Levered vs Unlevered Beta: When and Why to Unlever

Understanding Beta in Valuation

Beta measures a stock's sensitivity to overall market movements and serves as a key input in the Capital Asset Pricing Model (CAPM) for calculating cost of equity. A beta of 1.0 means the stock moves in line with the market. Beta above 1.0 indicates the stock is more volatile than the market, while beta below 1.0 indicates lower volatility.

The concept matters for valuation because beta determines the risk premium investors require to hold a particular stock. Higher beta stocks demand higher expected returns to compensate for greater systematic risk. When you calculate WACC for a DCF valuation, cost of equity depends directly on your beta assumption.

However, the beta you observe for a publicly traded company reflects two distinct types of risk: business risk from the company's operations and financial risk from its capital structure. Separating these risks is essential when applying beta from comparable companies to value a target with a different capital structure.

This distinction between levered and unlevered beta appears frequently in investment banking interviews and is fundamental to proper valuation methodology. Understanding when and why to unlever beta demonstrates technical sophistication that interviewers expect from strong candidates.

What is Levered Beta?

Levered beta, also called equity beta or observed beta, is what you find when you look up a company's beta on Bloomberg, Capital IQ, or Yahoo Finance. It measures the volatility of a company's stock returns relative to market returns and reflects both the underlying business risk and the additional risk from financial leverage.

When a company uses debt financing, equity holders bear amplified risk. If the business generates lower than expected returns, debt payments still must be made, leaving less for equity holders. Conversely, if returns exceed expectations, equity holders capture the upside after debt obligations. This leverage effect makes equity returns more volatile than the underlying business returns.

Consider two identical businesses with the same operating risk. Company A is financed entirely with equity, while Company B uses 50% debt. Company B's equity will be more volatile because the fixed debt obligations amplify gains and losses for shareholders. Company B's levered beta will be higher than Company A's, even though the underlying businesses have identical risk profiles.

This combined measure is appropriate when valuing a company as it currently exists with its current capital structure. However, it becomes problematic when comparing companies with different leverage levels or applying beta to a company with a different target capital structure.

What is Unlevered Beta?

Unlevered beta, also called asset beta, strips out the effect of financial leverage to isolate pure business risk. It represents the beta a company would have if it were financed entirely with equity and had no debt.

Unlevering beta removes the financial risk component, leaving only the operating risk inherent in the business itself. Two companies in the same industry with similar operations should have similar unlevered betas regardless of how they choose to finance themselves.

The key insight is that capital structure is a choice, not an inherent characteristic of the business. A company can change its leverage over time through debt issuance, repayment, or equity offerings. Unlevered beta captures the risk that cannot be changed through financing decisions.

Understanding the relationship between levered and unlevered beta is essential for properly applying comparable company analysis to valuation.

The Unlevering Formula

To convert levered beta to unlevered beta, use this formula:

The formula shows that higher leverage increases levered beta relative to unlevered beta. The (1-T) term accounts for the tax shield benefit of debt, which partially offsets the risk-increasing effect of leverage.

Example calculation:

The unlevered beta of 1.00 represents the pure business risk, while the observed beta of 1.30 reflects both business risk and the financial risk from 40% debt-to-equity leverage.

The Relevering Formula

Once you have unlevered beta (typically by averaging across comparable companies), you must relever to the target company's capital structure to calculate its cost of equity:

This is simply the unlevering formula rearranged to solve for levered beta.

Example calculation:

The relevered beta of 1.45 is higher than the unlevered beta because the target company uses more leverage than the average comparable company. This higher beta will increase the cost of equity in your WACC calculation.

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When to Unlever and Relever Beta

Understanding when this process is necessary is as important as knowing the mechanics. Not every situation requires unlevering and relevering.

When You Must Unlever and Relever

Using comparable company betas: When you derive beta from publicly traded comparable companies, you must unlever their observed betas, calculate an average or median unlevered beta, then relever to your target's capital structure. The comparables likely have different leverage than your target, making direct use of their levered betas inappropriate.

Valuing private companies: Private companies have no observable beta. You must estimate beta using public comparables, which requires the unlever-relever process to adjust for capital structure differences.

Analyzing leverage changes: If you are modeling a scenario where the company changes its capital structure (such as in an LBO), you need to relever beta to the new capital structure to properly calculate cost of equity.

Target capital structure differs from current: Even for public companies, if you believe the optimal or target capital structure differs from current leverage, you should relever beta to the target structure for valuation purposes.

When Direct Use May Be Appropriate

Valuing the company as-is: If you are valuing a public company with no expected capital structure changes and using its own historical beta, direct use of observed beta may be appropriate.

Single comparable with identical structure: In the rare case where you have one perfect comparable with the same capital structure as your target, you might use its levered beta directly. However, this situation is uncommon in practice.

Quick approximations: For rough analysis or screening purposes, direct beta comparisons may suffice. Formal valuations for transactions always require proper adjustment.

The Step-by-Step Process

Here is the complete process for deriving beta from comparables and applying it to a target company:

Step 1: Identify comparable companies

Select 4-8 publicly traded companies with similar business characteristics to your target. Consider industry, size, growth profile, and geographic exposure. The companies need not have identical capital structures since you will adjust for this.

