It appears as if Virginia looks at the value of estate assets at the time of death for the purposes of the probate tax. Of course that is merely what the state requires.
You will also need to consider federal taxes as well. In my experience the IRS will tax the estate for the value as the sale price of the stock minus the value at the time of death. I have to point out that I have yet to see a situation quite like this one where the property is discovered this long after death so you will want to seek out a local probate attorney for guidance.
As administrator you will also need to consider any tax liability for your great aunt's last year of life. In Georgia the administrator is responsible for filing the last tax return for the deceased. If a tax return was filed an amended return may be necessary. In order to determine if this is necessary you will need to find out if the realized value of the stocks is enough to trigger additional tax liability. The stock value is usually determined by the difference between the value of the stock on the day it was purchased and the value on the date of death.
You will definitely want to contact a probate or tax attorney to assist you in this matter as you will be liable for any unpaid tax obligations as administrator.
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Generally, the income of the estate is only income after the death of the decedent, and the basis is the value as of the date of death. Speaking of which, you should also confirm that someone on her behalf filed a tax return for her last year of life -- if these assets sat unnoticed for so long, it may be that there are other issues that need to be wrapped up.
You should still contact a probate attorney or a CPA who handles estate tax returns regularly. You can ask them to prepare (or to confirm) only those specific documents, and that should keep the costs low (although with an estate this old, you may have additional issues you need them to address).
As the administrator, you have liability for mistakes that you make, so it is best to rely on professionals to take on the responsibility for these types of decisions. And it is especially best not to mess with ambiguous tax issues!
If you have questions, feel free to email me at firstname.lastname@example.org or call my office at (434) 296-7138.
I am licensed to practice law in Virginia. Please note that this answer does not constitute legal advice, and should not be relied on, as each situation is fact specific, and it is not possible to evaluate a legal problem without a comprehensive consultation and review of all the facts and court pleadings filed in the case. This answer does not create an attorney-client relationship.
My colleagues are correct in their assessment of your fact pattern. Your best bet is to contact a local probate attorney that is also familiar with the tax code for assistance.
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