The American Economic Review VOLUME XLVIII JUNE 1958 NUMBER THREE THE COST OF CAPITAL,CORPORATION FINANCE AND THE THEORY OF INVESTMENT By FRANCO MODIGLIANI AND MERTON H.MILLER* What is the "cost of capital"to a firm in a world in which funds are used to acquire assets whose yields are uncertain;and in which capital can be obtained by many different media,ranging from pure debt instru- ments,representing money-fixed claims,to pure equity issues,giving holders only the right to a pro-rata share in the uncertain venture? This question has vexed at least three classes of economists:(1)the cor- poration finance specialist concerned with the techniques of financing firms so as to ensure their survival and growth;(2)the managerial economist concerned with capital budgeting;and (3)the economic theorist concerned with explaining investment behavior at both the micro and macro levels.1 In much of his formal analysis,the economic theorist at least has tended to side-step the essence of this cost-of-capital problem by pro- ceeding as though physical assets-like bonds-could be regarded as yielding known,sure streams.Given this assumption,the theorist has concluded that the cost of capital to the owners of a firm is simply the rate of interest on bonds;and has derived the familiar proposition that the firm,acting rationally,will tend to push investment to the point The authors are,respectively,professor and associate professor of economics in the Grad- uate School of Industrial Administration,Carnegie Institute of Technology.This article is a revised version of a paper delivered at the annual meeting of the Econometric Society,Decem- ber 1956.The authors express thanks for the comments and suggestions made at that time by the discussants of the paper,Evsey Domar,Robert Eisner and John Lintner,and subse- quently by James Duesenbercy.They are also greatly indebted to many of their present and former colleagues and students at Carnegie Tech who served so often and with such remark- able patience as a critical forum for the ideas here presented. 1 The literature bearing on the cost-of-capital problem is far too extensive for listing here. Numerous references to it will be found throughout the paper though we make no claim to completeness.One phase of the problem which we do not consider explicitly,but which has a considerable literature of its own is the relation between the cost of capital and public utility rates.For a recent summary of the"cost-of-capital theory"of rate regulation and a brief dis- cussion of some of its implications,the reader may refer to H.M.Somers [20J. This content downloaded from 202.120.21.61 on Thu,30 Nov 201707:07:36 UTC All use subject to http://about.jstor.org/terms
The American economic Revlew VOLUME XLVIII JUNE 1958 NUMBER THREE THE COST OF CAPITAL, CORPORATION FINANCE AND THE THEORY OF INVESTMIENT By FRANCO MODIGLIAN1 AND MERTON H. MILLER* What is the "cost of capital" to a firm in a world in which funds are used to acquire assets whose yields are uncertain; and in which capital can be obtained by many different media, ranging from pure debt instru- ments, representing money-fixed claims, to pure equity issues, giving holders only the right to a pro-rata share in the uncertain venture.? This question has vexed at least three classes of economists: (1) the cor- poration finance specialist concerned with the techniques of financing firms so as to ensure their survival and growth; (2) the managerial economist concerned with capital budgeting; and (3) the economic theorist concerned with explaining investment behavior at both the micro and macro levels.' In much of his formal analysis, the economic theorist at least has tended to side-step the essence of this cost-of-capital problem by pro- ceeding as though physical assets-like bonds-could be regarded as yielding known, sure streams. Given this assumption, the theorist has concluded that the cost of capital to the owners of a firm is simply the rate of interest on bonds; and has derived the familiar proposition that the firm, acting rationally, will tend to push investmnent to the point * The authors are, respectively, professor and associate professor of economics in the Grad- uate School of Industrial Administration, Carnegie Institute of Technology. This article is a revised version of a paper delivered at the annual meeting of the Econometric Society, Decem- ber 1956. The authors express thanks for the comments and suggestions made at that time by the discussants of the paper, Evsey Domar, Robert Eisner and John Lintner, and subse- quently by J'ames Duesenberry. They are also greatly indebted to many of their present and former colleagues and students at Carnegie Tech who served so often and with such remark- able patience as a critical forum for the ideas here presented. 1 The literature bearing on the cost-of-capital problem is far too extensive for listing here. Numerous references to it will be found throughout the paper though we make no claim to completeness. One phase of the problem which we do not consider explicitly, but which has a considerable literature of its own is the relation between the cost of capital and public utility rates. For a recent summary of the "cost-of-capital theory" of rate regulation and a brief dis- cussion of some of its implications, the reader may refer to H. M. Somers [201. 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
