What formula is used to unlever and relever beta?

The formula used to unlever and relever beta involves a calculation that considers the debt-to-equity ratio and the tax shield provided by debt. In this context, the correct equation is expressed as BL = Bu(1 + (1 - T)(D/E)), where:

• BL represents the levered beta,

• Bu denotes the unlevered beta,

• T is the corporate tax rate,

• D represents the market value of debt,

• E represents the market value of equity.

The significance of this formula lies in the adjustment of the beta for the leverage effect on a company’s risk. Unlevered beta (Bu) reflects the risk of the firm's assets without the impact of debt, while levered beta (BL) accounts for the financial risk introduced by leverage. This adjustment is crucial for evaluating the potential returns and risk profile of equity investors who bear the additional volatility caused by the company's debt level.

This formula also incorporates the tax advantage of debt, which lowers the effective cost of borrowing. As such, recognizing the tax shield effect (1 - T) is vital for accurately reflecting the firm's risk under its capital structure.