Breakeven and Leverage
Part of Chapter 13
 Read parts of chapter related to breakeven
and leverage (DOL, DFL, DTL)
 Breakeven
 Operating, financial and total leverage


Risk
Capital structure is a risk decision and that is
why this is in chapter 13, but the parts we are
pulling out of chapter 13 now rely on the
income statement and fit well with what we
have covered in chapter 3 and AFN.
2
Breakeven Analysis
 Used to determine the level of sales a firm
must achieve to stay in business in the long
run
 Shows the mix of fixed and variable cost and
the volume required for zero profit/loss

Profit/loss generally measured by EBIT
(operating profit/loss)
3
Breakeven Analysis
 Breakeven Diagrams
 Sales level is considered the big uncertainty

Operating Breakeven occurs at the intersection
of revenue and total operating cost





Represents the level of sales at which revenue
equals cost
Usually operating breakeven (interest ignored)
And financial breakeven
Need variable cost–fixed cost breakdown
Variable cost per unit assumed constant
4
Figure 13.5: The Breakeven
Diagram
Write Equations for Cost and
Revenue on the board
REV=PQ
Total Cost = VQ + FC
5
Breakeven Analysis
 The Contribution Margin
 Every sale makes a ‘contribution’ per unit of
the difference between price (P) and variable
cost (V)


Ct = P – V
Can be expressed as a percentage of the
price


Known as the contribution margin (CM)
CM = (P – V) / P
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Example
Breakeven Analysis—Example
Q: Suppose a company can make a unit of product for $7 in
variable labor and materials, and sell it for $10. What are the
contribution and contribution margin?
A: The contribution per unit is $3, or $10 - $7, while the contribution
margin is $3 / $10, or 30%.
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Operating Breakeven Analysis
 Calculating the Breakeven Sales Level
 EBIT is revenue minus cost, or



EBIT = PQ – VQ – FC
Find breakeven quantity by setting EBIT equal
to zero and solve for Q.
Breakeven occurs when revenue (PQ) equals
total cost (VQ + FC):

Look at
the math
on the
board
QB/E = FC / (P – V)
 Breakeven tells us how many units have to be sold to
contribute enough money to pay for fixed costs
 Can also be expressed in terms of dollar sales
 SB/E = P(FC) / (P – V) or FC / CM
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Example
Breakeven Analysis—Example
Q: What is the breakeven sales level in units and dollars for a
company that can make a unit of product for $7 in variable costs
and sell it for $10, if the firm has fixed costs of $1,800 per
month?
A: The breakeven point in units is $1,800  ($10 - $7) = 600 units.
The breakeven point in dollars (sales) is $10 per unit times 600
units, or $6,000, which could also be calculated as $1,800 
0.30. Thus, the firm must sell 600 units per month to cover fixed
costs.
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skim
Risk in the Context of Leverage
 Leverage potentially affects the stock price
Alters the risk/return relationship in an equity
investment
 Measures of performance
 Operating income (AKA: EBIT)




Unaffected by leverage because it is calculated prior to the
deduction for interest
Return on Equity (ROE) is Net Income 
Stockholders’ Equity
Earnings per Share (EPS) is Net Income  number
of shares

Investors regard EPS as an important indicator of future
profitability
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Risk in the Context of Leverage
 Redefining Risk for Leverage-Related
Issues
 Leverage-related
risk is variation in ROE
and EPS
Business risk—variation in EBIT
 Financial risk—additional variation in
ROE and EPS brought about by
financial leverage

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Leverage and Risk—Two Kinds
 1. Operating leverage (operating risk) and
2.Financial leverage (financial risk)
 Operating leverage affects a firm’s business
risk
 Relates to a company’s cost structure

Involves relative use of fixed versus
variable costs (more fixed cost is more
operating leverage)

