Capital Structure: Theory And Taxes
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Capital Structure
Can a firm increase its value by choosing the right mix of debt and
equity (i.e., the right capital structure) to finance its operations?
Capital structures vary across firms, industries, and
countries.
Is debt better than equity because it is cheaper?
Is equity better than debt because firms that borrow may go
bankrupt?
2
Evidence on Capital Structure
1) More profitable firms tend to use less leverage.
2) High-growth firms borrow less than mature
firms do.
3) Firms’ product market strategies and asset
bases influence capital structure choice.
4) Stock market generally views leverageincreasing events positively.
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5) Tax deductibility of interest gives firms an
incentive to use debt.
Market Value Debt Ratios, Selected
U.S. Corporations, July 2002
Debt to total
assets
L-T debt to
total capital
Market to
book ratio
Microsoft
0
0
5.54
Intel
0
0
4.03
ExxonMobil
0.04
0.03
3.72
Procter & Gamble
0.12
0.07
10.13
Boeing
0.27
0.24
3.65
Walt Disney
0.27
0.25
1.92
American Electric Power
0.54
0.36
1.62
Georgia Pacific
0.69
0.55
1.19
Delta Air Lines
0.77
0.75
0.82
General Motors
0.84
0.83
4.12
Company
Source: Firm-specific data taken from each company’s financial information at
http://money.cnn.com of June 12, 2002.
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Theoretical Models Of Capital
Structure
Modigliani and Miller’s (M&M) capital structure
model
The agency cost/tax shield trade-off model
The pecking order theory
The signaling model
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The M&M Capital Structure Model
First model to show that capital structure decision
may be irrelevant
Assumes perfect markets, no taxes or transactions
costs
Firm value is determined by:
Key insight
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Cash flows
generated
Underlying
business risk
Capital structure merely determines how cash flows and risks are
allocated between bondholders and stockholders.
M&M Proposition
Proposition I: Market value of a firm is driven by two factors:
cash flow and risk (determines the discount rate).
The mix of debt and equity merely determines how the cash flows and
the risks are divided.
NOI
V = E  D  =
r
D
rl  r  (r  rd )
E
Proposition II: The expected return on a levered firm’s equity,
rl, is a linear function of firm’s debt to equity ratio.
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Though the cost of debt is lower than the cost of equity, substituting
debt for equity causes the cost of equity to rise, negating any cost
savings from the switch.
M&M Proposition I
Use arbitrage arguments to prove proposition I
Proposition I: Market value of a firm is driven by two factors:
cash flow and risk (determines the discount rate).
Firms U and L belong to same risk class and have same
expected EBIT $2,000,000 per year in perpetuity.
Firm U has no debt.
Firm L has both debt and equity.
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Required return r for firms of this
risk class is 10%.
Under proposition I, market value of firms U and L should be identical.
M&M Proposition I
Market value of assets
should be $20,000,000
Earnings before interest (no taxes)
Required return on assets
Market value of assets
Debt
$2,000,000
10%
$2,000,000
10%
Firm U
Firm L
$2,000,000
$2,000,000
10%
10%
$20,000,000 $20,000,000
$0
Interest rate on debt
6%
Interest expense
Shares outstanding
Price per share
Market value of equity
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$10,000,000
$600,000
1,000,000
500,000
$20
$20
$20,000,000
$10,000,000
Market value of firm U = 1,000,000 x $20 = $20,000,000
Market value of firm L = 500,000 x $20 + $10,000,000 = $20,000,000
M&M Proposition I
What is the return the shareholders of the two firms expect on their
shares?
Firm U has no
debt
Required return on equity equals
required return on assets of 10%
Required return on equity = 10%
Firm L pays
$600,000 interest.
EBIT is
$2,000,000
Shareholders receive a cash
dividend of $1,400,000, or
$2.80/share. Share price = $20.
Required return on equity =
$2.80/$20 = 14%
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M&M Proposition I
What if the shares of the levered firm are selling at premium?
Firm L
Stock price
Total firm value
Debt value
$25
$20
$22,500,000
$20,000,000
$10,000,000
Shares outstanding
500,000
Dividend per share
$2.80
Required return on equity
0.112
0.14
Assume the stock price of
firm L is $25.
Total firm value increases
to $22,500,000.
The price of $25 per
share implies a return of
$2.80/$20 = 0.112.
Firm L stockholders can use “homemade leverage” to generate
arbitrage profit.
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M&M Proposition I
Assume investor
owns 5,000
shares of firm L
• The investor owns 1% of firm L.
• He earns $2.80 per share in dividends.
• The shares will generate $14,000 each
year.
The investor could earn an arbitrage profit from the
following:
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Sell 5,000 of firm L at $25 per share
• Proceeds of $125,000
Borrow an amount equal to 1% of
firm L debt
• $100,000 at 6% interest
Buy 1% of firm U equity
• 10,000 shares at $20 per
share
M&M Proposition I
Trades
Proceeds from stock sale
$125,000
Proceeds from borrowing
$100,000
Total proceeds
Cost of firm U shares
Net proceeds
The net return on
the new portfolio
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$225,000
-$200,000
$25,000
Using homemade
leverage, investor has
built a portfolio of
$200,000 of firm U's stock
and $100,000 in personal
debt. Investor has
$25,000 remaining.
• $2 dividend per share of firm U,
$20,000 for 10,000 shares
• $6,000 interest expense on borrowed
money
• $14,000 cash inflow next year on the
new portfolio
The same return expected on the original 1% stake in firm L's shares!
The cost of building this portfolio is just $200,000 , $25,000 less than
the cost of 5,000 firm L shares.
M&M Proposition II
Proposition II: The expected return on a levered firm’s equity is
a linear function of firm’s debt to equity ratio.
Required return on firm’s assets
D
rl = r + r - r d 
E
Required return on equity
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Required return on debt
Firm U return
on equity
rl = 0.10  0.10  rd  0  0.10
Firm L return
on equity
rl = 0.10  0.10  0.061  0.14
M&M Proposition II
Proposition II rearranged is just the WACC :
 E 
 D 
r  rl 
  rd 

