Question

33. A firm will pay a dividend of $0 one year from today and $5.00 two years from today (that is, D S0 and D 5.00). Thereafter, the dividend is expected to grow at a constant rate forever. The price of this stock today is $100 and the required rate of retun on the stock is 10%. What is the expected constant growth rate of the dividend stream from year 2 to infinity?

Answer 1

D1 =0
D2 =5
Terminal Value =D2*(1+g)/(Required rate-Growth )=5*(1+g)/(10%-g)

Price of Stock =D2/(1+r)^2+Terminal Value/(1+r)^2
100 =5/1.1^2+5*(1+g)/((10%-g)*1.1^2)
100*1.1^2 =5 +5*(1+g)/(0.1-g)
121 =5 +5*(1+g)/(0.1-g)
121-5 =5*(1+g)/(0.1-g)
116/5 =(1+g)/(0.1-g)
116/5 =(1+g)/(0.1-g)
23.2*(0.1-g) =1+g
2.32-23.2g =1+g
g =1.32/24.2 =5.45%