Corbin Inc. currently has $$900$ million in market cap and $$100$ million in debt, and at the company's current debt ratio, the cost of equity is $7\mathrm{.}90\%$ and the pre$-$tax cost of borrowing is $4\%.$ The company is considering doubling its debt to capital ratio and if it does so$,$ you expect the default spread on debt to also double. If the risk free rate is $3\%,$ the equity risk premium is $5\%$ and the marginal tax rate is $20\%,$ estimate the cost of capital at the new debt ratio.