Chapte
16
Slides Developed by:
Terry Fegarty
Seneca College
Capital Structure and
Leverage
Chapter 16 – Outline (1)
• Background
 Capital Structure and Financial Leverage
 The Central Issue
 Risk in the Context of Leverage
• Financial Leverage
 Financial Leverage and Financial Risk
 Putting the Ideas Together—The Effect on Share
Price
 Real Investor Behavior and the Optimal Capital
Structure
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2
Chapter 16 – Outline (2)
 Finding the Optimum—A Practical Problem
 The Target Capital Structure
 The Degree of Financial Leverage (DFL)—A
Measurement
• EBIT-EPS Analysis
• Operating Leverage
 Breakeven Analysis
 The Effect of Operating Leverage
 The Degree of Operating Leverage (DOL)—A
Measurement
 Comparing Operating and Financial Leverage
 The Compounding Effect of Operating and Financial
Leverage
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3
Chapter 16 – Outline (3)
• Capital Structure Theory
Background—The Value of the Firm
The Early Theory by Modigliani and Miller
Relaxing the Assumptions—MM Theory with Taxes
Relaxing the Assumptions—MM Theory with Taxes
and Bankruptcy Costs
 Other Considerations




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4
Capital Structure and Financial
Leverage
• Capital structure: mix of firm’s debt and
common equity
 Preferred shares treated as part of firm’s debt
• Financial leverage: using borrowed money to
enhance effectiveness of invested equity
 Financial leverage of 10% means firm’s capital
structure contains 10% debt and 90% equity
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5
The Central Issue
• Can use of debt increase value of firm’s equity?
 Specifically, firm’s share price?
• Under certain conditions, changing leverage
increases share price
 An optimal capital structure maximizes share price
• Relationship between capital structure and
share price not precise nor fully understood
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6
Risk in the Context of Leverage
• Leverage influences share price
 Alters risk/return relationship in equity investment
• Measures of performance
 Earnings Before Interest and Taxes (EBIT)
• Unaffected by leverage because calculated prior to
deduction for interest
 Return on Equity (ROE)
• Net Income  Shareholders’ Equity
 Earnings per Share (EPS)
• Net Income  number of shares
• Investors regard EPS as important indicator of future
profitability
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7
Risk in the Context of Leverage
• Leverage-related risk is variation in
ROE and EPS
• Two components
 Business risk—variation in EBIT
• Influenced by operating leverage—presence of
fixed costs
 Financial risk—additional variation in ROE
and EPS from using financial leverage (debt)
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8
Figure 16.1:
Business and
Financial Risk
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9
Financial Leverage
• Under certain conditions, financial
leverage can improve firm’s EPS and ROE
 If shares are replaced with debt, number of
shares and equity are reduced, increasing
EPS and ROE
 May increase share price
• However, at other times it may worsen
EPS and ROE
• Financial leverage increases risk
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10
Effect of Increasing Financial
Leverage When the Return on Capital
Employed Exceeds the Cost of Debt
Table 16.1:
As the firm’s debt
ratio rises, both
EPS and ROE
rise dramatically.
While NI falls, the
number of shares
outstanding falls
at a faster rate as
debt replaces
equity.
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11
Financial Leverage
• Return on Capital Employed (ROCE)
 Measures profitability of operations before financing charges,
but after taxes, on basis comparable to ROE
ROCE =
E B IT  1 - tax rate 
debt + equity


When ROCE more than after-tax cost of debt, more
leverage improves ROE and EPS
 Increase borrowing?
When ROCE less than after-tax cost of debt, more
leverage makes ROE and EPS worse
 Avoid borrowing?
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12
Table 16.2: Effect of Increasing Financial
Leverage When the Cost of Debt
Exceeds the Return on Capital Employed
ABC is now
doing rather
poorly—ROE and
ROCE are quite
low. As the firm
adds leverage,
EPS and ROE
decrease.
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13
Example 16.1:
Financial Leverage
Q: Financial information for the Scanterbury Corporation follows:
Scanterbury Corporation at $10M Debt
($000 except for per-share amounts)
$23,700
EBIT
Debt
Example
Interest (@12%)
EBT
Tax (@40%)
NI
1,200
$22,500
9,000
Equity
$10,000
90,000
Capital
$100,000
Number of shares=
9,000,000
$13,500
Share price = $10
ROE = NI  equity = $13,500  $90,000 = 15%
EPS = Ni  number of shares = $13,500  9,000,000 = $1.50
Will borrowing more money and retiring shares raise EPS, and
if so what capital structure will achieve an EPS of $2.00?
