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《投资学原理 Investments》课程教学资源（阅读资料）Dividend Policy, growth and the valuation of shares

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THE JOURNAL OF BUSINESS The Graduate School of Business of the University of Chicago VOL. XXXIF OCTOBER 1961 No 4 DIVIDEND POLICY, GROWTH, AND THE VALUATION OF SHARES* MERTON H MILLERT AND FRANCO MoDIGLIANIt [E effect of a firms dividend policy of dividend policy. Lacking such a state on the current price of its shares is a ment, investigators have not yet been matter of considerable importance, able to frame their tests with sufficient not only to the corporate officials who precision to distinguish adequately be must set the policy, but to investors tween the various contending hypothe planning portfolios and to economists ses. Nor have they been able to give a seeking to understand and appraise the convincing explanation of what their test functioning of the capital markets. Do results do imply about the underlying companies with generous distribution process of valuation. policies consistently sell at a premium In the hope that it may help to over- over those with niggardly payouts? Is the come these obstacles to effective empiri reverse ever true? If so, under what con- cal testing, this paper will attempt to fill ditions? Is there an optimum payout the existing gap in the theoretical litera- ratio or range of ratios that maximizes ture on valuation. We shall begin, in Sec the current worth of the shares? tion I, by examining the effects of differ Although these questions of fact have ences in dividend policy on the current been the subject of many empirical stud- price of shares in an ideal economy char ies in recent years no consensus has yet acterized by perfect capital markets,ra been achieved. One reason appears to be tional behavior, and perfect certainty the absence in the literature of a com- Still within this convenient analytical plete and reasonably rigorous statement framework we shall go on in Sections II of those parts of the economic theory of and iii to consider certain closely related valuati on bearing directly on the matter issues that appear to have been respon- The authe who read and comment pns of.an sible for considerable misunderstanding their thanks of the role of dividend policy. In d especially to lar. Section II will focus on the long onsiderable simplification of a number of the proofs. standing debate about what investor Professor of finance and economics, University "really "capitalize when they buy shares Professor of economics, Northwestern Univer- and Section III on the much mooted rela tions between price, the rate of growth of his content downloaded from 202.. 18.13 on Wed, 1 1 Sep 2013 02: 04: 42 AM All use subject to JSTOR Terms and Conditions

THE JOURNAL OF BUSINESS The Graduate School of Business of the University of Chicago VOL. XXXIV OCTOBER 1961 No. 4 DIVIDEND POLICY, GROWTH, AND THE VALUATION OF SHARES* MERTON H. MILLERt AND FRANCO MODIGLINIt Tz i~xeffect of a firm's dividend policy on the current price of its shares is a matter of considerable importance, not only to the corporate officials who must set the policy, but to investors planning portfolios and to economists seeking to understand and appraise the functioning of the capital markets. Do companies with generous distribution policies consistently sell at a premium over those with -niggardly payouts? Is the reverse ever true? If so, under what conditions? Is there an optimum payout ratio or range of ratios that maximizes the current worth of the shares? Although these questions of fact have been the subject of many empirical studies in recent years no consensus has yet been achieved. One reason appears to be the absence in the literature of a complete and reasonably rigorous statement of those parts of the economic theory of valuation bearing directly on the matter of dividend policy. Lacking such a statement, investigators have not yet been able to frame their tests with sufficient precision to distinguish adequately between the various contending hypotheses. Nor have they been able to give a convincing explanation of what their test results do imply about the underlying process of valuation. In the hope that it may help to overcome these obstacles to effective empirical testing, this paper will attempt to fill the existing gap in the theoretical literature on valuation. We shall begin, in Section I, by examining the effects of differences in dividend policy on the current price of shares in an ideal economy characterized by perfect capital markets, rational behavior, and perfect certainty. Still within this convenient analytical framework we shall go on in Sections II and III to consider certain closely related issues that appear to have been responsible for considerable misunderstanding of the role of dividend policy. In particular, Section II will focus on the longstanding debate about what investors "really" capitalize when they buy shares; and Section III on the much mooted relations between price, the rate of growth of * The authors wish to express their thanks to all who read and commented on earlier versions of this paper and especially to Charles C. Holt, now of the University of Wisconsin, whose suggestions led to considerable simplification of a number of the proofs. t Professor of finance and economics, University of Chicago. t Professor of economics, Northwestern University. 411 This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 02:04:42 AM All use subject to JSTOR Terms and Conditions

