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 20% 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 5%. The most recent annual dividend was DIV 0= $1 per share. 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 rateis 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 stocknow and sells it in 1 year?

Explanation:

Growth rate = 20%

DIV 0= $1 per share

a)

D1 =D0(1+g)  = 1*(1+0.20 ) =$1.2

D2= 1.2*(1+0.2) =$1.44

D3 = 1.44(1+0.2) =$1.728  

D4 = 1.728(1+0.2)=$2.0736

b)

Sustainable growth rate = 5%

Discount rate = 10%

D5 =D4*(1+g)  = 2.0736*(1+0.05) = $2.17728

price in 4 year =D5/(r-g)  = 2.17728 /(0.10-0.05)  = 2.17728 /0.05  = $ 43.5456

c)

price today = P0 = [PVF10%,1*D1]+[PVF10%,2*D2] +[PVF10%,4*TV]

= [0.90909*1.2]+[0.82645*1.44]+[0.75131*1.728]+[0.68301*2.0736]+[0.68301*43.5456]

= 1.0909+ 1.1901+ 1.2983+ 1.4163+ 29.7421

= $34.74 per share

D)dividend yield =D1/P0

= 1.2/34.74

= 0.0345 = 3.45%

e)

next year price = [0.90909*1.44]+[0.82645*1.728]+[0.75131*2.0736]+[0.75131*34.74]

= 1.3091+ 1.4281+ 1.5579+ 26.1005

= $ 30.40 per share

f)

expected rate of return =[ p1-p0+D1]/P

= [30.40-34.74+1.2]/34.74

= -3.14/ 34.74  = -0.0904 = -9.04%

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