How to Calculate Levered and Unlevered Beta

Beta measures a company’s systematic risk, quantifying how its stock price moves relative to the market. While observed beta reflects current realities, adjustments can provide deeper insights into financial structure and debt use. This article explains levered and unlevered beta, and how to calculate and use them for financial analysis and valuation.

Understanding Levered and Unlevered Beta

Beta, in its most basic form, indicates the sensitivity of an asset’s returns to the returns of the broader market. A beta of 1 suggests the asset moves in line with the market, while a beta greater than 1 indicates higher volatility, and a beta less than 1 suggests lower volatility. This market-derived beta inherently includes both the risk associated with a company’s operations and the risk stemming from its financing decisions.

Financial leverage, primarily through debt, introduces additional risk to equity holders. Fixed interest payments amplify earnings volatility, meaning small changes in operating income can lead to larger percentage changes in net income per share. This magnified risk directly impacts the company’s equity beta.

Levered beta, also known as equity beta, captures the total risk borne by a company’s shareholders. This includes both the inherent business risk of its operations and the financial risk introduced by its debt. It is the beta figure commonly observed when analyzing publicly traded stocks, as it reflects the company’s existing capital structure. This measure is directly influenced by the amount of debt a company employs.

Unlevered beta, often called asset beta, isolates a company’s pure business risk by theoretically removing the impact of financial leverage. It represents the beta of a hypothetical company with no debt, financed entirely by equity. This “pure” measure of operational risk is valuable because it allows for a direct comparison of the underlying business risk of different companies, irrespective of their varied debt levels. By stripping away the effects of financing, unlevered beta provides a clearer picture of the volatility inherent in a company’s core operations.

Applications of Beta Adjustment

Adjusting beta is important for several practical applications in finance, enabling more accurate comparisons and valuations. One significant application is in company valuation, particularly when comparing firms with different capital structures. By unlevering the beta of comparable public companies, analysts can determine the pure business risk inherent in their operations, then re-lever it to reflect the target company’s specific debt-to-equity ratio. This process helps establish a more appropriate discount rate for valuing the target firm’s equity.

Project valuation, often part of capital budgeting decisions, also benefits greatly from beta adjustment. When evaluating a new project, it is important to assess its specific risk profile rather than simply using the company’s overall levered beta. An unlevered beta from comparable projects or companies in the same industry can be used to determine a suitable discount rate for the project’s cash flows, isolating the project’s business risk from the parent company’s financial risk. This ensures that the project is assessed based on its standalone operational characteristics.

Comparables analysis, a widely used valuation technique, heavily relies on the ability to adjust beta. When valuing a private company or a specific division of a larger firm, direct market betas are unavailable. Analysts therefore look to publicly traded companies with similar business operations. By unlevering the betas of these comparable public firms, an average unlevered beta can be derived, representing the industry’s inherent business risk. This unlevered beta can then be re-levered to match the target company’s anticipated capital structure, providing a more robust basis for valuation.

Calculating Unlevered Beta

Calculating unlevered beta involves removing the effect of financial leverage from a company’s observed levered beta. The most common approach utilizes a formula derived from the Modigliani-Miller theorem, often referred to as Hamada’s equation. This formula considers the company’s levered beta, its debt-to-equity ratio, and its corporate tax rate to estimate the unlevered beta. The core idea is that debt provides a tax shield on interest payments, which influences the relationship between levered and unlevered beta.

The formula to calculate unlevered beta (βU) from levered beta (βL) is:

βU = βL / [1 + (1 – T) (D/E)]

In this formula, βL represents the company’s observed levered beta, typically obtained from financial data providers. T is the corporate tax rate, typically 21% for C corporations in the United States. This tax rate accounts for the tax deductibility of interest payments, which reduces the effective cost of debt and partially offsets the risk added by leverage. D is the market value of the company’s debt, and E is the market value of its equity.

Levered beta is often found on financial websites or through software. The market value of equity (E) for publicly traded companies is the current stock price multiplied by outstanding shares. The market value of debt (D) is more complex; if publicly traded bonds exist, their market prices can be used. Otherwise, analysts might estimate market value by discounting future interest and principal payments.

For example, consider a company with a levered beta of 1.2, a market value of debt of $100 million, and a market value of equity of $400 million. Assuming a corporate tax rate of 21%, the unlevered beta would be calculated as follows:

βU = 1.2 / [1 + (1 – 0.21) (100,000,000 / 400,000,000)]
βU = 1.2 / [1 + (0.79) (0.25)]
βU = 1.2 / [1 + 0.1975]
βU = 1.2 / 1.1975
βU ≈ 1.002

This calculation shows that the company’s underlying business risk, without the effect of its financial leverage, is approximately 1.002.

Calculating Levered Beta

Calculating levered beta involves reintroducing the effect of financial leverage to an unlevered beta, which is particularly useful when valuing a private company or a new project. This process allows financial analysts to determine the appropriate equity beta for a target company or project, considering its specific capital structure. The formula used for this calculation is essentially a rearrangement of the Hamada equation, reflecting how financial leverage impacts the risk to equity holders.

The formula to calculate levered beta (βL) from unlevered beta (βU) is:

βL = βU [1 + (1 – T) (D/E)]

Here, βU represents the unlevered beta, which is typically derived from comparable companies in the same industry that share similar business risks. T is the corporate tax rate. D is the market value of the target company’s or project’s debt, and E is the market value of its equity. This formula demonstrates how increasing the debt-to-equity ratio, while accounting for the tax shield, increases the levered beta, signifying higher risk for equity investors.

To apply this formula, unlevered beta is obtained from comparable firms. For a private company or new project, market values for debt and equity must be estimated. Equity market value can be estimated through valuation methods like discounted cash flow or recent equity transactions. Debt market value can be estimated by discounting projected interest and principal payments, or by using book values as a proxy if market data is unavailable.

For instance, imagine a private company with an estimated unlevered beta of 1.05, derived from comparable public companies. The private company plans to have a market value of debt of $75 million and a market value of equity of $250 million. With a corporate tax rate of 21%, the levered beta would be:

βL = 1.05 [1 + (1 – 0.21) (75,000,000 / 250,000,000)]
βL = 1.05 [1 + (0.79) (0.30)]
βL = 1.05 [1 + 0.237]
βL = 1.05 1.237
βL ≈ 1.299

This calculation provides a levered beta of approximately 1.299 for the private company, reflecting the impact of its specific financial leverage on its equity risk.