Court Opinion

ID: 4334773
Source: CourtListenerOpinion
Date Created: 2018-11-14 01:52:28.277964+00
Date Added: 2024-06-11T14:20:28.206521
License: Public Domain

ESTATE OF EMANUEL TROMPETER, DECEASED, ROBIN CAROL TROMPETER GONZALEZ AND JANET ILENE TROMPETER POLACHEK, CO-EXECUTORS, Petitioner v. COMMISSIONER OF INTERNAL REVENUE, Respondent *Estate of Trompeter v. Comm'rNo. 11170-95 United States Tax CourtT.C. Memo 2004-27; 2004 Tax Ct. Memo LEXIS 31; 87 T.C.M. 851; February 4, 2004, Decided Trompeter v. Comm'r (Estate of Emanuel Trompeter), 279 F.3d 767">279 F.3d 767, 2002 U.S. App. LEXIS 1252">2002 U.S. App. LEXIS 1252 (9th Cir., 2002)Findings of fact and conclusions of law, on remand from U.S. Court of Appeals for Ninth Circuit.                   Jan. 15,     Dec. 31,   Dec. 31,Class of Debt            1991       1991     1992Senior subordinated notes      $ 347,765    $ 744,820   $ 1,194,431Subordinated notes           -0-       309,241    1,071,628Series B subordinated debentures   291,132     488,889     711,294Unsecured notes            48,645      82,936     129,198                  ________     ________   __________                  687,542    1,625,886    3,106,551 Laro, David LAROSUPPLEMENTAL MEMORANDUM OPINION2004 Tax Ct. Memo LEXIS 31">*32 LARO, Judge: This case is before the Court upon remand from the Court of Appeals for the Ninth Circuit. We issued our initial report in this case on January 27, 1998, and filed that report as T.C. Memo. 1998-35 (Trompeter I). In Trompeter I, we set forth findings of fact as to the substantive issues arising from the notice of deficiency, and we set forth our Memorandum Opinion with respect to those issues. Subsequently, on July 22, 1998, we issued a Supplemental Opinion in this case and filed that Supplemental Opinion as 111 T.C. 57">111 T.C. 57 (Trompeter II). Our Supplemental Opinion in Trompeter II decided the parties' disagreement over the mechanics of their computations under Rule 155.1 On March 18, 1999, we entered our decision in this case.Through an opinion dated January 30, 2002, and reported at 2004 Tax Ct. Memo LEXIS 31">*33 279 F.3d 767">279 F.3d 767, the Court of Appeals for the Ninth Circuit vacated our decision and remanded the case to us to "articulate sufficiently the basis for * * * [our] ruling on omitted assets and * * * [our] rationale with respect to the valuation of certain stock". 279 F.3d 767"> Id. at 769. Specifically, the court directed us to clarify: (1) The manner in which we arrived at a $ 4.5 million figure for omitted assets, including a description of the assets and the related fair market values which were included within that figure, (2) our reasoning and analysis behind the use of a 4-percent discount rate in valuing the series A exchangeable preferred stock (series A preferred stock) of Sterling Holding Co. (Sterling), and (3) the "well accepted present value formulae" referenced and applied in our report. 279 F.3d 767"> Id. at 771-773. The court also stated that, upon remand and following the requisite clarification, we shall consider whether it is appropriate to revisit our conclusions as to fraud. 279 F.3d 767"> Id. at 773-774. The court noted that "In directing this approach, we do not pass judgment on the Tax Court's multiple, careful, and well-documented findings in this2004 Tax Ct. Memo LEXIS 31">*34  arena, nor do we suggest that a remand will necessarily result in a different outcome with respect to fraud." 279 F.3d 767"> Id. at 774.We divide this Supplemental Memorandum Opinion into the following three primary sections: (1) "Omitted Assets", (2) "Present Value Formulae and Discount Rate of Four Percent", and (3) "Determination of Fraud in Trompeter I". We made and set forth in Trompeter I extensive findings of fact.  For purposes of this Supplemental Memorandum Opinion, we repeat those findings and find additional facts only to the extent necessary. For purposes of convenience and clarity, we include those findings in our analysis. 2 As we did in Trompeter I, we refer to Emanuel Trompeter as the decedent, we refer to the decedent's estate as the estate, and we refer collectively to Robin Carol Trompeter Gonzalez (Gonzalez) and Janet Ilene Trompeter Polachek (Polachek) as the coexecutors. The parties routinely refer to the weight of gold and gemstones as karat (kt.) and carat (ct.), respectively, and points. We note that one point equals 1/10 of a karat (or carat) and simply refer to the weight of gold and gemstones as karat (or kt.) and carat (or ct.), respectively.2004 Tax Ct. Memo LEXIS 31">*35  I. Omitted AssetsWe determined in Trompeter I that the coexecutors failed to include $ 4.5 million of assets in the estate's taxable estate (taxable estate). The Court of Appeals for the Ninth Circuit has directed us "to provide sufficiently detailed findings regarding the assets (including their valuation)" underlying the $ 4.5 million.The decedent died on March 18, 1992. On the Federal estate tax return of his estate, the coexecutors valued the gross estate at $ 26,422,781 and reported that the taxable estate equaled $ 12,002,201. Respondent determined in the notice of deficiency that the coexecutors underreported the taxable estate by $ 22,833,693. As part of that determination, respondent determined that the taxable estate had omitted $ 14 million of assets.Respondent's determination of the unreported assets was based mainly on a creditor claim filed against the estate by Joe Pasko (Pasko), the son of a former female acquaintance of the decedent, and a document (finder's fee document) dated October 17, 1990. Pasko's claim alleged that he was entitled to a $ 1.4 million commission because, he alleged, the decedent had retained him to sell assets worth at least $ 14 million2004 Tax Ct. Memo LEXIS 31">*36  in return for a 10-percent commission. These assets, Pasko alleged, included the decedent's diamonds, jade and ivory collections, ancient Chinese artifacts, and handmade unique wool rug. 3 The finder's fee document, signed in the name of the decedent, provided that Pasko had the authority to sell for $ 20 million the decedent's "ancient ornamental Chinese artifacts for a period from Oct. 20 to Nov. 20, 1990 with no extension allowed. This lot also includes a hand made [sic] unique wool 4' x 8' rug of Moslem theme." The finder's fee document provided that Pasko would receive a commission equal to 10 percent of the sales price and that "Any and all commissions to be paid by the buyer as finders [sic] fee". 4 Although diamonds were not specifically mentioned in the finder's fee agreement, Pasko understood this agreement to include the decedent's diamonds.2004 Tax Ct. Memo LEXIS 31">*37  In addition to Pasko's claim and the finder's fee document, respondent based his determination of unreported assets on information furnished by certain individuals and on the value of assets seized from safe deposit boxes in the name of the decedent's trust (Trust) during the audit of the estate's Federal estate tax return. Respondent conversed primarily with four of the decedent's intimate friends and the decedent's two main suppliers of many of the assets collected by him. The first friend, Vivian Ballard Wong (Wong), had a personal relationship with the decedent from February 1987 through June 1991. Wong described to respondent a collection of jewels in the possession of the decedent in 1991. The other friends, Ira and Larry Goldberg and Robert Hesselgesser (Hesselgesser), generally relayed to respondent facts establishing that they had personal knowledge of the decedent's gemstone and jewelry collections, and they described to respondent certain gemstones and items of jewelry which they had seen in the decedent's possession near the time of his death. One of the decedent's suppliers, Dr. Nathan Mamiye (Mamiye) of New York, New York, confirmed selling loose gemstones, jewelry,2004 Tax Ct. Memo LEXIS 31">*38  jade, and ivory to the decedent and provided respondent with receipts reflecting a large dollar amount of diamonds which he (Mamiye) had recently sold to the decedent. The other supplier, Lloyds Fine Jewels (Lloyds) of New York, New York, provided respondent with receipts reflecting more than $ 1 million of sales which it had recently made to the decedent, and it informed respondent that those receipts did not necessarily reflect all of the sales which it had made to the decedent. Respondent's determination of the estate's unreported assets also was supported by respondent's examination of canceled checks of the decedent payable primarily to Mamiye and Lloyds, respondent's comparison of the items on the receipts furnished by Mamiye and Lloyds with the assets described by the individuals with whom respondent conversed, and respondent's seizure from the Trust's safe deposit box at Union Bank (safe deposit box) of unreported assets consisting of various bullion coins, 41 gold coins, 14 loose gemstones, and 11 items of jewelry.Following our trial of this case and our detailed review of the record, we agreed with respondent that the estate had failed to report a significant amount of2004 Tax Ct. Memo LEXIS 31">*39  assets. The estate conceded that this amount was a little over $ 1 million. We were persuaded that the amount was much greater. We also were persuaded, however, that this amount was less than the $ 14 million determined by respondent. We proceeded to make an approximation of the fair market value of assets omitted from the taxable estate, recognizing that valuation is not an exact science and that the task before us was difficult in that the coexecutors had concealed information and assets from their accountants, respondent, and this Court.The assets which we find were omitted from the taxable estate generally fall within three categories. First, there is approximately $ 1 million of assets which the estate concedes were unreported. Nineteen of these assets were seized by respondent from the safe deposit box and were sold at an auction held by Christie's, Inc. (Christie's). 5 Second, there are six other assets which respondent seized from the safe deposit box but which Christie's did not sell at auction. The parties agree that these six assets are includable in the taxable estate but disagree on their applicable fair market values. Third, there are still other assets as to which2004 Tax Ct. Memo LEXIS 31">*40  the parties dispute both fair market value and inclusion in the taxable estate. The coexecutors admit that they removed from the decedent's home after his death some of the assets included within this third category, but they deny the existence of most of the other assets. Respondent has never recovered any of these assets, but he has established to our satisfaction that they exist and are includable in the taxable estate. Respondent has done so through the introduction of credible testimony and documentary evidence that includes receipts and checks from purchases made by the decedent. We infer from this evidence that the decedent paid for and owned the assets listed in the receipts, see, e.g.,  Estate of Hodgdon v. Commissioner, 11 T.C.M. 898">11 T.C.M. 898, 1952 T.C.M. (P-H) par. 52,259 (1952), and that those assets, not having been shown to have been relinquished by the decedent, were includable in the taxable estate, see, e.g.,  Estate of Bograd v. Commissioner, T.C. Memo. 1988-34, affd. 887 F.2d 1084">887 F.2d 1084 (5th Cir. 1989). We also infer from this evidence that the taxable estate includes other assets which were not listed in the receipts but2004 Tax Ct. Memo LEXIS 31">*41  which the decedent possessed and controlled near the time of his death and were not shown by the estate to have been relinquished by him. As we stated in Trompeter I, the assets in this third category "consist mainly of gems, jewelry, furniture, and a music collection."  Estate of Trompeter v. Commissioner, T.C. Memo. 1998-35. As detailed below, these assets also include cash at home, 31 coins, rugs, jade, and ivory.We set forth below by these three categories the assets which we find were omitted from the taxable estate and the fair market values which we find as of the applicable valuation date. 6These fair market values represent our findings as to "the price at which the property would change hands between a [hypothetical] willing buyer and a [hypothetical] willing seller, neither being under any compulsion to buy or to sell and both having reasonable knowledge of relevant facts." Sec. 20.2031-1(b)2004 Tax Ct. Memo LEXIS 31">*42  , Estate Tax Regs.; see also  Propstra v. United States, 680 F.2d 1248">680 F.2d 1248, 680 F.2d 1248">1251-1252 (9th Cir. 1982). See generally  Bank One Corp. v. Commissioner, 120 T.C. 174">120 T.C. 174, 120 T.C. 174">302-306 (2003), for a detailed discussion of the criteria underlying a determination of fair market value. In deciding these fair market values, we note that:  The fair market value of a particular item of property   includible in the decedent's2004 Tax Ct. Memo LEXIS 31">*43  gross estate is not to be   determined by a forced sale price. Nor is the fair market value   of an item of property to be determined by the sale price of the   item in a market other than that in which such item is most   commonly sold to the public, taking into account the location of   the item wherever appropriate. Thus, in the case of an item of   property includible in the decedent's gross estate, which is   generally obtained by the public in the retail market, the fair   market value of such an item of property is the price at which   the item or a comparable item would be sold at retail. For   example, the fair market value of an automobile (an article   generally obtained by the public in the retail market)   includible in the decedent's gross estate is the price for which   an automobile of the same or approximately the same description,   make, model, age, condition, etc., could be purchased by a   member of the general public and not the price for which the   particular automobile of the decedent would be purchased by a   dealer in used automobiles. * * * The value is2004 Tax Ct. Memo LEXIS 31">*44  generally to be   determined by ascertaining as a basis the fair market value as   of the applicable valuation date of each unit of property. * * *  [Sec. 20.2031-1(b), Estate Tax Regs.]Respondent retained an expert, Charles I. Carmona (Carmona), Graduate Gemologist in Residence, Accredited Senior Appraiser, who, on direct examination, testified through his written report, see Rule 143(f)(1), that he had ascertained the applicable fair market values of 25 of the seized assets (25 seized assets) and that those values were as stated in that report. (We attach hereto as appendix A Carmona's description of each of the 25 seized assets, its appraised value, and, in the case of 19 of the assets sold by Christie's at auction, its auction price.) We considered Carmona to be helpful to our valuations of some of the disputed assets, and we relied on his opinion, which was credible and without contradiction.Carmona examined and researched each of the 25 seized assets and opined that the fair market value of those assets for Federal estate tax purposes was the "average price that each item in its current (used) condition might resell to the public in its most common retail2004 Tax Ct. Memo LEXIS 31">*45  outlets in the Estate's local area". 7 He opined that the proper resale prices for jewelry were the prices obtained at a retail jewelry store and that the proper resale prices for loose gemstones were their wholesale prices increased by the commissions charged by brokers on their sales of gemstones to the public. He opined that the public usually buys jewelry at retail from jewelry stores that sell estate jewelry, that the majority of buyers at public auctions are dealers, that the lowest level of sales prices for jewelry is found at auction, and that jewelry usually passes from the dealer to the public through retail jewelers with a dealer-to-retail-jeweler markup of 25 to 50 percent over cost and a retail-jeweler-to-public markup of 50 to 100+ percent over cost. He opined that the wholesale prices paid for gemstones by brokers was best ascertained from personal experience and comparable sales and offers to sell. He opined that a broker's commission on a sale of loose gemstones to the public was typically 15 to 25 percent of the wholesale price.2004 Tax Ct. Memo LEXIS 31">*46  The assets which we find were omitted from the taxable estate and the fair market values which we find for these assets are as follows: 8Assets Stipulated as to Existenceand Fair Market ValueSt. Gauden and other bullion coinsseized by respondent from the safedeposit box $ 50,00041 gold coins (different than theSt. Gauden and bullion coins justlisted) seized by respondent fromthe safe deposit box104,500 The decedent's gun collection2,08519 assets seized by resondent andsold at auction:1. Lady's 18-kt. yellow gold,sapphire, and channel-set diamondring (2a)$ 1,8002. Lady's 18-kt, yellow gold, ruby,and channel-set diamond ring (2b)1,8003. Lady's 14-kt. yellow gold and diamond ring (2c)20,0004. 14-kt, yellow gold and diamondtie tack (2f)4,5005. Lady's 18-kt, yellow gold and diamond necklace (2h)32,0006. Lady's 18-kt yellow gold, emerald and diamond necklace (2i)19,0007. One loose round-brilliant-cut1.9-ct. diamond (3c)9,6008. One loose round-brilliant-cut2.01-ct. diamond (3b)7,5009. One loose emerald-cut 3.35-ct.diamond (3n)25,00010. One loose heart-shape 4.03-ct.diamond (3g)7,50011. One loose round-brilliant-cut4.32-ct. diamond (3m)105,00012. One loose octagon-ct. 5.01-ct.diamond (3d)35,00013. One loose round-brilliant-cut6.62-ct. diamond (3f)20,00014. One loose round-brilliant-cut6.65-ct. diamond (3j)24,00015. One loose emerald-cut 7.57-ct.diamond (3e)30,00016. One loose round-brilliant-cut7.74-ct. diamond (3k)27,00017. One loose square-emerald-cut11.13-ct. diamoand (3i)44,00018. One loose octagon-shape 18.28-ct. diamond (3l)210,00019. One loose octagon-cut 40.02-ct.diamond (3a)22,000843,7001,000,285Six Seized Assets Disputed as to Fair Marke Value1. Lady's 18-kt. yellow gold,sapphire, and diamond necklace (2d)4,4002. Lady's 18-kt. yellow fold, ruby,and diamond necklace (2e)5,8003. Cultured pearl necklace with14-kt. white gold clasp (2g)4004. Lady's 18-kt. yellow gold, emerald, and diamondnecklace (2j)19,0005. Lady's 18-kt. yellow and whitegold, opal, and diamond pin/pendantcombination with treated opalnecklace (2k)7,6006. One loose cushion-shape-natural18.2-ct. sapphire (3h)9,10046,300Assets Disputed as to Fair MarketValue and Inclusion in the Taxable EstateMusic collection50,000Sofa table4,4161 Three Baker's tables 6,624"Thousand dollar" watch1,000Cash at home50,00031 coins425,847Rugs69,530Jade collection247,500Ivory collection1,500,000Loose gemstones:Emerald-cut 2.08-ct. diamond15,510Emerald-cut 2.28-ct. diamond17,010Round-cut 3.04-ct. diamond47,436Masterpiece 4.39-ct diamond106,680Heart-shaped-baguette five-ct.diamond75,000Round-cut 5.22-ct. diamond78,150Round-cut 7.75-ct. diamond35,800Eight-ct. emerald16,150Two other emeralds32,300Two opals32,30018-ct. ruby7,50018-ct. sapphire6,000Genuine masterpiece 18.02-ct.sapphire9,100Bracelets:18-kt. gold bracelet with 9.5-ct.diamonds108,000Six other diamond tennisbraclets187,140Ruby bracelet5,800Sapphire bracelet4,400Necklaces:Diamond necklace13,33018-kt. gold necklace w/ 26.73-ct.diamond74,00030,02-ct. graduated-diamond necklace66,404Ruby necklace13,300Sapphire necklace13,300Turquoise necklace21,250Rings:Man's diamond pinkie ring4,500man's three to four-ct.diamond ring15,750Ruby ring6,665Sapphire ring6,665Diamond stud earrings9,000Three to four-ct. diamond tie tack15,750Pins:Ruby pin5,800Sapphire pin4,400Pendants:18-kt. gold, ruby, and diamondpendant18,400Sapphire pendant with rounddiamonds 15,000Furniture26,0513,471,2182 4,517,803 2004 Tax Ct. Memo LEXIS 31">*47 We now discuss the specifics of our decision as to the existence and fair market value of the disputed assets.   