412 THE JOURNAL OF BUSINESS profits, and the rate of growth of divi- vestor as to the future investment pro- dends per share. Once these fundamen- gram and the future profits of every cor- tals have been established, we shall pro- poration. Because of this assurance ceed in Section IV to drop the assump- there is, among other things, no need tion of certainty and to see the extent to distinguish between stocks and bonds as which the earlier conclusions about divi sources of funds at this stage of the anal- dend policy must be modified. Finally, in ysis. We can, therefore, proceed as if Section V, we shall briefly examine the there were only a single type of financial implications for the dividend policy instrument which, for convenience, we problem of certain kinds of market im- shall refer to as shares of stock The fundamental principle of valua- lion.Under these assumptions the valu I. EFFECT OF DIVIDEND POLICY WITH PER- ation of all shares would be governed by FECT MARKETS, RATIONAL BEHAVIOR, the following fundamental principle: the AND PERFECT CERTAINTY price of each share must be such that the The meaning of the basic assumptions. rate of return(dividends plus capital S lthough the terms"perfect markets, gains per dollar invested)on every share rational behavior, and"perfect cer- will be the same throughout the market tainty"are widely used throughout eco- over any given interval of time. That is y spelling out the precise me. to start if we let nomic theory, it may be helpft of these assumptions in the present context d,0=dividends per share paid by firm j du capital markets, "no P:(0 ice(ex any dividend buyer or seller(or issuer)of securities is of a share in firmi at the start of large enough for his transactions to have orice. All traders have equal and costless we must have access to information about the ruling d, (2)+p:(+1)-pi (2) price and about all other relevant charac teristics of shares ( to be detailed spe- =p(t) independent of j cifically later). No brokerage fees, trans- fer taxes, or other transaction costs are or, equivalently, incurred when securities are bought sold,or issued, and there are no tax dif- p (0)-1+p(ld (0)+p; ( +1)1(2) ferential either between distributed and undistributed profits or between divi- for each i and for all t. Otherwise, holders dends and capital gains. of low-return(high-priced)shares could 2. " Rational behavior"means that increase their terminal wealth by selling investors always prefer more wealth to these shares and investing the proceeds less and are indifferent as to whether a in shares offering a higher rate of return given increment to their wealth takes the This process would tend to drive down form of cash payments or an increase in the prices of the low-return shares and the market value of their holdings of drive up the prices of high-return shares until the differential in rates of return 3.“ Perfect certainty olies com- had been eliminated plete assurance on the part of every in The effect of dividend policy. The im- his content downloaded from 202.. 18.13 on Wed, 1 1 Sep 2013 02: 04: 42 AM All use subject to JSTOR Terms and Conditions

412 THE JOURNAL OF BUSINESS profits, and the rate of growth of dividends per share. Once these fundamentals have been established, we shall proceed in Section IV to drop the assumption of certainty and to see the extent to which the earlier conclusions about dividend policy must be modified. Finally, in Section V, we shall briefly examine the implications for the dividend policy problem of certain kinds of market imperfections. I. EFFECT OF DIVIDEND POLICY WITH PERFECT MARKETS, RATIONAL BEHAVIOR, AND PERFECT CERTAINTY The meaning of the basic assumptions. -Although the terms "perfect markets," "rational behavior," and "perfect certainty" are widely used throughout economic theory, it may be helpful to start by spelling out the precise meaning of these assumptions in the present context. 1. In "perfect capital markets," no buyer or seller (or issuer) of securities is large enough for his transactions to have an appreciable impact on the then ruling price. All traders have equal and costless access to information about the ruling price and about all other relevant characteristics of shares (to be detailed specifically later). No brokerage fees, transfer taxes, or other transaction costs are incurred when securities are bought, sold, or issued, and there are no tax differentials either between distributed and undistributed profits or between dividends and capital gains. 2. "Rational behavior" means that investors always prefer more wealth to less and are indifferent as to whether a given increment to their wealth takes the form of cash payments or an increase in the market value of their holdings of shares. 3. "Perfect certainty" implies complete assurance on the part of every investor as to the future investment program and the future profits of every corporation. Because of this assurance, there is, among other things, no need to distinguish between stocks and bonds as sources of funds at this stage of the analysis. We can, therefore, proceed as if there were only a single type of financial instrument which, for convenience, we shall refer to as shares of stock. The fundamental principle of valuation.-Under'these assumptions the valuation of all shares would be governed by the following fundamental principle: the price of each share must be such that the rate of return (dividends plus capital gains per dollar invested) on every share will be the same throughout the market over any given interval of time. That is, if we let dj(t) = dividends per share paid by firm j during period t pj(t) = the price (ex any dividend in t - 1) of a share in firm j at the start of period t, we must have dj(t) +pj(t+ 1) -pj(t) pj(t) ~~~(1) = p ( t ) independent of j; or, equivalently, pj( t)= [dj(t)+pj(t+)] (2) for each j and for all t. Otherwise, holders of low-return (high-priced) shares could increase their terminal wealth by selling these shares and investing the proceeds in shares offering a higher rate of return. This process would tend to drive down the prices of the low-return shares and drive up the prices of high-return shares until the differential in rates of return had been eliminated. The effect of dividend policy.-The imThis content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 02:04:42 AM All use subject to JSTOR Terms and Conditions

