Two firms, $LL$ and HL each has $$50m$ in invested capital, $$12m$ of operating profit, a tax rate of $25\%.$ Firm $LL$ has a debt$-$to$-$capital $($D$/$C$)$ ratio of $20\%$ and pays $10\%$ interest on their debt. Firm HL has a D$/$C ratio of $35\%$ with an interest rate of $8\%$ on their debt. Calculate the following:

a$.$ Return on invested capital for firm HL and ROE for cach firm

b$.$ If LL$\text{'}$s CFO is thinking of raising the D$/$C ratio from $20\%$ to $35\%,$ which will lower their interest rate further from $10\%$ to $9\%,$ calculate the new ROE for LL$.$