1

Analysis and Impact Chapter 15

of Leverage
 3
Goal of a firm
Managers' objective is to maximize stockholders'
wealth--maximize the price of the firm's stock. We
noted in an earlier chapter that the capital structure
that produces the lowest WACC (risk) is also the one
that maximizes share price.
 4
Risk
Variability of the expected net income (EPS)
 5
Risk
Variability of revenues from expected
Two types of Risk: Business Risk & Financial Risk
 6
Risk
Variability of revenues from expected
Two types of Risk: Business Risk & Financial Risk

Revenue
-Variable Cost
Contribution margin
-Fixed cost
=EBIT/operating profits
-Interest
=NI
 7
Risk
Variability of revenues from expected
Two types of Risk: Business Risk & Financial Risk

Business Risk
Risk Due to Operations
 8
Risk
Variability of revenues from expected
Two types of Risk: Business Risk & Financial Risk

Business Risk
Risk Due to Operations

Measured by variability of EBIT (earnings before

interest and taxes)
 9
Risk
Variability of revenues from expected
Two types of Risk: Business Risk & Financial Risk

Business Risk
Risk Due to Operations
Measured by variability of EBIT (earnings before
interest and taxes)
Coefficient of Variation of EBIT

Standard Deviation of EBIT

= Expected EBIT
 10
Risk
Variability of revenues from expected
Two types of Risk: Business Risk & Financial Risk

Financial Risk
Risk due to raising money with fixed income securities
 11
Business Risk
Major determinants of business risk

1. Demand Variability

2. Sales Price Variability
3. Input Price variability.
4. Inability to adjust output prices for a change in input
prices-a utility can transfer costs more easily
5. Operating Leverage--the extent to which costs are
'fixed' (the ratio of fixed cost to total cost).

Business risk not only varies from industry to industry,

it varies among firms in a given industry.

Business risk of a firm can change over time.

 12
Risk

Financial Risk
Risk due to raising money with fixed income securities
Financial risk is high with high levels of debt financing
 13
Risk

Financial Risk
Risk due to raising money with fixed income securities
Financial risk is high with high levels of debt financing
Financial leverage - the use of fixed income securities
to finance a portion of assets
 14
Risk

Financial Risk
Risk due to raising money with fixed income securities
Financial risk is high with high levels of debt financing
Financial leverage - the use of fixed income securities
to finance a portion of assets
Example
Firm A is an all equity firm -- it has no financial leverage
 15
Risk
Financial Risk
Risk due to raising money with fixed income securities
Financial risk is high with high levels of debt financing
Financial leverage - the use of fixed income securities
to finance a portion of assets
Example
Firm A is an all equity firm -- it has no financial leverage
Firm B is financed by 50% debt and 50% equity -- it uses
financial leverage
 16
Risk
Notes:

1. Business risk is largely determined by technology and

by industry/market conditions, although management
decisions, to some extent, do matter.

2. Financial risk is largely management determined.

3. If business risk is high, financial risk (leverage) should

be restrained.
 17
Break-even Analysis
The point of sales where operating profits are zero.
The point where revenues barely cover all costs.

Steps to Solution
Determine the quantity of output which results in an
EBIT = $0
 18
Break-even Analysis
Steps to Solution
Determine the quantity of output which results in an
EBIT = $0
Shows output necessary to cover operating (not
financial) costs
 19
Break-even Analysis
Steps to Solution
Determine the quantity of output which results in an
EBIT = $0
Shows output necessary to cover operating (not
financial) costs
Calculate EBIT at various output levels
 20
Break-even Analysis
Steps to Solution
Determine the quantity of output which results in an
EBIT = $0
Shows output necessary to cover operating (not
financial) costs
Calculate EBIT at various output levels
Applications
Capital Expenditure Analysis
 21
Break-even Analysis
Steps to Solution
Determine the quantity of output which results in an
EBIT = $0
Shows output necessary to cover operating (not
financial) costs
Calculate EBIT at various output levels
Applications
Capital Expenditure Analysis
Determining Prices
Evaluating Fixed vs. Variable Costs
 22
Break-even Analysis
Assumptions
Fixed costs remain constant as quantity changes
Fixed Costs Includes:
Salaries, Depreciation, Rent
 23
Break-even Analysis
Assumptions
Fixed costs remain constant as quantity changes
Fixed Costs Includes:
Salaries, Depreciation, Rent
 Variable costs vary as quantity of output changes:
they are constant per unit of output
Variable Costs Includes:
Materials, Labor, Commissions

