Hamada's Equation

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In corporate finance, Hamada’s Equation is used to separate the financial risk of a levered firm from its business risk. The equation combines the Modigliani-Miller theorem with the Capital Asset Pricing Model. It is used to help determine the levered beta and, through this, the optimal capital structure of corporate firms.

Hamada’s Equation 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[1]

βL = βU[1 + (1 − T)φ]
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 separates 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. 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.

[edit] References

  1. ^ Hamada, R.S. (1972) “The Effect of the Firm's Capital Structure on the Systematic Risk of Common Stocks,” The Journal of Finance, May issue, p.435.
  • Cohen, R.D. (2007) "Incorporating Default Risk Into Hamada's Equation for Application to Capital Structure", Wilmott Magazine (download paper)
  • Conine, T.E. and Tamarkin, M. (1985) “Divisional Cost of Capital Estimation: Adjusting for Leverage,” Financial Management 14, Spring issue, p.54.