Carol Feely is a junior credit analyst at one of the major international credit rating agencies. She understands that in the standard structural models, equity is interpreted as a call option on the asset value of the company. However, she is not comfortable with the assumption that it is the debtholders who implicitly own the assets and write a call option on them. She claims that the model should start with the understanding that the shareholders own the net value of the company, which is A(T ) − K, and that their limited liability is essentially the value of a long position in a put option at a strike price of K. Furthermore, the debtholders own a “risk-free” bond having a value of K at time T and a short position in the put that is held by the shareholders.

Demonstrate that Ms. Feely’s “embedded put option” interpretation provides the same values for debt and equity at time T as does the more customary call option structural model.