Degree of Combined Leverage (DCL) (alternate 2):
DCL = DOL × DFL where: DOL = Degree of operating leverage DFL = Degree of financial leverage Equation 13-10. ercentage Change in Net Income (NI):
%Δ NI = %Δ Sales × DOL × DFL where: %∆ Sales = Percentage change in sales DOL = Degree of operating leverage DFL = Degree of financial leverage Equation 13-11. he Breakeven Point in Unit Sales, Qb.e.:
Q b.e. = where: FC
p − vc Qb.e. = Quantity unit sales breakeven level
FC = Total fixed costs p = Sales price per unit vc = Variable cost per unit Equation 13-12. otal Revenue, TR:
TR = p × Q where: p = Sales price per unit Q = Unit sales (Quantity sold) T
Equation 13-13. otal Costs, TC:
TC = FC + (vc × Q) where: FC = Fixed costs vc = Variable costs per unit Q = Units produced 405 406 Part IV Long-Term Financing Decisions Self-Test
ST-1. r. Marsalis’s firm has fixed costs of $40,000,
variable costs per unit of $4, and a selling
price per unit of $9. What is Mr. Marsalis’s
breakeven level of sales (in units)?
ST-2. AL’s computer store has sales of $225,000,
fixed costs of $40,000, and variable costs of
$100,000. Calculate the degree of operating
leverage (DOL) for this firm.
ST-3. AL’s computer store has operating income
(EBIT) of $85,000 and interest expense
of $10,000. Calculate the firm’s degree of
financial leverage (DFL).
ST-4. ane Newspapers, Inc., has an after-tax cost
of debt of 6 percent. The cost of equity is 14
percent. The firm believes that its optimal capital structure is 30 percent debt and 70
percent equity, and it maintains its capital
structure according to these weights. What is
the weighted average cost of capital?
ST-5. ohnny Ringo’s Western Shoppe expects its
sales to increase by 20 percent next year. If
this year’s sales are $500,000 and the degree
of operating leverage (DOL) is 1.4, what is the
expected level of operating income (EBIT) for
next year if this year’s EBIT is $100,000?
ST-6. arion Pardoo’s Bookstore has a degree of
operating leverage (DOL) of 1.6 and a degree
of financial leverage (DFL) of 1.8. What is
the company’s degree of combined leverage
(DCL)? Review Questions
1. hat is the operating leverage effect and what
causes it? What are the potential benefits and
negative consequences of high operating leverage?
2. oes high operating leverage always mean high
business risk? Explain.
3. hat is the financial leverage effect and what
causes it? What are the potential benefits and
negative consequences of high financial leverage? 5. Give two examples of types of companies that
would be best able to handle high debt levels.
6. What is an LBO? What are the risks for the equity
investors and what are the potential rewards?
7. If an optimal capital structure exists, what are the
reasons that too little debt is as undesirable as too
much debt? 4. ive two examples of types of companies likely to
have high operating leverage. Find examples other
than those cited in the chapter. Build Your Communication Skills
CS-1. sing publicly available sources, identify four
companies having very high debt ratios and
four having very low debt ratios. Write a one- to
two-page report describing the characteristics
of the companies with high debt ratios and
those with low debt ratios. Can you identify
characteristics that seem to be common to the
four high-debt firms? What are characteristics
common to the four low-debt firms? CS-2. nterview the owner of a small business in
your community. Ask that person to describe
the fixed operating costs and the variable costs
of the business. Write a report or give an oral
presentation to your class on the nature of the
business risk of this firm. 407 Chapter 13 Capital Structure Basics Problems
ilies, a flower shop, has the following data for the most recent fiscal year:
Fixed Costs Breakeven Point $2,300/month Variable Costs (per unit):
Packets $ 0.75 Décor $ 3.00 Misc $ 2.00
$50.00 Sales Price a. hat is Lilies’ breakeven point in sales per month?
The owner of Lilies is planning on moving to a new location that will cut
fixed costs by 30 percent. The price can be lowered to $45 per unit. What
is the new breakeven point in sales (per month)?
ViSorb sells its deluxe cell phone model for $125, its advanced model for
$90, and its basic model for $55. The company has fixed costs of $10,000
per month, and variable costs are $15 per unit sold. a.
Calculate the total revenue if 30 units of each model are sold. b.
What are the total costs if 30 units of each model are sold? c.
What is the company’s total revenue if it sells 10 deluxe models, 15
advanced models, and 35 basic models? d. hat would its total costs be at the sales level in (c)?
