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I understand that when a person dies and leaves an asset as a bequest, then a new cost basis is established for the asset. This can possibly be advantageous for taxes, but I don't see exactly how.

For example, let's say that a man has a 1924 Rolls Royce Silver Ghost which might sell at auction for $750,000 or something like that. However, he bought the Rolls Royce for $400 in 1924 has its cost basis is negligible which means if he sells the car, he will pay capital gains on the whole amount.

Now, let's imagine that the man dies and leaves the car to his son. The car is appraised as part of the estate at $600,000. This creates a new cost basis. So, if the son then sells the car for $750,000 he pays capital gains only the difference ( $150,000 ).

However, what about taxes on the $600,000? When the car goes from $400 to $600,000 in probate, will the estate owe capital gains on the car somehow, or does it get the new basis "for free"?

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When the car goes from $400 to $600,000 in probate, will the estate owe capital gains on the car somehow, or does it get the new basis "for free"?

No there are no taxes due on this part of the gain (assuming the overall estate is small enough to be exempt from estate taxes) - that's why the "step-up" in basis is so powerful.

It's also why "giving" assets before death can be disastrous from a tax standpoint. If the dad had instead just signed over the title to the son, then the son would owe capital gains tax on $759,600, not $150,000.

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