The Hamada Equation

A company's observed equity beta reflects both the riskiness of its underlying business and the extra risk added by financial leverage, debt magnifies the swings in equity value even if the business itself is stable. The Hamada equation separates these two effects:

where $\beta_L$ is the levered (observed equity) beta, $\beta_U$ is the unlevered (asset) beta reflecting only business risk, $t$ is the tax rate, and $D/E$ is the debt-to-equity ratio. Running this backward, dividing out the leverage term, recovers $\beta_U$ from a known $\beta_L$, which is exactly what analysts do when comparing companies with different capital structures: unlever each comparable's beta to strip out financing effects, average the unlevered betas, then re-lever that average to the target company's own capital structure.

For example, a company with $\beta_L = 1.5$, tax rate $t = 25\%$, and $D/E = 1.0$ has $\beta_U = 1.5 / [1 + (0.75)(1.0)] = 1.5/1.75 \approx 0.857$, its business risk alone, stripped of the leverage that inflated the observed 1.5. Re-levering that same $\beta_U = 0.857$ to a different target capital structure, say $D/E = 2.0$ at the same tax rate, gives $\beta_L' = 0.857 \times [1 + (0.75)(2.0)] = 0.857 \times 2.5 \approx 2.14$, a much higher equity beta purely from the heavier debt load, with the underlying business risk held fixed.