If doing a task with a fixed cost is cheaper than
doing it with a variable cost then operating
leverage will improve a firm’s ROE and EPS
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The Effect of Operating Leverage
 As volume moves away from breakeven, profit or loss increases
faster with more operating leverage
 The Risk Effect
 More operating leverage leads to larger variations in EBIT,
or business risk
 The Effect on Expected EBIT
 Thus, when a firm is operating above breakeven, more
operating leverage implies higher operating profit

If a firm is relatively sure of its sales level, it is in the firm’s best
interests to trade variable costs for fixed cost (assuming the
firm is operating above breakeven)
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Figure 13.6: Breakeven Diagram at High
and Low Operating Leverage
Diagram shows the common tradeoff of higher
fixed cost and lower variable cost (lower slope
on total cost line)
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The Degree of Operating Leverage
(DOL)—A Measurement
 Operating leverage amplifies changes in
sales volume into larger changes in EBIT
 DOL relates relative changes in volume (Q) to
relative changes in EBIT
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The Degree of Operating Leverage
(DOL)—A Measurement
Example
Q: The Albergetti Corp. sells its product at an average price of $10. Variable costs
are $7 per unit and fixed costs are $600 per month. Evaluate the degree of
operating leverage when sales are 5% and then 50% above the breakeven
level.
A: First, compute the breakeven volume: $600  ($10 - $7) = 200 units.
Breakeven plus 5% is 200 x 1.05 or 210 units, while breakeven plus 50% is 200
x 1.50 or 300 units. DOL at 210 units is:
DOLQ=210 =
210($10 - $7)
 21
210($10 - $7) - $600
DOL at 300 units is:
DOLQ=300
300($10 - $7)
=
3
300($10 - $7) - $600
Note that DOL decreases
as the output level
increases above
breakeven.
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Financial Leverage
 The use of borrowed money incurs
interest,
which is like a fixed cost
 If returns are greater than the interest rate
then financial leverage will improve a firm’s
ROE and EPS
 However, if returns are lower than the interest
rate then borrowing money will worsen EPS
and ROE
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Financial Leverage
 Return on Capital Employed, ROCE (also called Basic Earnings
Power, BEP)
 Measures the profitability of operations before financing charges
but after taxes on a basis comparable to ROE
EBIT 1 - tax rate 
ROCE =
debt + equity


When the ROCE exceeds the after-tax cost of debt,
more leverage improves ROE and EPS
When ROCE is less than the after-tax cost of debt,
more leverage makes ROE and EPS worse
20
Table 13.1 (the good side of debt)
As the firm’s debt
ratio rises, both
EPS and ROE rise
dramatically. While
EAT falls, the
number of shares
outstanding falls at
a faster rate as
debt replaces
equity.
21
Table 13.2 (the bad side of debt)
ABC is now
doing rather
poorly—ROE and
ROCE are quite
low. As the firm
adds leverage,
EPS and ROE
decrease.
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Financial Leverage and Financial
skim
Risk
 Financial leverage is a two-edged sword
 Multiplies good results into great results
 Multiplies bad results into terrible results
 ROE and EPS for leveraged firms experience
more variation
 Financial risk is the increased variability in
financial results that comes from additional
leverage
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The Degree of Financial Leverage
(DFL)—A Measurement
 Financial leverage magnifies changes in EBIT into
larger changes in ROE and EPS

The degree of financial leverage (DFL) relates relative
changes in EBIT to relative changes in EPS
DFL =

