Question

A major new client, Ms. Victoria, has requested that Houston Financial presents an investment seminar on the stock price of Sugar Land Inc. Bonnie will analyze Sugar Land Inc (SL).

1. Assume that Sugar Land (SL) has a beta coefficient of 1.3, that the risk-free rate, K_F (the yield on 10 year T-bonds) is 7 percent, and that the market risk premium (K_M – K_F) is 5 percent. What is the required rate of return on SL’s stock according to CAPM?

Assume that SL is a constant growth company whose last dividend (D0), which was paid yesterday) was $2.00, and whose dividend is expected to grow indefinitely at a 6 percent rate. Assume the required rate of return for SL is 13%, (Different from your estimate of 1 above).

2. What is the firm’s expected dividend stream over the next 3 years?
3. What is the firm’s current stock price?
4. What is the stock's expected value 1 year from now?
5. What is the expected dividend yield, the capital gains yield, and the total return during the first year?

Now assume that the stock is currently selling at $32.29, no other changes.

6. What is the expected rate of return on the stock?
7. What would the stock price be if its dividends were expected to have zero growth?

Answer 1

1. Required Rate of Return =Risk Free Rate+Beta*Market Risk Premium =7%+1.3*5% =13.5%

2. D0 =2
Growth =6%
Dividend Year 1(D1) =D0*(1+growth) =2*(1+6%)=2.12
D2=D0*(1+growth)^2 =2*(1+6%)^2 =2.2472 or 2.25
D3=D0*(1+growth)^3 =2*(1+6%)^3 =2.382 or 2.38

3.Current Stock Price(P0) =D0*(1+Growth)/(Required Rate-growth) =2*(1+6%)/(13%-6%) =30.2857 or 30.29

4. Expected Price after 1 year(P1) =P0*(1+g) =30.2857*(1+6%) =32.1029 or 32.10

5.Expected Dividend Yield =D1/P0 =2.12/30.2857 =7%
Capital Gain =(P1-P0)/P0 =(32.1029-30.2857)/30.2857 =6%
Total Return =Dividend Yield +Capital Gain =7%+6% =13%

6. If stock is currently selling at 32.29
Required Rate =D1/Price+growth =2.12/32.29+6% =12.57%

7. If 0 growth then Stock Price =D0/Required Rate =2/13% =15.38