Merton Miller and Modern Finance

Financial Management (Financial Management Association), Winter, 2000 by Rene M. Stulz

The 1958 article explained superbly why arbitrage arguments have contributed so much to the success of finance in pricing securities. In their proof, Modigliani and Miller emphasized that arbitrage is profitable to the one who undertakes it "quite independently of his attitudes towards risk" (Modigliani and Miller (1958), p. 269). Throughout the years, finance has found it difficult to understand exactly how to measure and price risk for securities. Arbitrage arguments bypass this problem altogether. They lead to a theory of pricing of securities that does not rely on attitudes towards risk. In a world without arbitrage opportunities, we can price securities by discounting their expected payoffs at the risk-free rate as if investors were indifferent towards risk. This approach to pricing securities is now not only one that is present throughout the academic literature but one applied in the business world.

II. Arbitrage and Corporate Finance

Though arbitrage arguments are now pervasive throughout finance, the more immediate and direct impact of the arbitrage proof of Proposition I was to provide the foundation for modern corporate finance because it specifies sufficient conditions for leverage not to matter. Because of the proof, we know that if financial markets are perfect, the value of a firm cannot be affected by leverage. As a result, practitioners and academics alike know that if leverage affects value, it must be that some of the assumptions required by the arbitrage proof do not hold. The arbitrage proof assumes a world where contracting is costless, all parties have the same information, transaction costs do not exist, there are no taxes, there are no limitations to short-sales, and firms and investors take prices as given. Of these assumptions, the absence of taxes was quickly identified as posing substantial difficulties for the result that leverage is irrelevant for firm value in the real world.

In their papers, Modigliani and Miller eliminated once and for all the argument that leverage is costly because it increases the cost the corporation pays for its debt. Their work made clear that an increase in the coupon paid on debt as leverage increases is not a cost of leverage in a world of perfect markets. As leverage increases in a world of perfect markets, the coupon paid on debt increases, but that is because bondholders bear more risk and have to be compensated for this additional risk. This will happen even though the firm's cash flows are unaffected by the additional leverage and hence, as Merton Miller pointed out in his Nobel lecture, the increase in the risk of debt has no social costs because the firm's total risk is unaffected by the change in leverage. [2] However, when looking at the cost of debt, Modigliani and Miller immediately realized that with corporate income taxes, the cost of debt for the firm is the cost after taxes. Since coupon payments are tax deductible, Modigliani and Miller saw that corporate taxes could make leverage valuable. The tax shield of debt with corporate income taxes was large since "the deductibility of interest could amount to a subsidy of as much as 50 cents on each dollar of debt capital raised by the firm." [3]