Data Loading...
THE MODIGLIANI-MILLER THEOREM Overview Flipbook PDF
MODIGLIANI-MILLER IRRELEVANCE THEOREM Modigliani and Miller (1958, 1961) Modigliani-Miller Theorem: Under some assumptio
142 Views
80 Downloads
FLIP PDF 164.05KB
THE MODIGLIANI-MILLER THEOREM
Overview: • The Modigliani-Miller Theorem • Illustration: — Capital Structure — Dividend Policy • Using MM sensibly: — Practitioners — Academics
D. Gromb
The Modigliani-Miller Theorem
1
FINANCIAL POLICY
• Investment policy: Business decisions — CAPX — R&D — Etc.
• Financial policy: — Financing decisions: Internal funds (i.e. cash reserves), debt, trade credit, equity, etc. — Capital structure — Long-term vs. short-term debt — Floating vs. fixed interest rate debt — Debt’s currency denomination — Dividend, share repurchases, etc. — Risk management (e.g. interest rate hedging) — Etc.
D. Gromb
The Modigliani-Miller Theorem
2
MODIGLIANI-MILLER IRRELEVANCE THEOREM Modigliani and Miller (1958, 1961) Modigliani-Miller Theorem: Under some assumptions, a firm’s value is independent of its financial policy Assumptions: 1. Perfect financial markets: • Competitive: Individuals and firms are price-takers • Frictionless: No transaction costs, etc. • All agents are rational
2. All agents have the same information 3. A firm’s cashflows do not depend on its financial policy (e.g. no bankruptcy costs) 4. No taxes
• ⇒ No point studying corporate financial policy D. Gromb
The Modigliani-Miller Theorem
3
Proof • Value additivity: — Arbitrage opportunity: Ability to make a risk-free profit by trading financial claims — Equilibrium ⇒ No arbitrage opportunity ⇒ If and are risky cashflow streams ( + ) = () + ()
• Firm value: — By definition, a firm’s value is the sum of the values of all its financial claims — The cashflows all its claims receive must add up to the total cashflow its assets generate — Value additivity ⇒ The firm’s value must equal that of the assets’ cashflow stream
— Intuition: Economic equivalent of the accounting identity between assets and liabilities
• Consider identical firms with different financial policies: — Same assets ⇒ Same cashflow streams ⇒ Same firm values
D. Gromb
The Modigliani-Miller Theorem
4
Remarks
The original propositions: • MM-Proposition I (MM 1958): A firm’s total market value is independent of its capital structure • MM-Proposition II (MM 1958): A firm’s cost of equity increases with its debt-equity ratio • Dividend Irrelevance (MM 1961): A firm’s total market value is independent of its dividend policy • Investor Indifference (Stiglitz 1969): Individual investors are indifferent to all firms’ financial policies Different approaches: • MM’s proof requires two identical firms • Alternatives: — Arbitrage approach with a single firm (Miller 1988) — General Equilibrium approach (Stiglitz 1969) • Firm-level irrelevance does not imply aggregate indeterminacy (e.g. Miller 1977)
D. Gromb
The Modigliani-Miller Theorem
5
ILLUSTRATION: CAPITAL STRUCTURE MM-Proposition I: A firm’s value is independent of its capital structure • At = 1 2 , firm 1 and firm 2 yield the same random cashflow • At = 0, they have different capital structures: — Firm 1 has no debt — Firm 2 has equity and a constant level debt that is risk-free (for simplicity) • At = 0: — — — —
Risk-free rate, constant (for simplicity): Market value of firm ’s debt: Market value of firm ’s equity: Market value of firm : = +
• Hence, at = 1 2 — Firm 1’s equityholders receive: — Firm 2’s debtholders receive: 2 — Firm 2’s equityholders receive: − 2 D. Gromb
The Modigliani-Miller Theorem
6
Step 1: 1 ≤ 2 • Suppose 1 2 • At = 0, an investor could: — Short sell a fraction of firm 1’s shares for 1 — Keep (1 − 2)
— Use 2 to buy a fraction of firm 2’s debt and equity as: 2 = · 2 + · 2 • At = 0, the investor would get (1 − 2) 0 • At = 1 2, the investor would get: − + 2 + · ( − 2) = 0
