ABC Boat Corporation has pulled off a miraculous recovery. Ten years ago, it was near bankruptcy. Now the firm has just announced a $$4$ per share dividend for the next year, the first since the crisis hit. Analysts expect that this dividend per share will increase at

the rate of $20\%$ per share as the company completes its recovery over the next three years $($$$4\mathrm{.}80$ in year one, $$5\mathrm{.}76$ in year two, and $$6\mathrm{.}92$ in year $3).$ After that, dividend growth is expected to settle down to a moderate long$-$term growth rate of $5\%).$

a$)$ What is the intrinsic value of this stock if the appropriate discount rate for the companies in the same risk class is $10\%?$

b$)$ Suppose now that stocks in the XYZ Boat Company are available. These stocks are expected to pay a dividend of $$7\mathrm{.}00$ per share next year. Thereafter, dividend growth is expected to be $5$ percent a year forever. Are these securities more valuable than those of the ABC Boat Company? Show your work. $($assume $10\%$ discount rate$)$

c$)$ What portion of the values XYZ calculated in part $($b$)$ is attributed to the present value of growth opportunities? Assume the year one earnings per share $($EPS$)$ for the XYZ Corp will be $$10$:$00.$ Show your work.