A. Seized Assets Disputed as to Fair Market ValueBefore Christie's auctioned the 25 seized assets, it had assigned to each of these assets a lower and upper estimated value. (We attach hereto as appendix B a list of each item's lower and upper estimated values, agreed reserve (i.e., the minimum price at which an asset could be sold by Christie's at auction), auction price (in the case of the 19 items sold at auction), high bid (in the case of the six items not sold at auction), and Carmona's appraised value.9) These lower and upper estimated values are estimates by Christie's of the likely amounts that bidders would bid at an auction for the assets. These estimated values do not reflect2004 Tax Ct. Memo LEXIS 31">*48  the requirement of Christie's that buyers also pay to Christie's on each sale a commission equal to 15 percent of the first $ 50,000 of the purchase price and 10 percent of any excess. Nor do the estimates (or the ultimate sales prices) include sales tax that is payable on the sales.The 25 seized assets consist of 11 items of jewelry and 14 loose gemstones. Of those assets, six items of jewelry and 13 loose gemstones were sold at the auction held by Christie's. The remaining six assets (i.e., five items of jewelry and one loose gemstone) did not sell at the auction.The six items of jewelry sold at auction for a total auction price (exclusive of buyer's commissions) of $ 79,100. Christie's estimated that these six items had a total lower estimated value of $ 70,000 and a total upper estimated value of $ 107,500. 2004 Tax Ct. Memo LEXIS 31">*49 Carmona ascertained that the fair market value of these six items totaled $ 146,200. Carmona's total fair market value for these six items is 84.83 percent (($ 146,200 - $ 79,100)/$ 79,100) greater than the total of their auction prices.The 13 loose gemstones sold at auction for a total auction price (exclusive of buyer's commissions) of $ 764,600. Christie's estimated that these 13 gemstones had a total lower estimated value of $ 488,000 and a total upper estimated value of $ 656,000. Carmona ascertained that the fair market value of these 13 gemstones totaled $ 1,100,000. Carmona's total fair market value for these 13 gemstones is 43.87 percent (($ 1,100,000 - $ 764,600)/$ 764,600) greater than the total of their auction prices.Christie's estimated that the five items of jewelry which did not sell at auction had a total lower estimated value of $ 28,000 and a total upper estimated value of $ 39,500. Carmona ascertained that the fair market value of these five items of jewelry totaled $ 37,200. Christie's estimated that the one loose gemstone which did not sell at auction had a lower estimated value of $ 14,000 and an upper estimated value of $ 16,000. Carmona ascertained that2004 Tax Ct. Memo LEXIS 31">*50  the fair market value of this single gemstone was $ 9,100.We find that, as of the applicable valuation date, the fair market value of each of the six assets which did not sell at auction equaled its fair market value as ascertained by Carmona. In other words, we find that the fair market values of the five items of jewelry which did not sell at auction totaled $ 37,200 and that the fair market value of the single gemstone that did not sell at auction was $ 9,100. We find that the individual values of these six assets are as follows:JewelryLady's 18-ky. yellow gold, sapphire, and diamond necklace$ 4,400lady's 18-kt. yellow gold, ruby, and diamond necklace5,800Cultured pearl necklace with 14-kt. white gold clasp400lady's 18-kt. yellow gold, emerald,and diamond necklace19,000Lady's 18-kt. yellow and whitegold, opal, and diamond pin/pendantcombination with treated opalnecklace7,600GemstoneOne loose cushion-shape-natural18.2-ct. sapphire9,10046,300We consider Carmona to be most helpful to our valuation of each of these six assets. Carmona testified as to jewelry in general that the typical buyer2004 Tax Ct. Memo LEXIS 31">*51  of jewelry at auction is a dealer and that jewelry usually passes from a dealer to the public through retail jewelers with a dealer-to-retail-jeweler markup of 25 to 50 percent over cost and a retail-jeweler-to-public markup of 50 to 100+ percent over cost. As to the six items of jewelry which sold at auction for a total price of $ 79,100, a markup of that total price by the minimum dealer-to-retailer and retail-jeweler-to-public markups referenced by Carmona (i.e., 25 and 50 percent, respectively) results in a total retail price of $ 148,312.50 ($ 79,100 + ($ 79,100 x .25) = $ 98,875; $ 98,875 + ($ 98,875 x .50) = $ 148,312.50)), 10 or, in other words, approximately the same as the total fair market value of $ 146,200 ascertained by Carmona for those items.2004 Tax Ct. Memo LEXIS 31">*52 Carmona testified as to gemstones in general that the public usually buys a gemstone at an amount that equals the gemstone's wholesale price plus 15 to 25 percent of the wholesale price. As to the 13 gemstones which sold at auction for a total price of $ 764,600, we do not find in the record any persuasive evidence that would indicate whether the auction price of those gemstones represents their wholesale price. We would imagine that, generally speaking, the auction price of a gemstone is at least 15 percent less than its wholesale price. Otherwise, why would a broker/dealer pay a double digit commission at auction (15 percent of the first $ 50,000, 10 percent thereafter) to buy a gemstone "as is", when the broker/dealer could buy a "similar" gemstone from a wholesaler without the payment of a commission? When we increase the $ 764,600 total auction price paid for the 13 gemstones by the $ 95,440 of commissions payable to Christie's on the respective sales, 11 and then mark up the sum of $ 860,040 ($ 764,600 + $ 95,440) to reflect the 15- to 25-percent commissions referenced by Carmona, we arrive at a range of retail value for the gemstones from $ 989,046 ($ 860,040 x 1.15) to $ 2004 Tax Ct. Memo LEXIS 31">*53  1,075,050 ($ 860,040 x 1.25). This range approximates the $ 1.1 million total fair market value ascertained by Carmona for the 13 gemstones.We recognize that none of the six assets in question actually sold at auction for even the lower estimated value ascertained by Christie's. We do not consider any of these lower estimated values to be a proper measure of the price at which a hypothetical willing buyer and a hypothetical willing seller would consummate a sale of those assets. The auction was a single auction that included many precious gemstones and many valuable items of jewelry. The mere fact that each of the six assets offered for sale at the auction did not sell there for even its lower estimated value does not mean under the facts herein that its fair market value is necessarily2004 Tax Ct. Memo LEXIS 31">*54  less than its lower estimated value. Cf.  CTUW Hollingsworth v. Commissioner, 86 T.C. 91">86 T.C. 91, 86 T.C. 91">101 (1986) (unaccepted offer to purchase land is not conclusive evidence of the value of the land). We also do not know, for example, whether the bidders at the auction consisted of actual consumers who were willing to buy an item at its fair market value or, as Carmona persuasively opined in the setting of jewelry auctions, primarily dealers who bid substantially less than fair market value in order to resell their purchases at a fair market value price which, to them, would be inclusive of a businessman's profit. In fact, we know little about the composition or number of bidders at the auction, let alone the tone of the actual bidding that took place. On the record before us, we simply cannot conclude as to any of the six items in question that the auction market is the "market * * * in which such item is most commonly sold to the public". Sec. 20.2031-1(b), Estate Tax Regs.We are mindful that this Court has on occasion determined that an item's auction price was its fair market value. E.g., 2004 Tax Ct. Memo LEXIS 31">*55  Estate of Scull v. Commissioner, T.C. Memo. 1994-211;  Lightman v. Commissioner, T.C. Memo. 1985-315. In contrast with the case at hand, the auction markets in those cases were shown to be the appropriate retail markets for the assets under consideration, and the sales at auction were shown to be to the ultimate consumer. Where as here such is not the case, the Court has rejected equating the auction price of an item with its fair market vale. E.g.,  McGuire v. Commissioner, 44 T.C. 801">44 T.C. 801 (1965) (prices paid at auction for art, furnishings, and other personal property did not reflect fair market value in that the bidders at auctions were generally wholesalers or dealers who were buying for resale); cf.  Stollwerck Chocolate Co. v. Commissioner, 4 B.T.A. 467">4 B.T.A. 467, 4 B.T.A. 467">471 (1926) (auction price determined to be fair market value where evidence established that "There were some twenty buyers present [at the auction], seven or eight of whom made bids for the property."). We also note as to the facts at hand that the auction by Christie's involved assets seized by respondent to satisfy a perceived Federal tax obligation, which, in turn, suggests2004 Tax Ct. Memo LEXIS 31">*56  that the auction at hand had an element of a forced sale. A forced sale is inconsistent with the willing seller requirement of fair market value and is not probative of fair market value. See, e.g., sec. 20.2031- 1(b), Estate Tax Regs.We also are mindful of Rev. Proc. 65-19, 1965-2 C.B. 1002, 1965 IRB LEXIS 135, Rev. Proc. 65-19. As relevant herein, that revenue procedure applies to "certain items of tangible personal property which, while generally available to a member of the general public at retail establishments, frequently are obtained by members of the general public at a public auction". Under this revenue procedure, the Commissioner presumes for purposes of section 20.2031-1(b), Estate Tax Regs., that the auction price of an item of tangible personal property is its retail sales price. By extension of this presumption, the fair market value of an item of tangible personal property not sold at auction could be presumed to be no greater than its high bid at auction.We do not believe that the presumption of Rev. Proc. 65- 19, supra, applies to set conclusively the fair market value of the six assets in question. Five of those assets are items of jewelry. We find pursuant2004 Tax Ct. Memo LEXIS 31">*57  to Carmona's testimony that the public does not frequently purchase jewelry at auction. As to the sixth item, a loose 18.2-ct. sapphire, we are unable to find in the record that loose sapphires are typically sold to the public at auction. However, even if the presumption were to apply to one or more of these six assets, we conclude from the record that the high bids for those six assets are not reflective of their retail sales price. We bear in mind especially our findings herein as to the much higher prices which the decedent paid to Mamiye and Lloyds for the comparable and other items shown on the receipts.We recognize that respondent stipulated that the applicable values of 19 of the 25 seized assets were the same as their auction prices and that those prices were in most instances lower than Carmona's appraised values. In valuing the assets in dispute, we do not find in the record that respondent has presumed under Rev. Proc. 65-19, 1965-2 C.B. 1002, 1965 IRB LEXIS 135, Rev. Proc. 65-19, that the fair market values of the 19 assets equaled their auction prices. In fact, given that the auction prices stipulated by respondent did not reflect the commissions paid by the buyers, we conclude2004 Tax Ct. Memo LEXIS 31">*58  to the contrary. See  Estate of Scull v. Commissioner, T.C. Memo. 1994-211 (when the appropriate retail market for an item is the auction, the fair market value of an auctioned item equals its auction price plus buyer's commission). See generally 2003 Fed. Tax Coordinator 2d (RIA), vol. 21, par. P-6009, at 42,252. More importantly, the fact that these assets sold at auction, presumably to dealers, suggests in this case that respondent's pursuance and the Court's redetermination of a fair market value for any of the 19 assets greater than its auction price would have made little or any difference in the deficiency in that the estate would have been entitled to deduct the additional value as an administration expense. See sec. 20.2053-3(d)(2), Estate Tax Regs.; see also  Estate of Joslyn v. Commissioner, 566 F.2d 677">566 F.2d 677 (9th Cir. 1977), revg. 63 T.C. 478">63 T.C. 478 (1975).B. Assets Disputed as to Fair Market Value and Inclusion in   The Taxable Estate1. Overview The decedent was a longtime, avid collector of various valuable items which included specially minted, limited edition gold coins, precious gemstones, expensive jewelry, exquisite2004 Tax Ct. Memo LEXIS 31">*59  rugs and furniture, and guns. 12 He was a wealthy man who enjoyed the finer and more expensive things in life, and he had the financial means to fulfill his desire of collecting only the best pieces of the items which he collected. He was an astute and shrewd businessman who was very knowledgeable about and proud of his collections, and he received much enjoyment flaunting his possessions before others when he entertained at home or was a guest at someone else's home.In early 1988, the decedent divorced Sylvia Trompeter, his wife of 37 years. They had separated on August 8, 1984, and the decedent's relationship with the coexecutors suffered as a result of his separation and ensuing divorce. The decedent following his divorce began devoting most of his time to his collections and, more specifically, to the fulfillment of his intent to own the world's finest pieces in the categories of items which he collected. 2004 Tax Ct. Memo LEXIS 31">*60  The decedent at that time had various female friends, one or more of whom lived with him on different occasions. In addition to his motive of investment, the decedent collected many of the referenced assets to impress these women.In early 1991, the decedent learned that he had terminal cancer, and he relayed this information to the coexecutors. At that time, Gonzalez, the decedent's oldest daughter, 13 began discussing with the decedent the specifics of the assets which he owned. Gonzalez, and to a lesser extent Polachek, became knowledgeable of the specifics of the decedent's vast wealth, and Gonzalez in conjunction with Polachek deliberately undertook to maximize their receipt of that wealth by, among other things, undervaluing his assets and excluding assets from the taxable estate.Receipts and canceled checks show that the decedent bought from Mamiye and Lloyds (primarily at its Fifth Avenue store in New York) various2004 Tax Ct. Memo LEXIS 31">*61  assets which included diamonds, rubies, sapphires, and emeralds, either loose or as pieces of jewelry, and ivory, jade, rugs, furniture, and Chinese artifacts. We set forth these receipts and checks in four categories.a. Receipts From Lloyds to the DecedentLloyds gave to the decedent nine receipts reflecting $ 1,421,000 of merchandise that it sold to him during 1988 and 1989. Three of the nine receipts relate to purchases of $ 650,000 made on January 16, 1988. One of the nine receipts relates to purchases of $ 235,000 made on May 4, 1988. One of the nine receipts relates to purchases of $ 235,000 made on May 5, 1988. Three of the nine receipts relate to purchases of $ 276,000 made on December 5, 1988. One of the nine receipts relates to purchases of $ 25,000 made on May 4, 1989.The writing on the receipts is not always easily readable. We set forth below our reading of that writing. We have been unable to decipher one word (apparently the surname of a collector) that appears in the receipts in four different places. We show that word as "illegible". The nine receipts read as follows:Receipt No. 562, dated January 16, 1988 1   ADHOXO = Masterpiece Genuine Diamond2004 Tax Ct. Memo LEXIS 31">*62     40 ct 2 pt. Wt. Emerald Cut2   Z20118 Heart Shape Baguette Diamond 5 ct Wt.   [ST>ZHOXO<ST] Round Cut, Diamond 5 ct 22 pt Wt.3   Z2014 PHOXO = Genuine Pear Shape Diamond   8 ct 69 pt Wt. Baguette 4 ct 75 pt Wt. Necklace4   Z2008 H8HOX Emerald 6 ct. 48 pt. Wt.   Baguette 32 ct. 50 pt Wt.5   GIA certificate, Emerald Cut 3 ct. 35 pt Wt. Clarity 1F,   Color F, report # 5186298 POAOX = AU6   GIA certificate, Round 3 ct. 4 pt Wt. Clarity VVS2   Color I # 5186303 = ALOXO7   Bracelet, Diamond 9 ct. 5 pt Wt. BK003   12400-SOXO 18 Ct. U. Gold8   Diamond, Heart 4 ct. 03 pt Wt. Fine Quality =   RHROX9   Diamond, Emerald Cut # 5181374   2 ct 08 pt Wt. GVSI = RASOX =10   Diamond [ST>Round<ST] Emerald Cut 2 ct 28 pt Wt.   RPOXO F VSIReceipt No. 563, dated January 16, 198811   Diamond # 5175260 2 ct 01 pt. Wt. Round #   1F-1= RAOXO Magnificent Diamond Round12   Diamond, Round 1 ct. 90 pt. Wt.   