Theorems on the Relation between Equity and Debt
Ruben D. Cohen
We illustrate here the effects of the Modigliani-Miller theorems on
capital structuring, emphasising especially on the relationship between
equity and debt.
This is carried out numerically via a simplified
financial statement, which takes us through the methodology that leads to
the ROE, WACC and firm’s value, all plotted against leverage.
Originally June, 2001.
Revised August 2004.
I am grateful to Professors Narayan Naik and Michel Habib, of the London Business School, for their
I express these views as an individual, not as a representative of companies with
which I am connected.
Citigroup, London E14 5LB
The Modigliani and Miller (M&M)
theorems on capital structuring have,
inarguably, laid down the foundations for
modern corporate finance.
several principles that underlie these
theorems and two of these, which are most
relevant to this paper, may, very simply,
be reiterated as follows:
1. In the absence of taxes, there are no
benefits, in terms of value creation, to
In the presence of taxes, such benefits,
by way of interest tax shield, do
accrue when leverage is introduced
An outcome of the above, whose
proof can be found in almost any academic
[see, for instance, chapter 16
(1998) or chapter 18 of
Brealey and Myers (1996)], is that the
value added to a firm by taking on a debt
of, let us say,
is the incremental value added
is the tax rate.
It, thus, follows that
, of the levered firm becomes:
is the value of the unlevered
Simply stated, therefore, the value
of the levered firm is that of its unlevered
counterpart, plus the present value of the
interest tax shield, which is
We will now implement the above
to illustrate how debt and equity are
coupled to each other when a firm decides
to take on debt to buy back its shares - or
alternatively, when it issues shares to pay
The approach used here will
be simplistic and numerical in nature, with
intent to illustrate how a firm’s financial
statement [income statement and balance
sheet] is affected when the amount of debt
For the sake of simplicity, and