Hamada equation

The Hamada equation splits a levered equity beta into business and financial risk: levered beta = unlevered beta × [1 + (1 − tax rate) × debt-to-equity ratio].

FrameworkModigliani-Miller with corporate taxes

What it is

See it move

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A firm has an unlevered beta of 0.80, a 25% tax rate, and a debt-to-equity ratio of 0.50. Its gearing multiplier is 1 + (1 − 0.25) × 0.50 = 1.375. Multiplying gives the levered equity beta: 0.80 × 1.375 = 1.10, higher purely because the firm carries debt, not because its business risk changed.

The formula

LaTeX

\beta_L = \beta_U\left[1+(1-t)\frac{D}{E}\right]

Variables

$β_{L}$: Levered equity beta (ratio)
$β_{U}$: Unlevered (asset) beta (ratio)
$t$: Tax rate (%)
$D / E$: Debt-to-equity ratio (ratio)

Converts a business's unlevered (asset) beta into the levered equity beta shareholders actually bear, given its tax rate and gearing.