The cost basis of in inherited mutual fund is its value at closing on the date of the decedent's passing, unless the executor has chosen an alternate valuation method. See "Alternate Valuation" on page 11 of this IRS Publication for a detailed explanation:
https://www.irs.gov/pub/irs-pdf/i706.pdf
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
