OPINION
In this action plaintiff, the Estate of William E. Newcomer, Deceased, William A. Newcomer, Executor, seeks refund of federal estate taxes paid in accordance with an Internal Revenue Service (“IRS”) review. The sole issue is to determine the fair market value of 45,955 shares of common stock of Newcomer Products, Inc. (“NPI”) on July 6,1967, the date of death of William E. Newcomer (the “decedent”). This question is one of fact. See, e.g., Diefenthal v. United States, 343 F.Supp. 1208, 1210 (E.D.La.1972). Jurisdiction is provided by 28 U.S.C. § 1346(a)(1).
Applicable Law
§ 2031 of the Internal Revenue Code of 1954, 26 U.S.C. § 2031, defines the value of the gross estate of the decedent to include the value of all intangible personal property owned by the decedent at the time of his death. For unlisted stock, in the absence of sales thereof, subsection (b) prescribes that the valuation of such stock shall be determined, inter alia, by reference to stock of similar corporations traded on an exchange.
Treas.Reg. § 20.2031-2 (26 C.F.R. § 20.-2031) provides that the value of stock is the fair market value per share on the applicable valuation date. Subsection (b) thereof fixes the fair market value based on selling prices, and subsection (d) thereof defines the fair market value based on incomplete selling prices or bid and asked prices. The fair market value is “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.” Treas.Reg. § 20.2031-1(b).
Treas.Reg. § 20.2031-2(f) states that, where selling prices and bona fide bid and asked prices are unavailable, the fair market value of stock is to be determined by taking into consideration the company’s net worth, prospective earning power and other relevant factors, including:
“The good will of the business; the economic outlook in the particular industry; the company’s position in the industry and its management; the degree of control of the business represented by the block of stock to be valued; arid the values of securities of corporations engaged in the same or similar lines of business which are listed on a stock exchange.”
In addition, the IRS has outlined factors to consider in valuing stock of closely-held corporations. § 4 of Rev.Rul. 59-60,1959-1 C.B. 237 provides:
“Sec. 4. Factors to Consider.
It is advisable to emphasize that in the valuation of the stock of closely held corporations or the stock of corporations where market quotations are either lacking or too scarce to be recognized, all available financial data, as well as all relevant factors affecting the fair market value, should be considered. The following factors, although not all-conclusive are fundamental and require careful analysis in each case:
The nature of the business and the history of the- enterprise from its inception.
The economic outlook in general and the condition and outlook of the specific industry in particular.
*1370The book value of the stock and the financial condition of the business.
The earning capacity of the company.
The dividend-paying capacity.
Whether or not the enterprise has goodwill or other intangible value.
Sales of the stock and the size of the block of stock to be valued.
The market price of stocks of corporations engaged in the same or a similar line of business having their stocks actively traded in a free and open market, either on an exchange or over-the-counter.”
Evidence of events subsequent to the date of a decedent’s death is irrelevant to the valuation of decedent’s property at the time of death. Ithaca Trust Co. v. United States, 279 U.S. 151, 155, 49 S.Ct. 291, 73 L.Ed. 647 (1929); Walter v. United States, 341 F.2d 182, 185 (6th Cir. 1965). Nor, by the reasoning of Ithaca Trust, is such evidence probative of the correctness of an expert’s valuation procedure. Although at trial we allowed plaintiff to introduce evidence of a sale shortly after decedent’s death, we did not consider any evidence as to post-death events for either of the above purposes.
Findings of Fact
After a trial without a jury, the court, pursuant to Fed.R.Civ.P. 52(a), makes the following findings of fact. We adopt in part the statements of facts submitted by the parties.
