LOKEN, Chief Judge.

Leo Polack gave 1,040,000 shares of Zip Sort, Inc. nonvoting common stock to his children. On his 1992 gift tax return, he reported $520,000 in taxable gifts, relying on appraiser Gerald Gray's opinion that the shares were worth $.50 each at the time of the gifts. The Commissioner of Internal Revenue valued the shares at $1.65 each and assessed a gift tax deficiency of $442,200. Polack paid the assessed tax and petitioned the United States Tax Court for a redetermination of the deficiency. At trial, the Commissioner did not contend that the stock was worth $1.65 per share, instead relying on appraiser Brad Cashion's valuation of $.88 per share. The Tax Court found that the evidence supported the Commissioner's valuation and redetermined the gift tax based on a value of $.88 per share. Polack v. Commissioner, 83 T.C.M. (CCH) 1811 (2002). Polack appeals, challenging the court's exclusion of Zip Sort's 1993 and 1994 financial statements and the court's valuation determination. We affirm.

For gift tax purposes, the amount of a gift is the value of the property on the date of the gift. 26 U.S.C. § 2512(a). "The value of the property is the price at which such property would change hands between a willing buyer and a willing seller, neither being under any compulsion to buy or to sell, and both having reasonable knowledge of relevant facts." 26 C.F.R. § 25.2512-1. The value of publicly traded stock is usually based on market prices. See 26 C.F.R. § 25.2512-2(b)(1). For closely held companies such as Zip Sort, stock value is best ascertained by relying on arms-length sales or transfers near the valuation date. See Estate of Fitts v. Commissioner, 237 F.2d 729, 731 (8th Cir. 1956). If as in this case there were no contemporaneous transfers of the stock, or of stock in similar companies, the Commissioner and the courts examine a variety of factors in determining the fair market value of the company and its stock on the date in question. See Rev. Rul. 59-60, 1959-1 C.B. 238-39.

Polack purchased Zip Sort in 1987. The company prints bulk mail pieces and prepares them for mailing. Prior to 1991, Zip Sort pre-sorted bulk mail according to United States Postal Service criteria to obtain a four-cent postage discount, which Zip Sort shared equally with its customers. In 1991, the company qualified for a new value-added refund program, in which USPS granted a nine-tenths of a cent discount for pre-sorted bulk mail bearing printed bar codes. Zip Sort retained all the value-added refund income (VARI) that it received in 1991, resulting in the pre-sorting division's first profitable year. In 1992, as a result of customer pressure to share VARI, Zip Sort retained $1,029,674 of its $1,147,100 in gross VARI. Thus, to determine the value of Zip Sort common stock at the time of the December 1992 gifts, it was important to estimate both the amount of future VARI and the portion of future VARI that Zip Sort would share with its customers.

Gerald Gray prepared his valuation report at Polack's request a few months after the December 1992 gifts. Based on discussions in which Polack estimated that Zip Sort would retain only 25-35% of future VARI, Gray projected that Zip Sort's net VARI would equal 3.89% of its future sales, or $350,000 in 1993. Gray also projected that Zip Sort's future capital expenditures would be $200,000 per year from 1993 through 1995 and $150,000 per year thereafter, and he excluded a $170,000 non-operating asset reflected on Zip Sort's unaudited financials because Polack advised that it was substantially offset by a $150,000 debt to Polack.

Brad Cashion prepared his appraisal of the Zip Sort stock many years later, at the Commissioner's request. Cashion's report was based in part on an April 1999 tour of Zip Sort's facilities during which he questioned Dana Rhoads, Zip Sort's president in charge of operations, to gather background information. Based on Rhoads's answers, Cashion projected that, as of December 31, 1992, the date of the gifts to be valued, Zip Sort's gross VARI would equal 18% of future sales and that Zip Sort would retain 50% of its VARI receipts, resulting in net VARI of $810,000 in 1993. Cashion projected Zip Sort's annual capital expenditures to be $100,000 in most years, and he included the $170,000 non-operating asset in estimating the company's value at the time of the gifts.

The appraisals by Gray and Cashion were in substantial agreement except for three significant items — future net VARI, future capital expenditures, and whether to include the non-operating asset. Thus, the decision whether to value the Zip Sort nonvoting common shares at $.50 or $.88 per share at the time of the gifts turned on whether Gray or Cashion made the more credible analysis of these three items. The Tax Court credited Cashion. With respect to net VARI, the court found that Cashion reasonably relied on what Rhoads told him, that Cashion's projection of 50% VARI retention was consistent with Zip Sort's retention of other USPS discounts, and that Gray's "bald projection of $350,000" was not based on credible evidence. With respect to capital expenditures, the court found Cashion's projections "reliable and probative of [Zip Sort's] value" because they were based on Rhoads's statements and Zip Sort's operational history. With respect to the non-operating asset, the court rejected Polack's uncorroborated testimony of an offsetting debt "in the face of the evidence that the asset was listed on [Zip Sort's] balance sheet at a value approximating $170,000."

