A few jurisdictions that generally have low taxes anyway, such as Hong Kong, abolished the estate tax without seeking any compensating capital gains tax or income tax.
The majority adopt an alternative in which there is no step-up in the cost basis of the decedent's assets at death. Instead of receiving a new cost basis equal to current fair market value (as under a step-up basis), beneficiaries will inherit the cost basis and pay capital gains tax when they sell the assets.
Under this option, capital gains tax is assessed on the increase in market value over the cost basis of the assets before they pass to the heirs. This approach has been proposed by both President Obama and President Trump for implementation in the U.S.
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