CHAPTER 16: CAPITAL STRUCTURE – BASIC CONCEPTS
Topics:
– 16.1-16.2
– 16.3-16.4
The Basics
Capital Structure in Perfect Markets
• Modigliani and Miller: Proposition I (No Taxes)
• Modigliani and Miller: Proposition II (No Taxes)
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Nobel Price Winners in your Textbook
• Harry Markowitz (1990)
• William Sharpe (1990)
– CAPM
• Merton Miller (1990)
• Franco Modigliani (1985)
– Capital structure
• To come
– Myron Scholes (1997)
– Robert Merton (1997)
• Option pricing
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16.1 The Definition
•
•
What is capital structure?
The pie
S B
Firm value V = B (market value of
debt) + S (market value of equity)
A capital structure ratio: Debtequity ratio: B/S
•
Two Questions in Capital Structure
1. What happens to the cost of various sources of funds when
the capital structure is changed?
2. Is there an optimal capital structure?
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Cost of Equity Capital Review
• CAPM: Cost of equity = rS = rf+ β [E(rM) − rf]
– β= Cov(rs,, rM) / Var(rM)
• Other sources of funds: what if there is leverage?
– Cost of debt = rB = expected return on firm’s debt, i.e., the rate
of interest paid
– The weighted average cost of capital (WACC) is given by
• Note that for now we ignore the tax deductibility of interest
payments
• Read over chapters 11 and 13 to review these concepts
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16.2 Management objective revisited
• Objective of management: Maximizing S
• However, as long as there is no costs of bankruptcy,
maximizing S is equivalent to maximizing V
An example: Firm has 10,000 shares. Share price = $25. Debt has a
market value of $100,000.
V = B + S = 100,000 + 10,000 * 25 = 350,000
Now suppose firm borrows another $50,000 and pays it immediately
as a special dividend.
B = 100,000 + 50,000 = 150,000
What would be shareholder gain/loss if firm value changes?
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Example cont’d
Consider Three Possibilities:
V increases to
$380,000
V stays constant
at $350,000
S
Shareholder gain
from dividend
V decreases to
$320,000
170,000
$50,000
$50,000
$50,000
Capital loss
-80,000
Net gain/loss to
shareholders
-30,000
• Changes in capital structure benefit the stockholders if and only if the value
of the firm increases.
•Managers should choose the capital structure that they believe will have the
highest firm value (to make the pie as big as possible).
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What is the optimal capital structure, if any,
that maximizes firm value?
• Assume Perfect Capital Markets (PCM):
– Information is free and available to everyone on an equal
basis.
– No transaction costs
– No taxes
– No costs of bankruptcy
– Firms and investors can borrow / lend at the same rate
• MM Proposition I (no taxes): The market value of any
firm is independent of its capital structure.
– Let VU be the value of an “unlevered” firm (i.e., all equity
financing), and VL be the value of an otherwise identical
“levered” firm (i.e. some debt financing): VL = VU.
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16.3 Proof of MM Proposition I (No taxes): VL = VU
• Assume that all cash flows are perpetuities (just to make the
calculations easier). Let X be the identical cash flow stream generated
by each firm (i.e. U and L); VU = SU be the value of the unlevered firm,
and VL = SL + BL be the value of the levered firm.
• Consider an investor who owns some fraction α (e.g. 5%) of the shares
of U:
• This investor can get the same return by investing in L:
• If Vu > VL the investor would not buy any shares in U since the same
return is available on a similar investment in L
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Proof cont’d
• Consider an investor who owns α of L’s equity
• This investor can get the same return by investing in U and
borrowing on personal account:
• If VL > VU the investor would not buy any shares in L since
the same return is available on a smaller investment in U
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Proof cont’d
• We have shown that no one would buy shares in U if VU >
VL and that no one would buy shares if VL > VU
• Therefore VU = VL is the only solution consistent with
market equilibrium
• The same arguments apply to more complicated capital
structures
• The same arguments apply if cash flows are not perpetuities
and/or not constant.
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Some observations
• MM’s result is based on a no-arbitrage argument: if two
investments give the same future returns, they must cost the
same today
• A key (implicit) assumption is that individuals can borrow as
cheaply as corporations
– One way to do this is through buying stock on margin
– With a margin purchase, the broker lends the investor a
portion of the cost (e.g., to buy $10,000 of stock on 40%
margin, put up $6,000 of your own money and borrow $4,000
from the broker)
– Since the broker holds the stock as collateral, brokers
generally charge relatively low rates of interest
– Firms, on the other hand, often borrow using illiquid assets as
collateral (and get charged higher rates)
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Example #1
• Given VU = $100m, X = $10m, r = 5%, BL = $50m, then MM
Proposition I implies SL = 50M
• Suppose SL = $40m
• Suppose SL = $60M
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Example #2: Uncertain cash flows
Consider an all-equity firm, Trans Can, that is considering going
into debt. (Maybe some of the original shareholders want to cash
out.)
