Final answer:
Lucinda's recognized gain from the like-kind exchange of real estate is $0. She exchanged property and cash for a lesser valued property, which would imply a loss, but losses are not recognized in a like-kind exchange. Thus, there is no recognized gain and her basis in the new property is $40,000.
Step-by-step explanation:
The student is asking about the consequences of a like-kind exchange for tax purposes under the United States tax code. When Lucinda exchanges real estate used in her business for like-kind real estate owned by Brandon, and the properties are not of equal value, the difference is considered boot. In this example, Lucinda has a basis of $50,000 in her real estate and provides Brandon with $10,000 cash plus her real estate, in exchange for Brandon's real estate worth $46,000.
Since Lucinda received property of a lesser value and she also paid cash, the next step is to calculate her recognized gain. No loss is recognized in a like-kind exchange. The formula for calculating recognized gain when boot is received is the lesser of the gain realized or the boot received. The gain realized is the fair market value of the property received minus the adjusted basis of the property given up. Here, Lucinda's gain realized is $46,000 (fair market value of Brandon's property) minus her own basis of $50,000, which would imply a loss. However, losses are not recognized in a like-kind exchange. Therefore, since there's no realized gain, there's no recognized gain, and the boot of $10,000 doesn't trigger any gain recognition.
Lucinda's recognized gain in this transaction is $0 because the potential loss on the exchange is not recognized. Lucinda's basis in the new property would be the same as the basis in her old property ($50,000) minus the cash given ($10,000) plus any gain recognized (which is $0 in this case), resulting in a basis of $40,000 for the property acquired from Brandon.