Levered vs Unlevered Beta: Which One to Use for Cost of Equity

Use a levered beta in the CAPM cost of equity formula, and make sure it reflects the debt level of the company you’re valuing. An unlevered beta strips out the effect of debt, so it’s mainly a tool for moving a beta from one capital structure to another. The Hamada equation does the conversion: an unlevered beta of 0.9 with a 0.5 debt-to-equity ratio and a 21% tax rate relevers to 1.2555, or about 1.26.

If you’re using the cost of equity calculator with a beta pulled from a finance site, that number is almost always levered already. The rest of this guide explains when that’s fine and when you need to adjust it.

What each beta measures

A levered beta (also called equity beta) measures how much a company’s shares move with the market. It includes two kinds of risk: the risk of the business itself and the extra risk shareholders take on because the company has debt.

An unlevered beta (also called asset beta) removes the debt effect. It measures only the business risk, as if the company had no debt at all.

	Levered beta	Unlevered beta
Also called	Equity beta	Asset beta
Includes debt risk	Yes	No
What you see on finance sites	Usually this one	Rarely
Used directly in CAPM	Yes	No (relever first)
Main use	Calculating cost of equity	Comparing companies with different debt

Why debt raises beta

Debt holders get paid first. Shareholders get whatever’s left. When a company borrows more, the same swings in operating profit cause bigger swings in what’s left for shareholders.

Picture two identical businesses, one with no debt and one with heavy debt. A 10% drop in operating profit hurts the shareholders of the indebted company more, because the interest bill stays fixed. Their shares move more with the market, so their beta is higher. That’s also why the FAQ on whether cost of equity increases with debt answers yes.

The Hamada equation

Robert Hamada published the relationship in a 1972 Journal of Finance paper, “The Effect of the Firm’s Capital Structure on the Systematic Risk of Common Stocks.” It’s the standard formula for converting between the two betas:

Levered beta = Unlevered beta x (1 + (1 - t) x D/E)
Unlevered beta = Levered beta / (1 + (1 - t) x D/E)

• t is the corporate tax rate. The US federal rate is 21%.
• D/E is debt divided by equity, ideally at market values.

The (1 - t) term is there because interest is tax deductible, which softens the effect of debt on shareholders.

The formula assumes the company’s debt carries no market risk of its own (a debt beta of zero). That’s a fair approximation for companies with modest debt. For heavily indebted companies, some analysts use versions that give debt a beta, but Hamada’s version is what most people use.

Worked example: relevering

Say the industry’s average unlevered beta is 0.9. The company you’re valuing has a debt-to-equity ratio of 0.5 and pays a 21% tax rate.

Step 1. After-tax factor: 1 - 0.21 = 0.79.

Step 2. Multiply by D/E: 0.79 x 0.5 = 0.395.

Step 3. Add 1: 1.395.

Step 4. Multiply by the unlevered beta: 0.9 x 1.395 = 1.2555.

The levered beta is about 1.26. With a 5% risk-free rate and a 5% equity risk premium, CAPM gives:

Ke = 5% + 1.2555 x 5% = 11.28% (rounded)

Here’s how the same 0.9 unlevered beta relevers at different debt levels:

D/E	Levered beta	Cost of equity (Rf 5%, ERP 5%)
0.00	0.90	9.50%
0.25	1.08	10.39%
0.50	1.26	11.28%
1.00	1.61	13.06%
1.50	1.97	14.83%

The business risk is the same in every row. Only the debt changes, and the cost of equity rises with it.

Worked example: unlevering comparables

When you’re valuing a private company or a division, you often start with several public companies and their levered betas. Each has a different debt load, so you unlever each one, average them, and then relever at your company’s debt level.

Company	Levered beta	D/E	Unlevered beta
Comparable A	1.10	0.20	0.95
Comparable B	1.39	0.80	0.85
Comparable C	1.18	0.40	0.90
Average			0.90

For Comparable A: 1.10 / (1 + 0.79 x 0.20) = 1.10 / 1.158 = 0.95. The others follow the same pattern with a 21% tax rate.

The average unlevered beta is 0.90. Relevered at a 0.5 D/E, that’s the 1.2555 from the first example. Notice that Comparable B had the highest levered beta but the lowest business risk. Its beta was high because of its debt.

The private company guide shows how this relevered beta feeds into a cost of equity with size and company-specific premiums added.

Where to find betas

You have three main options.

1. Calculate it from price data. Regress the stock’s returns against a market index. The Excel guide shows how with =SLOPE(). This gives a levered beta.
2. Use a published beta for the stock. Most finance sites and data terminals list one. Again, it’s levered, and different providers use different time periods and indexes, so numbers vary.
3. Use an industry average. Aswath Damodaran publishes betas by industry for US companies, with both levered and unlevered averages and the average debt-to-equity ratio for each sector.

Industry averages are often more reliable than a single company’s regression beta, because averaging across many companies cancels out some of the noise.

Which beta should you use?

Use the company’s own levered beta directly when:

• The company is listed and has enough trading history.
• Its debt level isn’t expected to change much.
• The regression looks reasonable (not wildly different from peers).

Unlever and relever when:

• The company is private, so there’s no beta to measure.
• You’re using an industry or peer average instead of the company’s own beta.
• The company plans to change its debt level, such as after a buyout or recapitalization.
• You’re valuing a division with a different risk profile from the parent.

Never plug an unlevered beta straight into CAPM for a company that has debt. It will understate the cost of equity, because it ignores the extra risk shareholders carry.

Related reading

Beta is one of three inputs in CAPM. For a plain definition, see the glossary entry on beta and on systematic risk, the type of risk beta measures. Once you have the cost of equity, the WACC guide shows how debt shows up a second time, this time on the cost of debt side.