DE
DE
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Firm U WACC
r = 0.10
Firm L WACC
1
1
rl = 0.14   0.06   0.10
2
2
If proposition II holds, WACC is independent of capital structure.
Firm’s Cost Of Equity Under M&M
Proposition II
Required
Return
rl (cost of equity)
WACC
r
rd (cost of debt)
D/E (debt to equity ratio)
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M&M with Taxes
1) Most countries allow firms to deduct interest as
an expense, but not dividends.
2) Deductibility lowers the after-tax cost of debt.
3) By using more debt, firms shelter more cash
flow from taxes.
4) Maximum firm value is reached at 100% debt.

Tc  rd  D 
PV interest t ax shields =
=T
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rd
c
D
Models Of Capital Structure:
With Corporate Income Taxes
Debt
25%
Taxes
25%
Equity
50%
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Equity
10%
Taxes
10%
Debt
80%
The M&M Model With Corporate
And Personal Taxes
Incorporating corporate income taxes yields a straightforward result: use 100% leverage.
This is not observed in the market. How can we explain
that firms use less than 100% debt?
•
Two obvious candidates: personal taxes and deadweight costs of
corporate bankruptcy
– Perhaps personal taxes offset corporate taxes.
– Direct bankruptcy costs are small, indirect costs are larger but not
large enough.
• Equity has a personal tax advantage (capital gains and sometimes
dividends taxed at lower rates than interest income).
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Miller (1977) And The Gain From
Leverage
Miller proposed a model where corporate tax benefits of
leverage are partially or fully offset by personal taxes.
Gains from
leverage

1 - T c  1 - T ps 
G L = 1 D
1 - T pd  

Tc = Tax rate on corporate profits
Tps = Personal tax rate on income from stock (capital gain and dividends)
Tpd = Personal tax rate on income from debt (interest income)
D = Market value of a firm's outstanding debt
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This is a general formulation. It includes original no-tax model as special
case, where GL=0. Also includes case with only corporate taxes.
Capital Structure: Theory And Taxes
Capital structures vary across firms, industries, and
countries
Modigliani and Miller showed that in a world of
frictionless capital markets capital structure is
irrelevant
Most of the assumptions of M&M model have been
successfully weakened