Drop Semivariable costs

 24
Break-even Analysis
Assumptions
Fixed costs remain constant as quantity changes

 Variable costs vary as quantity of output changes:

they are constant per unit of output
Costs
$

Variable Costs

Fixed Costs

Quantity Sold
 25
Break-even Analysis
Assumptions
Fixed costs remain constant as quantity changes
Fixed Costs Includes:
Salaries, Depreciation, Rent
 Variable costs vary as quantity of output changes:
they are constant per unit of output
Variable Costs Includes:
Materials, Labor, Commissions
 Revenues are quantity sold times price per unit
 26
Break-even Analysis
Calculation of Break-even Quantity

EBIT = Sales – Variable Costs - Fixed Costs

Find Quantity which results in EBIT = $0

 27
Break-even Analysis
Calculation of Break-even Quantity
Trial and Error Method
Choose arbitrary output level
Calculate EBIT
If EBIT < 0, choose a larger output level
If EBIT > 0, choose a lower output level
Continue until find a level of output which results in EBIT
= $0
 28
Break-even Analysis
Calculation of Break-even Quantity
Algebraic Analysis

QB = F
P–V
Where:
QB = Break-even Quantity
P = Price per Unit
F = Total Fixed Costs
V = Variable Costs per Unit
 29
Break-even Analysis
Calculation of Break-even Quantity
Example:

QB = F
P–V
Fixed Costs = $1,000,000 per year
Price = $800/unit
Variable Costs = $400/unit
 30
Break-even Analysis
Calculation of Break-even Quantity
Example:

QB = F
P–V
Fixed Costs = $1,000,000 per year
Price = $800/unit
Variable Costs = $400/unit
$1,000,000
QB =
$800 – $400
 31
Break-even Analysis
Calculation of Break-even Quantity
Example:

QB = F
P–V
Fixed Costs = $1,000,000 per year
Price = $800/unit
Variable Costs = $400/unit
$1,000,000
QB =
$800 – $400
= 2,500 Units
 32
Break-even Analysis
Calculation of Break-even Sales Level (S*)
To Find S* for a single product use Break-even Quantity (QB):

S* = QB x P
 33
Break-even Analysis
Calculation of Break-even Sales Level (S*)
To Find S* for a single product use Break-even Quantity (QB):

S* = QB x P

S* = 2,500 units x $800

 34
Break-even Analysis
Calculation of Break-even Sales Level (S*)
To Find S* for a single product use Break-even Quantity (QB):

S* = QB x P

S* = 2,500 units x $800

= $2,000,000
 35
Break-even Analysis
Calculation of Break-even Sales Level (S*)
May want to Calculate the Break-even Sales Level (S*)
for the entire firm with many products
 36
Break-even Analysis
Calculation of Break-even Sales Level (S*)
May want to Calculate the Break-even Sales Level (S*)
for the entire firm with many products
Calculate from Income Statement data at a particular
Sales Level
 37
Break-even Analysis
Calculation of Break-even Sales Level (S*)
May want to Calculate the Break-even Sales Level (S*)
for the entire firm with many products
Calculate for Income Statement at one Sales Level
F
S* =
1 - VC
S
S = Dollar Level of Sales
VC = Total Dollar Variable Costs
 38
Break-even Analysis
Calculation of Break-even Sales Level (S*)
May want to Calculate the Break-even Sales Level (S*)
for the entire firm with many products
Calculate for Income Statement at one Sales Level
F
S* =
1 - VC
Example: S
S = Dollar Level of Sales = $3,000,000
VC = Total Dollar Variable Costs = $1,500,000

