The asset beta of a levered firm is 1.1. The beta of debt is 0.3. If the debt equity ratio is 0.5, what is the equity beta? (Assume no taxes.)
A)1.50
B)1.10
C)0.30
D)0.15

Question

Quizplus · Accepted Answer

The formula for levered beta is:
Levered beta = Unlevered beta * (1 + (1 - tax rate) * debt/equity)
Since there are no taxes, the formula simplifies to:
Levered beta = Unlevered beta * (1 + debt/equity)
Plugging in the numbers:
1.1 = Unlevered beta * (1 + (0.5))
Unlevered beta = 0.7333
The equity beta is:
Equity beta = Unlevered beta / (1 + (1 - tax rate) * debt/equity)
Since there are no taxes, the formula simplifies to:
Equity beta = Unlevered beta / (1 + debt/equity)
Plugging in the numbers:
Equity beta = 0.7333 / (1 + (0.5))
Equity beta = 0.7333 / 1.5
Equity beta = 0.4889
Therefore, the answer is A) 1.50.

The Asset Beta of a Levered Firm Is 1