Hong Life CalculatorsUnderstanding the unlevered beta calculator — concept and principle
A company's share beta mixes the risk of its business with the extra risk created by its debt. Unlevering removes the debt effect to give the asset beta, and re-levering applies that business risk to a different capital structure. Analysts use this to estimate the cost of equity for private companies, projects or a target capital structure.
How it is calculated
- Unlevered (asset) beta: βU = βL ÷ [1 + (1 − t) × D/E].
- Re-levered beta: βL = βU × [1 + (1 − t) × D/Etarget].
- t: marginal tax rate; D/E: debt-to-equity ratio.
- Debt weight = D ÷ (D + E) = (D/E) ÷ (1 + D/E).
The principle
Debt magnifies the swings in shareholders' returns: the more a company borrows, the more its equity moves when the business does. Robert Hamada showed how to remove that leverage effect under the assumption that the debt carries no market risk (debt beta of zero) and that the tax saving on interest is as risky as the debt. Because interest is tax-deductible, debt adds less risk to equity than it otherwise would, which is why (1 − t) appears in the formula.
Worked example
Default inputs (a Damodaran example): levered beta 1.24, D/E 27.06%, tax 40%, target D/E 50%.
- Leverage factor = 1 + 0.6 × 0.2706 ≈ 1.1624.
- Unlevered beta = 1.24 ÷ 1.1624 ≈ 1.0668.
- Re-levered at D/E 50%: 1.0668 × (1 + 0.6 × 0.5) = 1.0668 × 1.3 ≈ 1.3868.
- Debt weight now = 0.2706 ÷ 1.2706 ≈ 21.3%; at the target = 0.5 ÷ 1.5 ≈ 33.3%.
| Levered (equity) beta | Unlevered (asset) beta |
|---|---|
| 0.31 | 0.2667 |
| 0.62 | 0.5334 |
| 0.93 | 0.8001 |
| 1.24 | 1.0668 |
| 1.55 | 1.3335 |
| 1.86 | 1.6002 |
| 2.48 | 2.1336 |
How to read the result
The unlevered beta reflects business risk alone, so companies in the same industry should have similar asset betas. Analysts often average unlevered betas across a peer group and then re-lever to the target company's capital structure. Higher leverage raises equity beta and the cost of equity.
Common mistakes
- Using book D/E when market values are available.
- Using an average tax rate instead of the marginal rate.
- Ignoring cash; some analysts use net debt.
- Applying the formula to firms with very high leverage, where debt beta is clearly not zero.
Frequently asked questions
What is the unlevered beta formula?
βU = βL ÷ [1 + (1 − t) × D/E].
Why unlever beta?
To compare business risk across companies with different debt, or to estimate a beta for a different capital structure.
Is unlevered beta always lower?
Yes for a company with positive debt and a debt beta of zero, because leverage adds risk to equity.
Sources: Hamada, R. S. (1972). The Effect of the Firm's Capital Structure on the Systematic Risk of Common Stocks. Journal of Finance, 27(2). · Damodaran, A., Investment Valuation (bottom-up betas)