$1,000,000
S* = 1 – $1,500,000
$3,000,000
 39
Break-even Analysis
Calculation of Break-even Sales Level (S*)
May want to Calculate the Break-even Sales Level (S*)
for the entire firm with many products
Calculate for Income Statement at one Sales Level
F
S* =
1 - VC
Example: S
S = Dollar Level of Sales = $3,000,000
VC = Total Dollar Variable Costs = $1,500,000

$1,000,000
S* = 1 – $1,500,000 = $2,000,000
$3,000,000
 40
Break-even Analysis
Graphical Analysis of Break-even Point
Sales
&
Costs
$

$1,000,000 Fixed Costs

Quantity of Units
 41
Break-even Analysis
Graphical Analysis of Break-even Point
Sales
&
Costs
$

Variable Costs

$1,000,000 Fixed Costs

Quantity of Units
 42
Break-even Analysis
Graphical Analysis of Break-even Point
Sales
&
Costs
$ Total Costs

Variable Costs

$1,000,000 Fixed Costs

Quantity of Units
 43
Break-even Analysis
Graphical Analysis of Break-even Point
Sales
&
Sales
Costs
$ Total Costs

Variable Costs

$1,000,000 Fixed Costs

Quantity of Units
 44
Break-even Analysis
Graphical Analysis of Break-even Point
Sales
&
Sales
Costs
$ Total Costs

$2,000,000 Variable Costs

$1,000,000 Fixed Costs

QB = 2,500 Quantity of Units

 45
Break-even Analysis
Limitations:
1. The sales-volume-cost-profit relationship is
assumed to be linear—it may not be. In the real
world It is not, except for a small range of sales.
2. Cost-price structure of the firm is assumed to
remains constant. It generally does not.
3. Sales price per unit is assumed to be constant
regardless of the output. This is not the case in the
real world—you have to ? Price if you want to sell
more.
 46
Operating Leverage
Degree of Operating Leverage

• With FIXED operating costs, there will be operating

leverage

• DOL measures the sensitivity of EBIT to changes in

sales. DOL of a company is different at different levels of
sales.

• High DOL implies that a relatively small change in

sales will result in large change in the operating
income (EBIT)
 47
Operating Leverage
Degree of Operating Leverage
Operating Leverage is responsiveness of a firm’s EBIT
to fluctuations in Sales
 48
Operating Leverage
Degree of Operating Leverage
Operating Leverage is responsiveness of a firm’s EBIT
to fluctuations in Sales
Degree of Operating Leverage (DOL)
Measurement of Operating Leverage
For a unique level of sales, DOL changes as sales
change.
 49
Operating Leverage
Degree of Operating Leverage
Operating Leverage is responsiveness of a firm’s EBIT
to fluctuations in Sales
Degree of Operating Leverage (DOL)
Measurement of Operating Leverage
For a unique level of sales, DOL changes as sales
change.

% Change in EBIT
DOLS =
% Change in Sales

Unique Level of Sales

 50
Operating Leverage
Measurement of DOL
Calculation using per unit information:

Q(P – V)
DOLS =
Q(P – V) – F
 51
Operating Leverage
Measurement of DOL
Calculation using per unit information:

Q(P – V)
DOLS =
Q(P – V) – F
Example: Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.
 52
Operating Leverage
Measurement of DOL
Calculation using per unit information:

Q(P – V)
DOLS =
Q(P – V) – F
Example: Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.
3,750(800 – 400)
DOL3,750 units = 3,750(800 – 400) – 1,000,000
 53
Operating Leverage
Measurement of DOL
Calculation using per unit information:

Q(P – V)
DOLS =
Q(P – V) – F
Example: Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.
3,750(800 – 400)
DOL3,750 units = 3,750(800 – 400) – 1,000,000

= 3 times
 54
Operating Leverage
Measurement of DOL
Calculation using per unit information:

