$8.$ Assume that the risk$-$free rate of interest is $6\%$ and the expected rate of return on the market is $16\%.$

a$.$ 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 $1\mathrm{.}2.$ What do investors expect the stock to sell for at the end of the year?

b$.$ I am buying a firm with an expected perpetual cash flow of $$1,000$ but am unsure of its risk. If I think the beta of the firm is $\mathrm{.}5,$ when in fact the beta is really $1,$ how much more will I offer for the firm than it is truly worth?

c$.$ A stock has an expected rate of return of $4\%.$ What is its beta?