Acort Industries owns assets that will have a$($n$)70\%$ probability of having a market value of $$50$ million in one year. There is a $30\%$ chance that the assets will be worth only $$20$ million. The current risk$-$free rate is $9\%,$ and Acort's assets have a cost of capital of $18\%.$

a$.$ If Acort is unlevered, what is the current market value of its equity?

b$.$ Suppose instead that Acort has debt with a face value of $$19$ million due in one year. According to $MM,$ what is the value of Acort's equity in this case?

c$.$ What is the expected return of Acort's equity without leverage? What is the expected return of Acort's equity with leverage?

d$.$ What is the lowest possible realized return of Acort's equity with and without leverage?

a$.$ If Acort is unlevered, what is the current market value of its equity?

The current market value of the unlevered equity is $ $q,$ million. $($Round to three decimal places.$)$

b$.$ Suppose instead that Acort has debt with a face value of $$19$ million due in one year. According to MM$,$ what is the value of Acort's equity in this case?

According to MM$,$ the current market value of the levered equity is $ million. $($Round to three decimal places.$)$

c$.$ What is the expected return of Acort's equity without leverage? What is the expected return of Acort's equity with leverage?

The expected return of Acort's equity without leverage is

$\%.($Round to two decimal places.$)$

The expected return of Acort's equity with leverage is

$\%.($Round to two decimal places.$)$

d$.$ What is the lowest possible realized return of Acort's equity with and without leverage?

The lowest possible realized return of Acort's equity without leverage will be

$\%.($Round to two decimal places.$)$

The lowest possible realized return of Acort's equity with leverage will be $\%.($Round to two decimal places.$)$