Question

North Pole Fishing Equipment Corporation and South Pole Fishing Equipment Corporation would have identical equity betas of 1.22 if both were all equity financed. The market value information for each company is shown here: North Pole South Pole Debt $ 3,070,000 $ 3,980,000 Equity $ 3,980,000 $ 3,070,000 The expected return on the market portfolio is 12.5 percent and the risk-free rate is 4.5 percent. Both companies are subject to a corporate tax rate of 22 percent. Assume the beta of debt is zero.

a. What is the equity beta of each of each company? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

b. What is the required rate of return on equity for each company?

Answer 1

a. The EQUITY beta  for North Pole :

The equity beta of a firm financed entirely by equity is equal to its unlevered beta. Since each firm has an unlevered beta of 1.22, we can find the equity beta for each

βEquity= [1 + (1 – tC)(total debt/total equity )] βUnlevered

βEquity= [1 + (1 – .22)($3,070,000/$3,980,000](1.22)

= 1.95 (rounded off to two decimal places)

Similarly the asset beta for South Pole:

βEquity= [1 + (1 – tC)(total debt/total equity )] Beta (unlevered)

βEquity= [1 + (1 – .22)($3,980,000/$3,070,000](1.22)

βEquity= 2.45

B.  What is the required rate of return on equity for each company:

Re = Rf + beta (Rm - Rf)

=  4.5 + 1.95( 12.5 - 4.5)

= 20.1 %

Re = Rf + beta (Rm - Rf)

= 4.5 + 2.45 (12.5 - 4.5)

= 24.1%