On October 3, 1968, the plaintiff filed a Federal Estate Tax Return listing, as part of the gross estate, 45,955 shares of stock in NPI (42.4% of the shares outstanding) owned by the decedent at his death. As reported on the return, the stock was valued at $7.50 per share, for a total value of $344,662.50. The Estate Tax Return was then examined by the IRS, which determined the value of the stock to be $32.50 per share, for a total value of $1,493,537.50. Due to this adjustment, an estate tax deficiency in the amount of $413,167.81 was assessed against the plaintiff. Under § 6166 of the Internal Revenue Code of 1954, the plaintiff qualified to make deferred tax payments of this deficiency. On October 3, 1972, the plaintiff filed a claim for refund in the amount of $194,470.93, being the deferred estate tax payments made to that date. The plaintiff alleges that, on October 6, 1976, the final deferred payment was made and so, as of that date, the entire assessment of $423,591.58 has been satisfied. On April 9, 1973, the plaintiff waived statutory notification of disallowance of the claim for refund and thereafter filed this tax refund suit.
NPI is a Pennsylvania corporation established in 1948. In its early years the company manufactured both cemented carbide cutting inserts and blanks and the tools holding such inserts and blanks. In the 1950’s NPI ceased production of the tools themselves and concentrated its efforts on the cemented carbide cutting blanks and inserts.
The manufacturing operation was conducted at a special use facility located in Latrobe, Pennsylvania, the present plant being completed in 1964. The majority of capital equipment used in such facility was specifically designed and made for the production of cemented carbide cutting inserts.
The competitive advantages NPI enjoyed in the industry were 1) the reputation of William E. Newcomer as a founder and innovator in the cemented carbide industry, and 2) the method, once a trade secret, that William E. Newcomer devised to recover tungsten scrap for reprocessing into new cutting edges, thereby reducing raw material costs. This advantage had diminished in the mid-1960's as other competitors began to utilize that process or similar processes to reclaim scrap tungsten as a low cost material for manufacturing new inserts or blanks. Approximately sixty percent of NPI’s products were sold to the steel industry, with the balance going to railroad, auto, aircraft and other metal working industries.
*1371At the time of William E. Newcomer’s death, NPI sold its products exclusively through the Greenleaf Corporation, an unaffiliated, independent sales organization. The sales arrangement, which, by contract, was to continue until August 1, 1969, gave Greenleaf a set percentage of gross sales of NPI products. Greenleaf used sub-distributors to market NPI products, and toward the end of the relationship Greenleaf restricted such sub-distributors for one year after a termination of the Greenleaf sub-distributor relationship from dealing in cemented carbide products other than those offered by Greenleaf. Thus, a termination of Greenleaf by NPI would result in a one year separation of NPI from its former Greenleaf sub-distributors, which would be detrimental to such a relationship. Prior to the decedent’s death, the'relationship between the decedent and Greenleaf became strained, and it appeared that the marketing contract would not be renewed when it expired. During the time Greenleaf acted as sole sales agent for NPI, Greenleaf began its own tool holder manufacturing, and it has since acquired a competing cemented carbide cutting insert and blank manufacturing company. Greenleaf Corporation was owned by Walter J. Greenleaf, Sr. Greenleaf family members and Greenleaf Corporation owned 15,546 shares of NPI common stock (14.3%) as of the date of William E. Newcomer’s death.
Although NPI’s earnings were variable from 1954 through 1967, earnings in the 1960’s showed a marked improvement. The Viet Nam war and NASA space program stimulated the steel, aircraft and auto industries, which are the principal users of NPI’s products. The following chart shows NPI’s improving financial position:
YEAR ENDED MARCH 31 SALES PROFITS AFTER TAXES EARNINGS PER SHARE BOOK VALUE 1108.300 shares) PER SHARE
1963 ; 1,538,555 $ 80,421 0.74 4.86
1964 1,883,243 118,776 1.10 5.49
1965 2,400,670 210,143 1.94 7.47
1966 3,175,866 379,503 3.50 10.82
1967 4,208,573 529,186 4.87 15.40
In 1966 and 1967, however, shipments of the primary metals industry increased by 3%, and new orders declined by 8%.
