101 T.C. 412">*412 CHABOT, Judge: Respondent determined a deficiency in Federal estate tax against petitioner in the amount of $ 2,396,902.92. By amendment to answer, respondent asserts 101 T.C. 412">*413 an addition to tax of $ 719,070.90 under section 6660¹ (valuation understatement).

After concessions by both sides, the issues are as follows:

(1) What the fair market value of decedent's 168,600 shares of Jung Corp. stock was on the1993 U.S. Tax Ct. LEXIS 69">*70 date of her death (Oct. 9, 1984); and

(2) whether petitioner is liable for an addition to tax under section 6660.

FINDINGS OF FACT ²

1993 U.S. Tax Ct. LEXIS 69">*71 Some of the facts have been stipulated; the stipulation and the stipulated exhibits are incorporated herein by this reference.

When the petition was filed in the instant case, petitioner was an Ohio estate with a legal residence in Cincinnati, Ohio. Decedent died a resident of Ohio on October 9, 1984. Decedent's estate was probated in Hamilton County, Ohio.

At her death decedent owned 168,600 voting shares of Jung Corp., which represented 20.83 percent of the outstanding voting shares and 20.74 percent of all the outstanding shares of Jung Corp. ³

In the early 1900's decedent's husband cofounded Jung Arch Brace Co., the predecessor to Jung Corp. In 1949, a year after decedent's husband died, Jung Corp. was incorporated in Ohio as Jung Products, 1993 U.S. Tax Ct. LEXIS 69">*72 Inc. As of January 1, 1982, the name was changed to Jung Corp. Jung Corp.'s principal place of business was in Cincinnati, Ohio.

101 T.C. 412">*414 On October 9, 1984, Jung Corp. owned all of the outstanding stock of the following companies: Jung International, Inc. (hereinafter sometimes referred to as JII), J.R.A. Industries, Inc. (hereinafter sometimes referred to as JRA), Rampon Products (hereinafter sometimes referred to as Rampon), Ione Realty (hereinafter sometimes referred to as Ione), and Calley & Currier; Jung Corp. also owned 96.3 percent of the stock of Theradyne.

Jung Corp and its subsidiaries were primarily operating companies, except that Ione was a holding company for the real estate occupied by the operating companies. Jung Corp. consisted of two divisions -- (1) the corporate division, which provided management services to the Jung Corp. subsidiaries, and (2) the Futuro division (hereinafter sometimes referred to as Futuro), which manufactured and marketed health care products and other products, including the products of Jung Corp. subsidiaries. ⁴ Jung Corp. and its subsidiaries together comprised an integrated manufacturer and distributor of elastic textile goods and1993 U.S. Tax Ct. LEXIS 69">*73 products, including elastic braces and supports, support stockings, and thermo comforters (elastic gloves and braces knitted with wool, which provide warmth and compression to swollen joints).

Futuro marketed health supports (such as elastic braces, athletic supporters, support socks and stockings, and hernia belts), patient aids (such as wheelchairs, canes, crutches, walkers, bed pans, and sitz baths), and thermo comforters. Futuro products were marketed almost entirely through drugstores, both nationally and internationally. About 95 percent of the health supports and 70-75 percent of the patient aids that Futuro marketed were manufactured by Jung Corp. and its subsidiaries. Futuro also marketed sporting goods through its All American and Grid lines. Futuro was Jung Corp.'s most profitable business. Futuro's health supports products were number one or number1993 U.S. Tax Ct. LEXIS 69">*74 two in drug stores.

JII, incorporated in 1968, was the export sales agent for Jung Corp. products. JII bought goods for resale only from Jung Corp. or its subsidiaries. JII was a domestic international sales corporation (DISC) until December 31, 1984, at 101 T.C. 412">*415 which time the DISC was liquidated and its successor was incorporated as a foreign sales corporation (FSC).

JRA, incorporated in 1969, primarily produced coarse yarns for sale to other Jung Corp. subsidiaries and to third parties. JRA also used the yarns to make elastic webbing, and it made fine elastic yarn from which Rampon (acquired by Jung Corp. in 1965) and third parties made stockings. In 1983 JRA acquired the property, plant, and equipment of a yarn covering operation in Raeford, North Carolina, and the Raeford operations became part of JRA. The industry in which JRA competed is very capital-intensive and has very low profit margins. JRA had a low profit margin in 1984.

Rampon produced knitted products including hosiery.

Theradyne manufactured wheelchairs for sale to Jung Corp. subsidiaries and to third parties. Jung Corp. acquired 70 percent of Theradyne's stock in 1973. Most of the remaining stock was held1993 U.S. Tax Ct. LEXIS 69">*75 by Jung family members. In 1983 Jung Corp. acquired most of the rest of Theradyne in a stock-for-stock transaction. On October 9, 1984, Jung Corp. held 96.3 percent of Theradyne's stock. In 1984 Theradyne was either marginally profitable or losing money.

Jung Corp. acquired Calley & Currier in March 1984. Calley & Currier principally manufactured wooden crutches; it was the second largest wooden crutch manufacturer, with about one-third of the domestic market.

Ione was incorporated in 1949 by Jung family members and was transferred to Jung Corp. in 1973. Its primary purpose was to hold real and personal property which was used by Jung Corp.'s operating subsidiaries. Ione owned the manufacturing facility that Futuro occupied, the plant that Theradyne occupied, and the Richard Grey plant (which was a part of Rampon). Ione also owned a condominium in Florida. Ione charged rent for the facilities it owned, but the rent charged was not market value.

Jung Corp. had industrial revenue bond (hereinafter referred to as IRB) financing for Futuro's manufacturing site. As of October 9, 1984, the outstanding balance of Jung Corp.'s IRB loan for Futuro was $ 970,000. JRA also had IRB1993 U.S. Tax Ct. LEXIS 69">*76 financing. As of October 9, 1984, the outstanding balance of JRA'S IRB loan was $ 3,030,000. The interest rate on JRA'S IRB loan was computed at 69 percent of the current prime rate at the time of payment.

101 T.C. 412">*416 Jung Corp. kept its books and records on a calendar year basis. Jung Corp. and its subsidiaries filed consolidated tax returns. The net income after taxes of Jung Corp. and its subsidiaries for 1970 through 1979 is shown in table 1:

Table 1

The audited financial statements for 1980 through 1986 show net sales and net income after taxes for the consolidated operations of Jung Corp. in the rounded amounts set forth in table 2:

Table 2

The unaudited interim financial statement for September 30, 1984 (9 days before decedent's death), shows year-to-date1993 U.S. Tax Ct. LEXIS 69">*77 net sales (rounded) of $ 52,271,000, and year-to-date net income after taxes (rounded) of $ 2,192,000. A portion of Jung Corp.'s unaudited interim consolidated balance sheet for September 30, 1984, is attached as the appendix. Complete information concerning 1984 yearend adjusting entries is not available. However, for 1984 Jung Corp. made at least three yearend adjustments as follows: (1) The inventory of Theradyne was decreased by $ 426,677, most of which was because of the discontinuance of the Titann wheelchair line, 101 T.C. 412">*417 (2) the inventory of Futuro was increased by an unknown amount to account for the increased costing of freight, and (3) deferred Federal income tax was decreased by $ 541,000.

Jung Corp. paid dividends of 4 cents per share from 1979 through 1983; in 1984 it paid dividends of 25 cents per share.

In November 1984 Jung Corp. employed 1,025 people.

In the early 1980s, Jung Corp. developed and installed computer programs which controlled its manufacturing and operating systems and produced financial statements, invoices, etc.

In the 1980s, governmental policies were introduced which were designed to reduce Medicare costs by discouraging hospital stays and1993 U.S. Tax Ct. LEXIS 69">*78 encouraging home health care. Because Jung Corp. marketed its products primarily through drugstores rather than through hospitals, Jung Corp. stood to benefit from this trend. Almost all the products in Jung Corp.'s product lines would benefit from an increase in home health care expenditures.

Jung Corp. had formulated 5-year business forecast plans since 1975, but the emphasis was only on sales projections. In 1984 Jung Corp. began an in-depth analysis of its strengths, weaknesses, and opportunities, and it began to formulate specific business strategies. By mid-1984 Jung Corp. began to implement these strategies. Also, in 1984 Jung Corp. began involving employees in the planning and forecasting process. In mid-1984, to help with financial planning, Jung Corp. hired Jim Cox, a partner from Ernst & Whinney, and retained the services of an accounting firm. Jung Corp. decided to actively promote future growth through expanded domestic sales, and through acquisitions of other companies. It decided that Jung Corp. would become global in both sales and purchases, and it began searching for European companies to acquire. During 1984 Jung Corp. introduced additional products into1993 U.S. Tax Ct. LEXIS 69">*79 the home health care market, and improved its then-current products. Beginning in 1984, each of Jung Corp.'s subsidiaries added a medical-surgical distribution service in order to provide products to surgical supply dealers, hospitals, and professionals. The year 1984 was the best sales and profit year in the history of Jung Corp.