Q(P – V)
DOLS =
Q(P – V) – F
Example: Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.
3,750(800 – 400)
DOL3,750 units = 3,750(800 – 400) – 1,000,000
Interpretation: If sales change 1%, then
= 3 times EBIT will change 3% in the same direction.
 55
Operating Leverage
Measurement of DOL
Calculation using Income Statement Information

S – VC
DOLS =
S – VC – F
 56
Operating Leverage
Measurement of DOL
Calculation using Income Statement Information

S – VC
DOLS =
S – VC – F
Example: Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.
 57
Operating Leverage
Measurement of DOL
Calculation using Income Statement Information

S – VC
DOLS =
S – VC – F
Example: Q = 3,750 units x Sales
$3,000,000
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.
 58
Operating Leverage
Measurement of DOL
Calculation using Income Statement Information

S – VC
DOLS =
S – VC – F
Example: Q = 3,750 units
Price = $800 per unit x Variable Costs
Variable costs = $400 per unit $1,500,000
Fixed Costs = $1,000,000 per year.
 59
Operating Leverage
Measurement of DOL
Calculation using Income Statement Information

S – VC
DOLS =
S – VC – F
Example: Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.
3,000,000 – 1,500,00
DOL3,750 units = 3,000,000 – 1,500,000 – 1,000,000
 60
Operating Leverage
Measurement of DOL
Calculation using Income Statement Information

S – VC
DOLS =
S – VC – F
Example: Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.
3,000,000 – 1,500,00
DOL3,750 units = 3,000,000 – 1,500,000 – 1,000,000

= 3 times
 61
Operating Leverage
Measurement of DOL
Calculation using Income Statement Information

S – VC
DOLS =
S – VC – F
Example: Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.
3,000,000 – 1,500,00
DOL3,750 units = 3,000,000 – 1,500,000 – 1,000,000

= 3 times Same Answer as before

 62
Operating Leverage
Degree of Operating Leverage
Degree of Operating Leverage is highest when the firm
is closest to break-even point--DOL falls as sales rise

Quantity DOL
2,500 (QB) Undefined
3,250 4.33
3,750 3
5,000 2
 63
Operating Leverage
Degree of Operating Leverage
Degree of Operating Leverage is highest when the firm
is closest to break-even point--DOL falls as sales rise
Quantity DOL
2,500 (QB) Undefined
3,250 4.33
3,750 3
5,000 2

The higher the sales level above break-even, the less

EBIT (in %) changes as sales change
 64
Operating Leverage
Degree of Operating Leverage
Degree of Operating Leverage is highest when the firm
is closest to break-even point--DOL falls as sales rise
Quantity DOL
2,500 (QB) Undefined
3,250 4.33
3,750 3
5,000 2

The higher the sales level above break-even, the less

EBIT(in %) changes as sales change
If Fixed Costs = $0, Degree of Operating Leverage = 1
 65
Financial Leverage
Degree of Financial Leverage
Finance a portion of the firm’s assets with securities
that have fixed financial costs
Debt
Preferred Stock
 66
Financial Leverage
Degree of Financial Leverage
Finance a portion of the firm’s assets with securities
that have fixed financial costs
Debt
Preferred Stock
Financial Leverage measures changes in earnings per
share (NI) as EBIT changes.
 67
Financial Leverage
Degree of Financial Leverage
Finance a portion of the firm’s assets with securities
that have fixed financial costs
Debt
Preferred Stock
Financial Leverage measures changes in earnings per
share as EBIT changes.
Degree of Financial Leverage (DFL) at one level of
EBIT:

% Change in EPS
DFLEBIT =
% Change in EBIT

Unique Level of EBIT

 68
Financial Leverage
Measurement of DFL

EBIT
DFLEBIT =
EBIT – I
 69
Financial Leverage
Measurement of DFL

EBIT
DFLEBIT =
EBIT – I Total Fixed
Financing
Costs
 70
Financial Leverage
Measurement of DFL

EBIT
DFLEBIT =
EBIT – I
Example: EBIT = $500,000
Interest Charges = $200,000
 71
Financial Leverage
Measurement of DFL

