Faris currently has a capital structure of 40 percent debt and 60 percent equity, but is considering a new product that will be produced and marketed by a separate division. The new division will have a capital structure of 70 percent debt and 30 percent equity. Faris has a current beta of 1.1 but is not sure what the beta for the new division will be. AMX is a firm that produces a product similar to the product under consideration by Faris. AMX has a beta of 1.6, a capital structure of 40 percent debt and 60 percent equity, and a marginal tax rate of 40 percent. Assuming Faris's tax rate is 40 percent, estimate the levered beta for the new product division.
A) 2.44
B) 1.14
C) 2.74
D) 3.88

Question

Quizplus · Accepted Answer

First, we need to find the unlevered beta of the new division:
Unlevered beta of AMX = 1.6
AMX D/E ratio = 0.40/0.60 = 0.67
Unlevered beta of new division = Unlevered beta of AMX / [1 + (1 - tax rate)*(debt/equity)]
= 1.6 / [1 + (1-0.4)*(0.7/0.3)]
= 1.16

Next, we need to find the levered beta of the new division:
Debt/equity of new division = 0.7/0.3 = 2.33
Levered beta of new division = Unlevered beta of new division * [1 + (1 - tax rate)*(debt/equity)]
= 1.16 * [1 + (1-0.4)*(2.33)]
= 2.74

Therefore, the answer is C) 2.74.

Faris Currently Has a Capital Structure of 40 Percent Debt