R $12-1$ A company currently has $$100$ million in assets. In one year it may have either $$120$ million or $$80$ million in assets, with equal probability. The company has $$90$ million in debt $($at the end of the year$).$ The firm's cost of debt capital is $5\%$ and the cost of equity capital is $15\%.$ If the company goes bankrupt, bankruptcy costs are $$20$ million. Ignore the effect of taxes.

$($a$)$ Calculate the value of the company.

$($b$)$ Determine the value of the company if it had no debt.