E VS2 = ROROX     including Furniture          Bulk for all          650,000.00        Ck 1 @ 250,000.002004 Tax Ct. Memo LEXIS 31">*63  1-16-88        Ck 2 200,000.00 2-28-88        Ck 3 200,000.00 3-15-88Receipt No. 564, dated January 16, 19889   pc Mother of Pearl Dining Room set   Set W/8 chairs2   Curio Cabin Mother of pearl inlay   With Lite, Lock, Shelfs [sic]HOX Black, Artwork Laqueor [sic] DeskAOX " Ming ChairAHO Carved pedestal = For tableRNO 48 inch Beveled glass 48 inch6 Chairs, Corner Work Mother of Pearl   RNH ea for table setLOX= 1 Sofa table for Back of couchRXO 1 Chair Laqueor [sic] Black          Complete for all        650,000.00        BulkReceipt No. 596, dated May 4, 1988Ivory erotic giga     RPHOX" Wise Mens        RPHOX" Erotic          RXOXO" "            RSHOX" 40 tall 3 figure     ROXOX   Delivered 26 items   for Bulk Lot special         235000Diamond NecklaceSapphire "Ruby "Ruby RingSapphire "Masterpiece Diamond       4 ct 39 ptFaint Blue     Bulk Lot Special      235000.00Receipt No. 2004 Tax Ct. Memo LEXIS 31">*64  597, dated May 5, 1988Ruby    18 ct. AR00 7500-0.60Sapphire  "     "   6000  "Diamond   "  Necklace  "   Dia 26 ct. 73 pt. "   74000-PO77Sapphire pendant # 6886 w/ Diamonds Rd.KHM 55= 18 ct., 15000-Ruby Pendant Diamond 072 pt. Ruby18 ct. gold 18400- # 6885 Bagget KHM 58Ivory Maiden     Bulk for          235000.00ck 812 Paid by Checks 100000- 5-5-88     100000-813    "            6-10-88     67000-814    "            7-12-88     67500-             for am in full   235000.00          received 3 cks    #812-813 814Receipt No. 565, dated December 5, 19881   AHO Turquoise Necklace, 11mm 30 inch   Wall of IVORY Art piece NSO   in exchange of Netsukie [sic] 12 YPOXO= Ivory Crab in Cage3 PSOOX= Magnificent pair, Genuine JadeTempess Urns, Black Jade Fish Waves 32 1/2 x 12 3/4 3 in.4 the Royal Kingdom in Temple UrnsAPOXO = w/21 inch x 16 x 42 top 31 x 145 Jade Screen Picture Hand Carved = 17 1/2 x 25 1/2With Wood Frame 23 x 38 pair2004 Tax Ct. Memo LEXIS 31">*65  6 Ivory Boat, PLHO = 22 x 16=x 15 1/2 Hand Carved7 Ivory Wall 11 x 7 1/2 x 3 (NSO)8 Genuine Ivory, apples 5 3/4 x 3 pair9 Silk Hand Made [illegible] Dragon Hand Made4-5 x 7 feet, 93000L 10 Round Diamond 1F 7ct. 75 pt. Wt.11 Diamonds graduated Necklace total wt. 30 ct 02 pt Wt., Fine QualityReceipt No. 566, dated December 5, 198812   Ceylon[ 1 ] Sapphire -- genuine Masterpiece   18 ct 02 pt Wt.13   Pair Diamond Stud Ear Ring14   tree of Life, Pure Silk, 2004 Tax Ct. Memo LEXIS 31">*66  Hand Made   3 x 5 feet = [illegible] Colection [sic] = 9150015   Silk, prayer Rug " 91800 3 x 5 By [illegible]   Hand Made pure Silk, Gold Mesheda16   Rose Wood Curio Stand 9400L = 4-piece   2 tables 9200L17   Netsukie [sic] cases 9360E18   5 assorted Beige Hand Made, Pure Silk   3x5 2x4 6x9 3x5 2x419   Isfahan Hand Made Fine Quality Wool   5 x 7 = feet20   a true Masterpiece aprox 6 x 9 feet   Hand Made 922000 Hand Made   Pure Silk21   Genuine Ivory Eagle arrived brokenReceipt No. 567, dated December 5, 1988to 21 assorted items   Bulk for all          276000-                Paid in full   With Furniture Delivered     with Eli Ezra [illegible]     and Complete Order   Jade Urns 45000- to apraisel [sic] preUnnumbered2004 Tax Ct. Memo LEXIS 31">*67  receipt dated May 4, 1989Nestkies [sic] collection             25,000.00These nine receipts do not reflect all of the merchandise which the decedent purchased from Lloyds. Lloyds was unable to locate all of its receipts relating to purchases by the decedent. 14b. Checks From the Decedent to LloydsFrom 1987 through 1989, the decedent wrote Lloyds the following 13 checks for his purchase of merchandise:Check NumberCheck DateCheck Amount696October 14, 1987$ 2,000697October 14, 198715,000 711October 28, 198780,500 731December 4, 1987276,000765January 16, 1988250,000774February 18, 1988 200,000775April 14, 1988200,000812May 5, 1988100,000813June 10, 198867,000 814July 12, 198867,500 846August 15, 198827,500 992May 4, 198925,000 4751April 15, 1989275,000 1,585,5002004 Tax Ct. Memo LEXIS 31">*68  Check numbers 765, 774, 775, 812, 813, and 814, totaling $ 884,500 in payments, are referenced in the receipts just discussed. The other checks, representing the balance of $ 701,000, reference no receipt in the record, nor are referenced in those receipts.c. Receipts From Mamiye to the DecedentTwo receipts which Mamiye gave to the decedent reflect the decedent's purchase from Mamiye of $ 485,000 of diamonds in 1989. The first receipt reflects the decedent's February 16, 1989, purchase from Mamiye of a round 6.62-ct. diamond with VS1 clarity, a round 6.65-ct. diamond with VS1 clarity, and a round 7.81-ct. diamond with VS1 clarity. The receipt states that the decedent purchased these items at the "bulk special" price of $ 125,000. The receipt states that the decedent was required to pay $ 50,000 down and $ 75,000 in 30 days, and that the decedent had "left as trade 7 ct. 74 pt. Round until sold, and to be set' for sale and ownership to Ed'".The second receipt reflects the decedent's May 5, 1989, purchase from Mamiye of a yellow 5.01-ct. diamond, an 8.53-ct. diamond, and an 11.13-ct. diamond. This receipt states that the decedent purchased these items in a "Bulk Lot" for a "Special" 2004 Tax Ct. Memo LEXIS 31">*69  price of $ 175,000 and that the price for the diamonds, if purchased separately, would have been $ 75,000, $ 85,000, and $ 200,000, respectively.In 1989, the decedent made a $ 100,000 pledge to a charity. In connection therewith, the decedent donated the 7.81 and 8.53-ct. diamonds to the charity during 1990 and 1991. The other four referenced diamonds purchased from Mamiye were included in the assets seized by respondent from the safe deposit box.  d. Checks From the Decedent to MamiyeDuring 1988 and 1989, the decedent wrote Mamiye the following checks for the purchase of merchandise:Check NumberCheck DateCheck Amount764Jan. 16, 1988$ 6,000954Feb. 16, 198950,000 981Apr. 6, 198975,000 982Apr. 9, 198945,000 993May 5, 1989175,000 1080Sept. 7, 19897,000 1183Dec. 22, 198915,000 373,000 Check numbers 764, 982, 1080, and 1183 do not relate to any receipt in the record.e. Relationship of Receipts and Checks to Disputed AssetsAs to the assets whose existence the parties do not dispute, some, but not all of these assets, are listed in these receipts.As to the assets whose existence2004 Tax Ct. Memo LEXIS 31">*70  the parties do dispute, the receipts reveal that 22 items which are not included in the seized assets were purchased by the decedent from Lloyds but were not reported on the estate's Federal estate tax return. 15 We find that the decedent retained ownership of these 22 assets at his death. These 22 assets are:   1. Emerald-cut 2.08-ct. diamond   2. Emerald-cut 2.28-ct. diamond   3. GIA certificate round 3.04-ct. diamond   4. Masterpiece 4.39-ct. diamond with faint blue color   5. Heart-shape-baguette five-ct. diamond   6. Round-cut 5.22-ct. diamond   7. Round 7.75-ct. diamond   8. 18-ct. ruby   9. 18-ct. sapphire   10. Ceylon genuine masterpiece 18.02-ct. sapphire   11. 18-kt. gold bracelet with2004 Tax Ct. Memo LEXIS 31">*71  9.05 ct. diamond   12. Diamond necklace   13. 18-kt. gold necklace with 26.73-ct. diamond   14. 30.02-ct. graduated-diamond necklace   15. Ruby necklace  16. Sapphire necklace   17. Turquoise necklace 11mm, 30 inches long   18. Ruby ring   19. Sapphire ring   20. Pair of diamond stud earrings   21. 18 kt. gold, ruby, and diamond pendant   22. Sapphire pendant with round diamondsThe checks and receipts from Lloyds also reveal that 18 items were either not reported on the estate's Federal estate tax return or, to the extent that they were so reported, were not included in the taxable estate at their fair market values as of the applicable valuation date. We find that the decedent retained ownership of these 18 assets at his death. These 18 assets are:   1. Sofa table with 48-inch beveled glass   2. Silk handmade dragon rug, four-five x seven feet   3. Silk handmade tree of life rug, three x five feet   4. Silk handmade prayer rug, three x five feet   5. Silk handmade beige rug, two x four feet   6. Silk handmade beige2004 Tax Ct. Memo LEXIS 31">*72  rug, two x four feet   7. Silk handmade beige rug, three x five feet   8. Silk handmade beige rug, three x five feet   9. Silk handmade beige rug, six x nine feet   10. Isfahan handmade fine quality wool, five x seven feet   11. Silk handmade masterpiece rug, six x nine feet   12. Three items of jade   13. Various items of ivory   14. Mother-of-pearl inlay dining room set with a carved pedestaland 14 chairs   15. Two curio cabinets with mother-of-pearl inlay   16. Black artwork lacquer desk and chair   17. Black Ming chair   18. Four-piece, two table rosewood curio standTestimony and documentary evidence also establish the existence of other unreported assets which were includable in the taxable estate. Hesselgesser, who like the decedent was a collector, testified credibly that he met with the decedent on a few occasions to discuss and inspect the decedent's collections of guns, gold coins, jewelry, ivory, and music. Hesselgesser's testimony persuades us that the decedent had "several" collections of ivory and that the decedent in the summer of 1991 owned several2004 Tax Ct. Memo LEXIS 31">*73  large diamonds (e.g., 30 and 40 carats), several tennis bracelets, and several large necklaces with emeralds and diamonds. Hesselgesser's wife testified credibly that the decedent near his death possessed several diamond necklaces and an extensive music collection. The decedent's friend, Joanne Standard (Standard), testified credibly that the decedent possessed eight to 10 tennis bracelets, some of which had one-ct. diamonds all around the bracelet, "fabulous" emerald necklaces, and all kinds of "lovely" jewelry. 16 Testimony also establishes that the decedent owned various other items of jewelry and numerous diamonds, emeralds, and opals. In sum, the testimony and documentary evidence establish that the decedent owned the following 18 assets which were not included in either the 25 seized assets or the known receipts and that were not reported on the estate's Federal estate tax return:2004 Tax Ct. Memo LEXIS 31">*74     1. Music collection consisting primarily of reel-to-reel tapes   2. Three Baker's tables   3. "Thousand dollar" watch   4. Cash at home   5. 31 coins   6. Various pieces of jade   7. Various pieces of ivory   8. One eight-ct. emerald and two other emeralds   9. Two opals   10. Tennis bracelet with many one-ct. diamonds   11. Six other diamond tennis bracelets   12. Ruby bracelet matching seized ruby necklace and ring   13. Sapphire bracelet matching seized sapphire necklace and ring   14. Pinkie ring with three to four-ct. diamond   15. Man's three- to four-ct. diamond ring   16. Tie tack with three- to four-ct. diamond   17. Ruby pin matching seized ruby necklace and ring   18. Sapphire pin matching seized sapphire necklace and ringWe find that the decedent retained ownership of these 18 assets at his death.2. Specific Assetsa. Music collectionWhen he died, the decedent owned a music collection consisting of reel-to-reel tapes (and to a lesser extent records) and three or four tape players. The decedent2004 Tax Ct. Memo LEXIS 31">*75  had been collecting reel-to- reel tapes for approximately three decades, and his life's goal was to own the best collection of reel-to-reel tapes which money could buy. The decedent's music collection was unique and of fine quality, consisting mainly of music from the 1920s and 1930s and including tapes of the famous Italian tenor Caruso and numerous other tapes of music from Latin America through music of the present day. The decedent kept his tapes at home in several rooms. In one room, in particular, the room where he routinely listened to his tapes on a high quality, highly sensitive sound system, the decedent covered one wall completely with his tapes.Henry Schiffer (Schiffer) was the decedent's accountant and a long-time friend. Once or twice a month, Schiffer would visit the decedent at his home to handle his accounting requirements or simply to converse with him in his music room or in his gazebo. For estate tax purposes, Schiffer prepared a one-page document entitled "ED TROMPETER ASSET LIST (NOT INCLUDING COINS) AS OF FEBRUARY 21, 1992". This document listed Schiffer's understanding of some (but not all) of the assets owned by the decedent as of that date and each asset's2004 Tax Ct. Memo LEXIS 31">*76  estimated fair market value. Schiffer generally obtained these estimates by asking the decedent his opinion as to each asset's value. Beforehand, Schiffer had advised the decedent that he should be conservative in estimating value for this purpose because the higher the value, the greater the estate tax. The document listed that the decedent's music collection had an estimated fair market value of $ 50,000 as of February 21, 1992.Gonzalez took the decedent's music collection to her home in Florida after he died, and the coexecutors did not report any value for this collection on the Federal estate tax return. We find on the basis of Schiffer's document and testimony that the fair market value of this collection was $ 50,000 as of the applicable valuation date. We are mindful that the fair market value of this collection could be significantly higher than $ 50,000 given the voluminous size of the collection, the decedent's earnest desire to have the finest collection of reel-to-reel tapes which money could buy, the decedent's financial ability to fulfill that desire, and Schiffer's advice to the decedent to estimate the value of the listed assets conservatively.b. Baker's tables/sofa2004 Tax Ct. Memo LEXIS 31">*77  tableBy her own admission, Polachek removed three Baker's tables and a long sofa table from the decedent's home after he died. While Polachek suggested that these tables were of minimal dollar value, we find it more likely that these assets had a significant dollar value in light of the decedent's wealth, lifestyle, and desire to own (and be seen as owning) only the best of everything. In fact, the value of these four assets caused Polachek to expend her time, effort, and money to transport them from the decedent's home in Southern California to her home in Northern California. 17 Given our added understanding of the location and value of the decedent's home, 18 as well as the fact that he was a flamboyant individual who filled his home extensively with the finest, most beautiful, and most valuable pieces of art, artifacts, gemstones, and jewelry (as well as a noteworthy collection of music recordings), we simply do not see the decedent sparing an expense when it came to furnishing his home with tables and other furniture. Such is especially so given that the decedent regularly entertained at his home, that he purchased at least some of his home's furniture from the Fifth Avenue2004 Tax Ct. Memo LEXIS 31">*78  location of Lloyds, and that he obviously paid a significant amount of money to ship that furniture cross-country to his home in California.We find as of the applicable2004 Tax Ct. Memo LEXIS 31">*79  valuation date that the fair market values of the sofa table and each of the three Baker's tables were $ 4,416 and $ 2,208, respectively. 19 Lloyds gave to the decedent three sequentially numbered receipts for his purchases of January 16, 1988, totaling $ 650,000. Receipt number 564, the last of these three receipts, listed nine pieces of furniture purchased by the decedent. Neither party has suggested that this sale was not a valid, arm's-length sale, and we consider it as such. 20 The parties stipulated that item numbers 1, 3, 4, 5, and 8 on receipt number 562 and the only two items on receipt number 563 had as of the applicable valuation date a total fair market value of $ 320,600. 21 As discussed infra pp. 56-58, 62-63, we find that the fair market values of the remaining items on receipt number 562 totaled $ 245,506 as of the applicable valuation date. 22 When we take into account credible testimony in the record to the effect that the value of jewelry and gemstones has remained virtually the same throughout the relevant time period, we conclude that the balance of the $ 650,000 sales price, i.e, $ 83,894 ($ 650,000 - ($ 320,600 + $ 245,506)), must be attributable to the2004 Tax Ct. Memo LEXIS 31">*80  nine items of furniture on receipt number 564.2004 Tax Ct. Memo LEXIS 31">*81  The nine items of furniture basically consist of: (1) A mother-of-pearl inlay dining room set with a carved pedestal and 14 chairs, (2) two curio cabinets with mother-of-pearl inlay, (3) a black artwork lacquer desk and matching chair, (4) a sofa table with 48-inch beveled glass, and (5) a black Ming chair. On the basis of our perception of the value of the items in these five categories, we assign the following weights to these categories to apportion the $ 83,894 amongst them: 8, 4, 4, 2, and 1, respectively. 23 In that the sum of these weights totals 19 (8 + 4 + 4 + 2 + 1 = 19), we apportion 8/19, 4/19, 4/19, 2/19, and 1/19 of the $ 83,894 to the respective categories. Our apportionment of the $ 83,894 to the five categories is $ 35,324, $ 17,662, $ 17,662, $ 8,831, and $ 4,415, respectively. We decide that, as of the applicable valuation date, a date that is approximately 5 years after this furniture was purchased, the fair market value of each of these categories is 50 percent of the amount which we apportion to it, or, in other words, $ 17,662, $ 8,831, $ 8,831, $ 4,416, and $ 2,208, respectively.24 We decide that the sofa table taken by Polachek is the sofa table in category2004 Tax Ct. Memo LEXIS 31">*82  4. We decide that the applicable fair market value of each of the Baker's tables is 1/2 of the fair market value of the sofa table, i.e., $ 2,208 ($ 4,416/2), and that the fair market values of the three Baker's tables on the applicable valuation date totaled $ 6,624 ($ 2,208 x 3).2004 Tax Ct. Memo LEXIS 31">*83  We are mindful that the estate's Federal estate tax return contains an "appraisal" opining that the decedent's home was filled mainly with minimal value assets. That document was prepared by Butterfield & Butterfield (Butterfield) on or about May 13, 1993, and purports to list the fair market values as of March 18, 1992, and September 18, 1992, 25 of 161 single or groups of assets which were viewed by Butterfield within the decedent's home. The document states that only three single assets were worth more than $ 1,000, 26 that 87 of the 161 assets were worth less than $ 100, and that 143 of the 161 assets were worth less than $ 500. The document lists, for example, that the fair market value of a "CHINESE MOTHER-OF-PEARL INLAY ROSEWOOD DINING SET" was $ 800, that the fair market value of a "PAIR OF CHINESE MOTHER-OF-PEARL INLAY ROSEWOOD DISPLAY CABINETS" was $ 1,500, that the fair market value of "SIX CHINESE MOTHER-OF-PEARL INLAY ROSEWOOD CORNER CHAIRS" was $ 300, that the fair market value of a "CHINESE BLACK LACQUER GILT DECORATED ARMCHAIR" was $ 50, and that the fair market value of a "PAIR OF CHINESE CARVED ROSEWOOD RECTANGULAR STANDS" was $ 800. The document also lists that2004 Tax Ct. Memo LEXIS 31">*84  the fair market values of 10 rugs were as follows: 27DescriptionAppraised ValueAuction PriceOriental rug (Rams)$ 200312.50Chinese silk rug(Banzai Trees), 34 x 56 inches300200.00Chinese silk rug(Dragons)49 x 86 inches300312.50Chinese silk yellowrug, 56 x 28 inches30037.50Chinese silk yellowrug, 68 x 98 inches150150.00Chinese silk yellowrug, 49 x 74 inches300137.50Chinese silk yellowrug, 56 x 28 inches15037.50Indian rug, 55 x 86 inches400250.00Chinese silk red andyellow rug,62 x 36 inches300125.00Chinese silk rug(Tabriz design)72 x 106 inches6003725.502004 Tax Ct. Memo LEXIS 31">*85 We give little regard to this "appraisal". We do not believe that an astute, strong-minded, self-made multimillionaire like the decedent, who indisputably collected only the finest and most valuable gold coins, gemstones, and items of jewelry, and who received enormous pleasure from flaunting his possessions before others, would purchase assets with such minimal values as listed by Butterfield. 