Hamada Equation

What Is the Hamada Equation?

The Hamada equation is a fundamental analysis method of investigating a firm's cost of capital as it utilizes extra financial leverage, and how that connects with the overall riskiness of the firm. The measure is utilized to sum up the effects this type of leverage has on a firm's cost of capital — far beyond the cost of capital as though the firm had no debt.

How the Hamada Equation Works

Robert Hamada is a former teacher of finance at the University of Chicago Booth School of Business. Hamada began educating at the university in 1966 and filled in as the senior member of the business school from 1993 to 2001. His equation showed up in his paper, "The Effect of the Firm's Capital Structure on the Systemic Risk of Common Stocks" in the Journal of Finance in May 1972.

The formula for the Hamada equation is:
$\begin &\beta_L = \beta_U \left [ 1 + ( 1 - T) \left ( \frac \right ) \right ]\ &\textbf \ &\beta_L = \text \ &\beta_U = \text{Unlevered beta*} \ &T = \text \ &D/E = \text{Debt to equity ratio*} \ \end$

• Unlevered beta is the market risk of a company without the impact of debt.

• Debt-to-equity ratio is a measure of a company's financial leverage.

The most effective method to Calculate the Hamada Equation

The Hamada equation is calculated by:

1. Separating the company's debt by its equity.
2. Finding one less the tax rate.
3. Increasing the outcome from no. 1 and negative. 2 and adding one.
4. Taking the unlevered beta and increasing it by the outcome from no. 3.

What Does the Hamada Equation Tell You?

The equation draws upon the Modigliani-Miller theorem on capital structure and stretches out an analysis to measure 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, at that point, shows how the beta of a firm changes with leverage. The higher the beta coefficient, the higher the risk associated with the firm.

Illustration of the Hamada Equation

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 expands the overall risk by a beta amount of 0.30, which is 1.05 less 0.75 or 40% (0.3/0.75).

Or on the other hand consider retailer Target (NYSE: TGT), which has a current unlevered beta of 0.82. Its debt-to-equity ratio is 1.05 and the effective annual tax rate is 20%. Consequently, the Hamada coefficient is 0.99, or 0.82 [1 + (1 - 0.2) (0.26)]. Consequently, leverage for a firm builds the beta amount by 0.17, or 21%.

The Difference Between Hamada Equation and Weighted Average Cost of Capital (WACC)

The Hamada equation is part of the weighted average cost of capital (WACC). The WACC includes unlevering the beta to relever it to track down an optimal capital structure. The act of relevering the beta is the Hamada equation.

Limitations of Using the Hamada Equation

The Hamada equation is utilized in finding optimal capital structures, yet the equation does exclude default risk. While there have been changes to account for such a risk, they actually lack a robust method for consolidating credit spreads and the risk of default. To gain a better comprehension of how to utilize the Hamada equation, it's valuable to comprehend what the beta is and how to work out it.

Features

• It draws upon the Modigliani-Miller theorem on capital structure.
• The Hamada equation is a method of examining a firm's cost of capital as it utilizes extra financial leverage.
• The higher the Hamada equation beta coefficient, the higher the risk associated with the firm.