If the expected return on the market is 13.8 percent and the risk-free
rate is 6.4 percent and a certain company stock has a beta of 1.2,
then what is the expected rate of return on the stock and if the risk
free rate decreases to 3.5 percent, what is the expected return on the
stock?

lola5 --

Your answer with a 6.4% risk-free rate is 15.28%.  
Your answer with a 3.5% risk-free rate is 15.86%


Here is how you can reproduce it for yourself.  

Since you know the risk-free rate(s), the expected market return and the
beta of the stock, you can use the calculator at this linked site to
quickly determine the return on each stock in the portfolio:

Money Chimp: CAPM Calculator
http://www.moneychimp.com/articles/valuation/capm.htm


Using that calculator, you can simply plug in the risk-free rate, the
market rate and the beta of the stock.  The calculated result is
termed the "risk-adjusted discount rate," which, according to the
formula explained at the linked site, is "the expected return rate . .
 .   ."


A fuller definition or "expected return" of a stock can be found in
the Forbes Financial Glossary:

"Expected return  
The expected return on a risky asset based on a probability
distribution for the possible rates of return. Expected return equals
some risk free rate (generally the prevailing U.S. Treasury note or
bond rate) plus a risk premium (the difference between the historic
market return, based upon a well diversified index such as the S&P 500
and the historic U.S. Treasury bond) multiplied by the assets beta.
The conditional expected return varies through time as a function of
current market information."


Search Strategy:

I found the calculator (and much other information about expected
rates of return) using the following Google search:

expected market return equals beta
://www.google.com/search?num=100&hl=en&lr=&safe=off&c2coff=1&rls=GGLD%2CGGLD%3A2004-01%2CGGLD%3Aen&q=expected+market+return+equals+beta
  

I am confident that this is answer you are seeking.  If anything is
unclear, please ask for clarification before rating the answer.


markj-ga