The basis of inherited property is stepped-up to its value on the date of death of the owner, or a slightly later date if chosen by the executor of a taxable estate. In other words, tax on any appreciation during his or her lifetime is forgiven. The heir uses the higher basis to figure his or her gain when the property is ultimately sold. If the value of property declined while it was owned by the decedent, the basis is stepped-down to date of death value.