I am confused because I see different formulae to lever and unlever betas in different books (Damodaran, McKinsey, Brealey & Myers …). Which is the correct one? IESE Business School-University of Navarra – 7 (Finance Interview Questions With Answers)

The Beta Conundrum: Unraveling the Discrepancies in Levered and Unlevered Beta Formulas

The concept of beta, a measure of a stock’s volatility relative to the market, is fundamental in finance. It plays a crucial role in the Capital Asset Pricing Model (CAPM), which is used to calculate the expected return on an investment. However, when it comes to levered and unlevered betas, different textbooks and financial institutions often present seemingly conflicting formulas, leaving many students and professionals confused. This article aims to clarify the discrepancies and provide a comprehensive understanding of the different approaches to calculating levered and unlevered betas.

Understanding Levered and Unlevered Betas

Before delving into the formulas, it’s essential to grasp the distinction between levered and unlevered betas:

  • Unlevered Beta (βU): This represents the risk of a company’s assets, excluding the impact of debt financing. It reflects the inherent business risk associated with the company’s operations.
  • Levered Beta (βL): This reflects the total risk of a company, including both business risk and financial risk (risk associated with debt financing). It considers the company’s capital structure and the impact of debt on its volatility.

The Discrepancies in Formulas

The confusion arises from the different approaches taken by various sources, particularly when it comes to the formula for converting unlevered beta to levered beta. Here’s a breakdown of the common formulas:

1. Damodaran’s Approach

Ashton Damodaran, a renowned finance professor, uses the following formula:

βL = βU [1 + (1 – Tax Rate) (Debt/Equity)]

2. McKinsey’s Approach

McKinsey & Company, a global management consulting firm, employs a slightly different formula:

βL = βU [1 + (Debt/Equity)]

3. Brealey & Myers’ Approach

Brealey & Myers, authors of the widely-used textbook “Principles of Corporate Finance,” present a formula similar to Damodaran’s:

βL = βU [1 + (1 – Tax Rate) (Debt/Equity)]

4. IESE Business School’s Approach

IESE Business School, a leading business school in Spain, uses a formula that incorporates the debt-to-equity ratio and the tax rate:

βL = βU [1 + (1 – Tax Rate) (Debt/Equity)]

Resolving the Discrepancies

The key difference lies in the inclusion of the tax rate. Damodaran, Brealey & Myers, and IESE Business School all incorporate the tax rate, while McKinsey’s formula omits it. This discrepancy stems from the fact that interest payments on debt are tax-deductible, reducing the effective cost of debt. By incorporating the tax rate, the formulas acknowledge this tax shield effect, which lowers the overall risk of the company.

Which Formula is Correct?

The “correct” formula depends on the specific context and the assumptions made. In most cases, the formulas that incorporate the tax rate (Damodaran, Brealey & Myers, IESE Business School) are more accurate and reflect the real-world impact of debt financing. However, if the tax rate is negligible or the analysis focuses solely on the business risk, the McKinsey formula might be appropriate.

Practical Implications

The choice of formula can have significant implications for investment decisions. For example, if a company has a high debt-to-equity ratio and a low tax rate, using a formula that omits the tax rate could underestimate the levered beta and lead to an underestimation of the company’s risk. This could result in an investor overpaying for the stock.

Case Study: Tesla

Consider Tesla, a company with a high debt-to-equity ratio and a relatively low tax rate. Using Damodaran’s formula, which incorporates the tax rate, would result in a higher levered beta compared to McKinsey’s formula. This higher beta would reflect the increased risk associated with Tesla’s high debt levels and the tax shield effect. An investor using McKinsey’s formula might underestimate Tesla’s risk and potentially overpay for the stock.

Conclusion

The discrepancies in levered and unlevered beta formulas highlight the importance of understanding the underlying assumptions and the context in which these formulas are applied. While different sources may present seemingly conflicting formulas, the key takeaway is that the formulas incorporating the tax rate are generally more accurate and reflect the real-world impact of debt financing. Investors and analysts should carefully consider the specific context and the assumptions made when choosing a formula to calculate levered and unlevered betas. By understanding the nuances of these formulas, investors can make more informed investment decisions and avoid potential pitfalls.

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