Currently, Bloom Flowers Inc. has a capital structure consisting of $20\%$ debt and $80\%$ equity. Bloom$$s debt currently has an $4\mathrm{.}6\%$ yield to maturity. The risk$-$free rate $($rRF$)$ is $2\mathrm{.}6\%,$ and the market risk premium $($rM $$ rRF$)$ is $7\%.$ Using the CAPM, Bloom estimates that its cost of equity is currently $15\mathrm{.}7\%.$ The company has a $36\%$ tax rate.

Bloom$$s financial staff is considering changing its capital structure to $40\%$ debt and $60\%$ equity. If the company went ahead with the proposed change, the yield to maturity on the company$$s bonds would rise to $9\mathrm{.}5\%.$ The proposed change will have no effect on the company$$s tax rate.

What would be the company$$s new cost of equity if it adopted the proposed change in capital structure?