Hamada Equation

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Definition: Hamada Equation

Hamada equation shows the effect of debt or financial leverage on the risk coefficient of the firm. It is used to separate the financial risk of a firm from its business risk. It shows the relationship between the type of leverage and the firm’s cost of capital.

To understand the impact of leverage on a firm’s risk coefficient i.e. β, we know that

Asset = Equity + Debt

Beta Asset = (E/(D+E))*Beta Equity + (D/(D+E))*Beta Debt

Where D- Debt, E- Equity

Beta Equity = Beta Asset + (D/E)*(Beta Asset- Beta Debt)

Beta Asset is not dependent on how the assets of a firm are financed and hence it is equivalent to a firm’s unlevered beta. T being the tax rate, the relationship between the levered and unlevered beta can be written as

Beta Levered = Beta Unlevered * (1+{(D/E)*(1-T)}) – {Beta Debt * [(D/E)*(1-T)]}

If the Beta debt is taken as zero, then the equation is known as Hamada’s equation

Beta Levered = Beta Unlevered * (1+{(D/E)*(1-T)})


For e.g. If the Debt free beta for a company is 0.73 and market value of debt is $300,000 and market value of equity is $700,000 and tax rate is 40%, then Levered Beta can be calculated as

Beta Levered = 0.73 * (1 + {(300,000/700,000)*(1-0.40)}) = 0.92

This means that if the firm goes for leverage then it will increase its overall risk by 0.92-0.73 = 0.19 or 26%. So the Hamada equation shows the effect that the financial leverage can have on a firm’s overall risk.



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