LECTURE15

# LECTURE15 - Lecture 15 Lecture Capital Structure Basic...

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Lecture 15 Lecture 15 Capital Structure Capital Structure

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Basic Concepts Focus on common stock and straight debt as representative financial instruments. We ignore default for now. The market value of the firm is V = B + S. 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 share- holders. Alternatively, if a firm borrows to pay a dividend, the increase in debt will reduce the market value of the equity. (dividends paid out) = (change in market value of B) (net value of the transaction to shareholders) = (change in market value of S) + (change in market value of B)
Modigliani-Miller Proposition I (MMI) The firm’s market value is independent of its capital structure, if Investors care only about risks and returns there is perfect competition everyone is price taker firms and investors (using equities as collateral) can borrow and lend at the same rate there is equal access to all relevant information there are no transaction costs or market frictions such as taxes, issue costs or bankruptcy costs All investors share common view of securities returns Capital markets are perfect in the sense that

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Proof of the Proposition MMI A proportion of the stock of an unlevered firm, paying annual earnings as dividends, will earn α E α E The value of an otherwise identical levered firm, with debt and equity , will be B L S B S V L L + = If the firm pays to bondholders, without default possibility. I ( 29 0 I E dividends - = A proportion of the equity gives α ( 29 ( 29 I E dividends - = α Investors can also engage in homemade leverage. They borrow on margin to buy of the equity in the unlevered firm at the cost , and get annual dividend income of α u V α E α
Proof of the Proposition MMI (continued) Assume their loans are of the total debt of the levered firm. α If the investors and levered firm pay the same interest rate, the annual interest cost of the loan will also be I α Net income from joint investment will be , which is identical to the income on of the outstanding equity of the levered firm. ( 29 I E - α α Net investment under the joint strategy is , and the investment in of levered firm equity costs . Hence, ( 29 B V u α α - α L S α L u S B V α α α = - L L u L u V B S V S B V = + = = -

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An Arbitrage argument for MMI Arbitrage opportunities would exist if the result did not hold : If , a portfolio, with zero net cash flow but positive value, could be created by buying stock and debt in the levered firm in the proportions issued, and shorting unlevered firm equity. L u V V If , a portfolio, with zero net cash flow but positive market value, could be created by buying the stock in the unlevered firm, borrowing on margin and shorting stock in the levered firm.
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