Assets
Debt
Equity
Debt/Equity ratio
Interest rate
Shares outstanding
Share price
Current
$8,000
$0
$8,000
0
n/a
400
$20
Proposed (50% debt)
$8,000
$4,000
$4,000
1
10%
200
$20
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Example #2 cont’d: Unlevered ROE
Current Shares Outstanding = 400 shares
Probability
EBI
Interest
Net income
EPS
ROE
Recession
0.5
$400
0
$400
$1.00
5%
Expansion
0.5
$2,000
0
$2,000
$5.00
25%
Expected
$1,200
0
$1,200
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Example #2 cont’d: Levered ROE
Proposed Shares Outstanding = 200 shares
Probability
EBI
Interest
Net income
EPS
ROE
Recession
0.5
$400
(400)
0
0
0%
Expansion
0.5
$2,000
(400)
1,600
$8
40%
Expected
$1,200
(400)
800
$4
20%
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Example #2 cont’d
• Since the expected ROE is higher under 50% debt, should
the firm switch to this capital structure?
• Not only have expected returns increased, but so has risk
• The MM argument is that it doesn’t matter, because
investors can effectively create the payoffs from the
alternative capital structure themselves (“homemade
leverage”)
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Example #2 cont’d: Replicate the higher EPS with only an
unlevered firm and borrowing: homemade leverage
Assume that you buy 200 shares of unlevered firm using $2,000 of
your own money and borrowing the rest $2,000 at 10% on margin
from your broker.
Recession Expansion
Expected
EPS of Unlevered Firm
$1
$5
$3
Earnings for 200 shares
$600
Less interest on $2000
(200)
Net Profits
$400
ROE (Net Profits / $2,000)
20%
Same ROE as if we bought into a levered firm! What’s the trick?
• Our personal debt equity ratio (personal leverage) is the same as
the levered equity
– Personal Debt contribution/equity contribution
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Example #2 cont’d: Law of One Price
Let’s call the portfolio in previous slide Strategy A. Suppose the investor
engages in the following alternate investment strategy (“Strategy A”) with
levered firm only:
• Buy 100 shares of levered firm. Also 50% of equity ownership. Initial
cost = 20*100 = 2,000.
Recession Expansion
Expected
EPS of Levered Firm
$0
$8
$4
Earnings for 100 shares
$0
$800
$400
ROE (Net Profits / $2,000)
0%
40%
20%
• Same initial investment & same ROE in every scenario:
– Value of strategy A must equal value of strategy B (Law of one
price).
– Or:
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How is no-arbitrage principle used in proving MM?
• Arbitrage opportunity, in principle, allows you to:
– have non-negative profit in every state of the world
with an initial investment of $0.
• We’ll show that if VL ≠ VU there exists an arbitrage
opportunity.
• By Law of One Price the arbitrage opportunity will
disappear instantaneously.
• Suppose instead PL=21, so that SL = 4,200 and VL =
8,200 > VU
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No arbitrage cont’d
• What to do?
– Buy low and sell high
• We consider a simple occasion where buy and sell involve same
percentage of equity
– Borrow or lend to make initial investment be zero
• Synthetic strategy:
(1) Buy low: buy 50% of U’s equity, costs 200 shares * 20 =
4,000
(2) Sell high: (short) sell 50% of L’s equity, proceeds 100 shares *
21 = 2,100
(3) Zero initial investment: borrow 1,900 at 10%.
• What’s my payoff?
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No arbitrage cont’d
Cashflow (dividend income)
Buy 50% of U (200 sh.)
Short 50% of L (100 sh.)
Borrow 1,900 at 10%
Net Profits
ROE (Net Profits /0)
Recession Expansion
$200
$1000
Expected
$600
(400)
(190)
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+∞
At time T, you clear your position by reversing (1) (2) (3) in the
previous slide and receive 0 back.
• I will make $ in every scenario with zero initial investment.
• But everyone else can do it…
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How does leverage affect shareholder returns?
• Note that from previous example that leverage increases the
expected return and risk of equity, even if there is no chance
of bankruptcy
• Recall the weighted average cost of capital formula
• MM proposition I implies that the WACC is constant (i.e.,
independent of capital structure)
• In the previous example:
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16.4 MM Proposition II: Cost of equity
• Define
• Since r0 = rWACC , we have
• This can be re-arranged to yield MM Proposition II
– Leverage increases the risk and return to stockholders
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Cost of capital: r (%)
The Cost of Equity, the Cost of Debt, and the Weighted Average
Cost of Capital: MM Proposition II with No Corporate Taxes
rS  r0 
r0
rW ACC 
rB
rB
B
 (r0  rB )
SL
B
S
 rB 
 rS
BS
BS
Debt-to-equity Ratio B
S
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Example #2 cont’d
• Cost of equity of unlevered firm
r0 = expected earnings to unlevered firm/unlevered equity
= 1200/8000 = 15%
15%  rW ACC 
B
S
 rB 
 rS
BS
BS
rs =
Is this right:
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• Assigned Problems # 16.2, 3, 4, 6, 8, 10, 11
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