Last year Rosenberg Corp. had $$195,000$ of assets, $$18,775$ of net income, and a debt$-$to$-$total$-$assets ratio of $32\%.$ Now suppose the new CFO convinces the president to increase the debt ratio to $48\%.$ Sales and total assets will not be affected, but interest expenses would increase. However, the CFO believes that better cost controls would be sufficient to offset the higher interest expense and thus keep net income unchanged. By how much would the change in the capital structure improve the ROE?

Question $5$ options:

$4\mathrm{.}36\%$

$4\mathrm{.}57\%$

$4\mathrm{.}80\%$

$5\mathrm{.}04\%$