28 Nor does the appraisal state the rationale underlying its low values; it merely recites a brief general description of the asset with its proffered value. We also know little about the appraiser (e.g., her credentials) or the terms or conditions underlying the appraisal. We do know, however, that the appraiser2004 Tax Ct. Memo LEXIS 31">*86  generally walked through the decedent's home, eyed most of the items in the home, and appraised them on the spot. We also know that Gonzalez testified that she took three of the decedent's rugs to her home in Florida, that she later had those rugs appraised in Florida by what she described as a "legitimate company", and that the company appraised the rugs at $ 4,000. Gonzalez effectively conceded at trial that Butterfield did not recognize the value of those rugs and did not meaningfully appraise them. 292004 Tax Ct. Memo LEXIS 31">*87  c. Thousand dollar watchSchiffer testified that the decedent wore a "thousand dollar" watch. The coexecutors did not report any watch on the estate's Federal estate tax return. On the basis of Schiffer's testimony, we find that the fair market value of the decedent's "thousand dollar" watch was $ 1,000 as of the applicable valuation date.d. Cash at homeThe coexecutors reported on the estate's Federal estate tax return that all of his money (exclusive of coin collections) as of the applicable valuation date was held in financial institutions. 30 The coexecutors did not report any cash that the decedent had at home. The decedent kept cash at home in a burlap bag secured in a large safe in his den, and he routinely went to the safe when he needed money to spend. The decedent was very private about the contents of this safe, and he generally did not tell his closest friends about its existence, nor allow them to enter the den.2004 Tax Ct. Memo LEXIS 31">*88  A few days before the decedent died, he gave the combination to his home safe to Polachek and taught her how to open the safe by herself. Polachek testified that the safe had cash in it at this time but that it had no cash in it when she and Gonzalez opened the safe together following the decedent's death. Gonzalez was regularly in the decedent's home following his death, including the period of time before she and Polachek opened the safe together. Gonzalez testified to the effect that she did not know how to open the safe alone, but needed Polachek's assistance to do so. We find that testimony incredible. Gonzalez was deeply involved with the decedent and his wealth for approximately 1 year before his death, and we believe it incredible that the decedent would have taught Polachek to open the safe but not Gonzalez. This is especially so given the fact that the decedent informed Gonzalez as to the specifics of his extensive holdings.We find that the decedent when he died had cash of $ 50,000 at home. The decedent when he died had amassed at his home valuable assets worth hundreds of thousands of dollars, and we believe under the facts and circumstances of this case that it is reasonable2004 Tax Ct. Memo LEXIS 31">*89  to conclude that the decedent also kept at home a significant amount of cash. This is especially so given that the decedent tended to keep his assets secreted at home rather than in banks (e.g., he kept many of his coins hidden in his garage) and that he had a history of giving large sums of cash (not checks) to at least Gonzalez, Polachek, and Wong. He gave $ 16,000 in cash to Wong in or about 1987. He gave $ 50,000 in cash to Gonzalez and Polachek in 1991. He gave to Wong in or about 1991 cash of $ 77,000 and additional money to pay off approximately $ 250,000 of her debts. We also note that some of the receipts in evidence do not relate to the decedent's checks in evidence, which indicates to us that the decedent on various occasions paid large sums of cash for his purchases of the items which he collected.e. CoinsRespondent did not recover all of the coins omitted from the taxable estate. Gonzales understood that the decedent had approximately 500 coins in the possession of Superior Stamp & Coin (Superior) before the auction of February 25, 1992. Given the fact that Gonzalez was well informed as to the extent of the decedent's holdings, we conclude that the decedent near the2004 Tax Ct. Memo LEXIS 31">*90  time of his death owned 500 coins. Of these coins, 201 (209-8) were sold in the auction and 227 (191 + 36) were reported on the estate's Federal estate tax return. 31 This leaves 72 coins (500 - (201 + 227)), 41 of which were seized and 31 of which have not been recovered by respondent. In light of the tough and thorough litigation with Superior, we believe that those of the 500 coins in Superior's possession which were not sold were returned to the decedent.We find a fair market2004 Tax Ct. Memo LEXIS 31">*91  value of $ 425,847 for the 31 coins which were not recovered by respondent. The 201 coins, which consisted primarily of $ 1, $ 2-1/2, and $ 3 gold coins and certain pattern gold coins, sold at the first auction for the total amount of $ 3,850,622 (an average of $ 19,157 per coin). The 191 coins, which consisted of $ 5, $ 10, and $ 20 gold pieces and the Amazonian set, were valued by the Court at $ 7,635,000 (an average of $ 39,974 per coin) as of the applicable valuation date. The 36 coins, which were similar to the 191 coins, were valued by the Court at $ 494,523 (an average of $ 13,737 per coin) as of the applicable valuation date. We find the applicable fair market value of the 31 coins using the $ 13,737 average value (31 x $ 13,737 = $ 425,847). 32f. RugsBy her own admission, 2004 Tax Ct. Memo LEXIS 31">*92  Gonzalez removed three rugs from the decedent's home. While the estate asserts that these rugs had little dollar value, we believe that these rugs were worth a lot of money in light of the decedent's wealth, lifestyle, and desire to own (and be seen as owning) only the best of everything. In fact, the value of these assets caused Gonzalez to expend the time, effort, and expense to transport them cross-country from the decedent's home in Southern California to her home in Florida. 33The decedent purchased 10 handmade rugs from Lloyds on December 5, 1988. The receipts for that day indicate that the decedent paid $ 276,000 to Lloyds for all of the items listed therein and that the listed jade urns had been appraised at $ 45,000. The parties stipulated that the coexecutors did not report the Isfahan rug on the estate's Federal estate tax return. 2004 Tax Ct. Memo LEXIS 31">*93  At trial, the Court granted the estate's request to vacate that stipulation. The estate had pointed to the fact that the Lloyds's receipts in evidence listed 10 rugs and that the coexecutors included in the taxable estate the 10 rugs shown on Butterfield's appraisal. The estate alleged that the Isfahan rug was reported by the coexecutors as the "Indian rug, 55 x 86 inches" with a value of $ 400. The Court informed the parties that the issue of whether the coexecutors included the applicable fair market value of the Isfahan rug in the taxable estate would be decided on the basis of the record.On the basis of the record, we conclude that the Isfahan rug was not the referenced Indian rug. Isfahan (or Esfahan as it is more commonly spelled) is a city in Iran. It is not a city in India. We also conclude that the 10 rugs reported on the estate's Federal estate tax return did not represent the total fair market value of the 10 rugs purchased from Lloyds on December 5, 1988. As explained below, we find that the coexecutors failed to include within the taxable estate $ 59,530 for rugs owned by the decedent when he died.The December 5, 1988, receipts show that the decedent paid a bulk price2004 Tax Ct. Memo LEXIS 31">*94  of $ 276,000 for 24 items (the 20 items shown in item numbers 2 through 21 inclusive of five rugs shown in item number 18). 34 Of those 24 items, 10 are rugs, five are pieces of ivory, three are pieces of jade, one is a 30.02-ct. graduated-diamond necklace, one is a pair of diamond earrings, one is a 7.75 ct. diamond, one is a genuine masterpiece 18.02 ct. sapphire, one is netsukes, and one is two rosewood tables. We apportion the $ 276,000 sales price among these items in the following manner.First, we apportion $ 45,000 to the three items of jade to reflect their appraised value.  Second, we apportion $ 18,750 to the five pieces of ivory to reflect what we decide was a reasonable $ 3,750 per piece value for ivory. We ascertain that per piece2004 Tax Ct. Memo LEXIS 31">*95  value taking into account the fact that Butterfield appraised two of the decedent's ivory urns at a per piece value of $ 2,000 and that Carmona testified in the setting of jewelry sales that the fair market value of an item purchased at auction generally equals the auction price plus a 25 to 50 percent dealer-to-retailer markup and a 50 to 100+ percent retailer-to-public markup. On the basis of the record before us, we consider the sale of jewelry as sufficiently similar to the sale of ivory for purposes of valuing the latter, and we conservatively apply the lower range of the estimated markups. In other words, we find for purposes of our analysis that the retailer's price for ivory was $ 2,500 per item ($ 2,000 + ($ 2,000 x .25)), and that the retail sales price for ivory was $ 3,750 per item ($ 2,500 + ($ 2,500 x .50)).Third, we apportion $ 25,000 to the item of netsukes to reflect the fact that the decedent had on May 4, 1989, paid that amount for other netsukes. Fourth, we apportion $ 4,416 to the two rosewood tables to reflect our finding supra p. 42 that the Baker's tables were each worth $ 2,208 and our decision that the Baker's tables are a good measure of the value of the2004 Tax Ct. Memo LEXIS 31">*96  rosewood tables. Fifth, we apportion $ 66,404 to the diamond necklace, $ 9,000 to the diamond earrings, $ 35,800 to the 7.75-ct. diamond, and $ 9,100 to the 18.02-ct. sapphire to reflect our findings infra pp. 58, 62, 69-70, 73, of those fair market values. Sixth, we apportion the remaining $ 62,530 of the $ 276,000 sales price to the 10 rugs. 35 We allow the estate credit for $ 3,000 of rugs reported on its estate tax return and conclude that $ 59,530 of value was unreported by the coexecutors primarily for the Isfahan rug, but for other rugs as well.g. Jade collectionThe Schiffer document lists the value of the decedent's jade collection at $ 250,000 as of February 21, 1992. Schiffer obtained this value from the decedent. The decedent purchased2004 Tax Ct. Memo LEXIS 31">*97  $ 45,000 of jade from Lloyds on December 5, 1988. The decedent purchased other items of jade at other times.The coexecutors reported on the estate's Federal estate tax return that the only jade included in the taxable estate was two jade plaques with a fair market value of $ 2,500. The reported value equaled the amount on the Butterfield appraisal shown for those items. Taking into account the decedent's own valuation of his jade collection and allowing the estate credit for the reported value of the plaques, we find the fair market value of the remainder of the jade collection at $ 247,500 as of the applicable valuation date ($ 250,000 - $ 2,500).h. Ivory collectionOn May 4 and December 5, 1988, the decedent purchased from Lloyds numerous items of ivory. The decedent purchased other items of ivory at other times. On December 7, 1992, the estate's accountants prepared a preliminary summary of the estate which listed the value of the decedent's ivory collection at $ 1.5 million as of March 18, 1992. Gonzalez believed that the ivory collection was worth an amount consistent with that valuation.We decide that the decedent had a significant ivory collection when he died. We find2004 Tax Ct. Memo LEXIS 31">*98  consistent with the preliminary statement and Gonzalez's understanding of the decedent's ivory holdings that the fair market value of the decedent's ivory collection was $ 1.5 million as of the applicable valuation date. 36i. Loose Gemstonesi. DiamondsThe Schiffer document lists the value of the decedent's diamond collection at $ 500,000 as of February 21, 1992. Schiffer obtained this value from the decedent. The decedent estimated this value conservatively and not as an accurate gauge of the fair2004 Tax Ct. Memo LEXIS 31">*99  market value of his diamonds. Respondent seized 13 loose diamonds from the safe deposit box, and those diamonds were appraised by Carmona at a fair market value of $ 1.1 million and sold at auction for a total price (exclusive of buyer's commissions) of $ 764,600. The seized diamonds, their values as appraised by Carmona, and their auction prices (exclusive of buyer's commission) are as follows:CaratCarmona'sAuction PriceWeightAppraised Valueof Christie's1.9$ 11,800$ 9,6002.0115,0007,5003.3552,30025,0004.0319,6007,5004.3297,000105,0005.0148,00035,0006.6221,50020,0006.6522,00024,0007.5748,00030,0007.8435,80027,00011.1359,00044,00018.28210,000210,00040,02460,000220,0001,100,000764,600Carat      Carmona's       Auction PriceWeight     Appraised Value    of Christie's1.9       $ 11,800        $ 9,6002.01       15,000         7,5003.35       52,300         25,0004.03       19,600         7,5004.2004 Tax Ct. Memo LEXIS 31">*100  32       97,000        105,0005.01       48,000         35,0006.62       21,500         20,0006.65       22,000         24,0007.57       48,000         30,0007.74       35,800         27,00011.13       59,000         44,00018.28       210,000        210,00040.02       460,000        220,000        ________       _________       1,100,000        764,600The decedent also purchased from Lloyds in 1988 seven loose diamonds which were not reported on the Federal estate tax return and which were not included in the 25 seized assets. Five of these diamonds were purchased on January 16, 1988, one was purchased on May 4, 1988, and one was purchased on December 5, 1988. The five diamonds purchased on January 16, 1988, are an emerald-cut 2.08-ct. diamond, an emerald-cut 2.28-ct. diamond with VS1 clarity, a GIA certificate round 3.04-ct. diamond with VVS2 clarity and I color, a heart-shape-baguette 5-ct. diamond,2004 Tax Ct. Memo LEXIS 31">*101  and a round-cut 5.22-ct. diamond. The diamond purchased on May 4, 1988, was a masterpiece 4.39-ct. diamond with a faint blue color. The diamond purchased on December 5, 1988, was a round 7.75-ct. diamond. We find that the decedent retained ownership of these seven diamonds at his death.We find the fair market value of these seven diamonds through a three-step process. First, we look to the prices at which Mamiye sold similarly weighted diamonds. 37 We consider those arm's-length retail prices to be the best indicia of fair market value on the basis of the record before us. If a diamond sold by Mamiye was similar in weight to one of the seven diamonds in question, we use that comparable diamond to measure the fair market value of the diamond in question.2004 Tax Ct. Memo LEXIS 31">*102  By its weight, the 5.01-ct. diamond that Mamiye was selling for $ 75,000, if purchased separately, is comparable to the five-ct. and 5.22-ct. diamonds in question. We decide that the five- ct. diamond was for practical purposes the same weight as the 5.01- ct. diamond sold by Mamiye and observe that the 5.22-ct. diamond was 4.2 percent larger in weight than the 5.01-ct. diamond ((5.22 - 5.01)/5.01 = .042). We find on the basis of the $ 75,000 price that the fair market values of the five-ct. and 5.22-ct. diamonds were $ 75,000 and $ 78,150 ($ 75,000 + ($ 75,000 x .042)), respectively, as of the applicable valuation date.We do not find in the record that Mamiye sold a diamond that was comparable to one or more of the five remaining diamonds. As to these five diamonds, we turn to Carmona's opinion as set forth in his expert report. If a diamond that was valued by Carmona was similar in weight to one of the five remaining diamonds, we use that comparable diamond to measure the fair market value of the diamond in question, unless the record establishes that Carmona's appraised value was not indicative of the diamond's retail sales price. Under the facts herein, we believe that Carmona's2004 Tax Ct. Memo LEXIS 31">*103  opinion is the second best measure of the fair market value of four of the five remaining diamonds.Carmona opined that the fair market value of the 2.01-ct. diamond was $ 15,000. We decide that the 2.01-ct. diamond was the best measure of value for the 2.08 and 2.28-ct. diamonds. On the basis of Carmona's appraisal of the 2.01-ct. diamond at $ 15,000, and the fact that the 2.01 diamond is 3.4 and 13.4 percent smaller in weight than the 2.08-ct. and 2.28-ct. diamonds, respectively ((2.08 - 2.01)/2.01 = .034; (2.28 - 2.01)/2.28 = .134), we find that the fair market values of the 2.08 and 2.28-ct. diamonds were $ 15,510 ($ 15,000 + ($ 15,000 x .034) and $ 17,010 ($ 15,000 + ($ 15,000 x .134)) respectively.Carmona opined that the fair market value of the 3.35-ct. diamond was $ 52,300. We decide that the 3.35-ct. diamond was the best measure of value for the 3.04-ct. diamond. On the basis of the $ 52,300 value and the fact that the 3.04-ct. diamond was 9.3 percent smaller than the 3.35-ct. diamond ((3.35 - 3.04)/3.35 = .093), we find that the fair market value of the 3.04-ct. diamond was $ 47,436 ($ 52,300 - ($ 52,300 x .093)).Carmona opined that the fair market value of the 7.74-ct. 2004 Tax Ct. Memo LEXIS 31">*104  diamond was $ 35,800. We decide that the 7.74-ct. diamond was the best measure of value for the 7.75-ct. diamond. On the basis of the $ 35,800 value and the fact that the 7.74-ct. diamond was for practical purposes the same weight as the 7.75-ct. diamond, we find that the fair market value of the 7.75-ct. diamond was $ 35,800.Lastly, we turn to the auction prices to find the value of the remaining diamond. A faint blue 4.32-ct. diamond sold at auction for $ 105,000. Whereas the 4.32 ct. diamond actually sold at auction for more than its $ 97,000 value as appraised by Carmona, we do not consider Carmona's appraised value to be the best measure of value for the faint blue 4.39 ct. diamond. 