The stock of Robotic Atlanta Inc. is trading at $40 per share. In the
past, the firm has paid a constant dividend of $5 per share and it has
just paid an annual dividend. However, the company will announce today
new investments that the market does not know about. It is expected
that with these new investments, the dividends will grow at 5%
forever.  Assuming that the discount rate remains the same, what will
be the price of the stock after the announcement?

Hi!!


To solve this you must use the Constant Growth Stock Valuation formula.

Let me define the variables:
Pi = price at year i
P0 = today's price
Di = dividends in period i
r = rate of return on the stock
g = constant growth rate


Since stock initially pays constant dividends (0-growth), then 
r = D0/P0 = 5/40 = 0.125  (12.5%)

After the announcement the stock will become from a 0%-growth to a
4%-growth, and the new price, according to the Constant Growth Stock
Valuation formula, will be:
New P0 = D1/(r-g) = 
       = D0*(1+g)/(r-g) =
       = 5*(1.04)/(0.085) =
       = 61.18

The new price will be $61.18 .


For a references about the formula see:
"Constant Growth Stock Valuation":
http://www.globusz.com/ebooks/Valuation/00000020.htm


Regards,
livioflores-ga