# Summary Modigliani & Miller

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

pk= 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

α = 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:

s1 = fraction/amount invested in stocks

S1 = total stocks outstanding

To see why this should be true,...

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