Unlevered Beta Calculator
This calculator helps you determine a company's Unlevered Beta (Asset Beta) by removing the impact of debt financing from its Levered Beta (Equity Beta). This is useful for comparing the inherent business risk of companies with different capital structures.
Enter the company's Levered Beta, Tax Rate, and Debt-to-Equity Ratio.
Enter Company Data
Understanding Unlevered Beta and the Hamada Formula
What is Beta?
Beta (β) is a measure of a stock's volatility in relation to the overall market. A Beta of 1 means the stock's price tends to move with the market. A Beta greater than 1 means it's more volatile, and less than 1 means it's less volatile. Negative Beta is possible but rare, indicating movement opposite to the market.
Levered Beta vs. Unlevered Beta
- Levered Beta (βL): This is the Beta you typically find on financial websites. It reflects both the company's inherent business risk *and* its financial risk (the risk introduced by using debt). It measures the volatility of the company's *equity*.
- Unlevered Beta (βU): Also called Asset Beta. This value theoretically removes the effect of debt from the Beta. It aims to isolate only the systematic business risk of the company's assets, assuming it had no debt.
Why Calculate Unlevered Beta?
Unlevering Beta allows you to compare the fundamental business risk of companies in the same industry that have different levels of debt. Once you have the Unlevered Beta for comparable companies, you can average them and then "re-lever" that average Unlevered Beta to reflect the capital structure of the specific company you are analyzing. This is a key step in calculating the Cost of Equity using the Capital Asset Pricing Model (CAPM).
The Hamada Formula
The most common formula used to unlever Beta is the Hamada formula, which accounts for the tax shield benefits of debt:
βU = βL / [1 + (1 - Tax Rate) * (Debt / Equity Ratio)]
Where:
- βU = Unlevered Beta
- βL = Levered Beta
- Tax Rate = Corporate Tax Rate (as a decimal, e.g., 0.25 for 25%)
- Debt / Equity Ratio = Market Value of Debt / Market Value of Equity (Book values are often used as a proxy if market values are unavailable)
This calculator applies this formula.
Assumptions of the Hamada Formula
The Hamada formula makes several simplifying assumptions:
- Debt is risk-free.
- Debt capacity is fixed (constant D/E ratio).
- Tax shields are permanent and certain.
- No costs of financial distress.
In reality, these assumptions may not hold perfectly, especially for highly leveraged companies.
Unlevered Beta Calculation Examples
See how Unlevered Beta is calculated in various scenarios:
Example 1: Moderately Leveraged Company
Scenario: Company A is in the retail sector.
Inputs: Levered Beta (βL) = 1.2, Tax Rate = 25%, Debt/Equity = 0.4
Formula: βU = βL / [1 + (1 - Tax Rate) * (D/E)]
Calculation: βU = 1.2 / [1 + (1 - 0.25) * 0.4] = 1.2 / [1 + 0.75 * 0.4] = 1.2 / [1 + 0.3] = 1.2 / 1.3
Result: βU ≈ 0.923
Conclusion: The underlying business risk of Company A, before considering debt, corresponds to an Unlevered Beta of about 0.923.
Example 2: Highly Leveraged Company
Scenario: Company B is in a capital-intensive industry.
Inputs: Levered Beta (βL) = 1.5, Tax Rate = 30%, Debt/Equity = 1.5
Formula: βU = βL / [1 + (1 - Tax Rate) * (D/E)]
Calculation: βU = 1.5 / [1 + (1 - 0.3) * 1.5] = 1.5 / [1 + 0.7 * 1.5] = 1.5 / [1 + 1.05] = 1.5 / 2.05
Result: βU ≈ 0.732
Conclusion: Despite a high Levered Beta, removing the significant debt effect shows a lower underlying business risk (Unlevered Beta) compared to Company A in Example 1.
Example 3: Company with Zero Debt
Scenario: Company C is funded entirely by equity.
Inputs: Levered Beta (βL) = 0.8, Tax Rate = 20%, Debt/Equity = 0
Formula: βU = βL / [1 + (1 - Tax Rate) * (D/E)]
Calculation: βU = 0.8 / [1 + (1 - 0.2) * 0] = 0.8 / [1 + 0.8 * 0] = 0.8 / [1 + 0] = 0.8 / 1
Result: βU = 0.8
Conclusion: For a company with no debt, Levered Beta equals Unlevered Beta, as there is no financial risk to remove.