THE VALUATION OF SHARE 413 ications of this principle for our prob- able information as to what that future lem of dividend policy can be seen some- dividend policy would be. The first possi what more easily if equation (2)is re- bility being the relevant one from the stated in terms of the value of the enter- standpoint of assessing the effects of divi- prise as a whole rather than in terms of dend policy, it will clarify matters to as- the value of an individual share. Drop- sume, provisionally, that the future divi ping the firm subscript i since this will dend policy of the firm is known and ad to no ambiguity in the present con- given for t+ 1 and all subsequent peri text and letting ods and is independent of the actual divi- n(= the number of shares of record dend decision in 4. Then V(+ 1) will at the start of t also be independent of the current divi- m(t+ 1)=the number of new shares(if dend decision, though it may very well any) sold during t at the ex be affected by D(t+1)and all subse- dividend closing price p(+ 1), quent distributions. Finally, current div idends can influence v through the v(2=n(0)p(t)= the total third term, -m(t+1)p(t+1), the val the enterprise and ue of new shares sold to outsiders during D(=n(ed(o= the total the period. For the higher the dividend id during t to hold ord at the start of t, rout in capital that must be raised from external we can rewrite(2) sources to maintain any desired level of investment 1+p() D()+#()(+1)] The fact that the dividend decision effects price not in one but in these two 1+p(4)[D()+v(4+1) conflicting ways-directly via D()and inversely via -me)p(t-+ 1)-is, of m(L+1)P(L+1)].(3)course, precisely why one speaks of there being a dividend policy problem. If the The advantage of restating the funda- firm raises its dividend in t, given its in- mental rule in this form is that it brings vestment decision, will the increasein the into sharper focus the three possible cash payments to the current holders be routes by which current dividends might more or less than enough to offset their affect the current market value of the lower share of the terminal value? Which firm V(), or equivalently the price of its is the better strategy for the firm in individual shares, P. Current divi- financing the investment: to reduce divi- dends will clearly affect v(o via the first dends and rely on retained earnings or to term in the bracket, D(. In principle, raise dividends but float more new current dividends might also affect v shares? indirectly via the second term, V(E+ 1), In our ideal world at least these and the new ex dividend market value. since related questions can be simply and v(t+1)must depend only on future mediately answered: the two dividend and not on past events, such could be the effects must always exactly cancel out so case, however, only if both(a)v(+ 1)that the payout policy to be followed in t were a function of future dividend policy will have no effect on the price at t. and(b)the current distribution D() We need only express m(+1). P(t+1) served to convey some otherwise unavail- in terms of d( to show that such must his content downloaded from 202.. 18.13 on Wed, 1 1 Sep 2013 02: 04: 42 AM All use subject to JSTOR Terms and Conditions

