Ultimate Electric, Inc. has just developed a solar panel capable of generating $200$ percent more

electricity than any solar panel currently on the market. As a result, Ultimate is expected to

experience a $15$ percent annual growth rate for the next five years. When the five$-$year period ends,

other firms will have developed comparable technology, and Ultimate's growth rate will slow to $5$

percent per year indefinitely. Stockholders require a return of $12$ percent on Ultimate's stock. The

firm's most recent annual dividend $(D_0),$ which was paid yesterday, was $$1\mathrm{.}75$ per share.

a$.$ Calculate the value of the stock today.

b$.$ Calculate the dividend yield, hat$\frac{(D{)}_1}{P_0},$ the expected capital gains yield, and the expected total

return $($dividend yield plus capital gains yield$)$ for this year. Calculate these same three yields

for Year $5.$