Hamada's Equation

Implemented widely in the area of corporate finance, Hamada’s Equation enables one to separate the financial risk of a levered firm from its business risk. The relationship, which results from combining the Modigliani-Miller capital structuring theorems with the Capital Asset Pricing Model, is used extensively in practice to help determine the levered beta and, through it, the optimal capital structure of corporate firms.

Hamada’s Equation basically relates the beta of a levered firm to that of its unlevered counterpart. It has proved useful in several areas of finance, including capital structuring, portfolio management and risk management, to name just a few.

The equation is presented by $$\beta_{L} = \beta_{U}[1+(1-T)\phi]$$ where βL and βU are the levered and unlevered betas, respectively, T the tax rate and φ the leverage, defined here as the ratio of debt, D, to equity, E, of the firm. The importance of Hamada's Equation is that it allows one to separate the risk of the business, reflected here by the beta of an unlevered firm, βU, from that of its levered counterpart, βL, which contains the financial risk of leverage. Hence, apart from the effect of the tax rate, which is generally taken as constant, the discrepancy between the two betas can be attributed solely to how the business is financed.