A NOTE ON THE "COST OF CAPITAL" RICHARD L. CARSON.

CARLLTON UNIVERSITY

In a wen-known article, hfodigliani and Miller have rramted the classical vicar that the marginal cost of investible funds' is independent of h e means of investment financing [ 8 1. This cost is no longer the "rate of interest" of the classical world of perfect certainty, but a wei ted average of the e x p e d yields on all kinds of sia%

market value of the firm in each kind of issue. ?he principal contending point of view has been advanced by Professor Duesenberry

[ 4, ch. 5 I . His marginal cost schedule breaks up into three parts correspondin to the three major ways of financing investment open to the finn. The enterprise k d s it cheapest of all to use retained earnings for lower rates of investment, but, as more and more projects are undertaken, the opportunity cost of not paying dividends rises, eventually making it profitable to borrow. Here, the schedule becomes inelastic, for as the firm's newly contracted debt grows, so does its debt-to-equity ratio, dong with the fixed burden of future interest charges on profits which may fluctuate, making the firm a riskier venture. At last, equity issue becomes the cheapest form of invest- ment financing and the schedule begins to flatten out again, although it does not be-

Modigliani and Miller (hereafter to be called MM) were tincipdy interested in showing that a firm's cost of capital is independent of its d eg t -bei@y ratio. How- ever, the full force of their argument is to flatten Duesenberry's mar@ cost schedule on the basis of the existence of arbitrage by investors in the securities of the various corpotations listed on the stock and bond markets. In a sense, the MM marginal cost of funds schedule is the "resolution" of Duesenberry's, for this cost may be lowest for retained earnings, next lowest for borrowing, and highest for equity issues before arbitraging reestablishes equilibrium after any act of investing, borrowing, or stock sale by the firm. In arbitraging, MM discovered an element affecting the marginal cost of capital that had been neglected by Duesenberry and alI previous well-known writers on the subject. The two cost schedules are illustrated in the diagram below.

Since the appearance of their classic paper, MM have had to withstand a fair amount of criticism. They themselves have had to admit that their conclusions can only be valid, for example, when the tax deductibility of interest charges is ignored [ 71. When this is taken into account, however, we reach the rather uncomfortable conclusion that, in the words of Ezra Solomon, "companies ought to be financed 99.9 per cent with pure debt" [11, p. 1031. Others have argued that individual investors may not be able to borrow on terms as attractive as those available to corporations (corporations, for example, possess limited liability) [9] [lo] [ 11 I . If this were the case, arbitrage would not work as MM hypothesize; historically spealung, however, inkrest rates on brokers' loans have not differed significantly from rates on loans to corporations 18, p. 2741.

and bonds issued by the P rm, the weights in question being the parentage of the

tome perfectly dastic.

*The author wishes to thank Professors J. G. Witte, Jr., Franz Gehrels, and Elmw R. Wicker, of Indiana University, dong with Keith Hay, of Carleton University, for their excellent comments and suggestiom. Residual errors are, of course, the fault of the writer.

r. the terms "cost of capital" and "marginal cost of investible funds' an used interchangcabf;eto mean the marginal cost at which enterprises may acquire funds for invest- ment purposes.

In this pa

282

CARSON: COST OF CAPITAL

Figurc 1

cost of Capita I

0

Duesenberry

Mod ig I iani - Miller

lnterna I Financing

Gross Investment

Finally, Professor Solomon, among others, argues that, in ractice, capital markets are not so perfect as assume them to be in their m o d 2 The interest rate that a firm must pay on its borrowings will rise signrficantly as its debt-toquity ratio is increased “beyond levels acceptable to the market” [ 11, p. 110 1. From this, it may be shown that, for any given firm and investment mgram, there is an optimal debt- to-equity ratio (or, at least, an optimal range of d&-tocquity ratios) which this firm should try to maintain in order to keep its financing costs as low as possible. This optimal ratio will cxist whether or not one takes tax deductibility of interest charges into consideration although, of course, such deductibility afFects the value of the opti- mum. Solomon’s conclusion is in fact a *mation of the traditional viewpoint as stated, for example, by Durand. It is also one implication of Duesenbeq’s Sshaped marginal cost of investible funds schedule.

