THE AMERICAN ECONOMIC REVIEW ll structure, shares of different companies, even in the same class, can give rise to different probability distributions of returns. In the language of finance, the shares will be subject to different degrees of financial risk or "leverage"and hence they will no longer be perfect substitutes for To exhibit the mechanism determining the relative prices of shares under these conditions, we make the following two assumptions about the nature of bonds and the bond market, though they are actually stronger than is necessary and will be relaxed later:(1) All bonds(in cluding any debts issued by households for the purpose of carrying shares)are assumed to yield a constant income per unit of time, and this income is regarded as certain by all traders regardless of the issuer (2)Bonds, like stocks, are traded in a perfect market, where the term perfect is to be taken in its usual sense as implying that any two com- modities which are perfect substitutes for each other must sell, in equi- librium, at the same price. It follows from assumption(1)that all bonds Qmption(2)that they must all sell at the same price per doe.from as- return, or what amounts to the same thing must yield the same rate of return. This rate of return will be denoted by r and referred to as the rate of interest or, equivalently, as the capitalization rate for sure streams. We now can derive the following two basic propositions with respect to the valuation of securities in companies with different capital Proposition I Consider any company j and let X, stand as before he expected return on the assets owned by the company(that is, its expected profit before deduction of interest). Denote by Di the market value of the debts of the company; by S, the market value of its com- mon shares; and by Vi=S,+D, the market value of all its securities or as we shall say, the market value of the firm. Then, our Proposition I serts that we must have in equilibrium ViE(S,+ D)=X,/, for any frm j in class k That is, the arket value of any firm is independent of its capital structure and is given by capitalizing its expected return at the rate Pk appropriate to This proposition can be stated in an equivalent way in terms of the firm's"average cost of capital, "'Xi/Vi, which is the ratio of its expected return to the market value of all its securities. Our proposition then is: X, X, (4) (S,+D )V-Pe, for any firm i, in class k That is, the average cost of capital to any firm is completely independent of