Jung Corp. also experienced growth from October 1984 through 1986. During this time Futuro became number one 101 T.C. 412">*418 in the drugstore market. During 1985 or 1985, Jung Corp. introduced neoprene athletic products, which increased sales in Futuro's Grid line by 3 to 5 percent. In 1985 and 1986 Jung Corp. upgraded its equipment, installed new computer programs to manage inventory, and trained personnel to use the computers. Jung Corp. bought two English companies, Solport and Lastonet. It began sending managers to management training schools at Harvard, Stanford, and Massachusetts Institute of Technology. The planning and forecasting procedures which Jung Corp. had begun in 1984 helped it to identify both weaknesses and opportunities, and helped to give it needed impetus for growth in 1985 and 1986. Jung Corp.'s net sales in 1985 were higher than1993 U.S. Tax Ct. LEXIS 69">*80 1984 net sales; however, Jung Corp.'s profits for 1985 and 1986 were lower than 1984 profits. See supra table 2. The decline in profits in 1985 and 1986 was due to the above-mentioned increased expenditures, which ultimately helped Jung Corp. Also, in 1985 and 1986 JRA and Calley & Currier changed from profitable companies to unprofitable companies. Because of the foregoing activities, and changes in the market, Jung Corp. increased in value substantially between 1984 and 1986.

Since at least 1979, Jung Corp. had received letters inquiring about the possibility of acquiring Jung Corp. The standard response to these letters was that Jung Corp. was not for sale. In 1984 Jung Corp. was not for sale. From 1979 through 1986 there were not any arm's-length sales of the stock of Jung Corp. Jung Corp. stock was not publicly traded.

On October 9, 1984, Ruth J. Conway, decedent's daughter, was treasurer of Jung Corp., and Ruth J. Conway's husband, Robert A. Conway (hereinafter sometimes referred to as Conway), was chairman of the board of directors. Thomas H. Clark (hereinafter sometimes referred to as Clark), decedent's nephew, was legal counsel and secretary for Jung Corp. 1993 U.S. Tax Ct. LEXIS 69">*81 Mary Lois Jung, also a daughter of decedent, was a member of the board of directors of Jung Corp. and was one of two doctors who reviewed and approved the new product development literature that Jung Corp. distributed. No other members of decedent's family were employed by, or involved in, the management of Jung Corp. After a series of strokes in the period 1975-77, decedent had not been involved in the management of Jung Corp. Decedent's death had no impact 101 T.C. 412">*419 on the running of Jung Corp. The Conways had eight children, none of whom was involved in the business. As of October 1984, Conway (then 57 years old) was not considering retirement; however, he was concerned about who his successor would be because none of his children was involved in the business.

The holders of voting common shares of record on the date of decedent's death were as shown in table 3:

Table 3

1993 U.S. Tax Ct. LEXIS 69">*82 In May 1986, Kendall Co. (hereinafter sometimes referred to as Kendall) contacted Jung Corp. in regard to an acquisition of Jung Corp. Conway told Kendall's representatives that he was not interested in selling. In the summer of 1986, Conway was invited to meet with Kendall's representatives in Boston, Massachusetts. Conway then consulted with Ruth Conway and Mary Lois Jung. Conway raised the matter at a meeting of Jung Corp.'s board of directors in September 1986. The board of directors advised that, if Conway did not plan to have family succession at Jung Corp., then he should treat Jung Corp. as any other asset, to be held or sold when he thought appropriate.

Jung Corp. began negotiations with Kendall concerning the sale of certain assets of Jung Corp. The board of directors of Jung Corp. recommended that any sale be completed by December 31, 1986, because of changes in the tax law enacted by the Tax Reform Act of 1986. On December 29, 101 T.C. 412">*420 1986, Kendall bought certain assets of Jung Corp. for about $ 59.5 million. On the date of decedent's death this sale was not foreseeable.

The remaining assets of Jung Corp. were sold in transactions separate from the sale to 1993 U.S. Tax Ct. LEXIS 69">*83 Kendall. On July 7, 1986, Jung Corp. sold Theradyne to Surgical Appliances Industries, Inc., for $ 1 million. On December 1, 1986, Jung Corp. sold assets of Futuro's Grid line to CDC Liquidators for $ 552,705. On December 23, 1986, Jung Corp. sold certain assets of JRA to Spanco Co. for $ 5,076,200. On December 29, 1986, Calley & Currier was sold for $ 750,000.

In 1986 Jung Corp. did not discuss the possible sale of Jung Corp. assets with any entities other than those to which sales actually took place.

On December 15, 1986, the shareholders of Jung Corp. adopted a plan of liquidation. According to the plan of liquidation, Jung Corp. was to be liquidated upon the sale to Kendall, which was to be on December 29, 1986, and dissolved by December 31, 1986. In order to accommodate the liquidation, the Jung-Conway Trust was established to serve as a conduit for transferring assets from Jung Corp. to its shareholders. The total trust equity of about $ 64 million is net of liquidation expenses, and after the buyout of the voting and nonvoting stock and stock options. The buyout price was $ 75 per share. On the date of decedent's death, this liquidation was not foreseeable.

In connection1993 U.S. Tax Ct. LEXIS 69">*84 with the preparation of the estate tax return, decedent's executrix relied on Clark's law firm to find an appraiser for decedent's stock in the Jung Corp. Clark's law firm retained Edwin T. Robinson (hereinafter sometimes referred to as Robinson) to prepare an appraisal report. On April 8, 1985, Robinson submitted his written valuation report to Clark, in which he valued decedent's Jung Corp. stock at $ 2,671,973 as of October 9, 1984. This valuation report was the basis for the estate's estate tax return's use of that amount as the reported value of decedent's Jung Corp. stock. Petitioner's estate tax return was filed timely, on July 9, 1985.

On the estate tax return, petitioner elected under section 6166 to pay the appropriate portion of the estate tax in installments. In the course of making this election, petitioner represented that the $ 2,671,973 reported value of decedent's 101 T.C. 412">*421 Jung Corp. stock is 88.1 percent of the value of the adjusted gross estate. On the estate tax return, petitioner reported the value of the gross estate as $ 3,418,971.52. The reported value of decedent's Jung Corp. stock is 78.2 percent of the value of the gross estate.

Robinson is a certified1993 U.S. Tax Ct. LEXIS 69">*85 public accountant and an attorney. Robinson does not have formal training or accreditation in valuation. In 1966, after being graduated from law school, Robinson spent 6 years working for the Arthur Andersen accounting firm; his work there involved some valuation questions. In 1972 Robinson joined a law firm as a tax specialist. His work at the law firm included some valuation issues. From 1979 to 1984 Robinson worked for SHV North America Corp. (hereinafter sometimes referred to as SHV), which is a U.S. holding company for a privately owned Dutch company. Robinson was vice president of acquisitions, and president of the SHV Investment Fund (hereinafter sometimes referred to as the fund), a venture capital fund. His job was to make investments for the fund in privately held businesses. Although Robinson did not prepare formal appraisal reports while he was employed by SHV, his job involved valuing companies for potential acquisition, or valuing a company held by SHV for purposes of selling it.

In July 1984 Robinson joined Mayfield & Co., Inc. (hereinafter sometimes referred to as Mayfield). Mayfield provides consultation services for clients who wish to acquire businesses. 1993 U.S. Tax Ct. LEXIS 69">*86 Robinson's work for Mayfield involved valuing companies, and helping clients to negotiate price, contracts, and financing. Although Robinson was not in the business of issuing written appraisals until he began working for Mayfield in 1984, he already had extensive experience for several years in valuing businesses.

In preparing the appraisal report for petitioner, Robinson visited Jung Corp.'s facilities in Cincinnati and interviewed officers of Jung Corp. In his appraisal report, Robinson considered the history, economic outlook, products, and financial condition of Jung Corp. He valued Jung Corp. by (1) calculating its return on equity and its return on capital employed, and (2) using a price/earnings multiple based on market comparables and applying the multiple to Jung Corp.'s weighted earnings for 1980 through 1984. Robinson 101 T.C. 412">*422 concluded that Jung Corp. should be valued at less than book value.

Table 4 shows the positions of the parties, of their expert witnesses, and of the Court as to the fair market value of decedent's 168,600 shares of Jung Corp. stock on October 9, 1984.