A BRIEF DESCRIPTION OF THE MODIGLIANI-MILLER MODEL

It has been mentioned above that the MM model may be looked upon as the “reso- lution” of Duesenberry’s Sshapd marginal cost of investible funds schedule. Let us now try to see how this resolving takes place. MM begin by supposing that all firms in the economy are corporations which may issue only common stocks-no bonds or preferred stock-to raise investible funds from external sources. All corporate man- agers are, in effect, profit maximizers and the enterprises that they manage 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 (and, hence, perfectly correlated with) the return on the shares issued by any other firm in the same dass . . . . this assump tion . . . . permits us to dassify firms into groups within which the shares of differ- ent firms are . . . . perfect substitutes for one another . . . . To complete this analogy with Marshallian price theory, we shall assume . . . . that the shares are traded in perfect markets under conditions of atomistic competition . . . . in equilibrium . . . . the price per dollar’s worth of expected return must be the same for all shares in any given class. Or, equivalently, in any given class, the price of every share must be po- portional to the expected return” [ 8, pp. 266-671.

Let us denote this factor of proportionality in the k‘* “equivalent return” class by I / p k , and let Pj be the price and F j the expected return per share of j t* firm in

’These are equivdence classes in the mathematical sense-i.e., classes that are mutuaIIy a- clusire and exhaustive.

284 ;WESTERN ECONOMIC JOURNAL

class R. Then, the last statement of the above paragraph says:

where pr is a constant for all firms in class A. ation (I), MM drop the assumption that firms cannot issue

bonds. However, suchxnds are assumed, like stocks, to be traded in perf& markets and to be completely riskless assets, each bond, in effect, yielding the same rate of interest. The appearance of bonds on the securities exchange therefore merely creates one more “cqu~valent return” class in which all assets traded are riskless. MM are now set to prove their Proposition I from which vimLolly all of their basic

conclusions derive. It may be stated as follows:

After establishing

Where V, is the market value of the firm j regardless of its debt-bequity ratio and X, is the value of its expected annual earnings or profits. A thus takes on a new sig- nificance. It is the equilibrium marpa l cost of investible funds for all firms whose stocks fall into equivalence class k. In particular, it is independent of the firm’s capi- tal struclute.

The proposition is proved by showing that if the marginal capt of investible funds for an unlevered firm is higher or lower than for a levered firm in the same equiva- lence class, holders of stock in one of the com ‘es can arbitrage so as to increase their (expected) earnings per doliar’s worth o portfoIio holdings. ’Ihis d i t m does not ‘depcnd upon any assumption about individual risk preferences,” the au OR assert. ‘Nor do fthe Propitions] involve any assertion as to what is an adequate

sation to investors for assuming a given degree of risk. They rely merely on

market . . . . ” 18, p. 2791. Thus, a corporation that tries to reduce its cost of investible funds by adding debt

to its capital structure is presumed by MM to be ando us to a dairy farmer trying

uilibrium conditions prevail, his efTorts are doomed to failure because have equated the pnce of whole milk with the sum of the pr im of

skim milk and butter fat. Furthermore, as soon as these prices get out of line, buying in the cheap mke t ( s ) and selling in the dear one(s) will take place immediately so as to restore the previous equilibrium.

In a similar fashion, whenever a corporation succeeds in reducing its cost of capital tern orarily by borrowing, it simultaneously reduces yields on its stocks relative to pie& on other stocks in the same equivalence dass. The same thing happens if the management tries to apply a lower opportunity cost to retained earnings than to debt

. In either of these circumstances, investors can increase their return by selling some Or qui7 o the firm’s stock and buying shares of other corporations in the same equiva- lence dass. Thus, they have the market p e r to dictate, via arbitrage, what the mar- ginal cost of investible funds shall be to the management of any corporation. If man- agemement consistently ignores thew dictates (say by confining its investment largely to what it feels can be “safely” financed from internal sources), stockholders will be of the unanimous opinion that their funds are being misused and will vote the man- agers out of ofice.

-

irg

the cmr act that a given commodity cannot consistentIy sell at more than one price in the

to earn more for the milk he produces by skimming o P the butter fat and selling it

p““

THE NATURE OF THE “CORPORATE EARNINGS” MARKET

T h e bulk of the controversy over the MM thesis has centered on the cost of debt vis-A-vis the cost of equity investment financing. In this note, I wish to shift the focus of the debate. Modigliani and Miller explicitly assume [8 , pp. 265-661 that investors are fully agreed as to the expected or average annual return on each type of stock or

CARSON: Con OF CAF'ITAL 28)

bond offered for sale. In a footnote [8, p. 2661, they contend that allowing investors to disagree over yields would merely constitute a "refinement" in their model. The contrasting claim made here is that such disagreement destroys the MM analogy be- tween a matket for dairy roduce and a market for corporate earning assets. In con-

ginal cost of investible funds is inde ndent of the method of finance).

when investors buy and sell streams of future earnings in stocks and bonds while not knowing, for sure, just what the expected annual value of any particular stream will be. Any two investors may differ in their estimates of the yield of a given stream. We may, therefore, observe two investors utilizing the same information, one of whom is selling shares in company A to buy shares in B while the other is doing precisely the opposite. In these conditions, Duesenberry's S-shaped cost of capital schedule is not necessarily resolved into the horizontal line that MM propose. Such behavior is not inconsistent with income optimization on the part of either investor nor is either actor necessarily behaving irrationally.

