MM Propositions Research Articles

Enhancing Student Understanding of the 1958 Modigliani-Miller Propositions

In their 1958 paper, Franco Modigliani and Merton Miller show that, in a theoretical “perfect world,” a company’s value and its cost of capital do not vary across levels of leverage. As a consequence, a linear relationship must exist between the debt-to-equity ratio and the cost of equity. Most textbooks first explore these fundamental theoretical relationships before transitioning on to “real world” issues such as corporate taxes and bankruptcy. In this teaching note, we suggest that textbook presentations of the 1958 MM propositions allow for confusion on the part of students because of ambiguity in discussions and graphical representations. To help avoid confusion on the students’ part in this regard, we present a series of exercises that instructors may use to supplement and enhance textbook content

Proof that MM Proposition I is Illogical

Despite some initial misgivings, the Modigliani-Miller proposition about the neutrality of the structure of capital was (enthusiastically) accepted by most academics and CEOs, and (reluctantly) agreed by most investors. In this paper we show that by ignoring the bidirectionality between the balance sheet and total revenue the proposition is logically inconsistent.

Perfect Market, Arbitrage, and Value Creation in the MM Proposition

The real contributions of the MM Proposition are its central assumptions of perfect capital markets and the associated arbitrage argument. In this text, we review the perfect market assumptions and no-arbitrage principle. Then, to explain the evolution of the understanding of arbitrage from a deterministic world into an uncertain world, we restate and comment on the proofs of the MM Proposition in current perspectives. With the no-arbitrage principle in mind, we clearly read the circular justification in the MM Proposition and the misleading concept of cost of equity. From the perspective of the distribution of a corporation's value creation, we find that shareholders prefer a maximum degree of debt. However, we believe that the capital structures are mainly constrained by industry characteristics and the market timing of equity and debt financing.

Cost of capital: spot rate or forward rate?

ABSTRACTIn this study, we intend to reveal some problems with the classic valuation method – the weighted average cost of capital (WACC) method. We first address a fundamental question about WACC, that is, should WACC be interpreted as a spot rate, a forward rate or any kind of average of either of them? We show that the nature of WACC is the expected forward rate. We next demonstrate that without understanding this nature, we may misinterpret the famous MM formula and MM Proposition II, as well as develop incorrect valuation framework. Our findings provide insightful implications to academia and practitioners for the proper interpretation and implementation of the WACC method.

Cost of Capital: Spot Rate or Forward Rate?

In this study, we intend to reveal some problems with the classic valuation method - the Weighted Average Cost of Capital (WACC) method. We first address a fundamental question about WACC, i.e. should WACC be interpreted as a spot rate, a forward rate, or any kind of average of either of them? We show that the nature of WACC is the expected forward rate. We next demonstrate that without understanding this nature, we may misinterpret the famous MM formula and MM Proposition II, as well as develop incorrect valuation framework. Our findings provide insightful implications to academia and practitioners for the proper interpretation and implementation of the WACC method.

(Ir)Relevance of MM Propositions in Explaining Leverage Strategies of Real Estate Companies

(Ir)Relevance of MM Propositions in Explaining Leverage Strategies of Real Estate Companies

Trade Off Theory or Pecking Order Theory: What Explains the Behavior of the Indian Firms?

The proposed research is intended to study the financing behavior of the Indian firms. The theory of capital structure is important for firms as they are constantly making investment decisions driven by financing decisions. Corporate decisions on capital structure policy have long been a subject of debate and still remain an unresolved issue. Out of the four major theories: the MM proposition, the Trade off theory, the Pecking order theory and the Agency theories, the present study focuses on the Trade off theory and the Pecking order theory Since the validity of the implications of these theories is mostly an empirical issue, correct model specification is very important. New models for the times series-trade off theory and the cross sectional diagnosis are proposed here. It is important to note that factors that affect these theories are very country specific. It depends on the factors like corporate governance, corporate and personal tax system, law & regulations, development of the capital and debt markets, etc which are highly economy specific (Alves and Ferreira, 2005; La Porta et al., 1997, 1998, 2000; Demirgue-Kunt and Levine, 1999; Demirgue-Kunt and Maksimovic, 1996). Hence it is important to carry out the study for Indian firms and not rely on the results from other economies. The models are tested for a sample dataset and the results are reported. The data consists of firms from ten industries (automobiles, drugs & pharmaceuticals, textile, polymers, electronics, health services, information technology, dairy, tea & coffee and electricity) for the period 1991-2007. The results seem to suggest the existence of the trade off theory in the Indian firms (contrary to the results found by Farhat, Cotei and Abugri, 2006).