Step 2: Gather data for each comparable

Step 3: Unlever each comparable's beta

Apply the unlevering formula to each company:

Step 4: Calculate central tendency

Take the median or mean of the unlevered betas. Median is often preferred because it reduces the impact of outliers. This gives you the industry unlevered beta representing typical business risk for companies like your target.

Step 5: Determine target capital structure

Step 6: Relever to target capital structure

Apply the relevering formula:

Step 7: Use relevered beta in CAPM

The relevered beta becomes your input for calculating cost of equity:

This cost of equity then flows into your WACC calculation and ultimately your DCF valuation.

Practical Example

Let's work through a complete example with multiple comparables.

Target company: Private manufacturing company Target capital structure: 35% debt, 65% equity (D/E = 0.54) Target tax rate: 25%

Comparable company data:

Median unlevered beta: (0.96, 1.02, 1.04, 1.05) → Median = 1.03

Relever to target capital structure:

The target company's levered beta is 1.45, which you would use in CAPM to calculate cost of equity.

Notice how the comparables' levered betas ranged from 1.10 to 1.55, but unlevering narrows this range to 0.96 to 1.05. Much of the observed beta variation was due to capital structure differences rather than business risk differences.

Common Interview Questions

Beta concepts appear frequently in technical interviews. Here are questions you should be prepared to answer.

"What is the difference between levered and unlevered beta?"

Levered beta is the observed equity beta that reflects both business risk and financial risk from debt. Unlevered beta strips out financial leverage to isolate pure business risk. We unlever when using comparable company betas to value a target with different capital structure.

"Why do we unlever beta?"

Capital structure differs across companies, but business risk should be similar for comparable businesses. Unlevering removes the leverage effect so we can compare pure operating risk, then relever to the target's specific capital structure for an accurate cost of equity estimate.

"What happens to beta as a company increases leverage?"

Levered beta increases because equity holders bear more risk when debt increases. Fixed debt obligations amplify equity returns in both directions. The unlevered beta remains unchanged since it reflects only business risk.

"Walk me through calculating cost of equity using comparable company betas."

Gather levered betas and D/E ratios for comparables. Unlever each beta using the formula. Take the median unlevered beta. Relever to the target's capital structure. Use the relevered beta in CAPM with risk-free rate and equity risk premium to calculate cost of equity.

"Why do we multiply by (1-T) in the beta formulas?"

The tax shield from interest expense reduces the effective cost of debt and partially offsets leverage risk. The (1-T) term accounts for this tax benefit. Higher tax rates mean a larger tax shield, so the leverage adjustment is smaller.

Understanding these concepts helps you tackle DCF-related interview questions with confidence.

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Common Mistakes to Avoid

Several errors frequently occur when working with levered and unlevered beta.

Using book values instead of market values: The D/E ratio should use market value of debt and market value of equity. Book values can significantly differ from market values, leading to incorrect beta adjustments.

Forgetting to relever: Some analysts unlever comparable betas but forget to relever to the target capital structure. The median unlevered beta is an intermediate step, not the final answer for cost of equity.

Using inconsistent tax rates: Apply each company's own tax rate when unlevering. When relevering, use the target company's tax rate. Mixing tax rates introduces errors.

Ignoring outliers: One comparable with unusual leverage or beta can skew your analysis. Use median rather than mean, and consider excluding clear outliers from your comparable set.

Applying beta adjustments inappropriately: Not every situation requires unlevering. If you are using a company's own beta with its current capital structure, direct use may be appropriate.

Circular reference issues: In some models, capital structure depends on equity value, which depends on WACC, which depends on capital structure. Be aware of these dynamics and iterate or use target weights.

Alternative Formulas

The formula presented above is the Hamada equation, which is most common in practice. However, you may encounter variations:

Hamada equation (standard):

Alternative assuming debt has beta:

Most practitioners assume debt beta is zero for investment-grade companies, simplifying to the standard formula. For highly leveraged or distressed companies, incorporating debt beta may be more accurate.

Fernandez formula and other variations exist in academic literature but are less common in practice. For interviews and most professional applications, the Hamada equation is standard.

Key Takeaways

Conclusion

The distinction between levered and unlevered beta is fundamental to proper valuation methodology. When you use comparable company betas without adjusting for capital structure differences, you introduce errors that can materially affect your cost of equity and ultimately your valuation conclusions.

The mechanics are straightforward: unlever to remove financial risk, find central tendency across comparables, relever to the target's structure. The key is understanding why this process matters and when it applies. Interviewers test this understanding because it reveals whether you grasp the relationship between capital structure, risk, and value.

For investment banking interviews, be prepared to explain the concept, walk through the formulas, and discuss the intuition behind why leverage affects beta. Demonstrating command of this topic signals technical competence that interviewers expect from candidates who will build and review valuation models daily.

As you build DCF models and calculate WACC, proper beta treatment ensures your cost of capital reflects appropriate risk for the specific company you are valuing rather than the risk profile of different companies with different financing choices.