262 THE AMERICAN ECONOMIC REVIEW where the marginal yield on physical assets is equal to the market rate of interest.?This proposition can be shown to follow from either of two criteria of rational decision-making which are equivalent under certain- ty,namely (1)the maximization of profits and(2)the maximization of market value. According to the first criterion,a physical asset is worth acquiring if it will increase the net profit of the owners of the firm.But net profit will increase only if the expected rate of return,or yield,of the asset exceeds the rate of interest.According to the second criterion,an asset is worth acquiring if it increases the value of the owners'equity,i.e.,if it adds more to the market value of the firm than the costs of acquisi- tion.But what the asset adds is given by capitalizing the stream it gen- erates at the market rate of interest,and this capitalized value will exceed its cost if and only if the yield of the asset exceeds the rate of interest.Note that,under either formulation,the cost of capital is equal to the rate of interest on bonds,regardless of whether the funds are acquired through debt instruments or through new issues of common stock.Indeed,in a world of sure returns,the distinction between debt and equity funds reduces largely to one of terminology. It must be acknowledged that some attempt is usually made in this type of analysis to allow for the existence of uncertainty.This attempt typically takes the form of superimposing on the results of the certainty analysis the notion of a "risk discount"to be subtracted from the ex- pected yield (or a"risk premium"to be added to the market rate of interest).Investment decisions are then supposed to be based on a com- parison of this"risk adjusted"or"certainty equivalent"yield with the market rate of interest.3 No satisfactory explanation has yet been pro- vided,however,as to what determines the size of the risk discount and how it varies in response to changes in other variables. Considered as a convenient approximation,the model of the firm constructed via this certainty-or certainty-equivalent-approach has admittedly been useful in dealing with some of the grosser aspects of the processes of capital accumulation and economic fluctuations.Such a model underlies,for example,the familiar Keynesian aggregate invest- ment function in which aggregate investment is written as a function of the rate of interest-the same riskless rate of interest which appears later in the system in the liquidity-preference equation.Yet few would maintain that this approximation is adequate.At the macroeconomic level there are ample grounds for doubting that the rate of interest has 2 Or,more accurately,to the marginal cost of borrowed funds since it is customary,at least in advanced analysis,to draw the supply curve of borrowed funds to the firm as a rising one. For an advanced treatment of the certainty case,see F.and V.Lutz [13]. The classic examples of the certainty-equivalent approach are found in J.R.Hicks [8]and O.Lange [11]. This content downloaded from 202.120.21.61 on Thu,30 Nov 201707:07:36 UTC All use subject to http://about.jstor.org/terms
262 THE AMERICAN ECONOMIC REVIEW where the marginal yield on physical assets is equal to the market rate of interest.2 This proposition can be shown to follow from either of two criteria of rational decision-making which are equivalent under certain- ty, namely (1) the maximization of profits and (2) the maximization of market value. According to the first criterion, a physical asset is worth acquiring if it will increase the net profit of the owners of the firm. But net profit will increase only if the expected rate of return, or yield, of the asset exceeds the rate of interest. According to the second criterion, an asset is worth acquiring if it increases the value of the owners' equity, i.e., if it adds more to the market value of the firm than the costs of acquisi- tion. But what the asset adds is given by capitalizing the stream it gen- erates at the market rate of interest, and this capitalized value will exceed its cost if and only if the yield of the asset exceeds the rate of interest. Note that, under either formulation, the cost of capital is equal to the rate of interest on bonds, regardless of whether the funds are acquired through debt instruments or through new issues of common stock. Indeed, in a world of sure returns, the distinction between debt and equity funds reduces largely to one of terminology. It