An unlevered company $($just common stock, no preferred$)$ with a cost of equity of $13\%$ generates $$2$ million in earnings before interest and taxes $($EBIT$)$ each year. The decides to alter its capital structure to include debt by adding $$8$ million in debt with a pre$-$tax cost of $4\%$ to its capital structure and using the proceeds to reduce equity by a like amount as to keep total invested capital unchanged. The firm pays a tax rate of $33\%.$

Assuming that the company's EBIT stream can be earned into perpetuity and that the debt can be perpetually issued $($or rolled$),$ what is the firm's new weighted average cost of capital?