Example 4: Company with Negative Levered Beta
Scenario: Company D's stock tends to move opposite the market.
Inputs: Levered Beta (βL) = -0.3, Tax Rate = 35%, Debt/Equity = 0.2
Formula: βU = βL / [1 + (1 - Tax Rate) * (D/E)]
Calculation: βU = -0.3 / [1 + (1 - 0.35) * 0.2] = -0.3 / [1 + 0.65 * 0.2] = -0.3 / [1 + 0.13] = -0.3 / 1.13
Result: βU ≈ -0.265
Conclusion: A negative Levered Beta results in a negative Unlevered Beta, scaled down by the debt factor.
Example 5: Impact of High Tax Rate
Scenario: Comparing the unlevering effect with a high tax rate.
Inputs: Levered Beta (βL) = 1.1, Tax Rate = 40%, Debt/Equity = 0.8
Formula: βU = βL / [1 + (1 - Tax Rate) * (D/E)]
Calculation: βU = 1.1 / [1 + (1 - 0.4) * 0.8] = 1.1 / [1 + 0.6 * 0.8] = 1.1 / [1 + 0.48] = 1.1 / 1.48
Result: βU ≈ 0.743
Conclusion: A higher tax rate means the tax shield benefits of debt are larger, which amplifies the difference between Levered and Unlevered Beta for a given D/E ratio.
Example 6: Impact of Low D/E Ratio
Scenario: Company with minimal debt.
Inputs: Levered Beta (βL) = 0.9, Tax Rate = 30%, Debt/Equity = 0.1
Formula: βU = βL / [1 + (1 - Tax Rate) * (D/E)]
Calculation: βU = 0.9 / [1 + (1 - 0.3) * 0.1] = 0.9 / [1 + 0.7 * 0.1] = 0.9 / [1 + 0.07] = 0.9 / 1.07
Result: βU ≈ 0.841
Conclusion: With a low D/E ratio, the Unlevered Beta is only slightly lower than the Levered Beta.
Example 7: Re-levering Beta for a Project
Scenario: A company wants to use the Unlevered Beta of a comparable company (from Ex. 1, βU ≈ 0.923) but their project will have a D/E ratio of 0.6 and their tax rate is 28%. What is the Levered Beta for the project?
Inputs (for Re-levering): Unlevered Beta (βU) = 0.923, Tax Rate = 28%, Debt/Equity = 0.6
Formula (Re-levering): βL = βU * [1 + (1 - Tax Rate) * (D/E)]
Calculation: βL = 0.923 * [1 + (1 - 0.28) * 0.6] = 0.923 * [1 + 0.72 * 0.6] = 0.923 * [1 + 0.432] = 0.923 * 1.432
Result: βL ≈ 1.322
Conclusion: The relevant Levered Beta for the project, incorporating its specific financial risk, is approximately 1.322.
Example 8: Using Book Value D/E (Proxy)
Scenario: Market values for debt/equity are hard to find; using book values instead.
Inputs: Levered Beta (βL) = 1.3, Tax Rate = 21%, Book Debt/Equity = 0.7
Note: Using book values is a common approximation but less theoretically accurate than market values for the Hamada formula.
Formula: βU = βL / [1 + (1 - Tax Rate) * (D/E)]
Calculation: βU = 1.3 / [1 + (1 - 0.21) * 0.7] = 1.3 / [1 + 0.79 * 0.7] = 1.3 / [1 + 0.553] = 1.3 / 1.553
Result: βU ≈ 0.837
Conclusion: Using book values provides an estimate of Unlevered Beta.
Example 9: Comparing Two Companies Unlevered
Scenario: Compare the business risk of Company X and Company Y.
