Levered Beta Calculator
This tool calculates the Levered Beta (Equity Beta) of a company using the Hamada equation. Levered Beta reflects a company's systematic risk, including the risk added by debt.
Input the company's Unlevered Beta, its Debt-to-Equity Ratio, and the Corporate Tax Rate.
Calculate Levered Beta
Understanding Levered Beta & The Hamada Equation
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 suggests higher volatility (more sensitive to market swings), while a beta less than 1 suggests lower volatility.
Unlevered vs. Levered Beta
- Unlevered Beta (Asset Beta, βU): Represents the systematic risk of a company's assets *without* considering the impact of debt (leverage). It isolates the business risk inherent in the company's operations.
- Levered Beta (Equity Beta, βL): Represents the systematic risk of a company's stock *including* the impact of debt. Debt increases the risk to equity holders because interest payments are fixed obligations that must be paid before profits can be distributed to shareholders.
The Hamada Equation (Levering Beta)
The most common way to calculate Levered Beta from Unlevered Beta is using the Hamada equation:
βL = βU * [1 + (1 - Tax Rate) * (D/E Ratio)]
Where:
- βL = Levered Beta (Equity Beta)
- βU = Unlevered Beta (Asset Beta)
- Tax Rate = Corporate Tax Rate (in decimal form)
- D/E Ratio = Debt-to-Equity Ratio
This formula shows how financial leverage (debt) increases the equity beta relative to the asset beta. The tax rate is included because interest payments on debt are often tax-deductible, providing a "tax shield" that slightly reduces the cost of debt and its impact on volatility compared to a world without taxes.
Why is Levered Beta Important?
Levered Beta is a crucial input in the Capital Asset Pricing Model (CAPM), which is widely used to calculate the required rate of return on equity (Cost of Equity). The Cost of Equity is a key component in valuing a company or project using discounted cash flow (DCF) analysis.
Levered Beta Calculation Examples
Here are 10 examples demonstrating the calculation using the formula βL = βU * [1 + (1 - Tax Rate) * (D/E Ratio)].
Example 1: Moderately Levered Company
Scenario: A company with typical debt levels.
Given: Unlevered Beta (βU) = 0.9, Debt/Equity (D/E) = 0.6, Tax Rate = 30% (0.30).
Formula: βL = βU * [1 + (1 - Tax Rate) * (D/E)]
Calculation: βL = 0.9 * [1 + (1 - 0.30) * 0.6] = 0.9 * [1 + 0.70 * 0.6] = 0.9 * [1 + 0.42] = 0.9 * 1.42
Result: βL = 1.278
Interpretation: The company's stock is slightly more volatile than the market due to its moderate debt.
Example 2: Highly Levered Company
Scenario: A company with significant debt.
Given: Unlevered Beta (βU) = 0.7, Debt/Equity (D/E) = 2.0, Tax Rate = 25% (0.25).
Formula: βL = βU * [1 + (1 - Tax Rate) * (D/E)]
Calculation: βL = 0.7 * [1 + (1 - 0.25) * 2.0] = 0.7 * [1 + 0.75 * 2.0] = 0.7 * [1 + 1.5] = 0.7 * 2.5
Result: βL = 1.75
Interpretation: The high debt level significantly increases the stock's volatility relative to the market.
Example 3: Company with No Debt
Scenario: A company that is entirely equity-financed (no debt).
Given: Unlevered Beta (βU) = 0.85, Debt/Equity (D/E) = 0, Tax Rate = 35% (0.35).
Formula: βL = βU * [1 + (1 - Tax Rate) * (D/E)]
Calculation: βL = 0.85 * [1 + (1 - 0.35) * 0] = 0.85 * [1 + 0.65 * 0] = 0.85 * [1 + 0] = 0.85 * 1
Result: βL = 0.85
Interpretation: With no debt, the Levered Beta equals the Unlevered Beta, indicating lower volatility than the market.
Example 4: Low Unlevered Beta, High Debt
Scenario: A stable industry company using a lot of debt.
