Fall 2009

Homework 8

Instructions: please read carefully

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You should show your work how to get the answer for each calculation question to get full credit

The due date is Tue Dec 15, 2009. Late homework will not be graded.

Name(s):

Student ID

1. A constant-growing stock just paid $2 dividend and has a current market price of $30. Determine the stock's required rate of return if the company's constant growth rate is 5%. a. 5%

b. 7%

c. 12%

d. 14%

1. c

R = D1/Po + g = 2(1+0.05)/30 + 0.05 = 0.12

2. Stock analysts just predicted that Hybrid Engine Company's earnings and dividends will grow at 20% each year for the next two years due to its new invention. After that, its growth rate will stabilize at 5% per year indefinitely. Assume that the rate of return on the stock is 14% and its last dividend was $1 per share. Determine the current price of the company's stock. a. $16.8

b. $15.1

c. $16.1

d. $13.8

2. b

Step 1: compute D1, D2

D1 = D0(1+g*) = 1(1+.2)= 1.2

D2 = D1(1+g*) = 1.2(1+1.2) = 1.44

Step 2: compute P2 = D3/(k-g)

D3 = D2(1+g) = 1.44(1+0.05)= 1.512

P2 = 1.512/(0.14-0.05) = 16.8

Step 3: Compute P0 by discounting D1, D2, and P2 to present

P0 =

1.2

1.44

16.8

+

+

= 15.1

1

2

(1 + 0.14)

(1 + 0.14)

(1 + 0.14) 2

3. Southwest Technology's common stock is selling at $30 per share today. Southwest just paid a $2 dividend. Its dividend is expected to grow by 5% in the coming year. The required rate of return on Southwest is 15%. Determine the common stock's dividend yield and capital gain yield for the first year.

a. 10%; 5%

b. 7%; 8%

c. 5%; 10%

d. 6.7%; 8.3%

3. b

dividend yield = D1/P0

D1 = D0(1+g) = 2(1+0.05) = 2.1

So dividend yield = 2.1/30 = 0.07

We have total return = dividend yield + capital gain yield

15% = 7% + capital gain yield

So capital gain yield = 15% - 7% = 8%

4. Heavenly Hotels, Inc. will not pay any dividends for the next three years. Heavenly will pay its first dividend of $2.00 per share at the end of year four and its dividends will stay the same forever. The required rate of return on the company's common stock is 10%. What price should the stock be selling now?

a. $20

b. $16

c. $12

d. $15

Step 1: Compute D1, D2, D3, D4

D1 = D2 = D3 = 0

D4 = 2

Step 2: compute P4 = D5/(k-g)

P4 = 2/(0.1-0) = 20

Step 3: Find P0 by discounting D1, D2, D3, D4 to present. In this case, D1 = D2= D3 = 0, so we only need to discount D4 and P4

P0 =

2.0

20

+

= 15

4

(1 + 0.1)

(1 + 0.1) 4

5. If two firms have the same current dividend and the same expected growth rate, their stocks must sell at the same current price or else the market will not be in equilibrium. a. True.

b. False.

5.b

P0 = D1/(k-g), so the current stock price not only depends on dividend, growth rate, but also on required return k

6. According to the dividend discount model, the current stock price of a company is ______________. a. the sum of all future dividends

b. the sum of the present values of all future dividends

c. zero if the company does not pay dividends

d. All of the above are correct.

6.b

7. If two firms have the same current P/E ratio and the same EPS, their stocks must sell at the same current price or else the market will not be in equilibrium.

a. True.

b. False.

7. a

8. A company's stock price will rise with an increase of its plowback ratio if ______________. a. the company's ROE = its required rate of return

b. the company's ROE < its required rate of return

c. the company's ROE = its growth rate

d. the company's ROE > its required rate of return

8. d

9. Which of the following statements is most correct for a zero growth stock? a. The stock's price one year from now should be the same as its current price. b. The stock's dividend yield is larger than the stock's required rate of return. c. The stock pays zero dividends.

d. None of the above is correct.

9. a

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