In the exam le of the dairy farmer referred to above, however, a similar statement

rices of butter fat and skim milk p us the cost of separating the two. Then, there is gut one logical course of action for a dairy farmer or anyone else with separating machinery, and that is to buy whole milk, separate it into butter fat and skim milk, and sell these. If a number of persons do this the price of whole milk will rise and the prices of butterfat and skim milk will fall until the ga that caused the arbitrage

fat, mix them into whole milk, and sell the latter. Yet, if some individuals insisted on doing this anyway they could undo the arbitrage of the former group. The prices of whole and skim milk might not move together at a l l ; they might even move apart.

Such cancelling behavior is not irrational when it comes to buying stocks and bonds. Hence, MM's analogy between this market and the dairy market breaks down. De- spite their claims to the contrary, MM have not "dealt with" uncertainty regarding streams of future earnings on corporate assets. Ironically, it is this very uncertainty that may lead different investors to regard the same stock or bond as a different com- modity (i.e., a different stream of future interest or dividend earnings) and, in con- sequence, fail to engage in the arbitrage upon which MM rely so heavily.

It is worth noting, in this connection, that no reputable stockbroker will claim to be certain as to whether a given equity is under- or overvalued and by how much. And, in sharp contrast to the price information yielded by a dairy market, the educated guess of a fulltime expert on stock-price information is not free.S

Given these circumstances investors will, in general, differ b o d in the way they classify corporate earning assets by "equivalent return" class and in the yield they assign to each class. For our pu s a , it is enough to restrict disagreement to the

sequence, the way is pave B for the downfall of their central thesis (i.e., that the mar-

The reason, essentially, is that e r ective arbitrage cannot be guaranteed to take place

P cannot be ma P e. Suppose that the rice of whole milk lies below the sum of the

to begin is erased. It would be completely irrational to E uy skim milk and butter

latter point,' and for simplicity o 'p" notation, this will be done. Each investor, there-

'It is interesting to note that one characteristic of a "well-managed" company, in the eys of many of these "experts," is that it consistent1 finance its capital upenditures internally. Thus. the value of the firm is not considered inLpendently of the way in which investments are financed.

T o see this, let there be two equivalent return classes and two investors. The first investor assigns yields pu and pu to these classes and the second assigns yields pn and pn. Suppose further that the first class contains the more speculative stocks and that the second investor is much more of a risk averter than the first so that pu > pn while < pn. Assume linally that firm A is initially placed in the second equivalent return class by both investors when its management uses retained earnings to invest in what is, for it, an unusually r isky venture. Both investors reassign it to the first class, but the first investor may now want to buy shrm in A while the second wishes to sell them.

266 ;\IQESTERN ECONOMIC JOURNAL

fore, p u p s the “market” into the same collection of equivalence classes, but different investors view any given class as a different commodity and, in consequence, assign different yields to this class. The cost of capital to a representative firm in the ktL class can no loager be uniquely written as m. Instead, it is necessary to assOciate avcctor of costs [Ar, m, ...A,,] with such a company where the sub& (2 ... n) denote present or pros ve investors in its earning assets and the first 2 ript refers to its

in the following section, but first, let us give a summary of our basic argument up to management.6 #? e reason for assigning a prime role to the latter will be taken up

3- generate. The size o P this earnings stream is uncertain, but we assume that, for each

now : (a) Investors in the st& and bonds issued by any corporation arc, in effea,

ers and sellers of its future earnings. The known price of a share of common s for instance, is the

investor, it has an expected or average annual value (in the probabilistic sense). (b) Because any stream of earnings to be paid out over future intern& is uncer-

tain, the expected annual vdue of such a stream may vary from one investor to an- other. To say the same thing, investors may disagree u to the yield or return of a given stock or bond, this yield or return being the expected annual earnings divided by the price, 0) the amount of enpeacd annual eamings that a dollar will buy. Hence, there can, in general, be no predictable arbitraging in the “market” for the future earnings of these portfolio assets. Indeed, one may well ask whether a “market” for such eamings even exists in the same sense, say, as a market for dairy produce.

