Hamada equation
DCFThe formula linking levered and unlevered beta through the debt to equity ratio and the tax rate.
The Hamada equation states that levered beta equals asset beta multiplied by one plus one minus the tax rate times debt over equity. Rearranged, it lets you strip leverage out of an observed beta or add it back at a different capital structure.
The one minus tax rate term is the tax shield. Because interest is deductible, debt does not amplify equity risk quite as much as it otherwise would, since the government absorbs part of the interest burden.
The standard use is a three step procedure: unlever each comparable using its own debt to equity and tax rate, average the asset betas to get a sector view, then relever at the target's target capital structure rather than its current one.
It assumes debt itself is riskless, or at least that debt beta is zero, which is a reasonable simplification at investment grade and a poor one for a heavily levered credit where the debt genuinely carries market risk.
Worked example
Three peers with observed levered betas of 1.45, 1.10 and 1.62, at debt to equity ratios of 0.60, 0.20 and 0.85, all at a 25% tax rate.
Unlevered, they become 1.00, 0.96 and 0.99, so a sector asset beta of about 0.98. The spread collapsed once financing was stripped out, which is the point: their businesses really are similar and only their balance sheets differed.
Relevered at a target 0.35 debt to equity: 0.98 times one plus 0.75 times 0.35, giving 1.24.