Consider four different stocks, all of which have a required return of $11\%$ and a most recent dividend of $$3\mathrm{.}50$ per share. Stocks W$,$ X and Y are expected to maintain constant growth rates in dividends for the foreseeable future of $10\%,0\%,$ and $16\%$ per year, respectively. Stock Z is a growth stock that will increase its dividend by $12\%$ for the next two years and then maintain a constant $9\%$ growth rate thereafter.

a$.)$ For all four stocks, what is the dividend yield and the expected capital gains yield? Explain your results for each stock.

b$.)$ Identify the relationship between the various returns, in terms of growth and income, that you find for each of these stocks.

You must show all your work to get marks for answers including equations, values and, if using a financial calculator, provide key functions and inputs.