W Total Revenue, Total Costs 13-3. The following is an income statement for Gabotti Enterprises: Degree of Operating Leverage 2009 2010 $15,000,000 $25,000,000 Fixed Costs 3,800,000 3,800,000 Variable Costs 1,980,000 3,300,000 Net Sales Operating Income $17,900,000 1,710,000 1,710,000 EBT 7,510,000 16,190,000 Taxes (30%) 2,253,000 4,857,000 Net Income $9,220,000 Interest Expense $5,257,000 $11,333,000 Calculate Gabotti Enterprises’ DOL. Use both methods and compare results. 13-4.
From the table in problem 13-3, calculate Gabotti Enterprises’ DFL using
both methods. Degree of Financial Leverage 408 Part IV Long-Term Financing Decisions Breakeven Analysis 13-5.
Howard Beal Co. manufactures molds for casting aluminum alloy test
samples. Fixed costs amount to $20,000 per year. Variable costs for each unit
manufactured are $16. Sales price per unit is $28. a.
What is the contribution margin of the product? b.
Calculate the breakeven point in unit sales and dollars. c.
What is the operating profit (loss) if the company manufactures and sells (i) 1,500 units per year? (ii) 3,000 units per year? d. lot a breakeven chart using the foregoing figures.
P Breakeven Analysis 13-6.
UBC Company, a competitor of Howard Beal Co. in problem 13-5, has a
comparatively labor-intensive process with old equipment. Fixed costs are
$10,000 per year and variable costs are $20 per unit. Sales price is the same,
$28 per unit. a.
What is the contribution margin of the product? b.
Calculate the breakeven point in unit sales and dollars. c.
What is the operating profit (loss) if the company manufactures and sells (i) 1,500 units per year? (ii) 3,000 units per year? d. lot a breakeven chart using the foregoing figures.
Comment on the profit and loss potential of UBC Company compared
with Howard Beal Co. Operating Leverage 13-7.
Use the same data given in problem 13-5 (fixed cost = $20,000 per year,
variable cost = $16 per unit, and sales price = $28 per unit) for Howard Beal
Co. The company sold 3,000 units in 2009 and expects to sell 3,300 units
in 2010. Fixed costs, variable costs per unit, and sales price per unit are
assumed to remain the same in 2009 and 2010. a.
Calculate the percentage change in operating income and compare it with
the percentage change in sales. b.
Comment on the operating leverage effect. c.
Calculate the degree of operating leverage using (i) data for 2009 and 2010 (ii) data for 2009 only d. xplain what the results obtained in (c) tell us.
E Financial Leverage 13-8.
Use the same data given in problems 13-5 and 13-7 (fixed cost = $20,000
per year, variable cost per unit = $16, sales price per unit = $28, 2009 sales
= 3,000 units, and expected 2010 sales = 3,300 units) for Howard Beal Co.
Fixed costs, variable costs per unit, and sales price per unit are assumed to
remain the same in 2009 and 2010. The company has an interest expense of
$2,000 per year. Applicable income tax rate is 30 percent. Chapter 13 Capital Structure Basics 409 a.
Calculate the percentage change in net income and compare it with the
percentage change in operating income (EBIT). b.
Comment on the financial leverage effect. c.
Calculate the degree of financial leverage using (i) data for 2009 and 2010 (ii) data for 2009 only d. xplain what the results obtained in (c) tell us about financial leverage.
Tony Manero owns a small company that refinishes and maintains the
wood flooring of many dance clubs in Brooklyn. Because of heavy use, his
services are required at least quarterly by most of the clubs. Tony’s annual
fixed costs consist of depreciation expense for his van, polishing equipment,
and other tools. These expenses were $9,000 this year. His variable costs
include wood-staining products, wax, and other miscellaneous supplies.
Tony has been in this business since 1977 and accurately estimates his
variable costs at $1.50 per square yard of dance floor. Tony charges a rate of
$15 per square yard. a.
How many square yards of dance floor will he need to work on this year
to cover all of his expenses but leave him with zero operating income? b.
What is this number called? c.
Calculate the breakeven point in dollar sales. d. ony has little competent competition in the Brooklyn area. What happens
to the breakeven point in sales dollars if Tony increases his rate to $18 per
square yard? e. the $18 per square yard rate, what are Tony’s operating income and net
income if he completes work on 14,000 square yards this year? Assume
his tax rate is 40 percent and he has a $25,000 loan outstanding on which
he pays 12 percent interest annually. Breakeven Analysis 13-10. tis Day’s company manufactures and sells men’s suits. His trademark gray
flannel suits are popular on Wall Street and in boardrooms throughout the
East. Each suit sells for $800. Fixed costs are $200,000 and variable costs
are $250 per suit. a.
What is the firm’s operating income on sales of 600 suits? On sales of
3,000 suits? b.
