Borrow the beta, not the balance sheet
When you value a private company or a division, there is no stock price to regress — so you borrow a beta from a publicly traded peer. But that beta was measured on the peer’s shareholders, who bear the peer’s leverage. Robert Hamada’s 1972 result, built on the Modigliani–Miller propositions with corporate taxes, gives the conversion: strip the peer’s capital structure out to isolate the pure business (asset) beta, then re-dress that asset beta in your own target debt-to-equity ratio. The relevered beta is what belongs in theCAPM calculatorto estimate a cost of equity, which in turn feeds theWACC calculatorand the discount rate of aDCF calculator.
The Hamada equation, both directions
βU = βL ÷ [1 + (1 − t) · (D/E)] (unlever)
βL = βU × [1 + (1 − t) · (D/E)] (relever)
where βL = levered (equity) beta, βU = unlevered (asset) beta, t = corporate tax rate, and D/E = the debt-to-equity ratio. The bracket 1 + (1 − t)·(D/E) is the leverage factor: it is exactly 1 for an all-equity firm and grows with debt, shrunk slightly by the tax shield. Dividing by it removes financial risk; multiplying by it adds financial risk back at whatever D/E you choose.
Worked example
Take a peer trading with a beta of 1.3 at a debt-to-equity ratio of 0.5, and suppose your target structure carries a D/E of 1 with a 21% tax rate. The chain runs in three steps:
| Step | Amount |
|---|---|
| Peer levered beta (βL)observed at the peer's debt-to-equity of 0.5, with a 21% tax rate | 1.3 |
| Step 1 — unlever at the peer’s D/EβU = 1.3 ÷ [1 + (1 − 0.21) × 0.5] = 1.3 ÷ 1.395 | βU = 0.9319 |
| Step 2 — relever at the target D/EβL = 0.9319 × [1 + (1 − 0.21) × 1] = 0.9319 × 1.79 | × 1.79 |
| = Relevered beta at D/E 1business risk 0.9319 + financial risk 0.7362 (up from 0.3681 at the peer's lighter leverage) | 1.6681 |
Computed with this calculator's default settings — open the tool above and you'll see the same numbers, then swap in your own peer beta and capital structures.
Business risk, financial risk, and what the formula assumes
The decomposition is the real insight. In the example above, the peer’s shareholders experience a beta of 1.3, but only0.9319 of that is the business itself — the rest,0.3681, is amplification from borrowing. Relever the same business at twice the leverage and the financial-risk premium grows to 0.7362, even though nothing about the underlying operations changed. That is why comparing raw betas across firms with different balance sheets misleads: you are comparing financing choices as much as businesses.
Be honest about the assumptions, because the formula bakes in three. It treats the beta of debt as zero, so lenders bear none of the market risk — a fair approximation for investment-grade leverage, a poor one for distressed balance sheets. It assumes aconstant debt-to-equity ratio, so a firm planning to pay down or lever up over time is only approximately described. And it lives in the Modigliani–Miller world with corporate taxes, where the interest tax shield is the only reason capital structure matters — no distress costs, no agency effects. Within those limits it is the workhorse of practice; outside them, treat the output as a starting point rather than an answer.
Frequently asked questions
What is the Hamada equation?
The Hamada equation links a company’s equity beta to its capital structure: βL = βU × [1 + (1 − t) × D/E], where βL is the levered (observed) beta, βU the unlevered (asset) beta, t the corporate tax rate, and D/E the debt-to-equity ratio. Robert Hamada derived it in a 1972 Journal of Finance paper by combining the Modigliani–Miller capital-structure propositions with the CAPM. Rearranged, it strips leverage out of an observed beta; applied forward, it puts a chosen capital structure back on. It is the standard bridge between a beta measured at one firm and a cost of equity estimated for another.
Why would I unlever a beta?
Because an observed beta belongs to a specific capital structure, not to the business itself. If you borrow a peer’s regression beta to value a private company or a division, you inherit the peer’s leverage along with its business risk — and the two firms rarely borrow alike. Unlevering divides that leverage effect out, leaving an asset beta that reflects only the economics of the business. You can then relever it at your own target debt-to-equity ratio, so the beta that feeds your CAPM cost of equity matches the capital structure you are actually valuing. Every comparable-company DCF runs this exact chain.
What is the difference between levered and unlevered beta?
Levered (equity) beta is what a regression against the market measures: the volatility shareholders actually experience, which bundles two risks together. Unlevered (asset) beta is the business-risk component alone — how sensitive the firm’s operations are to the economy, independent of financing. The gap between them is the financial-risk premium: debt magnifies equity returns in both directions, so shareholders in a levered firm ride bigger swings from the same underlying business. At a debt-to-equity ratio of zero the two betas are identical; as leverage rises, the levered beta climbs above the asset beta by the factor 1 + (1 − t) × D/E.
What tax rate should I use?
Use the marginal corporate tax rate — the rate applied to the next dollar of income — because that is the rate at which the interest tax shield accrues. For US companies the 21% federal statutory rate is the common starting point, often adjusted upward a few points for state taxes. Many practitioners avoid the effective tax rate (taxes paid ÷ pre-tax income), which is distorted by credits, loss carryforwards, and one-off items that will not apply to future interest deductions. Whatever you choose, use the same rate when unlevering the peer and relevering at your target so the chain stays consistent.
What are the limitations of the Hamada equation?
The formula assumes the beta of debt is zero — that lenders bear no market risk — which is reasonable at modest leverage but understates the asset beta of highly levered firms, where debt holders clearly share the business risk. It also assumes the debt-to-equity ratio is constant and that the tax shield is discounted at the cost of debt, per Modigliani–Miller with corporate taxes; if the firm plans to change leverage over time, alternatives such as the Harris–Pringle or Miles–Ezzell formulas fit better. Finally, the output is only as good as the peer beta going in — a noisy regression beta stays noisy after relevering.
Sources
- Hamada, "The Effect of the Firm’s Capital Structure on the Systematic Risk of Common Stocks", Journal of Finance 27(2), 1972 (JSTOR)
- Modigliani & Miller, "The Cost of Capital, Corporation Finance and the Theory of Investment", American Economic Review 48(3), 1958 (JSTOR)
The official figures this page quotes are drawn from the primary sources above — check them (or a qualified professional) before relying on a result.
Disclaimer: This calculator is foreducation and illustration only. Unlevering and relevering betas rests on simplifying assumptions — riskless debt, a constant capital structure, and a taxes-only view of leverage — and the result inherits every flaw of the peer beta you start from. The output is a textbook calculation, not a valuation, and nothing here is investment, tax, or trading advice.