EMBA in Management & Finance
Corporate Finance
Eric Jondeau
EMBA in Management & Finance
Lecture 3:
Capital Structure
Modigliani and Miller
Eric Jondeau
Corporate Finance
Outline
1 The Capital-Structure Question
2 Financial Leverage and Firm Value
3 Modigliani - Miller Propositions (No Taxes)
4 Modigliani - Miller Propositions (With Taxes)
5 Summary and Conclusions
Eric Jondeau
EMBA
3/27
Corporate Finance
1. The Capital Structure Question
• The value of a firm is defined to be the sum of the value of the
firm’s debt and the firm’s equity.
• V=B+S
If the goal of the management of the
firm is to make the firm as valuable
as possible, then the firm should pick
the debt-equity ratio that makes the
pie as big as possible.
Eric Jondeau
EMBA
S
B
4/27
Corporate Finance
The Capital Structure Question
There are really two important questions:
1. Why should the stockholders care about maximizing
firm value? Perhaps they should be interested in
strategies that maximize shareholder value.
2. What is the ratio of debt-to-equity that maximizes the
shareholder’s value?
As it turns out, changes in capital structure benefit the
stockholders if and only if the value of the firm
increases.
Eric Jondeau
EMBA
5/27
Corporate Finance
2. Financial Leverage and Firm Value
Consider an all-equity firm that is considering going into debt.
(Maybe some of the original shareholders want to cash out.)
Current
Assets
$20,000
Debt
$0
Equity
$20,000
Debt/Equity ratio
0.00
Interest rate
n/a
Shares outstanding
400
Share price
$50
Eric Jondeau
EMBA
Proposed
$20,000
$8,000
$12,000
2/3
8%
240
$50
6/27
Corporate Finance
EPS and ROE under current capital structure
EBIT
Interest
Net income
EPS
ROA
ROE
Recession
$1,000
0
$1,000
$2.50
5%
5%
Expected
$2,000
0
$2,000
$5.00
10%
10%
Expansion
$3,000
0
$3,000
$7.50
15%
15%
Current Shares Outstanding = 400 shares
Eric Jondeau
EMBA
7/27
Corporate Finance
EPS and ROE under proposed capital structure
EBIT
Interest
Net income
EPS
ROA
ROE
Recession
$1,000
640
$360
$1.50
5%
3%
Expected
$2,000
640
$1,360
$5.67
10%
11%
Expansion
$3,000
640
$2,360
$9.83
15%
20%
Proposed Shares Outstanding = 240 shares
Eric Jondeau
EMBA
8/27
Corporate Finance
EPS and ROE under both capital structures
AllAll-Equity
Recession
EBIT
$1,000
Interest
0
Net income
$1,000
EPS
$2.50
ROA
5%
ROE
5%
Current Shares Outstanding = 400 shares
Levered
Recession
EBIT
$1,000
Interest
640
Net income
$360
EPS
$1.50
ROA
5%
ROE
3%
Proposed Shares Outstanding = 240 shares
Eric Jondeau
EMBA
Expected
$2,000
0
$2,000
$5.00
10%
10%
Expansion
$3,000
0
$3,000
$7.50
15%
15%
Expected
$2,000
640
$1,360
$5.67
10%
11%
Expansion
$3,000
640
$2,360
$9.83
15%
20%
9/27
Corporate Finance
Financial leverage and EPS
EPS 12.00
(dollars) 10.00
Debt
8.00
6.00
No Debt
Break-even
point
Advantage
to debt
4.00
Disadvantage
to debt
2.00
0.00
1,000
2,000
EBIT in dollars, no taxes
(2.00)
Eric Jondeau
3,000
EMBA
10/27
Corporate Finance
3. Modigliani-Miller Propositions (No Taxes)
Assumptions of the Modigliani-Miller model
• Homogeneous Expectations
• Homogeneous Business Risk Classes
• Perpetual Cash Flows
• Perfect Capital Markets:
–
–
–
–
–
Eric Jondeau
Perfect competition
Firms and investors can borrow/lend at the same rate
Equal access to all relevant information
No transaction costs
No taxes
EMBA
11/27
Corporate Finance
Homemade Leverage: An Example
Recession
EPS of Unlevered Firm
$2.50
Expected
$5.00
Earnings for 40 shares
$100
Less interest on $800 (8%) $64
Net Profits
$36
ROE (Net Profits / $1,200)
3%
$200
$64
$136
11%
Expansion
$7.50
$300
$64
$236
20%
We are buying 40 shares of a $50 stock on margin.