(c) Without arbitrage in predictable directions, there need be no market force tending to quate the marginal costs of investible funds to a given firm for all the various ways of financing investment. Indeed, each ential investor may have his own idea about the ex

, rice of the discounted earnings stream which that share will

ed yield on ead~ of the f!z ’s earning assets, and all of these valuations may d’ IF er to an extent.

THE ROLE Or THE MANAQEMENT

Ultimately, it is the management of any corporation that makes investment decisions and, therefore, we should be especially interested in how a representative corporation management views the marginal cost of invisibIe funds schedule to its firm. In the MM model, the opinion of the management as to what the cost of capital to its firm is or should be is of no importance because investors in the firm’s earning assets vir- tually dictate this cost just as a perfectly competitive market dictates a price of the product to individual producers. When we deprive investors of their unanimity, how- ever, they also lose their dictatorial power and allow managers a certain amount of what has come to be known as “organizational slack’ in investment decisionmaking. Modem behavioral theories of the firm stress this freedom of management from stockholder restraint, although the existence of the latter is not denied [ 2 ) [ 31.

Moreover, if managers did effectively face cost of capital schedules that were en- tirely independent of the means of investment financing, they would not be expected to exhibit any particular bias in selecting means of investment finance unless such bias were induced by tax laws. And, while these laws should exert their bias in favor of debt financing over uity financing, it is well known that enterprises, by and large, show a ronouncg preference for using internal funds-exactl as Duesen- berry’s S-shaJcost of capital schedule would suggest. To cite but one f? gure on this,

‘This notation implicitly assumes that the management of each firm in equivalence class R has the same view of the cost of capital facing its own company. This sup sitiw does not affect the course of any subsequent argument and is made, once again, to g p the notation simple.

CARSON: COST OF CAPITAL 287

the author’s own work with 23 major rations shows that through the yeats 1947-67, the combined investment o f these Yrn was about 75 to 80 percent financed from internal sources.

What, then, might force the marginal cost of funds, h1 for a reprerentah’we firm, to rise as the corporation moves from internal to external hancing? Professor Duesenberry gives reasons for thii, and the literature on managerial behavior brings to light others (see, for example, [2 ] and 131)- From this literature, it would a p pear reasonable to hypothesize that successful corporate managers have at least one of the following traits: (i) They are more buoyant about their own firm’s investment opportunities (as an outlet for internal funds) than resent and prospective investors

(e.g. by banks )in their own firms’ affairs than do investors. The first trait may simply be allied to the fact that the representative corporate

manager tends to feel it his primary responsibility to improve his own enterprise [ 3, ch. 271. This could lead him to ignore lucrative investment op rtunities involv-

feeling that it alone is best qualified to run the enterprise, or it might mirror a gen- eral irritation with oukide dictates. In either instance, a giuen investment opportunity will be more readily undertaken, on the average, when it can be internally financed. Hence, the cost of capital tends to be lower for interml funds and is not, as Modig- liani and Miller believe, independent of the means of financing.

ian co

in general tend to be. (ii) They look more skeptica If y upon any outside participation

ing the earning assets of other corporations. The second might re r ect management’s

REFERENCES

1. Council of Economic Advisers. Economic Zndicdors. Washington, March 19%. J n n q 1963 nad h r i l 1966.

2. &d M.-C&t and J m a G. Mar4 A Bebaviord T b e g of the Firm. Eaglewood CUh. N.J. 1963.

3. Paa-F. Drucker, Tbc Practice of Mmurgrment. New York 1954. 4. Junes S. -. Business Cycles and Economic Growb. New YO& 1960. 5. David Durand, “Costs of Debt and Equity Funds for Busineu: Treads and Problems of

Meuuranent.” Conference on Rescarcb in BnsinesJ Finance. Nat. Bur. of Ron. R w c h . New York 1952.

6. John Lintner, ‘The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets,” Rev. of Econ. md Stur., February 1965, 47, 13-37.

7. Franc0 Modigliani a d M. H. Miller, “Corporate Taxes and the Cost of Capital: A Cor- d o n , ” Amu. Econ. Rev., June 1963,53, 433-43.

8. - and -, “The Cost of Capital, Corporation Finance, and the Theory of Investment,” Amm*can Econ. Rev., June 1958, 48, 261-97.

9. J. R. Rose, “The Cost of Capital, Corporation Finance, and the Tbeory of Investment: Comment.” hu. &on. Rev., September 1959.49, 638-39.

10. Scott E. Scpga, “Leverage and the Cost of Cppital,” National Banking Review, JW 1966. 3, 497-500.

11. E m Solom011, Tbe Tbeory of Pinanrial Mumgment. New York 1%3.