Leverage

Operating Leverage:



The use of fixed operating costs as opposed to variable
operating costs
A firm with relatively high fixed operating costs will
experience more variable operating income if sales
change
Financial Leverage:

The use of fixed-cost sources of financing (debt,
preferred stock) rather than variable-cost sources
(common stock)
Slide 1

Leverage Analysis
Operating Leverage



Affects a firm’s business risk
Business risk is the variability or uncertainty of a
firm’s operating income (EBIT)
Financial Leverage


Affects a firm’s financial risk
Financial risk is the variability or uncertainty of a
firm’s earnings per share (EPS) and the increased
probability of insolvency that arises when a firm uses
financial leverage
Slide 2
Breakeven Analysis




Illustrates the effects of operating leverage
Useful for forecasting the profitability of a firm,
division or product line
Useful for analyzing the impact of changes in
fixed costs, variable costs, and sales price
Terms:

P: price per unit, Q: quantity produced, V: variable
costs per unit, VC; total variable costs, F; total fixed
costs, TC: total cost (VC+F), S: sales ($)
Slide 3
Breakeven Analysis
Total Revenue
(PQ)
$
Quantity
Slide 4
Costs

Suppose the firm has both fixed operating costs
(administrative salaries, insurance, rent, property
tax) and variable operating costs (materials,
labor, energy, packaging, sales commissions)
Slide 5
Breakeven Analysis
Total Revenue
$
+
}
Total Cost
(QV)+F or
VC+F
EBIT
FC
{
Breakeven EBIT
Q
Quantity
Slide 6
Operating Leverage

What happens if the firm increases its fixed
operating costs and reduces (or eliminates) its
variable costs?
Slide 7
Breakeven Analysis
With high operating leverage, an increase in
sales produces a relatively larger increase in
operating income.
Total Revenue
$
Trade-off: the firm has a higher breakeven
point. If sales are not high enough, the firm
will not meet its fixed expenses!
+
{
FC
}
EBIT
Total Cost
= Fixed
-
Q1
Breakeven EBIT
Quantity
Slide 8
Breakeven Calculations – Quantity
F
QB =
P-V
where
Q B : breakeven level of Q
F : total anticipate d fixed costs
P : sales price per unit
V : variable cost per unit
P - V is the Contributi on Margin
Slide 9
Breakeven Calculations – Sales
F
S* =
VC
1S
where
S* : breakeven level of sales
F : total fixed costs
S : total sales
VC : total variable costs
VC
Note that
is assumed to be constant
S
Slide 10
Analytical Income Statement
-
sales
contribution margin
variable costs
fixed costs
operating income (EBIT)
interest
EBT (1 – t) = Net Income,
EBT
so,
taxes
Net Income / (1 – t) = EBT
net income
}
Slide 11
Degree of Operating Leverage (DOL)


Operating leverage: by using fixed operating
costs, a small change in sales revenue is
magnified into a larger change in operating
income
This “multiplier effect” is called the degree of
operating leverage
Slide 12
Degree of Operating Leverage
from Sales Level (S)

change in EBIT
% change in EBIT
EBIT
DOL S 

change in sales
% change in sales
sales
Above calculation requires two analytical
income statements, one for the base period and
one for the following period using the new level
of sales
Slide 13
Degree of Operating Leverage
from Sales Level (S)

If we have the base level data, we can use this formula:
Sales - Variable Costs
Q( P  V )
DOL S 

EBIT
Q( P  V )  F



Implicit assumption is that Variable Costs / Sales and
Fixed Costs stay the constant
If DOL = 2, then a 1% increase in sales will result in a
2% increase in operating income (EBIT) and vice versa
%Δ in EBIT = DOLSales x %Δ in Sales
Slide 14
Degree of Financial Leverage (DFL)


Financial leverage: by using fixed cost financing,
a small change in operating income is magnified
into a larger change in earnings per share (EPS)
This “multiplier effect” is called the degree of
financial leverage
Slide 15
Degree of Financial Leverage
DFLEBIT

change in EPS
% change in EPS
EPS


% change in EBIT change in EBIT
EBIT
Each financing or capital structure (relative use
of debt and equity) alternative will have a
different degree of financial leverage (DFL)
Slide 16
Degree of Financial Leverage


