One of your new employees notes that your debt has a lower cost of capital $(5\%)$ than your equity $(12\%).$So$,$ he suggests that the firm swap its capital structure from $35\%$ debt and $65\%$ equity to $65\%$ debt and $35\%$ equity instead. He estimates that after the$$ swap, your cost of equity would be $21\%.$

a$.$ What would be your new cost of$$ debt? Make your calculations based on your$$ firm's pretax WACC.

b$.$ Have you lowered your overall cost of$$ capital?