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:

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

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.