MEMORANDUM FINDINGS OF FACT AND OPINION

CHIECHI, JUDGE: Respondent determined a deficiency of $512,881 in petitioner's Federal estate tax. The sole issue remaining for decision is the fair market value of the stock interest in a closely held corporation that was owned by Thomas A. Fleming (decedent) at the date of his death.

FINDINGS OF FACT

Some of the facts have been stipulated and are so found.

Decedent died testate 1997 Tax Ct. Memo LEXIS 566">*567 on November 22, 1991 (the valuation date). Cathy J. Hirt (Ms. Hirt), the independent successor executrix of decedent's estate (the estate), resided in Tyler, Texas, at the time the petition was filed.

At the time of his death, decedent owned, inter alia, a 50-percent community property interest (decedent's 50-percent stock interest) in the 100,000 shares of the common stock of B&W Financial Corporation of Longview, Inc. (B&W Longview), that were outstanding at that time, and his spouse, Jeanette T. Fleming, owned the remaining 50-percent community property interest in that stock. Decedent's spouse died in December 1992.

On the valuation date, B&W Longview, which had three offices in Tyler, Longview, and San Antonio, Texas, was engaged, inter alia, in the business of making small loans that were regulated by the Office of Consumer Credit in Texas. (The parties refer to those loans as trade notes receivable, and we shall do the same.) Pursuant to Texas law and/or regulations, on the valuation date, the amount of a loan reflected by a trade note receivable could not exceed $380. ¹ Although B&W Longview's trade notes receivable did not bear interest, under Texas law and/or regulations, 1997 Tax Ct. Memo LEXIS 566">*568 B&W Longview was permitted to charge for each such note a $10 acquisition fee (acquisition fee) and a handling charge (handling charge), the amount of which varied according to the amount and duration of the trade note receivable. If a debtor of B&W Longview prepaid that debtor's trade note receivable, B&W Longview was required under Texas law and/or regulations to refund a portion of the acquisition fee and/or the handling charge. The amount of any such refund, which was regulated by the Office of Consumer Credit in Texas, depended upon the amount and duration of the trade note receivable.

In addition to the trade notes receivable, on the valuation date, B&W Longview had in its portfolio of loans 11 demand loans (demand loans), each of which bore monthly interest of one percent of the unpaid balance of the loan. Five of those loans were in amounts exceeding $100,000, one loan to decedent was in the amount of $6,200, and one loan was for less than $1,000. As of the date of the trial of this case, two of the demand loans remained outstanding.

On the valuation date, the assets of B&W Longview consisted of cash totaling $1997 Tax Ct. Memo LEXIS 566">*569 760,953, the gross amount of the trade notes receivable totaling $1,012,177, ² nondepreciable assets totaling $75,323, the demand loans totaling $652,139, and other assets totaling $22,630. On that date, B&W Longview had total liabilities of $253,166 and equity of $2,168,839 consisting of $100,000 of capital stock, $9,412 of paid-in capital, and $2,059,427 of retained earnings. The book value of B&W Longview on the valuation date was $2,168,839.

Prior to the valuation date, decedent participated in the following transactions involving corporations in which he had an interest and which had portfolios of business loans that were similar to B&W Longview's trade notes receivable: ³ (1) The purchase during 1987 (Young transaction) by decedent from Tommy Young (Mr. Young) of Mr. Young's 50-percent stock interest in TA&T Finance Corporation (TA&T Finance); (2) the purchase during 1989 (B&W El Paso transaction) by an unidentified individual from decedent of decedent's1997 Tax Ct. Memo LEXIS 566">*570 100-percent stock interest in B&W El Paso (B&W El Paso); and (3) the purchases during 1991 (FNFS transaction) by FNFS, Inc. (FNFS), from decedent of decedent's respective 100-percent stock interests in five corporations. (We shall sometimes refer collectively to the foregoing transactions as the precedent transactions.)