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14
Example 16.1:
Financial Leverage
A: EPS will rise if ROCE exceeds the after-tax cost of debt.
ROCE

$23.7 M (1  0.4)
 14.2%
Example
100.0 M
The after-tax cost of debt is 12% x (1 – 0.4), or 7.2%. Since
7.2% < 14.2%, trading equity for debt will increase EPS.
Using trial and error, we can determine that $45 million of debt is
the approximate amount of debt that makes the firm’s EPS
equal $2.00.
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15
Financial Leverage—
An Alternate Approach
Example 16.1:
Example
A: If we set EPS to $2 we can solve for the value of Debt
$2 
$23.7M - (.12)(Debt )(1 - .4)
$100.0M - Debt
$ 10 
Debt  $45,156,25 0
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16
Financial Leverage and Financial
Risk
• Financial leverage is a two-edged sword
 Multiplies good results into great results
 Multiples bad results into terrible results
• Leverage magnifies changes in EBIT into
larger changes in ROE and EPS
• Financial risk is increased variability in
financial results that comes from
additional leverage
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17
Table 16.3:
Financial Leverage and
Risk
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18
Putting the Ideas Together—The
Effect on Share Price
• Leverage enhances performance while it
adds risk, pushing share prices in
opposite directions
 Enhanced performance makes expected
return on shares higher, driving up share’s
price
 Increased risk drives down share’s price
• Which effect dominates, and when?
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19
Real Investor Behavior and the
Optimal Capital Structure
• When leverage is low, increase in debt
has positive effect on investors
• At high debt levels, concerns about risk
dominate and adding more debt
decreases share’s price
• As leverage increases, effect goes from
positive to negative, which results in an
optimal capital structure
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The Effect of Leverage
on Share Price
Figure 16.2:
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21
Finding the Optimum—A Practical
Problem
• No way to determine exact optimum
amount of leverage for particular
company at particular time
 Appropriate level tends to vary according to
• Nature of company’s business
• If firm has high business risk it should use less leverage
• Economic climate
• If outlook is poor investors are likely to be more
sensitive to risk
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22
Finding the Optimum—A Practical
Problem
• General guidelines
 1. Profitable firm with little or no debt should
probably increase borrowing if interest rates
are reasonable
 2. For most businesses, optimal capital
structure is somewhere between 30% and
50% debt
 3. Debt levels above 60% create excessive
risk and should be avoided unless cash flows
are very stable (for example, those of a
public utility)
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The Target Capital Structure
• Firm’s target capital structure is
management’s estimate of optimal capital
structure
 An approximation as to amount of debt that
will maximize firm’s share price
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The Degree of Financial Leverage
(DFL)—A Measurement
• Financial leverage magnifies changes in EBIT
into larger changes in ROE and EPS
 The degree of financial leverage (DFL) relates
relative changes in EBIT to relative changes in EPS
DFL =

%  EPS
%  E B IT
o r %  E P S = D F L  %  E B IT
Somewhat
tedious
Easier method of calculating DFL is:
DFL =
E B IT
E B IT - In te re st
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The Degree of Financial
Leverage (DFL)—A Measurement
Example 16.2:
Q:
Selected income statement and capital information for the Mallaig
Manufacturing Company follow ($000):
Capital
Revenue
Example
Cost/expense
EBIT
$5,580
4,200
$1,380
Debt
Equity
Total
$1,000
7,000
$8,000
Currently 700,000 common shares are outstanding. The firm pays 15%
interest on its debt.. The income tax rate is 40%
Management is considering restructuring capital to 50% debt in the hope
that the increased EPS will have increase the price of its shares. Mallaig’s
shares sell for their book value of $10 per share.
Estimate the effect of the proposed restructuring on EPS. Then use the
degree of financial leverage to assess the increase in risk involved.
