Radical VenOil, Inc. has a cost of equity capital equal to 22.8 percent. If the risk-free rate of return is 10 percent and the expected return on the market is 18 percent, then what is the firm's beta if the marginal tax rate is 35 percent?

Question

Quizplus · Accepted Answer

Radical VenOil's cost of equity (ke) = 22.8%
Risk-free rate of return (rf) = 10%
Expected return on the market (rm) = 18%
Marginal tax rate (T) = 35%

We can use the following formula to calculate the beta of the firm:

ke = rf + β(rm -rf) + T[β(rm - rf) - D], where D is the dividend yield

22.8% = 10% + β(18% - 10%) + 35%[β(18% - 10%) - 0]

Simplifying the equation, we get:

0.128β = 0.1188
β = 0.1188 / 0.128
β = 0.93

However, this is the unlevered beta of the firm. To get the levered beta, we need to use the following formula:

βL = βU[1 + (D/E)(1-T)], where D/E is the debt-to-equity ratio

As the debt-to-equity ratio is not given, we cannot calculate the levered beta directly. Therefore, we cannot use choices A and B.

We also cannot use choice D as the calculated beta is much lower than 4.10.

The correct answer is C, 1.60, as it is the only option that can potentially be correct based on the calculated unlevered beta of 0.93.