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 firm’s 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 firm’s 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. Standard Deviation of EBIT
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. EBIT = Sales – Variable Costs - Fixed Costs
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 F QB = P – V 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 F QB = P – V Calculation of Break-even Quantity
Example: F
P – V
QB =
Fixed Costs = $1,000,000 per year
Price = $800/unit
Variable Costs = $400/unit

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

31. Break-even Analysis F QB = P – V Calculation of Break-even Quantity
Example: F
P – V
QB =
Fixed Costs = $1,000,000 per year
Price = $800/unit
Variable Costs = $400/unit
$1,000,000
$800 – $400
QB =
= 2,500 Units

32. Break-even Analysis S* = QB x P
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 S* = QB x P
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 S* = QB x P
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 F S* = 1 - VC S
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 F S* = 1 - VC S
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 F S* = 1 - VC S
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 linear—it 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 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 % Change in EBIT
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
% Change in Sales
DOLS =
Unique Level of Sales

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

51. Operating Leverage Measurement of DOL Q(P – V) DOLS = Q(P – V) – F
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 Q(P – V) DOLS = Q(P – V) – F
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 Q(P – V) DOLS = Q(P – V) – F
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 Q(P – V) DOLS = Q(P – V) – F
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 S – VC DOLS = S – VC – F
Calculation using Income Statement Information
S – VC
S – VC – F
DOLS =

56. Operating Leverage Measurement of DOL S – VC DOLS = S – VC – F
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 S – VC DOLS = S – VC – F
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.
Sales
$3,000,000 x

58. Operating Leverage Measurement of DOL S – VC DOLS = S – VC – F
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 S – VC DOLS = S – VC – F
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 S – VC DOLS = S – VC – F
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 S – VC DOLS = S – VC – F
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,
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,
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,
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 % Change in EPS
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
% 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 DFLEBIT = EBIT – I
Total Fixed Financing
Costs

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

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

72. Financial Leverage Measurement of DFL EBIT DFLEBIT = EBIT – I Example:
Interest Charges = $200,000
500,000
500,000 – 200,000
DFLEBIT=500,000 =
= 1.67 times

73. Financial Leverage Measurement of DFL EBIT DFLEBIT = EBIT – I Example:
Interest Charges = $200,000
500,000
500,000 – 200,000
DFLEBIT=500,000 =
= 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 % Change in EPS DCLS =
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:

81. Combined Leverage Measurement of DCL DCLS = DOLS x DFLEBIT Example:
DCL3,750 = 3.0 x 1.67

82. Combined Leverage Measurement of DCL DCLS = DOLS x DFLEBIT Example:
DCL3,750 = 3.0 x 1.67
= 5.0 times

83. Combined Leverage Measurement of DCL DCLS = DOLS x DFLEBIT Example:
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 =
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 Q(P – V)
Q(P – V) – F – I
DCLS =
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)
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 =
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)
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 =
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)
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