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Just want to add that, in the U.S., correct me if I am wrong, the 'cost basis' of the inherited stock or property is determined at decedent's the date of death....

Calculating the Basis of Inherited Property

The general rule, which is usually favorable to taxpayers, is that the recipient’s basis for inherited property is stepped up (or stepped down) from the decedent’s cost to the asset’s fair market value at the decedent’s date of death. The advantage of a step-up in basis is demonstrated by the example of a decedent who owns shares of stock for $500 and held on to the investment until his death, at which time the stock had appreciated to a value of one million dollars.  The person who receives the stock upon the decedent’s death will take a stepped-up basis of one million dollars, the stock’s fair market value at the decedent’s death.  Therefore, upon the recipient’s subsequent sale of the stock, the appreciation in value between $500 and one million dollars will NOT be recognized for income tax purposes, and the recipient of the stock will be taxed only on the gain represented by any appreciation of the stock beyond one million dollars.