An unlevered firm with a cost of capital of $10\%$ announces that it will issue bonds. The firm's new capital structure will be a mix of $30\%$ equity and $70\%$ debt. Find the new cost of equity if the cost of debt is $6\%$ and the tax rate is $40\%.$

A$.$

$14\mathrm{.}20\%$

B$.$

$11\mathrm{.}03\%$

C$.$

$10\mathrm{.}77\%$

D$.$

$13\mathrm{.}24\%$

E$.$

$15\mathrm{.}60\%$