ABC has a debt$-$equity ratio of $0\mathrm{.}20$ and the market value of equity is $$125$ billion. ABC$$s equity cost of capital is $7\%,$ it can borrow at $4\mathrm{.}20\%$ and its tax rate is $35\%.$ ABC announces that it will raise its debt$-$ equity ratio to $0\mathrm{.}5$ through a leveraged recapitalization. Borrowing costs will rise to $4\mathrm{.}50\%.$ What is ABC$$s new cost of equity?