MODIGLIANI AND MILLER:THEORY OF INVESTMENT 267 analysis to follow that the shares concerned are traded in perfect mar- kets under conditions of atomistic competition. From our definition of homogeneous classes of stock it follows that in equilibrium in a perfect capital market the price per dollar's worth of expected return must be the same for all shares of any given class.Or, equivalently,in any given class the price of every share must be propor- tional to its expected return.Let us denote this factor of proportionality for any class,say the kth class,by 1/p&.Then if denotes the price and is the expected return per share of the jth firm in class k,we must have: 1 (1) =一元； Pk or,equivalently, (2) =p&a constant for all firms j in class k. 帖 The constants pr(one for each of the k classes)can be given several economic interpretations:(a)From (2)we see that each pa is the ex- pected rate of return of any share in class k.(b)From (1)1/p&is the price which an investor has to pay for a dollar's worth of expected re- turn in the class k.(c)Again from(1),by analogy with the terminology for perpetual bonds,P can be regarded as the market rate of capitaliza- tion for the expected value of the uncertain streams of the kind gen- erated by the kth class of firms.10 B.Debt Financing and Its Efects on Security Prices Having developed an apparatus for dealing with uncertain streams we can now approach the heart of the cost-of-capital problem by drop- ping the assumption that firms cannot issue bonds.The introduction of debt-financing changes the market for shares in a very fundamental way.Because firms may have different proportions of debt in their capi- Just what our classes of stocks contain and how the different classes can be identified by outside observers are empirical questions to which we shall return later.For the present,it is sufficient to observe:(1)Our concept of a class,while not identical to that of the industry is at least closely related to it.Certainly the basic characteristics of the probability distributions of the returns on assets will depend to a significant extent on the product sold and the tech- nology used.(2)What are the appropriate class boundaries will depend on the particular prob- lem being studied.An economist concerned with general tendencies in the market,for example, might well be prepared to work with far wider classes than would be appropriate for an inves- tor planning his portfolio,or a firm planning its financial strategy. 10 We cannot,on the basis of the assumptions so far,make any statements about the rela- tionship or spread between the various p's or capitalization rates.Before we could do so we would have to make further specific assumptions about the way investors believe the proba- bility distributions vary from class to class,as well as assumptions about investors'preferences as between the characteristics of different distributions. This content downloaded from 202.120.21.61 on Thu,30 Nov 201707:07:36 UTC All use subject to http://about.jstor.org/termsMODIGLIANI AND MILLER: THEORY OF INVESTMENT 267 analysis to follow that the shares concerned are traded in perfect mar- kets under conditions of atomistic competition.9 From our definition of homogeneous classes of stock it follows that in equilibrium in a perfect capital market the price per dollar's worth of expected return must be the same for all shares of any given class. Or, equivalently, in any given class the price of every share must be propor- tional to its expected return. Let us denote this factor of proportionality for any class, say the kth class, by l/Pk. Then if pi denotes the price and sj is the expected return per share of the jth firm in class k, we must have: (1) pj =-xj; Pk or, equivalently, (2) = Pk a constant for all firms j in class k. pi The constants Pk (one for each of the k classes) can be given several economic interpretations: (a) From (2) we see that each Pk iS the ex- pected rate of return of any share in class k. (b) From (1) l/Pk is the price which an investor has to pay for a dollar's worth of expected re- turn in the class k. (c) Again from (1), by analogy with the terminology for perpetual bonds, Pk can be regarded as the market rate of capitaliza- tion for the expected value of the uncertain streams of the kind gen- erated by the kth class of firms.10 B. Debt Financing and Its Effects on Security Prices Having developed an apparatus for dealing with uncertain streams we can now approach the heart of the cost-of-capital problem by drop- ping the assumption that firms cannot issue bonds. The introduction of debt-financing changes the market for shares in a very fundamental way. Because firms may have different proportions of debt in their capi- 9 Just what our classes of stocks contain and how the different classes can be identified by outside observers are empirical questions to which we shall return later. For the present, it is sufficient to observe: (1) Our concept of a class, while not identical to that of the industry is at least closely related to it. Certainly the basic characteristics of the probability distributions of the returns on assets will depend to a significant extent on the product sold and the tech- nology used. (2) What are the appropriate class boundaries will depend on the particular prob- lem being studied. An economist concerned with general tendencies in the market, for example, might well be prepared to work with far wider classes than would be appropriate for an inves- tor planning his portfolio, or a firm planning its financial strategy. 10 We cannot, on the basis of the assumptions so far, make any statements about the rela- tionship or spread between the various p's or capitalization rates. Before we could do so we would have to make further specific assumptions about the way investors believe the proba- bility distributions vary from class to class, as well as assumptions about investors' preferences as between the characteristics of different distributions. This content downloaded from 202.120.21.61 on Thu, 30 Nov 2017 07:07:36 UTC All use subject to http://about.jstor.org/terms