"If the debt is risky, there is no guarantee the principal amount will be repaid in full. Specifically, if the value of the firm falls below the principal amount, if V(T) < F, then the firm is insolvent and the debt holders can only recover the firm's value. Therefore, the payoff to debt holders is Min[V(T), F]; i.e., their payoff must be at least equal to the firm's value but cannot be greater than the principal amount. Further, Min[V(T), F] = F - Max[F - V(T), 0], which illustrates that the debt holders' payoff is economically equivalent to the debt principal minus the payoff of a put option on the firm's assets, V(T), with an exercise price equal to K. Consider the same example where F = $100. If V(T) = $120, then debt holders receive Min(100, 120) = 100 - Max(100 - 120, 0) = $100. But if V(T) = $80, then debt holders receive Min(100, 80) = 100 - Max(100 - 80, 0) = $80."
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