$(10$ points$)$ Dong Hwa and I$-$lan are identical, tax$-$free firms except that I$-$lan is more levered. These two firm will do their business for only one more year. The financial economists predict the probability of expansion this year is $80\%$ and the chance of recession is $20\%.$ These firms are expected to generate an EBIT of $2\mathrm{.}7$ million in expansion and $1\mathrm{.}1$ million in recession. Dong Hwa and I$-$lan's debt obligations are $0\mathrm{.}9$ and $1\mathrm{.}2$ million at the end of the coming year. Assuming the appropriate discount rate is $13\%$ for both equity and debt, and no bankruptcy costs.

$(1)$ What are the values of the equity and debt for these two firms?

$(2)$ President Hsu of Dong Hwa considers the valuation of his firm should be higher than I$-$lan because of lower default risk. Do you agree or not?

Answer: