Understanding Beta within the Capital Asset Pricing Model (CAPM) can be tricky, especially when figuring out whether to use levered or unlevered beta. It's a question that often pops up, and getting it right is crucial for accurate investment analysis. So, let's dive into this topic and break it down in a way that’s easy to understand.

Understanding Beta

Before we tackle the levered versus unlevered debate, let's make sure we're all on the same page about what beta actually represents. In simple terms, beta measures a stock's volatility relative to the overall market. A beta of 1 means the stock's price tends to move in the same direction and magnitude as the market. A beta greater than 1 suggests the stock is more volatile than the market, while a beta less than 1 indicates lower volatility. Essentially, it quantifies the systematic risk of an asset.

Beta is a key input in the CAPM, which is used to calculate the expected return on an investment. The formula for CAPM is:

Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)

Here, beta is the lever that adjusts the market risk premium (Market Return - Risk-Free Rate) to reflect the specific risk of the asset you're evaluating. Now, let's dig into the heart of the matter: levered versus unlevered beta.

Levered Beta: Reflecting Debt

Levered beta, also known as equity beta, reflects the risk of a company's equity, considering the impact of its debt. When a company takes on debt, it introduces financial leverage, which amplifies both gains and losses. This increased volatility is captured in the levered beta. Think of it this way: levered beta shows how much a company's stock price tends to move compared to the market, taking into account its debt levels.

Using levered beta is appropriate when you're evaluating the risk of a company's equity as it currently stands. It's the beta you'll typically find quoted by financial data providers because it's directly based on the company's stock price movements. If you're trying to determine the expected return for an investment in a specific company's stock, using its levered beta is generally the way to go. Remember, this beta already incorporates the effect of the company's capital structure (i.e., the mix of debt and equity).

However, there are situations where levered beta might not be the best choice. For instance, when comparing companies with significantly different capital structures, the levered betas can be misleading. A company with a lot of debt will naturally have a higher levered beta than a company with little or no debt, even if their underlying business operations are equally risky. This is where unlevered beta comes in handy.

Unlevered Beta: Isolating Business Risk

Unlevered beta, also known as asset beta, measures the risk of a company's assets without considering the impact of debt. It essentially strips out the financial leverage to isolate the inherent business risk. This beta tells you how volatile a company's assets are compared to the market, assuming it has no debt. Calculating unlevered beta involves removing the effect of debt from the levered beta, allowing for a more direct comparison of the underlying business risks of different companies.

The formula to unlever beta is:

Unlevered Beta = Levered Beta / (1 + (1 - Tax Rate) * (Debt / Equity))

Where:

• Levered Beta is the company's observed beta.
• Tax Rate is the company's corporate tax rate.
• Debt is the market value of the company's debt.
• Equity is the market value of the company's equity.

Why bother with unlevered beta? It's particularly useful when you want to compare the risk profiles of companies with different capital structures or when you're trying to estimate the beta of a project or division within a company. By removing the effect of debt, you can focus on the fundamental business risk and make more apples-to-apples comparisons. For example, if you're evaluating two companies in the same industry, but one has significantly more debt than the other, using unlevered betas will give you a clearer picture of which company's underlying business is actually riskier.

When to Use Levered vs. Unlevered Beta

Okay, so when should you use levered beta, and when should you use unlevered beta? Here’s a breakdown to help you decide:

Use Levered Beta When:

• Evaluating the risk of a specific company's stock: If you're trying to determine the expected return for an investment in a particular company's shares, the levered beta is generally the appropriate choice. It reflects the actual risk that investors in that company's stock are exposed to, considering its current debt levels.
• The company's capital structure is stable: If you believe that the company's debt-to-equity ratio is unlikely to change significantly in the foreseeable future, using the levered beta is a reasonable assumption.
• You're using CAPM for a single company analysis: When you're focused on valuing a specific company and not comparing it to others with different capital structures, levered beta is usually sufficient.

Use Unlevered Beta When:

• Comparing companies with different capital structures: If you're analyzing multiple companies and they have vastly different debt-to-equity ratios, using unlevered betas allows you to compare their underlying business risks on a more level playing field. This helps you avoid being misled by the impact of financial leverage.
• Estimating the beta of a project or division: When you're evaluating a specific project or division within a company, you often need to estimate its beta. In this case, you can use the unlevered beta of comparable companies in the same industry and then relever it based on the project's or division's expected capital structure.
• The company's capital structure is expected to change: If you anticipate that a company will significantly alter its debt-to-equity ratio in the future (e.g., through a major debt issuance or repayment), using the current levered beta may not be accurate. In such cases, it's better to use the unlevered beta and then relever it based on the expected future capital structure.

Practical Example

Let's illustrate with an example. Suppose we have two companies, Company A and Company B, in the same industry. Company A has a levered beta of 1.2 and a debt-to-equity ratio of 0.5, while Company B has a levered beta of 1.5 and a debt-to-equity ratio of 1.5. At first glance, it might seem that Company B is riskier because it has a higher levered beta. However, this doesn't account for the fact that Company B has significantly more debt.

To get a clearer picture, we need to calculate the unlevered betas. Assuming a tax rate of 25%, the unlevered beta for Company A is:

1. 2 / (1 + (1 - 0.25) * 0.5) = 0.96

And the unlevered beta for Company B is:

1. 5 / (1 + (1 - 0.25) * 1.5) = 0.86

Now we see that Company A actually has a higher unlevered beta than Company B, indicating that its underlying business is riskier, despite Company B having a higher levered beta. This example highlights the importance of using unlevered beta when comparing companies with different capital structures.

Relevering Beta

Once you've calculated the unlevered beta, you might need to relever it to reflect a different capital structure. This is often necessary when you're estimating the beta of a project or division that has a different debt-to-equity ratio than the comparable companies you used to calculate the unlevered beta. The formula to relever beta is:

Levered Beta = Unlevered Beta * (1 + (1 - Tax Rate) * (Debt / Equity))

For example, suppose you've determined that the unlevered beta for a particular project is 0.8, and the project is expected to have a debt-to-equity ratio of 0.6. Assuming a tax rate of 25%, the relevered beta would be:

0. 8 * (1 + (1 - 0.25) * 0.6) = 1.16

This relevered beta can then be used in the CAPM to estimate the expected return for the project.

Conclusion

In summary, understanding the difference between levered and unlevered beta is essential for accurate investment analysis. Levered beta reflects the risk of a company's equity, considering the impact of debt, while unlevered beta measures the risk of a company's assets without considering debt. Use levered beta when evaluating the risk of a specific company's stock and the capital structure is stable. Use unlevered beta when comparing companies with different capital structures or estimating the beta of a project or division. By mastering these concepts, you'll be better equipped to make informed investment decisions.