MM Corp currently maintains a fixed capital structure of $80\%$ equity and $20\%$ debt. Its cost of equity is $10\%$ and it pays an interest rate of $5\%$ on its debt. Its CFO believes the company could continue to issue debt at the same interest rate as long as the debt$-$to$-$value ratio doesn't rise above $50\%.$ There are no taxes or financial frictions $($bankruptcy costs, agency costs, etc....$).$

$($a$)$ What is MM Corp's cost of capital $($WACC$)?$

$($b$)$ Calculate MM Corp's WACC if it changes its capital structure to maintain a debt$-$to$-$value ratio of $40\%.$

$($c$)$ Now assume instead that the tax rate is $25\%$ and interest is tax exempt $($as it is in practice$).$ Under this assumption, what is the $($after$-$tax$)$ WACC in $($b$)?$

$($d$)$ Should the CFO increase the debt$-$to$-$value ratio to $40\%$ in part $($b$)$ of this question? How about in part $($c$)?$ Give a brief explanation of your reasoning in each case.