WIENER, Circuit Judge: Petitioners-Appellants Margaret Elise Joseph and Leslie Keith Sasser (“Petition *445 ers”), as Independent Executors of the Estate of their deceased father, James A. Elkins, Jr. (“Decedent”), petitioned the United States Tax Court (“Tax Court”) to review and eventually eliminate the federal estate tax deficiency assessed against the Estate by Respondent-Appellee, the Commissioner of Internal Revenue (“the Commissioner”). That deficiency resulted solely from the Commissioner’s disallowance of the “fractional-ownership discount” applied by the Estate in determining the taxable values of Decedent’s pro rata shares of the jointly stipulated fair market values (“FMV”) of 64 original works of modern and contemporary art in which the Decedent owned only fractional interests at his death. In the Tax Court, the Commissioner steadfastly maintained that absolutely no fractional-ownership discount was allowable. This presumably accounts for his failure to adduce any affirmative evidence—either factual or expert opinion— as to the quantum of such discounts in the event they were found applicable by the court. The Tax Court rejected the Commissioner’s zero-discount position, but also rejected the quantums of the various fractional-ownership discounts adduced by the Estate through the reports, exhibits, and testimony of its three expert witnesses— the only substantive evidence of discount quantum presented to the court. 1 Instead, the Tax Court concluded that a “nominal” fractional-ownership discount of 10 percent should apply across the board to Decedent’s ratable share of the stipulated FMV of each of the works of art; this despite the absence of any record evidence whatsoever on which to base the quantum of its self-labeled nominal discount. We agree in large part with the Tax Court’s underlying analysis and discrete factual determinations, including its rejection of the Commissioner’s zero-discount position (which holding we affirm). We disagree, however, with the ultimate step in the court’s analysis that led it not only to reject the quantums of the Estate’s proffered fractional-ownership discounts but also to adopt and apply one of its own without any supporting evidence. We therefore affirm in part, reverse in part, and render judgment in favor of Petitioners, holding that the taxable values of Decedent’s fractional interests in the works of art are the net amounts reflected for each on Exhibit B of the Tax Court’s opinion. This, in turn, produces an aggregate refund owed to the Estate of $14,359,508.21, plus statutory interest. 2 I. FACTS AND PROCEEDINGS A. Issue on Appeal Despite the size and complexity of Decedent’s estate and the millions of dollars of federal estate tax that it returned and paid, the single question presented in this appeal is narrow, straightforward, and easily posed: *446 Given the parties’ stipulation of the FMV of each of the works of art in which Decedent owned fractional interests at his death, is the Estate taxable on Decedent’s undiscounted pro rata share of those FMVs, as the Commissioner contended on audit and throughout the Tax Court proceedings, or is it taxable only on those values reduced by fractional-ownership discounts of either (1) a uniform 10 percent each, as …
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