Final answer:
The recognized gain or loss on the transfer in a §351 transaction is $0.
Step-by-step explanation:
In a §351 transaction, when Byron transfers property with a value of $100,000 (adjusted basis = $80,000) to Allen Corp. for stock worth $50,000, and Allen assumes the $50,000 mortgage against the property, the recognized gain or loss on the transfer is $0 (option a).
According to §351 of the Internal Revenue Code, no gain or loss is recognized if property is transferred to a corporation by one or more persons solely in exchange for stock in the same corporation, and immediately after the exchange, the person(s) transferring the property are in control of the corporation.