Company X Inputs: βL = 1.4, Tax Rate = 30%, D/E = 1.0
Company X Calc: βU = 1.4 / [1 + (1 - 0.3) * 1.0] = 1.4 / [1 + 0.7] = 1.4 / 1.7 ≈ 0.824
Company Y Inputs: βL = 1.1, Tax Rate = 25%, D/E = 0.3
Company Y Calc: βU = 1.1 / [1 + (1 - 0.25) * 0.3] = 1.1 / [1 + 0.75 * 0.3] = 1.1 / [1 + 0.225] = 1.1 / 1.225 ≈ 0.898
Conclusion: Although Company X has a higher Levered Beta, its Unlevered Beta (0.824) is slightly *lower* than Company Y's (0.898), suggesting Company X has slightly less fundamental business risk before accounting for debt.
Example 10: Tax Rate = 0%
Scenario: Calculating Unlevered Beta for a situation where the tax rate is zero (e.g., theoretical model, or if debt interest is not tax deductible).
Inputs: Levered Beta (βL) = 1.2, Tax Rate = 0%, Debt/Equity = 0.5
Formula: βU = βL / [1 + (1 - Tax Rate) * (D/E)]
Calculation: βU = 1.2 / [1 + (1 - 0) * 0.5] = 1.2 / [1 + 1 * 0.5] = 1.2 / [1 + 0.5] = 1.2 / 1.5
Result: βU = 0.8
Conclusion: When the tax rate is zero, the formula simplifies to βU = βL / (1 + D/E).
Notes on Inputs
Ensure your inputs are accurate:
- Levered Beta: Use a reliable source. Beta values can vary depending on the market index used (e.g., S&P 500, Nasdaq) and the time period of data.
- Tax Rate: Use the marginal corporate tax rate relevant to the company.
- Debt-to-Equity Ratio: Ideally, use market values for both debt and equity. If market values of debt are unavailable, use book values of debt as a proxy. Market value of equity is typically easier to obtain (share price * shares outstanding). Using book values for both is a less precise but sometimes necessary approximation. Ensure the ratio is calculated consistently.
Frequently Asked Questions about Unlevered Beta
1. What is Unlevered Beta used for?
Unlevered Beta is primarily used in corporate finance and valuation to estimate the cost of equity for a company or project, especially when comparing companies with different debt levels. It isolates business risk from financial risk.
2. How is Unlevered Beta different from Levered Beta?
Levered Beta includes both business risk and financial risk (due to debt), reflecting the volatility of equity. Unlevered Beta theoretically removes the financial risk, showing only the business risk of the company's assets.
3. Which formula does this calculator use?
It uses the standard Hamada formula: βU = βL / [1 + (1 - Tax Rate) * (Debt / Equity Ratio)].
4. What Tax Rate should I use?
You should use the marginal corporate tax rate applicable to the company's profits. Enter it as a percentage in the input field (e.g., 25 for 25%). The calculator converts it to a decimal for the formula.
5. Should I use market values or book values for the Debt/Equity Ratio?
The Hamada formula is theoretically based on market values. Market value of equity is readily available (share price * shares outstanding). Market value of debt is harder to obtain, so the book value of debt is often used as a practical proxy in the ratio calculation.
6. Can Unlevered Beta be negative?
Yes. If the Levered Beta is negative, the calculated Unlevered Beta will also be negative, although scaled by the debt factor.
7. What does a high Unlevered Beta mean?
A high Unlevered Beta suggests that the company's core business operations have high systematic risk, meaning their asset returns are highly sensitive to overall market movements, independent of how the company is financed.
8. What does a low Unlevered Beta mean?
A low Unlevered Beta suggests the company's core business operations have low systematic risk; its asset returns are less sensitive to overall market movements.
9. How is Unlevered Beta related to CAPM?
Unlevered Beta is a key component in estimating the cost of equity (Re) using the CAPM: Re = Rf + βL * (Rm - Rf). To apply this to a project or division with a different capital structure than the parent company, you might unlever comparable companies' Betas, average them, and then re-lever using the project's target D/E ratio and tax rate to get the appropriate βL for the project.
10. Does the formula work for companies with zero debt?
Yes. If the Debt/Equity ratio is 0, the formula simplifies to βU = βL / [1 + (1 - Tax Rate) * 0] = βL / 1 = βL. This correctly shows that for an all-equity firm, Levered Beta equals Unlevered Beta.