must be acknowledged that some attempt is usually made in this type of analysis to allow for the existence of uncertainty. This attempt typically takes the form of superimposing on the results of the certainty analysis the notion of a "risk discount" to be subtracted from the ex- pected yield (or a "risk premium" to be added to the market rate of interest). Investment decisions are then supposed to be based on a com- parison of this "risk adjusted" or "certainty equivalent" yield with the market rate of interest.3 No satisfactory explanation has yet been pro- vided, however, as to what determines the size of the risk discount and how it varies in response to changes in other variables. Considered as a convenient approximation, the model of the firm constructed via this certainty-or certainty-equivalent-approach has admittedly been useful in dealing with some of the grosser aspects of the processes of capital accumulation and economic fluctuations. Such a model underlies, for example, the familiar Keynesian aggregate invest- ment function in which aggregate investment is written as a function of the rate of interest-the same riskless rate of interest which appears later in the system in the liquidity-preference equation. Yet few would maintain that this approximation is adequate. At the macroeconomic level there are ample grounds for doubting that the rate of interest has 2 Or, more accurately, to the marginal cost of borrowed funds since it is customary, at least in advanced analysis, to draw the supply curve of borrowed funds to the firm as a rising one. For an advanced treatment of the certainty case, see F. and V. Lutz [131. a The classic examples of the certainty-equivalent approach are found in J. R. Hicks [8] and 0. Lange [11]. 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
MODIGLIANI AND MILLER:THEORY OF INVESTMENT 263 as large and as direct an influence on the rate of investment as this analysis would lead us to believe.At the microeconomic level the cer- tainty model has little descriptive value and provides no real guidance to the finance specialist or managerial economist whose main problems cannot be treated in a framework which deals so cavalierly with uncer- tainty and ignores all forms of financing other than debt issues. Only recently have economists begun to face up seriously to the prob- lem of the cost of capital cum risk.In the process they have found their interests and endeavors merging with those of the finance specialist and the managerial economist who have lived with the problem longer and more intimately.In this joint search to establish the principles which govern rational investment and financial policy in a world of uncer- tainty two main lines of attack can be discerned.These lines represent, in effect,attempts to extrapolate to the world of uncertainty each of the two criteria-profit maximization and market value maximization- which were seen to have equivalent implications in the special case of certainty.With the recognition of uncertainty this equivalence vanishes. In fact,the profit maximization criterion is no longer even well defined. Under uncertainty there corresponds to each decision of the firm not a unique profit outcome,but a plurality of mutually exclusive outcomes which can at best be described by a subjective probability distribution. The profit outcome,in short,has become a random variable and as such its maximization no longer has an operational meaning.Nor can this difficulty generally be disposed of by using the mathematical expecta- tion of profits as the variable to be maximized.For decisions which affect the expected value will also tend to affect the dispersion and other characteristics of the distribution of outcomes.In particular,the use of debt rather than equity funds to finance a given venture may well in- crease the expected return to the owners,but only at the cost of in- creased dispersion of the outcomes. Under these conditions the profit outcomes of alternative investment and financing decisions can be compared and ranked only in terms of a subjective "utility function"of the owners which weighs the expected yield against other characteristics of the distribution.Accordingly,the extrapolation of the profit maximization criterion of the certainty model has tended to evolve into utility maximization,sometimes explicitly, more frequently in a qualitative and heuristic form.5 The utility approach undoubtedly represents an advance over the certainty or certainty-equivalent approach.It does at least permit us 4 Those who have taken a "case-method"course in finance in recent years will recall in this connection the famous Liquigas case of Hunt and Williams,19,pp.193-96]a case which is often used to introduce the student to the cost-of-capital problem and to poke a bit of fun at the economist's certainty-model. 5 For an attempt at a rigorous explicit development of this line of attack,see F.Modigliani and M.Zeman [14]. This content downloaded from 202.120.21.61 on Thu,30 Nov 201707:07:36 UTC All use subject to http://about.jstor.org/terms
