Leverage Chapter 10 247 | Page The biggest challenge that a corporate financial manager faces is to have an optimal capital structure that results in an optimal capital balance between risk and return and at the same time maximizes the firm’s earning per share. Learning objectives After learning this chapter, you should be able to: 1. Know the term leverage. 2. Examine each type of leverage: operating and financial. 3. Understand and compute Degree of Leverage. 4. Understand and compute Indifference point. Leverage GOAL
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Leverage Chapter 10
247 | P a g e
The biggest challenge that a corporate financial
manager faces is to have an optimal capital structure
that results in an optimal capital balance between risk
and return and at the same time maximizes the firm’s
earning per share.
Learning objectives
After learning this chapter, you should be able to:
1. Know the term leverage.
2. Examine each type of leverage: operating and financial.
3. Understand and compute Degree of Leverage.
4. Understand and compute Indifference point.
Leverage
GOAL
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10.0 INTRODUCTION
What is leverage? Leverage exists from the firms’s investment and financing decisions that
directly affect the asset structure and the financial structure of the firm. For example looking
at the financial structure, when a particular company carries debt in its capital structure, the
company is leveraged. The more debt a company has the more is its leverage. What does
leverage do to a company then? In essence, leverage that exists in the asset structure and
financial structure accelerates the profitability of a company. It existence enable a company
to achieve greater rate of profit as compared to without leverage.
However, the use of leverage is goes hand in hand with risk that is the higher the leverage,
the higher the risk. This is because the use of leverage in the firm’s operations and financing
involves risk-return tradeoff. Our focus in this chapter is therefore, concerning the firm's
capital structure and the impact of leverage, and thus the risk-return tradeoff.
10.1 OPERATING LEVERAGE a) Fixed Operating Costs
It represents the costs incurred by the firm in a given period regardless of the sales
volume. It has no direct relationship with sales; that is the total amount will remains
constant and thus, per unit basis will declines with an increase in sales. These costs
include depreciation, rentals, lease charges, interest expenses, salaries and general
and administrative expenses.
b) Variable Operating Costs
It represents the costs that vary in direct proportion to the firm's productions and
sales; that are total variable costs will increase in direct proportions with sales, but
per unit basis will remains constant. These costs include labor, materials, selling
expenses, sales commissions, and direct overhead.
For certain type of costs such as salaries and office expenses, clear classifications
cannot be made. These semi-variable costs remain fixed over a given range of sales,
and tend to increase drastically in a step up fashion as sales reach certain maximum
point. For the purpose of the analysis, these costs will be included in variable costs'
component if it represents a small percentage of the firm's total operating costs.
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Under normal conditions, the existence of high fixed costs relate to high capital
investment made by the firm such as in a highly automated manufacturing facilities.
This mode of operations refers to capital-intensive operations that result in high fixed
costs and low variable costs.
10.1.1 Break Even Analysis
Break even analysis focus on the relationship between sales volume and
profitability, that relates directly to the firm's total cost structure; fixed
operating costs and variable or direct costs. The understanding of break-even
analysis is utmost important in profit planning.
Determining Break Even Point
The break-even analysis or cost-volume-profit analysis involves
finding the level of sales where operating profit or earnings before interest and tax (EBIT) equals zero; that is total revenues equal total
costs. In essence, it is the point where the all costs are covered and
any sales above that level will contribute directly (price minus variable
cost) to the operating profit. EBIT is given by:
EBIT = TR – TC
= QP – QV – FC
= Q (P – V) – FC
Where FC : Fixed operating costs including depreciation
V : Variable cost per unit
Q : Sales volume in units
P : Price per unit
QV : Total variable costs, also presented as VC
TR : Total operating revenues (QP) or sales (S)
TC : Total operating costs; FC + QV
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At break-even point, EBIT is zero; therefore the above equation can
be used to solve for Q or break-even point in units (BEunits):
EBIT = Q (P – V) – FC
Q = BEunits = FC / (P – V)
To illustrate, consider Marisa Manufacturing that sells its only product
at RM1.00 per unit, has a variable cost of RM0.60 per unit, and fixed
costs of RM20,000. Therefore, the company must sell 50,000 units to
break even:
BEunits = 20,000 / (1.00 – 0.60)
= 50,000 units
A graphic illustration of the break-even concept is presented in Figure
10-1. It shows that Marisa has to sell at least 50,000 units or
RM50,000 (=50,000 x 1) to break even. If sales are greater than
50,000 units, it will show a positive EBIT; or else, EBIT will be
negative.
