please show work for better rating investors require a 15 percent rate of return

Question

please show work for better rating

investors require a 15 percent rate of return on Goulet COmpanys stock (rs=15%)

a. what will be goulets stock value if the previous divided was D0=$2 and if investors expect dividends to prow at a constant compund annual rate of (1)-5% (2) 0% (3) 5% (4) 10%

b. using data from part a calcualte the value for goulets stock if the required rate of return is 15% and the expected growth rate is (1) 15% or (2) 20%. Are these rates reasonable?

c. is it resonable to expect that a constant growth stock would have g > rs?

Explanation / Answer

a. required arte of return = 15%

D0 = $2

(1) g=-5%

ergo D1 = 2*(.95), D2 = 2*(0.95)^2......and so on continue

ergo , Price = D1/(r-g) = 2*0.95/(.15+.05)

= $ 9.5

(2) g=0%

ergo D1 = 2, D2 = 2......and so on continue

ergo , Price = D1/r= 2/.15

= $ 13.33

(3) g=5%

ergo D1 = 2*(1.05), D2 = 2*(1.05)^2......and so on continue

ergo , Price = D1/(r-g) = 2*1.05/(.15-.05)

= $ 21

(4) g=10%

ergo D1 = 2*(1.1), D2 = 2*(1.1)^2......and so on continue

ergo , Price = D1/(r-g) = 2*1.1/(.15-.1)

= $ 44

b. if growth rate = 15%

then price = D1/(r-g) since r=g= 15%,

price of the stock would be ...not possible

if growth rate is 20%...not possible becos thsi would imply that company is growing more then the co==economy and hence the value of the company is more then the value of the econmy....this may be possible in the short run but not in the long run

c. henc it is not reasonalbe to expect that a constant growth stock would have g > rs..this may be possible in the short run but not in the long run

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