Table 4

On October 9, 1984, Jung Corp. was worth about $ 32-34 million; decedent's shares amounted to 20.74 percent of the total and were worth about $ 6.7 to $ 7 million, without regard to discounts; the value of decedent's shares should be discounted 35 percent for lack of marketability and should not be further discounted for lack of control; and the fair market value of decedent's shares was $ 4,400,000.

When Robinson prepared the appraisal report for petitioner, he was an experienced expert appraiser. Petitioner acted in good faith in claiming the valuation reported on the estate tax return. There was a reasonable basis for the valuation claimed on the estate tax return.

Respondent's refusal to waive the addition to tax under section 6660 was an abuse of discretion.

101 T.C. 412">*423 OPINION

I. Value of1993 U.S. Tax Ct. LEXIS 69">*88 Decedent's Stock

The value of decedent's gross estate includes the fair market value of the stock in Jung Corp. that decedent owned at her death. Sec. 2031(a); ⁵United States v. Cartwright, 411 U.S. 546">411 U.S. 546, 411 U.S. 546">551 (1973); sec. 20.2031-1(b), Estate Tax Regs. Because Jung Corp.'s stock was not listed on an exchange and cannot be valued with reference to bid and asked prices or historical sales prices, the statute requires us to consider the value of stock in comparable corporations engaged in the same or a similar line of business. Sec. 2031(b).

1993 U.S. Tax Ct. LEXIS 69">*89 The parties have not agreed on the fair market value of decedent's stock, and so we will have to find the fair market value. Buffalo Tool & Die Manufacturing Co. v. Commissioner, 74 T.C. 441">74 T.C. 441, 74 T.C. 441">451-452 (1980).

Generally, the fair market value of property is the price at which a willing buyer will purchase the property from a willing seller, when neither is acting under compulsion and both are fully informed of the relevant facts and circumstances. E.g., 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, 62 T.C. 684">696 (1974); McShain v. Commissioner, 71 T.C. 998">71 T.C. 998, 71 T.C. 998">1004 (1979). Respondent's determination in the notice of deficiency as to the fair market value of the subject property is presumptively correct, and petitioner bears the burden of proving that the fair market value is lower. Rule 142; Welch v. Helvering, 290 U.S. 111">290 U.S. 111 (1933).

At trial, both sides presented the testimony of expert witnesses to establish the fair market value of the Jung Corp. stock. It would serve no useful purpose to make a detailed analysis1993 U.S. Tax Ct. LEXIS 69">*90 of the testimony of these experts to explain item by item the extent to which we agree or disagree with their analysis. Valuation is a not precise science, and the determination 101 T.C. 412">*424 of the fair market value of property on a given date is a question of fact ( Kaplan v. Commissioner, 43 T.C. 663">43 T.C. 663, 43 T.C. 663">665 (1965)), to be resolved on the basis of the entire record ( McShain v. Commissioner, 71 T.C. 998">71 T.C. 1004), and without necessarily being bound by the opinions of the expert witness, Silverman v. Commissioner, 538 F.2d 927">538 F.2d 927, 538 F.2d 927">933 (2d Cir. 1976), and cases there cited, affg. T.C. Memo. 1974-285; Palmer v. Commissioner, 523 F.2d 1308">523 F.2d at 1310. However, we will note considerations that we have taken into account in our determination and explain how we reach our conclusions. See Akers v. Commissioner, 798 F.2d 894">798 F.2d 894, 798 F.2d 894">897 (6th Cir. 1986), revg. and remanding T.C. Memo. 1984-208.

Petitioner contends that the value of decedent's stock on October 9, 1984, was $ 2,997,708 (after applying discounts). 1993 U.S. Tax Ct. LEXIS 69">*91 Petitioner averages the per-share amounts determined by its three experts and multiplies this average ($ 17.78) by the number of shares (168,600) to arrive at its position. This position is about 12 percent greater than the amount shown on the estate tax return. On brief, in regard to the prediscount value of Jung Corp., petitioner does not offer substantive criticism of respondent's expert witness reports.

In contrast, respondent finds error in all of the expert witness reports, including those of her own expert witnesses. Respondent contends that all the experts undervalued Jung Corp. Respondent criticizes each report on various grounds, and urges this Court to determine a value for Jung Corp. by determining each element used in the discounted cash-flow (hereinafter sometimes referred to as DCF) approach, ⁶ and by recomputing value based on that approach. Respondent contends that the DCF approach gives decedent's shares a prediscount value of $ 46.20 per share. Respondent contends that if we choose to rely in whole or in part on the comparable market approach, then we should refer to ratios of companies selected by both parties' expert witnesses, as compiled by respondent. 1993 U.S. Tax Ct. LEXIS 69">*92 Respondent contends that Jung Corp. is two-thirds health care operations and one-third elastic textile operations. Respondent contends that the Court would need 101 T.C. 412">*425 only to determine the appropriate normalized income to be used in the market comparable analysis, and the emphasis to be given to the home health care and elastic textile segments of Jung Corp. Respondent contends that under the comparable market approach the prediscount value of decedent's shares is $ 56.11 per share. Respondent contends that the Court should give the comparable market approach twice the weight as the DCF approach, so that the prediscount value of decedent's shares is $ 52.81 per share. As to discounts, respondent contends that a minority discount should not be applied, and that a marketability discount of 10 percent should be applied, giving decedent's stock a value after discounts of $ 47.53 per share, which results in a total that respondent rounds to $ 8 million. Respondent also contends that in valuing decedent's stock, proceeds of the 1986 sale and liquidation of Jung Corp. should be considered. Respondent's position on brief is about 4 percent less than the amount shown on the notice1993 U.S. Tax Ct. LEXIS 69">*93 of deficiency and about 43 percent greater than the revised amount presented by her own expert witnesses.

We agree with petitioner in part, and we agree with respondent in part.

First, we briefly summarize the approaches and conclusions of the experts. Then we analyze the value of Jung Corp. as of October 9, 1984. Then we consider the appropriateness and magnitude of discounts for marketability and minority interests. Finally, we reach our conclusion as to the1993 U.S. Tax Ct. LEXIS 69">*94 fair market value of the property (i.e., decedent's 168,600 shares of Jung Corp.).

Both sides submitted expert witness reports and presented expert witness testimony in regard to the value of decedent's stock at the date of death. Three expert witnesses testified for petitioner, and two expert witnesses testified for respondent.

Robinson is a 50-percent owner of Mayfield. He is an attorney and an accountant, and has had extensive experience in valuing businesses. Robinson submitted his report to petitioner on April 8, 1985, before the estate tax return was 101 T.C. 412">*426 filed, and his valuation was the amount used on the tax return -- $ 2,671,973.

Robinson concluded that the best measure of value for Jung Corp. was by reference to Jung Corp.'s earning capacity. Robinson did not use the comparable sales method of valuation because he concluded that there were no public companies whose business was reasonably comparable to Jung Corp.'s. In particular, although there were publicly traded hosiery companies about the size of Jung Corp., "they are not significant participants in the health care or sports business in the [same] sense that1993 U.S. Tax Ct. LEXIS 69">*95 Jung is. Competitors * * * in the sports and health care market are typically so large overall that comparisons are meaningless." Robinson concluded that Jung Corp. should be valued at less than book value, which he determined to have been $ 19,857,000, as adjusted to the first in, first out, method of inventory valuation. Robinson also valued Jung Corp. using a price earnings multiple of 9, which produced a value for Jung Corp. of $ 18,405,000 at the date of death, and which Robinson concluded was the value of Jung Corp. This led to his determination of a prediscount value of $ 3,817,104, or $ 22.64 per share for decedent's stock. Robinson then discounted this value by 30 percent to account for both lack of control and lack of marketability. Robinson did not assign separate discount rates to the control and marketability factors. This resulted in a value for decedent's stock of $ 2,671,973.

David O. McCoy (hereinafter sometimes referred to as McCoy) has more than 20 years of experience in business valuation. McCoy used three approaches in his appraisal: A market comparable approach, a discounted cash-flow approach, and a capitalization of earnings 1993 U.S. Tax Ct. LEXIS 69">*96 approach. The amounts McCoy obtained for the value of Jung Corp. are shown in table 5.

Table 5

101 T.C. 412">*427 McCoy averaged the eight amounts, and rounded the result, obtaining a prediscount value of Jung Corp. of $ 18,966,000, and a prediscount value for decedent's stock of $ 23.34 per share. McCoy then applied a discount of 35 percent for lack of marketability, but no minority discount, giving decedent's stock a value of $ 15 (rounded) per share. This comes to a total of $ 2,529,000 for the 168,600 shares.

At trial, McCoy conceded a number of errors, and estimated the effects of correcting certain of these errors. As a result, petitioner evaluates McCoy's revised valuation estimate as $ 17.50 per share, which comes to a total of $ 2,950,500 for the 168,600 shares.