38 On the basis of the price at which the 4.32 ct. diamond sold at auction and taking into account the fact that the 4.39-ct. diamond was 1.6 percent larger than the 4.32-ct. diamond ((4.39 - 4.32)/4.32 = .016), we decide that the fair market value of the 4.39-ct. diamond was no less than $ 106,680 ($ 105,000 + ($ 105,000 x .016)) and, indeed, most likely more than that amount.39On the basis of the record, we find the fair market value of the 4.39-ct. diamond at its minimum value of $ 106,680. 2004 Tax Ct. Memo LEXIS 31">*105 ii. EmeraldsThe coexecutors did not include any loose emeralds in the taxable estate. When he died, the decedent owned numerous loose emeralds including at least one that weighed eight carats. With the exception of the eight-ct. emerald, the record does not establish the carat weight or specifics of any of the other loose emeralds owned by the decedent.Respondent did not seize any loose emeralds from the safe deposit box, but he did seize two 18-kt. gold, emerald, and diamond necklaces. One of those necklaces, item 2j in2004 Tax Ct. Memo LEXIS 31">*106  the appendices, had a 6.07-ct. emerald and 270 small diamonds with a total weight of 10.44 carats. We find supra p. 18 that the applicable fair market value of this necklace was $ 19,000. The other seized necklace, item 2i in the appendices, had a 6.48-ct. emerald and 245 small diamonds with a total weight of 32.5 carats. The parties stipulated that the applicable fair market value of this necklace was $ 19,000.We decide that the fair market values of the two emerald necklaces is most probative of the fair market value of the eight-ct. emerald. On the basis of the $ 19,000 value, we find as of the applicable valuation date that the fair market value of the eight-ct.  emerald was $ 16,150. We find the $ 16,150 fair market value by increasing the $ 19,000 by 27.5 percent ($ 19,000 x .275 = $ 5,225) to reflect the fact that the eight-ct. emerald is 27.5 percent larger than 6.275 ((8 - 6.275)/6.275 = .275), which is the average weight of the emeralds on the necklaces in items 2i and 2j, and then decreasing the total of $ 24,225 ($ 19,000 + $ 5,225) by one-third ($ 24,225/3 = $ 8,075) to account for the fact that the $ 24,445 value included a necklace that was 18-kt. gold and had an assortment2004 Tax Ct. Memo LEXIS 31">*107  of small diamonds ($ 24,225 - $ 8,075 = $ 16,150).We find a fair market value of $ 32,300 for other emeralds owned by the decedent when he died. Although the record does not establish the exact number of other loose emeralds owned by the decedent when he died, we surmise from the record that the decedent must have then owned at least two other loose emeralds. We decide conservatively that the decedent owned two other emeralds when he died, that the value of each of those emeralds was the same as the eight-ct. emerald, and that the total fair market value of those two other emeralds was two times the fair market value of the eight-ct. emerald ($ 16,150 x 2 = $ 32,300).iii. OpalsThe coexecutors did not include any loose opals in the taxable estate. Testimony establishes that the decedent owned "numerous" opals when he died. Whereas the record does not establish the number or specifics of any of these "numerous" opals, we decide conservatively that the decedent owned two opals when he died.We believe that it is reasonable on the basis of the facts and circumstances at hand to conclude that the fair market value of each of the decedent's two opals was the same as the fair market2004 Tax Ct. Memo LEXIS 31">*108  value of each of the decedent's emeralds. We find that the fair market value of the opals totaled $ 32,300 (2 x $ 16,150).iv. RubyLloyds's receipt number 597, dated May 5, 1988, reported that the decedent purchased an 18-ct. ruby from Lloyds for the price of $ 7,500. We find that the decedent retained ownership of this ruby at his death. On the basis of the price listed on the receipt, we find that the fair market value of the 18-ct. ruby was $ 7,500 as of the applicable valuation date.v. SapphiresThe coexecutors did not include any loose sapphires in the taxable estate. Respondent seized from the safe deposit box one loose blue sapphire, 18.2 carats in size, which we valued supra p. 18 at $ 9,100. That sapphire was not the same sapphire as either the Ceylon genuine masterpiece 18.02-ct. sapphire shown on the pertinent Lloyds's receipt of December 5, 1988, or the 18-ct. sapphire shown on the Lloyds's receipt of May 5, 1988. We find that the decedent retained ownership of the 18-ct. sapphire and the 18.02-ct. sapphire at his death.We find that the fair market value of the 18-ct. sapphire was $ 6,000 as of the applicable valuation date. Lloyds listed that amount on the May 5, 1988, receipt2004 Tax Ct. Memo LEXIS 31">*109  as the price of that sapphire. On the basis of our valuation of the seized 18.2-ct. sapphire and the fact that the 18.2-ct. sapphire was for practical purposes the same weight as the 18.02-ct. sapphire, we find that the fair market value of the 18.02 sapphire was $ 9,100 as of the applicable valuation date. We attribute the differential between the valuations of $ 6,000 for the 18-ct. sapphire and $ 9,100 for each of the 18-ct. and 18.02 ct. sapphires to the fact that the two more expensive sapphires were a "blue" sapphire and a "genuine masterpiece" "Ceylon" sapphire, respectively.j. Braceletsi. DiamondOn January 16, 1988, the decedent purchased from Lloyds an 18-kt. gold bracelet with a 9.5-ct. diamond. The receipt for that item reported that its price was $ 12,400. We find that the decedent retained ownership of this bracelet at his death. On the basis of the price listed on the receipt, we find that the fair market value of this bracelet was $ 12,400 as of the applicable valuation date.The decedent typically purchased diamond bracelets with one-ct. diamonds set all the way around each bracelet. Hesselgesser and his wife saw decedent with "several" bracelets, and Standard2004 Tax Ct. Memo LEXIS 31">*110  saw 8 or 10 diamond tennis bracelets and believed that at least 1 of those bracelets had an assortment of diamonds which were 1 carat each. The decedent gave Wong two diamond tennis bracelets, one with 10.5 carats of diamonds and the other with approximately seven carats of diamonds. The decedent bought one of the bracelets given to Wong at a coin show, and he bought the other bracelet given to Wong from Mamiye. We decide that the taxable estate included seven unreported diamond tennis bracelets (average of nine bracelets seen by Standard less the two bracelets given to Wong), and that one of these seven bracelets had one-ct. diamonds all around it.For the diamond tennis bracelet with one-ct. diamonds all around it, we find that its fair market value was $ 108,000 as of the applicable valuation date. The parties stipulated that the tie tack with a one-ct. diamond had an applicable fair market value of $ 4,500. On the basis of our review of the pictures and descriptions of the items displayed in the auction catalogue of Christie's in evidence (auction catalogue), we decide that this tennis bracelet was 6 1/2 inches long and contained 24 one-ct. diamonds. We use the tie tack as a measure2004 Tax Ct. Memo LEXIS 31">*111  of the minimum value for each one-ct. diamond (24 x $ 4,500 = $ 108,000). 40As to the six other diamond tennis bracelets, we find that their total fair market value was $ 191,568 as of the applicable valuation date. Item number 293 in the auction catalogue is a 6 5/8 inch bracelet with 44 rectangular-cut diamonds weighing approximately 17.5 carats in total. Christie's estimated that the value of this bracelet was $ 20,000 to $ 25,000. We decide on the basis of the record at hand that this bracelet is the best measure of the fair market value of the six diamond tennis bracelets in question. As to the 11 seized items of jewelry, Christie's had ascertained that their lower and upper estimated values totaled $ 98,000 ($ 70,000 of sold items + $ 28,000 of unsold items) and $ 147,000 ($ 107,500 of sold items + $ 39,500 of unsold items), respectively. Carmona ascertained that their2004 Tax Ct. Memo LEXIS 31">*112  fair market values totaled $ 183,400 ($ 146,200 of sold items + $ 37,200 of unsold items). The total value ascertained by Carmona is 24.76 percent greater than the total upper estimated value for these 11 items (($ 183,400 - $ 147,000)/$ 147,000 = .2476)). Consistent with Carmona's valuation of the 11 items of jewelry vis-a-vis their total upper estimated values as ascertained by Christie's, we find that the fair market value of each of the six bracelets was $ 31,190 as of the applicable valuation date; i.e., 24.76 percent greater than the higher estimated value of $ 25,000 for item number 293 ($ 25,000 + ($ 25,000 x .2519) = $ 31,190). We find accordingly that the fair market values of these six diamond tennis bracelets totaled $ 187,140 as of the applicable valuation date ($ 31,190 x 6 = $ 187,140).ii. Ruby/SapphireThe decedent owned a sapphire bracelet that was part of the set that included the seized sapphire necklace and the seized sapphire ring. The decedent owned a ruby bracelet that was part of the set that included the seized ruby necklace and the seized ruby ring. We find that the decedent retained ownership of these bracelets at his death.We decide that the fair market2004 Tax Ct. Memo LEXIS 31">*113  value of each of these bracelets was the same as the fair market value of the matching necklace. 41 Thus, we find that the fair market value of the sapphire bracelet was $ 4,400 as of the applicable valuation date; i.e., the same fair market value that we find for the sapphire necklace listed as item 2d in the appendices. We find that the fair market value of the ruby bracelet was $ 5,800 as of the applicable valuation date; i.e., the same fair market value that we find for the ruby necklace listed as item 2e in the appendices.k. NecklacesRespondent seized seven necklaces from the safe deposit box. The receipts from Lloyds establish that the decedent purchased six other necklaces which were not seized by respondent. The May 4, 1988, receipt indicates that the decedent purchased on that date a diamond necklace, a sapphire necklace, and a ruby necklace. Testimony establishes that the diamonds on the diamond necklace were all2004 Tax Ct. Memo LEXIS 31">*114  the same size and were set in yellow gold. The May 5, 1988, receipt indicates that the decedent purchased on that date a necklace with a 26.73-ct. diamond. The December 5, 1988, receipt indicates that the decedent purchased on that date an 11-millimeter-wide, 30-inch-long turquoise necklace and a necklace with graduated diamonds weighing 30.02 carats. Testimony establishes that the diamonds on the graduated necklace sloped down in size to one carat on the front stones and were set in white gold with yellow gold on the bottom. We find that the decedent retained ownership of these six unseized necklaces at his death.i. Diamond Necklaces of May 4, 1988As to the three necklaces purchased on May 4, 1988, the May 4, 1988, receipt shows that the decedent paid a bulk price of $ 235,000 for 26 items. Included in those items are ivory, a diamond necklace, a sapphire necklace, a ruby necklace, a ruby ring, a sapphire ring, and a faint blue masterpiece 4.39-ct. diamond. We apportion the $ 235,000 sales price among these categories in the following manner.First, we apportion $ 75,000 to the ivory. Exclusive of the ivory, the May 4, 1988, receipt lists six items. We conclude that the remaining2004 Tax Ct. Memo LEXIS 31">*115  20 items referenced in the receipt were pieces of ivory that are included within the ivory shown on the receipt in the categories "erotic giga", "Wise mens", "Erotic", or "40 tall 3 figure". On the basis of our decision supra pp. 51-52 that $ 3,750 was a reasonable amount to attribute to each piece of ivory, we conclude that the fair market value of the ivory referenced in this receipt totals $ 75,000 (20 x $ 3,750). Second, we apportion $ 106,680 to the 4.39-ct. diamond to reflect our valuation of that diamond supra pp. 58-59. Third, we decide that the balance of $ 53,320 ($ 235,000 - ($ 75,000 + $ 106,680)) was attributable to the remaining three necklaces and two rings. We apportion the $ 53,320 to those items using a weighing process under which we decide (following, in part, our examination and comparison of the appraised values of the necklaces and rings shown in appendix A) that each of the necklaces was worth the same amount and that each of the rings was worth 1/2 of the value of a necklace. 42 As we did similarly above, we assign a weight of two to each of the three necklaces and a weight of one to each of the two rings. In that the sum of these weights totals eight (22004 Tax Ct. Memo LEXIS 31">*116  + 2 + 2 + 1 + 1 = 8), we apportion 2/8 of $ 53,320 to each of the three necklaces (2/8 x $ 53,320 = $ 13,330) and 1/8 of $ 53,320 to each of the two rings (1/8 x $ 53,320 = $ 6,665).43 We find accordingly that the fair market value of each of the three necklaces shown on the May 4, 1988, receipt was $ 13,330 as of the applicable valuation date.2004 Tax Ct. Memo LEXIS 31">*117  ii. Diamond Necklaces of May 5, 1988On May 5, 1988, the decedent purchased from Lloyds an 18- kt. gold necklace with a 26.73-ct. diamond. The receipt for that item reported that its price was $ 74,000. We find that the fair market value of this necklace was the same as of the applicable valuation date.     iii. Turquoise and Diamond Necklaces of December 5,        1988We find that the fair market value of the turquoise necklace was $ 21,250 as of the applicable valuation date. Lloyds gave the turquoise necklace and a wall of ivory art piece to the decedent in exchange for netsukes. The May 4, 1989, Lloyds's receipt reports that the decedent on that date bought from Lloyds other netsukes worth $ 25,000, 44 and we find supra p. 52 that the decedent also paid $ 25,000 for still other netsukes on December 5, 1988. We decide on the basis of these receipts that the value of the exchanged netsukes referenced as item one on the December 5, 1988, receipt also was $ 25,000. Having decided above that the value of each ivory item was $ 3,750, we apportion the $ 21,250 difference between $ 25,000 and $ 3,750 to the turquoise necklace.2004 Tax Ct. Memo LEXIS 31">*118  As to the necklace with graduated diamonds weighing 30.02 carats, we find that the fair market value of this necklace was $ 66,404 as of the applicable valuation date. On the basis of our review of the pictures and descriptions of items displayed in the auction catalogue, we decide that item numbers 295 and 299 shown therein were proper measures of the fair market value of the graduated-diamond necklace in question. Item number 295 was a 16 3/4- inch platinum necklace set with 55 graduated heart-shape diamonds with a total weight of approximately 60.5 carats. Christie's estimated that this necklace would sell at auction for $ 120,000 to $ 150,000. Item number 299 was a 16-inch platinum necklace set with 80 graduated oval-cut diamonds with a total weight of approximately 48 carats. Christie's estimated that this necklace would sell at auction for $ 70,000 to $ 90,000. We valued the six seized assets which did not sell at auction at the values as appraised by Carmona. Carmona's total appraised value for the five items of jewelry which did not sell at auction was approximately the same as the total of the upper estimated values for those items as ascertained by Christie's. We decide2004 Tax Ct. Memo LEXIS 31">*119  in the case of the graduated-diamond necklace in question that its applicable fair market value equals the average of the estimated highest values of item numbers 295 and 299, as adjusted to reflect the fact that the graduated-diamond necklace in question had only 30.02 carats of diamonds. In other words, we average the two highest estimated values (($ 150,000 + $ 90,000)/2 = $ 120,000), divide the average value by the average carat weight of item numbers 295 and 299 ((60.5 + 48)/2 = 54.25; $ 120,000/54.25 = $ 2,211.9816), and multiply the resulting amount by 30.02 ($ 2,211.9816 x 30.02 = $ 66,404).        l. Rings          i. Man's Diamond Pinkie RingThe decedent wore a "pinkie ring" with a noticeable diamond in it. We find that the decedent retained ownership of this pinkie ring at his death. The receipts from Lloyds and Mamiye do not list any diamond that was purchased by the decedent that was less than one carat. We decide that the decedent's pinkie ring had a diamond weighing at least one carat and value that ring as if it had a one-ct. diamond in it. Consistent with our valuation of the one- ct. diamonds in the decedent's diamond2004 Tax Ct. Memo LEXIS 31">*120  tennis bracelet that we valued supra pp. 63-64 at $ 108,000, we decide that the one-ct. diamond in the pinkie ring had an applicable fair market value of $ 4,500. We find that the fair market value of the decedent's pinkie ring was $ 4,500 as of the applicable valuation date.          ii. Other High Quality Man's Diamond RingThe decedent owned a man's ring with a high quality three- to four-ct. diamond in it. We find that the decedent retained ownership of this ring at his death. On the basis of the average of the range of the size of the diamond (i.e., we view the diamond as weighing 3.5 carats), and the fact that a 3.5-ct. diamond weighs 250 percent more than a 1-ct. diamond ((3.5 - 1)/1 = 2.5), we find that the fair market value of the decedent's three-to four-ct. diamond ring was 250 percent more than the value of the 1-ct. pinkie ring. In other words, we find that the fair market value of the decedent's three-to four-ct. diamond ring was $ 15,750 as of the applicable valuation date ($ 4,500 + ($ 4,500 x 2.5) = $ 15,750).          