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IN order to use stepped up basis for the property - the property should be considered as inherited - means - included into the estate.
In this case - the stepped up basis is the FMV at time of death. That basis is adjusted by improvements after the death.
If the estate keep the property and not distribute the property to beneficiaries - that is OK.The estate may pay operating expenses such as utilities, etc - that is not an issue - however if the property is used for personal purposes - these operating expenses may not be deducted by the estate.
The estate will be able to deduct real estate taxes and mortgage interest.
Let me know if you need any help with reporting.