If F be the face value of a firm’s debt, V the value of its assets and E the market value of equity, then according to the option pricing approach a default on debt occurs when:

If F be the face value of a firm’s debt, V the value of its assets and E the market value of equity, then according to the option pricing approach a default on debt occurs when:
A . F > V
B . V < E
C . F < V
D . F – E < V

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Answer: A

Explanation:

According to the option pricing approach developed by Merton, the shareholders of a firm have a put on the assets of the firm where the strike price is equal to the face value of the firm’s debt. This is just a more complicated way of saying that the debt holders are entitled to all the assets of the firm if these assets are insufficient to pay off the debts, and because of limited liability of the shareholders of a corporation this part payment will fully extinguish the debt.

A firm will default on its debt if the value of the assets falls below the face value of the debt.

Therefore Choice ‘a’ is the correct answer. All other choices are incorrect.

(There are two ways to consider this sort of optionality, and I have mentioned only one for this question: