Hamada Equation

What is the Hamada Equation?

The Hamada equation is the fundamental analysis method of evaluating the cost of Capital of a company as it uses extra financial leverage and how that is associated with the overall risks of the company.

This measure is used to summarize the impact this leverage type will leave on the company’s cost of capital in comparison to what would have been the cost of capital if the company didn’t have any debts.

History of Hamada Equation

Robert Hamada, the former finance professor at the University of Chicago Booth School of Business, began teaching at this university back in 1966 and served as the dean from 1993 to 2001. His equation first appeared in the paper, “The Effect of the Firm’s Capital Structure on the Systemic Risk of Common Stocks” in May 1972 in the Journal of Finance.

Hamada Equation Formula

The Hamada equation formula is:

βL=βU[1+(1−T) (ED)]

Here,

• βL=Levered Beta
• βU=Unlevered beta
• T=Tax Rate
• D/E=Debt to equity ratio

Calculating the Hamada Equation

To calculate the Hamada equation:

• Divide the firm’s debt by the equity
• Find one less the tax rate
• Multiply the result from number 1 and number 2 and add one
• Multiply the unlevered data by the result acquired from number 3

What do you Learn for the Hamada Equation?

This equation helps drawing upon the Modigliani-Miller theorem on capital structure and to extend the analysis to quantify the impact of financial leverage on the company. Beta is the measurement of the Volatility of systematic risk relevant to the overall Market.

Then, the Hamada equation shows how the beta of the company alters with leverage. The higher the beta, the higher is the risk for the company.

Example of the Hamada Equation

Let’s consider an example here. Suppose a company has a debt-to-equity ratio of 0.60, unlevered beta of 0.75 and a tax rate of 33%. Now, the Hamada coefficient would be:

0.75 [1 + (1 – 0.33) (0.60)] = 1.05

This simply means that the financial leverage for the company increases the risk by a beta amount of 0.30, which is less than 0.75 or overall 40$.

Let’s consider another example. Suppose there is a retail company which has the current unlevered beta of 0.82. The company’s debt-to-equity ratio is 1.05, and the annual tax rate is 20%. This way, the Hamada coefficient will be:

0.82 [1 + (1 – 0.2) (0.26)] = 0.99

Therefore, the company’s leverage has increased the beta amount by 21% or 0.17.