What is the formula for calculating unlevered beta?

What is the formula for calculating unlevered beta?

• A. Levered beta / (1+(1-tax rate)*(total debt/equity))
• B. Levered beta * (1+(1-tax rate)*(total debt/equity))
• C. (1-tax rate) * (total debt/equity)
• D. Levered beta + (1-tax rate) * total debt

Answer: (A)

Unlevered beta is a measure that reflects the risk of a firm's equity without the impact of debt. The formula for calculating unlevered beta effectively removes the financial leverage component from the levered beta, allowing for a clearer comparison of companies with different capital structures. The correct formula expresses unlevered beta in relation to levered beta, factoring in the company’s debt and the tax shield provided by that debt. By dividing the levered beta by the term \(1 + (1 - \text{tax rate}) \times \frac{\text{total debt}}{\text{equity}}\), the impact of debt is appropriately adjusted for the tax advantages associated with interest payments, resulting in a clearer picture of the underlying business risk. This adjustment is crucial because it separates the operational risk inherent in the business from the financial risk introduced by leveraging, thus providing a more accurate measure of the company's intrinsic risk profile.

Unlevered beta is a measure that reflects the risk of a firm's equity without the impact of debt. The formula for calculating unlevered beta effectively removes the financial leverage component from the levered beta, allowing for a clearer comparison of companies with different capital structures.

The correct formula expresses unlevered beta in relation to levered beta, factoring in the company’s debt and the tax shield provided by that debt. By dividing the levered beta by the term (1 + (1 - \text{tax rate}) \times \frac{\text{total debt}}{\text{equity}}), the impact of debt is appropriately adjusted for the tax advantages associated with interest payments, resulting in a clearer picture of the underlying business risk.

This adjustment is crucial because it separates the operational risk inherent in the business from the financial risk introduced by leveraging, thus providing a more accurate measure of the company's intrinsic risk profile.