In the Young transaction, decedent, who owned 50 percent of the stock of TA&T Finance, purchased during 1987 Mr. Young's 50- percent stock interest in that corporation, thereby resulting in decedent's owning 100 percent of the stock of TA&T Finance. ⁴ Although Mr. Young and decedent were not related, Mr. Young had previously worked for decedent. In calculating the price for Mr. Young's 50-percent stock interest in TA&T Finance, the parties to the Young transaction added to the book value of that company a premium of 23 percent of the trade notes receivable that were held by TA&T Finance at the time of that transaction.

1997 Tax Ct. Memo LEXIS 566">*571 In the B&W El Paso transaction, an unidentified individual who was not related to decedent purchased during 1989 decedent's 100- percent stock interest in B&W El Paso. In calculating the price for decedent's 100-percent stock interest in B&W El Paso, the parties to the B&W El Paso transaction added to the book value of that company a premium of 15 percent of the trade notes receivable that were held by B&W El Paso at the time of that transaction.

In the FNFS transaction, FNFS purchased during 1991 decedent's respective 100-percent stock interests in B&W Brownsville, B&W Harlingen, B&W Mission, B&W Austin, and B&W Finance. At the time of that transaction, FNFS was a holding company owned equally by David Harwood (Mr. Harwood) and Wayne McKinney, who were not related. Mr. Harwood, who was not related to decedent, negotiated on behalf of FNFS in the FNFS transaction. In calculating the price for each of decedent's respective stock interests in B&W Brownsville, B&W Harlingen, B&W Mission, B&W Austin, and B&W Finance, the parties to the FNFS transaction added to the book value of each of those companies a premium of 23 percent of the trade notes receivable that were held by each such company1997 Tax Ct. Memo LEXIS 566">*572 at the time of that transaction.

On or about August 7, 1992, the estate filed Form 706, United States Estate (and Generation-Skipping Transfer) Tax Return (estate tax return). In that return, the estate listed the value of 100 percent of the stock of B&W Longview as $2 million and claimed a value of $1 million for decedent's 50-percent stock interest in that corporation.

On or about November 17, 1993, the estate filed an amended estate tax return (amended estate tax return) in which the estate listed the value of 100 percent of the stock of B&W Longview as $1,452,000 and claimed a value of $726,000 for decedent's 50-percent stock interest in that corporation. Respondent treated the amended estate tax return as a claim for refund and denied it.

OPINION

Respondent determined in the notice of deficiency, inter alia, that on the valuation date the fair market value of decedent's 50-percent stock interest in B&W Longview was $1,251,460. Respondent modified that determination and claims on brief that the value of that stock interest was $1,110,000. The estate also modified on brief its prior positions as to the value on the valuation date of the stock interest1997 Tax Ct. Memo LEXIS 566">*573 in question. The estate now claims that that value was $604,777.

As is customary in valuation cases, the parties rely extensively on the opinions of their respective experts to support their differing views about the fair market value on the valuation date of decedent's 50-percent stock interest in B&W Longview. The estate relies on Richard P. Bernstein (Mr. Bernstein), a member of the American Society of Appraisers, who is the founder and president of the business valuation firm of Bernstein, Phalon & Conklin. Respondent relies on Monty L. Harrell (Mr. Harrell), who is employed by the Internal Revenue Service as an economist. Although Mr. Harrell is not a member of the American Society of Appraisers, he has taken business valuation courses offered by that organization.