Roger J. Grabowski (hereinafter sometimes referred to as Grabowski) is a principal and director of Price Waterhouse Valuation Services, 1993 U.S. Tax Ct. LEXIS 69">*97 and he has had extensive experience in valuing businesses. In valuing Jung Corp., Grabowski divided the various subsidiary companies of Jung Corp. into three separate groups. The health care product operations group comprises Futuro, JII, Theradyne, and Calley & Currier. The elastic textile operations group comprises JRA, Rampon, and the activities of the Richard Grey Co. (which was a part of Rampon). The third group comprises the real estate assets and machinery and equipment assets of Ione. Grabowski used the market comparable approach and the DCF approach, see supra note 6, in valuing the first two groups.

In Grabowski's revised report, his market comparable approach gave the following values shown in table 6.

101 T.C. 412">*428 Table 6

1993 U.S. Tax Ct. LEXIS 69">*98 Grabowski also used the DCF approach in valuing the health care products operations and the elastic textile operations.

In Grabowski's revised report, his DCF approach gives the values shown in table 7.

Table 7

101 T.C. 412">*429 Grabowski concluded that the average of the two approaches was the value of decedent's stock. He concluded that decedents's Jung. Corp. stock was worth $ 20 per share (rounded). This comes to a total of $ 3,372,000 for the 168,600 shares.

Martin D. Hanan (hereinafter sometimes referred to as Hanan) 1993 U.S. Tax Ct. LEXIS 69">*99 and Mark L. Mitchell (hereinafter sometimes referred to as Mitchell) prepared a joint expert witness report, and both of them testified. Hanan is the founder and president of Business Valuation Services and Mitchell manages the financial valuation services for Business Valuation Services. Both Hanan and Mitchell have extensive experience in valuing businesses. Hanan and Mitchell computed value by using the market comparable approach and the DCF approach. Hanan and Mitchell did not rely on the market comparable approach because they had difficulty in developing a reliable sample of comparable firms.

In Hanan and Mitchell's revised report, their DCF approach gives the values shown in table 8.

Table 8

The conclusions of the expert witnesses and the Court may be summarized as shown in table1993 U.S. Tax Ct. LEXIS 69">*100 9.

101 T.C. 412">*430 Table 9

B. Value of Jung Corp.

Respondent contends that, in valuing Jung Corp. stock, this Court should consider the sale to Kendall, the other sales, and the ensuing liquidation of Jung Corp. Petitioner contends the 1986 sales and the liquidation are irrelevant because the sales and liquidation were unforeseeable at the valuation date.

We agree in part with respondent and in part with petitioner.

101 T.C. 412">*431 A distinction may usefully be drawn between later-occurring events which affect fair market value as of the valuation date, and later-occurring events1993 U.S. Tax Ct. LEXIS 69">*102 which may be taken into account as evidence of fair market value as of the valuation date.

If a prospective October 9, 1984, buyer and seller were likely to have foreseen the 1986 sale to Kendall, and the other activities leading to the liquidation, then those later-occurring events could affect what a willing buyer would pay and what a willing seller would demand as of October 9, 1984. We conclude, and we have found that, on October 9, 1984, Jung Corp. was not for sale, the sale to Kendall was not foreseeable, and the liquidation was not foreseeable. Accordingly, we conclude that those later-occurring events did not affect the October 9, 1984, fair market of decedent's stock. Estate of Gilford v. Commissioner, 88 T.C. 38">88 T.C. 38, 88 T.C. 38">51-55 (1987).

However, we have stated that "for purposes of determining fair market value, we believe it appropriate to consider sales of properties occurring subsequent to the valuation date if the properties involved are indeed comparable to the subject properties." Estate of Thompson v. Commissioner, 89 T.C. 619">89 T.C. 619, 89 T.C. 619">628-629 n.7 (1987), revd. on other grounds 864 F.2d 1128">864 F.2d 1128 (4th Cir. 1989).1993 U.S. Tax Ct. LEXIS 69">*103 To the same effect are, e.g., Krapf v. United States, 977 F.2d 1454">977 F.2d 1454, 977 F.2d 1454">1458-1460 (Fed. Cir. 1992); Estate of Kaplin v. Commissioner, 748 F.2d 1109">748 F.2d 1109, 748 F.2d 1109">1111 (6th Cir. 1984), revg. T.C. Memo. 1982-440; Estate of Brown v. Commissioner, 425 F.2d 1406">425 F.2d 1406, 425 F.2d 1406">1407 (5th Cir. 1970), affg. T.C. Memo. 1969-91. See Estate of Jung v. Commissioner, T.C. Memo. 1990-5, and cases cited therein.

Of course, appropriate adjustments must be made to take account of differences between the valuation date and the dates of the later-occurring events. For example, there may have been changes in general inflation, people's expectations with respect to that industry, performances of the various components of the business, technology, and the provisions of tax law that might affect fair market values between October 9, 1984, and the sales and liquidation some 2 years later. Although any such changes must be accounted for in determining the evidentiary weight to be given to the later-occurring events, those changes ordinarily are not justification1993 U.S. Tax Ct. LEXIS 69">*104 for ignoring the later-occurring events (unless other comparables 101 T.C. 412">*432 offer significantly better matches to the property being valued).

When viewed in this light -- as evidence of value rather than as something that affects value -- later-occurring events are no more to be ignored than earlier-occurring events.

Accordingly, we do not consider the sales and eventual liquidation as affecting the October 9, 1984, value of Jung Corp., but we do consider these events as evidence of the October 9, 1984, value.

Robinson did not consider the 1986 events in his expert witness report. This is to be expected -- his report was submitted to petitioner on April 8, 1985, and was the foundation for the valuation on the estate tax return, which was filed on July 9, 1985.

At trial, on re-cross-examination, Robinson was asked if he considered Jung Corp. to be an acquisition candidate, and whether, if a company were about to be acquired at a premium, that would affect its value. Robinson agreed that one would take that into account. However, he went on to emphasize that he was not aware of that potential, and that he did not think that Jung Corp. was an 1993 U.S. Tax Ct. LEXIS 69">*105 attractive acquisition candidate on October 9, 1984.

McCoy did not consider the 1986 events in his expert witness report. At trial, on direct examination, he stated that he was aware of the sale, but did not know any details about it. He testified that he considered whether he should take into account the liquidation values, and made a decision that he should not take them into account. He said that the reasons the liquidation values are not relevant were (1) in 1984 there was no intention to sell Jung Corp., and (2) a minority interest holder has no power to force a liquidation or sale.

Hanan and Mitchell considered the liquidation proceeds in their appraisal. After taking into account the changes in the market and the changes in Jung Corp. between October 9, 1984, and the 1986 sales and liquidation, they concluded that the proceeds obtained in the 1986 liquidation supported their date of death valuation.

Grabowski did not consider the liquidation proceeds in his initial report. In his rebuttal report Grabowski contended that Hanan and Mitchell made errors in their calculations. 101 T.C. 412">*433 Nevertheless, after taking into account his view of how the intervening events should 1993 U.S. Tax Ct. LEXIS 69">*106 be accounted for, he concluded that the proceeds obtained by the shareholders in liquidation were consistent with his date of death valuation.

Thus, Grabowski and Hanan and Mitchell evaluated the 1986 events in the manner we described supra as being appropriate (i.e., as evidence of fair market value as of the valuation date, and not as events affecting fair market value as of the valuation date) and concluded that this evidence was consistent with the results they derived from using the DCF approach.

Respondent urges us "to determine the appropriate rate or amount for each DCF element." Respondent also urges us to give twice the weight to the comparable market approach as to the DCF approach. Respondent concludes that Jung Corp. was worth $ 52.81 per share, which amounts to a total of about $ 43 million.

In the instant case, we believe the DCF approach to valuing Jung Corp. is more reliable than the market comparable approach. The market comparable approach does not work well in the instant case because the comparable corporations do not have the same product mix (health and elastic textile) as Jung Corp. None of the experts relied exclusively on the market1993 U.S. Tax Ct. LEXIS 69">*107 comparable approach, and Hanan and Mitchell and Robinson rejected the market comparable approach because they had difficulty finding companies which were similar to Jung Corp. At trial, Grabowski also stated that he did not rely on the market comparable approach.

Finally, the 1986 sales of parts of Jung Corp. have been shown by Grabowski and by Hanan and Mitchell to be consistent with their conclusions of an October 9, 1984, value of $ 32-34 million for Jung Corp. See supra table 9. The lower valuations by Robinson and McCoy (about $ 18.4 and $ 22.1 million, respectively) were not reconciled with the 1986 events, and we doubt that they could be so reconciled.

