The value of equity in a firm is $$6$ million and its annual volatility is $40\%.$ All the firm's debt is a five$-$year, zero$-$coupon bond with a face value of $$10$ million. The risk$-$free rate is $5\%.$

A$)$ Use Excel to calculate the value of the firm's assets and its volatility.

B$)$ Find the expected loss on debt from the firm's default in $5$ years, and the recovery rate in this case.

C$)$ Calculate the distance$-$to$-$default and interpret it$.$