Under the Merton model framework for structural credit risk, a firm's equity can be viewed as a European call option on the firm's assets with a strike price equal to the face value of the debt. The debt is viewed as a risk-free bond minus a European put option on the firm's assets.

At maturity $T$, the value of equity ($E_T$) and debt ($D_T$) are strictly determined by the value of the firm's assets ($V_T$) and the principal face value of the debt ($F$):

• Equity Payoff: $E_T = \max(V_T - F, 0)$
• Debt Payoff: $D_T = \min(V_T, F)$

Given the firm's asset value at maturity ($V_T$) is $80 million and the face value of the debt ($F$) is $100 million:

• Value of Equity = \max(80 - 100, 0) = \`0`$
• Value of Debt = \min(80, 100) = \`80` \text{ million}$

Because the firm's value at maturity ($80 million) is less than the face value of the debt ($100 million), the firm defaults. By the rules of absolute priority, debt holders claim the entire remaining value of the firm's assets ($80 million), and the equity holders are wiped out and receive nothing.