We get the same ROE as if we bought into a levered firm.
Our personal debt equity ratio is:
Eric Jondeau
B $800 2
=
=
S $1, 200 3
EMBA
12/27
Corporate Finance
Homemade (Un)Leverage: An Example
Recession
EPS of Levered Firm
$1.50
Expected Expansion
$5.67
$9.83
Earnings for 24 shares
$36
Plus interest on $800 (8%) $64
Net Profits
$100
ROE (Net Profits / $2,000)
5%
$136
$64
$200
10%
$236
$64
$300
15%
Buying 24 shares of an otherwise identical levered firm along
with the some of the firm’s debt gets us to the ROE of the
unlevered firm.
This is the fundamental insight of MM.
Eric Jondeau
EMBA
13/27
Corporate Finance
The MM Propositions I & II (No Taxes)
• Proposition I
– Firm value is not affected by leverage:
VL = VU
• Proposition II
– Leverage increases the risk and return to stockholders
rS = r0 + ( B / S L )(r0 − rB )
rB is the interest rate (cost of debt)
rS is the return on (levered) equity (cost of equity)
r0 is the return on unlevered equity (cost of capital)
SL is the value of levered equity
B is the value of debt
Eric Jondeau
r0 =
Expected earnings to unlevered firm
Unlevered equity
EMBA
14/27
Corporate Finance
The MM Proposition I – Derivation
Shareholders in a levered firm receive
EBIT − rB B
Bondholders receive
rB B
Total cash flow to all stakeholders: ( EBIT − rB B ) + rB B
The present value of this stream of cash flows is VL
Clearly
( EBIT − rB B) + rB B = EBIT
The present value of this stream of cash flows is VU
VL = VU
Eric Jondeau
EMBA
15/27
Corporate Finance
The MM Proposition II – Derivation
rWACC
B
S
=
rB +
rS
B+S
B+S
B
S
rB +
rS = r0
B+S
B+S
rWACC is constant for a firm regardless
of its capital structure. It is therefore
equal to the cost of capital for an allequity firm rWACC = r0 .
Multiply both sides by B + S
S
B+S B
B+S S
B+S
rB +
rS =
r0
S B+S
S B+S
S
B
B+S
rB + rS =
r0
S
S
B
B
rB + rS = r0 + r0
S
S
Eric Jondeau
B
rS = r0 + (r0 − rB )
S
EMBA
16/27
Corporate Finance
The MM Proposition II – Derivation
Cost of
Capital
r (%)
B
rS = r0 + (r0 − rB )
SL
rWACC
r0
B
S
=
rB +
rS
B + SL
B + SL
rB
rB
Debt-to-equity Ratio (B/S)
Eric Jondeau
EMBA
17/27
Corporate Finance
4. Modigliani-Miller Propositions (With Taxes)
• Proposition I (with Corporate Taxes)
– Firm value increases with leverage:
VL = VU + τ C B
• Proposition II (with Corporate Taxes)
– Some of the increase in equity risk and return is offset
by interest tax shield
rS = r0 + ( B / S L )(1 − τ C )(r0 − rB )
rB is the interest rate (cost of debt)
rS is the return on equity (cost of equity)
r0 is the return on unlevered equity (cost of capital)
B is the value of debt
S is the value of levered equity
Eric Jondeau
EMBA
18/27
Corporate Finance
The MM Proposition I – Derivation
Shareholders in a levered firm receive
( EBIT − rB B ) × (1 − τ C )
Bondholders receive
rB B
Total cash flow to all stakeholders: ( EBIT − rB B ) × (1 − τ C ) + rB B
The present value of this stream of cash flows is VL
Clearly ( EBIT − rB B ) × (1 − τ C ) + rB B
= EBIT × (1 − τ C ) − rB B × (1 − τ C ) + rB B
= EBIT × (1 − τ C ) + τ C rB B
The present value of the first term is VU
The present value of the second term is τCB
VL = VU + τ C B
Eric Jondeau
EMBA
19/27
Corporate Finance
The MM Proposition II – Derivation
Start with MM Proposition I with taxes: VL = VU + τ C B
Since
VL = S + B ⇒ S + B = VU + τ C B
