How the Hamada factor works

The Hamada factor is the piece that turns an equity beta into an asset beta, assuming debt beta is zero:

$$H = 1 + (1 - t)\frac{D}{E}$$

Equity beta 1.2, tax 25 percent, D/E 0.5. After-tax D/E is $0.75 \times 0.5 = 0.375$. The factor is $1 + 0.375 = 1.375$. Unlevered beta is then $1.2 / 1.375 = 0.8727$. Relevered at the same D/E: $0.8727 \times 1.375 = 1.2$.

The unlevered beta calculator on this page prints the factor and both betas. How unlevered beta works owns 0.8727. This page owns 1.375. How leverage ratio works is the D/E sitting inside the factor. Unlevered against levered beta is the two betas on one sheet.

Keep equity beta at 1.2 and tax at 25 percent. Set D/E to 0. After-tax D/E is 0. The Hamada factor is 1. Asset beta is $1.2 / 1 = 1.2$, equal to equity beta.

An all-equity firm has no financial leverage in the beta. Unlevering is multiplying and dividing by 1. That is the check that the identity is doing what it claims: the gap between 1.2 and 0.8727 on the first sheet is the 1.375 factor, not a change in the operations.

Equity beta 1.5, tax 21 percent, D/E of 1. After-tax D/E is $0.79 \times 1 = 0.79$. The Hamada factor is $1 + 0.79 = 1.79$. Asset beta is $1.5 / 1.79 = 0.8380$. Relevered at the same D/E is 1.5.

The equity beta is higher than 1.2 and the D/E is higher than 0.5. The factor rose from 1.375 to 1.79. The asset beta, 0.8380, sits close to the first sheet's 0.8727. Most of the extra equity beta was the larger factor, not the operations. That is the point of reading the factor before you compare two names.

It is not asset beta. Asset beta is 0.8727 on the first sheet. The factor is the 1.375 you divide by.

It is not D/E. D/E is 0.5. The factor is 1 plus after-tax D/E. Quoting 0.5 as if it were the unlevering multiplier skips the tax term and skips the leading 1.

It is not a WACC weight. How WACC works blends costs by market share. This factor is a beta identity. Put the relevered equity beta into the cost of equity, then into WACC. Do not paste 1.375 into a WACC weight box.

The $(1-t)$ is there because interest is deducted, so a unit of debt does not add a full unit of equity risk. At 25 percent tax and D/E of 0.5, after-tax D/E is 0.375 rather than 0.5, and the factor is 1.375 rather than 1.5. Asset beta is then 0.8727 rather than $1.2 / 1.5 = 0.8$.

Set tax to zero in your head and the factor becomes $1 + D/E$. That is a different identity. Type the tax rate the sheet actually uses. Distressed debt has a beta of its own. This page assumes it is zero.

It is not a CAPM cost of equity, not a debt-beta estimate, and not a WACC. The three sheets are a factor of 1.375 on D/E of 0.5 (asset beta 0.8727), a factor of 1 on no debt (asset beta 1.2), and a factor of 1.79 on D/E of 1 (asset beta 0.8380). This is educational material, not financial advice.