$(1)$ Questions on the DuPont Identity and Cost of Capital $(15$ points$)$

Assume that Company A and Company B have the same conditions except for the different debt ratios $($total debts$/$total assets$)$ and borrowing rates. Both companies have total assets of $$20,000,000,$ earnings before interest and tax $($EBIT$)$ of $$4,000,000$ with a profit margin of $14\%,$ and a marginal tax rate of $40\%.$ Company A has a debt ratio of $50\%$ and a borrowing interest rate of $12\%$; Company $B$ has a debt ratio of $30\%$ and a borrowing interest rate of $10\%.$ Please answer the following questions based on the above information.

What is the return on equity $($ROE$)$ of Company A and Company B respectively? Which company outperforms the asset$-$use efficiency? Explain.

Suppose the required rate of return for shareholders of the two companies is the same level at $18\%,$ which company produces the lower cost of capital? Why?

If Company B expects to increase its debt ratio to $60\%,$ and its borrowing rate will also increase to $15\%,$ what is the ROE of Company B after the increase in debt ratio? Please comment on the appropriateness of using ROE vs$.$ ROA $($return on asset$)$ to measure a company's profitability.