MODIGLIANI AND MILLER: THEORY OF INVESTMENT 263 as large and as direct an influence on the rate of investment as this analysis would lead us to believe. At the microeconomic level the cer- tainty model has little descriptive value and provides no real guidance to the finance specialist or managerial economist whose main problems cannot be treated in a framework which deals so cavalierly with uncer- tainty and ignores all forms of financing other than debt issues.4 Only recently have economists begun to face up seriously to the prob- lem of the cost of capital cum risk. In the process they have found their interests and endeavors merging with those of the finance specialist and the managerial economist who have lived with the problem longer and more intimately. In this joint search to establish the principles which govern rational investment and financial policy in a world of uncer- tainty two main lines of attack can be discerned. These lines represent, in effect, attempts to extrapolate to the world of uncertainty each of the two criteria-profit maximization and market value maximization- which were seen to have equivalent implications in the special case of certainty. With the recognition of uncertainty this equivalence vanishes. In fact, the profit maximization criterion is no longer even well defined. Under uncertainty there corresponds to each decision of the firm not a unique profit outcome, but a plurality of mutually exclusive outcomes which can at best be described by a subjective probability distribution. The profit outcome, in short, has become a random variable and as such its maximization no longer has an operational meaning. Nor can this difficulty generally be disposed of by using the mathematical expecta- tion of profits as the variable to be maximized. For decisions which affect the expected value will also tend to affect the dispersion and other characteristics of the distribution of outcomes. In particular, the use of debt rather than equity funds to finance a given venture may well in- crease the expected return to the owners, but only at the cost of in- creased dispersion of the outcomes. Under these conditions the profit outcomes of alternative investment and financing decisions can be compared and ranked only in terms of a subjective "utility function" of the owners which weighs the expected yield against other characteristics of the distribution. Accordingly, the extrapolation of the profit maximization criterion of the certainty model has tended to evolve into utility maximization, sometimes explicitly, more frequently in a qualitative and heuristic form.5 The utility approach undoubtedly represents an advance over the certainty or certainty-equivalent approach. It does at least permit us 4 Those who have taken a "case-method" couirse in finance in recent years will recall in this connection the famous Liquigas case of Hunt and Williams, 19, pp. 193-961 a case which is often used to introduce the student to the cost-of-capital problem and to poke a bit of fun at the economist's certainty-model. 6 For an attempt at a rigorous explicit development of this line of attack, see F. Modigliani and M. Zeman [141. 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
264 THE AMERICAN ECONOMIC REVIEW to explore(within limits)some of the implications of different financing arrangements,and it does give some meaning to the"cost"of different types of funds.However,because the cost of capital has become an essentially subjective concept,the utility approach has serious draw- backs for normative as well as analytical purposes.How,for example, is management to ascertain the risk preferences of its stockholders and to compromise among their tastes?And how can the economist build a meaningful investment function in the face of the fact that any given investment opportunity might or might not be worth exploiting depend- ing on precisely who happen to be the owners of the firm at the moment? Fortunately,these questions do not have to be answered;for the alter- native approach,based on market value maximization,can provide the basis for an operational definition of the cost of capital and a workable theory of investment.Under this approach any investment project and its concomitant financing plan must pass only the following test:Will the project,as financed,raise the market value of the firm's shares?If so,it is worth undertaking;if not,its return is less than the marginal cost of capital to the firm.Note that such a test is entirely independent of the tastes of the current owners,since market prices will reflect not only their preferences but those of all potential owners as well.If any current stockholder disagrees with management and the market over the valuation of the project,he is free to sell out and reinvest elsewhere, but will still