We conclude that Hanan and Mitchell and Grabowski accurately valued Jung Corp. using the DCF approach. We conclude (and we have found) that the prediscount value of Jung Corp. was about $ 32-34 million. Decedent's shares 101 T.C. 412">*434 amounted to 20.74 percent of the total and were worth about $ 6.7 to $ 7.0 million, without giving effect to discounts.

The parties agree that the date-of-death value to be assigned to decedent's shares should be discounted in some manner. Cases involving the valuation of1993 U.S. Tax Ct. LEXIS 69">*108 minority holdings in close corporations ordinarily consider a discount or discounts because the stock is a minority holding and is not publicly traded. Conceptually, (1) a minority discount reflects a minority shareholder's inability to compel liquidation and thus inability to realize a pro rata portion of the corporation's net assets value, while (2) a marketability discount reflects the hypothetical buyer's concern that there will not be a ready market when that buyer decides to sell the stock. Each of these prospects (lack of control and lack of ready market) is likely to depress the price that a hypothetical buyer is likely to be willing to pay for the stock. Although we analyze them separately, it is likely that there is a significant real-world overlap between these two discounts. Estate of Andrews v. Commissioner, 79 T.C. 938">79 T.C. 938, 79 T.C. 938">952-953 (1982).

Respondent does not dispute that a marketability discount should be applied. The only dispute is the amount of the discount. Respondent contends that a marketability discount of 10 percent is appropriate. Petitioner contends that decedent's stock should be discounted 35 percent for lack of marketability.

1993 U.S. Tax Ct. LEXIS 69">*109 Petitioner contends that decedent's stock also should be discounted 25 percent because it is a minority interest in Jung Corp. Respondent acknowledges that a minority discount often is appropriate, but contends that under the DCF approach to valuation used in the instant case, no minority discount should be applied because the DCF approach used in the expert witness reports values the stock by reference to minority positions, so that the value obtained in the instant case is inherently the value of a minority interest.

Under petitioner's approach, the combined discounts amount to a 51.25-percent reduction ⁷ from the undiscounted 101 T.C. 412">*435 value of decedent's shares. Respondent's approach would allow an overall 10-percent discount. The experts' views, and the Court's conclusions, are shown supra, in table 9.

1993 U.S. Tax Ct. LEXIS 69">*110 We agree with petitioner as to the marketability discount and with respondent as to the minority discount. Thus, we apply a 35-percent reduction from the undiscounted value of decedent's shares.

Grabowski reviewed six studies of transactions involving restricted stock. Grabowski's report indicated that these studies showed marketability discounts as follows:

Based on these studies, Grabowski concluded that a 35-percent discount for lack of marketability was appropriate. Grabowski's rebuttal report considered two additional studies, the Baird and Willamette studies. These studies compared initial public offerings to private transactions before the public offering. The Baird and Willamette studies showed median discounts in the private transactions of 66 percent and 74 percent, respectively.

McCoy consulted a trade magazine that publishes information about private placements of common stock. The stocks are1993 U.S. Tax Ct. LEXIS 69">*111 securities of companies that have other common shares that are registered with the SEC and are publicly traded in an active market. These securities are typically bought under an "investment letter" agreement. He reviewed all the private placements shown to have occurred in the 6 years from January 1, 1979, through December 31, 1984. After excluding certain categories of placements, he found 75 private transactions in the common stock of actively traded companies. Of 101 T.C. 412">*436 the 75, 11 occurred at small premiums over the freely traded market price, 1 occurred at that market price, and 63 occurred at discounts (ranging up to 90 percent) from that market price. The average of these private placements was a discount of 27 percent. Under SEC rule 144(b), ⁸17 C.F.R. sec. 230.144 (1984), such restricted securities will eventually become freely tradable through either registration or the passage of time. McCoy reasoned that, if such stocks with a temporary market restriction sold at an average discount of 27 percent, then Jung Corp. stock with a permanent market restriction should sell at a discount greater than 27 percent; he chose 35 percent. McCoy's rebuttal report added 1993 U.S. Tax Ct. LEXIS 69">*112 comments about a Maher study and a Solberg study that supported average and modal discounts of 35 percent. In his rebuttal, he also indicated that Hanan's and Mitchell's discussions about the marketability of Jung Corp. are irrelevant to the question of marketability of a minority interest in Jung Corp.

Robinson merely stated in his report: "We believe that a discount of 30% should apply to an interest such as Mrs. Jung's to account for the lack of control and lack of marketability." Robinson's report did not favor us with an explanation of his conclusion.

Hanan and Mitchell concluded that a 20-percent marketability discount was appropriate. They based this conclusion on the SEC Institutional Investor Study for 19661993 U.S. Tax Ct. LEXIS 69">*113 through 1969. This was a study of publicly traded stock which was restricted from trading on the open market for a certain period of time. The study shows average discounts of about 25 percent for companies with earnings similar to Jung Corp. Hanan and Mitchell concluded that because a majority of Jung Corp. stock was controlled by the Jung family, the sale of Jung Corp. could be easily accomplished. Hanan and Mitchell also concluded that Jung Corp.'s size, history of profitability, and relatively strong position in the market, and the quality of its management, indicated that the marketability discount should be less than the average marketability discount in the SEC Institutional Investor 101 T.C. 412">*437 Study. Hanan and Mitchell determined the appropriate discount to be 20 percent.

Here, too, respondent disagrees in part with her expert witnesses. Respondent contends that a 10-percent marketability discount is appropriate because Jung Corp. was an attractive acquisition candidate in 1984. Respondent states "that, without consideration of the acquisition potential, the marketability discount appropriate for Jung is between 15% and 20%, as was opined by BVS" (i.e., Hanan and Mitchell).

1993 U.S. Tax Ct. LEXIS 69">*114 We are persuaded by the materials and analyses presented by McCoy and Grabowski. We believe that respondent, and to a lesser extent Hanan and Mitchell, gave too much weight to acquisition potential, or ease of sale, of Jung Corp. as a whole. We have found that, on October 9, 1984, Jung Corp. was not for sale, the sale to Kendall was not foreseeable, and the liquidation was not foreseeable. Also, as McCoy pointed out, we are concerned with the marketability of decedent's interest. We try to evaluate a market for decedent's 20.74-percent interest, not a market for Jung Corp. We assume a hypothetical willing seller of decedent's interest, not a hypothetical willing seller of Jung Corp. The hypothetical willing seller of decedent's shares would have to contend with an actual absence of interest in selling the entire corporation.

Neither respondent nor Hanan and Mitchell presented an explanation of why the inquiries about acquiring Jung Corp. would translate into a significant market for decedent's shares, and we decline to speculate on this point.

We conclude, and we have found, that a 35-percent marketability discount should be allowed.

Respondent contends that a small marketability1993 U.S. Tax Ct. LEXIS 69">*115 discount should be applied because Jung Corp. itself would have repurchased decedent's shares in order to keep ownership in the family. ⁹ Respondent supports this argument by noting 101 T.C. 412">*438 that in 1972 Jung Corp. bought a 20-percent block of stock from a shareholder who was not a family member. This argument is not persuasive. Firstly, although Conway testified that he would rather decedent's stock did not fall into the hands of a third party, he also testified that Jung Corp. could tolerate a 20-percent shareholder who was not a family member. Further, the fair market value test under section 20.2031-1(b), Estate Tax Regs., contemplates a hypothetical willing buyer and a hypothetical willing seller. Propstra v. United States, 680 F.2d 1248">680 F.2d 1248, 680 F.2d 1248">1251-1252 (9th Cir. 1982); Estate of Bright v. United States, 658 F.2d 999">658 F.2d 999, 658 F.2d 999">1005-1006 (5th Cir. 1981); Minahan v. Commissioner, 88 T.C. 492">88 T.C. 492, 88 T.C. 492">499 (1987); Estate of Andrews v. Commissioner, 79 T.C. 938">79 T.C. 952-956. We will not cast Jung Corp. in the role of the hypothetical willing buyer.

1993 U.S. Tax Ct. LEXIS 69">*116 We hold, for petitioner, that a 35-percent marketability discount shall be applied.

As may be seen from table 9, supra, Grabowski did not provide for a minority discount under his market comparables approach (except for the minor matter discussed supra in table 9 note 3); McCoy did not provide for minority discount under any of the approaches he considered (see supra table 5; three-eighths of his final figures depend on a DCF approach); and Robinson's 30-percent discount was intended to take care of both marketability and minority considerations. Hanan and Mitchell provided for a 25-percent minority discount, but only for about 1 percent of the overall value, and so that minority discount had practically no effect on their conclusion. See supra table 9 note 6.

