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Hamada’s Equation

Updated on April 12, 2024
Article byRutan Bhattacharyya
Edited byRutan Bhattacharyya
Reviewed byDheeraj Vaidya, CFA, FRM

What Is Hamada’s Equation?

Hamada’s equation refers to a fundamental analysis technique that involves analyzing an organization’s capital cost as it utilizes extra financial leverage and what connection that has with the business’s overall riskiness. It helps summarize the impact of the additional leverage on a business’s riskiness.

Hamada's Equation

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This concept combines the CAPM or Capital Asset Pricing Model and the Modigliani Miller (M&M) theorems. The structure of this equation is such that it can help determine an organization’s levered beta and hence, the ideal way in which the firm can structure its capital. A finance professor named Robert Hamada introduced this equation.

Key Takeaways

  • Hamada’s equation method is a concept utilized in fundamental analysis to differentiate the financial threat of a firm from its business threat. It summarizes the impact additional financial leverage has on a firm’s cost of capital compared to what its cost of capital would have been if there was no debt.
  • This equation is a part of the weighted average cost of capital.
  • The elements included in this formula are levered beta, tax rate, debt-to-equity ratio, and unlevered beta.
  • Robert Hamada, who was a Finance professor, created this equation. It helps determine a company’s optimal capital structure.

Hamada’s Equation Explained

Hamada’s equation refers to an equation used in corporate finance to differentiate between a levered organization’s financial and business risks. This measure helps determine a levered business’s cost of capital based on comparable organizations’ cost of capital. In this case, the comparable businesses have similar business risks. Hence, these firms’ unlevered betas are similar to those of the levered businesses.

A levered firm is a business that has both equity and debt in its capital structure. Assessing a levered business against an unlevered one is useful in multiple areas, such as portfolio management, capital structuring, and risk management.

This equation falls back on the M&M theorem and offers analysis for quantifying financial leverage‘s impact on a company. Beta measures systemic risk or volatility relative to the entire market. Then, the equation shows individuals how a company’s beta alters with leverage. That said, one must remember that the higher an organization’s beta coefficient, the higher its business risk.

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Formula

Hamada’s equation formula is as follows:  

ΒL = ΒU {1+ (1-T) (D/E)}

Where:

  • ΒU is unlevered beta
  • ΒL is levered beta
  • D/E is debt-to-equity ratio
  • T is the tax rate

Examples

Let us look at some of Hamada’s equation examples to understand the concept better.

Example #1

Suppose the debt-to-equity ratio of ABC, a company is 0.70. Moreover, it’s unlevered beta and tax rate are 0.80 and 32%, respectively. In this case, one can apply Hamada’s equation formula to analyze how financial leverage impacts the risk associated with the business.

Therefore, the Hamada coefficient is:

= 0.80{1 +(1 – 0.32)(0.70)}

= 1.1808.

This means the financial leverage raises the overall risk of ABC by a beta of 0.3808, which is (1.1808 – 0.80) or 38.08%.

Example #2

Suppose DBC, a tire manufacturer, has a tax rate, debt-to-equity ratio, and an unlevered beta of 30%, 0.80, and 0.60, respectively. The levered beta after applying Hamada’s equation, in this case, will be 0.60{1+(1-0.30)(0.80)}, i.e., 0.936.

This means DBC’s financial leverage increases its overall business risk by a beta of 0.136 (0.936-0.80) or 13.6.

Thus, as the coefficient’s beta increases, the risk of having more debt also increases.  

Importance

This equation is very useful for individuals because it provides a comprehensive analysis of an organization’s cost of capital, which shows how various aspects concerning financial leverage are connected to a firm’s overall riskiness. Besides showing how the beta of a firm alters with leverage, Hamada’s equation formula is a useful tool that allows individuals to conduct comparable company analyses.

Limitations

Although people utilize this equation to determine the right capital structure, it does not consider default risk. Although experts made modifications to the equation to factor in this risk, a robust way to include default risk and credit spreads is still absent in the case of this concept.  

Hamada’s Equation vs Weighted Average Cost of Capital

Hamada’s equation and WACC, or the weighted average cost of capital, can be quite confusing, especially if individuals have read about either of the two topics for the first time. One can learn about the key differences highlighted in the table below to avoid confusion.

Hamada’s EquationWeighted Average Cost Of Capital
Hamada’s EquationWeighted Average Cost Of Capital
This equation is a method businesses or individuals use in fundamental analysis.It refers to the overall amount a business has to pay to cover the cost of its operations.
One can use this equation to analyze the cost of capital of companies as they utilize additional financial leverage.The WACC helps determine the rate a business has to pay for raising funds from every source.
This refers to the act of relevering beta in WACC.This involves unrelevering and then relevering it to determine the optimal capital structure.  

Frequently Asked Questions (FAQs)

1. Is Hamada’s Equation accurate?

This equation is accurate if the dollar amount of a firm’s borrowings remains the same over time. The equation will not provide an accurate result if a company adopts a constant leverage strategy.

2. What are the assumptions of Hamada’s equation?

There are certain assumptions based on which Hamada’s equation was formed. Let us look at them.
– A firm’s debt remains constant in dollar value. Thus, the formula will be incorrect if a business implements a constant leverage strategy.
– The discount rate that a company uses to compute tax shield is the same as the debt capital’s cost.
– Another key Hamada’s Equation assumption is that the beta of debt or βD is 0.

3. What is Hamada’s equation for unlevered beta?

The equation for unlevered data is as follows:
βU = βL ÷ {1 + (1 – T)(D/E)}
Where:
– βL is levered beta
– D/E is debt-to-equity ratio
– T is the tax rate
– βU is unlevered beta

4. Is Hamada’s equation applicable to all types of companies?

The equation can only apply to companies with debt in their capital structure. Moreover, the debt’s dollar amount must remain unchanged over time.

This has been a guide to what is Hamada’s Equation. Here, we explain its examples, formula, importance, limitations, and differences with WACC. You can learn more about it from the following articles –

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