The Seamy Side of the MM Irrelevance Propositions: A Break-Through Through the Haze

This paper reexamines MM's dividend and capital structure irrelevance theorems, refuting the first and confirming the latter from the inside out framework. The paper cooperates with Garry and Linda DeAngelo's papers on the irrelevance of the MM's dividend irrelevance theorem and refutes arguments of MM dividend irrelevance theorem advocates. The paper provides alternative proofs to MM's Propositions I and II for the capital structure irrelevance absent taxes and exclusive costs and benefits for shareholders, which holds even for two-way deals in an uninhabited island in the absent of markets. The argumentation is built upon the differences in time value of money and risk redistribution mechanism for the firm's stakeholders. The proofs presented take away the necessity in arbitrage and possibilities for shareholders to produce homemade leverage or escape from leverage for the capital structure irrelevance to hold in perfect markets and relax a long number of non-realistic assumptions. The only assumption that keeps is the investors' rational behavior that is endeavoring for net benefits and avoiding losses. The paper also considers firm valuation under imperfect market conditions and derives extended universal formula for estimating cost of levered equity, which includes MM's Proposition II formula as a special case. This formula addresses to internal causes of value relevance-irrelevance and is able to catch financial leverage value effect and is well-suited also for imperfect markets and unequal transactions. The implications of uncritical application of idealized models and valuation techniques are discussed as well. The paper investigates the shortcoming of CAPM, WACC, NPV and conventional proxies for capital budgeting and valuation in the light of new insights into MM's Propositions and suggests precautionary measures and improvements for financial applications.

U-Shaped Cost of Equity Function? Digging Into Modigliani-Miller (1958) Mistake

Modigliani and Miller (1958, The cost of capital, corporation finance and the theory of investment, The American Economic Review, Vol. 48, No 3) assert that, beyond some high level of leverage, the cost of equity curve may be decreasing. Despite the lack of rigour of their argument, this proposition received a small amount of criticism. However, it is wrong: in an MM world, the cost of equity function must be increasing, because under the dynamics of MM Proposition II, the marginal cost of debt must be lower than the cost of equity. Should, by any chance, the marginal cost of debt be higher than the cost of equity, arbitrage opportunities, incompatible with market equilibrium, would emerge. In this way, the intuitive idea that the cost of equity may increase unboundedly is recovered. Nevertheless, the cost of equity function will tend to infinity only if the first derivative of the interest cost function also tends to infinity. Otherwise, in the limit, the cost of equity will tend to a finite number. These findings reinforce the theoretical validity of MM propositions.

Capital Structure of Firms with Negative EBIT - Applying the MM Propositions

This abstract was created post-production by the JFI Editorial Board. This paper presents a model combining the MM Model and the CAPM to estimate the optimal level of debt for a firm with negative EBIT. Unlike most textbook examples, this model does not require making an assumption on the present value of bankruptcy costs which is often unrealistic. In addition to the theoretical construct, this paper illustrates the model's applicability with a numerical example using financial data from a real company. At present, one of the most frustrating aspects of investigating capital structure is that most research papers provide only qualitative guidance. There is a dearth of applicable quantitative results. This paper therefore fills the gap by providing practical quantitative guidance in identifying the optimal leverage of a firm, even if it has negative EBIT.

The One and Only Standard WACC - Cost of Capital versus Return on Capital

A lot of finance textbooks present calculation of WACC (Weighted Average Cost of Capital) as: WACC = Kd - (1 -/- T)- D % Ke - E %, whereas Kd is opportunity cost of debt before taxes, T is tax rate, D % is percentage of debt to total value, Ke is opportunity cost of equity and E % is percentage of equity to total value. Numerous textbooks state that D % and E % are market values, but the correct interpretation of these values is not sufficiently dealt with: which market values, what D/E-ratio? No matter how the financing is done, there is actually only one standard net WACC.WACC changes in time, one needs an up-to-date WACC, yes indeed, but what and how exactly? In short, many questions still remain, but up to the present they do not have unequivocal answers. The purpose of this paper is to clear up these questions and emphasize in some ideas that usually are overlooked. Famous writers, e.g., Pablo Fernandez, Ignacio Velez-Pareja and Joseph Tham, claim: to calculate the firm's value it is necessary to know the WACC-figure, but to calculate WACC, the firm's value (among other data like the financing profile) is needed. Indeed, one needs to know the WACC in order to calculate the firm's value. However, to calculate WACC, several data are truly needed, just not the firm's value. Many misconceptions exist about firm valuation and the valuation of tax shields (VTS) as well as the correct calculation of WACC.Although Franco Modigliani and Merton Miller (MM for short) were awarded the Nobel Prize in Economics, their Propositions I and II appear to be clearly incorrect. Many theories and much advise is flawed by the demasque of MM's Proposition I (1958, equation 3), which states in the absence of taxes, the firm's value is independent of its debt. The so-called proof given by MM is not a mathematical proof. It was and is a statement that cannot stand the test. Proposition I is not true; re SSRN_ID609102. Consequently, everything based on Proposition I is not true either. This paper repudiates Proposition II, constituting Ke being a cost to the firm and similarly a return to the equity investor. Ke and WACC are measuring costs, just costs. Return and cost values coincide at intersect-points only of clearly divergent return and respectively cost functions.

