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 thedebt.
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:
1. The equity holders can sell the assets of the firm to the debt holders at a price equal to the face value of the debt, ie a put. (ie they can extinguish their liability to the debt holders in full by handing them the assets of the firm, effectively selling them the assets at the value of the debt)
2. The equity holders have a long position in a call option where they can keep the assets of the firm by paying a price equal to the face value of the debt (ie, they can pay off the debt holders and keep the assets)
For this question, perspective 1 applies but you should be aware of the second one too as a question may reference that view point.)
