$1)$ Diana Ltd$.$ paid a $$2\mathrm{.}50$ per share dividend yesterday. The dividend is expected to grow at $10$ percent per year for the foreseeable future. Diana Ltd$.$ has a beta of $1\mathrm{.}6,$ a standard deviation of returns of $30$ percent, and a required return of $18\%.$ What is the value of a share of Diana Ltd$.$ common stock?

$2)$ You are considering the purchase of Zee Company stock. You anticipate that the company will pay dividends of $$3\mathrm{.}50$ per share next year and $$4\mathrm{.}00$ per share the following year. You believe that you can sell the stock for $$20\mathrm{.}00$ per share two years from now. If your required rate of return is $10$ percent, what is the maximum price that you would pay for a share of Zee Company stock?

$3)$ The price of DDS Corporation stock is expected to be $$45$ in $5$ years. Dividends are anticipated to increase at an annual rate of $10$ percent from the most recent dividend of $$1\mathrm{.}00.$ If your required rate of return is $15$ percent, how much are you willing to pay for DDS stock?

$4)$ You purchased one share of Sophia Enterprises common stock for $$30$ today. If the stock pays a dividend of $$6\mathrm{.}50$ in one year, and sells for $$32\mathrm{.}50$ at that time, what will the dividend yield, growth rate, and total rate of return be for the year?

$5)$ Tannerly Worldwide's common stock is currently selling for $$48$ a share. If the expected dividend at the end of the year is $$2\mathrm{.}40$ and last year's dividend was $$2\mathrm{.}00,$ what is the rate of return implicit in the current stock price?