A share of stock with a beta of .75 now sells for $50. Investors
expect the stock to pay a year-end dividend of $2. The T-bill rate is
4 percent, and the market risk premium is 8 percent. If the stock is
perceived to be fairly priced today, what must be investors?
expectation of the price of the stock at the end of the year?

Using the CAP-M model, we calculate r=beta(rm-rf)+rf = 0.75(8%-4%)+4% = 7%.

Using the Gordon Dividend Model Po=Div1/(r-g), we can solve for g
given an r of 7%, Div1 of $2, and Po of $50.  g=6.96%.  To determine
P1 at year end, we calculate Div2 by multiplying Div1 by 1+g
($2*1.0696) to get $2.1392.  $2.1392/(7%-6.96%) = $53.48.  This is the
expectation of the stock price at year end.

Source:  "Security Analysis" QuickMBA (2004)
http://www.quickmba.com/finance/securities/

Search terms:  "stock price" year end dividend CAPM

Sincerely,

Wonko

Thank you.

USing capm r = 4%+(0.750*(8%) = 10%
growth = 10%-2/50 = 6%

Div at the end of year 2  = 2 * (1+6%) = 2.12

Stock price = 2.12 / (10% - 6%) = 53