If an estate is valued at $4.5 million, which form does not need to be filed?

In the context of estates and taxes, Form 706 is the United States Estate (and Generation-Skipping Transfer) Tax Return, which is required when the gross estate exceeds the federal estate tax exemption limit. As of 2023, this exemption is set at $12.92 million. Since the estate in the question is valued at $4.5 million, it is below the exemption threshold, meaning that the estate is not subject to federal estate taxes and therefore does not require Form 706 to be filed.

Form 1040, the individual income tax return, may still need to be filed depending on the income of the deceased's estate during the year of death. Similarly, Form 1041, the U.S. Income Tax Return for Estates and Trusts, would be required for reporting the estate's income if the estate generates taxable income. However, since the estate's value does not trigger the need for the estate tax return, this makes Form 706 the correct response as the form that does not need to be filed in this specific scenario.