Only Grabowski, among the expert witnesses, argues for a minority discount, and then only if we accept the DCF approach to valuation of decedent's interest in Jung Corp. As noted supra, (1) we accept the DCF approach to valuation of decedent's interest in Jung Corp., and (2) we accept the general concept of a minority discount in appropriate circumstances.

101 T.C. 412">*439 The matter now before1993 U.S. Tax Ct. LEXIS 69">*117 us is whether we should allow a minority discount in addition to the 35-percent marketability discount we have already determined to allow, and, if so, then in what amount. The resolution of this issue depends on the workings of the DCF approach as used by the expert witnesses before us and explained on the record in the instant case.

Grabowski contends that his DCF approach was designed to produce a control value, but concedes that a DCF approach could be used to produce a minority interest value (i.e., a value as to which a minority discount would not be appropriate). Hanan and Mitchell contend that their DCF approach embodies a minority interest value.

Grabowski contends that his DCF approach leads to a control value because (a) his cash-flow assumptions for Jung Corp. were based on what a controlling interest could do to Jung Corp. to make it run better, (b) the discount rate he used did not reflect minority interest evaluation, and (c) his equity risk premium assumed large company financing synergies. We consider these contentions seriatim.

(a) Grabowski's initial expert witness report states that a minority discount is needed because his DCF valuation was done on a controlling1993 U.S. Tax Ct. LEXIS 69">*118 interest basis. The expert witness report states: "We presume that an investor is able to take the steps necessary to realize the projected results; therefore, a controlling interest is implicit." In his rebuttal expert witness report, Grabowski states as follows:

Third, we have included one, quantifiable major synergy into our calculation which causes the formulation of the discounted cash flow approach to be a control value. Premiums for control are paid in buying entire businesses. That is, the controlling shareholders of Jung could realize a higher price if they could sell the business to a buyer who could affect [effect?] savings or synergies. (Such synergies are oftentimes categorized as operating, financial and tax synergies.)

Operating savings on [or?] synergies result from increased sales or reduced costs by operating the business differently or combining businesses with a specific acquiring company.

Financial synergy results form [from?] lower costs of funds because the acquiring firm or combined firms are perceived as less risky. Tax synergy results from tax savings peculiar to combining with a specific buyer (i.e., operating loss carryforwards to a specific1993 U.S. Tax Ct. LEXIS 69">*119 buyer).

We did not discover any major operating savings that a control-buyer of Jung could realize from changing the operations of Jung as a stand-along 101 T.C. 412">*440 [alone?] company. Operating synergies and tax synergies are unique to each potential purchaser and could not be measured by the controlling shareholders of Jung. However, we did account for financing synergies which could only be realized if the existing controlling shareholders of Jung were to take action and sell their shares.

In his oral testimony, Grabowski explained as follows:

So we have measured available cash flow based on what we observe to be a reasonable way Jung Corp. was being run. We did not make, I grant you, any operating changes to Jung Corp. in the calculations of the cash flow. Sometimes, Your Honor, when you are doing a control basis, you will find that the controlling shareholder is taking $ 5 million of salary out. And if you are valuing on a control basis, you will add back the excess salary; he may or may not be worth $ 5 million. But if you determine that he is not, you would add that back. Because if I controlled the business, I would not run it that way.

But there was no excessive amounts1993 U.S. Tax Ct. LEXIS 69">*120 of compensation that we determined, excessive items that required extensive adjustments, et cetera, in valuing the control interest.

In neither his expert witness reports nor his oral testimony did Grabowski suggest any other element of his calculation of the amount of the available cash-flow that would make his DCF approach a valuation of a controlling interest.

From the foregoing, we gather that the only element of Grabowski's calculation of the amount of the available cash-flow that would make his DCF approach a valuation of a controlling interest is the financing synergy, which we discuss infra. As far as we can tell, in all other respects Grabowski's calculation of the amount of the available cash-flow was done on a basis which, by itself, would not result in a control premium, or minority discount.

(b) The second area of dispute is whether the discount rate applied by the expert witnesses puts the DCF approach valuations on a minority basis. In their initial expert witness report, Hanan and Mitchell stated that no minority discount was needed in their DCF valuation because their discount rate was derived by using equity return data from the trading of minority interests1993 U.S. Tax Ct. LEXIS 69">*121 in publicly traded companies.

As explained previously, supra note 6, the DCF approach involves calculating the sum of the present value of the available cash-flow and the present value of the terminal value. A discount rate, which represents the required rate of return of an investor in an alternate investment opportunity, is used in this calculation. The discount rate is the weighted 101 T.C. 412">*441 average of the required rate of return on equity capital and the required rate of return on debt capital. Both Grabowski and Hanan and Mitchell determined the required rate of return on equity capital by using the capital asset pricing model (hereinafter sometimes referred to as CAPM). The CAPM is the risk-free rate plus the product of the beta ¹⁰ for the specific company and an equity risk premium.

1993 U.S. Tax Ct. LEXIS 69">*122 The risk-free rate is the yield to maturity on 20-year (Grabowski) or 30-year (Hanan and Mitchell) U.S. Treasury bonds on the valuation date. This yield is available to investors in the market, without regard to control or minority status. Accordingly, this element of the discount rate does not affect the question of whether the DCF approach results in a controlling interest value or a minority interest value.

Although the establishment of a beta for Jung Corp. involves consideration of many matters (e.g., selecting comparable companies the securities of which are commonly traded on stock exchanges, "unlevering" and "relevering"), it is enough for our purposes to observe that Grabowski and Hanan and Mitchell agree that the Jung Corp. beta was a little under 1. Also, because the betas for the companies and industries that these expert witnesses used are derived from reported stock exchange trading data, which is almost entirely the data of trading in minority interests, this element of the discount rate suggests that ordinarily the DCF approach results in a minority interest value.

Grabowski and Hanan and Mitchell based their equity risk premiums on Ibbotson and Associates' publication, 1993 U.S. Tax Ct. LEXIS 69">*123 "Stocks, Bonds, Bills, and Inflation". Grabowski based his calculations --

on the arithmetic mean of actual investor returns over the period of 1950-1984 and consists of an overall excess return for the stock market as a 101 T.C. 412">*442 whole of 7.34% (the additional return common stock investors earned in excess of the return on long-term government bonds).

Hanan and Mitchell used the same source and --

concluded that the market risk premium [a different term for equity risk premium] equals 6.9%, the average annualized total return on equity investments (defined as the S&P 500) in excess of the average annualized bond yield (income) return on long-term government bonds over the period January 1926 to December 1983.

The modest difference between Grabowski's equity risk premium and that used by Hanan and Mitchell is one of many differences between them that were largely balanced out so that their bottom-line values for Jung Corp. differed by less than 3 percent. See supra table 9. What is important for purposes of the minority discount question is that the basic data these experts used are the data of stock market trading, which is almost entirely the data of trading in minority1993 U.S. Tax Ct. LEXIS 69">*124 interests. Thus, this element of the discount rate also suggests that ordinarily the DCF approach results in a minority interest value.

In his rebuttal expert witness report Grabowski contends that the discount rate represents the minimum rate of return which the corporation must earn on its investments, including acquisitions of controlling interests. He notes that the prospective controlling investor will control the total available cash-flow of the acquired corporation. However, this explanation does not persuade us that the discount rate in Grabowski's DCF calculation implies control, because this rate of return is developed from data that reflect the actions of minority investors and generally not the actions of controlling investors.

We agree with respondent that the discount rates used by the expert witnesses in the instant case reflect the minority position. ¹¹

1993 U.S. Tax Ct. LEXIS 69">*125 101 T.C. 412">*443 (c) Grabowski's main argument is his third argument. He contends that his equity risk premium assumed large company financing synergies. He contends that his equity risk premium of 7.34 percent is appropriate only if Jung Corp. were to be acquired by a large company which could incorporate financing synergies into Jung Corp. He contends that Hanan and Mitchell also assumed financing synergies in determining their equity risk premium of 6.9 percent. In his rebuttal expert witness report Grabowski contends that taking into account Jung Corp.'s small size, the equity risk premium should be 16.73 percent rather than 7.34 percent. Grabowski asserts that a premium of 16.73 percent is appropriate based on the equity risk premiums of the smallest companies traded on the New York Stock Exchange. Stated otherwise, Grabowski is contending that a "small stock" premium of 16.73 percent should have been applied in the DCF valuation, and that because he did not apply a small stock premium, a minority discount is needed to make up for his error. Grabowski did not make this contention in his initial expert witness report. He made this contention only when his minority discount1993 U.S. Tax Ct. LEXIS 69">*126 was challenged. We do not agree that a small stock premium is appropriate in the instant case, and we do not agree that a minority discount is appropriate in the instant case.

