# Summary Modigliani & Miller

L1 – Modigliani & Miller (1958) ‘The Cost of Capital, Corporation Finance and the Theory of Investment’ This article mainly discusses the cost of capital, the required return necessary to make a capital budgeting project worthwhile.Cost of capital includes the cost of debt and the cost of equity.Theorist conclude that the cost of capital to the owners of a firm is simply the rate of interest on bonds.

**Summary Modigliani & Miller**

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In a world without uncertainty the rational approach would be (1) to maximize profits and (2) to maximize market value.

When uncertainty arises, these statements vanish and change into a utility maximization. The goal is to get more insight in the effect of financial structure on market valuations. I. Valuation of Securities, Leverage and the Cost of Capital A. The Capitalization Rate for Uncertain Streams In the paper, M&M (1958) assume that firms can be divided into equivalent return classes such that the return on the shares issued by any firm in any given class is proportional to the return on shares issued by any other firm in the same class.

This implies that various shares within the same class can differ at most by a scale factor. The significance of this assumption is that it permits us to clarify firms into groups where shares of different firms are homogeneous (perfect substitutes of each other). This again means that in equilibrium in a perfect capital market the price per dollars worth of expected return must be the same for all shares of any given class. This will result in the following formula’s: = pj = the price xj = expected return per share of the firm in class k k= expected rate of return of any share in class k 1/pk = the price which an investor has to pay for a dollars worth of expected return in the class k B. Debt Financing and its Effects on Security Prices In this case, shares will be subject to different degrees of financial risk or leverage and hence will no longer be perfect substitutes for each other. Companies will have different proportions of debt in their capital structure and gives a different probability distribution of returns.

To exhibit the mechanism determining the relative price of shares under these conditions two assumption are made 1)all bonds yield a constant income per unit of time 2)bonds, like stocks, are trade in perfect market (perfect substitutes) Proposition 1 ‘The value of an unlevered firm is the same as the value of a levered firm’ V = value of the firm S = market value of common stock D = market value of the debts X = expected return on the assets owned by the company (cost of capital)

The market value of any firm is independent of its capital structure and is given by capitalizing its expected return at the rate pk appropriate to its class. This shows that the average cost of capital to any firm is completely independent of its capital structure and is equal to the capitalisation rate of a pure equity stream of its class. Capitalization rate (or “cap rate”) is a measure of the ratio between the net operating income produced by an asset (usually real estate) and its capital cost (the original price paid to buy the asset) or alternatively its current market value.

The pure equity stream is showed in the next example: If proposition 1 did not hold, an investor could buy and sell stocks and bonds in such a way as to exchange one income stream for another stream, but selling at a lower price. It would be corrected through arbitrage. Return on a levered portfolio can be written as: Y2 = return from this (levered) portfolio ? = fraction of the income available for the stockholders of the company/fraction total shares outstanding X = expected return rD2 = interest charge Return on a unlevered portfolio looks like this: 1 = fraction/amount invested in stocks S1 = total stocks outstanding To see why this should be true, suppose an investor is considering buying one of the two firms U or L. Instead of purchasing the shares of the levered firm L, he could purchase the shares of firm U and borrow the same amount of money D that firm L does. The eventual returns to either of these investments would be the same. Therefore, the price of L must be the same as the price of U minus the money borrowed D, which is the value of L’s debt. Proposition 2 > re = ro + (ro – rd) x D/E = required rate of return on equity (cost of equity) pk = cost of capital for an all equity firm r = required rate of return on borrowings (i. e. , cost of debt or interest rate) D/S = debt to equity ratio That is, the expected yield of a share of stock is equal to the appropriate capitalization rate pk for a pure equity stream in the class, plus a premium related to financial risk equal to the debt-to-equity ratio time the spread between pk and r. C. Some Qualifications and Extensions of the Basic Propositions Effects of Present Method of Taxing Corporations

Proposition 1 becomes (with taxes): ? = average rate of corporate income tax ? = expected net income accruing to the common stock holder Proposition 2 becomes (with taxes): pk can no longer be indentified with the average cost of capital when taxes come into play. Yet, to simplify things the writers will still do this. Effects of a Plurality of Bonds and Interest Rates Economic theory and market experience both suggest that the yields demanded by lenders tend to increase with the debt-equity ratio of the borrowing firm (or individual).

The increased cost of borrowed funds as leverage increases will tend to be offset by a corresponding reduction in the yield of common stock. Proposition 1 remains unaffected as long as the yield curve is the same for all borrowers. However, the relation between common stock yields and leverage will no longer be the strictly linear one given by the original Proposition 2. If r increases with leverage, the yield i will still tend to rise as D/S increases, but at a decreasing rather than a constant rate. Yield curve: D. The Relation of Propositions 1 en 2 to Current Doctrines.

Proposition 1 asserts that the average cost of capital is a constant for all firms j in class k, independently of their financial structure. II. Implications of the Analysis for the Theory of Investments A. Capital Structure and Investment Policy Proposition 3 (Proposition 4 in lecture slides): A firm will exploit investment opportunities if and only if the rate of return on the investment p* is as large as or larger than pk . This will be completely unaffected by the type of security used to finance the investment (bonds or stocks).

So the main conclusion is that companies should invest when . Capital structure is a matter of indifference and the problem of the optimal capital structure is no problem at all. B. Proposition 3 and Financial Planning by Firms Misinterpretation of the scope of Proposition 3 can be avoided by remembering that this Proposition 3 tells us only that the type of instrument used to finance an investment is irrelevant to the question of whether or not the investment is worth while.

This does not mean that the owners (or managers) have no grounds whatever for preferring one financing plan to another; or that there are no other policy or technical issues in finance at that level. C. The Effect of the Corporate Income Tax on Investment Decisions The cost of capital now depends on the debt ratio, decreasing , as D/V rises, at the constant rate of . Thus with a corporate income tax under which interest is a deductible expense, gains can accrue to stockholders from having debt in the capital structure, even when capital markets are perfect. L1 – Fama & French (1998) ‘Taxes, Financin