-The historical returns data for the past three years for Company A's stock is -6.0%, 15%,
15% and that of the market portfolio is 10%, 10% and 16%. If the risk-free rate of return is
4%, what is the cost of equity capital (required rate of return of company A's common stock)
Using CAPM?
A) 18%
B) 14%
C) 12%
D) None of the above

Question

Quizplus · Accepted Answer

Calculating the beta of Company A's stock using the historical returns data:

Beta = (Company A's annual return - Risk-free rate) / (Market portfolio's annual return - Risk-free rate)

Year 1: Beta = (-6% - 4%) / (10% - 4%) = -1

Year 2: Beta = (15% - 4%) / (10% - 4%) = 1.75

Year 3: Beta = (15% - 4%) / (16% - 4%) = 0.722

Average Beta = (-1 + 1.75 + 0.722) / 3 = 0.491

Using CAPM:

Required rate of return = Risk-free rate + Beta * (Market risk premium)

Market risk premium = Market portfolio's annual return - Risk-free rate = 16% - 4% = 12%

Required rate of return = 4% + 0.491 * 12% = 10.89%

Therefore, the cost of equity capital (required rate of return of Company A's common stock) using CAPM is 10.89%, which is closest to answer A) 18%.

-The Historical Returns Data for the Past Three Years for Company