%  EPS
or %  EPS = DFL  %  EBIT
%  EBIT
Calculate DFL:
DFL =
EBIT
EBIT - Interest
Write this down to
use as we go along
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EPS = [(EBIT – I)(1 – t)] / shares
dEPS EBIT
(1  t ) EBIT
DFL 


dEBIT EPS shares EPS
(1  t ) EBIT
EBIT
 DFL 
( EBIT  I )(1  t )
EBIT  I
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The Degree of Financial Leverage
(DFL)—A Measurement—Example
Q: Selected income statement and capital information for the Moberly Manufacturing Company
follow ($000):
Capital
Revenue
Cost/expense
Example
EBIT
$5,580
4,200
$1,380
Debt
Equity
Total
$1,000
7,000
$8,000
Currently 700,000 shares of common stock are outstanding. The firm pays 15% interest
on its debt and anticipates that it can borrow as much as it reasonably needs at that rate.
The income tax rate is 40%
Moberly is interested in boosting the price of its stock. To do that management is
considering restructuring capital to 50% debt in the hope that the increased EPS will have
a positive effect on price. However, the economic outlook is shaky, and the company’s
CFO thinks there’s a good chance that a deterioration in business conditions will reduce
EBIT next year. At the moment Moberly’s stock sells for its book value of $10 per share.
Estimate the effect of the proposed restructuring on EPS. Then use the degree of financial
leverage to assess the increase in risk that will come along with it.
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The Degree of Financial Leverage
(DFL)—A Measurement (Example)
A: Since the equity is trading at book value, this is a relatively simple example.
Current
Proposed
Capital
Debt
Example
Equity
Total
Shares outstanding
$1,000
$4,000
7,000
4,000
$8,000
$8,000
700,000
400,000
Current
EBIT
Proposed
$1,380
$1,380
150
600
$1,230
$780
492
312
EAT
$738
$468
EPS
$1.054
$1.170
Interest (15% of debt)
EBT
Tax (@40%)
If business conditions
remain unchanged, a
higher EPS will result
with the addition of
debt.
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The Degree of Financial Leverage
(DFL)—A Measurement—Example
Example
A: Next, calculate DFL:
$1,380
 1.12
$1,380 - $150
$1,380
=
 1.77
$1,380 - $600
DFLCurrent =
DFLProposed
EPS will be much more volatile under the proposed plan. When EBIT
changes, EPS will change by a factor of 1.77 vs. 1.12.
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Comparing Operating and Financial
Leverage
 Financial and operating leverage are similar in that both can




enhance results while increasing variation
Financial leverage involves substituting debt for equity in the firm’s
capital structure
Operating leverage involves substituting fixed costs for variable
costs in the firm’s cost structure
Both methods involve substituting fixed cash outflows for variable
cash outflows
Both kinds of leverage make their respective risks larger as the
levels of leverage increase

However, financial risk is non-existent if debt is not present, while
business risk would still exist even if no operating leverage
existed
 Financial leverage is more controllable than operating leverage
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The Compounding Effect of Operating
and Financial Leverage
 The effects of financial and operating leverage compound one
another
 Changes in sales are amplified by operating leverage into larger
relative changes in EBIT
 Which in turn are amplified into still larger relative changes in
ROE and EPS by financial leverage

The effect is multiplicative, not additive
Thus, fairly modest changes in sales can lead to dramatic
changes in ROE and EPS
 The combined effect can be measured using degree of total
leverage (DTL)
 DTL = DOL × DFL

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The Compounding Effect of Operating and
Financial Leverage—Example
Example
Q: The Allegheny Company is considering replacing a manual production process
with a machine. The money to buy the machine will be borrowed. The
replacement of people with a machine will alter the firm’s cost structure in favor
of fixed costs, while the loan will move the capital structure in the direction of
more debt. The firm’s leverage positions at expected output levels with and
without the project are summarized as follows:
DOL
DFL
Current
2.0
1.5
Proposed
3.5
2.5
The economic outlook is uncertain and some managers fear a decline in sales of
as much as 10% in the coming year. Evaluate the effect of the proposed project
on risk in financial performance.
A: The firm’s current DTL is 2 x 1.5, or 3, meaning a 10% decline in sales could
result in a 30% decline in EPS. Under the proposal, the DTL will be much
higher: 8.75, or 3.5 x 2.5, meaning a 10% drop in sales could lead to a 87.5%
drop in EPS.
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