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better mousetraps has come out with an improved product, and the world is beating a path to its door. as a result, the firm projects growth of 21 percent per year for 4 years. by then, other firms will have copycat technology, competition will drive down profit margins, and the sustainable growth rate will fall to 6 percent. the most recent annual dividend was div 0 = $1 per share. (15 points)
a. What are the expected values of DIV 1, DIV 2, DIV 3, and DIV 4?
b. What is the expected stock price 4 years from now? The discount rate
is 10%.
c. What is the stock price today?
d.Find the dividend yield, DIV 1/ P 0 .
e. e. What will next year’s stock price, P1, be?
f. What is the expected rate of return to an investor who buys the stock
now and sells it in 1 year?

Sagot :

As per the given information, there is a growth rate of the firm by 21% or 0.21. The same firm has a dividend that has been divided on the basis of $1. There has been few situations given, in according to the same, solutions will be as follow:

(a) DIV 1 =Do (1+g)  = 1*(1+0.21 ) =$1.21

DIV 2= 1.21*(1+0.21) =$1.46

DIV 3 = 1.46 *(1+0.21) =$1.77  

DIV 4 = 1.77 * (1+0.21)=$2.14

(b) Sustainable growth rate is 6% or 0.06

Discount rate is 10% or 0.10.

DIV 5 =DIV 4*(1+g)  = 2.14 *(1+0.06) = $2.2684

Price in 4 year =DIV 5/(r-g)  = 2.2684 /(0.10-0.06)  = 2.2684 /0.04  

= $ 56.71

(c)  Price today = Po = [PVF10%,1*D1]+[PVF10%,2*D2] +......[PVF10%,4*TV]

= [0.90909*1.21]+[0.82645*1.46]+[0.75131*1.77]+[0.68301*2.14]+ [0.68301*56.71]

= 1.089+ 1.197+ 1.327+ 1.455+ 38.56

= $43.63 per share

(D)Dividend yield =D1/P0

= 1.21/43.63

= 0.00277 = 2.77%

(e) Next year price = [0.90909*1.46]+[0.82645*1.77]+[0.75131*2.14]+ [0.75131*43.63 ]

= 1.314+ 1.451+ 1.605+ 32.722

= $ 37.09 per share

(f) Expected rate of return =[ P1-Po+D1]/Po

=(37.09 - 43.63 + 1.21)/43.63

=-5.33 /43.63

= -0.122   or = -1.22%

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