for all
• ⇒ An arbitrage opportunity exists ⇒ Contradiction • Intuition: Arbitrageurs can “unlever” firm 2 by buying equal proportions of its debt and equity so that interest paid and received cancel out
D. Gromb
The Modigliani-Miller Theorem
7
Step 2: 2 ≤ 1 • Suppose 2 1 • At = 0, an investor could: — Short sell a fraction of firm 2’s shares for 2 — Borrow 2 — The total is 2 + 2 = 2 — Keep (2 − 1)
— Use 1 to buy a fraction of firm 1’s shares as: 1 + 1 = · 1 • At = 1 2 , the investor would receive: and pay interests × 2: − ( − 2) − 2 + = 0
for all
• ⇒ An arbitrage opportunity exists ⇒ Contradiction • Intuition: Arbitrageurs can “lever up” firm 1 by borrowing on their own accounts (“homemade leverage”)
D. Gromb
The Modigliani-Miller Theorem
8
Note: Shareholders are Indifferent to Capital Structure • Consider a firm with no debt: 1 ≡ 1 + 1 = 1 • Assume the firm undertakes a leveraged recapitalization (“recap”): — Borrow an amount 2 — Shareholders get a large dividend: = 2 — They also retain shares worth 2 • Shareholders use to own 100% of the firm • Now, they must share it with the debtholders, i.e. surely 2 1 • How can they be indifferent? • Without the recap, shareholders’ equity would be worth 1 • With the recap, they receive 2 + 2 — The equity is worth 2 — They receive a dividend = 2 • MM says 1 = 2 + 2 ⇒ Shareholders are indifferent to the recap D. Gromb
The Modigliani-Miller Theorem
9
ILLUSTRATION: DIVIDEND POLICY • Each “period”, the firm: — Invests (Investment Policy) — Raises new capital (Financing Policy) — Retains cash and pays dividends (Payout Policy)
• Accounting identity: — Taking investment as given, a change in payout has to be met by a change in financing — Example: A dividend increase/decrease can be financed with a new debt issue/retirement • Current and new investors trade among themselves ⇒ Total claims’ value is unchanged • Competitive investors ⇒ They break even ⇒ The current shareholders claims’ value is unchanged • Raises an important question: Why do firms pay dividends? • Good news for MM: The arbitrage proof requires the firms to have the same cashflows (largely business driven) but not the same dividends (more discretionary) D. Gromb
The Modigliani-Miller Theorem
10
USING MM SENSIBLY: PRACTITIONERS CORNER
• MM is not a literal statement about the real world • It obviously leaves important things out • But it gets you to ask the right question: How is this financial move going to change the size of the pie? • MM’s most basic message: — Value is created only (i.e. in practice mostly) by operating assets, i.e. on LHS of B/S — A firm’s financial policy should be (mostly) a means to support the operating policy, not (generally) an end in itself • MM helps you avoid first-order mistakes
D. Gromb
The Modigliani-Miller Theorem
11
MM vs. WACC Fallacy “Debt is Better Because Debt Is Cheaper Than Equity” Average rates of return 1926-2000 (in % per year) Portfolio Nominal Real Risk Premium (over T-bills) Treasury bills 3.9 0.8 0.0 Government bonds 5.7 2.7 1.8 Corporate bonds 6.0 3.0 2.1 Common stocks (S&P 500) 13.0 9.7 9.1 Small-firm common stocks 17.3 13.8 13.4
• A firm’s debt is (almost always) safer than its equity ⇒ Investors demand a lower return for holding debt than for equity (True) • The difference is significant: = 6% vs. = 13% expected return • Firms should always use debt finance because they have to give away less returns to investors, i.e. debt is a cheaper source of funds (False)
What is wrong with this argument? D. Gromb
The Modigliani-Miller Theorem
12
• The firm’s Weighted Average Cost of Capital (with no taxes) is: = • If is constant: =
+ + +
+∞ X =1
[] (1 + )
• [] and are independent of (MM Assumption and Prop. I) ⇒ So is WACC • Riskfree debt (for simplicity) ⇒ is linear in because: = ( − )
+
