Assume that the risk$-$free rate is $6\%$ and the expected rate of return on the market portfolio is

$16\%.$ A share of stock sells for $$50$ today. It will pay a dividend of $$6$ per share at the end of the

year. Its beta is $1\mathrm{.}2.$

a$.$ What is the expected price of the stock at the end of the year? Find the expected return using

SML and then use the one$-$year rate of return formula $E(r)=\frac{D_1+P_1-P_0}{P_0}$ to find the price.

b$.$ You buy a firm with an expected perpetual annual cash flow of $$1,000$ but unsure of its risk. If

you think the beta of the firm is $0\mathrm{.}5,$ when in fact the beta is really $1,$ how much more will you

offer for the firm than it is truly worth?