If the "prize" was from gambling, yes, the losses would be deductible on Schedule A.
Otherwise, no.
But the fact the business that issued the 1099 calls it a "prize" makes it very questionable if it was gambling.
I had a client who spent hundreds in postage every year entering sweepstakes. He would occasionally win a toaster. Oh, maybe that was for opening a bank account. I once had a client who had 11 IRA's and 11 toasters. But that's not the question. We deducted the postage as a miscellaneous deduction. Then they limited it with the 2% haircut. Then they suspended it altogether.
But what you have is not gambling, or it would have been reported on a W-2G.
I have made an offset to the "suggested retail price" of a prize won. e.g. Refrigerator with a MFSRP of $1,000 that I can produce an ad showing it on sale at $800, then I report the $1,000 with another "other income" of "adjustment to 1099-MISC" actual value of a -$200.
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