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
ΔV = DT
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 statement [income statement and balance sheet] is affected when the amount of debt changes. For the sake of simplicity, and for the time being, it shall be assumed that the cost of debt remains constant throughout – i.e. the firm experiences no
Originally June, 2001. Revised August 2004. http://rdcohen.50megs.com/MMabstract.htm I am grateful to Professors Narayan Naik and Michel Habib, of the London Business School, for their helpful comments. I express these views as an individual, not as a representative of companies with which I am connected. 2 Citigroup, London E14 5LB 3 E-mail: firstname.lastname@example.org
default risk as it raises its leverage. Including these effects is quite trivial, but shall not be pursued at this point. A companion paper, instead, focuses on it (Cohen, 2004). Analysis We plan to investigate here the evolution of a simple firm, which initially has all its assets backed by equity 4 . The firm then issues debt to buy back shares and, in the process, its value will rise, owing to debt-related tax benefits. We shall consider three scenarios, whereby: 1. The firm has an initial asset base [value] of 100 and no debt [Scenario 1]. The equity, E, of this firm is, therefore, 100 and should, thus, represent the unlevered firm’s value, Vu. We further assume that this firm has an “expected” EBIT 5 , of 20 and pays tax and interest at constant rates of 40% and 5%, respectively. Subsequently, this firm will have a financial statement similar to that shown in Figure 1. 2. In Scenario II, the firm takes on a debt, D, of 50 to buy back some of its shares. One of M&M’s outcomes, which is Equation 1, states that the firm’s value should increase by DT. According to our numbers, this equates to 20, which when added to the asset base, raises it from 100 to 120. It also follows that the firm must pay an interest of 2.5 [= 50 x 5%]. The consequence of the above is a financial statement that resembles the one shown in Figure 2. It is important to note...
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