What is Mr. Day’s degree of operating leverage (DOL) at a sales level of
600 suits? At a sales level of 3,000 suits? c.
Calculate Mr. Day’s breakeven point in sales units and sales dollars. d. f the cost of the gray flannel material increases so that Mr. Day’s variable
costs are now $350 per suit, what will be his new breakeven point in sales
units and sales dollars? e.
Considering the increase in variable costs, by how much will he need to
increase the selling price per suit to reach the original operating income
for sales of 3,000 suits calculated in part a? Operating Leverage and Breakeven Analysis 410 Part IV Long-Term Financing Decisions Operating Leverage 13-11.
Company A, Company B, and Company C all manufacture and sell identical
products. They each sell 12,000 units annually at a price of $10 per unit.
Assume Company A has $0 fixed costs and variable costs of $5 per unit.
Company B has $10,000 in fixed costs and $4 in variable costs per unit.
Company C has $40,000 fixed costs and $1 per unit variable costs. a.
Calculate the operating income (EBIT) for each of the three companies. b.
Before making any further calculations, rank the companies from highest
to lowest by their relative degrees of operating leverage. Remember what
you read about how fixed costs affect operating leverage. Operating Leverage 13-12.
Faber Corporation, a basketball hoop manufacturing firm in Hickory,
Indiana, plans to branch out and begin producing basketballs in addition to
basketball hoops. It has a choice of two different production methods for
the basketballs. Method 1 will have variable costs of $6 per ball and fixed
costs of $700,000 for the high-tech machinery, which requires little human
supervision. Method 2 employs many people to hand-sew the basketballs.
It has variable costs of $16.50 per ball, but fixed costs are estimated to be
only $100,000. Regardless of which method CEO Norman Dale chooses, the
basketballs will sell for $30 each. Marketing research indicates sales in the
first year will be 50,000 balls. Sales volume is expected to increase to 60,000
in year 2. a.
Calculate the sales revenue expected in years 1 and 2. b.
Calculate the percentage change in sales revenue. c.
Calculate the earnings before interest and taxes for each year for both
production methods. d. alculate the percentage change in EBIT for each method.
Calculate the year 1 degree of operating leverage for each method, using
your answers from parts b and d. f.
Calculate the degree of operating leverage again. This time use only
revenue, fixed costs and variable costs from year 1 (your base year) for
each production method. g.
Under which production method would EBIT be more adversely affected
if the sales volume did not reach the expected levels? h. hat would drive this adverse effect on EBIT?
Recalculate the year 1 base year EBIT and the degree of operating
leverage for both production methods if year 2 sales are expected to be
only 53,000 units. Financial Leverage 13-13.
Three companies manufacture and sell identical products. They each have
earnings before interest and taxes of $100,000. Assume Company A is an allequity company and, therefore, has zero debt. Company B’s capital structure
is 10 percent debt and 90 percent equity. It makes annual interest payments
of $2,000. Company C’s capital structure is just the opposite of B. It has 90
percent debt and 10 percent equity. Company C has annual interest expense
of $40,000. The tax rate for each of the three companies is 40 percent. 411 Chapter 13 Capital Structure Basics a.
Before making any calculations, rank the companies from highest to
lowest by their relative degrees of financial leverage (DFL). Remember
what you read about how debt and the interest expense that comes with it
affects financial leverage. b.
Calculate the degree of financial leverage for each company. Was your
answer to a correct? c.
Calculate the net income for each company.
Michael Dorsey and Dorothy Michaels each own their own companies. They
design and supply custom-made costumes for Broadway plays. The income
statement from each company shows they each have earnings before interest
and taxes of $50,000 this year. Mr. Dorsey has an outstanding loan for
$70,000, on which he pays 13 percent interest annually. When she started her
business, Ms. Michaels only needed to borrow $10,000. She is still paying
9 percent annual interest on the loan. Each company expects EBIT for next
year to be $60,000. The tax rate for each is 40 percent and is not expected to
change for next year. a.
Calculate the net income for each company for this year and next year. b.
Calculate the percentage change in net income for each company. c.
Calculate the percentage change in EBIT for each company. d. alculate this year’s degree of financial leverage for each company using
your answers from parts b and c. e.
Calculate the degree of financial leverage for each company again. This
time use only EBIT and interest expense for this year. f. earnings before interest and taxes do not reach the expected levels, in
which company would net income be more adversely affected? g.
