Mm Hypothesis
An Implication of the Modigliani-Miller Capital Structuring Theorems on the Relation between Equity and Debt1
Ruben D. Cohen 2,3
Abstract 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.
Introduction The Modigliani and Miller (M&M) theorems on capital structuring have, inarguably, laid down the foundations for modern corporate finance. There are 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 increasing leverage. 2. In the presence of taxes, such benefits, by way of interest tax shield, do accrue when leverage is introduced and/or increased. An outcome of the above, whose proof can be found in almost any academic finance text [see, for instance, chapter 16 of Ross et al (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, D, is
where ΔV is the incremental value added and T is the tax rate. It, thus, follows that the value, VL, of the levered firm becomes:
V L = Vu + DT
(1b)
ΔV = DT
1
(1a)
where Vu is the value of the unlevered firm. 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 DT. 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 down debt. The approach used here will be simplistic and numerical in nature, with intent to illustrate how a firm’s financial
Ruben D. Cohen 2,3
Abstract 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.
Introduction The Modigliani and Miller (M&M) theorems on capital structuring have, inarguably, laid down the foundations for modern corporate finance. There are 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 increasing leverage. 2. In the presence of taxes, such benefits, by way of interest tax shield, do accrue when leverage is introduced and/or increased. An outcome of the above, whose proof can be found in almost any academic finance text [see, for instance, chapter 16 of Ross et al (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, D, is
where ΔV is the incremental value added and T is the tax rate. It, thus, follows that the value, VL, of the levered firm becomes:
V L = Vu + DT
(1b)
ΔV = DT
1
(1a)
where Vu is the value of the unlevered firm. 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 DT. 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 down debt. The approach used here will be simplistic and numerical in nature, with intent to illustrate how a firm’s financial