What MM Have Wrought

I. An Assessment The influence of the MM propositions on financial economics is comparable to the impact of Keynes in macroeconomics. Keynes' General Theory [23] ushered in a new theoretical framework, stimulating the development of equation systems by modeling the economy and utilizing the national income accounts that had been under development during the 1920s. Even the analytics of the monetarist view were sharpened and improved by the need to confront the Keynesian models. So it was with MM. The traditional approaches in finance had to be reexamined and clarified.

Comment on the Modigliani-Miller Propositions

[This is a comment on “The Modigliani-Miller Propositions after Thirty Years” by Merton H. Miller in this same issue.] What a treat it is to have the opportunity to read Merton Miller's ruminations on the MM Propositions. A comment on Miller and Modigliani's work can easily become a discussion of any facet of modern finance. I will focus on the two areas of arbitrage and taxation. Since the original MM analysis, economists have learned an enormous amount about the role played by no arbitrage conditions in financial markets. Taxation is where the real world meets the theory. At first blush, the corporate deduction for interest seemed to doom the MM analysis to an academic curiosity, since it appeared to give debt an obvious cost advantage over equity. It was the genius of Miller to see that the arbitrage analysis went much too deeply into the workings of the financial markets and the economy as a whole to be easily unseated by even something as powerful as the tax code.

MM—Past, Present, Future

[This is a comment on “The Modigliani-Miller Propositions after Thirty Years” by Merton H. Miller in this same issue.] Before getting serious about the MM theorem's past and future, I would like to say a few words about its more personal history, including the origins of the Modigliani-Miller alliance. Miller has reviewed, in his usual masterly fashion, the validity and working of the MM theorem under conditions of perfect markets and no taxes. There seems little to add to that subject, especially since, by now, countless alternative proofs of the theorem have been provided. So I would like to come back to some issues that are still with us -- and probably will be for a long time. How should the MM propositions be modified in the presence of taxes and how well do they perform in accounting for observed behavior?

On Valuation, Beta, and the Cost of Equity Capital: A Note

The issue of capital structure has been intensively examined in the finance literature, particularly after the appearance of the landmark 1958 paper by Modigliani and Miller [8], hereafter MM. In that paper, MM derived a relationship in terms of the expected return on equity of a levered and unlevered firm, known as MM Proposition II. Their analysis was extended later by researchers such as Hamada [5] and Rubinstein [9] who derived the corresponding relationship in terms of the systematic risk (beta). Both these risk-return relationships have been derived for the case of perfect capital markets and the case in which corporate income taxes are the only type of market imperfection. Although effects of other types of market imperfections such as personal income taxes and bankruptcy costs have been examined in numerous studies, neither MM Proposition II nor the “beta” relationship were extended to include the effects of personal income taxes and bankruptcy costs.

GROWTH STOCKS AND CORPORATE CAPITAL STRUCTURE THEORY

MORE THAN A DECADE AGO, with respect to the validity of Modigliani and Miller's homemade leverage thesis-namely, their Propositions I and II (see [24, 25])-under growth, Durand [6] expressed pointed skepticism by arguing that the said thesis is valid only under perfect markets where the market value of stock equals its book value.' Since then many others have questioned the validity-and consistency-of the propositions under growth, resting their theoretical as well as empirical analysis on the traditional valuation model,2 eminently set forth by Williams [34]. On the other hand, MM [25, 29, 30] have not only reaffirmed their original conclusions under growth but also have provided extensive tests of their statistical model [29, p. 348], which, in view of the foregoing, is not unequivocal.3 The purpose of this paper is to examine some of the theoretical issues bearing on the specification of empirically testable models concerning the effect of capital structure on the firm valuation. The motivation for doing so stems in particular from Durand's arguments and in general from the controversial nature of the subject. Insofar as the validity of the capital structure irrelevance proposition is in the final analysis an empirical issue, this paper takes the consistency of the MM Propositions I and II as a useful guide in generating several hypotheses that could be imbedded in the structural form of econometric models. Section I provides a brief introduction to the relevant literature. In Section II, some earlier results (contained in [15, 16, 12]) are succinctly