iii. Ruby RingAs discussed above, the May 4, 1988, receipt from Lloyds shows that the decedent2004 Tax Ct. Memo LEXIS 31">*121  purchased a ruby ring as one of 26 items purchased for a bulk price of $ 235,000. We find that the decedent retained ownership of this ruby ring at his death. On the basis of our finding supra p. 68 that $ 6,665 of that price was attributable to the ruby ring, we find that the fair market value of that ring was $ 6,665 as of the applicable valuation date.          iv. Sapphire RingAs discussed above, the May 4, 1988, receipt from Lloyds shows that the decedent purchased a sapphire ring as one of 26 items purchased for a bulk price of $ 235,000. We find that the decedent retained ownership of this ring at his death. On the basis of our finding supra p. 68 that $ 6,665 of that price was attributable to the sapphire ring, we find that the fair market value of that ring was $ 6,665 as of the applicable valuation date.        m. EarringsRespondent did not seize any earrings from the safe deposit box. The December 5, 1988, receipt from Lloyds shows that the decedent had purchased on that day a pair of diamond stud earrings. We find that the decedent retained ownership of these earrings at his death.Consistent with our valuation of the decedent's2004 Tax Ct. Memo LEXIS 31">*122  pinkie ring, we decide that each of the earrings had a one-ct. diamond and that each of these diamonds had an applicable fair market value of $ 4,500. We find that the fair market value of the earrings was $ 9,000 as of the applicable valuation date.        n. Tie TackIn addition to the 1-ct. diamond tie tack that was seized by respondent from the safe deposit box, the decedent owned a tie tack with a three to four-ct. diamond. We find that the decedent retained ownership of this tie tack at his death. On the basis of our finding that the decedent's man's ring with a three to four-ct. diamond had a fair market value of $ 15,750 as of the applicable valuation date, we find that this tie tack, which had a similar size diamond, had a fair market value of $ 15,750 as of the applicable valuation date.        o. PinsThe decedent owned a sapphire pin that matched the sapphire bracelet valued above and the seized items consisting of the sapphire necklace and the sapphire ring. The decedent owned a ruby pin that matched the ruby bracelet valued above and the seized items consisting of the ruby necklace and the ruby ring. We find that the decedent2004 Tax Ct. Memo LEXIS 31">*123  retained ownership of these pins at his death.We decide that the fair market values of these sapphire and ruby pins were the same as the fair market values of the sapphire bracelet and the ruby bracelet, respectively. 45 We find supra p. 65 that the fair market value of the sapphire bracelet was $ 4,400 as of the applicable valuation date. We find supra pp. 65-66 that the fair market value of the ruby bracelet was $ 5,800 as of the applicable valuation date. Accordingly, we find that the fair market values of the sapphire and ruby pins were $ 4,400 and $ 5,800, respectively, as of the applicable valuation date.        p. PendantsThe May 5, 1988, receipt from Lloyds shows that the decedent purchased six items from Lloyds at a cost of $ 235,000. Two of these items were a sapphire pendant with round diamonds and an 18- kt. gold, ruby, and diamond pendant. The receipt indicates that the prices of those2004 Tax Ct. Memo LEXIS 31">*124  pendants were $ 15,000 and $ 18,400, respectively. 46 We find that the decedent retained ownership of these pendants at his death.We find that the fair market values of the sapphire and diamond pendant, on the one hand, and the 18 kt. gold, ruby, and diamond pendant, on the other hand, were $ 15,000 and $ 18,400, respectively, as of the applicable valuation date.        q. FurnitureThe coexecutors valued the2004 Tax Ct. Memo LEXIS 31">*125  decedent's dining room set at $ 1,100 ($ 800 + $ 300). We value it supra pp. 41-42 at $ 17,662. They valued his curio cabinets at $ 1,500. We value these cabinets supra pp. 41-42 at $ 8,831. They valued his Ming chair at $ 50. We value it supra pp. 41-42 at $ 2,208. The sum of these three items as valued by us, on the one hand, and by the coexecutors, on the other hand, is $ 28,701 ($ 17,662 + $ 8,831 + $ 2,208) and $ 2,650 ($ 1,100 + $ 1,500 + $ 50), respectively. We find as to these items that the coexecutors failed to report value of $ 26,051 ($ 28,701 - $ 2,650).II. Present Value Formulae and Discount Rate of Four Percent   A. OverviewIn Trompeter I, we decided the applicable fair market value of the series A preferred stock includable in the taxable estate. We detailed our valuation methodology but did not identify with specificity the present value formulae which were a part thereof. Nor did we state with specificity the reasons behind our use of a 4-percent discount rate. The Court of Appeals for the Ninth Circuit remanded this case to us to specify that formulae and to document the reasons for using the 4-percent rate.   B. Present Value Formulae2004 Tax Ct. Memo LEXIS 31">*126       1. Redemption Value of Series A Preferred StockThe certificate of designation underlying the series A preferred stock (certificate of designation) 47 required that Sterling redeem 1,000 shares of that stock on each December 31, 1993 through 1995. For each of those dates, we calculated in Trompeter I the amount of the redemption payment payable under the certificate of designation for the decedent's series A preferred stock using the following formula: P x (1 + i/n)y. In this context, "P" equals the 511.161 shares of the decedent's series A preferred stock required to be redeemed on December 31, 1993, 1994, or 1995, multiplied by the liquidation value of each redeemed share at the beginning of the applicable year; "i" equals the annual dividend rate; "n" equals the total number of days in the year; and "y" equals the number of days in a year over which dividends were compounded. 482004 Tax Ct. Memo LEXIS 31">*128  Preferential dividends accrued daily on each share of series A preferred stock at the annual rate of 8.5 percent during 1989, 9.83 percent during 1990, 11.17 percent during 1991, and 12.5 percent during 1992 and at all times thereafter until the share was either redeemed or exchanged. 492004 Tax Ct. Memo LEXIS 31">*127  Our methodology in Trompeter I reflected our finding that holders of series A preferred stock were entitled to receive dividends not simply at an annual rate of 8.5-, 9.83-, 11.17-, or 12.5-percent, but at those rates as adjusted to reflect daily compounding.Upon remand, we have redetermined that dividends were payable at the annual rates without compounding. In other words, the amount of dividends payable on a share of series A preferred stock was ascertained for each year simply by multiplying the applicable dividend rate by that share's liquidation value. 50 As of each December 31, the liquidation value of a share of series A preferred stock equaled its face value ($ 1,000) plus all preferential dividends that had not been paid as of the most recent January 15. Thus, assuming as we did in Trompeter I that the series A preferred stock was issued on March 15, 1989, the liquidation values of each share of that stock on Dec. 31, 1989, 1990, 1991, 1992, 1993, 1994, and 1995 (assuming that the share had not been redeemed, exchanged, or had dividends paid2004 Tax Ct. Memo LEXIS 31">*129  with respect thereto) were $ 1,000, $ 1,071.8068, $ 1,170.9871, $ 1,302.4101, $ 1,512.0629, $ 1,701.0708, and $ 1,913.7047, respectively. The following accrued dividends which were not included in the liquidation value were also payable on each of those shares as of those respective dates: $ 67.7671, $ 94.2603, $ 125.424, $ 156.1291, $ 181.2404, $ 203.8955, and $ 229.3824. Thus, as of December 31, 1993, 1994, and 1995, respectively, the redemption payments payable under the certificate of designation for the decedent's series A preferred stock were as follows:2004 Tax Ct. Memo LEXIS 31">*130         ($ 1,512.0629 + $ 181.2404) x 511.161 = $ 865,550.60        ($ 1,701.0708 + $ 203.8955) x 511.161 = $ 973,744.47        ($ 1,913.7047 + $ 229.3824) x 511.161 = $ 1,095,462.50   2. Discounted AmountsIn Trompeter I, we used the following formula to discount each of the redemption payments as of the applicable valuation date: P x (1 + i/n)-y. In this context, "P" equals the value of the series A preferred stock at the time of redemption (i.e., its liquidation value plus any unpaid accrued dividends not included in the liquidation value); "i" equals the discount rate; "n" equals the total number of days in the year; and "y" equals the total number of days over which the discount is compounded. In other words, we used in Trompeter I the basic formula for computing present value in the case of interest that is compounded annually, see generally Thorndike's Compound Interest and Annuity Tables 19 (1982), as adjusted to reflect our belief that the discount rate should be compounded daily consistent with our determination of the redemption payments. Now, consistent with our redetermination that the payment of dividends2004 Tax Ct. Memo LEXIS 31">*131  is compounded annually rather than daily, we modify our discount formula by deleting the "n" and using "y" to refer to a fraction the numerator of which is the total number of days over which the discount is compounded and the denominator of which is 365.C. 4 Percent Discount RateIn Trompeter I, we applied in our methodology a 4-percent discount rate to ascertain the discounted value on September 18, 1992, of each of the redemption payments which Sterling was obligated to pay as of the three referenced dates after September 18, 1992. The Court of Appeals for the Ninth Circuit questioned whether a 4-percent discount rate accurately reflects the risk that Sterling would not have redeemed its series A preferred stock as required by the certificate of designation. According to the Court of Appeals for the Ninth Circuit: "it seems a bit of a stretch to conclude that a buyer would have accepted a discount rate of only four percent to account for the time value of money and the risk that Sterling would not meet its contractual obligations." 2004 Tax Ct. Memo LEXIS 31">*132  Estate of Trompeter v. Commissioner, 279 F.3d 767">279 F.3d 767, 279 F.3d 767">773 (9th Cir. 2002) (emphasis added), vacating and remanding T.C. Memo. 1998-35, supplemented by 111 T.C. 57">111 T.C. 57 (1998).Our 4-percent discount rate did not reflect the risk that Sterling would fail to meet its contractual obligations but reflected only the time value of money; i.e., the fact that one dollar to be received in the future is not worth one dollar today. We believe that a 4-percent rate is a reasonable indicator of the time value of money as of the applicable valuation date. The T-bill rate was 2.954 for the week of September 14, 1992, and it was 2.9740 for the week of September 21, 1992. The annualized inflation rate was 2.99 percent for September 1992.As to the risk that Sterling would not meet its contractual obligation to redeem its series A preferred stock, we believe that a hypothetical buyer would have demanded minimal additional compensation to accept such a risk under the facts herein. Pursuant to the certificate of designation, the hypothetical buyer was already entitled to compensation for that risk in that, in the event of a default, dividends would continue to accrue2004 Tax Ct. Memo LEXIS 31">*133  daily at the annual rate of 12.5 percent on any share of series A preferred stock that was not redeemed. The hypothetical buyer also was deemed to know on the applicable valuation date that Sterling and its subsidiaries, with the consent of their creditors, had recently restructured certain of their debt and had issued additional equity so as not to default on debt and so that Sterling could redeem some of its other shares of stock. 51 Specifically, on June 29, 1989, Sterling replaced $ 1.5 million of senior subordinated notes with $ 2,450,000 of senior subordinated notes, TEI and QCI replaced $ 9 million of subordinated notes with $ 9 million of subordinated notes, and Sterling issued $ 181,452 of 1-year promissory notes. Sterling also on that date had issued 840,055 shares of class A common stock and 1,209,945 shares of class B common stock for an aggregate amount of $ 200,000 and had redeemed 550 shares of series S convertible preferred stock (series S preferred stock) and 1,500 shares of series T convertible preferred stock (series T preferred stock) at stated liquidation values totaling $ 102,500. We believe that a hypothetical buyer would have concluded on the applicable valuation2004 Tax Ct. Memo LEXIS 31">*134  date that Sterling was mindful of its contractual obligations both as to debt and as to equity and that Sterling would go to great lengths not to breach its contractual obligations, including its obligation to redeem its series A preferred stock timely.The decedent's shares of series A preferred stock also were part of Sterling's senior class of stock. Sterling had issued 3,000 shares of that stock to the decedent and his former wife in March 1989 in acquisition of TEI. The 3,000 shares were the only shares of series A preferred stock issued by Sterling, and holders of those2004 Tax Ct. Memo LEXIS 31">*135  share were generally entitled to more rights than holders of Sterling's other stock. As of the applicable valuation date, Sterling's other outstanding preferred shares consisted of 25,000 shares of series C exchangeable preferred stock, 5,450 shares of series S preferred stock, and 1,000 shares of series T preferred stock. Each share of these other classes of preferred stock accrued dividends whether or not declared, but holders of those shares (as well as holders of Sterling common shares) were generally precluded from receiving dividends or distributions as to their shares before the vested rights of the holders of series A preferred stock were satisfied in full. Accordingly, after the dates of the scheduled redemptions for the series A preferred stock, Sterling would need first to honor its redemption obligation before it could satisfy the requirements of its other shareholders.Although Sterling was prohibited by its senior debt and senior subsidiary debt agreements from redeeming any of its stock or paying any dividends on its stock in certain circumstances, we do not believe that a hypothetical buyer would have considered these agreements to have prevented Sterling from redeeming2004 Tax Ct. Memo LEXIS 31">*136  its series A preferred stock timely. In appendix C, we list on a consolidated basis Sterling's debt as of December 31, 1989 through 1992. The relevant provisions underlying this debt generally tied a redemption to Sterling's profitability. As of the applicable valuation date, Sterling was a viable entity that had a positive cashflow for that and the previous 2 years. Although it had reported losses for 1991 and 1992, those losses were attributable primarily to its amortization of intangible assets and deferred financing costs (the 1992 loss also was attributable to a one-time writeoff of $ 2,953,646), and it had reported significant net income for 1992. It also was timely paying interest and principal on its senior debt, and it had recently restructured its debt and equity as discussed supra pp. 81-82 so as not to default on debt and to redeem other preferred shares.In addition to the risk that Sterling would not redeem its series A preferred stock timely, however, is the risk that Sterling would not redeem its series A preferred stock for the contractual amount referenced in the certificate of designation but would redeem those shares at a lesser amount. 52 We did not take this2004 Tax Ct. Memo LEXIS 31">*137  risk into account in Trompeter I. Upon remand, we now believe that our 4- percent discount rate undercompensated the hypothetical buyer for this risk. In lieu of the 4-percent discount rate that we applied in Trompeter I, we now believe on the basis of the record before us that the more appropriate rate is an annual rate of 12.5 percent. This 12.5-percent rate is approximately three times the 4-percent rate that we believe reflects the time value of money and, as discussed above, is the same rate at which a holder of series A preferred stock would be compensated following an untimely redemption. A 12.5-percent rate also approximates the rate that as of the applicable valuation date was payable on the series B subordinated debentures, the debt into which the series A preferred stock was convertible, and is 5 percentage points greater than the rate that was payable on the senior term notes as of December 31, 1992. 532004 Tax Ct. Memo LEXIS 31">*138 The estate asserts on remand that we should determine the fair market value of the series A preferred stock by applying a 20- percent discount rate to the $ 1,947,845 actually paid to redeem the decedent's shares. We disagree. In addition to the fact that the estate's proffered rate does not take into account our finding that a holder of series A preferred stock would following a missed redemption be entitled to daily dividends at a 12.5-percent annual rate, the estate's rate ignores the solid history of Sterling in honoring its contractual obligations. We also are unpersuaded by the record before us that a rate approximately seven times the referenced T-bill and inflation rates is appropriate in this case, let alone that we should apply the discount rate to the amount actually paid for the stock after the applicable valuation date.2004 Tax Ct. Memo LEXIS 31">*139  Nor do we agree with the estate's assertion on remand that we should discount our redetermined value to take into account a lack of marketability for the series A preferred stock. The estate relies upon its expert, Herbert T. Spiro (Spiro), who testified in Trompeter I that the freely traded value of the decedent's series A preferred stock should be adjusted for lack of marketability. The estate's reliance on this testimony is misplaced. Spiro opined that the "freely traded value" of the decedent's shares should be discounted for lack of marketability, and our methodology does not determine the freely traded value of those shares. Where as here the value determined for shares of stock is not the freely traded value of those shares, a lack of marketability discount is inappropriate. As we noted in  Estate of Cloutier v. Commissioner, T.C. Memo. 1996-49, in rejecting a similar assertion, a marketability discount generally represents the additional price that an unlisted share would command if it were freely traded. We held in Estate of Cloutier that a marketability discount did not apply to the stipulated value of the company in question because that value was not representative2004 Tax Ct. Memo LEXIS 31">*140  of the company's freely traded value. Id.We use our modified formula with the 12.5-percent discount rate to calculate the discounted values of the December 31, 1993, 1994, and 1995, payments as follows:       $ 865,550.60 x (1 + .125)-47470/365 = $ 743,746.32  $ 973,744.47 x (1 + .125)-835/365 = $ 743,746.36  $ 1,095,462.50 x (1 + .125)-1200/365 = $ 743,746.53We conclude that the sum of these discounted values, $ 2,231,239.21, is the applicable fair market value of the decedent's series A preferred stock. 