Leverage Theory Essay

1461 words - 6 pages

THEORY OF CAPITAL STRUCTUREDetermination of an optimal capital structure has frustrated theoreticians for decades. The early work made numerous assumptions in order to simplify the problem and assumed that both the cost of debt and the cost of equity were independent of capital structure and that the relevant figure for consideration was the net income of the firm. Under these assumptions, the average cost of capital decreased with the use of leverage and the value of the firm (the value of the debt and equity combined) increased while the value of the equity remained constant.%KsKaKdDebt/EquityModigliani and Miller showed that this could not be the case. Their contention was that two identical firms, differing only in their capital structure, must have identical total values. If they did not, individuals would engage in arbitrage and create the market forces that would drive the two values to be equal.Their proof of this proposition was based upon several assumptions (many of which have subsequently been relaxed without changing the results):All investors have complete knowledge of what future returns will beAll firms within an industry have the same risk regardless of capital structureNo taxes (we will relax this assumption subsequently)No transactions costsIndividuals can borrow as easily and at the same rate of interest as the corporationAll earnings are paid out as dividends (thus, earnings are constant and there is no growth)The average cost of capital is constantSince no taxes has been assumed, the operating income (EBIT) is equivalent to the net income which is all paid out as dividends. Thus, the value of the firm is equal toSince the value of the firm is equal to the sum of the value of the debt and equity,Substituting the last equation into the preceding equation and solving for KsThus, ks must go up as debt is added to the capital structure.%KsKaKdDebt/EquityTo prove their point, they assumed two identical firms, an unlevered firm (all equity) and a levered firm with $4 million of debt carrying an interest rate of 7.5%, both firms generating an operating income (EBIT) of $900,000 annually. They adopted the assumption that stockholders of both firms would have the same required rate of return of 10% which, as previously mentioned, was the standard assumption at the time (that the cost of equity was constant regardless of capital structure).Unlevered Firm Levered FirmEBIT $ 900,000 $ 900,000-Interest 0 300,000Income $ 900,000 $ 600,000Since the required rate of return of shareholders is 10% in both casesUnlevered Firm Levered FirmValue of Equity =Value of Debt = $ 0 $ 4,000,000Total Value of Firm = $9,000,000 $10,000,000If this were true, then someone who owns 10% of the levered firm would have income of $60,000 ($600,000 * 10%) and could sell it for $600,000 ($6 million * 10%). With this $600,000 the individual could borrow another $300,000 at 7.5% and buy 10% of the unlevered firm for $900,000 ($9 million * 10%). What would this...

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