Question

# Suppose that firm A is considering entering a business similar to firm B, a relatively small...

Suppose that firm A is considering entering a business similar to firm B, a relatively small firm in a single line of business. Firm A is currently financed with 60% debt and 40% equity. Firm B, the pure-play firm, has a β of 0.95 and is financed with 40% debt and 60% equity. Firm B’s marginal tax rate is 30% and firm A’s marginal tax rate is 25%. Assume the riskless rate is 2% and the market return is 8%.

Q1. According to the CAPM, the market risk premium is _____________ percent.

Q2. What is Firm B's unleveraged beta?

Q3. What is Firm A's leveraged beta?

Q4. Estimate firm A’s cost of equity for the new business using the CAPM. Answer is decimal format.

Solution:

Q1.) The market risk premium = Market return - Risk-free rate = 8% - 2% = 6%

Q2) Levered Beta = Unlevered beta * ( 1+ D/E *(1-Tax rate))

0.95 = Unlevered beta * ( 1+ 0.4/0.6 *(1-30%))

0.95 = Unlevered beta * 1.46667

Unlevered Beta = 0.65

Q3)

Levered Beta = Unlevered beta * ( 1+ D/E *(1-Tax rate))

Levered Beta = 0.65 * ( 1+ 0.6/0.4 *(1-25%)) = 0.65*2.125= 1.38

Q4)

The cost of equity = Risk-free rate + Beta * Market Risk Premium

The cost of equity = 2% + 1.38 * 6% = 10.28%