5
Prepared by:
Terry Fegarty
Seneca College
Revised By
P Chua
McGraw-Hill Ryerson

Chapter 5 - Outline
 What is Leverage?
 Break-even Analysis
 Operating Leverage
 Financial Leverage
 Combined or Total Leverage
 Summary and Conclusions
PPT 5-2
© 2003 McGraw-Hill Ryerson Limited

PPT 5-3
What is Leverage?
 In general terms, leverage means the use of force and effects to produce a more than normal results from a given action
 In other words, leverage is the advantage generated by using a lever
 Example, using a jack to lift a car
 In Finance, leverage is the use of fixed costs to magnify the potential return to a firm
 2 types of fixed costs:
 fixed operating costs = rent, salaries, etc.
 fixed financial costs = interest costs from debt
© 2003 McGraw-Hill Ryerson Limited

What is Leverage?
 Leverage can magnify returns to common stockholders but can also increase risk
 Management has almost complete control over this risk introduced through the use of leverage (fixed costs)

The degree in the use of leverage depends on management’s attitude toward risk and the nature of its business , among others.

Three types of leverage with reference to the firm’s income statement:



Operating leverage,
Financial leverage, and
Combined (Total) leverage.
 Leverage is measured on the profitability range of operations.
© 2003 McGraw-Hill Ryerson Limited

What is Leverage?
Sales
Less: Cost of Goods Sold
Gross Margin
Less: Operating Expenses
Earnings Before Interest and Taxes (EBIT)
Less: Interest
Earnings Before Taxes
Less: Taxes
Earnings After Taxes (EAT)
Number of Shares Outstanding
Earnings Per Share
Operating leverage
Financial leverage
© 2003 McGraw-Hill Ryerson Limited

What is Leverage?
Sales
Less: Total variable Costs
Contribution Margin
Less: Fixed Cost
Earnings Before Interest and Taxes (EBIT)
Less: Interest
Earnings Before Taxes
Less: Taxes
Earnings After Taxes (EAT)
Number of Shares Outstanding
Earnings Per Share
Operating leverage
Financial leverage
© 2003 McGraw-Hill Ryerson Limited

Breakeven Analysis



Break-even Analysis is used by the firm:


To determine the level of operations necessary to cover all operating costs, and
To evaluate the profitability associated with various levels of sales.
The Operating Breakeven Point is the level of sales necessary to cover all operating costs.
The formula for determining operating breakeven is:
EBIT = (P

Q) – (VC

Q) – FC (1) where
P = sales price per unit
Q = sales quantity in units
FC = fixed operating cost per period
VC = variable operating cost per unit
EBIT = earnings before interest and taxes
© 2003 McGraw-Hill Ryerson Limited

Breakeven Quantity
 Equation (1) can be rewritten to solve for the sales quantity that will breakeven:
(2)
Q

FC
P

VC
 Since P – VC is the Contribution Margin per unit
(CM/unit), equation 2 becomes:
(3)
Q

FC
CM / unit
© 2003 McGraw-Hill Ryerson Limited

Breakeven Analysis
Plan A (Leveraged) Plan B (Less Leveraged-
Conservative)
Selling Price (/unit) = $2.00
Fixed Cost = $60,000 Fixed Cost = $12,000
Variable Cost (/unit) = $0.80
Variable Cost (/unit) = $1.60
Contribution Margin(/unit) = $1.20
Contribution Margin(/unit) = $0.40
Break-Even Point (units) = 50,000 Break-Even Point (units) = 30,000
© 2003 McGraw-Hill Ryerson Limited

PPT 5-4
Figure 5-1
Break-even chart: leveraged firm
Revenues and costs ($ thousands)
Total
Revenue
200
Profit
160
120
100
80
60
40
BE
Loss
Variable costs
Total costs
Fixed costs
20 40 50 60 80 100 120
Price ($2)
Variable costs per unit ($0.80)
Fixed costs ($60,000)
Units produced and sold (thousands)
© 2003 McGraw-Hill Ryerson Limited

Table 5-2
Volume-cost-profit analysis: Leveraged firm
PPT 5-5
Total
Units Variable Fixed
Sold Costs Costs
Total Total
Operating
Income
Costs Revenue (loss)
0 0 $60,000 $ 60,000 0 $(60,000)
20,000 16,000 60,000 76,000 $ 40,000 (36,000)
40,000 32,000 60,000 92,000 80,000 (12,000)
50,000 40,000 60,000 100,000 100,000 0
60,000 48,000 60,000 108,000 120,000 12,000
80,000 64,000 60,000 124,000 160,000 36,000
100,000 80,000 60,000 140,000 200,000 60,000
© 2003 McGraw-Hill Ryerson Limited

Figure 5-2
Break-even chart: conservative firm
Total
Revenue
Revenues and costs ($ thousands)
200
Profit
Total costs
PPT 5-6
160
120
80
40
BE Variable costs
Loss
Fixed costs
20 40 60 80 100 120
Units produced and sold (thousands)
Fixed costs ($12,000) Price ($2) Variable costs per unit ($1.60)
© 2003 McGraw-Hill Ryerson Limited

