Question

ABC is financed with debt and the rest equity. ABC has an equity beta of ​, a debt beta of 0 and a marginal tax rate of . If ABC issues debt to repurchase equity so that the new firm is now ​% ​debt, what will be its new equity​ beta? ​ (Continue to assume the debt beta remains at​ 0.) Ans is 2.25 but i do not know how to calculate

Answer 1

The new equity beta after ABC issues debt to repurchase equity can be calculated using the levered beta formula, which incorporates the company's tax rate and new debt-to-equity ratio. It involves the equity beta before leverage, the marginal tax rate, and the proportion of financing that is now debt.

Step-by-step explanation:

When a company like ABC issues debt to repurchase equity, it changes its capital structure and this affects its equity beta. The formula for calculating the new equity beta (levered beta) when there is a change in the capital structure is:

Beta_Levered = Beta_Unlevered * [1 + ((1 - Tax Rate) * (Debt/Equity))]

Assuming the initial equity beta is given and represented as Beta_Unlevered, and the firm is using its debt to repurchase equity so that the new structure is X% debt. Since the debt beta is 0, we can simplify the formula as Beta_Levered = Beta_Unlevered * [1 + ((1 - Tax Rate) * X/(1-X))],

Inserting the appropriate values into this formula would yield the new levered beta of the equity. The provided answer of 2.25 implies that these values were calculated accordingly.