Instead of calculating DFL for each alternative capital
structure we can use the following formula with the base
EBIT and differing interest expenses
Note that interest expense would be based on how much
debt is used financing the assets of the firm
DFLEBIT


EBIT

EBIT  I
If DFL = 3, then a 1% increase in operating income will
result in a 3% increase in earnings per share and vice
versa
%Δ in EPS = DFLEBIT x %Δ in EBIT
Slide 17
Degree of Combined Leverage (DCL)


Combined leverage: by using operating
leverage and financial leverage, a small change
in sales is magnified into a larger change in
earnings per share
This “multiplier effect” is called the degree of
combined leverage
Slide 18
Degree of Combined Leverage
DCLS  ( DOL S ) X ( DFLEBIT )
% change in EPS
DCLS 
% change in Sales
change in EPS
EPS
DCLS 
change in Sales
Sales
Slide 19
Degree of Combined Leverage

If we have the base level data, we can use this formula:
Sales - Variable Costs
DCLS 
EBIT - I
Q( P  V )
DCLS 
Q( P  V )  F  I


If DCL = 4, then a 1% increase in sales will result in a
4% increase in earnings per share
%Δ in EPS = DCLSales x %Δ in Sales
Slide 20

Example
Based on the following information on a
Levered Company, answer these questions:
1) If sales increase by 10%, what should happen
to operating income?
2) If operating income increases by 10%, what
should happen to EPS?
3) If sales increase by 10%, what should be the
effect on EPS?
Slide 21
Levered Company – Data
Sales (100,000 units)
Variable Costs
Fixed Costs
Interest paid
Tax rate
Shares outstanding
$1,400,000
$800,000
$250,000
$125,000
34%
100,000
Slide 22
Leverage
Sales
DCL
DOL
EPS
EBIT
DFL
Slide 23
Levered Company – Base Level Data
Sales (100,000 units)
$1,400,000
Variable Costs
($800,000)
Fixed Costs
($250,000)
EBIT (Operating Income)
$350,000)
Interest paid
($125,000)
EBT
$225,000
Tax @ 34%
($75,500)
EAT (Net Income)
$148,500
EPS = $148,500 / 100,000 = $1.485
Slide 24
Degree of Operating Leverage from Sales Level (S)
Sales - Variable Costs
DOL S 
EBIT
1,400,00  800,000
DOL D 
 1.714
350,000



Answer to part 1:
%Δ in EBIT = DOLSales x %Δ in Sales
%Δ in EBIT = 1.714 x 10% = 17.14%
Slide 25
Degree of Financial Leverage
DFLEBIT
DFLEBIT




EBIT

EBIT  I
350,000

 1.556
225,000
Answer to part 2:
%Δ in EPS = DFLEBIT x %Δ in EBIT
%Δ in EPS = 1.556 x 10% = 15.56%
%Δ in EPS = 1.556 x 17.14% = 26.67% (cumulative
impact of part 1
Slide 26
Degree of Combined Leverage
Sales - Variable Costs
DCLS 
EBIT - I
1,400,000  800,000
DCLS 
 2.667
225,000




Answer to part 3:
Alternatively DCL = DOL x DFL
DCL = 1.714 x 1.556 = 2.667
%Δ in EPS = 2.667 x 10% = 26.67%
Slide 27
Levered Company
Sales
DCL = 2.667
EPS
DOL = 1.714
EBIT
DFL =
1.556
Slide 28
Levered Company
10% increase in sales
Sales (110,000 units)
Variable Costs
Fixed Costs
EBIT
Interest
EBT
Taxes (34%)
Net Income
EPS
1,540,000
(880,000)
(250,000)
410,000 ( +17.14%)
(125,000)
285,000
(96,900)
188,100
$1.881 ( +26.67%)
Slide 29