On appeal, Polack first argues that the Tax Court abused its discretion when it excluded Zip Sort's 1993 and 1994 financial data and refused to permit Polack's expert Gray to use that data to refute or impeach Cashion's 1999 estimate of the common stock's fair market value in December 1992. The Tax Court sustained the Commissioner's objection, observing that "what happened in 1994 is not going to change the Court's view on what was a reasonable appraisal." Counsel for Polack then made the following offer of proof:

The 1993 and 1994 financial statements indicate, in fact, that the income numbers that Zip Sort experienced were less than the appraisal that has been submitted by [Gray], and were over $650,000 less than the appraisal that's been submitted by [Cashion], which would drastically decrease the value [of the nonvoting common stock].

In an offer of proof, a party must "express precisely the substance of the excluded evidence" to inform both the trial court and the appellate court why exclusion of the evidence was prejudicial error. Strong v. Mercantile Trust Co., N.A., 816 F.2d 429, 432 (8th Cir. 1987), cert. denied, 484 U.S. 1030, 108 S.Ct. 759, 98 L.Ed.2d 771 (1988); see FED. R. EVID. 103(a)(2), made applicable to Tax Court proceedings by 26 U.S.C. § 7453. The Tax Court's decision to exclude evidence is reviewed for abuse of discretion. See Sather v. Commissioner, 251 F.3d 1168, 1176 (8th Cir. 2001).

Whether evidence relating to subsequent events is admissible in determining the fair market value of property on an earlier date is an issue of relevance. Most subsequent events are not relevant because "the measure of the tax must be determined according to the situation as it existed on the date [in question], and not according to subsequent events." Morris v. Commissioner, 761 F.2d 1195, 1201 (6th Cir. 1985), quoting Walter v. United States, 341 F.2d 182, 185 (6th Cir. 1965). "Information that the hypothetical willing buyer could not have known is obviously irrelevant to this calculation." First Nat'l Bank of Kenosha v. United States, 763 F.2d 891, 894 (7th Cir. 1985); accord Saltzman v. Commissioner, 131 F.3d 87, 93 (2d Cir. 1997). But subsequent events that shed light on what a willing buyer would have paid on the date in question are admissible, such as "evidence of actual sales prices received for property after the date [in question], so long as the sale occurred within a reasonable time . . . and no intervening events drastically changed the value of the property." First Nat'l Bank of Kenosha, 763 F.2d at 894; see Schnorbach v. Kavanagh, 102 F.Supp. 828, 834 (W.D.Mich. 1951).

Based on Polack's offer of proof, the 1993 and 1994 unaudited financials were not relevant. In general, courts exclude "post-transaction earnings [because they] would not have been known to a prospective purchaser on the critical date." Krapf v. United States, 977 F.2d 1454, 1460 (Fed. Cir. 1992), citing Fehrs v. United States, 223 Ct.Cl. 488, 620 F.2d 255, 264 n. 6 (1980). Here, Polack asserts on appeal that the 1993 and 1994 financials were relevant because they show that Zip Sort "certainly did not achieve the percentage of value added refund that Cashion projected." But that assertion was not part of the offer of proof at trial, and from our review of the record it is inaccurate. The proffered 1993 income statement reflected gross VARI of $1,402,484 that year with $201,131 remitted to Zip Sort customers. This left net VARI of over $1,200,000 retained by Zip Sort in 1993, $390,000 more than Cashion estimated and $850,000 more than Gray estimated. Zip Sort's net income in 1993 was less than either expert projected for a different reason — they both estimated sales of $9,000,000 in 1993, whereas the actual sales were $7,378,051. In these circumstances, the Tax Court did not abuse its discretion in excluding Zip Sort's 1993 and 1994 financials and rebuttal testimony by Gray based on those financials.

Polack next argues that the Tax Court's valuation determination was clearly erroneous because Cashion's stock valuation opinion was based on "speculation, conjecture and unwarranted assumptions." The valuation of property for federal tax purposes is a question of fact we review for clear error. Estate of Ford v. Commissioner, 53 F.3d 924, 926 (8th Cir. 1995). In this case, the fact intensive valuation issue required the Tax Court to weigh the credibility of experts Gray and Cashion in order to resolve their conflicting projections of Zip Sort's future net VARI and future capital expenditures and their disagreement over whether to exclude a non-operating asset reflected on Zip Sort's 1992 financials because of an unrecorded offsetting debt to Polack. Based on our careful review of the record and the Tax Court's lengthy explanation of why it found Cashion's treatment of these disputed items more reliable, we conclude that the court's determination of fair market value for gift tax purposes was not clearly erroneous.

Finally, Polack argues that the Tax Court erred in not shifting the burden of proof after the Commissioner abandoned his initial valuation theory in favor of expert Cashion's valuation opinion. The Tax Court noted but did not decide the burden of proof issue because it concluded that a preponderance of the evidence supported the Commissioner's valuation. This was not error. "The shifting of an evidentiary burden of preponderance is of practical consequence only in the rare event of an evidentiary tie. . . ." Cigaran v. Heston, 159 F.3d 355, 357 (8th Cir. 1998).

The judgment of the Tax Court is affirmed.