We evaluate the opinions of experts in light of the demonstrated qualifications of each expert and all other evidence in the record. Anderson v. Commissioner, 250 F.2d 242">250 F.2d 242, 250 F.2d 242">249 (5th Cir. 1957), affg. in part and remanding in part T.C. Memo. 1956-178; Parker v. Commissioner, 86 T.C. 547">86 T.C. 547, 86 T.C. 547">561 (1986). We have broad discretion to evaluate1997 Tax Ct. Memo LEXIS 566">*574 "'the overall cogency of each expert's analysis.'" Sammons v. Commissioner, 838 F.2d 330">838 F.2d 330, 838 F.2d 330">334 (9th Cir. 1988) (quoting Ebben v. Commissioner, 783 F.2d 906">783 F.2d 906, 783 F.2d 906">909 (9th Cir. 1986), affg. in part and reversing in part T.C. Memo. 1983-200). We are not bound by the formulae and opinions proffered by expert witnesses, especially when they are contrary to our judgment. Silverman v. Commissioner, 538 F.2d 927">538 F.2d 927, 538 F.2d 927">933 (2d Cir. 1976), affg. T.C. Memo. 1974-285; IT&S of Iowa, Inc. v. Commissioner, 97 T.C. 496">97 T.C. 496, 97 T.C. 496">508 (1991). Instead, we may reach a determination of value based on our own examination of the evidence in the record. Lukens v. Commissioner, 945 F.2d 92">945 F.2d 92, 945 F.2d 92">96 (5th Cir. 1991), affg. Ames v. Commissioner, T.C. Memo. 1990-87 (citing 538 F.2d 927">Silverman v. Commissioner, supra). The persuasiveness of an expert's opinion depends largely upon the disclosed facts on which it is based. See Tripp v. Commissioner, 337 F.2d 432">337 F.2d 432, 337 F.2d 432">434 (7th Cir. 1964), affg. T.C. Memo. 1963-244.1997 Tax Ct. Memo LEXIS 566">*575 Where experts offer divergent estimates of fair market value, we shall decide what weight to give those estimates by examining the factors used by those experts to arrive at their conclusions. Casey v. Commissioner, 38 T.C. 357">38 T.C. 357, 38 T.C. 357">381 (1962). While we may accept the opinion of an expert in its entirety, Buffalo Tool & Die Manufacturing Co. v. Commissioner, 74 T.C. 441">74 T.C. 441, 74 T.C. 441">452 (1980), we may be selective in the use of any part of such an opinion, 86 T.C. 547">Parker v. Commissioner, supra at 562. We also may reject the opinion of an expert witness in its entirety. Palmer v. Commissioner, 523 F.2d 1308">523 F.2d 1308, 523 F.2d 1308">1310 (8th Cir. 1975), affg. 62 T.C. 684">62 T.C. 684 (1974); 86 T.C. 547">Parker v. Commissioner, supra at 562-565.

In their respective original reports (expert reports), both experts relied on the market approach in determining the fair market value on the valuation date of decedent's 50-percent stock interest in B&W Longview. In applying that approach, each of those experts used a combination of the transaction method and the market multiple or guideline company method1997 Tax Ct. Memo LEXIS 566">*576 (market multiple method) in order to arrive at his opinion of that value. At trial, Mr. Bernstein and Mr. Harrell modified and/or abandoned portions of their respective expert reports, as follows: In applying the market approach to valuing the stock interest in question, petitioner's expert modified his application of the market multiple method (modified market multiple method), and respondent's expert modified his application of the transaction method (modified transaction method) and abandoned his determination of value under the market multiple method. Consequently, both experts modified their respective opinions of the fair market value on the valuation date of decedent's 50-percent stock interest in B&W Longview. We have problems with the opinions of both experts.

Mr. Bernstein relied on the market approach and applied an equally weighted combination of the transaction method and his modified market multiple method under that approach because he did not believe that either method alone produced what he considered to be an accurate estimate of the fair market value on the valuation date of the stock interest in question.

In applying the transaction method, Mr. Bernstein examined1997 Tax Ct. Memo LEXIS 566">*577 the precedent transactions that occurred in 1987, 1989, and 1991, respectively. He concluded that under that method the value of decedent's 50-percent stock interest in B&W Longview should be derived by (1) adding to the book value of B&W Longview on the valuation date a premium equal to 23 percent of the gross amount of the trade notes receivable held by that corporation on that date and (2) multiplying the resulting sum by 50 percent to reflect the fact that decedent owned only a 50-percent stock interest in B&W Longview. Mr. Bernstein determined that, under the transaction method and before considering any discounts that he believed are warranted because of the lack of control and the lack of marketability inherent in that stock interest on the valuation date, its value was $1,200,801.

