1 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)
Slide 2
2 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
Slide 3
3 16.1 The Definition What is capital structure? The pie 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? Firm value V = B (market
value of debt) + S (market value of equity) A capital structure
ratio: Debt- equity ratio: B/S
Slide 4
4 Cost of Equity Capital Review CAPM: Cost of equity = r S = r
f + [E(r M ) r f ] = Cov(r s,, r M ) / Var(r M ) Other sources of
funds: what if there is leverage? Cost of debt = r B = 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
Slide 5
5 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?
Slide 6
6 Example contd V increases to $380,000 V stays constant at
$350,000 V decreases to $320,000 S170,000 Shareholder gain from
dividend $50,000 Capital loss-80,000 Net gain/loss to shareholders
-30,000 Consider Three Possibilities: 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).
Slide 7
7 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 V U be the value of an unlevered firm (i.e., all equity
financing), and V L be the value of an otherwise identical levered
firm (i.e. some debt financing): V L = V U.
Slide 8
8 16.3 Proof of MM Proposition I (No taxes): V L = V U 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); V U = S U be the value of the unlevered firm,
and V L = S L + B L be the value of the levered firm. Consider an
investor who owns some fraction (e.g. 5%) of the shares of U: This
investor can get the same return by investing in L: If Vu > V L
the investor would not buy any shares in U since the same return is
available on a similar investment in L
Slide 9
9 Proof contd Consider an investor who owns of Ls equity This
investor can get the same return by investing in U and borrowing on
personal account: If V L > V U the investor would not buy any
shares in L since the same return is available on a smaller
investment in U
Slide 10
10 Proof contd We have shown that no one would buy shares in U
if V U > V L and that no one would buy shares if V L > V U
Therefore V U = V L 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.
Slide 11
11 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)
Slide 12
12 Example #1 Given V U = $100m, X = $10m, r = 5%, B L = $50m,
then MM Proposition I implies S L = 50M Suppose S L = $40m Suppose
S L = $60M
Slide 13
13 Example #2: Uncertain cash flows Current Assets$8,000 Debt$0
Equity$8,000 Debt/Equity ratio0 Interest raten/a Shares
outstanding400 Share price$20 Consider an all-equity firm, Trans
Can, that is considering going into debt. (Maybe some of the
original shareholders want to cash out.) Proposed (50% debt) $8,000
$4,000 1 10% 200 $20
Slide 14
14 Example #2 contd: Unlevered ROE Current Shares Outstanding =
400 shares RecessionExpansionExpected Probability0.50.5
EBI$400$2,000$1,200 Interest000 Net income$400$2,000$1,200
EPS$1.00$5.00 ROE5%25%
Slide 15
15 Example #2 contd: Levered ROE Proposed Shares Outstanding =
200 shares RecessionExpansionExpected Probability0.50.5
EBI$400$2,000$1,200 Interest(400)(400)(400) Net income01,600800
EPS0$8$4 ROE0%40%20%
Slide 16
16 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)
Slide 17
17 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.
RecessionExpansionExpected 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
Slide 18
18 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 = 20*100 = 2,000.
RecessionExpansionExpected 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:
Slide 19
19 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 V L V U there exists an arbitrage opportunity. By Law
of One Price the arbitrage opportunity will disappear
instantaneously. Suppose instead P L =21, so that S L = 4,200 and V
L = 8,200 > V U
Slide 20
20 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?
Slide 21
21 No arbitrage contd Cashflow (dividend income)
RecessionExpansionExpected Buy 50% of U (200 sh.)$200$1000$600
Short 50% of L (100 sh.)(400) Borrow 1,900 at 10% (190) Net
Profits10 ROE (Net Profits /0) + 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
Slide 22
22 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:
Slide 23
23 16.4 MM Proposition II: Cost of equity Define Since r 0 = r
WACC, we have This can be re-arranged to yield MM Proposition II
Leverage increases the risk and return to stockholders
Slide 24
24 Debt-to-equity Ratio Cost of capital: r (%) r0r0 rBrB rBrB
The Cost of Equity, the Cost of Debt, and the Weighted Average Cost
of Capital: MM Proposition II with No Corporate Taxes
Slide 25
25 Example #2 contd Cost of equity of unlevered firm r 0 =
expected earnings to unlevered firm/unlevered equity = 1200/8000 =
15% r s = Is this right: