Question

Question 1 (14 marks) Assume the risk-free rate is 3% and the expected rate of return on the market is 10%. a. AXB stock is now selling for $45 per share. It will pay a dividend of $2 per share at the end of the year. Its beta is 1.3. What do you expect the stock to sell for at the end of the year? (4 marks) b. Peter is buying a firm with an expected perpetual cash flow of $1,200 but is unsure of its risk. If Peter thinks the beta of the firm is 0.8, when the beta is really 1.2, how much more will he offer for the firm than it is truly worth? (8 marks) [Hint: Value of perpetual cash flow = CF/r] c. A stock has an expected rate of return of 9%. What is its beta? (2 marks)

Answer 1

(1) Risk-Free Rate = Rf = 3 % and Market Return = Rm = 10%

(a) Current Stock price = P0 = $ 45, Expected Dividend = D1 = $ 2 and Let the expected Stock price be $ P1

Stock Beta = 1.3

Expected Stock Return = 3 + 1.3 x (10-3) = 12.1 %

Therefore, [(P1-P0) + D1] / P0 = 0.121

P1 - 45 + 2 = 5.445

P1 = 5.445 + 45 - 2 = $ 48.445

(b) Perpetual Cash Flows = $ 1200, Expected Beta = 0.8 and Actual beta = 1.2

Expected Return = 3 + (10-3) x 0.8 = 8.6 %

Expected Firm Value = 1200 / 0.086 = $ 13953.49

Actual Return = 1.2 x 7 + 3 = 11.4 %

Actual Firm Value = 1200 / 0.114 = $ 10526.32

Extra Price Paid for Firm = 13953.49 - 10526.32 = $ 3427.17

(c) Expected Return = 9%

Let the firm beta be B

Therefore, 9 = 3 + B x (10-3)

9 = 3 + 7B

B = 6/7 = 0.8571 ~ 0.86