54III. Determination of Fraud in Trompeter IPursuant to the direction of the Court of Appeals for the Ninth Circuit, we have set forth in detail our findings as to the omitted assets. Our ultimate finding that the value of these assets totals $ 4.52004 Tax Ct. Memo LEXIS 31">*141  million is the same as in Trompeter I. We also have clarified our reasoning as to the valuation methodology that we applied in Trompeter I. We continue to adhere to that methodology. Although we have now slightly modified it to compound the dividends annually, rather than daily, and to recognize the need for an increase in the discount rate to an amount greater than 4 percent, neither of these modifications changes the decision that we entered on March 18, 1999.Pursuant to the direction of the Court of Appeals for the Ninth Circuit, we now consider whether it is appropriate to revisit our conclusions as to fraud. We do not believe it is. Although the Court of Appeals for the Ninth Circuit has not asked us to restate the legal basis for our finding of fraud, and thus we do not, we emphasize our belief that the coexecutors' willing and conscious failure to disclose to respondent the assets of the estate, coupled with their deliberate undervaluation of some of the assets which were disclosed to respondent, constitutes clear and convincing evidence of fraud deserving of the section 6663 penalty.Decision will be entered as previously entered on Mar. 18, 1999.      2004 Tax Ct. Memo LEXIS 31">*142           APPENDIX A                       Appraised   Auction                       Value     Price   Description of Jewelry   2a. Lady's 18 kt. yellow gold,sapphire and diamond ring: The ringweighs 7.7 grams and has 27 2.5 to 3 mm.square cut natural sapphires, totalweight (TW) approx. 3.1 ct., medium-darkslightly grayish-blue, flawless to theunaided eye, and 18 2 mm. square cutdiamonds, TW apx. .7 ct., "F-G" colorrange, "VS" clarity range, good cuts.The sapphires are invisibly set in threerows across the center of the ring withone row of channel set diamonds on eachedge.                       $ 1,500  $ 1,800   2b. Woman's 18 kt. yellow gold,ruby, and diamond ring (same mounting asin 2a, but with rubies instead ofsapphires): The ring weighs 7.6 gramsand has 27 2.5 to 3 mm. square cutnatural rubies, TW apx. 3.1 ct., mediumred, lightly included to the unaided eye,and 18 2 mm. square cut diamonds, TW apx..70 ct., F-G/VS (avg.), good cuts. Therubies are invisibly2004 Tax Ct. Memo LEXIS 31">*143  set in three rowsacross the center of the ring with onerow of channel set diamonds on each edge.      1,800   1,800   2c. Man's 14 kt. yellow gold anddiamond ring: The geometric ribbeddesign ring weighs 13.1 grams and has(set in 4 posts in the center) one roundbrilliant cut (RBC) diamond, apx. 3.6 ct.(apx. 10 x 5.8 mm.), "E-F-G" color range,"VS" clarity range (based on a cluster ofincluded crystals in the center of thetable), depth apx. 58%, table apx. 66%,good symmetry and polish. Channel set oneach side of the center are 4 full cutround diamonds (total of 8), apx. .06 to.07 ct. each, TW apx. .50ct., G-H/SI-I1(avg.), good cuts.                 37,500   20,000   2d. Woman's 18 kt. yellow gold,sapphire, and diamond necklace: Thepanther link chain with inverted leafcenter is 16" long by 6.3 mm. wide andweighs 44.8 grams, clasp stamped 18KPATPEND milor", back of leaf stamped18kt". The leaf has 100 square andcustom cut natural sapphires (62 are apx.2.5 mm. square), TW apx. 10.0 ct.,medium-dark slightly grayish-blue,flawless to the unaided eye, and 65 fullcut round (FC) diamonds,2004 Tax Ct. Memo LEXIS 31">*144  TW apx. 1.5 ct.,F-G/VS (avg.). The sapphires areinvisibly set in the center with a borderof channel set diamonds and a stem ofbead set diamonds.                 4,000   ---   2e. Woman's 18 kt. yellow gold,ruby, and diamond necklace: The pantherlink chain with inverted leaf center is16" long by 6.3mm. wide and weighs 42.5grams, clasp stamped "18KTPATPEND milor".The leaf has 141 square and custom cutnatural Rubies (118 are apx. 2.5 mm.square), TW apx. 15.5 ct., mediumslightly purplish-red, lightly includedto the unaided eye, and 18 square cutdiamonds, TW apx. .72 ct., F-G/VS (avg.).The rubies are invisibly set with acentral stem of channel set diamonds.        5,800   ---   2f. One 14 kt. yellow gold anddiamond tie tack: The 6-prong mountingweighs .9 grams and has one RBC diamond,apx. 1.02 ct., E-F-G/VS, good symmetryand polish.                     5,400   4,500   2g. One cultured pearl necklacewith 14 kt. white gold clasp: The 24"uniform strand has 75 7 to 7.5 mm. roundcultured pearls, cream white color, lowluster, slightly2004 Tax Ct. Memo LEXIS 31">*145  blemished, with afishhook clasp.                    400   ---   2h. Woman's 18 kt. yellow gold anddiamond necklace: The drop necklace is18" long, weighs 93.6 grams, is stamped"18kt" with a <<small "D" inside a large<para>"L"> hallmark, and has one pear shapebrilliant cut diamond, apx. 8.69 ct.(19.5 x 12.5 x 7.2 mm.), light browncolor, "I-1" clarity (feather on lowerleft), 61 baguette diamonds, TW apx. 4.75ct., F-G-H/VS-SI (avg.), good cuts, and440 FC diamonds, TW apx. 13.02 ct. F-GH/VS-SI (avg.), good cuts. The pearshape diamond is bezel set in the dropand surrounded by channel set baguetteand bead set round diamonds. Thenecklace portion also has channel setbaguette and bead set round diamonds.       44,000   32,000   2i. Woman's 18 kt. yellow gold,emerald and diamond necklace: Thenecklace is 16--1/2" long, weighs 93.6grams, is stamped "18k" with the "LD"hallmark, and has one emerald cut naturalemerald, apx. 6.48 ct. (13.7 x 9.8 x 6.8mm.), medium slightly bluish-green,moderately included, and 245 baguette cutdiamonds, apx. .08 to .25 ct. each, TWapx. 32.50 ct., 2004 Tax Ct. Memo LEXIS 31">*146  F-G-H/VVS-VS (avg.), goodcuts. The emerald is 4-prong set in thecenter with pairs and single diamondsprong set in fringe style links.       56,000 19,000   2j. Woman's 18 kt. yellow gold,emerald, and diamond necklace: Thenecklace is 17" long, weighs 97.5 grams,is stamped "18ktK" with the "LD"hallmark, and has one heart shape naturalemerald, apx. 6.07 ct. (13.5 x 12.5 x 6.4mm.), medium slightly bluish-green,moderately included, 176 diamonds, TWapx. 5.22 ct., and 94 baguette cutdiamonds, TW apx. 5.22 ct., F-G-H/VVS-VS(avg.), good cuts. The emerald is bezelset in the center and surrounded bychannel set baguette diamonds and beadset round diamonds.                19,000   ---   2k. Woman's 18 kt. yellow and whitegold, opal, and diamond pin/pendantcombination with treated opal necklace:The necklace is 23" long with 42 - 10.3mm. round very dark brown color opalbeads and six 11 to 11.5 mm. round whiteopal beads with faint play of color. Thedark beads have been treated by animpregnation process to give them theappearance of black opals. The drop hasa leafy design yellow2004 Tax Ct. Memo LEXIS 31">*147  gold frame around acenter removable white gold frame withone oval cabochon cut natural semi-blackopal with moderate green/blue pay-of-color,apx. 30 ct. (38 x 26 x 5.5 mm.),20 marquise cut diamonds, TW apx. 1.8ct., H-M/VS (avg.), and 28 baguette cutdiamonds, TW apx. 1.1 ct., H-I-J/VS(avg.). The opal is multi-prong set inthe center and surrounded by prong setdiamonds.                      7,600   ---                        _______   ______Total for 11 jewelry items            183,400   79,100   Description of Loose Gemstones   3a. One loose octagon cut diamond:The diamond weighs apx. 40.02 ct andmeasures apx. 21.3 x 17.7 x 11.85 mm.,fair to good symmetry and polish. Thediamond was subsequently graded on GIAreport #8812646 as fancy yellow naturalcolor, VS2 clarity.                460,000  220,000   3b. One loose round brilliant cutdiamond: The diamond weighs apx. 2.01ct. and measure apx. 7.98-8.1 x 5.02 mm.,good symmetry and polish. The diamond isaccompanied by a note of "I/IF"color/clarity2004 Tax Ct. Memo LEXIS 31">*148  and a notation of "GIA#517260". The stone appears to matchthis grading.                   15,000   7,500   3c. One loose round brilliant cutdiamond: The diamond weighs apx. 1.9 ct.and measures apx. 7.72-7.81 x 5.01 mm.,good symmetry and polish. The diamond isaccompanied by a note of "E/VS2"color/clarity and a notation of "GIA#5172800". The stone appears to matchthis grading.                   11,800   9,600   3d. One loose octagon shapediamond: The diamond weighs apx. 5.01ct. and measures apx. 9.6 x 8.61 x 6.22mm., good symmetry and polish. Thediamond is accompanied by an altered noteof "Intense Yellow/VS-2" and a notationof "GIA #5234002". The diamond wassubsequently graded on GIA report#8812648 as fancy yellow natural color,VS2 clarity.                      48,000   35,000   3e. One loose emerald cut diamond:The diamond weighs apx. 7.57 ct andmeasures apx. 13.12 x 9.46 x 6.65 mm.,good symmetry and polish. The diamondhas a note of "VVS-J(?)", but appears tohave a color grade in the range of "J-K"and2004 Tax Ct. Memo LEXIS 31">*149  in the clarity range of "VS".           48,000   30,000   3f. One loose round brilliant cutdiamond: The diamond weighs apx. 6.62 ctand measures apx. 12.18-12.2 x 7.28 mm.,good symmetry and polish. The diamondhas a note of "VS-1/N", but appears tohave a color grade in the range of "R-V"and in the clarity range of "VS".       21,500 20,000   3g. One loose heart shape diamond:The diamond weighs apx. 4.03 ct. andmeasures apx. 11.1 x 10.78 x 5.27 mm.,good symmetry and polish. The diamondhas a note of "SI-1/K", but appears tohave a color grade in the range of "J-K"and a clarity grade of "SI-1".       19,600 7,500   3h. One loose cushion shape naturalsapphire: The sapphire weighs apx. 18.2ct. and measures apx. 17.15 x 13.5 x 8.32mm., good symmetry and polish. The coloris medium-dark blue to violetish-blue andthe clarity is lightly included to theunaided eye.                    9,100   ---   3i. One loose square emerald cutdiamond: The diamond weighs apx. 11.13ct. and measures apx. 12.63 x 12.32 x 8.3mm., good symmetry and polish. 2004 Tax Ct. Memo LEXIS 31">*150  Thediamond has a note of "VVS-1/K", butappears to have a color grade in therange of "K-L" and in the clarity gradeof "VS".        59,000 44,000   3j. One loose round brilliant cutdiamond: The diamond weighs apx. 6.65ct. and measures apx. 12.5-12.59 x 7.13mm., good symmetry and polish. Thediamond has a note of "VS-1/N", butappears to have a color grade in therange of "Q-U" and in the clarity rangeof "VS".        22,000 24,000   3k. One loose round brilliant cutdiamond: The diamond weighs apx. 7.74ct. and measures apx. 13.42-13.45 x 7.28mm., good symmetry and polish. Thediamond has a note of "I-1/I-J" and itappears to match this grading.        35,800 27,000   3l. One loose octagon shapediamond: The diamond weighs apx. 18.28ct and measures apx. 15.67 x 15.66 x 8.65mm., good symmetry and polish. Thediamond is accompanied by a note of"Fancy Yellow/IF" color/clarity and "GIA#7085087." The stone appears to matchthis grading.                   210,000  210,000   3m. One loose round brilliant cutdiamond: The diamond weighs apx. 4.32ct. 2004 Tax Ct. Memo LEXIS 31">*151  and measures aprx. 10.41-10.51 x 6.3mm., good symmetry and polish. Thediamond is accompanied by a note of"Faint Blue/IF" color/clarity and "GIA#5117323." The diamond was subsequentlygraded on GIA report #8812982 as "E"color, "VVS1" clarity (and markedpotentially flawless).               97,000  105,000   3n. One loose emerald cut diamond:The diamond weighs apx. 3.35 ct. andmeasures apx. 10.01 x 7.5 x 4.84 mm.,good symmetry and polish. The diamondhas a note of "F/IF" color/clarity "GIA#5186298". The stone appears to matchthis grading.                   52,300   25,000                       _________  _______   Total for 14 loose gemstones        1,109,100  764,600                       _________  _______Total                      1,292,500  843,700               APPENDIX B                                 Carmona's   2004 Tax Ct. Memo LEXIS 31">*152               Estimated Value   Agreed   Auction AppraisedProperty Description       Lower    Upper   Reserve  Price   ValueSold at Auction   JewelryLady's 18-kt. yellow gold,invisibly-set sapphire,and channel-set diamondring (2a)            $ 2,000   $ 3,000 $ 1,800  $ 1,800  $ 1,500Lady's 18-kt. yellow gold,invisibly-set ruby, andchannel-set diamond ring(2b)               2,000    3,000   1,800   1,800   1,800Lady's 14-kt. yellow goldand diamond ring (2c)      15,000   20,000  13,500   20,000   37,50014-kt. yellow gold anddiamond tie tack (2f)       1,000    1,500    900   4,500   5,400Lady's 18-kt. yellow goldand diamond necklace (2h)    30,000   50,000  27,000   32,000   44,000Lady's 18-kt. yellow gold,emerald, and diamondnecklace (2i)          20,000   30,000  18,000   19,000   56,000               _______   ______  ______   ______   ______                70,000  2004 Tax Ct. Memo LEXIS 31">*153  107,500  63,000   79,100  146,200   Loose GemstonesLoose round brilliant-cutdiamond weighingapproximately 1.9 carats(3c)               8,000   10,000   7,200   9,600   11,800Loose round brilliant-cutdiamond weighingapproximately 2.01 carats(3b)               8,000   10,000   7,200   7,500   15,000Loose emerald-cut diamondweighing approximately3.35 carats (3n)         25,000   35,000  22,500   25,000   52,300Loose heart-shaped diamondweighing approximately4.03 carats (3g)         8,000   10,000   7,200   7,500   19,600Loose round brilliant-cutdiamond weighingapproximately 4.32 carats(3m)               35,000   45,000  31,500  105,000   97,000Loose octagon-shaped yellowdiamond weighingapproximately 5.01 carats(3d)               30,000   50,000  27,000   35,000   48,000Loose round brilliant-cutdiamond weighingapproximately 6.62 carats(3f)               18,000   22,000  16,200   20,000   21,500Loose2004 Tax Ct. Memo LEXIS 31">*154  round brilliant-cutdiamond weighingapproximately 6.65 carats(3j)               18,000   22,000  16,200   24,000   22,000Loose emerald diamondweighing approximately7.57 carats (3e)         28,000   32,000  25,200   30,000   48,000Loose round brilliant-cutdiamond weighingapproximately 7.74 carats(3k)               30,000   50,000  27,000   27,000   35,800Loose square emerald-cutdiamond weighingapproximately 11.13 carats(3i)               40,000   60,000  36,000   44,000   59,000Loose octagon-shapeddiamond weighingapproximately 18.28 carats(3l)              100,000   150,000  90,000  210,000  210,000Loose modified rectangular-cut light fancy yellowdiamond weighingapproximately 40.02 carats(3a)              140,000   160,000 126,000  220,000  460,000               _______   _______ _______  _______  _______               488,000   656,000 439,200  764,600 1,100,000       2004 Tax Ct. Memo LEXIS 31">*155          558,000   763,500 502,200  843,700 1,246,200Not Sold At Auction                            High Bid   JewelryLady's 18-kt. yellow gold,sapphire, and diamondleaf necklace (2d)        4,000    6,000   3,600  $ 2,800   4,400Lady's 18-kt. yellow gold,ruby, and diamond leafnecklace (2e)           5,000    7,000   4,500   3,800   5,800Cultured pearl necklacewith 14-kt. white goldfishhook clasp (2g)        1,000    1,500    900    650    400Lady's 18-kt. yellow gold,heart-shaped emerald,and diamond necklace (2j)    15,000   20,000  13,500    1 -0-   19,000Treated opal necklace with18-kt. yellow and whitegold, opal, and diamondpin/pendant (2k)         3,000    5,000   2,700   2,600   7,600               _______   _______ _______  _______  _______                28,000   39,500  25,200   9,850   37,200   Loose GemstoneLoose cushion-shaped naturalsapphire2004 Tax Ct. Memo LEXIS 31">*156  weighingapproximately 18.2 carats(3h)               14,000   16,000  12,600   10,000   9,100               _______   _______ _______  _______  _______                42,000   55,500  37,800   19,850   46,300Totals             600,000   819,000 540,000    --     --APPENDIX CConsolidated Debt Outstanding 1Senior term notes, due in quarterly installments through Dec. 28,1995 at lender's reference rate plus 1 1/2 percent (12%, 11.5%, 8%, and 7.5% at Dec. 31 of the respective years). Payment is secured by Sterling's assets (Dec. 31, 1991, book value of $ 25,683,252) and prepayments may be required if sufficient cashflow.2    1989     2004 Tax Ct. Memo LEXIS 31">*157  1990     1991     1992$ 20,075,000 $ 17,450,000 $ 14,075,000 $ 10,575,000Consolidated Debt Outstanding 1Senior subordinated notes, due in two equal installments at Dec. 15,1998 and 1999. Interest payments at 14 percent are due annually.Payment is unsecured and subject to the noted requirements of thesenior term notes.    1989     1990     1991     1992 2,450,000   2,450,000   2,450,000   2,450,000Consolidated Debt Outstanding 1Subordinated notes, due in three installments at Mar. 15, 1996, 1997,and 1998. Interest payments vary from 13.5 to 14.5 percent (14%, 14%,13,5%, and 13.5% at December 31 of the respective years) and are duequarterly. Payment is unsecured and subject to the noted requirementsof the senior term notes. The additional $ 175,000 of notes shown for1992 were issued on Oct. 23, 1992, as consideration for the holdersof the subordinated notes waiving and amending certain covenants.1989     1990     1991     1992 9,000,000   9,000,000   9,000,000   9,175,000Consolidated Debt Outstanding 1Series B2004 Tax Ct. Memo LEXIS 31">*158  subordinated debentures, due in three equal installments atDec. 31, 1993, 1994, and 1995. Interest payments are due annually atincremental rates, increasing from 8 percent in 1989 to 12 percent in1992 and thereafter. Payment is subject to the noted requirements ofthe senior term notes.1989     1990     1991     1992 1,428,000   1,428,000   1,428,000   1,428,000Consolidated Debt Outstanding 1Unsecured notes, due June 29, 1990. Interest at 14 percent increasingto 18 percent past the due date. Payment is subject to the notedrequirements of the senior debt. 1989     1990     1991     1992  181,452    181,452    181,452    181,452Consolidated Debt Outstanding 1Contractual obligation, discounted, secured by $ 400,000 series Bsubordinated debentures. 