Introduction
The Modigliani-Miller (MM) theory of corporate
finance has been subject to considerable debate
and interest for over 30 years. Today it is the
dominant theory in the field. This paper highlights
an intuitively unappealing implication of the
MM model that has remained unnoticed or at least
has not received due attention. Modigliani &
Miller (hereafter MM) revolutionized corporate
finance. The ideas presented in their major articles
(1958,1963,1966) have become central to the capital
structure and cost of capital theories.
The basic assumptions of the original MM papers
(perfect capital markets, rational investor behavior,
no tax differentials, and the implicit assumption
of no bankruptcy costs) are retained.
The Modigliani-Miller Theory
According to MM (1963), the value of a levered
firm (VL) with a permanent level of debt (D) in
its capital structure is given by:
VL = VU + tauD = (l - tau)E(X)/ rho + tauR / r
(Copeland et al, 1988)----------(1)
where:
VU = The value of an unlevered firm;
tau = The corporate tax rate;
E(X) = The expected level of average annual earnings
generated by the assets of the firm;
1/p = The market capitalization rate for an unlevered
firm in the firm's risk class;
r = The rate of interest, assumed to be constant
and independent of the size of debt; and
R = The size of the interest bill = rD.
Further, the value of a firm naturally must be
equal to the sum of the values of equity (S) and
debt (D), so that:
VL= S+D. (DeThomas, 1985)--------(2)
The line of reasoning leading to the central formula
of the MM theory is broadly as follows. The after
tax return (earnings after interest and taxes,
plus interest), denoted by the random variable
Xtau, can be expressed as:
xtau = (l - tau)(X- R) + R = (l - tau)X + tauR.
(Fama, 1968)---------(3)
MM (1963) argue that from the investor's point
of view, the long-run average stream of after
tax returns appears as a sum of two components:
an uncertain stream, (1- tau)X, and a sure stream,
tauR. This suggests that the equilibrium market
value of the combined stream can be found by capitalizing
each component separately.
The Inconsistency Implicit in the MM Model
The cost of equity capital, i*, is defined as
the rate of return required on a firm's equity
by the market. In the MM framework, i* can be
derived as follows. Utilizing (3):
E(Xtau) - tauR = (l- tau)E(X). (Hamada, 1969)-----------(4)
Therefore, equation (1) can be expressed equivalently
as:
VL = E(Xtau) - tauR / rho + tauD = E(Xtau - taurD
+ rhotauD / rho (Levy, 1986) ----------(5)
= E(Xtau) + tau(rho - r)D / rho.
Xtau also can be considered to consist of the
following two streams (see equation (3)):
• The net profit after interest and taxes
accruing to common shareholders. Deducting from
earnings before interest and taxes, (EBIT), X,
the amounts of taxes, (X-R)tau, and interest charges,
R, yields the net profit, pi, which belongs to
the shareholders:
pi = X- (X - R)tau- R = (l- tau)(X - R). (Miller,
1966) --------------(6)
The expected size of the annual profit stream
will be:
E(pi) = (l- tau)[E(X) - R]. (Modigliani, 1958)
------------(7)
• The second part of Xtau is the amount
of interest charges, R = rD.
The value of the firm now can be expressed as:
VL = E(pi) + rD + tau(rho - r)D / rho, (Modigliani,
1963)------------(8)
and the value of equity is:
S=VL - D= E(pi) + rD + tau(rho - r)D - rhoD /
rho (Osteryoung, 1977) -----------(9)
= E(pi) -(l-tau)(rho - r)D / rho
whereby:
rho = E(pi) / S - (l I tau)(rho - r)D / S. (Phillips,
1983) ---------(10)
As growth is excluded from the model, the expected
rate of return to the shareholders (the cost of
equity), i*, is obtained directly by dividing
the expected net profit by the market value of
equity (e.g., Hamada, 1969; Rubinstein, 1973,
and Copeland and Weston, 1988). Consequently,
rearranging equation (10) yields the MM (1963)
expression of i*:
i* = E(pi) / S = rho + (l - tau)(rho - r)D/S.
(Rubinstein, 1973) --------------(11)
One can argue, however, that it is basically the
required rate of return, i*, that determines S
in the market, not vice versa. Thus, a more specific
expression for i* is needed than is provided by
equation (11) above. Although not given by MM,
this can be accomplished in the MM framework as
follows.
Based on equations (1) and (2), the value of equity,
S, can be written as:
S = VL - D =(l - tau)E(X) . rho + tauR / r - R
/ r (Sharpe, 1964) ----------(12)
= (l - tau)E(X) / rho - (l - tau)R / r.
By noting that the expected net profit to the
shareholders is E(pi) = (1- tau)(E(X) R), i* can
be expressed as:
Multiple line equation(s) cannot be represented
in ASCII text. (Sharpe & Cooper, 1972) ---------(13)
To illustrate, assume:
E(X) = 1000
r = .05
p =.10
tau = 0 or, alternatively, tau = .50.
