Mountain Sports Inc. currently has no debt, annual earnings before interest and taxes of $$75$ million and an average tax rate of $34\%.$ Net income is expected to stay constant forever. The firm pays out $100\%$ of net income as dividends.

Using the CAPM, the firm estimates that its cost of equity is $10\%.$ The risk$-$free rate is $2\%$ and the expected equity market risk premium $($MRP$)$ is $7\%.$ There are $8$ million shares outstanding.

The firm is considering issuing bonds worth $$45$ million to repurchase its own shares at the higher market price after announcing the recapitalization. An investment bank has estimated that the coupon rate and yield to maturity on the bonds would be $8\%.$

Stock Price before the recapitalization $=61\mathrm{.}88$

Debt$-$to$-$equity ratio after the capitalization $=\mathrm{.}0967$

What will be the cost of equity after the recapitalization?