Question

A company currently pays a dividend of $4 per share (D0= $4). It is estimated that the company’s dividend will grow at a rate of 10% per year for the next 2 years, and then at a constant rate of 5% thereafter. The company’s stock has a beta of 1.6, the risk-free rate is 4% and the market risk premium is 2%. What is your estimate of the stock’s current price?

Answer 1

D(t+1) = D(t)*(1+g1)
D0	4
For the first two years
g1	0.1
D1	4*(1+.1)
D1	4.4
D2	4.4*(1+.1)
D2	4.84
Find the price of the stock in year 3
g2	0.05
D3	4.84*(1+.05)
D3	5.082
D4	5.082*(1+.05)
D4	5.3361
According to the dividend growth model.
P3 = D4/(R-g2)
Use the CAPM model to find the expected return on the stock.
Under the Capital Asset pricing model
R = Rf + Beta*(Rm-Rf)
Rf is the risk free rate that is .04.
Beta of the stock is 1.6
Rm - Rf is the market risk premium that is .02.
R = .04 + (1.6*.02)
R = .072.
In other words the expected return on the stock is 7.2%.
P3	5.3361/(.072 - .05)
P3	242.55
Cash flow in year 3	P3 +D3
Cash flow in year 3	247.632
The price of the stock today = sum of present value of future cash flows.
Using R = .072
Year	1	2	3
Cash flow	4.4	4.84	247.632
Present value	4.10	4.21	201.01
sum of present values	209.33
The estimate of the stocks current price is equal to $209.33.