Leverage and Capital Structure


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1 Leverage and Capital Structure Ross Chapter 16 Spring Leverage Financial Leverage Financial leverage is the use of fixed financial costs to magnify the effect of changes in EBIT on EPS. Fixed financial costs can be, for instance, interest payments and dividends on preferred shares. 2
2 10.1 Leverage Financial Leverage Let T denote the tax rate, let I denote interest expense and let NS denote the number of shares outstanding. Then earnings per share (EPS) are given by EPS = (1 T )(EBIT I). NS Leverage Financial Leverage At a given EBIT level, how do percentage changes in EBIT translate into percentage changes in EPS? EPS EPS (1 T )(EBIT I) NS ( (1 T )(EBIT I) NS = (1 T )(EBIT I) NS = (1 T )(EBIT EBIT) (1 T )(EBIT I) = = EBIT (1 T )EBIT EBIT EBIT (1 T )(EBIT I) EBIT EBIT I EBIT EBIT ) 4
3 10.1 Leverage Financial Leverage That is, when EBIT increases by 1%, the percentage increase in EPS is EBIT EBIT I = EBIT EBIT I. This the degree of financial leverage (DFL) at base level EBIT. 5 Types of Capital Assets Debt & Equity NWC LongTerm Debt (D) Fixed Assets Equity (E) 6
4 Capital Structure Theory Modigliani and Miller s propositions: Proposition I: The market value of a firm is constant regardless of the amount of leverage that it uses to finance its assets. Proposition II: The expected return on a firm s equity is an increasing function of the firm s leverage. 7 Capital Structure Theory: M&M Proposition I The value of a firm is given by the present value of all the cash flows its assets are expected to generate in the future. The value of a firm is equal to the value of its assets. Unlevered Firm: V U = E U Levered Firm: V L = D + E L. 8
5 Capital Structure Theory: M&M Proposition I M&M Proposition I states that V U = V L. Why? Consider an allequity firm with value V U = E U. Suppose there existed a way to finance this firm s assets with debt and equity such that V L = D + E L > V U. 9 Capital Structure Theory: M&M Proposition I An arbitrageur could buy α shares of the above firm, place them in a trust and sell debt and equity claims against these shares in proportions such that making then a riskless profit. α(d + E L ) > αe U, 10
6 Capital Structure Theory: M&M Proposition I Similarly, someone could buy all of the firm s shares for E U and modify the firm s capital stucture to have V L = D + E L > E U and then resell the firm for a riskless profit of V L V U. 11 Capital Structure Theory: M&M Proposition I In a frictionless market, this arbitrage oppotunity would lead to an increase in the firm s unlevered equity to the point where for any level of D and E L. V U = E U = D + E L = V L 12
7 Capital Structure Theory: M&M Proposition I with Taxes Consider an unlevered firm, denoted U, that expects constant earnings before interest and taxes, denoted EBIT, forever. Each period, if the corporate tax rate is T, shareholders receive and the government receives (1 T )EBIT T EBIT. 13 Capital Structure Theory: M&M Proposition I with Taxes Let E U = V U denote the present value of the payment (1 T )EBIT forever. Let G U denote the present value of the payment T EBIT forever. Let k 0 denote the firm s WACC when unlevered. Then E U = V U = (1 T )EBIT k 0. 14
8 Capital Structure Theory: M&M Proposition I with Taxes Consider a levered firm, Firm L, with the same EBIT as U, but with a perpetual debt issue D with coupon rate i. Interest payments are tax exempt. Shareholders receive (1 T )(EBIT id) each period forever, bondholders receive id each period forever, and the government receives T (EBIT id) each period forever. 15 Capital Structure Theory: M&M Proposition I with Taxes Each period, the total cash flow to shareholders and bondholders of Firm L is (1 T )(EBIT id) + id = (1 T )EBIT + TiD. The value of the levered firm is then the sum of two perpetuities, i.e. (1 T )EBIT forever and TiD forever. 16
9 Capital Structure Theory: M&M Proposition I with Taxes As before, the present value of (1 T )EBIT forever is V U. Discounting the tax shield cash flows TiD at the bonds coupon rate i, their present value is TiD i = T D, and thus the value of the levered firm is V L = V U + T D. 17 Capital Structure Theory: Financial Distress In a world with uncertainty, however, increasing D also increases the risk of bankruptcy. Financial distress creates some costs. Business risk is not affected by the level of debt but has an impact on the firm s capability to meet in financial obligations. Financial risk is directly affected by the firm s level of debt. 18
10 The Optimal Capital Structure The value of the levered firm can also be obtained using V = (1 T )EBIT k a, where k a is the firm s cost of capital. 19 The Optimal Capital Structure Suppose we have D D+E k e k d WACC (k a ) 0% 13.00% 8.00% 13.00% 20% 13.20% 8.20% 12.20% 40% 13.80% 8.80% 11.80% 50% 14.25% 9.25% 11.75% 60% 14.80% 9.80% 11.80% 80% 16.20% 11.20% 12.20% 20
11 The Optimal Capital Structure Then the value of the firm V = k a is minimized. (1 T )EBIT k a, is maximized when 21 The Optimal Capital Structure Suppose EBIT = 1,000 and T = 40%. Then D D+E k e k d WACC (k a ) V = (1 T )EBIT k a 0% 13.00% 8.00% 13.00% % 13.20% 8.20% 12.20% % 13.80% 8.80% 11.80% % 14.25% 9.25% 11.75% % 14.80% 9.80% 11.80% % 16.20% 11.20% 12.20%
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