THE VALUATION OF SHARES 413 plications of this principle for our problem of dividend policy can be seen somewhat more easily if equation (2) is restated in terms of the value of the enterprise as a whole rather than in terms of the value of an individual share. Dropping the firm subscript j since this will lead to no ambiguity in the present context and letting n(t) = the number of shares of record at the start of t m(t + 1) = the number of new shares (if any) sold during t at the ex dividend closing price p(t + 1), so that n(t + 1) = n(t) + m(t + 1) V(t) = n(t) p(t) = the total value of the enterprise and D(t) = n(t) d(t) = the total dividends paid during t to holders of record at the start of t, we can rewrite (2) V(t l +,) 1[D(t)+n(t)p(t+1) I 1+0 -1+ (t) [ D(t) + V(t+ 1) -m (t+ 1) p (t+ 1)I. (3) The advantage of restating the fundamental rule in this form is that it brings into sharper focus the three possible routes by which current dividends might affect the current market value of the firm V(t), or equivalently the price of its individual shares, p(t). Current dividends will clearly affect V(t) via the first term in the bracket, D(t). In principle, current dividends might also affect V(t) indirectly via the second term, V(t + 1), the new ex dividend market value. Since V(t + 1) must depend only on future and not on past events, such could be the case, however, only if both (a) V(t + 1) were a function of future dividend policy and (b) the current distribution D(t) served to convey some otherwise unavailable information as to what that future dividend policy would be. The first possibility being the relevant one from the standpoint of assessing the effects of dividend policy, it will clarify matters to assume, provisionally, that the future dividend policy of the firm is known and given for t + 1 and all subsequent periods and is independent of the actual dividend decision in t. Then V(t + 1) will also be independent of the current dividend decision, though it may very well be affected by D(t + 1) and all subsequent distributions. Finally, current dividends can influence V(t) through the third term, -m(t + 1) p(t + 1), the value of new shares sold to outsiders during the period. For the higher the dividend payout in any period the more the new capital that must be raised from external sources to maintain any desired level of investment. The fact that the dividend decision effects price not in one but in these two conflicting ways-directly via D(t) and inversely via -m(t) p(t + 1)-is, of course, precisely why one speaks of there being a dividend policy problem. If the firm raises its dividend in t, given its investment decision, will the increase in the cash payments to the current holders be more or less than enough to offset their lower share of the terminal value? Which is the better strategy for the firm in financing the investment: to reduce dividends and rely on retained earnings or to raise dividends but float more new shares? In our ideal world at least these and related questions can be simply and immediately answered: the two dividend effects must always exactly cancel out so that the payout policy to be followed in t will have no effect on the price at t. We need only express m(t+l) 1 p(t+1) in terms of D(t) to show that such must This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 02:04:42 AM All use subject to JSTOR Terms and Conditions

THE JOURNAL OF BUSINESS indeed be the case. Specifically, if I( once you think of it. "It is, after all, is the given level of the firms invest- merely one more instance of the genera ment or increase in its holding of physical principle that there are no "financial il- assets in t and if X( is the firms total lusions""in a rational and perfect econom- net profit for the period, we know that ic environment. Values there are deter- the amount of outside capital required mined solely by "real"considerations- will be in this case the earning power of the m(+1)φ(t+1)=I(4) firms assets and its investment policy IX(E)-D(/. (4) and not by how the fruits of the earning power are "packaged"for distribution Substituting expression(4)into(3), the, Obvious as the proposition may be, D( cancel and we obtain for the value however, one finds few references to it in of the firm as of the start of t the extensive literature on the problem.' It is true that the literature abounds with V()≡()夕(4) statements that in some <theoretical 1+p(IX(O-I(0+V\+/ C 5)sense, dividend policy ought not to count; but either that sense is not clearly specified or, more frequently and espe D (does not appear directly cially among eco onomists, it is(wrongly) the arguments and since X o, identified with a situation in which the r (t+ 1)and p(o are all independ- firm's internal rate of return is the same ent of D((either by their nature or by as the external or market rate of re ssumption) it follows that the current turn 2 value of the firm must be independent of A major source of these and related the current dividend decision misunderstandings of the role of the divi- Having established that V( is unaf- dend policy has been the fruitless concern fected by the current dividend decision and controversy over what investors it is easy to go on to show that v()must "really" capitalize when they buy shares also be unaffected by any future dividend We say fruitless because as we shall now decisions as well. Such future decisions proceed to show, it is actually possible to can influence V(O)only via their effect on derive from the basic principle of valua V(t+1). But we can repeat the reason- tion(1) not merely one, but several valu- ing above and show that V(t+ 1-and ation formulas each starting from one of hence V(O-is unaffected by dividend the "classical"views of what is being policy in t+1; that V(+ 2)-and capitalized by investors. Though differ- hence V(t+ 1)and v(t-is unaffected ing somewhat in outward appearance, by dividend policy in t+ 2; and so on the various formulas can be shown to be for as far into the future as we care to equivalent in all essential respects in look. Thus, we may conclude that given a cluding, of course, their implication that firm's investment policy, the dividend dividend policy is irrelevant. While the payout policy it chooses to follow will af 1 Apart from the references to it in our earlie fect neither the current price of its shares papers, especially [161, the closest nor the total return to its shareholders seems to be that in Bodenborn [1 Like many other propositions in ec his treatment of the role of divi policy is not nomics, the irrelevance of dividend pol mpletely explicit. (The numbers in brackets refer references listed below, pp. 432-33 icy, given investment policy,is“obⅵious, See below p 424 his content downloaded from 202.. 18.13 on Wed, 1 1 Sep 2013 02: 04: 42 AM All use subject to JSTOR Terms and Conditions