1989     1990     1991     1992  400,000    400,000    400,000    400,000Consolidated Debt Outstanding 1Unsecured notes payable, interest rates range from 11.25 to 12.5percent, due in monthly installments through Nov. 1994.2004 Tax Ct. Memo LEXIS 31">*159      1989     1990     1991     1992   18,853    22,013    15,770     -0-Consolidated Debt Outstanding 1Obligations under capital leases 1989     1990     1991     1992  509,866    140,722    21,084     -0-Consolidated Debt Outstanding 1Other1989     1990     1991     1992   -0-      -0-      -0-      8,716Consolidated Debt Outstanding 1Total long-term debt1989     1990     1991     199234,063,171  31,072,187  27,571,306  24,218,168Consolidated Debt Outstanding 1Less current portion1989     1990     1991     1992 2,942,325   3,671,964   3,709,589   3,921,015Consolidated Debt Outstanding 1Long-term debt less current portion1989     1990     1991     199231,120,846  27,400,223  23,861,717  20,297,1532004 Tax Ct. Memo LEXIS 31">*160 2004 Tax Ct. Memo LEXIS 31">*161   Footnotes*. This Supplemental Memorandum Opinion supplements our prior Memorandum Opinion in Estate of  Trompeter v. Commissioner, T.C. Memo. 1998-35, supplemented by 111 T.C. 57">111 T.C. 57 (1998), vacated and remanded 279 F.3d 767">279 F.3d 767↩ (9th Cir. 2002).1. Rule references are to the Tax Court Rules of Practice and Procedure. Unless otherwise indicated, section references are to the applicable versions of the Internal Revenue Code.↩2. We also in our analysis set forth various calculations underlying our findings and our Supplemental Memorandum Opinion. We round the results of those calculations as appropriate.↩3. The estate's Federal estate tax return did not report that the decedent owned at his death any jewelry or loose gemstones. Nor were either of those items reported as a gift on any of the gift tax returns filed by or on behalf of the decedent, his trust, or the estate. The estate's Federal estate tax return also did not report that the decedent owned at his death a significant amount of jade, ivory, Chinese artifacts, or rugs. The coexecutors reported on the estate's Federal estate tax return that the value of the decedent's collection of ivory, jade, rugs, and other collectibles totaled $ 39,065.↩4. The fact that the buyer was liable for the 10-percent commission on $ 20 million means that the buyer would need to pay $ 22 million for the specified items in order for Pasko to collect his $ 2 million commission.↩5. The purchasers of the items auctioned by Christie's bought those items "as is".↩6. The coexecutors elected to have the estate valued as of the alternate valuation date of sec. 2032(a). Thus, the applicable valuation date is generally Sept. 18, 1992. See generally sec. 20.2031-1(b), Estate Tax Regs. ("The value of every item of property includible in a decedent's gross estate under sections 2031 through 2044 is its fair market value at the time of the decedent's death, except that if the executor elects the alternate valuation method under section 2032↩, it is the fair market value thereof at the date, and with the adjustments, prescribed in that section.").7. Carmona noted in his report that "the [25] items listed have been examined and researched to the best of my ability, but not under ideal conditions (cramped quarters, time constraints, artificial light)." When Carmona examined the 11 items of jewelry included within the 25 seized assets, he observed that most of those items still had tags on them and that none of the items showed any signs of wear.↩8. We provide below a brief description of the 25 seized assets and list in parenthesis at the end of each description the number and letter that corresponds to Carmona's specific description in appendix A.↩1. As discussed below, Polachek used the term 'Baker's" to describe three tables which she removed from the decedent's home. We understand from this reference that these tables were manufactured by Baker's furniture, Inc., and refer to the tables as 'Baker's tables".↩2. We round this number to $ 4.5 million.↩9. The descriptions of the assets in appendix B also are cross-referenced to the specific descriptions in Carmona's report by way of the number and letter in the parenthesis following the description.↩10. We note that $ 148,312.50 is 87.5 percent greater than $ 79,100 (($ 148,312.50 - $ 79,100)/$ 79,100) and that the 25- and 50-percent minimum markups referenced by Carmona translate into a single 87.5-percent markup (.25 + (.50 + (.25 x .50)) = .875).↩11. As to the total auction price of $ 764,600 paid for the 13 loose gemstones, $ 379,600 was subject to a 15-percent commission and $ 385,000 was subject to a 10-percent commission (($ 379,600 x .15) + ($ 385,000 x .10) = $ 95,440).↩12. The decedent's guns (approximately 10) were not as valuable as the other assets which he collected.↩13. When the decedent died, Gonzalez and Polachek were 38 and 33 years old, respectively.↩1. A netsuke (the plural of which is netsuke or netsukes, not netsukie) is "a small and often intricately carved toggle (as of wood, ivory, or metal) used to fasten a small container to a kimono sash". Merriam-Webster's Collegiate Dictionary 780 (10thed. 1999). We understand the decedent to have received the referenced turquoise necklace and wall of ivory art piece in exchange fornetsukes and not as consideration for any of the $ 276,000 purchase price related to the receipts of Dec. 5, 1988.↩1. "Ceylon" was the former name of Sri Lanka. Merriam-Webster's Collegiate Dictionary, supra at 1456, 1516.↩14. We note as to the nine referenced receipts that Lloyds first gave the decedent receipt numbers 562, 563, and 564, then, approximately 4 months later, gave him receipt numbers 596 and 597 and then, approximately 7 months after that, gave him receipt numbers 565, 566, and 567.↩15. Although the two receipts from Mamiye do not list any item the existence of which is disputed by the parties, these receipts reflect only the sales from Mamiye to the decedent of the six loose diamonds.↩16. The decedent generally collected sets of jewelry that included necklaces, earrings, brooches/pins, and bracelets.↩17. The estate has not established that Polachek transported any of these four assets to her home for sentimental reasons. In fact, the record leads us to a contrary conclusion.↩18. The decedent owned a four-bedroom, 3,928 square-foot one-story home in Thousand Oaks, California. It was sited on approximately one acre of land and, when built in 1975, had two two- car garages and a double car port. (The decedent when he died owned a 1992 Lexus four-door sedan and a 1991 Jeep Cherokee four-wheel drive, the blue book values of which were $ 28,500 and $ 19,050 as of the date of his death.) The decedent for purposes of Schiffer's statement had valued his home at just over $ 1 million.↩19. We understand the sofa table to be much larger than each of the Baker's tables, which we understand are the same size. Although Polachek suggested that the sofa table had a broken leg that made it worthless, we find this suggestion incredible.↩20. The decedent also must have considered this sale to have been on good terms as he proceeded afterwards to frequent Lloyds continually and to spend large sums of money there.↩21. Those items correspond respectively to item numbers 19, 5, 6, 9, 10, 8, and 7 on our list of assets stipulated as to existence and fair market value.↩22. We find that the fair market values of the two diamonds in item number 2 were $ 75,000 and $ 78,150 and that the fair market values of the items in item numbers 6, 7, 9, and 10 were $ 47,436, $ 12,400, $ 15,510, and $ 17,010, respectively.↩23. In other words, we decide that the item in category 1 was worth twice as much as each of the items in category 2 and 3, four times as much as the item in category 4, and eight times as much as the item in category 5.↩24. We believe that a 50-percent reduction of the apportioned amounts adequately compensates for the fact that the decedent purchased this furniture approximately 5 years before the applicable valuation date and that furniture in general tends to decrease in value over time. Judging by the prices which the decedent paid for this furniture, we conclude that it was furniture of the highest quality. We also note that the decedent purchased this furniture in "Bulk" at a "special" price that apparently was less than the total retail price of that furniture if each piece of it had been purchased separately. The decedent also was an elderly man who tended to live either alone or with one other person, a factor which we believe would conserve the condition of the furniture.↩25. In all cases, the amount shown as fair market value is the same on both dates.↩26. Specifically, Butterfield appraised a "PAIR OF MASSIVE CHINESE IVORY VENEER COVERED URNS" at $ 4,000, a "PAIR OF LARGE CHINESE CARVED JADE PLAQUES" at $ 2,500, and a "LARGE CHINESE CARVED IVORY TUSK ON WOOD STAND" at $ 1,400.↩27. Butterfield later in 1993 sold each of these rugs at auction. The amounts paid by the buyers for these rugs (including applicable commission) is shown in the column to the right. We list the amounts in that column for completeness and do not rely on these amounts to value any of the disputed assets herein.↩28. We also find that many of Butterfield's listed values are considerably low when compared to the actual price for similar assets per the receipts. Although we understand that some of the items appraised by Butterfield ultimately sold at prices near the appraised values, we do not know who bought the items at those prices (e.g., dealer or consumer). Nor do we know whether Butterfield had been instructed by the coexecutors to sell those items for at least a set minimum value.↩29. For similar reasons, we also give little weight to the fact that Christie's wrote a letter to Gonzalez stating that it was unable to prepare an insurance appraisal of some of the Chinese artifacts in the decedent's home because "Most of these items are of modern or late production. * * * I would suggest that you either call in a local appraiser or insure at the cost prices."↩30. The coexecutors reported that the decedent had at financial institutions two money market accounts and two checking accounts. They reported that the balance in the money market accounts was approximately $ 412,000 and that the balance in one of the checking accounts was $ 822. They reported that the other checking account had a $ 109,760 deficit.↩31. The decedent consigned to Superior 209 gold proof coins for auction on Feb. 25, 1992. Of those coins, 201 were sold and eight were not. The coins reported on the return were those coins held by Superior when the decedent died. The 191 coins were at that time consigned to Superior for auction on Oct. 13, 1992. As to the 36 coins, eight of them were the unsold coins above, and the other 28 were from other consignments made to Superior before 1991 and for which Superior was awaiting a written request from the decedent for their return.↩32. We recognize that the parties stipulated that the value of the 41 seized gold coins totaled $ 104,500 (an average of $ 2,549 per coin). We do not believe that the stipulated value is a proper measure of the value of the 31 coins.↩33. The estate has not established that Gonzalez transported any of these rugs to her home for sentimental reasons. In fact, the record leads us to a contrary conclusion.↩34. Item 1 in receipt number 565 is the "Turquoise Necklace" and "Wall of IVORY Art piece". Whereas receipt 565 states that this necklace and wall of ivory were given to the decedent in exchange for netsukes, we do not attribute any of the $ 276,000 to those two items.↩35. To summarize:↩Three pieces of jade$ 45,000Five pieces of ivory18,750Netsukes25,000Rosewood tables4,416Diamond necklace66,404Diamond earrings9,000Loose diamond35,800Loose sapphire9,10010 rugs62,530276,00036. As stated supra note 29, we give little weight to a letter written by Christie's stating that "most" of the decedent's Chinese artifacts were of modern or late production. In addition to the fact that we do not know whether Christie's examined all of the decedent's ivory collection, or actually considered ivory to be a Chinese artifact, we note that Christie's acknowledged in its letter by its use of the word "most" that some of the Chinese artifacts which it examined were not of modern or late production.↩37. We understand that the value of gemstones depends not just on weight but on color, cut, and clarity as well. The record before us generally does not allow us to factor color, cut, or clarity into our valuations as to gemstones which are "comparable" to the gemstones in question.↩38. We note that Carmona had stated in his report that his valuations were not under ideal conditions.↩39. As noted above, we do not consider the auction prices of Christie's to be a good gauge of the fair market value of the related items; we generally view those prices as significantly less than fair market value.↩40. As discussed supra pp. 20-24, we consider the auction prices, and hence the stipulated values, to be less than fair market value.↩41. We decide that a bracelet is more similar in size to a necklace than to a ring.↩42. The May 4, 1988, receipt states no specific information on these necklaces and rings, but for the gemstones.↩43. To summarize: Ivory$ 75,0004.39-ct. diamond106,680Diamond necklace13,300 Sapphire necklace13,300 Ruby necklace13,300 Ruby ring6,665 Sapphire ring6,665 Ivory $ 75,0004.39-ct. diamond 106,680Diamond necklace 13,330Sapphire necklace 13,330Ruby necklace 13,330Ruby ring 6,665Sapphire ring 6,665 ________ 235,000↩44. Whereas this receipt lists the only purchased item as "Nestkies", we understand this description to refer to netsukes.↩45. We decide that the pins are more similar in size to the bracelets than to the rings.↩46. Of the items listed on the May 5, 1988, receipt, the only item that did not have a listed price was the "Ivory Maiden". The listed prices of the other items on that receipt totaled $ 120,900 ($ 7,500 + $ 6,000 + $ 74,000 + $ 15,000 + $ 18,400 = $ 120,900). We decide that the difference between $ 235,000 and $ 120,900 ($ 114,100) was paid for the ivory maiden. We decide in this regard that the ivory maiden was either significantly more valuable than the other pieces of ivory which we valued at $ 3,750 apiece or that it was not one piece of ivory but was a multipiece collection.↩47. In Trompeter I, we referred to the certificate of designation as a "purchase agreement". In that we now broaden our findings of fact to address the specific attributes of that stock, and not simply to address the fact that the stock was redeemed, we herein refer to that document by its given title.↩48. In other words, we used the basic formula for computing future value in the case of interest that is compounded annually, see generally Thorndike's Compound Interest and Annuity Tables 7 (1982), and adjusted that formula to reflect our finding in Trompeter I that the preferential dividends payable on the series A preferred stock compounded daily.↩49. Holders of series A preferred stock were entitled, subject to minimal restrictions, to exchange their series A preferred stock for Sterling's series B subordinated debentures due Dec. 31, 1995. See appendix C.↩50. The certificate of designation provides that "dividends on each share of the Series A Preferred Stock * * * will accrue on a daily basis at the rates per annum computed with respect to the Redemption Price thereof" and that Sterling "will be obligated on the Redemption Date to pay to the holder * * * [of each share to be redeemed] an amount in immediate available funds equal to the Liquidation Value thereof (the "Redemption Price")." The certificate of designation also provides that "all dividends which have accrued on each Share outstanding during the twelve-month period * * * ending upon each * * * [Jan. 15] will be added to the Liquidation Value of such Share and will remain a part thereof until such dividends are paid."↩51. Sterling's consolidated group included itself and its wholly owned subsidiaries Trompeter Electronics, Inc. (TEI), Quality Components, Inc. (QCI), and TQ Management Company (TQM). TEI, QCI, and Sterling were incorporated on Nov. 22, 1988, to facilitate the March 1989 leveraged transaction described in Trompeter I. TQM was formed on Apr. 25, 1989, to perform managerial services for Sterling in relation to the operations of TEI and QCI.↩52. We note but do not rely upon the fact that Sterling eventually did such a thing when, after the applicable valuation date, it agreed to redeem its series A preferred stock at approximately $ 1,270.21 per share ($ 1,947,845 redemption price paid to the Trust/1,533.482 redeemed shares). We also note but do not rely upon the fact that this lesser amount reflected the payment of 5 percent interest in lieu of the accrued dividends which were payable under the certificate of designation.↩53. We recognize that Dec. 31, 1992, postdates the applicable valuation date. We believe that a hypothetical buyer on the applicable valuation date could have ascertained this rate.↩54. For completeness, we note that a discount rate of 19.45 percent would under our methodology result in a fair market value approximately equal to the fair market value of $ 1,947,845 determined by respondent.↩1. This item was withdrawn from the auction.↩1. The specific debtors on the consolidated debt listed below are: (1) Sterling -- senior subordinated notes; series B subordinated debentures; unsecured notes, (2) TEI -- senior term notes (jointly with QCI); subordinated notes (jointly with QCI); obligations under capital lease, and (3) QCI--contractual obligations; unsecured notes payable; obligations under capital leases.↩2. Sterling's other debt was all subordinate to the senior term notes and was restricted as to payment unless Sterling met certain financial criteria. In that this criteria had not been met as of the applicable valuation date, the restrictions had in previous years prevented Sterling from making any payment on the senior subordinated notes, subordinated notes, series B subordinated debentures, and unsecured notes. As of Jan. 15, 1991, and Dec. 31, 1991 and 1992, the amount of accrued interest due but restricted from payment was as follows:                  Jan. 15,     Dec. 31,   Dec. 31,Class of Debt            1991       1991     1992Senior subordinated notes      $ 347,765    $ 744,820   $ 1,194,431Subordinated notes           -0-       309,241    1,071,628Series B subordinated debentures   291,132     488,889     711,294Unsecured notes            48,645      82,936     129,198                  ________     ________   __________                  687,542    1,625,886    3,106,551 ↩