benefit from the capital appreciation resulting from man- agement's decision. The potential advantages of the market-value approach have long been appreciated;yet analytical results have been meager.What ap- pears to be keeping this line of development from achieving its promise is largely the lack of an adequate theory of the effect of financial struc- ture on market valuations,and of how these effects can be inferred from objective market data.It is with the development of such a theory and of its implications for the cost-of-capital problem that we shall be con- cerned in this paper. Our procedure will be to develop in Section I the basic theory itself and to give some brief account of its empirical relevance.In Section II, we show how the theory can be used to answer the cost-of-capital ques- tion and how it permits us to develop a theory of investment of the firm under conditions of uncertainty.Throughout these sections the approach is essentially a partial-equilibrium one focusing on the firm and "industry."Accordingly,the "prices"of certain income streams will be treated as constant and given from outside the model,just as in the standard Marshallian analysis of the firm and industry the prices of all inputs and of all other products are taken as given.We have chosen to focus at this level rather than on the economy as a whole because it This content downloaded from 202.120.21.61 on Thu,30 Nov 201707:07:36 UTC All use subject to http://about.jstor.org/terms
264 THE AMERICAN ECONOMIC REVIEW to explore (within limits) some of the implications of different financing arrangements, and it does give some meaning to the "cost" of different types of funds. However, because the cost of capital has become an essentially subjective concept, the utility approach has serious draw- backs for normative as well as analytical purposes. How, for example, is management to ascertain the risk preferences of its stockholders and to compromise among their tastes? And how can the economist build a meaningful investment function in the face of the fact that any given investment opportunity might or might not be worth exploiting depend- ing on precisely who happen to be the owners of the firm at the moment? Fortunately, these questions do not have to be answered; for the alter- native approach, based on market value maximization, can provide the basis for an operational definition of the cost of capital and a workable theory of investment. Under this approach any investment project and its concomitant financing plan must pass only the following test: Will the project, as financed, raise the market value of the firm's shares? If so, it is worth undertaking; if not, its return is less than the marginal cost of capital to the firm. Note that such a test is entirely independent of the tastes of the current owners, since market prices will reflect not only their preferences but those of all potential owners as well. If any current stockholder disagrees with management and the market over the valuation of the project, he is free to sell out and reinvest elsewhere, but will still benefit from the capital appreciation resulting from man- agement's decision. The potential advantages of the market-value approach have long been appreciated; yet analytical results have been meager. What ap- pears to be keeping this line of development from achieving its promise is largely the lack of an adequate theory of the effect of financial struc- ture on market valuations, and of how these effects can be inferred from objective market data. It is with the development of such a theory and of its implications for the cost-of-capital problem that we shall be con- cerned in this paper. Our procedure will be to develop in Section I the basic theory itself and to give some brief account of its empirical relevance. In Section II, we show how the theory can be used to answer the cost-of-capital ques- tion and how it permits us to develop a theory of investment of the firm under conditions of uncertainty. Throughout these sections the approach is essentially a partial-equilibrium one focusing on the firm and "industry." Accordingly, the "prices" of certain income streams will be treated as constant and given from outside the model, just as in the standard Marshallian analysis of the firm and industry the prices of all inputs and of all other products are taken as given. We have chosen to focus at this level rather than on the economy as a whole because it 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
MODIGLIANI AND MILLER:THEORY OF INVESTMENT 265 is at the level of the firm and the industry that the interests of the vari- ous specialists concerned with the cost-of-capital problem come most closely together.Although the emphasis has thus been placed on partial- equilibrium analysis,the results obtained also provide the essential building blocks for a general equilibrium model which shows how those prices which are here taken as given,are themselves determined.For reasons of space,however,and because the material is of interest in its own right,the presentation of the general equilibrium model which rounds out the analysis must be deferred to a subsequent paper. I.The Valuation of Securities,Leverage,and the Cost of Capital A.The Capitalization Rate for Uncertain Streams As a starting point,consider an economy in which all physical assets are owned by corporations.For the moment,assume that these corpora- tions can finance their assets by issuing common stock only;the intro- duction of bond issues,or their equivalent,as a source of corporate funds is postponed until the next part of this section. The physical assets held by each firm will yield to the owners of the frm一its stockholders--a stream of“profits'”over time;but the ele- ments of this series need not be constant and in any event are uncertain. This stream of income,and hence the stream accruing to any share of common stock,will be regarded as extending indefinitely into the future. We assume,however,that the mean value of the stream over time,or average profit per unit of time,is finite and represents a random vari- able subject to a(subjective)probability distribution.We shall refer to the average value over time of the stream accruing to a given share as the return of that share;and to the mathematical expectation of this average as the expected return of the share.6 Although individual inves- tors may have different views as to the shape of the probability distri. These propositions can be restated analytically as follows:The assets of the ith firm gener- ate a stream: X(1),X(2)···X(T) whose elements are random variables subject to the joint probability distribution: xX:(1),X(2)···X(0 The return to the ith firm is defined as: Xi=lim xi(). X;is itself a random variable with a probability distribution(Xi)whose form is determined uniquely by x.The expected return X;is defined as X;=E(Xi)=/x;X;(Xi)dXi.If N:is the number of shares outstanding,the return of the ith share is x;=(1/N)X:with probability distribution (xdxs=(Nxi)d(Nx;)and expected value=(1/N)Xi. This content downloaded from 202.120.21.61 on Thu,30 Nov 201707:07:36 UTC All use subject to http://about.jstor.org/terms
MODIGLIANI AND MILLER: THEORY OF INVESTMENT 265 is at the level of the firm and the industry that the interests of the vari- ous specialists concerned with the cost-of-capital problem come most closely together. Although the emphasis has thus been placed on partial- equilibrium analysis, the results obtained also provide the essential building blocks for a general equilibrium model which shows how those prices which are here taken as given, are themselves determined. For reasons of space, however, and because the material is of interest in its own right, the presentation of the general equilibrium model which rounds out the analysis must be deferred to a subsequent paper. I. Tihe Valuation of Securities, Leverage, and tihe Cost of Capital A. T'he Capitalization Rate for Uncertain Streams As a starting point, consider an economy in which all physical assets are owned by corporations. For the moment, assume that these corpora- tions can finance their assets by issuing common stock only; the intro- duction of bond issues, or their equivalent, as a source of corporate funds is postponed until the next part of this section. The physical assets held by each firm will yield to the owners of the firm-its stockholders-a stream of "profits" over time; but the ele- ments of this series need not be constant and in any event are uncertain. This stream of income, and hence the stream accruing to any share of common stock, will be regarded as extending indefinitely into the future. WTe assume, however, that the mean value of the stream over time, or average profit per unit of time, is finite and represents a random vari- able subject to a (subjective) probability distribution. We shall refer to the average value over time of the stream accruing to a given share as the return of that share; and to the mathematical expectation of this average as the expected return of the share.6 Although individual inves- tors may have different views as to the shape of the probability distri 6 These propositions can be restated analytically as follows: The assets of the ith firm gener- ate a stream: Xi (I), Xi (2) ... Xi (T) whose elements are random variables subject to the joint probability distribution: Xi [Xi (1), Xi (2) .. *X\i (t)J. The return to the ith firm is defined as: liT Xi-= lim - Xsit). 7--co T t= Xi is itself a random variable with a probability distribution diW(Xi) whose form is determined uniquely by Xi. The expected return Xi is defined as Xi=E(Xi) =fxXib(X,)dX;. If Ni is the number of shares outstanding, the return of the ith share is xi= (1/N)X; with probability distribution Oi(xi)dx1=4i(Nxi)d(Nxi) and expected value 9i=(1/N)X,. 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