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)

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

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

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

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?

Example cont’d 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 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).

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.

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

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

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.

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)

Example #1 Given VU = $100m, X = $10m, r = 5%, BL = $50m, then MM Proposition I implies SL = 50M Suppose SL = $40m Suppose SL = $60M

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.) Proposed (50% debt) $8,000 $4,000 1 10% 200 $20 Current Assets $8,000 Debt $0 Equity $8,000 Debt/Equity ratio 0 Interest rate n/a Shares outstanding 400 Share price $20

Example #2 cont’d: 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%

Example #2 cont’d: 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%

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”)

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

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:

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

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?

No arbitrage cont’d 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) +∞ 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…

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:

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

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

Example #2 cont’d Cost of equity of unlevered firm r0 = expected earnings to unlevered firm/unlevered equity = 1200/8000 = 15% rs = Is this right:

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