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The Degree of Financial
Leverage (DFL)—A Measurement
Example 16.2:
A:
Current
Proposed
Capital
$1,000
$4,000
7,000
4,000
Total
$8,000
$8,000
Shares outstanding
700,000
400,000
Debt
Example
Equity
Current
EBIT
Interest (15% of debt)
EBT
Tax (@40%)
NI
EPS
Proposed
$1,380
$1,380
150
600
$1,230
$780
492
312
$738
$468
$1.054
$1.170
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If business conditions
remain unchanged,
more debt will result
in a higher EPS
27
The Degree of Financial
Leverage (DFL)—A Measurement
Example 16.2:
A: Next, calculate DFL:
Example
D FL C urrent =
D FL P roposed =
$1,380
 1.12
$1,380 - $150
$1,380
 1.77
$1,380 - $600
EPS will be much more volatile under the proposed plan. EPS will change
by a factor of 1.77 vs. 1.12.
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EBIT-EPS Analysis
• Managers need way to quantify and analyze
tradeoffs between risk and results when
changing leverage levels
• Analysis provides graphical portrayal of the
trade-off
 Involves graphing EPS as function of EBIT for each
leverage level
• Portrays results of leverage and helps to decide
how much to use
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Graphical Analysis of EBIT - EPS
Debt
Financing
EPS
Advantage to
equity financing
Equity
Financing
Advantage to
debt financing
EBIT
Indifference
Point
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Figure 16.3:
EBIT – EPS Analysis for
ABC Corporation
(from Table 13.1, Columns 1 and 2)
The
indifference
point occurs
when the
two plans
offer the
same EBIT
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The 50% Debt and
No Leverage lines
intersect. At the
point of intersection
ABC is indifferent
between the two
plans. To the left of
the intersection the
50% Debt plan is
preferable. To the
right of the point
the No Leverage
plan is preferable.
31
EBIT-EPS Analysis
• Comparing two capital structures,
indifference point is level of EBIT
where EPS is same under both
(E B IT - I )(1- T )
EPS=
N um ber of shares
Capital Structure A
Capital Structure B
(E B IT - I )(1- T )
(E B IT - I )(1- T )
=
N um ber of shares
N um ber of shares
Solve for EBIT
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EBIT-EPS Analysis
Example
For ABC Corporation:
No Leverage
50% Debt
(E B IT -$0)(1-0.4)
(EBIT -$50,000)(1-0.4)
100,000
=
50,000
EBIT = $100,000
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Operating Leverage
• Terminology and Definitions
 Business Risk—Risk in Operations
• Defined as variation in EBIT
• Most is caused by changes in sales level
 Fixed and Variable Costs and Cost Structure
• Fixed costs don’t change with level of sales,
while variable costs do
• Fixed costs include rent, amortization, utilities, salaries
• Variable costs include direct labour, direct materials,
sales commissions
• Mix of fixed and variable costs in a firm’s
operations is its cost structure
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Figure 16.4:
Fixed, Variable, and
Total Cost
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Operating Leverage
• Terminology and Definitions
 Operating Leverage
• Refers to amount of fixed costs in the cost
structure
• Increases business risk
• May combine with financial leverage for very
volatile ROE and EPS
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Breakeven Analysis
• Used to determine level of activity firm
must achieve to stay in business in long
run
• Shows mix of fixed and variable cost and
volume required for zero profit/loss
 Profit/loss generally measured by EBIT
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Breakeven Analysis
• Breakeven Diagrams
 Breakeven occurs at intersection of revenue
and total cost
• Represents level of sales at which revenue equals
cost
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Figure 16.5:
The Breakeven
Diagram
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Breakeven Analysis
• The Contribution Margin
 Every sale makes contribution (Ct) of
difference between price (P) and variable
cost (V)
• Ct = P – V
 Can be expressed as percentage of revenue
• Known as contribution margin (CM)
(P -V )
CM =
P
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Example
Example 16.3:
Breakeven Analysis
Q: Suppose a company can make a unit of product for $7 in
variable labour and materials, and sell it for $10. What are the
contribution and contribution margin?
A: The contribution per unit is $3, or $10 - $7, while the contribution
margin is $3  $10, or 30%.
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Breakeven Analysis
• Calculating Breakeven Sales Level
 EBIT is revenue minus cost, or
• EBIT = PQ – VQ – FC
 Breakeven occurs when revenue (PQ) equals
total cost (VQ + FC), or
Q BE =
FC
(P -V )
 Breakeven tells us how many units
have to be sold to contribute
enough money to pay for fixed costs
 Can also be expressed in terms of dollar sales
S BE =
P (FC )
(P -V )
=
FC
CM
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Example
Example 16.4:
Breakeven Analysis
Q: What is the breakeven sales level in units and dollars for a
company that can make a unit of product for $7 in variable costs
and sell it for $10, if the firm has fixed costs of $1,800 per
month?
A: The breakeven point in units is $1,800  ($10 - $7) = 600 units.
The breakeven point in dollars is $10 per unit times 600 units, or
$6,000, which could also be calculated as $1,800  0.30. Thus,
the firm must sell 600 units per month to cover fixed costs.
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The Effect of Operating Leverage
• As sales volume moves away from breakeven,
profit or loss increases faster with more
operating leverage
• The Risk Effect
 More operating leverage leads to larger variations in
EBIT, or business risk
• The Effect on Expected EBIT
 Above breakeven, more operating leverage implies
higher operating profit
• If firm is relatively sure of sales level, should
trade variable costs for fixed cost
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Breakeven at Low Operating
Leverage
Low Fixed Costs with High Variable Costs
Low Breakeven; Profits/Losses Increase Slowly
Revenue
Dollars
Profit
Variable
Cost
Breakeven
Quantity
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Total
Cost
Fixed
Cost
Quantity
45
Breakeven at High Operating
Leverage
High Fixed Costs with Low Variable Costs
High Breakeven; Profits/Losses Increase Quickly
Revenue
Dollars
Profit
Total
Cost
Variable Cost
Fixed Cost
Breakeven
Quantity
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Quantity
46
The Effect of
Operating Leverage
Example 16.5:
Example
Q: Suppose Firm A has fixed costs of $1,000 per period, sells its
product for $10, and has variable costs of $8 per unit. Further,
suppose Firm B has fixed costs of $1,500 and also sells its
product for $10 a unit. Both firms are at the same breakeven
point.
What variable cost must Firm B have if it is to achieve the same
breakeven point as Firm A? State the trade-off at the breakeven
point.
Which structure is preferred if there’s a choice?
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The Effect of
Operating Leverage
Example 16.5:
Example
A: Both firms have a breakeven point of 500 units (Firm A: $1,000  $2).
We need to solve the breakeven formula for Firm B’s variable costs per
unit:
QB/E = FC  (P – V)
500 units = $1,500  ($10 – V)
V = $7
Change in V = $8 - $7 = $1
Thus, at breakeven, a $1
differential in contribution
makes up for a $500
difference in fixed cost.
The preferred structure depends on volatility—if sales are expected to
be highly volatile, the lower fixed cost structure might be better in the
long run.
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The Degree of Operating Leverage
(DOL)—A Measurement
• Operating leverage amplifies changes in
sales volume into larger changes in EBIT
• DOL relates relative changes in volume
(Q) to relative changes in EBIT
DOL =
%  E B IT
%  Q
or
or
Q (P - V )
Q (P - V ) - FC
CM
E B IT
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Example 16.6: The Degree of Operating
Example
Leverage (DOL)—A Measurement
Q: The Cowichan Corp. sells its products at an average price of $10. Variable
costs are $7 per unit and fixed costs are $600 per month. Evaluate the
degree of operating leverage when sales are 5% and then 50% above the
breakeven level.
A: Breakeven volume = $600  ($10 - $7) = 200 units.
Breakeven plus 5% = 200 x 1.05 or 210 units
Breakeven plus 50% = 200 x 1.50 or 300 units.
DOL at 210 units is:
D O L Q =210 =
210($10 - $7)
 21
210($10 - $7) - $600
DOL at 300 units is:
D O L Q =300 =
300($10 - $7)
3
300($10 - $7) - $600
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DOL decreases
as the output level
increases above
breakeven.