Given: Unlevered Beta (βU) = 0.5, Debt/Equity (D/E) = 1.5, Tax Rate = 20% (0.20).
Formula: βL = βU * [1 + (1 - Tax Rate) * (D/E)]
Calculation: βL = 0.5 * [1 + (1 - 0.20) * 1.5] = 0.5 * [1 + 0.80 * 1.5] = 0.5 * [1 + 1.2] = 0.5 * 2.2
Result: βL = 1.1
Interpretation: Even with low business risk (low βU), high debt can push Levered Beta above 1.
Example 5: High Unlevered Beta, Low Debt
Scenario: A growth company with high business risk but little debt.
Given: Unlevered Beta (βU) = 1.3, Debt/Equity (D/E) = 0.2, Tax Rate = 28% (0.28).
Formula: βL = βU * [1 + (1 - Tax Rate) * (D/E)]
Calculation: βL = 1.3 * [1 + (1 - 0.28) * 0.2] = 1.3 * [1 + 0.72 * 0.2] = 1.3 * [1 + 0.144] = 1.3 * 1.144
Result: βL = 1.4872
Interpretation: High business risk dominates, resulting in a high Levered Beta despite low debt.
Example 6: Impact of Higher Tax Rate (vs Ex. 1)
Scenario: Same as Example 1, but with a higher tax rate.
Given: Unlevered Beta (βU) = 0.9, Debt/Equity (D/E) = 0.6, Tax Rate = 40% (0.40).
Formula: βL = βU * [1 + (1 - Tax Rate) * (D/E)]
Calculation: βL = 0.9 * [1 + (1 - 0.40) * 0.6] = 0.9 * [1 + 0.60 * 0.6] = 0.9 * [1 + 0.36] = 0.9 * 1.36
Result: βL = 1.224
Interpretation: A higher tax rate provides a larger tax shield, slightly *reducing* the impact of debt on beta compared to Example 1 (1.224 vs 1.278).
Example 7: Impact of Lower Tax Rate (vs Ex. 1)
Scenario: Same as Example 1, but with a lower tax rate.
Given: Unlevered Beta (βU) = 0.9, Debt/Equity (D/E) = 0.6, Tax Rate = 20% (0.20).
Formula: βL = βU * [1 + (1 - Tax Rate) * (D/E)]
Calculation: βL = 0.9 * [1 + (1 - 0.20) * 0.6] = 0.9 * [1 + 0.80 * 0.6] = 0.9 * [1 + 0.48] = 0.9 * 1.48
Result: βL = 1.332
Interpretation: A lower tax rate provides a smaller tax shield, slightly *increasing* the impact of debt on beta compared to Example 1 (1.332 vs 1.278).
Example 8: Unlevering Beta (Reverse Calculation)
Scenario: Use the formula to find Unlevered Beta if you know Levered Beta and debt levels.
Given: Levered Beta (βL) = 1.5, Debt/Equity (D/E) = 1.0, Tax Rate = 30% (0.30).
Formula: βL = βU * [1 + (1 - Tax Rate) * (D/E)] → βU = βL / [1 + (1 - Tax Rate) * (D/E)]
Calculation: βU = 1.5 / [1 + (1 - 0.30) * 1.0] = 1.5 / [1 + 0.70 * 1.0] = 1.5 / [1 + 0.70] = 1.5 / 1.70
Result: βU ≈ 0.8824
Interpretation: The underlying business risk (unlevered) is lower than the equity risk (levered).
Example 9: Company with Negative Beta (Rare)
Scenario: A theoretical company whose unlevered beta is negative (moves opposite the market - very rare).
Given: Unlevered Beta (βU) = -0.2, Debt/Equity (D/E) = 0.8, Tax Rate = 25% (0.25).
