Stock A pays an earnings of $5 per share in year 1. The return on equity is 20%.

Question

Stock A pays an earnings of $5 per share in year 1. The return on equity is 20%. The discount rate is 10%.

5. If there is no plow-back, what is the stock price now (P0) ? A) $40 B) $50 C) $60 D) $70 E) None of the above

6. If there is a plow-back of 40%, what is the dividend per share at year 1 (Div1)? A) $5 B) $4 C) $6 D) $3 E) None of the above

7)If there is a plow-back of 40%, what would be the price for stock A one year from now (P1)? A) $150 B) $162 C) $172 D) $ 182 E) None of the above

8)If there is a plow-back of 40%, what is the earnings per share at year 2? A) $5.0 B) $5.4 C) $5.8 D) $6.2 E) None of the above

9. According to the dividend discount model, the current value of a stock is equal to the: A) present value of all expected future dividends. B) sum of all future expected dividends. C) next expected dividend, discounted to the present. D) discounted value of all dividends growing at a constant rate. E) none of the above

10. If a stock’s P/E ratio is 13.5 at a time when earnings are $3 per year, what is the stock’s current price? A) $4.50 B) $18.00 C) $22.22 D) $40.50 E) None of the above

11. A stock paying $5 in annual dividends sells now for $100 and has an expected return of 20%. What might investors expect to pay for the stock one year from now? A) $182.00 B) $186.00 C) $115.00 D) $110.00 E) None of the above

12. How much should you pay for a share of stock that offers a constant dividend growth rate of 10%, has a discount rate of 16%, and pays a dividend of $3 next year? A) $42.00 B) $45.00 C) $45.45 D) $50.00 E) none of the above

13. The price of a stock will likely increase if: A) the investment horizon decreases. B) the growth rate of dividends increases. C) the discount rate increases. D) dividends are discounted back to the present. E) none of the above

14. What should be the price for a common stock paying $3.50 annually in dividends if the growth rate is zero and the discount rate is 8%? A) $22.86 B) $28.00 C) $42.00 D) $43.75 E) None of the above

15. What is the plowback ratio for a stock with current price of $30, earnings of $5 per share next year, a discount rate of 20% , and a rate of return on equity of 25% ? A) 0.5 B) 0.2 C) 0.4 D) 0.1 E) None of the above

16. What is the expected constant growth rate of dividends for a stock currently priced at $50, that is expected to pay a dividend of $5 next year, and has a required return of 20%? A) 13% B) 10% C) 11% D) 12% E) none of the above 17. If the (current) dividend yield is 5% and the stock price is $25, what will the year three dividend be if dividends grow at a constant 6%? A) $1.33 B) $1.49 C) $1.58 D) $1.67 E) none of the above

Explanation / Answer

Answer 9) A

According to the dividend discount model, the current value of a stock is equal to the present value of all expected future dividends.

Answer 10)D  

            P/E = 13.5

            Then P = 13.5 x $3

            Price = $40.50

Answer 11) c

EXPECTED RETURN= DIVIDEND+P1-P0 /P0

20% =$ 5+ p1-$ 100 /$ 100

p1=$ 115

Answer 12 ) D

P0=C1/(r-g)=3/0.06=$50

Answer 13) The price of a stock will likely increase if: the growth rate of dividends increases

Answer 14) d

Po= Div /r =3.50/0.08 = $ 43.75

Answer 15)

The idea to solve this problem is that you suppose that the plow-back ratio is the ratio in each choice, then you use the dividend growth model ( P0 = Div1/(r-g) ) to calculate the current stock price. If the calculated stock price is the same as the given stock price of $30, then that choice is the answer.        

For example, suppose that the plow-back ratio is 0.5 in choice A. Then the dividend growth rate g = plow-back ratio * the rate of return on equity (ROE) =0.5*0.25=12.5%. Div1 =earnings1 * payout ratio =5*(1-plow-back ratio)=$2.5. P0 =Div1/(r-g)=2.5/(0.2-0.125)=$33.3, which is not the same as $30. So choice A is not the answer. Then use the above procedure to test choice B and you will find out P0=4/(0.2-0.5)=$26.7 < $30. So Choice B is not the answer. For choice C,

            g= 0.4*0.25=10%; P0=Div1/(r-g)=0.6*5/0.1=$30. So choice C is the answer.

Answer 16) B

By using the dividend growth model, P0 =div1/(r-g), we have

            $50 = $5/(.2 – g).

            g = 0.1=10%

Answer 17) B

Dividend yield is Div1/P0, which is 5%. So

            Div1=.05 x 25 = 1.25

            then, Div3 = div1*(1+g)2=1.25 x (1.06)2 = $1.4045

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