Any changes in the price (P), unit variable cost (V), and/or fixed cost (FC) will alter the break-even point, hence the firm's profitability.
For example, if Marisa decides to change its mode of operations that
leads to the change in costs structure as follows: (1) fixed cost
RM8,000; (2) variable cost RM0.80; and (3) the selling price will
remain at RM1.00. This will shift the fixed cost line down, and the
break-even point declines to 40,000 units (=8,000 / (1.00 – 0.80)).
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Figure 10.1 Graphic Illustration Of Break Even
Sales Break Even
For a firm with more than one product line, break even can be
calculated in terms of Ringgits instead of units. It involves the same
formula except that sale break-even uses contribution margin (CM) in place of ringgit contribution to fixed cost and profit. Sales break
even (BEs) can be calculated as follows:
Using the same example for Marisa, break even sales equals to
RM50,000:
BEsales = 20,000 / (1 – (0.60 / 1.00))
= RM50,000
-30-20-10
0102030405060708090
0 10 20 30 40 50 60 70 80
Units in thousands
RM
in th
ousa
nds TR
TC
VC
FC
EBIT
CM = 1 – Variable cost ratio
= 1 – (V / P)
Alternatively CM = 1 – (QV / S)
BEsales = FC / [1 – (V / P)]
= FC / CM
Where V, QV : Variable cost per unit, Total variable costs
P, S : Price per unit, Total sales in Ringgits
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Break-even analysis can also be used in profit planning. For example,
Marisa Manufacturing would like to have at least RM20,000 of EBIT in
the coming period. Given that the cost structure remains constant, it
has to sell 100,000 units or RM100,000 in order to achieve that profit
target:
BEunits = (FC + Profit) / (P – V)
= (20,000 + 20,000) / (1.00 – 0.60)
= 100,000 units
BESales = (FC + Profit) / 1 – (V / P)
= (20,000 + 20,000) / 1 – (0.60 / 1.00)
= RM100,000
The break-even analysis is an important analysis in profit and
production capacity planning. It aids the financial manager to set the
appropriate capital structure and price structure that results in higher
firm's value in long-term.
Cash Break Even
The cash break-even (CBE) concerns with the sales level that the
firm must achieve to meet its operating cash requirements. This
analysis is important since cash receipts and expenditures do not
correspond directly with the sales and expenses as shown in the
income statements. It focuses on the non-cash expense (N), such as
depreciation, which is normally treated as part of the fixed cost's
component.
In the cash break even, the non-cash expenses are not included as
they will overstate the cash break even. Assuming that Marisa
Manufacturing in the previous example, has RM4000 of depreciation
charges are part of its fixed costs of RM20,000, then its cash break
even in units and sales can be computed as follows:
CBEunits = (FC – N) / (P – V)
= (20,000 – 4000) / (1.00 – 0.60)
= 40,000 units
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CBEsales = (FC – N) / [ 1 – (V / P)]
= (20,000 – 4,000) / [1 – (0.60 / 1.00)]
= RM40,000
Other things being equal, Marisa has to achieve at least RM40,000 in
sales to meet its cash operating needs. If sales level is below than
RM40,000, Marisa may face liquidity problems that will affect its
overall operation significantly.
Break Even Margin
The break-even margin is used to assess the margin of safety for a
given level of sales. It relates the firms' current sales levels to the
break even point, and it is a measure of risk; that is how much sales
can decline before it hits break even point that result in negative
operating earnings. For example, if Marisa's current sales (S0) are at
RM80,000, break-even margin (BEM) can be computed as follows:
BEM = (S0 – BEsales) / S0
= (80,000 – 50,000) / 80,000
= 37.5%
The above calculation shows that Marisa's sales could decline by
37.5% before it faces any financial problems. The margin is relatively
high, and therefore is preferred, because higher margin associates
with lower business risk.