Table 5-3
Volume-cost-profit analysis: Less
Leveraged (Conservative) firm
Total
Units Variable
Sold Costs
Fixed
Costs
Total Total
Costs Revenue
Operating
Income
(loss)
0 0 $12,000 $ 12,000 0 $(12,000 )
20,000 $ 32,000 12,000 44,000 $ 40,000 (4,000 )
30,000 48,000 12,000 60,000 60,000 0
40,000 64,000 12,000 76,000 80,000
60,000 96,000 12,000 108,000 120,000
80,000 128,000 12,000 140,000 160,000
100,000 160,000 12,000 172,000 200,000
4,000
12,000
20,000
28,000
PPT 5-7
© 2003 McGraw-Hill Ryerson Limited

PPT 5-10
Table 5-4
Operating income or loss
Units
Leveraged Less Leveraged
Plan (Conservative)
Plan
EBIT EBIT
0
20,000
$(60,000)
(36,000)
$(12,000)
(4,000)
30,000
40,000
(12,000) 0
(12,000) 4,000
50,000 0 8,000
60,000 12,000 12,000
80,000 36,000 20,000
100,000 60,000 28,000
© 2003 McGraw-Hill Ryerson Limited

PPT 5-8
Leverage Means Risk
 Leverage is a double-edged sword
It magnifies losses as well as profits
 An aggressive or highly leveraged firm has a relatively high break-even point (and high fixed costs)
 A conservative or less-leveraged firm has a relatively low break-even point (and low fixed costs)
© 2003 McGraw-Hill Ryerson Limited

PPT 5-9
Operating Leverage
 Measures the amount of fixed operating costs used by a firm
 Operating Leverage measures the sensitivity of a firm’s operating income to a  in sales
 a
 in Sales
 a larger
 in EBIT (or OI)
Degree of Operating Leverage (DOL)=
%age
 in EBIT ( or OI)
%age
 in Sales
© 2003 McGraw-Hill Ryerson Limited

Calculating the Degree of Operating
Leverage
 DOL can be computed using the following formula: or
DOL

Q (
Q ( P
P

VC

VC )

)
FC
DOL

S
S

TVC

TVC

FC or
DOL

CM
EBIT
© 2003 McGraw-Hill Ryerson Limited

PPT 5-12
Financial Leverage
 Measure of the amount of debt used and interest paid by a firm
 Financial Leverage measures the sensitivity of a firm’s earnings per share to a  in operating income
 a
 in EBIT (or OI)
 a larger
 in EPS
Degree of Financial Leverage (DFL) =
%age
 in EPS
%age
 in EBIT (or OI)
© 2003 McGraw-Hill Ryerson Limited

Calculating the Degree of Financial
Leverage
 DFL can be computed using the following formula:
DFL

EBIT
EBIT

I
© 2003 McGraw-Hill Ryerson Limited

Financing Plans
Debt (8%)
Common Stock
Total Financing
Total Assets = $200,000
Plan A (Leveraged)
$150,000 ($12,000 interest)
Plan B (Less
Leveraged-
Conservative)
$50,000 ($4,000 interest)
$50,000 (8,000 shares @
$6.25)
$150,000 (24,000 shares
@ $6.25)
$200,000 $200,000
© 2003 McGraw-Hill Ryerson Limited

PPT 5-13 Table 5-5a
Impact of financing plan on earnings per share
Plan A Plan B
(leveraged) (conservative)
1. EBIT (0 )
Earnings before interest and taxes (EBIT)
— Interest (I)
Earnings before taxes (EBT)
— Taxes (T) *
Earnings aftertaxes(EAT)
Shares
0
$(12,000
(12,000
(6,000
$ (6,000
8,000
.
.
.
.
)
)
)
)
0
$ (4,000
(4,000
(2,000
$ (2,000
24,000
Earnings per share (EPS) $ (0.75) $ (0.08)
2. EBIT ($12,000)
.
.
.
.
)
)
)
)
Earnings before interest and taxes (EBIT)
— Interest (I)
Earnings before taxes (EBT)
— Taxes (T)
Earnings aftertaxes (EAT)
Shares
Earnings per share (EPS)
$12,000
12,000
0
0
$ 0
8,000
0
$12,000
4,000
8,000
4,000
$ 4,000
24,000
$0.17
* The assumption is that large losses can be written off against other income, perhaps in other years, thus providing the firm with a tax savings benefit. The tax rate is 50 percent.
© 2003 McGraw-Hill Ryerson Limited