Firstly, if Grabowski had applied the small stock premium in his DCF approach to Jung Corp.'s value, then his prediscount value would be only about $ 20 million. ¹² That 101 T.C. 412">*444 number is even less than McCoy's revised estimate. See supra table 9. Grabowski has not shown us how a $ 20 million October 9, 1984, valuation (or any valuation calculated with Grabowski's small stock premium) could be reconciled with the 1986 sales and liquidation proceeds. We rejected McCoy's $ 22 million valuation in part because of McCoy's failure to so reconcile, and accepted Grabowski's $ 33 million valuation because it could be reconciled with the 1986 events.

1993 U.S. Tax Ct. LEXIS 69">*127 Accordingly, we reject Grabowski's contention that he had erred by failing to use a small stock premium in his initial expert witness report calculation in the instant case. Because a small stock premium would not have been appropriate in the instant case (whatever may be the general validity of the small stock premium concept), there is no force to Grabowski's contention that a minority discount is appropriate in order to make up for Grabowski's failure to use a small stock premium.

Secondly, Mitchell testified that small companies tend to be more risky because they tend to be in risky industries. Thus, the apparently greater equity risk premiums for small companies, on which Grabowski relies, are merely a reflection of the risk involved in the type of activity and not a greater risk arising merely or primarily because of corporate size. As a result, it is not at all clear that there is any general validity in the small stock premium concept, except as a substitute for a beta rating. See Pratt, Valuing a Business: The Analysis and Appraisal of Closely-Held Companies 76-77 (2d ed. 1989).

Thirdly, at trial when Grabowski was asked to explain the differences in risk and1993 U.S. Tax Ct. LEXIS 69">*128 rates of return in regard to an investment in a small company like Jung Corp., and an investment in a large publicly traded company, Grabowski discussed lack of control and lack of marketability, factors which are taken into account by the DCF approach and a discount for lack of marketability. Grabowski did not provide the Court with any evidence that Jung Corp. is a riskier investment simply because of its small size. In addition, Grabowski did not provide any explanation of why the size of the corporation affects 101 T.C. 412">*445 the appropriateness of a discount for a minority interest in the corporation.

We conclude that in the instant case financing synergies do not justify a minority discount, on top of the 35-percent marketability discount that we have already determined to allow.

At trial, the Court raised the question of whether some amount of minority discount is appropriate to account for the difference between a minority shareholder in a publicly traded corporation and a minority shareholder in a closely held corporation. On brief petitioner contends that there is a difference between minority shareholders in private and publicly traded companies, but petitioner provides1993 U.S. Tax Ct. LEXIS 69">*129 neither authority nor persuasive reasoning to support the contention. Respondent contends that although there may be differences, the differences generally do not affect the value of the stock, and in any event do not affect the value of decedent's stock in the instant case. The Court has not found any authority for using the public-private distinction as a basis for applying a minority discount. Accordingly, in the instant case we do not apply a minority discount based on the differences between public and private minority shareholders.

We conclude that the DCF calculations by Grabowski and by Hanan and Mitchell in the instant case were on a minority basis, and we have found that in the instant case no minority discount should be applied to the values determined using the DCF approach.

Petitioner contends that in Northern Trust Co., Transferee v. Commissioner, 87 T.C. 349">87 T.C. 349, 87 T.C. 349">383 (1986), affd. sub nom. Citizens Bank & Trust Co. v. Commissioner, 839 F.2d 1249">839 F.2d 1249 (7th Cir. 1988), this Court approved the use of a minority discount when the DCF approach is used in valuation. Respondent tells us that the instant case provides1993 U.S. Tax Ct. LEXIS 69">*130 us "with an opportunity to reconsider issues" in Northern Trust Co., Transferee.

In Northern Trust Co., Transferee, stock of a closely held corporation was valued. Grabowski submitted an expert witness report and testified in that case. Grabowski used the DCF approach, and he used the CAPM to determine the discount rate. After deciding on a value for the corporation, he applied a minority discount. 87 T.C. 349">87 T.C. 369. This Court concluded that the DCF approach correctly determined the value 101 T.C. 412">*446 of the stock. We also allowed both minority and marketability discounts. Id. However, in Northern Trust Co., Transferee, respondent did not contend that no minority discount was appropriate. Rather, respondent merely argued for a lower minority discount than the discount for which the taxpayer contended. Id. Because the parties in Northern Trust Co., Transferee did not present to the Court the question of whether a minority discount could be allowed in conjunction with the DCF approach, the opinion in that case did not explore whether the DCF approach that Grabowski used in that case was calculated on a control basis rather than1993 U.S. Tax Ct. LEXIS 69">*131 on a minority basis. See Estate of Fusz v. Commissioner, 46 T.C. 214">46 T.C. 214, 46 T.C. 214">215 n.2 (1966).

Thus, we do not accept respondent's invitation to reconsider our opinion in 87 T.C. 349">Northern Trust Co., Transferee v. Commissioner, supra, and we also conclude that that opinion does not require us to allow a minority discount in the instant case.

We hold, for respondent, that no minority discount shall be applied.

In determining the date-of-death value of decedent's shares in Jung Corp., we have concluded that the value of Jung Corp. was $ 32-34 million. We have concluded that the prediscount value of decedent's shares was $ 6.7 to $ 7 million, and that this must be discounted by 35 percent.

We are obligated to set a specific number on the value of decedent's interest. We are not so presumptuous as the parties, who claimed the wisdom in the estate tax return and in the notice of deficiency to determine the value to seven significant figures ($ 2,671,973 and $ 8,330,448, respectively). Taking into account the "inherently imprecise" nature of this issue, Messing v. Commissioner, 48 T.C. 502">48 T.C. 502, 48 T.C. 502">512 (1967),1993 U.S. Tax Ct. LEXIS 69">*132 we determine this value to two significant figures -- $ 4,400,000. We have so found.

We hold for neither party on this issue, although we note that our conclusion is significantly closer to petitioner's position than it is to respondent's position.

In her amendment to answer, respondent asserts an addition to tax under section 6660. See sec. 6214(a). Respondent asserts that the value claimed on the tax return is less than 40 percent of the correct value, and so the addition to tax should amount to 30 percent of the underpayment attributable to the valuation understatement. On brief, respondent does not specifically ask for the 30-percent rate, but rather asks for an addition to tax "in an amount to be computed based upon the value of the decedent's interest in Jung as determined by the Court." Respondent contends that petitioner did not have a reasonable basis for the valuation claimed on its tax return and that respondent did not abuse her discretion in refusing to waive the addition.

Petitioner contends that there should be no addition to tax because (1) there is no valuation understatement, and (2) even if there is a valuation understatement, 1993 U.S. Tax Ct. LEXIS 69">*133 the addition to tax should be waived because (a) there was a reasonable basis for the estate tax return value, (b) petitioner claimed this value in good faith, and (c) respondent "wrongfully refused to waive the addition to tax".

Respondent relies on our opinion in Mailman v. Commissioner, 91 T.C. 1079">91 T.C. 1079 (1988). Petitioner seeks to distinguish that case because (1) it is based on a different Code section (sec. 6661, not sec. 6660, as is the instant case), (2) in Mailman we relied on regulations under section 6661 while there are no regulations under section 6660, and (3) in Mailman there was no expert evidence or evidence of the taxpayer's efforts to determine proper tax liability, while in the instant case there is substantial evidence in both categories.

We agree with respondent that there is a valuation understatement, but we agree with petitioner that the resulting addition to tax should be waived.

Section 6660¹³ provides for an addition to tax if there is an underpayment of tax of at least $ 1,000 attributable to a 101 T.C. 412">*448 valuation understatement for purposes of estate or gift tax. There is a valuation understatement if the value 1993 U.S. Tax Ct. LEXIS 69">*134 stated on the tax return is 66 2/3 percent (or less) of the correct value. Respondent may waive all or part of this addition to tax if there was a reasonable basis for the valuation claimed on the return and the claim was made in good faith.

1993 U.S. Tax Ct. LEXIS 69">*135

Because respondent did not determine the addition to tax in the notice of deficiency, but asserted it in the amendment to answer, respondent has the burden of proof on all of the elements of section 6660. Rule 142(a); see Reiff v. Commissioner, 77 T.C. 1169">77 T.C. 1169, 77 T.C. 1169">1173 (1981); Achiro v. Commissioner, 77 T.C. 881">77 T.C. 881, 77 T.C. 881">889-891 (1981).

We consider first whether there is a valuation understatement and, if so, then whether the addition to tax should be waived.

