Firms HD and LD each have $$30$m in invested capital, $$8$m of EBIT, and a tax rate of $25\%.$ Firm HD has a D$/$E ratio of $50\%$ with an interest rate of $8\%$ on their debt. Firm LD has a debt$-$to$-$capital ratio of $30\%,$ however, pays $9\%$ interest on its debt. Calculate the following:

a$.$ Return on invested capital for firm LD

b$.$ Return on equity for each firm

c$.$ If HD$$s CFO is thinking of lowering the D$/$E from $50\%$ to $40\%,$ which will lower their interest rate further from $8\%$ to $7\%,$ calculate the new ROE for firm HD$.$