Chapter 13 Analysis and Impact of Leverage

1
Analysis and Impact of Leverage
Chapter 15
2

• Learning Objectives
• Understand the different between business risk
  and financial risk.
• Use the technique of break-even analysis in a
  variety of analytical settings.
• Calculate the firms break-even point in terms of
  units produced and sold, and in sales dollars.
• Distinguish among the financial concepts of
  operating leverage, financial leverage, and
  combined leverage.
• Calculate the firms degree of operating
  leverage, financial leverage, and combined
  leverage.
• Explain why a firm with a high business risk
  exposure might logically choose to employ a low
  degree of financial leverage in its financial
  structure.

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 lt 0, choose a larger output level
• If EBIT gt 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
F P V
QB
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
F P V
QB
Fixed Costs 1,000,000 per year Price 800/uni
t Variable Costs 400/unit
30
Break-even Analysis

• Calculation of Break-even Quantity

Example
F P V
QB
Fixed Costs 1,000,000 per year Price 800/uni
t Variable Costs 400/unit
1,000,000 800 400
QB
31
Break-even Analysis

• Calculation of Break-even Quantity

Example
F P V
QB
Fixed Costs 1,000,000 per year Price 800/uni
t Variable Costs 400/unit
1,000,000 800 400
QB
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 1 - VC
S
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 1 - VC
S
S
Example
S Dollar Level of Sales 3,000,000 VC Total
Dollar Variable Costs 1,500,000
1,000,000 1 1,500,000
S
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 1 - VC
S
S
Example
S Dollar Level of Sales 3,000,000 VC Total
Dollar Variable Costs 1,500,000
1,000,000 1 1,500,000
S
2,000,000
3,000,000
40
Break-even Analysis

• Graphical Analysis of Break-even Point

Sales Costs
Fixed Costs
1,000,000
Quantity of Units
41
Break-even Analysis

• Graphical Analysis of Break-even Point

Sales Costs
Variable Costs
Fixed Costs
1,000,000
Quantity of Units
42
Break-even Analysis

• Graphical Analysis of Break-even Point

Sales Costs
Total Costs
Variable Costs
Fixed Costs
1,000,000
Quantity of Units
43
Break-even Analysis

• Graphical Analysis of Break-even Point

Sales Costs
Sales
Total Costs
Variable Costs
Fixed Costs
1,000,000
Quantity of Units
44
Break-even Analysis

• Graphical Analysis of Break-even Point

Sales Costs
Sales
Total Costs
Variable Costs
2,000,000
Fixed Costs
1,000,000
QB 2,500
Quantity of Units
45
Break-even Analysis

• Limitations
• The sales-volume-cost-profit relationship is
  assumed to be linearit may not be. In the real
  world It is not, except for a small range of
  sales.
• Cost-price structure of the firm is assumed to
  remains constant. It generally does not.
• Sales price per unit is assumed to be constant
  regardless of the output. This is not the case
  in the real worldyou 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 firms
  EBIT to fluctuations in Sales

48
Operating Leverage

• Degree of Operating Leverage
• Operating Leverage is responsiveness of a firms
  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 firms
  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 Change in Sales
DOLS
Unique Level of Sales
50
Operating Leverage

• Measurement of DOL
• Calculation using per unit information

Q(P V) Q(P V) F
DOLS
51
Operating Leverage

• Measurement of DOL
• Calculation using per unit information

Q(P V) Q(P V) F
DOLS
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) Q(P V) F
DOLS
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) 3,750(800
400) 1,000,000
DOL3,750 units
53
Operating Leverage

• Measurement of DOL
• Calculation using per unit information

Q(P V) Q(P V) F
DOLS
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) 3,750(800
400) 1,000,000
DOL3,750 units
3 times
54
Operating Leverage

• Measurement of DOL
• Calculation using per unit information

Q(P V) Q(P V) F
DOLS
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) 3,750(800
400) 1,000,000
DOL3,750 units
Interpretation If sales change 1, then EBIT
will change 3 in the same direction.
3 times
55
Operating Leverage

• Measurement of DOL
• Calculation using Income Statement Information

S VC S VC F
DOLS
56
Operating Leverage

• Measurement of DOL
• Calculation using Income Statement Information

S VC S VC F
DOLS
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 S VC F
DOLS
Example
Sales 3,000,000
Q 3,750 units Price 800 per unit Variable
costs 400 per unit Fixed Costs 1,000,000
per year.
x
58
Operating Leverage

• Measurement of DOL
• Calculation using Income Statement Information

S VC S VC F
DOLS
Example
Q 3,750 units Price 800 per unit Variable
costs 400 per unit Fixed Costs 1,000,000
per year.
Variable Costs 1,500,000
x
59
Operating Leverage

• Measurement of DOL
• Calculation using Income Statement Information

S VC S VC F
DOLS
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
3,000,000 1,500,000 1,000,000
DOL3,750 units
60
Operating Leverage

• Measurement of DOL
• Calculation using Income Statement Information

S VC S VC F
DOLS
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
3,000,000 1,500,000 1,000,000
DOL3,750 units
3 times
61
Operating Leverage

• Measurement of DOL
• Calculation using Income Statement Information

S VC S VC F
DOLS
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
3,000,000 1,500,000 1,000,000
DOL3,750 units
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 firms assets with
  securities that have fixed financial costs
• Debt
• Preferred Stock

66
Financial Leverage

• Degree of Financial Leverage
• Finance a portion of the firms 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 firms 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 Change in EBIT
DFLEBIT
Unique Level of EBIT
68
Financial Leverage

• Measurement of DFL

EBIT EBIT I
DFLEBIT
69
Financial Leverage

• Measurement of DFL

EBIT EBIT I
DFLEBIT
Total Fixed Financing Costs
70
Financial Leverage

• Measurement of DFL

EBIT EBIT I
DFLEBIT
Example
EBIT 500,000 Interest Charges 200,000
71
Financial Leverage

• Measurement of DFL

EBIT EBIT I
DFLEBIT
Example
EBIT 500,000 Interest Charges 200,000
500,000 500,000 200,000
DFLEBIT500,000
72
Financial Leverage

• Measurement of DFL

EBIT EBIT I
DFLEBIT
Example
EBIT 500,000 Interest Charges 200,000
500,000 500,000 200,000
DFLEBIT500,000
1.67 times
73
Financial Leverage

• Measurement of DFL

EBIT EBIT I
DFLEBIT
Example
EBIT 500,000 Interest Charges 200,000
500,000 500,000 200,000
DFLEBIT500,000
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 Change in Sales
DCLS
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

Q(P V) Q(P V) F I
DCLS
85
Combined Leverage

• Measurement of DCL--Alternative Computation

Q(P V) Q(P V) F I
DCLS
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
Example
86
Combined Leverage

• Measurement of DCL--Alternative Computation

Q(P V) Q(P V) F I
DCLS
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
Example
3,750(800 400)
3,750(800 400) 1,000,000 200,000
DCLS
87
Combined Leverage

• Measurement of DCL--Alternative Computation

Q(P V) Q(P V) F I
DCLS
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
Example
3,750(800 400)
3,750(800 400) 1,000,000 200,000
DCLS
5 times
88
Combined Leverage

• Measurement of DCL--Alternative Computation

Q(P V) Q(P V) F I
DCLS
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
Example
3,750(800 400)
3,750(800 400) 1,000,000 200,000
DCLS
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