The answer is a$)12\mathrm{.}48\%$ but how? Simple Tech Inc is an Australian company operating in a pure imputation tax system. It is currently financed entirely $(100\%)$ by equity and has a beta of $0\mathrm{.}8.$ After examining its capital structure, Simple Tech finds that the optimal capital structure can be achieved at D$/$E ratio of $0\mathrm{.}4.$ The before$-$tax cost of debt capital for Simple Tech at the optimal capital structure is $10\%$ p$.$a$.$ The risk$-$free rate and market risk premium are $5\%$ p$.$a$.$ and $7\%$ p$.$a$.,$ respectively. If the statutory corporate tax rate is $30\%,$ which of the following is closest to the cost of equity at the optimal capital structure $($using the approach covered in the lecture$)?$

a$.12\mathrm{.}84\%$ p$.$a$.$

b$.12\mathrm{.}17\%$ p$.$a$.$

c$.12\mathrm{.}03\%$ p$.$a$.$

d$.11\mathrm{.}69\%$ p$.$a$.$

e$.10\mathrm{.}60\%$ p$.$a$.$