Formula: βL = βU * [1 + (1 - Tax Rate) * (D/E)]
Calculation: βL = -0.2 * [1 + (1 - 0.25) * 0.8] = -0.2 * [1 + 0.75 * 0.8] = -0.2 * [1 + 0.6] = -0.2 * 1.6
Result: βL = -0.32
Interpretation: Debt can still amplify a negative beta, making it 'more negative' in relative terms.
Example 10: Using Betas from Comparable Companies
Scenario: Estimating Levered Beta for a private company by using publicly traded peers.
Process:
1. Find publicly traded companies (Comparables) similar to your private company in industry and operations.
2. Obtain the Levered Beta (βL_Comp), Debt/Equity (D/EComp), and Tax Rate (TaxComp) for each Comparable.
3. Unlever each Comparable's beta: βU_Comp = βL_Comp / [1 + (1 - TaxComp) * (D/EComp)].
4. Calculate the average or median Unlevered Beta (Average βU) from the Comparables.
5. Obtain your private company's Debt/Equity (D/EPrivate) and Tax Rate (TaxPrivate).
6. Re-lever the average Unlevered Beta using your private company's financial structure: βL_Private = Average βU * [1 + (1 - TaxPrivate) * (D/EPrivate)].
Example Values (Step 6): Average βU from peers = 1.0, Your Company's D/E = 0.7, Your Company's Tax Rate = 25% (0.25).
Calculation: βL_Private = 1.0 * [1 + (1 - 0.25) * 0.7] = 1.0 * [1 + 0.75 * 0.7] = 1.0 * [1 + 0.525] = 1.0 * 1.525
Result: βL_Private = 1.525
Interpretation: This is the estimated Levered Beta for your private company.
Frequently Asked Questions about Levered Beta
1. What is the difference between Unlevered and Levered Beta?
Unlevered Beta measures the systematic risk of a company's core business operations, independent of its debt structure. Levered Beta adds the financial risk introduced by debt, showing the total systematic risk faced by equity holders.
2. Why do you use the Hamada Equation?
The Hamada equation is a standard model used to quantify how financial leverage (debt) affects the systematic risk of a company's equity relative to its assets. It helps separate business risk from financial risk.
3. What inputs are needed for the calculation?
You need the Unlevered Beta (Asset Beta), the company's Debt-to-Equity Ratio, and the Corporate Tax Rate.
4. Where can I find these input values?
- Unlevered Beta: This is often calculated by 'unlevering' the average Levered Beta of comparable public companies in the same industry. Financial data providers might also provide estimated unlevered betas.
- Debt-to-Equity Ratio: Calculated from the company's balance sheet (Total Debt / Total Shareholder Equity).
- Corporate Tax Rate: Can be the statutory rate, or an effective tax rate derived from the company's income statement, depending on the analysis context.
5. Why is the tax rate included in the formula?
Interest payments on debt are typically tax-deductible expenses. This tax shield reduces the effective cost of debt and mitigates some of the risk debt adds, which is reflected in the (1 - Tax Rate) term.
6. What does a Levered Beta greater than 1 mean?
A Levered Beta greater than 1 means the company's stock is expected to be more volatile than the overall market. Its price tends to rise and fall more sharply than the market average.
7. What does a Levered Beta less than 1 mean?
A Levered Beta less than 1 means the company's stock is expected to be less volatile than the overall market. Its price tends to be more stable than the market average.
8. Can Levered Beta be negative?
Yes, if the Unlevered Beta is negative (meaning the company's business is inversely correlated with the market, which is rare), the Levered Beta will also be negative, amplified by the debt factor.
9. Is this formula always accurate?
The Hamada equation is a simplification based on certain assumptions (e.g., constant debt-to-equity ratio, perpetual debt, taxes as the only market imperfection). Real-world beta estimation involves complex statistical analysis and judgment.
10. How is Levered Beta used in valuation?
Levered Beta is used in the Capital Asset Pricing Model (CAPM): Cost of Equity = Risk-Free Rate + Levered Beta * (Market Risk Premium). The Cost of Equity is used to discount future equity cash flows or is part of the Weighted Average Cost of Capital (WACC).
