CHAPTER 16: CAPITAL STRUCTURE

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CHAPTER 16 CAPITAL STRUCTURE BASIC CONCEPTS

• Topics
• 16.1-16.2 The Basics
• 16.3-16.4 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
• Two Questions in Capital Structure
• What happens to the cost of various sources of
  funds when the capital structure is changed?
• Is there an optimal capital structure?

Firm value V B (market value of debt) S
(market value of equity) A capital structure
ratio Debt-equity ratio B/S
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Cost of Equity Capital Review

• CAPM Cost of equity rS rf ß E(rM) - rf
• ß Cov(rs,, rM) / Var(rM)
• Other sources of funds what if there is
  leverage?
• Cost of debt rB expected return on firms
  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 contd
Consider Three Possibilities
V increases to 380,000 V stays constant at 350,000 V decreases to 320,000
S 170,000
Shareholder gain from dividend 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 a
  (e.g. 5) of the shares of U
• This investor can get the same return by
  investing in L
• If Vu gt 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 contd

• Consider an investor who owns a of Ls equity
• This investor can get the same return by
  investing in U and borrowing on personal account
• If VL gt 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 contd

• We have shown that no one would buy shares in U
  if VU gt VL and that no one would buy shares if VL
  gt 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

• MMs 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.)

• Current
• Assets 8,000
• Debt 0
• Equity 8,000
• Debt/Equity ratio 0
• Interest rate n/a
• Shares outstanding 400
• Share price 20

Proposed (50 debt) 8,000 4,
000 4,000 1 10 200 20
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Example 2 contd Unlevered ROE

• Current Shares Outstanding 400 shares
• Recession Expansion Expected
• Probability 0.5 0.5
• EBI 400 2,000 1,200
• Interest 0 0 0
• Net income 400 2,000 1,200
• EPS 1.00 5.00
• ROE 5 25

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Example 2 contd Levered ROE

• Proposed Shares Outstanding 200 shares
• Recession Expansion Expected
• Probability 0.5 0.5
• EBI 400 2,000 1,200
• Interest (400) (400) (400)
• Net income 0 1,600 800
• EPS 0 8 4
• ROE 0 40 20

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Example 2 contd

• 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 doesnt matter,
  because investors can effectively create the
  payoffs from the alternative capital structure
  themselves (homemade leverage)

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Example 2 contd 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!
  Whats 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 contd Law of One Price

• Lets 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 20100 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.
• Well show that if VL ? VU there exists an
  arbitrage opportunity.
• By Law of One Price the arbitrage opportunity
  will disappear instantaneously.
• Suppose instead PL21, so that SL 4,200 and VL
  8,200 gt VU

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No arbitrage contd

• 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 Us equity, costs 200
  shares 20 4,000
• (2) Sell high (short) sell 50 of Ls equity,
  proceeds 100 shares 21 2,100
• (3) Zero initial investment borrow 1,900 at
  10.
• Whats my payoff?

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No arbitrage contd

• Cashflow (dividend income)
• Recession Expansion Expected
• Buy 50 of U (200 sh.) 200 1000 600
• Short 50 of L (100 sh.) (400)
• Borrow 1,900 at 10 (190)
• Net Profits 10
• ROE (Net Profits /0) 8
• 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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The Cost of Equity, the Cost of Debt, and the
Weighted Average Cost of Capital MM Proposition
II with No Corporate Taxes
Cost of capital r ()
r0
rB
rB
Debt-to-equity Ratio
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Example 2 contd

• Cost of equity of unlevered firm
• r0 expected earnings to unlevered
  firm/unlevered equity
• 1200/8000 15
• rs
• Is this right

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• Assigned Problems 16.2, 3, 4, 6, 8, 10, 11