Capital Structure & WACC

Under MM Proposition II without taxes, why does more leverage not reduce $WACC$?

Higher leverage raises equity cost enough to exactly offset cheaper debt.

Under MM with taxes, how does greater leverage affect $WACC$?

It lowers $WACC$ because the debt tax shield reduces after-tax debt cost.

How does a higher corporate tax rate affect $WACC$, all else equal?

It tends to lower $WACC$ by increasing the debt tax shield.

In the $WACC$ formula, what do the weights $w_d$, $w_p$, and $w_e$ represent?

Target or market-value proportions of debt, preferred, and equity.