Question

1.    If the risk-free rate is 6.9%, the market risk premium is 7.0%, and the expected return on Security J is 29.4%, what is the beta for Security J? (Calculate your answer to two decimal places.)

Title: Preferred stock (solve for value)

2.    Timeless Corporation issued preferred stock with a par value of $700. The stock promised to pay an annual dividend equal to 19.0% of the par value. If the appropriate discount rate for this stock is 10.0%, what is the value of the stock?

Title: Supernormal growth (three years g(s))

3.    Growing, Inc. is a firm that is experiencing rapid growth. The firm yesterday paid a dividend of $5.60. You believe that dividends will grow at a rate of 24.0% per year for three years, and then at a rate of 10.0% per year thereafter. You expect that the stock will sell for $177.59 in three years. You expect an annual rate of return of 18.0% on this investment. If you plan to hold the stock indefinitely, what is the most you would pay for the stock now?

Title: Constant Growth Model (new div - CAPM)

4.    You are considering buying common stock in Grow On, Inc.  You have projected that the next dividend the company will pay will equal $7.60 and that dividends will grow at a rate of 6.0% per year thereafter.  The firm's beta is 0.93, the risk-free rate is 6.1%, and the market return is 13.6%.  What is the most you should pay for the stock now?

Answer 1

Q1) Expected return = risk free rate + beta ( market risk premium)

29.4% = 6.9% + Beta (7%)

Beta = 29.4% - 6.9% / 7%

= 22.5% / 7%

= 3.21

Q2) Dividend = preference share value × dividend rate

= 700 × 19%

= 133

Value of stock = dividend / cost of capital

= 133 / 0.10

= $1,330

Q3) Given:

Growth rate for 3 years = 24%

Cost of capital (r)= 18%

Dividend (D0)= 5.60

Expected price after 3 years = 177.59

D1= 5.60 × (1.24)= 6.944

D2= 6.944 × (1.24) = 8.611

D3= 8.611 × (1.24) = 10.6771

Value of stock = D1/(1+r)^n + D2/(1+r)^n + D3/(1+r)^n + Price / (1+r)^n

= 6.944 / (1.18)^1 + 8.611/(1.18)^2 + 10.6771/(1.18)^3 + 177.59 / (1.18)^3

= 6.944/1.18 + 8.611/1.3924 + 10.6771/1.643032 + 177.59/1.643032

= 5.8847 + 6.184 + 6.498 + 108.087

= $126.65

Q4) Cost of equity = Risk free rate + beta (market return - risk free rate)

= 6.1% + 0.93 ( 13.6% - 6.1%)

= 6.1% + 0.93 (7.5%)

= 6.1% + 6.975%

= 13.075%

Price = expected Dividend / cost of equity - growth rate

= 7.60 / 0.13075 - 0.06

= 7.60 / 0.07075

= $107.42