• In practice, (i.e. ) ⇒ increases with
• Intuition: Increasing debt makes existing equity more risky, increasing the expected return investors demand to hold it (NB: Even riskfree debt makes equity riskier, i.e. this is not about default risk)
MM-Proposition II: A firm’s cost of equity increases with its debt-equity ratio
D. Gromb
The Modigliani-Miller Theorem
13
MM vs. Win-Win Fallacy “Debt Is Better Because Some Investors Prefer Debt to Equity” Clientèles Theory (or Financial Marketing Theory): • Different investors prefer different consumption streams • ⇒ They may prefer different financial assets • ⇒ Financial policy serves these different clientèles • Example: All-equity firms might fail to exploit investors’ demands for safe and risky assets. It may be better to issue both debt and equity to allow investors to focus on their preferred asset mix Intuition for MM: • Investors’ preferences are over consumption, not assets • They (or intermediaries) can slice/dice/combine/retrade the firms’ securities • If investors can undertake the same transactions as firms, at the same prices, they will not pay a premium for firms to undertake them on their behalf ⇒ No value in financial marketing • NB: MM do not assume homogeneity but the preference-cashflow match need not be done by firms D. Gromb
The Modigliani-Miller Theorem
14
MM vs. EPS Fallacy “Debt is Better When It Makes EPS Go Up” • EPS can go up (or down) when a firm increases its leverage (True) • Firms should choose their financial policy to maximize their EPS (False) • EBI(T) is unchanged by a change in capital structure (Recall we assumed no taxes for now) • Creditors receive the safe (or the safest) part of EBIT • Expected EPS might increase but EPS has become riskier
• More generally, beware of accounting measures: They often fail to account for risk
D. Gromb
The Modigliani-Miller Theorem
15
MM vs. The “Bird-in-the-Hand” Fallacy
• Dividends now are safer than uncertain future payments (True) • ⇒ They increase firm value (False)
• MM show that this theory is flawed (“Bird-in-the-Hand” Fallacy)
D. Gromb
The Modigliani-Miller Theorem
16
USING MM SENSIBLY: ACADEMICS’ CORNER • MM is a paradigm shift, and the foundation of modern Corporate Finance • Turn MM’s result on its head • If we know what does not matter, we may be able to infer what does • One (or more) of the MM assumptions must be violated 1. Imperfect financial markets: • Markets are not perfectly competitive? • Transaction costs, short-sale constraints, ...? • Some investors are not fully rational 2. Information asymmetry? 3. Financial policy affects cashflows (e.g. bankruptcy costs + other ways in which RHS affects LHS)? 4. Taxes?
• We are going to relax each assumption in turn D. Gromb
The Modigliani-Miller Theorem
17
REFERENCES (s) denotes surveys, books, syntheses, etc. (s) Grinblatt, Mark, and Sheridan Titman (1998), Financial Markets and Corporate Strategy, Irwin/McGraw-Hill, chapter 13. Miller, Merton (1977), “Debt and Taxes,” Journal of Finance, 32, 261-276. (s) Miller, Merton (1988), “The Modigliani-Miller Propositions After Thirty Years,” Journal of Economic Perspective, 2, 99-120. (see the whole issue). Miller, Merton, and Franco Modigliani (1961), “Dividend Policy, Growth and the Valuation of Shares,” Journal of Business, 34, 411-433. Modigliani, Franco, and Merton Miller (1958), “The Cost of Capital, Corporation Finance, and the Theory of Investment,” American Economic Review, 48, 261-297. Stiglitz, Joseph E. (1969), “A Re-Examination of the Modigliani-Miller Theorem,” American Economic Review, 59, 784-793. Stiglitz, Joseph E. (1974), “On the Irrelevance of Corporate Financial Policy,” American Economic Review, 64, 851-866. Titman, Sheridan (2002), “The Modigliani and Miller Theorem and the Integration of Financial Markets,” Financial Management, 31, 101-115.