101 T.C. 412">*449 A. Valuation Understatement

As shown supra in table 4, we hold that the correct value of decedent's interest in Jung Corp. is $ 4,400,000, and petitioner claimed on its estate tax return that the value is $ 2,671,973. The claimed value thus is about 60.7 percent of the correct value. It follows that there is a valuation understatement, sec. 6660(c), and that the applicable percentage is 10 percent, sec. 6660(b). It is apparent that the underpayment of estate tax attributable to the valuation understatement is at least $ 1,000. Sec. 6660(d).

As a result, an addition to tax of 10 percent of the attributable underpayment is to be imposed on account of the valuation1993 U.S. Tax Ct. LEXIS 69">*136 understatement, unless the addition to tax is waived.

Section 6660(e) provides that the Secretary may waive all or part of the addition to tax under section 6660 if the taxpayer shows both (1) that there was a reasonable basis for the valuation claimed on the tax return, and (2) that the taxpayer acted in good faith in claiming that valuation. The denial of a waiver by the Secretary is reviewable by this Court on an abuse-of-discretion basis. Mailman v. Commissioner, 91 T.C. 1079">91 T.C. 1082-1084. ¹⁴1993 U.S. Tax Ct. LEXIS 69">*137 In other words, for petitioner to win on this issue it is not enough for us to conclude that we would have waived the addition to tax -- we would have to conclude that, in refusing to waive the addition to tax, respondent has exercised this discretion "arbitrarily, capriciously, or without sound basis in fact." Mailman v. Commissioner, 91 T.C. 1079">91 T.C. 1084; ¹⁵ see Capitol Fed. Sav. & Loan v. Commissioner, 96 T.C. 204">96 T.C. 204, 96 T.C. 204">213, 96 T.C. 204">223 (1991).

101 T.C. 412">*450 In the instant case, respondent has the burden of proof on the section 6660 addition to tax. If respondent were to prove that either (1) there was not a reasonable basis for the valuation claimed on the tax return, or (2) the valuation claim was not made in good faith, then1993 U.S. Tax Ct. LEXIS 69">*138 respondent would have proven that petitioner failed to meet the statutory predicate for consideration of a waiver. Failing that, respondent could prevail if she were to prove that her refusal to waive the addition to tax (1) was not arbitrary, (2) was not capricious, and (3) had a sound basis in fact.

We consider first whether the valuation claim was made in good faith, then whether there was a reasonable basis for the valuation, and finally whether respondent abused her discretion in failing to waive the addition to tax.

It was clear that decedent's interest in the Jung Corp. constituted substantially all of decedent's estate. The executrix proceeded promptly to retain the services of Robinson, an experienced appraiser. Robinson examined financial records and interviewed officials of Jung Corp. On April 8, 1985, he submitted a report which provided some explanation of his conclusions. Petitioner's estate tax return, incorporating Robinson's valuation, was filed timely, on July 9, 1985. Respondent does not direct our attention to any evidence pointing to lack of good faith.

We conclude (and we have found) that petitioner acted in good faith in claiming1993 U.S. Tax Ct. LEXIS 69">*139 the valuation reported on the estate tax return.

It is a close question whether there was a reasonable basis for the valuation claimed on the return.

On the one hand, Robinson undervalued decedent's stock by about $ 1.7 million -- an undervaluation of about 39 percent of what we have determined to be the correct value. Robinson's report is short, it is deficient in providing data and support for its conclusions, and the Court has given little weight to it in valuing the stock. ¹⁶

1993 U.S. Tax Ct. LEXIS 69">*140 101 T.C. 412">*451 On the other hand, Robinson's analysis does have some validity, and his conclusions were based on his extensive experience as an appraiser. Robinson's report, although poor for purposes of assisting the Court in determining the value of decedent's interest, does give some explanation of Robinson's conclusion, analysis, and process. Also, it is evident that valuing decedent's interest is a difficult task. After all, in the notice of deficiency respondent overvalued decedent's interest by about 89 percent. Even on brief, after having access to all the expert witness reports and other evidence of record (more than 3 1/2 linear feet of exhibits and almost 1,000 pages of transcript), respondent overvalued decedent's interest by about 82 percent. Thus, petitioner's valuation was much closer to the mark than was respondent's valuation.

Petitioner does not contend that Robinson's value for Jung Corp. ($ 18,405,000) can be reconciled with the proceeds which were obtained by the shareholders through the sale of Jung Corp.'s subsidiaries and assets; however, this does not negate our finding of a reasonable basis. When the appraisal report was prepared and the estate tax return1993 U.S. Tax Ct. LEXIS 69">*141 was filed, neither Robinson nor the executrix of the estate knew that Jung Corp.'s subsidiaries and assets would be sold, and what the liquidation proceeds would amount to.

Under the circumstances, we conclude (and we have found) that there was a reasonable basis for the valuation claimed on the estate tax return.

If our role were to determine whether petitioner had reasonable cause and acted in good faith, then our determinations under items 1 and 2, supra, would be enough, and petitioner would prevail. However, for the years before the Court our role is much more limited. See supra the last paragraph of note 13. As we stated in Mailman v. Commissioner, 91 T.C. 1079">91 T.C. 1079, 91 T.C. 1079">1084 (1988) --

101 T.C. 412">*452 Unlike other additions to tax such as for failure to timely file (sec. 6651(a)(1)), the statute does not provide that the taxpayer's proof of reasonable cause will excuse the taxpayer's misfeasance.

To put it another way, under the statute's language petitioner's showing of reasonable basis and good faith serve only to bring petitioner to the point where respondent "may waive all or any part of the addition to the tax". 1993 U.S. Tax Ct. LEXIS 69">*142 Sec. 6660(e) (emphasis added). That is, such a showing gets petitioner into the game; in order for petitioner to win the game, we must consider whether respondent's refusal to waive is an abuse of discretion. In the instant case we have to determine whether respondent has carried her burden of persuading us that her discretion was not exercised "arbitrarily, capriciously, or without sound basis in fact." Mailman v. Commissioner, 91 T.C. 1079">91 T.C. 1084.

On the one hand, petitioner's actions have satisfied the good faith and reasonable basis requirements, but not so clearly as to make respondent's refusal to waive arbitrary or capricious. On the other hand, it is evident that respondent's view of the situation was affected by a view of the facts that was far from the view that we took.

As we have noted, respondent overvalued the property by $ 3.6 million on brief, while petitioner undervalued the property by a little more than $ 1.7 on the tax return. From respondent's position on brief, petitioner's tax return undervaluation was enormous. From our view of the facts, the amount of petitioner's tax return undervaluation was less than one-half the amount 1993 U.S. Tax Ct. LEXIS 69">*143 of respondent's overvaluation on brief. We conclude that respondent's discretion was exercised "without sound basis in fact." Mailman v. Commissioner, 91 T.C. 1079">91 T.C. 1084.

We conclude, and we have found, that respondent's refusal to waive the addition to tax under section 6660 was an abuse of discretion.

In Estate of Berg v. Commissioner, T.C. Memo. 1991-279, affd. in part and revd. in part 976 F.2d 1163">976 F.2d 1163 (8th Cir. 1992), we held that respondent's discretion had not been abused in refusing to waive the section 6660 addition to tax. The Court of Appeals reversed on that issue. The record in the instant case is far more favorable to petitioner than the record presented by the taxpayer in Estate of Berg.

101 T.C. 412">*453 In Estate of Berg, the taxpayer did not commission an appraisal until more than 4 years after the decedent's death; in the instant case petitioner did commission an appraisal promptly, and the value on the timely filed estate tax return was based on that appraisal. In Estate of Berg, the estate tax return did not provide support for the claimed valuation, except for a reference1993 U.S. Tax Ct. LEXIS 69">*144 to another opinion of this Court; in the instant case, Robinson's appraisal was deficient in terms of evidentiary standards, but provided some substantive support for the claimed valuation. In Estate of Berg, we agreed with respondent's determination of value; in the instant case, respondent overvalued the property by more than twice as much as petitioner undervalued it. Thus, our conclusion in the instant case that respondent's discretion was abused is consistent with our conclusion in Estate of Berg that respondent's discretion was not abused.

In Estate of Berg, the Court of Appeals held that respondent's discretion was abused. This is the same result that we reach in the instant case.

We conclude that, under these circumstances, the instant case is not an appropriate vehicle for determining whether we agree with the analysis presented by the Court of Appeals for the Eighth Circuit in Estate of Berg v. Commissioner, 976 F.2d at 1166-1167.

We hold for petitioner on this issue.

To take account of the foregoing and concessions on other matters,

Decision will be entered under Rule 155.

APPENDIX

Jung Corp. -- Consolidated as of September1993 U.S. Tax Ct. LEXIS 69">*145 30, 1984