In applying his modified market multiple method, Mr. Bernstein selected three publicly traded companies (guideline companies) engaged to varying degrees in consumer lending that he determined were comparable or similar to B&W Longview. Mr. Bernstein did not explain in his report or adequately explain at trial why the three guideline companies that he chose were comparable to B&W Longview on 1997 Tax Ct. Memo LEXIS 566">*578 the valuation date and why he selected only three publicly traded companies as guideline companies. For these reasons, we are not persuaded that the results that Mr. Bernstein reached under his modified market multiple method are reliable, and we shall not give any weight to those results in determining the fair market value on the valuation date of the stock interest in question. ⁵ Consequently, we shall ignore Mr. Bernstein's opinion that, under his modified market multiple method and before considering any discounts that he believed are warranted because of the lack of control and the lack of marketability inherent in decedent's 50-percent stock interest in B&W Longview on the valuation date, its value was $660,050.

Although we shall not rely on Mr. Bernstein's modified market multiple method, for the sake of completeness we shall describe what Mr. 1997 Tax Ct. Memo LEXIS 566">*579 Bernstein did with the results that he derived under that method. After having arrived at the respective values of the stock interest in question under his modified market multiple approach and the transaction method and after having determined that each such value should be accorded equal weight in ascertaining the fair market value of that interest, Mr. Bernstein calculated the mean of those two values to be $930,425 (mean value). He applied a 35- percent combined minority and lack-of-marketability discount ⁶ (35- percent combined discount) to that mean value and arrived at an amount, viz., $604,777, that he determined was the fair market value on the valuation date of decedent's 50-percent stock interest in B&W Longview. We are not persuaded on the record presented to us that the 35-percent combined discount which Mr. Bernstein applied is appropriate.

1997 Tax Ct. Memo LEXIS 566">*580 When he prepared his expert report, Mr. Harrell, like Mr. Bernstein, believed that applying a weighted combination of the market multiple method and the transaction method generally would produce an accurate estimate under the market approach of the fair market value on the valuation date of the stock interest in question. ⁷ However, after he prepared his report and before trial, Mr. Harrell discovered deficiencies in the data which were provided to him and on which he relied in applying the market multiple method. Those deficiencies caused Mr. Harrell to conclude that the results that he reached under that method are not reliable. We agree, and we shall not give any weight to those results in determining the fair market value of the stock interest in question.

In applying his modified transaction method, Mr. Harrell, like Mr. Bernstein, examined the precedent transactions that occurred in 1987, 1989, and 1991, respectively. 1997 Tax Ct. Memo LEXIS 566">*581 Mr. Harrell testified that under that method the value of that interest was between approximately $1,110,000 and approximately $1,124,000, derived as follows: Mr. Harrell, like Mr. Bernstein, added to the book value of B&W Longview on the valuation date a premium equal to 23 percent of the gross amount of the trade notes receivable held by that corporation on that date. Mr. Harrell, unlike Mr. Bernstein, also added to that book value a premium on the demand loans that Mr. Harrell believed should be between 10 percent and 15 percent of those loans. Mr. Harrell reduced the resulting sum by 50 percent to reflect the fact that decedent held only a 50-percent stock interest in B&W Longview on the valuation date. Finally, Mr. Harrell applied a 10- percent minority discount, but, unlike Mr. Bernstein, he applied no discount for lack of marketability.

On the record before us, we are not persuaded that Mr. Harrell should have added any premium to the demand loans in determining the fair market value of the stock interest in question. We found Mr. Harrell's testimony about the propriety of such a premium to be tentative and unconvincing. Accordingly, we shall not accept Mr. Harrell's1997 Tax Ct. Memo LEXIS 566">*582 opinion that a premium should be applied to the demand loans.

We also are not convinced on the present record that Mr. Harrell was correct in not applying any lack-of-marketability discount in valuing the stock interest in question.

