## What is the 'Hamada Equation'

The Hamada equation is a fundamental analysis method of analyzing a firm's cost of capital as it uses additional financial leverage, and how that relates to the overall riskiness of the firm. The measure is used to summarize the effects this type of leverage has on a firm's cost of capital (over and above the cost of capital as if the firm had no debt). The equation is:

B(L) = B(U)[1 + (1-T)(D/E)]

where:

• B(L) = levered beta
• B(U) = unlevered beta
• T = tax rate
• D/E = debt to equity ratio
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The equation draws upon the Modigliani-Miller theorem on capital structure and extends an analysis to quantify the effect of financial leverage on a firm. Beta is a measure of volatility or systemic risk relative to the overall market. The Hamada equation, then, shows how beta of a firm changes with leverage.

The higher the beta coefficient, the higher the risk associated with the firm. For example, say a firm has a debt to equity ratio of 0.60, a tax rate of 33%, and an unlevered beta of 0.75. The Hamada coefficient would be 0.75[1 + (1-0.33)(0.60], or 1.05. This means that financial leverage for this firm increases the overall risk by 0.30 (1.05 - 0.75), or 40%.

Robert Hamada is a professor of finance at the University of Chicago Booth School of Business. Professor Hamada served as the dean of the business school from 1993-2001, and has taught at the University of Chicago since 1966. His equation appeared in his paper, "The Effect of the Firm's Capital Structure on the Systemic Risk of Common Stocks" in Journal of Finance in May 1972.

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