PPT 5-14 Table 5-5b
Impact of financing plan on earnings per share
Plan A Plan B
(leveraged) (conservative)
3. EBIT ($16,000)
Earnings before interest and taxes (EBIT) $ 16,000
— Interest (I) 12,000
Earnings before taxes (EBT)
— Taxes (T)
Earnings aftertaxes (EAT)
Shares
4,000
2,000
$ 2,000
8,000
Earnings per share (EPS) $0.25
$ 16,000
4,000
12,000
6,000
$ 6,000
24,000
$0.25
4. EBIT ($36,000)
Earnings before interest and taxes (EBIT)
— Interest (I)
Earnings before taxes (EBT)
— Taxes (T)
Earnings aftertaxes (EAT)
Shares
Earnings per share (EPS)
$ 36,000
12,000
24,000
12,000
$ 12,000
8,000
$1.50
$ 36,000
4,000
32,000
16,000
$ 16,000
24,000
$0.67
© 2003 McGraw-Hill Ryerson Limited

PPT 5-15 Table 5-5c
Impact of financing plan on earnings per share
Plan A Plan B
(leveraged) (conservative)
5. EBIT ($60,000)
Earnings before interest and taxes (EBIT) $ 60,000
— Interest (I)
12,000
Earnings before taxes (EBT)
— Taxes (T)
Earnings aftertaxes (EAT)
Shares
48,000
24,000
$ 24,000
8,000
Earnings per share (EPS) $3.00
$ 60,000
4,000
56,000
28,000
$ 28,000
24,000
$ 1.17
© 2003 McGraw-Hill Ryerson Limited

EBIT and EPS under both plans
EBIT
Leveraged Less Leveraged
Plan (Conservative)
Plan
EPS EPS
0 $ (0.75) $ (0.08)
12,000 0 $0.17
16,000 $0.25
36,000 $1.50
60,000 $3.00
$0.25
$0.67
$ 1.17
PPT 5-10
© 2003 McGraw-Hill Ryerson Limited

Figure 5-4
Financing plans and earnings per share
PPT 5-16
EPS ($)
4
Plan A
3
2
1
.25
0
-1
-2
0 12
16
25 50
EBIT ($ thousands )
75
Plan B
100
© 2003 McGraw-Hill Ryerson Limited

PPT 5-19
Combined or Total Leverage
 Represents maximum use of leverage
 a
 in Sales
 a larger
 in EPS
Degree of Combined Leverage (DCL ) =
%age
 in EPS
%age
 in Sales
Short-cut formula:
DCL = DOL x DFL
© 2003 McGraw-Hill Ryerson Limited

Calculating the Degree of Combined
Leverage
 DCL can be computed using the following formula:
DCL

Q ( P

VC )
Q ( P

VC )

FC

I
OR
DCL

S
S


TVC
TVC

FC

I
© 2003 McGraw-Hill Ryerson Limited

PPT 5-18
Operating, Financial and Combined Leverage under Leveraged
Plan
Sales (80,000 units @ $2) $160,000
Less: Variable costs ($0.80 per unit) 64,000
Contribution Margin 96,000
Less: Fixed costs 60,000
Earnings before interest and taxes
Less:Interest
$ 36,000
12,000
Earnings before taxes
Less:Taxes
Earnings aftertaxes
Shares
Earnings per share
24,000
12,000
$ 12,000
8,000
$1.50
Operating
Leverage
= 2.67
Financial
Leverage
= 1.5
Combined
Leverage=
4
© 2003 McGraw-Hill Ryerson Limited

Operating, Financial and Combined Leverage under Less
Leveraged (Conservative) Plan
PPT 5-18
Sales (80,000 units @ $2) $160,000
Less: Variable costs ($1.60 per unit) 128,000
Contribution Margin 32,000
Less: Fixed costs 12,000
Earnings before interest and taxes
Less:Interest
$ 20,000
4,000
Earnings before taxes
Less:Taxes
Earnings aftertaxes
Shares
Earnings per share
16,000
8,000
$ 8,000
24,000
$0.33
Operating
Leverage
= 1.6
Financial
Leverage
= 1.25
Combined
Leverage=
2
© 2003 McGraw-Hill Ryerson Limited

Calculating EBIT at Indifference Point

Level of EBIT where the firm’s EPS are equal between 2 financing plans
 This is computed using the following formula:
EBIT

( S
B *
I
A
S
B


S
A *
I
B
)
S
A
Where:
EBIT is the operating income at the indifference point
I is the interest cost under plan A and B
S is shares outstanding under plan A and B
© 2003 McGraw-Hill Ryerson Limited

PPT 5-22
Summary and Conclusions
 Leverage uses fixed costs to magnify the profits (or losses) of a business
 Operating leverage refers to fixed operating costs, such as lease or amortization expense
 The degree of operating leverage (DOL) measures the %age change in operating income from a %age change in sales
 Financial leverage refers to interest expense on debt
 The degree of financial leverage (DFL) measures the %age change in earnings from a %age change in operating income
 The higher the level of fixed costs, the greater the effect on net income of an increase in sales revenue (This is the degree of combined leverage (DCL) )
© 2003 McGraw-Hill Ryerson Limited