Table 1 shows how increasing leverage affects
key valuation variables in the MM framework. Figures
for the following variables are tabulated:
• Expected annual earnings, E(X);
• The assumed amounts of interest charges,
R;
• Required rate of return on equity i*,
obtained from equation (13); 1
• The value of the whole firm, V (from equation
(1));
• The amount of debt, D (= R/r);
• The value of equity, S (given, e.g., by
S = E(pi)/i*, by equation (9), or, simply,.S =
V - D);
• Net profits to common shareholders after
interest and taxes, E(pi) = (l- tau)(E(X) - R).
The tax rate is assumed to be zero in Table 1.
Table 2 is based on otherwise identical assumptions
except.that the tax rate is 50 percent (tau =
.50).
Table 1 shows that in the absence of taxes, the
value of the firm (v) does not depend on leverage.
With taxes, the value of the firm increases due
to the tax saving induced by leverage. Introducing
taxation does not cause differences in the rates
of return for stockholders, if leverage is measured
in terms of total earnings and interest payments.
(Note that if leverage is measured in terms of
market values (for instance by D/S), the i*- values
would differ.) And while the tax shield increases
the value of the firm with taxation, it does not
affect the rate of return on common stock, i*.
The troublesome aspect of the two tables is that
the value of equity becomes zero in both cases
when the interest bill (R) is only half of the
total earnings. The MM theory causes the value
of equity to become worthless too soon. (The figures
for the example are taken from MM (1958,p. 271),
where they restricted the illustration to a single
case in which R = 200, implying i* = .133.) If
the figures in Table 2 are in millions of dollars,
the shares of this firm, which is expected to
earn $250,000,000 annually, are worthless.
Note that a shareholder has limited liability.
In the worst possible case of bankruptcy, the
shareholder will receive nothing. The shareholder,
however, does not have to pay any of the firm's
losses or costs associated with bankruptcy.
The reason for the inconsistency in the MM model
becomes evident if equation (13) is examined.
The equity becomes zero (and i* infinite) when:
E(X) R
-------- - --- = 0
rho r
or
E(X) R
-------- = ---. (Worley & Green, 1989) ----------(14)
rho r
Because p is is expected to exceed the risk free
rate (r), both sides of equation (14) become equal
before E(x) = R. How much before depends on the
relation of p to r.
Thus, one can argue that the model does not give
realistic solutions. (Even the well-known extreme
corner solution, which suggests that a firm should
have nearly 100 percent debt, occurs when the
firm may have normal levels of R/E(X).)
Irrelevant Dividend Policy
Miller and Modigliani (1961) argue that dividend
policy is irrelevant for the cost of capital and
the value of the firm in a world without taxes
or transaction costs. They show that when investors
can create any income pattern by selling and buying
shares, the expected return required to induce
them to hold firm shares will be invariant to
the way the firm packages dividend payments and
new issues of stocks. Since the firm's assets,
investment opportunities, expected future net
cash flows and cost of capital are not affected
by the choice of dividend policy, its market value
is unaffected by any change in the firm's payout
pattern. Thus, dividend policy is irrelevant and
firms can choose any payout pattern without affecting
their value. Miller and Modigliani's (MM) theory
implies that dividend payout will fluctuate as
a by-product of the firm's investment and financing
decisions, and therefore, will not exhibit a systematic
pattern over time.
MM's irrelevance argument also applies to the
case with corporate taxes but without personal
taxes. It can be shown that the value of firms
with or without debts is not affected by dividend
policy if there are no transaction costs and investment
decisions are independent of dividend decisions.
The situation becomes more complicated when personal
taxes are considered. In general, dividend policy
becomes relevant if investors' dividend income
tax rates are higher than their capital gains
tax rates. However, Federal tax laws are complex
and individuals can shelter their income through
tax-exempt and tax-deferred investments.
Also, reducing the tax liability of dividend income
often involves transaction costs. The existence
of transaction costs may preclude individuals
front fully using tax-reduction strategies. Despite
these complications, dividends generally subject
individual investors to a higher income tax rate
than capital gains do. Thus, dividend policy may
affect investors' after-tax income and therefore,
the cost of capital and the value of the firm.
As Brennan (1970) indicates, for a given risk
level, investors require a higher total return
on a security, the higher its prospective dividend
yield is, if a higher tax rate is levied on dividends
than on capital gains.
Therefore, front the standpoint of maximizing
individuals' net after-tax income, firms should
pay the lowest cash dividends to reduce shareholders'
tax burden.
If taxes are relevant to the firm's value and
cost of capital, one should observe a change in
corporate dividend policy whenever there is a
change in personal income and/or capital gains
taxes. Firms and investors are expected to respond
to the change in the tax code in making their
dividend and investment decisions For instance,
when there is a decrease in the capital gains
tax rate relative to the regular income tax talc.
firms should reduce their dividend payout, and
vice versa.
The tax laws in the U.S. have gone through a couple
of changes since 1980. In 1981, people had the
largest tax cuts in the history of the United
States. Top individual tax rates decreased from
71) to 51) percent and allowable contributions
to Keoghs and other retirement systems were increased.
The Tax Reform Act of 1984 lowered the holding
period on capital gains from more than one year
to more than six months, while the minimum holding
period for the 85% exclusion for corporate investor,
was extended from 16 to 46 days.
In 1986, the most sweeping revision of the tax
code in the U.S. history took place. One of the
most significant changes in 1986 is the elimination
of the preferential tax treatment of long-term
capital gains.
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