Despite the deficiencies that we found in the respective expert reports and opinions of the parties' experts, we agree with both experts that, under the market approach to determining the fair market value on the valuation date of decedent's 50-percent stock interest in B&W Longview, the combined use of the market multiple method and the transaction method would produce a better indication of that value than the use of only the transaction method. However, as discussed above, we are not persuaded that the respective results of Mr. Bernstein's modified market multiple method and Mr. Harrell's market multiple method are reliable. Consequently, we are left with a deficient record from which to determine the effect of the proper application of the market multiple method on the determination of the value of the stock interest in question. Nonetheless, we shall determine the fair market value on the valuation date of decedent's 50-percent stock interest in B&W1997 Tax Ct. Memo LEXIS 566">*583 Longview by applying our best judgment to a record that we find to be inadequate in that and other respects ⁸ and bearing in mind that the valuation of that stock interest is a question of fact, Estate of Bonner v. United States, 84 F.3d 196">84 F.3d 196, 84 F.3d 196">197 (5th Cir. 1996); Estate of Andrews v. Commissioner, 79 T.C. 938">79 T.C. 938, 79 T.C. 938">940 (1982), on which petitioner has the burden of proof, Rule 142(a).⁹

The determination of the value of closely held stock is a matter of judgment, rather than of mathematics. Hamm v. Commissioner, 325 F.2d 934">325 F.2d 934, 325 F.2d 934">940 (8th Cir. 1963),1997 Tax Ct. Memo LEXIS 566">*584 affg. T.C. Memo. 1961-347. Moreover, since valuation is necessarily an approximation, it is not required that the value that we determine be one as to which there is specific testimony, provided that it is within the range of figures that properly may be deduced from the evidence. Silverman v. Commissioner, 538 F.2d 927">538 F.2d at 933; Anderson v. Commissioner, 250 F.2d 242">250 F.2d at 249.

The regulations define fair market value for purposes of the Federal estate tax as "the price at which the property would change hands between a willing buyer and a willing seller, neither being under any compulsion to buy or to sell and both having reasonable knowledge of relevant facts." Sec. 20.2031-1(b), Estate Tax Regs. In the case of unlisted stock, the price at which sales of stock are made in arm's-length transactions in an open market is the best evidence of its value. Champion v. Commissioner, 303 F.2d 887">303 F.2d 887, 303 F.2d 887">893 (5th Cir. 1962), revg. T.C. Memo. 1960-51; 79 T.C. 938">Estate of Andrews v. Commissioner, supra at 940. In the instant case, the record does not disclose1997 Tax Ct. Memo LEXIS 566">*585 any such sales of the stock interest in question. The record does disclose, however, information with respect to the precedent transactions that involved corporations in which decedent had an interest and which, like B&W Longview, had portfolios of trade notes receivable.

Where the value of unlisted stock cannot be determined from actual sale prices, section 2031(b) provides that value is to be determined by taking into consideration the value of stock of corporations listed on an exchange that are engaged in the same or similar business, as well as all other factors bearing on value. The factors we must consider are those that an informed buyer and seller would take into account. 325 F.2d 934">Hamm v. Commissioner, supra at 938. Section 20.2031-2(f), Estate Tax Regs., lists some of those factors, including the company's net worth, prospective earning power, dividend-earning capacity, goodwill, the economic outlook for its industry, its position in the industry, its management, the degree of control represented by the block of stock to be valued, and nonoperating assets to the extent not otherwise considered. Section 5 of Rev. Rul. 59-60, 1959-1 C.B. 237, 238-242,1997 Tax Ct. Memo LEXIS 566">*586 sets forth criteria that are virtually identical to those listed in section 20.2031-2(f), Estate Tax Regs., and "has been widely accepted as setting forth the appropriate criteria to consider in determining fair market value". Estate of Newhouse v. Commissioner, 94 T.C. 193">94 T.C. 193, 94 T.C. 193">217 (1990).