What would drive this adverse effect on net income? h. ecalculate the degree of financial leverage and the net income expected
for next year for both companies if EBIT only increases to $53,000. Financial Leverage In
13-15. 2009, Calaire had net income of $75,000 and sales of $230,000. John
Mastore, the financial manager, has forecast the 2010 net income to be
$200,000 and sales to be $400,000. What is Calaire’s degree of combined
leverage if these numbers become fact? Degree of Combined Leverage Fanny Brice, owner of Funny Girl Comics, has sales revenue of $200,000,
earnings before interest and taxes of $95,000, and net income of $30,000 this
year. She is expecting sales to increase to $225,000 next year. The degree of
operating leverage is 1.35 and the degree of financial leverage is relatively
low at 1.09. a.
Calculate the percentage change in EBIT Ms. Brice can expect between
this year and next year. b.
How much will EBIT be next year in dollars? c.
Calculate the percentage change in net income Ms. Brice can expect
between this year and next year. Challenge Problem 412 Part IV Long-Term Financing Decisions d. ow much net income should Ms. Brice expect next year?
Calculate this year’s degree of combined leverage (DCL). f.
Ms. Brice is considering a price increase. This would mean the percentage
change in sales revenue between this year and next year would be 20
percent. If this is true, what net income (in dollars) can she expect for
next year? Degree of Combined Leverage 13-17.
Clint Reno owns Real Cowboy, a western wear store that has current annual
sales of $2,800,000. The degree of operating leverage (DOL) is 1.4. EBIT is
$600,000. Real Cowboy has $2 million in debt, on which it pays 10 percent
annual interest. Calculate the degree of combined leverage for Real Cowboy. DOL, DFL, and DCL Interactions 13-18.
Chad Gates owns Strings Attached, a store that sells guitars. The company
has $5 million in current annual sales, fixed operating costs of $300,000, and
$700,000 in variable operating costs, for a total EBT of $2.5 million. The
firm has debt of $16,666,666.67, on which it pays 9 percent annual interest.
The degree of combined leverage (DCL) for Strings Attached is 1.72. a.
Calculate the degree of operating leverage (DOL). b.
What is the degree of financial leverage (DFL) for Strings Attached?
Calculate your answer using the EBIT and interest expense figures and
your knowledge of how DOL and DFL jointly determine DCL. c. sales next year increase by 20 percent, what will be the percent change
in net income? Comprehensive Problem Soccer International, Inc., produces and sells soccer balls. Partial
information from the income statements for 2005 and 2009 follows.
Soccer International, Inc., Income Statement for the Year
Ending December 31
2009 Sales Revenue 2010 $560,000 616,000 Variable Costs 240,000 264,000 Fixed Costs 160,000 160,000 EBIT Interest Expense 40,000 40,000
EBT Income Taxes (30%) Net Income Soccer International sells each soccer ball for $16. a. in the missing values in the income statements of 2009 and 2010.
Calculate Soccer International’s breakeven point in sales units for 2009
and 2010. c.
Calculate the breakeven point in dollar sales for 2009 and for 2010. d. ow many soccer balls need to be sold to have an operating income of
$200,000 in 2009? Chapter 13 Capital Structure Basics 413 e.
What is the operating profit (loss) if the company sells (i) 18,000 and (ii)
24,000 balls in 2009? f.
Calculate the degree of operating leverage for 2009 and for 2010. g. sales revenue is expected to increase by 10 percent in 2010, calculate
the percentage increase in EBIT and the dollar amount of EBIT for 2010. h. alculate the degree of financial leverage for 2009 and for 2010.
Calculate the percentage change in net income and the dollar amount of
net income expected in 2010. j.
Calculate the degree of combined leverage for 2009 and for 2010. k. ssume Soccer International raises its selling price and that sales revenue
increases to $650,000 in 2009. How much net income can be expected
13-20. Amigos has an operating income of $35,000 in 2009 and a projected
operating income of $50,000 in 2010. It estimates its DFL to be 1.71. At this
estimated DFL, what will be the change in net income? Answers to Self-Test
ST-1. ales breakeven point (in units)
S = $40,000 ÷ ($9.00 – $4.00) = 8,000 units
ST-2. egree of operating leverage (DOL)
D = $225,000 – $100,000) ÷ ($225,000 – $100,000 – $40,000) = 1.47
ST-3. egree of financial leverage (DFL)
D = $85,000 ÷ ($85,000 – $10,000) = 1.13
ST-4. eighted average cost of capital, ka
W = (.3 × 6%) + (.7 × 14%) = 11.6%
ST-5. ext year’s change in EBIT equals (this year’s EBIT × 20% × 1.4) + this
year’s EBIT ($100,000 × 20% × 1.4) + $100,000
ST-6. egree of combined leverage (DCL) = DOL × DFL
D = 1.6 × 1.8 = 2.88 Percentage Change in Net Income ...
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This note was uploaded on 02/15/2012 for the course GERM 200 taught by Professor Kuhmar during the Spring '10 term at SUNY Albany.
- Spring '10