EBIT
DFLEBIT =
EBIT – I
Example: EBIT = $500,000
Interest Charges = $200,000

500,000
DFLEBIT=500,000 = 500,000 – 200,000
 72
Financial Leverage
Measurement of DFL

EBIT
DFLEBIT =
EBIT – I
Example: EBIT = $500,000
Interest Charges = $200,000

500,000
DFLEBIT=500,000 = 500,000 – 200,000

= 1.67 times
 73
Financial Leverage
Measurement of DFL

EBIT
DFLEBIT =
EBIT – I
Example: EBIT = $500,000
Interest Charges = $200,000

500,000
DFLEBIT=500,000 = 500,000 – 200,000

= 1.67 times
Interpretation: For 1% change in EBIT (from an existing
level of $500,000) Earnings Per Share will change 1.67%
 74
DFL

S - VC - F
DFL = ---------------------
S - VC - F - I
 75
Combined Leverage
Degree of Combined Leverage
Measures changes in Earnings Per Share given
changes in Sales
 76
Combined Leverage
Degree of Combined Leverage
Measures changes in Earnings Per Share given
changes in Sales
Combines both Operating and Financial Leverage
 77
Combined Leverage
Degree of Combined Leverage
Measures changes in Earnings Per Share given
changes in Sales
Combines both Operating and Financial Leverage
Computed for a specific level of sales
 78
Combined Leverage
Degree of Combined Leverage
Measures changes in Earnings Per Share given
changes in Sales
Combines both Operating and Financial Leverage
Computed for a specific level of sales

% Change in EPS
DCLS =
% Change in Sales

Unique Level of Sales

 79
Combined Leverage
Measurement of DCL

DCLS = DOLS x DFLEBIT

 80
Combined Leverage
Measurement of DCL

DCLS = DOLS x DFLEBIT

Example:
DFLEBIT = 1.67
DOLS = 3.0
 81
Combined Leverage
Measurement of DCL

DCLS = DOLS x DFLEBIT

Example:
DFLEBIT = 1.67
DOLS = 3.0

DCL3,750 = 3.0 x 1.67

 82
Combined Leverage
Measurement of DCL

DCLS = DOLS x DFLEBIT

Example:
DFLEBIT = 1.67
DOLS = 3.0

DCL3,750 = 3.0 x 1.67

= 5.0 times
 83
Combined Leverage
Measurement of DCL

DCLS = DOLS x DFLEBIT

Example:
DFLEBIT = 1.67
DOLS = 3.0

DCL3,750 = 3.0 x 1.67

= 5.0 times

Interpretation: When sales change 1%, Earnings Per Share

(NI) will change 5.0%
 84
Combined Leverage
Measurement of DCL--Alternative Computation

DCLS = Q(P – V)
Q(P – V) – F – I
 85
Combined Leverage
Measurement of DCL--Alternative Computation

DCLS = Q(P – V)
Q(P – V) – F – I
Example: Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year
Interest = $200,000 per year
 86
Combined Leverage
Measurement of DCL--Alternative Computation

DCLS = Q(P – V)
Q(P – V) – F – I
Example: Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year
Interest = $200,000 per year
3,750(800 – 400)
DCLS = 3,750(800 – 400) – 1,000,000 – 200,000
 87
Combined Leverage
Measurement of DCL--Alternative Computation

DCLS = Q(P – V)
Q(P – V) – F – I
Example: Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year
Interest = $200,000 per year
3,750(800 – 400)
DCLS = 3,750(800 – 400) – 1,000,000 – 200,000
= 5 times
 88
Combined Leverage
Measurement of DCL--Alternative Computation

DCLS = Q(P – V)
Q(P – V) – F – I
Example: Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year
Interest = $200,000 per year
3,750(800 – 400)
DCLS = 3,750(800 – 400) – 1,000,000 – 200,000
= 5 times
Interpretation: When sales change 1%, Earnings Per Share
will change 5.0%
 89

Combined Leverage

Measurement of DCL--Alternative Computation-

Using income statement.

S - VC - F
DCLS = ---------------------
S - VC - F - I