There is no fixed formula for applying the foregoing factors. See Estate of Goodall v. Commissioner, 391 F.2d 775">391 F.2d 775, 391 F.2d 775">786 (8th Cir. 1968), vacating T.C. Memo. 1965-154. We have held, and the regulations provide, that the weight to be given to the various factors in arriving at fair market value depends upon the facts of each case. 79 T.C. 938">Estate of Andrews v. Commissioner, supra at 940-941; sec. 20.2031-2(f), Estate Tax Regs. As the trier of fact, we have broad discretion in assigning the weight to accord to the various factors and in selecting the method of valuation. Estate of O'Connell v. Commissioner, 640 F.2d 249">640 F.2d 249, 640 F.2d 249">251 (9th Cir. 1981), affg. on this issue T.C. Memo. 1978-191.

Each of the parties' experts agree that, under the transaction method that1997 Tax Ct. Memo LEXIS 566">*587 each applied under the market approach to valuation, the starting point for determining the fair market value of the stock interest in question should be the book value of B&W Longview on the valuation date plus a 23-percent premium on the gross amount of the trade notes receivable that that corporation held on that date. We accept that starting point under the transaction method as reasonable. According to the expert reports, market conditions on the valuation date, like market conditions in 1991 at the time of the FNFS transaction in which a 23-percent premium was applied to the trade notes receivable there involved, were more favorable than they were in 1989 at the time the B&W El Paso transaction occurred in which a 15-percent premium was applied to the trade notes receivable involved in that transaction.

A major difference between the parties' experts in valuing the stock interest in question relates to the discounts that each applied. Respondent's expert applied only a 10-percent minority discount, and petitioner's expert applied a 35-percent combined minority and lack-of-marketability discount. Discounts for a minority interest and for lack of marketability are conceptually1997 Tax Ct. Memo LEXIS 566">*588 distinct. 94 T.C. 193">Estate of Newhouse v. Commissioner, supra at 249. A minority discount reflects the minority shareholder's inability to compel liquidation and thereby realize a pro rata share of the corporation's net asset value. A discount for lack of marketability reflects the fact that there is no ready market for the stock of a closely held corporation. Id. The appropriate amount of a minority discount and/or a lack-of- marketability discount is a question of fact. Id.

We agree with both parties' experts that a minority discount should be applied in valuing decedent's 50-percent stock interest in B&W Longview. Although Mr. Harrell specified that he would apply a 10-percent discount, Mr. Bernstein did not specify how much of the 35-percent combined discount that he applied was attributable to the fact that decedent did not own a controlling stock interest in B&W Longview on the valuation date. On brief, petitioner, who has the burden of proof, does not insist that a minority discount in excess of 10 percent be applied in this case.

Respondent contends, and petitioner disputes, that, because the precedent transactions on which both experts, inter alia, relied1997 Tax Ct. Memo LEXIS 566">*589 involved stock for which there was no ready market, the respective prices paid for the stock sold in those transactions reflected some lack-of-marketability discount. While we generally agree with respondent, it is significant that the stock interests acquired in the precedent transactions were different from decedent's 50-percent stock interest in B&W Longview in that (1) the respective purchasers in the transactions involving (a) B&W El Paso and (b) B&W Brownsville, B&W Harlingen, B&W Mission, B&W Austin, and B&W Finance acquired 100 percent of the stock of each of those corporations; and (2) although decedent purchased only 50 percent of the stock of TA&T Finance in the Young transaction, after that purchase, decedent owned 100 percent of the stock of that corporation. On the record before us, we find that there was even less of a ready market for decedent's 50-percent stock interest in B&W Longview than there was for the stock interests sold in the precedent transactions. Consequently, we conclude that, in addition to a minority discount, some amount of lack-of-marketability discount should be applied in determining the fair market value on the valuation date of decedent's 50-percent1997 Tax Ct. Memo LEXIS 566">*590 stock interest in B&W Longview.

Based on our consideration of the entire record before us, and using our best judgment, we find that the fair market value on the valuation date of decedent's 50-percent stock interest in B&W Longview was $875,000.

To reflect the foregoing,

Decision will be entered under Rule 155.