Although break-even analysis is an important part in planning, it has
some limitations in its usage. It is applicable only over a relevant
range of operations as fixed and/or variable costs may change with a
higher level of operations. The classification of fixed versus variable
cost is sometimes difficult especially when the majority of the cost
components are semi-variable in nature. Other aspects of cautions are
that break-even analysis assumes that variable cost and the marginal
revenues remain constant over time, which may not be the case in
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real conditions. Therefore, the use of break-even analysis in planning
and financial decision-making must be done judiciously.
10.1.2 The Degree of Operating Leverage
The operating leverage is concern with the amount of fixed cost employed by
a firm in its cost structure. A high degree of operating leverage indicates that:
1. A high percentage of a firm's total costs is fixed; and
2. A relatively small change in sales will lead to a large change in
earnings before interest and taxes (EBIT) or operating income.
A high fixed costs in the firm's cost structure are a result of high capital
investment in its operations; capital intensive. The mode of operations is
highly automated with less labor in used that result in lower variable costs and
higher fixed costs. To further illustrate the effects the firm's investment in
capital asset on its potential return, consider the examples shown in Table
10.1.
Table 10.1 Marisa Inc., Mode of Operations and Relative DOL
Capital intensity Low Average High Price (P) RM1.00 RM1.00 RM1.00 Variable cost(V) RM0.80 RM0.60 RM0.40 Fixed cost (FC) RM8,000 RM20,000 RM36,000 Break even Sales RM40,000 RM50,000 RM60,000 Break even Units 40,000 units 50,000 units 60,000 units
In thousands of RM Sales (S=PQ) Less: Fixed cost (FC) Variable cost (VC=VQ)
The illustrations showed in Table 10.1 and 10.2 set forth a number of
important concepts in interpreting and understanding DOL:
1. DOL is associated with current sales level.
2. DOL will remain constant regardless of whether the change in
sales is positive or negative.
3. The value of DOL does not depend on the magnitude of
change.
4. DOL is positive if the current sales level is above break-even
point, and vice versa.
5. The DOL is associated with the firm's capital intensity, that is
higher DOL represents higher capital intensity, and vice versa.
6. DOL is undefined at the break-even point as any change in
sales will constitute an infinite fractional change.
In the event that DOL is negative, it associates with current sales level
below the break-even point, and thus losses. From Table 8.2, any 1%
increase in sales will result in 4% reduction in losses and likewise any
1% decrease in sales will result in 4% increase in losses.
The understandings of DOL provide insight of the relative impact of
operating leverage on EBIT or the degree of business risk. It is
important in capital investment decisions as it has a direct impact on
the firm's value without exposing the firm to unnecessary risk.
10.2 FINANCIAL LEVERAGE
The operating leverage concerns with firm's cost structure that concerns with the relationship
between sales and operating profit or EBIT. On the other hand, financial leverage concerns
with the effects of financing decision on the owners' return, that is the relationship between
firm's operating profit and earnings available to common stockholders (EPS). Figure 10-2
shows the relationship between operating leverage and financial leverage; how each
leverage has an impact on the firm's profitability: earnings before interest and tax (EBIT),
and (2) earnings available to common stockholders respectively (EACS). The combination of
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these leverages is the total leverage that shows the relationship of changes in sales and its
impact on earnings per share.
Figure 10-2 Relationship of DOL, DFL, and DTL
Net sales
Less: Cost of goods sold Operating
Gross profit leverage
Less: Operating expenses (DOL)
Operating profit (EBIT) Total leverage
Less: Interest and taxes (DTL)
Net profit Financial
Less: Preferred dividends leverage
0Earnings available to common shareholders (DFL)
Figure 10-1 shows that financial leverage relates to the financing cost of the firm, particularly
the cost of debt or interest. The extent to which the firm uses debt financing or financial
leverage has direct implications on risk and returns tradeoff. For example, if the firm utilizes
high volume of debt in its financial structure:
1. The stockholders have less control of the firm;
2. It represents higher risk to the creditors or lenders and the firm alike; and
3. Return on owners' capital is magnified or leveraged.
Our concern here is with the impact on earnings after tax (EAT), and thus earnings per share (EPS) if there is a change in earnings before interest and taxes (EBIT) due to
change in sales level.