414 THE JOURNAL OF BUSINESS indeed be the case. Specifically, if I(t) is the given level of the firm's investment or increase in its holding of physical assets in t and if X(t) is the firm's total net profit for the period, we know that the amount of outside capital required will be m(t+1)p(t+1) = I(t) (4) - [X (t) -D (t) ]. Substituting expression (4) into (3), the D(t) cancel and we obtain for the value of the firm as of the start of t V (t)-n (t) p (t) (5) = +p(t)[X 1 (t)-I(t) + V(t+ 1) Since D(t) does not appear directly among the arguments and since X(t), I(t), V(t + 1) and p(t) are all independent of D(t) (either by their nature or by assumption) it follows that the current value of the firm must be independent of the current dividend decision. Having established that V(t) is unaffected by the current dividend decision it is easy to go on to show that V(t) must also be unaffected by any future dividend decisions as well. Such future decisions can influence V(t) only via their effect on V (t + 1). But we can repeat the reasoning above and show that V(t + 1)-and hence V(t)-is unaffected by dividend policy in t + 1; that V(t + 2)-and hence V(t + 1) and V(t)-is unaffected by dividend policy in t + 2; and so on for as far into the future as we care to look. Thus, we may conclude that given a firm's investment policy, the dividend payout policy it chooses to follow will affect neither the current price of its shares nor the total return to its shareholders. Like many other propositions in economics, the irrelevance of dividend policy, given investment policy, is "obvious, once you think of it." It is, after all, merely one more instance of the general principle that there are no "financial illusions" in a rational and perfect economic environment. Values there are determined solely by "real" considerationsin this case the earning power of the firm's assets and its investment policyand not by how the fruits of the earning power are "packaged" for distribution. Obvious as the proposition may be, however, one finds few references to it in the extensive literature on the problem.' It is true that the literature abounds with statements that in some "theoretical" sense, dividend policy ought not to count; but either that sense is not clearly specified or, more frequently and especially among economists, it is (wrongly) identified with a situation in which the firm's internal rate of return is the same as the external or market rate of return.2 A major source of these and related misunderstandings of the role of the dividend policy has been the fruitless concern and controversy over what investors "really" capitalize when they buy shares. We say fruitless because as we shall now proceed to show, it is actually possible to derive from the basic principle of valuation (1) not merely one, but several valuation formulas each starting from one of the "classical" views of what is being capitalized by investors. Though differing somewhat in outward appearance, the various formulas can be shown to be equivalent in all- essential respects including, of course, their implication that dividend policy is irrelevant. While the 1 Apart from the references to it in our earlier papers, especially [16], the closest approximation seems to be that in Bodenborn [1, p. 4921, but even his treatment of the role of dividend policy is not completely explicit. (The numbers in brackets refer to references listed below, pp. 432-33). 2 See below p. 424. This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 02:04:42 AM All use subject to JSTOR Terms and Conditions

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