Skip to content

Unlevered beta calculator

Unlevered beta is equity beta divided by one plus after-tax D/E. An equity beta of 1.2, a 25 percent tax rate, and D/E of 0.5 produce an asset beta of 0.8727.

Unlevered beta

0.8727

Hamada factor 1.375. Relevered at the same D/E is 1.20.

Equity beta
1.20
1 + (1 minus t) times D/E
1.3750
Asset beta
0.8727

The levered beta. How the share moves with the market.

%

D/E, not debt over total capital. 0.5 means fifty cents of debt per dollar of equity.

The formula

βU=βE1+(1t)(D/E)\beta_U = \frac{\beta_E}{1 + (1 - t)(D/E)}

βE\beta_E is the equity beta, tt the tax rate as a decimal, and D/ED/E the debt-to-equity ratio. βU\beta_U is the asset beta, the beta the operations would have if they were all-equity financed. Debt beta is assumed to be zero.

Strip the financing out

Equity beta moves with financial leverage. The same swing in operating results lands on a thinner slice of equity when the firm has borrowed, so βE\beta_E is larger than the beta of the assets.

Hamada's identity, with debt beta taken as zero, undoes that. The Hamada factor is 1+(1t)(D/E)1 + (1 - t)(D/E). On this sheet that is 1+(10.25)×0.5=1.3751 + (1 - 0.25)\times 0.5 = 1.375. Divide the equity beta of 1.2 by 1.375 and the asset beta is 0.8727.

The same walk from the other side: treat equity as 1 and debt as 0.5, so after-tax firm value is 1+0.5×0.75=1.3751 + 0.5\times 0.75 = 1.375. Asset beta is equity beta times equity's share of that, 1.2×1/1.3751.2 \times 1 / 1.375. Both routes meet.

No debt, nothing to strip

Keep the equity beta at 1.2 and the tax rate at 25 percent. Set D/E to 0. The Hamada factor is 1. Asset beta equals equity beta: 1.2.

An all-equity firm has no financial leverage in the beta. Unlevering is a no-op. That is the check that the identity has not grown a constant of its own.

A higher beta on a more borrowed sheet

Equity beta 1.5, tax 21 percent, D/E of 1. The Hamada factor is 1+(10.21)×1=1.791 + (1 - 0.21)\times 1 = 1.79. Asset beta is 1.5/1.79=0.83801.5 / 1.79 = 0.8380.

Relevering at the same D/E must return 1.5, and it does: 0.8380×1.79=1.50.8380 \times 1.79 = 1.5. If you are putting this beta into a WACC for a different capital structure, relever at the target D/E, not at the firm's current one. That is the whole point of unlevering first.

What this page is not doing

It is not a regression. It will not estimate βE\beta_E from returns. Type the equity beta your data provider or your course printed. Two providers can publish 0.8 and 1.2 on the same name with neither of them doing the arithmetic wrong.

It also assumes debt beta is zero, which is the teaching-sheet Hamada convention and a worse fit for distressed debt. Miles-Ezzell and other identities exist. This page is the one-line unlevering a first deal model actually uses. This is educational material, not financial advice.

Worked examples

Equity beta 1.2, tax 25 percent, D/E 0.5

Equity beta is 1.2, the tax rate is 25 percent, and debt-to-equity is 0.5. What is unlevered beta?

  1. Hamada factor: 1+(10.25)×0.5=1.3751 + (1 - 0.25)\times 0.5 = 1.375.
  2. Asset beta: 1.2/1.375=0.8727271.2 / 1.375 = 0.872727, which prints as 0.8727.
  3. The other walk, with E = 1 and D = 0.5: 1.2×1/(1+0.5×0.75)=1.2/1.3751.2 \times 1 / (1 + 0.5\times 0.75) = 1.2 / 1.375.

Unlevered beta is 0.8727. The Hamada factor is 1.375. Relevered at the same D/E is 1.2.

The same beta with no debt

Keep equity beta at 1.2 and tax at 25 percent. Set D/E to 0. What is asset beta?

  1. Hamada factor: 1+(10.25)×0=11 + (1 - 0.25)\times 0 = 1.
  2. Asset beta: 1.2/1=1.21.2 / 1 = 1.2.

Asset beta is 1.2, equal to equity beta. There was no financial leverage to strip.

Equity beta 1.5, tax 21 percent, D/E 1

Equity beta 1.5, tax rate 21 percent, debt-to-equity 1. What is unlevered beta?

  1. Hamada factor: 1+(10.21)×1=1.791 + (1 - 0.21)\times 1 = 1.79.
  2. Asset beta: 1.5/1.79=0.8379881.5 / 1.79 = 0.837988, which prints as 0.8380.
  3. Relevered: 0.8380×1.79=1.50.8380 \times 1.79 = 1.5.

Unlevered beta is 0.8380. The Hamada factor is 1.79. Relevered at the same D/E is 1.5.

The mistake that costs the most

Unlevering with D/(D+E) in a formula that wants D/E, or forgetting the tax term.

On the first sheet, D/E is 0.5. Debt over total capital is 0.5 / 1.5, which is one third. Feeding one third into Hamada as if it were D/E produces the wrong asset beta, and then a WACC built on it prices the firm wrong.

Dropping (1t)(1-t) is the other unit error. At 25 percent tax and D/E of 0.5 the factor is 1.375, not 1.5. Dividing 1.2 by 1.5 prints 0.80 instead of 0.8727.

Common questions

Is this the beta I put into CAPM?

CAPM wants the equity beta of the claim you are pricing. If you are pricing the operations at a new capital structure, unlever, then relever at the target D/E, then put that equity beta into CAPM. Putting the current equity beta into a WACC for a different structure mixes two sheets.

Why is debt beta assumed to be zero?

That is the Hamada teaching convention: debt is treated as risk-free for this identity. Distressed debt has a beta of its own. This page does not estimate one.

Where does the 0.8727 go next?

Into a relevering at the target D/E, then into the cost of equity, then into WACC. The WACC guide is the next page if the question is the weighted cost of capital.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.