$($Medium$/$Hard$)$ Ballack Co$.\text{'}$s common stock currently sells for $$46\mathrm{.}75$ per share. The growth rate is a constant $12\%,$ and the company has an expected dividend yield of $5\%.$ The expected long$-$run dividend payout ratio is $25\%,$ and the expected return on equity $($ROE$)$ is $16\%.$ New stock can be sold to the public at the current price, but a flotation cost of $5\%$ would be incurred. What would be the cost of new equity?

A$)15\mathrm{.}24\%$

B$)15\mathrm{.}82\%$

C$)16\mathrm{.}13\%$

D$)14\mathrm{.}96\%$

E$)17\mathrm{.}26\%$