50
Comparing Operating and
Financial Leverage
• Both operating and financial leverage can
enhance results while increasing variation
 Operating leverage magnifies changes in
sales into larger changes in EBIT
 Financial leverage magnifies changes in EBIT
into larger changes in ROE and EPS
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Comparing Operating and
Financial Leverage
• Both methods substitute fixed cash
outflows for variable cash outflows
 Operating leverage substitutes fixed costs for
variable costs in cost structure
 Financial leverage involves substitutes fixed
interest on debt for discretionary dividends
on shares in capital structure
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Comparing Operating and
Financial Leverage
• Both kinds of leverage increase risks as
the levels of leverage increase
 However, no financial risk if no debt
 Business risk would still exist even if no
operating leverage
• Financial leverage is more controllable
than operating leverage
 Debt used at management’s discretion
 Technology may require fixed costs
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Figure 16.7: The
Similar Functions of
Operating and Financial Leverage
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The Compounding Effect of
Operating and Financial Leverage
• Effects of financial and operating leverage
compound one another
• Changes in sales are amplified by operating
leverage into larger relative changes in EBIT
 Which in turn are amplified by financial leverage
into still larger relative changes in ROE and EPS
 Modest changes in sales can lead to dramatic
changes in ROE and EPS
• The combined effect can be measured using
degree of total leverage (DTL)
 DTL = DOL × DFL
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Risk and Cost Relationships
Between Operating and Financial
Leverage
Figure 16.8:
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56
The Compounding Effect of Operating
Leverage and Financial Leverage
Type of
leverage
% Change
in
Operating
Financial
Total
Sales
EBIT
Sales
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Causes a
bigger %
change in
EBIT
EPS
EPS
57
Degree of Total Leverage
%
Change
in Sales
%
Change
in EBIT
DOL
DFL
%
Change
in EPS
DTL
DTL
Low
High
Small EPS
change
Large EPS
change
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Example 16.7: The Compounding Effect
of Operating and Financial Leverage
Example
Q: The Carragana Company is considering replacing a manual production
process with a machine. The money to buy the machine will be
borrowed. The firm’s cost structure will be altered in favour of fixed
cost. The capital structure will include more debt. Leverage positions
with and without the project are:
DOL
DFL
Current
2.0
1.5
Proposed
3.5
2.5
The economic outlook is uncertain and some managers fear a decline
in sales of as much as 10% in the coming year.
Evaluate the effect of the proposed project on risk in financial
performance.
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Example 16.7: The Compounding Effect
Example
of Operating and Financial Leverage
A: The firm’s current DTL is 2 x 1.5 = 3.
A 10% decline in sales could result in a 30% decline in EPS.
Under the proposal, the DTL will be 3.5 x 2.5 = 8.75.
A 10% drop in sales could lead to a 87.5% drop in EPS.
DTL
Current
Proposed
∆EPS
3
30%
8.75
87.5%
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60
Capital Structure Theory
• Studies the relationship between:
 Capital structure
• Mix of debt & equity securities in capital
 Cost of capital
• Return demanded by investors
• Impacts on value of firm
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61
Capital Structure Theory
• Does capital structure affect share price
and market value of firm?
• If so, is there optimal capital structure
that:
 Minimizes firm’s weighted average cost of
capital (WACC)?
 Maximizes share price and value of firm?
 Or both?
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62
Background—The Value of the
Firm
• Notation
 Vd = market value of firm’s debt
 Ve = market value of firm’s shares or equity
 Vf = market value of firm in total
• Vf = Vd + Ve
• Investors’ returns on firm’s securities will be
 kd = return on investment in debt
 ke = return on investment in equity
• Theory begins by assuming a world without taxes or
transaction costs
 Investors’ returns are exactly component capital costs
 ka = average cost of capital
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63
Background—The Value of the
Firm
• Value (Vf ) is based on cash flow which comes
from income (Operating income or OI)
 Earnings ultimately determine value because all cash
flows paid to investors come from earnings
 Consists of dividends (D) and interest payments (I)
(both assumed to be perpetuities)
• The firm’s market value is the sum of their present values
Vf =
I
kd
+
D
ke
=
OI
ka
Returns drive value
in an inverse
relationship.
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64
Figure 16.10: Variation in Value and
Average Return with Capital Structure
The value of the firm
and the firm’s share
price reach a
maximum when the
average cost of capital
is minimized.