10.2.1 Degree of Financial Leverage
The degree of financial leverage (DFL) is defined as the percentage of
change in EPS that results from a given percentage change in EBIT. To
illustrate, refer to Table 10-3 for relevant financial data for Marisa Inc., with
current production level of 70,000 units. Please note that this exercise is the
continuation of sample illustrations on DOL in the previous section.
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Note that the change in EPS is similar to change in EAT. This assumption
holds true if there no preferred dividends in the capital structure of the firm.
The basis for understanding DFL is similar to that of DOL previously
introduced. The DFL can be calculated by applying the following formula:
DFL = Percentage ∆ in EPS / Percentage ∆ in EBIT
= 112% / 70%
= 1.60
Therefore, a 1% change in EBIT would result in 1.60% change in earning per
share, and vice versa.
Table 10-3 Marisa Inc.; Operating Characteristics with Change in Sales
Capital intensity
Average
Price (P) RM1.00
Unit variable cost (V) RM0.60
Fixed cost (F) RM20,000
Break even Sales RM50,000
Break even Units 50,000 units
Current sales level 70,000 units
Ringgits in thousands
Current Sales
Expected Sales
Change
Sales Less: Fixed cost (F) Variable cost (VQ)
RM70.00 20.00 42.00
RM84.00 20.00 50.40
RM14.00
Operating profit (EBIT) Less: Interest (I)
RM 8.00 3.00
RM13.60 3.00
RM 5.60
Earnings before tax (EBT) Less: Tax (40%)
RM 5.00 2.00
RM10.60 4.24
Earnings after tax (EAT) RM 3.00 RM 6.36 RM 3.36
Change is sales Change in EBIT Change in EAT, hence EPS with no preferred dividends
1. The higher DOL or fixed operating cost, the more sensitive EBIT due
to change in sales; and
2. The higher DFL or fixed financial cost, the more sensitive EPS due to
change in EBIT.
Therefore, the net effect of any change in sales is significant to EPS and, thus
returns to common stockholders.
DFLU = (Q (P – V) – FC) / (Q (P – V) – FC – I) or, based on Ringgit sales: DFLS = (S – VC – FC) / (S – VC – FC – I) Where Q : Sales quantity units
P : Price per unit
V : Variable cost per unit
FC : Total fixed cost
I : Interest
VC : Total variable costs in RM that equals to QV
S : Sales revenue in RM that equals to QP
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10.3 DEGREE OF TOTAL LEVERAGE To determine the overall impact of leverage, the following formula for total degree of total leverage (DTL) utilizes both DOL and DFL is as follows:
DTL = DOL (DFL)
= 3.50 (1.60)
= 5.60x
Alternatively, by using the simplified equation that combined both DOL and DTL:.
DTLU = Q (P – V) / (Q (P – V) – FC – I)
= 70(1 – 0.60) / (70(1 – 0.60) – 20 – 3)
= 5.60x
DTLS = (S – VC) / (S – VC – FC – I)
= (70 – 42) / (70 – 42 – 20 – 3)
= 5.60x
The degree of total leverage shows that; if Marisa's sales increase by 1% then the earnings
per share will increase by 5.60%, and vice versa. The use DTL could provides an easy way
to estimate the expected earnings per share given any change in sales. To illustrate, let
assume that current EPS for Marisa's is RM0.30 and sales to increase by 20 %. Therefore,
the EPS1 for the next period equals to:
EPS1 = Current EPS (1 + [(Degree of total leverage)(Percentage change is sales)])
= EPS0 (1.0 + [(DTL)(∆S)])
= 0.30 (1.0 + (5.60)(0.20))
= RM0.64
The above calculations for DFL and DTL assume that the firm has no preferred stock. To
account for preferred stock dividends, the above formulas should be adjusted appropriately
by deducting before tax value of preferred stock dividends. For example, if Marisa's
preferred dividends is RM1,000; new DFLS for the company:
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DFLS = S – QV – FC / (S – QV – FC – I – (Dps / (1 – T))