A company due to its technology development expects to have 15% annual growth ra
ID: 2791959 • Letter: A
Question
A company due to its technology development expects to have 15% annual growth rate for the next 5 years, thereafter as other firms would have comparable technology, its growth is expected to slow down to 5% per year indefinitely. Stockholders required rate of return is 12% on company’s stock. The most recent annual dividend paid yesterday was $1 per share.
Calculate the present value of the company’s stock and the expected a)dividend yield, b) capital gain yield, and c) total return during
i.current year and
ii.5 years thereafter
Explanation / Answer
i.current year
Present value of the company’s stock = D1/(r-G)*(1-(1+G)^n/(1+r)^n) + D6/(r-g) *1/(1+r)^n
D1 = 1*(1+15%) = 1.15
r = 12%
G = 15%
n = 5
g = 5%
D6 =1*(1+15%)^5*(1+5%) = 2.111925
Present value of the company’s stock = 1.15/(12%-15%) *(1-(1+15%)^5/(1+12%)^5) + 2.111925/(12%-5%) *1/(1+12%)^5
Present value of the company’s stock = 22.54
a)
Dividend yield = D1/P0
Dividend yield = 1.15/22.54
Dividend yield = 5.10%
b)
Capital gain yield = Require return - Dividend yield
Capital gain yield = 12%-5.10%
Capital gain yield = 6.90%
c)
Total Return = Dividend yield+Capital gain yield
Total Return = 5.10%+6.90%
Total Return = 12%
ii 5 years thereafter
Value of the company’s stock in 5 year = D6/(r-g)
r = 12%
g = 5%
D6 =1*(1+15%)^5*(1+5%) = 2.111925
Value of the company’s stock in 5 year= 2.111925/(12%-5%)
Value of the company’s stock in 5 year = 30.17
a)
Dividend yield = D6/P5
Dividend yield = 2.111925/30.17
Dividend yield = 7.00%
b)
Capital gain yield = Require return - Dividend yield
Capital gain yield = 12%-7%
Capital gain yield = 5%
c)
Total Return = Dividend yield+Capital gain yield
Total Return = 5%+7%
Total Return = 12%
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