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65
The Early Theory by Modigliani
and Miller
• Modigliani & Miller (MM) were the
pioneers in developing the theory of
capital structure
• MM began by assuming perfect capital
markets
• MM also recognized that debt will always
cost less than equity because:
 Interest is tax deductible
 Debt securities are less risky than equity
securities
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66
The Early Theory by Modigliani
and Miller
• Restrictive Assumptions in the Original
Model (1958)
 No income taxes
 Securities trade in perfectly efficient capital
markets with no transaction costs
 No bankruptcy costs
• No administrative costs
• No losses on sale of assets
 Investors and companies can borrow as
much as they want at same interest rate
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MM’s Two Propositions
• Under MM’s initial set of restrictions:
• Proposition #1:
 Market value of firm is independent of capital
structure. Therefore, capital structure is irrelevant
• The independence hypothesis
• Proposition #2:
 The cost of capital remains constant as capital
structure changes. As quantity of debt rises, return
demanded by shareholders increases because of
increased risk, exactly offsetting benefit due to the
lower cost of debt
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68
Figure 16.11:
The Independence
Hypothesis
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The Early Theory by Modigliani
and Miller
• The Arbitrage Concept
 Arbitrage means making profit by buying and
selling same thing at same time in two different
markets
 MM proposed that arbitrage by equity investors
would hold value of firm constant as debt levels
changed
• If adding leverage increased value of firm, equity investors
could maximize returns by selling shares and borrowing to
buy shares in unleveraged firm
• Would lower price of leveraged firm and raise price of
unleveraged firm
• Value of firm should be constant as leverage increases
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The Early Theory by Modigliani
and Miller
• The Assumptions and Reality
 Realistically income taxes exist
 Realistically costs of bankruptcy are quite large
 Realistically individuals cannot borrow at the same
rate as companies and interest rates usually rise as
more money is borrowed
• Interpreting MM Result
 Leverage does affect value because of market
imperfections
• Such as taxes and transaction costs (including bankruptcy)
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Relaxing the Assumptions—MM
Theory with Taxes
• Financing and the Tax System
 Tax system favours debt financing over
equity financing
• Interest expense on debt is tax deductible while
dividends on shares are not
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72
Table 16.4:
The Tax System Favours
Debt Financing
The All Equity firm
pays more taxes
because it receives
no interest expense
deduction.
Total payments to
investors are higher
for the leveraged
company.
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73
Relaxing the Assumptions—MM
Theory with Taxes
• Including Corporate Taxes in the MM
Theory
 When taxes exist, operating income (OI) split
between investors and government
• Reduces firm’s value
• Amount of reduction depends on firm’s use of leverage
(debt)
• Interest on debt reduces taxable income which
reduces taxes
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74
Relaxing the Assumptions—MM
Theory with Taxes
• Interest provides tax shield that reduces
government’s share of firm’s earnings
 When firm uses debt financing, government’s take is
reduced by (corporate tax rate × interest expense)
every year
• Present value of tax shield = (corporate tax rate × interest
expense)  kd
• Since interest expense is amount of debt (B) times interest
rate on debt, equation can be written as
P V of tax shield =
corporate tax rate x B x k d
= TB
kd
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75
Relaxing the Assumptions—MM
Theory with Taxes
• Having debt in capital structure increases
firm’s value by amount of debt times tax
rate
• Benefit of debt accrues entirely to
shareholders because bond returns are
fixed
• In theory, firm can increase value of
shares by replacing equity with debt
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76
Figure 16.12:
MM Theory with Taxes
In the MM model with taxes, value
increases steadily as leverage is
added. Thus, the firm’s value is
maximized with 100% debt. Note
that kd remains constant across
all levels of debt.
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77
Relaxing the Assumptions—MM
Theory with Taxes
• If the value of firm increases with debt,
should conclusion be that all firms should
be financed with 100% debt?
• Conclusion defies logic and is counter to
customary practice
• What are we missing?
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Relaxing the Assumptions—MM Theory
with Taxes and Bankruptcy Costs
• As leverage increases past a certain point,
probability of bankruptcy failure increases
 Investors raise required rates of return
 However, effect on cost of capital offset by growing
tax shield
• Eventually average cost of capital will be
minimized and firm value will be maximized
 This is optimal capital structure
 Additional leverage beyond this point increases cost
of capital and reduces value
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MM Theory with Taxes
and Bankruptcy Costs
Figure 16.13:
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80
Other Considerations
• Industry effects
 Firms with stable cash flows tend to have
more debt
 More profitable firms tend to have less debt
ratios
 Market appears to reward firms with capital
structures appropriate to their industry
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