VU = S + (1 − τ C ) B
The cash flows from each side of the balance sheet must equal:
SrS + BrB = VU r0 + Bτ C rB
SrS + BrB = [ S + B(1 − τ C )]r0 + Bτ C rB
Divide both sides by S
rS + BS rB = [1 + BS (1 − τ C )]r0 + BS τ C rB
which reduces to
Eric Jondeau
B
rS = r0 + (1 − τ C )(r0 − rB )
S
EMBA
20/27
Corporate Finance
The Effect of Financial Leverage with Corp Taxes
B
rS = r0 + (r0 − rB )
SL
B
rS = r0 + (1 − τ C )(r0 − rB )
SL
Cost of
Capital
r (%)
r0
rWACC =
SL
B
(1 − τ C )rB +
rS
B+SL
B + SL
rB
Debt-to-equity Ratio (B/S)
Eric Jondeau
EMBA
21/27
Corporate Finance
Total Cash Flow to Investors Under Each Capital
Structure with Corporate Taxes
All-Equity
EBIT
Interest
EBT
Taxes (35%)
Total Cash Flow to S/H
Recession
$1,000
0
$1,000
$350
$650
Expected
$2,000
0
$2,000
$700
$1,300
Expansion
$3,000
0
$3,000
$1,050
$1,950
Expected
$2,000
$640
$1,360
$476
$468+$640
$1,524
$1,300+$224
$1,524
Expansion
$3,000
$640
$2,360
$826
$1,534+$640
$2,174
$1,950+$224
$2,174
Levered
EBIT
Interest ($8000 at 8% )
EBT
Taxes (35%)
Total Cash Flow
(to both S/H & B/H):
EBIT(1-τC)+τCrBB
Eric Jondeau
Recession
$1,000
$640
$360
$126
$234+640
$874
$650+$224
$874
EMBA
22/27
Corporate Finance
Total Cash Flow to Investors Under Each Capital
Structure with Corporate Taxes
All-equity firm
Levered firm
G
G
S
S
B
The levered firm pays less in taxes than does the all-equity
firm.
Thus, the sum of the debt plus the equity of the levered firm is
greater than the equity of the unlevered firm.
Eric Jondeau
EMBA
23/27
Corporate Finance
Total Cash Flow to Investors Under Each Capital
Structure with Corporate Taxes
All-equity firm
Levered firm
G
G
S
S
B
The sum of the debt plus the equity of the levered firm is
greater than the equity of the unlevered firm.
This is how cutting the pie differently can make the pie larger:
the government takes a smaller slice of the pie!
Eric Jondeau
EMBA
24/27
Corporate Finance
Summary: No Taxes
• In a world of no taxes, the value of the firm is unaffected by
capital structure.
• This is MM Proposition I:
VL = VU
• Proposition I holds because shareholders can achieve any
pattern of payouts they desire with homemade leverage.
• In a world of no taxes, MM Proposition II states that
leverage increases the risk and return to stockholders
B
rS = r0 + (r0 − rB )
SL
Eric Jondeau
EMBA
25/27
Corporate Finance
Summary: Taxes
• In a world of taxes, but no bankruptcy costs, the value of the
firm increases with leverage.
• This is MM Proposition I:
VL = VU + τ C B
• Proposition I holds because shareholders can achieve any
pattern of payouts they desire with homemade leverage.
• In a world of taxes, MM Proposition II states that leverage
increases the risk and return to stockholders.
B
rS = r0 + (1 − τ C )(r0 − rB )
SL
Eric Jondeau
EMBA
26/27
Corporate Finance
Prospectus: Bankruptcy Costs
• So far, we have seen MM suggest that financial leverage
does not matter, or imply that taxes cause the optimal
financial structure to be 100% debt.
• In the real world, most executives do not like a capital
structure of 100% debt because that is a state known as
“bankruptcy”.
• In the next chapter we will introduce the notion of a limit
on the use of debt: financial distress.
• The important use of this session is to get comfortable
with “MM algebra”.
Eric Jondeau
EMBA
27/27