15_Oheads

15_Oheads - Lecture Notes 15 Capital Structure: Basic...

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1 Lecture Notes 15 Capital Structure: Basic Concepts • Focus on “common stock” and “straight debt” as “representa- tive” financial instruments. For now, we ignore default. • The market value of the firm is: V = B + S (1) Maximizing total firm value is in the interest of shareholders • Without bankruptcy, a change in firm value, leaving the level of debt and its characteristics unchanged, accrues to shareholders. • Alternatively, if a firm borrows to pay shareholders a dividend, the increase in debt will reduce the market value of the equity. • Dividends paid out = the change in the market value of the debt. • The net value of the transaction to shareholders = the change in the market value of S + the value of the dividends = the change in the market value of S + the change in the market value of B .
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2 Modigliani-Miller Proposition I • Modigliani-Miller proposition I states that the firm’s market val- ue is independent of its capital structure under the assumptions: i. Investors care only about risks and returns; ii. All investors share a common view of securities returns; iii. Capital markets are “perfect” in the sense that: a. there is perfect competition — everyone is a price taker; b. firms and investors (using equities as collateral) can borrow and lend at the same rate r B ; c. there is equal access to all relevant information; d. investors can sell equities short to arbitrage price differences; e. there are no transaction costs or market frictions such as taxes, issue costs or bankruptcy costs. 1. Proof of the Proposition • A proportion α of the stock of an unlevered firm paying annual earnings E as dividends will earn α E . • The value of an otherwise identical levered firm, with debt B and equity S L will be:
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3 V L = S L + B . (2) • If the firm pays I to bondholders, dividends = E I > 0 with de- fault impossible. A share α of the equity costs α S L and yields dividends α ( E - I ). • Investors can also engage in “homemade” leverage: i. They borrow on margin to buy α of the equity in the unlevered firm, at cost α V U , and giving annual dividend income of α E . ii. Assume their loans are α of the total debt of the levered firm (so “homemade” and firm leverage are the same proportions) . iii. If the investor and levered firm pay the same interest rate, the annual interest cost of the loan will also be α I . iv. Net income from the joint investment will be α ( E - I ), identical to the income on α of the outstanding equity of the levered firm. v. If there are to be no arbitrage profits, the two identical income flows have to sell at the same price. • Net investment under the joint strategy is α V U α B , investment in α of levered firm equity costs α S L . Hence,
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4 α V U α B = α S L (3) so, S L = V U B (4) that is, using (2) with (4), V U = S L + B = V L . (5) 2. Exploiting arbitrage opportunities if MMI did not hold • This is how arbitrage opportunities could be exploited if the re- sult did not hold: i. If V L > V U , a portfolio with zero net cash flow but positive mar-
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15_Oheads - Lecture Notes 15 Capital Structure: Basic...

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