The Davidson Company will be an annual dividend of $2 in the coming
year.  THe dividend is expected to grow at a constant rate of 5
percent permanetly.  The market requires a 12 percent return on the
company.
a.  what is the current price of a share of the stock?
b.  what will the stock price be 10 years from today?

Hi!!


I start defining the variables:
Pt = price at time t
P0 = today's price
Dt = dividends in period t
r = market required rate of return
g = constant growth rate


a. What is the current price of a share of the stock?

P0 = D1/(r-g) = 
   = $2/(0.12-0.05) =
   = $28.57

The current price of a share of the stock is $28.57 .

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b. What will the stock price be 10 years from today?


We know that 
Pt = D_(t+1)/(r-g) 
and 
D_(t+1) = Dt*(1+g) = D1*(1+g)^t 

Then:
Pt = D1*(1+g)^t/(r-g) = 
   = P0*(1+g)^t

We will have that:

P10 = $28.57*(1.05)^10 =
    = $46.54 

The stock price 10 years from now will be $46.54 .

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I hope that this helps you. If you find something unclear feel free to
request for a clarification.

Best regards.
livioflores-ga