Welcome! My goal is to do my very best to understand your situation and to provide a full and complete answer for you.
Good morning. North Carolina is not a community property state
. Thus, when your father died, his 1/2 of the property
received a step up in basis to its fair market value; his wife's 1/2 did not so her basis in her 1/2 is the purchase price (plus any improvements). Then, when the wife transfers her interest
to you by gift, her basis carries over to you. So, when you sell it, presuming you sell it at the fair market value as of the date of death, you will have no gain on 1/2 of the sale; and you will have long term capital
gain on the 1/2 you received as a gift...that gain being $125,000 (less 1/2 of the closing costs) in excess of 1/2 of the purchase price (plus 1/2 the cost of any improvements).
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