Academic journal article Journal of Business Strategies

Response of the Cost of Equity to Leverage: An Alternative Perspective

Academic journal article Journal of Business Strategies

Response of the Cost of Equity to Leverage: An Alternative Perspective

Article excerpt

ABSTRACT

In this paper we examine the change in a corporation's cost of equity as the corporation increases leverage. Standard textbook treatments present the wellknown Modigliani-Miller hypothesis that the cost of leverage increases linearly with increases in the debt-to-equity ratio in keeping with a constant cost of capital for the firm. Less frequently, textbooks present the Modigliani-Miller argument that, if the cost of debt rises with high levels of leverage, the cost of equity will increase at a decreasing rate or even decline in order to keep the overall cost of capital constant. Standard textbook presentations continue with additional discussions concerning tax effects and bankruptcy costs but without mention of the cost of equity. These presentations leave the impression that the cost of equity remains as presented in the Modigliani-Miller framework. In this paper we present theoretical and empirical arguments in support of our claim that the cost of equity increases slowly with moderate increases in debt but increases dramatically as leverage increases sufficiently to cause equity investors to fear bankruptcy.

INTRODUCTION

What Should Students Know About the Cost of Equity?

Two fundamental relationships form the core knowledge base that students should possess about the cost of equity, both from a corporate finance perspective and an investment perspective. First, because debt has a senior payment claim both in the case of normal business operations and in the case of bankruptcy, equity has more risk and the cost of equity is greater than the cost of debt. This holds regardless if the firm uses very little leverage or a great deal of leverage. Second, because debt is cheaper than equity, increasing leverage may increase per unit payments to equity, but at the cost of increasing variability in these payments. This increase in financial risk causes equity owners to demand a higher percentage return. It is the path of this increased required return to equity that we argue is inadequately addressed by textbooks and provides the focus of this paper. Because textbook discussions of the relationship between the cost of equity and leverage typically depend on the theory developed by Modigliani and Miller, we continue with a discussion of their arguments.

Modigliani-Miller Model

Modigliani and Miller's (1958) Nobel Prize winning paper on capital structure still underpins textbook discussions of capital structure. At the core of their argument is the proposal that a firm's value is determined solely by the cash flow and the risk of the cash flow created by the firm's assets. Thus, under perfect market conditions, the value of the firm, and hence its overall cost of capital, is not influenced by the decision to finance the firm by debt or by equity. This result is referred to as the irrelevance proposal, or as Modigliani-Miller Proposition I (MM I), and is supported by the argument that investors can achieve whatever level of leverage they desire in their investment in a firm by borrowing on their own to supplement their personal equity investment (the "homemade leverage" argument).

Because using debt financing replaces the higher cost of equity with lower costing debt, in order for the cost of capital to remain constant, the cost of equity must increase with leverage and must do so at a prescribed rate as shown in equation (1) below. This relationship is referred to as Modigliani-Miller Proposition II (MM II).

[RR.sub.equity] = Unlevered Required Return of Equity + D/E * (ROA--Cost of Debt) (1)

Where: [RR.sub.requity] l is the required return on equity for a given level of leverage, D/E is the debt-to-equity ratio (measures leverage), and ROA is the expected return on assets.

The cost of debt is assumed to be constant across levels of leverage.

Thus, the required return to equity is a constantly increasing linear function of leverage as measured by the D/E ratio. …

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