Question

Suppose the company just paid dividend of $1. The dividends are expected to grow at 25% in Year 1 and 20% in Year 2, and 15% in Year 3. After that, the dividends will grow at a constant rate of 5% forever. If the required rate of return is 10%, compute today's price of the stock.

Answer 1

D(t+1) = D(t)*(1+g1)
D0	1
For the first year
g1	0.25
D1	1*(1+.25)
D1	1.25
For the second year
g2	0.2
D2	1.25*(1+.2)
D2	1.5
For the third year
g3	0.15
D3	1.5*(1+.15)
D3	1.725
For the fourth year
g4	0.05
D4	1.725*(1+.05)
D4	1.81125
According to the dividend growth model.
P4 = D5/(R-g4)
D5	1.81125*(1.05)
D5	1.9018125
R is the required rate of return that is 10%
P4	1.9018125/(.10 - .05)
P4	38.03625
Cash flow in year 4	D4+P4
Cash flow in year 4	39.8475
The price of the stock today = sum of present value of future cash flows.
Using R = .10
Year	1	2	3	4
Cash flow	1.25	1.5	1.725	39.8475
Present value	1.14	1.24	1.30	27.22
sum of present values	30.89
The price of the stock today is equal to $30.89.