D. Gromb
The Modigliani-Miller Theorem
18
PROBLEMS Problem 1 (MM Warm-up) Unless otherwise specified, assume throughout that the Modigliani-Miller conditions hold. ABC Corp. has 2 million shares outstanding and no debt. Each year, it generates (on average) a cash flow of $96 which is paid out to shareholders as a regular dividend. ABC pays no taxes and its cost of capital is 12%. (Since ABC has no debt, this is also its expected return on equity, which is also referred to as its cost of equity or cost of equity capital). a) What is ABC’s stock price? ABC’s CEO plans to borrow $8 and use the proceeds immediately to pay shareholders an exceptional dividend. This level of debt would be riskfree. The riskfree rate is constant and equal to 5%. Answer the following, assuming the transaction (borrowing + exceptional dividend) has already occurred. b) What is ABC’s new stock price? Compare it to the initial stock price. Explain. c) Are ABC’s shareholders happy about the CEO’s change in policy? d) Assume that ABC’s debt is perpetual, i.e., no principal is ever repaid.What is ABC’s annual interest expense? What is the new average regular annual dividend per share? What is ABC’s new expected return on equity? Compare it to the initial 12% return. Explain. Problem 2 (MM, The Single-Firm Proof) The standard proof of the Modigliani-Miller Theorem assumes that for each firm, comparable firms (i.e. in a similar business) exist that have different capital structures. This problem takes you through a proof of the theorem that does not rely on the existence of comparable firms. Consider a firm at = 0 that has (possibly risky) debt with face value maturing at = 1. At = 1, the value of the firm’s assets takes a random value and the firm is liquidated. The riskfree rate is . Assume there are no costs of bankruptcy. a) Write the value of the firm’s debt and equity as well as the total firm value (debt plus equity) as a function of those of a risk-free bond and of a call and a put on the firm’s assets. D. Gromb
The Modigliani-Miller Theorem
19
b) Use an arbitrage argument to prove MM Proposition I (i.e., the irrelevance of capital structure) without resorting to a comparable firm. c) Compare this proof to the comparable-firms proof. What are, in your view, its main merits and weaknesses? Problem 3 (MM, The General Equilibrium Approach) This problem illustrates a version of MM in a static GE model, and that all agents are indifferent to the firms’ capital structures (in a sense to be clarified soon). Consider an economy with a set of firms and a set of individual investors. At = 0, firm ∈ has risk-free debt with value , equity with value and total value = + . At = 1, it generates a random cashflow . At = 0, individual ∈ ’s wealth is invested in risk-free corporate debt and a fraction of firm ’s equity. The risk-free rate is and the gross ris-free rate ≡ 1 + . Show that for any given equilibrium, there exists another one with any firm having any other debt-equity ratio but with the value of all firms ˆ , there exists an and the risk-free rate being unchanged. That is, for any equilibrium with , and and for any ˆ , and . Proceed as follows. equilibrium with a) Write individual ’s wealth at = 1, , as a function of , , and . b) Consider an equilibrium with , and . Write the market clearing conditions for firm ’s equity and risk-free debt. ˆ and assume that, indeed, and are unchanged. Show that the are unchanged. c) Consider a change from to d) Show that the equity markets and the debt market clear. e) Conclude. f) Does this imply the irrelevance of the aggregate capital structure, i.e. of the economy-wide debt-equity ratio? g) Compare this GE version of MM with the more standard arbitrage approach. What are the differences and similarities? What are, in your view, the relative strengths and weaknesses of the two approaches? h) Consider the same model as before but now suppose that, at = 0, the firms can also issue call warrants, i.e. options to buy new equity, maturing at = 1. Show that for any given equilibrium, there exists another one with any firm issuing any debt/equity and warrants/equity ratios but with the value of all firms and the risk-free rate being unchanged. Problem 4 (MM Proposition II and CAPM) D. Gromb
The Modigliani-Miller Theorem
20
Assume that the conditions for MM Proposition I are satisfied and that CAPM holds. MM’s original Proposition II states that as a firm’s cost of equity capital increases linearly with its debt-equity ratio (as long as debt remains risk-free). What is the implicit assumption about the firm for this to hold? Explain.
D. Gromb
The Modigliani-Miller Theorem
21