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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

Debts currency denomination

Dividend, share repurchases, etc.

Risk management (e.g. interest rate hedging)

Etc.


MODIGLIANI-MILLER IRRELEVANCE THEOREM

Modigliani and Miller (1958, 1961)

Modigliani-Miller Theorem:Under some assumptions, a firms 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 firms cashflows do not depend on its financial policy (e.g. no bankruptcy costs)

4. No taxes

No point studying corporate financial policy


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 firms 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 firms value must equal that of the assets cashflow stream Intuition: Economic equivalent of the accounting identity between assets and liabilities

Consider identical firms with dierent financial policies: Same assets Same cashflow streams Same firm values


Remarks

The original propositions:

MM-Proposition I (MM 1958): A firms total market value is independent of its capital structure MM-Proposition II (MM 1958): A firms cost of equity increases with its debt-equity ratio Dividend Irrelevance (MM 1961): A firms total market value is independent of its dividend policy Investor Indierence (Stiglitz 1969): Individual investors are indierent to all firms financial policies

Dierent approaches:

MMs 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)


ILLUSTRATION: CAPITAL STRUCTURE

MM-Proposition I: A firms value is independent of its capital structure

At = 1 2 , firm 1 and firm 2 yield the same random cashflow At = 0, they have dierent 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 1s equityholders receive: Firm 2s debtholders receive: 2 Firm 2s equityholders receive: 2


Step 1: 1 2

Suppose 1 2 At = 0, an investor could: Short sell a fraction of firm 1s shares for 1 Keep (1 2) Use 2 to buy a fraction of firm 2s 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 sothat interest paid and received cancel out


Step 2: 2 1

Suppose 2 1 At = 0, an investor could: Short sell a fraction of firm 2s shares for 2 Borrow 2 The total is 2 + 2 = 2 Keep (2 1) Use 1 to buy a fraction of firm 1s 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 (homemadeleverage)


Note: Shareholders are Indierent 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 indierent?

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 indierent to the recap


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 (largelybusiness driven) but not the same dividends (more discretionary)


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?

MMs most basic message: Value is created only (i.e. in practice mostly) by operating assets, i.e. on LHS of B/S

A firms financial policy should be (mostly) a means to support the operating policy, not (gen-erally) an end in itself

MM helps you avoid first-order mistakes


MM vs. WACC FallacyDebt is Better Because Debt Is Cheaper Than Equity

Portfolio Nominal Real Risk Premium (over T-bills)Treasury bills 3.9 0.8 0.0Government bonds 5.7 2.7 1.8Corporate bonds 6.0 3.0 2.1Common stocks (S&P 500) 13.0 9.7 9.1Small-firm common stocks 17.3 13.8 13.4

Average rates of return 1926-2000 (in % per year)

A firms debt is (almost always) safer than its equity Investors demand a lower return for holdingdebt than for equity (True)

The dierence 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?


The firms 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 investorsdemand to hold it (NB: Even riskfree debt makes equity riskier, i.e. this is not about default risk)

MM-Proposition II: A firms cost of equity increases with its debt-equity ratio


MM vs. Win-Win FallacyDebt Is Better Because Some Investors Prefer Debt to Equity

Clientles Theory (or Financial Marketing Theory):

Dierent investors prefer dierent consumption streams They may prefer dierent financial assets Financial policy serves these dierent clientles

Example: All-equity firms might fail to exploit investors demands for safe and risky assets. It maybe 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 apremium 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


MM vs. EPS FallacyDebt 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


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)


USING MM SENSIBLY:ACADEMICS CORNER

MM is a paradigm shift, and the foundation of modern Corporate Finance Turn MMs 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 aects cashflows (e.g. bankruptcy costs + other ways in which RHS aects LHS)?

4. Taxes?

We are going to relax each assumption in turn


REFERENCES

(s) denotes surveys, books, syntheses, etc.

(s) Grinblatt, Mark, and Sheridan Titman (1998), Financial Markets and Corporate Strategy, Irwin/McGraw-Hill, chapter13.

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 ofBusiness, 34, 411-433.

Modigliani, Franco, and Merton Miller (1958), The Cost of Capital, Corporation Finance, and the Theory of Invest-ment, 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, FinancialManagement, 31, 101-115.


PROBLEMS

Problem 1 (MM Warm-up)

Unless otherwise specified, assume throughout that the Modigliani-Miller conditions hold. ABC Corp. has 2 million sharesoutstanding and no debt. Each year, it generates (on average) a cash flow of $96 which is paid out to shareholders asa regular dividend. ABC pays no taxes and its cost of capital is 12%. (Since ABC has no debt, this is also its expectedreturn on equity, which is also referred to as its cost of equity or cost of equity capital).a) What is ABCs stock price?ABCs CEO plans to borrow $8 and use the proceeds immediately to pay shareholders an exceptional dividend. Thislevel of debt would be riskfree. The riskfree rate is constant and equal to 5%. Answer the following, assuming thetransaction (borrowing + exceptional dividend) has already occurred.b) What is ABCs new stock price? Compare it to the initial stock price. Explain.c) Are ABCs shareholders happy about the CEOs change in policy?d) Assume that ABCs debt is perpetual, i.e., no principal is ever repaid.What is ABCs annual interest expense? Whatis the new average regular annual dividend per share? What is ABCs new expected return on equity? Compare it to theinitial 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 similarbusiness) exist that have dierent capital structures. This problem takes you through a proof of the theorem that doesnot 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 thefirms assets takes a random value and the firm is liquidated. The riskfree rate is . Assume there are no costs ofbankruptcy.a) Write the value of the firms debt and equity as well as the total firm value (debt plus equity) as a function of thoseof a risk-free bond and of a call and a put on the firms assets.


b) Use an arbitrage argument to prove MM Proposition I (i.e., the irrelevance of capital structure) without resorting toa 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 indierent to the firms capitalstructures (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, itgenerates a random cashflow . At = 0, individual s wealth is invested in risk-free corporate debt anda fraction of firm s equity. The risk-free rate is and the gross ris-free rate 1 + . Show that for any givenequilibrium, there exists another one with any firm having any other debt-equity ratio but with the value of all firmsand the risk-free rate being unchanged. That is, for any equilibrium with , and and for any , there exists anequilibrium with , and . Proceed as follows.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.c) Consider a change from to and assume that, indeed, and are unchanged. Show that the

are unchanged.

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 dierences 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. optionsto buy new equity, maturing at = 1. Show that for any given equilibrium, there exists another one with any firm issuingany 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)


Assume that the conditions for MM Proposition I are satisfied and that CAPM holds. MMs original Proposition II statesthat as a firms 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.


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