Operating and Financial Leverage
(Chapter 5)

Business and Financial Risk
 Employing Leverage
 Leverage and the Income Statement
 Operating Leverage and
Business Risk
 Breakeven Analysis
 Degree of Operating Leverage
 Degree of Financial Leverage
 Degree of Combined Leverage
 Illustration of Leverage Effects
Business and Financial Risk

Business Risk - Uncertainty inherent in the
firm’s operations if it used no debt.

Major Factors Affecting Business Risk:
– Total sales variability
– Total fixed operating expenses

Financial Risk – Additional risk incurred
through the use of debt financing.
Employing Leverage

Leverage:
– Use of “fixed cost” items in the process of
magnifying earnings.

Operating Leverage:
– Use of “fixed operating costs” in the process of
magnifying operating income (EBIT)

Financial Leverage:
– Use of “fixed financial costs” (e.g., debt and
preferred stock financing) in the process of
magnifying earnings per share EPS. Our
discussion focuses on the use of debt financing.
Leverage and the Income Statement
-
Sales
Fixed costs
Variable costs
EBIT
Interest
EBT
Taxes
EAT
Operating Leverage
Total
Leverage
Financial Leverage
Note: EPS = EAT/(# shares)
[assuming no pfd. stock]
Leverage Analysis: An Example
Webb’s Incorporated Income Statement
(Year Ended December 31, 2002)
-
Sales (30,000 units @ $25)
Variable costs ($7 per unit)
Fixed costs
EBIT
Interest expenses
EBT
Taxes
EAT
Given 20,000 shares outstanding:
EPS = $66,000/20,000 = $3.30
$ 750,000
(210,000)
(270,000)
$ 270,000
(170,000)
$ 100,000
( 34,000)
$ 66,000
Key to Symbols Used in
the Following Analyses
Note: The symbols used in the notes differ
somewhat from the symbols used in the text.








P = price per unit
Q = sales in units
V = variable cost per unit
F = fixed costs
VC = total variable costs
TC = F + VC = total costs
S = PQ = sales dollars
EBIT = S - TC
Operating Leverage and Business Risk

Calculating Breakeven Point in Units:
– (1) S - TC = 0
– (2) S - F - VC = 0
– (3) PQ - F - VQ = 0
– (4) PQ - VQ = F
F
Q
(P  V )
Webb’s Breakeven Point in Units:
F
$270,000
Q

 15,000 units
( P  V ) $25  $7

Calculating Breakeven Point in Dollars:
F
(multiply both sides by P)
P V
PF
PQ 
(divide numerator & denominator by P)
P V
F
S=
(multiply V / P by Q / Q)
V
1P
F
F
Result: S 

VQ
VC
1
1
PQ
S
F
$270,000
S

 $375,000
VC
$210,000
1
1
S
$750,000
Q
Breakeven Chart
Thousands of Dollars
1200
S
1000
800
TC
600
400
200
0
0
15
30
Thousands of Units
45
EBIT Chart
Thousands of Dollars
600
EBIT
500
400
300
200
100
0
-100
-200
-300
-400
15
30
45
Thousands of
Units
Degree of Operating Leverage
%  in EBIT
DOL 
%  in Sales
Q( P  V )
S  VC
=

Q( P  V )  F S  VC  F
S  VC
=
EBIT

Note: If F = 0, DOL = 1 (i.e., without any F, the %
change in EBIT would be equal to the % change in
sales). By employing F, the firm’s % change in EBIT
will be greater than the % change in sales.
Webb’s DOL When Q = 30,000 Units
30,000($25  $7)
DOL 
 2.0
30,000($25  $7)  $270,000
For every 1% change in sales, EBIT will change
2%.
 Operating Leverage is Risky: If sales
increase 5%, a DOL of 2.0 indicates that
EBIT would increase 10%. On the other hand,
if sales decline 7%, a DOL of 2.0 indicates
that EBIT would decline 14%.
Degree of Financial Leverage
%  in EPS
DFL 
%  in EBIT
EBIT
=
EBIT - I

Note: If interest expense = 0, DFL = 1.0 (i.e.,
without any debt financing, the % change in
EPS would be equal to the % change in
EBIT). By incurring interest expense (debt
financing) the firm’s % change in EPS will be
greater than the % change in EBIT.
Webb’s DFL When Q = 30,000 Units
$270,000
DFL 
 2.7
$270,000  $170,000
For every 1% change in EBIT, EPS will
change 2.7%
Financial Leverage is Risky: If EBIT increases
2%, a DFL of 2.7 indicates that EPS would
increase 5.4%. On the other hand, if EBIT
declines 4%, a DFL of 2.7 indicates that EPS
would decline 10.8%.
Degree of Combined Leverage
%  in EPS
%  in Sales
Q( P  V )
=
Q( P  V )  F  I
S  VC
S  VC
=

S  VC  F  I
EBT
 %  in EBIT  %  in EPS 
=


%

in
Sales
%

in
EBIT



= (DOL)(DFL)
DCL 

Note: If F = 0, and I = 0, DCL = 1.0 (i.e., without
F or I the % change in EPS would be equal to the
% change in sales). By employing F or I (or both),
the firm’s % change in EPS will be greater than
the % change in sales.
Webb’s DCL When Q = 30,000 Units
30,000(25  7)
DCL 
30,000(25  7)  270,000  170,000
= (DOL)(DFL)
= (2)(2.7)
= 5.4
Illustration of Leverage Effects
(A 10% Increase in Sales for Webb’s Inc.)
Bef. Sales Inc.
-
-
Sales (33,000 units @ $25)
Variable costs ($7 per unit)
Fixed costs
EBIT
Interest expense
EBT
Taxes
EAT
$ 825,000 $ 750,000
(231,000)
(210,000)
(270,000)
(270,000)
$ 324,000 $ 270,000
(170,000)
(170,000)
$ 154,000 $ 100,000
( 52,360)
(34,000)
$ 101,640 $ 66,000
EPS = $101,640/20,000 = $5.08
EPS = $3.30
DOL = 2.0
324,000  270,000
%  in EBIT =
 .2
270,000
= 2(%  in sales) = 20%
DFL = 2.7
5.08 - 3.30
%  in EPS =
= .54
3.30
= 2.7(%  in EBIT) = 54%
DCL = 5.4
%  in EPS = 5.4(%  in sales) = 54%