3-Milestones Page 84 Wednesday, February 4, 2004 12:47 PM
84 The Mathematics of Financial Modeling and Investment ManagementModigliani-Miller Irrelevance Theorems and the
Absence of Arbitrage
A major step was taken in 1958 when Franco Modigliani and Merton
Miller published a then-controversial article in which they maintained
that the value of a company does not depend on the capital structure of
the firm.^11 (The capital structure of a firm is the mix of debt and equity.)
The traditional view prior to the publication of the article by
Modigliani and Miller was that there existed a capital structure that
maximized the value of the firm (i.e., there is an optimal capital struc-
ture). Modigliani and Miller demonstrated that in the absence of taxes
and in a perfect capital market, the capital structure was irrelevant (i.e.,
the capital structure does not affect the value of a firm).^12
In 1961, Modigliani and Miller published yet another controversial
article where they argued that the value of a company does not depend
on the dividends it pays but on its earnings.^13 The basis for valuing a
firm—earnings or dividends—had always attracted considerable atten-
tion. Because dividends provide the hard cash which remunerates inves-
tors, they were considered by many as key to a firm’s value.
Modigliani and Miller’s challenge to the traditional view that capi-
tal structure and dividends matter when determining a firm’s value was
founded on the principle that the traditional views were inconsistent
with the workings of competitive markets where securities are freely
traded. In their view, the value of a company is independent of its finan-
cial structure: from a valuation standpoint, it does not matter whether
the firm keeps its earnings or distributes them to shareholders.
Known as the Modigliani-Miller theorems, these theorems paved the
way for the development of arbitrage pricing theory. In fact, to establish
their theorems, Modigliani and Miller made use of the notion of absence
of arbitrage. Absence of arbitrage means that there is no possibility of
making a risk-free profit without an investment. This implies that the
same stream of cash flows should be priced in the same way across dif-(^11) Franco Modigliani and Merton H. Miller, “The Cost of Capital, Corporation Fi-
nance, and the Theory of Investment,” American Economic Review (June 1958),
pp. 261–297. In a later article, they corrected their analysis for the impact of corpo-
rate taxes: Franco Modigliani and Merton H. Miller, “Corporate Income Taxes and
the Cost of Capital: A Correction,” American Economic Review (June 1963), pp.
433–443.
(^12) By extension, the irrelevance principle applies to the type of debt a firm may select
(e.g., senior, subordinated, secured, and unsecured).
(^13) Merton H. Miller and Franco Modigliani, “Dividend Policy, Growth, and the Val-
uation of Shares,” Journal of Business (October 1961), pp. 411–433.