As of July 6, 1967, the financial outlook of NPI was generally favorable. NPI had experienced excellent growth in the prior several years. Several factors, however, indicated that NPI’s growth would not continue at the same extraordinary rate: 1) NPI’s competitors would eventually all use the same or comparable scrap reclamation procedures; 2) the loss of decedent, one of NPI’s key persons; 3) the View Nam war and NASA space programs would be winding down, thus generating less demand for NPI products; and 4) the Greenleaf marketing agreement would expire in 1969 and probably not be renewed.
In the ten years before decedent died, dividends were paid only in 1961, 1966 and 1967, the highest dividend being $.45 per' share in 1967. Instead, the earnings were retained for improvement to NPI’s facilities.
The decedent was' the key administrative and production officer of NPI. Although his brother, Joseph Newcomer, who was president of NPI until 1968, maintained customer relations, and although decedent’s son, William A. Newcomer, was being trained in a management capacity, the decedent was the decision-maker aftd dominant force in NPI. As a result of a heart attack, the decedent “retired” in early 1967 and thereafter worked approximately 35 hours per week. George Brennan was hired in 1966 or early 1967 to take up the slack in the company when the decedent retired. James Fraunholtz was employed by NPI in *1372May, 1965 in an engineering capacity, and at all times before decedent’s death he took directions from the decedent. Although the decedent received substantial assistance in the day-to-day operation of NPI after his “retirement,” he remained highly important to the company up to the time of his death.
On a few occasions, NPI stock was traded over the counter, generally through local Pittsburgh brokers. When an owner offered his shares for sale, it was customary for brokers who could not find a buyer in the open market to refer that seller to the officers of the company. In many cases an officer purchased the offered.shares. Only nine such sales of NPI stock, made between 1964 and 1967 for a total of less than 5% of the outstanding stock, were effected. As the following table shows, except for the first sale early in 1964, all" sales were for less than .5% of the outstanding stock.
DATE PERCENTAGE NO. OF OF ALL SHARES SHARES SELLER PURCHASER PER SHARE PRICE
1/31/64 3,041 2.8% C. E. Lizza J. C. Newcomer 2.50
5/22/64 200 0.18% E. A. Conniff J. C. Newcomer 2.50
4/27/65 500 0.46% McRab & Co. W. F. Newcomer 3.00
5/11/65 200 0.18% H. M. Sheeder Singer, Deane and Scribner 4.00
7/9/65 200 0.18% Singer, Deane and Scribner W. A. Scott 4.00
7/23/65 100 0.09% J. C. Doherty R. A. Anderson 5.00
10/1/66 100 0.09% B. K. Norante M. J. Newcomer 5.00
5/10/66 200 0.18% H. E. Schweinsve W. E. Newcomer 5.00
11/2/67 100 0.18% V. R. Kaltenbaug W. R. Benshoff 7.50
The highest “bid” price for shares of NPI in 1967 as reflected by the National Daily Quotation Service was 6% in July, 1967. There were no “asked” prices, however.
Experts’ Analyses
Plaintiff’s expert witness, James L. Kenkel, has a Ph.D. degree in economics, is an associate professor of economics at the University of Pittsburgh, and has authored economics textbooks and articles. This case was the first instance in which he has valued corporate stock by analytical methods.
Dr. Kenkel first considered the actual sales of NPI stock, and he concluded that they are the best indicators of fair market value of the stock. In his view, the sales transactions apparently took place between willing buyers and willing sellers, neither under any compulsion to deal in the stock. The actual sales, Dr. Kenkel decided, were in sufficient quantities to provide a basis for valuation. Using the November, 1967 transaction (almost 4 months post-death) of 100 shares, he determined that $7.50 per share is the “best,” “reliable estimate” of fair market value of NPI stock.
Next Dr. Kenkel valued the stock using the intrinsic value approach, which reduces a future stream of income to present value. In his report, he assumed that future earnings would not grow, and for them he used the figure of $3.24, which was the average of the actual earnings for post-death years 1968 through 1972. Because future earnings were “highly variable and uncertain” and also due to NPI’s meager dividend policy, Dr. Kenkel used a 30% discount factor to arrive at an intrinsic value of $10.80, which, because the intrinsic value approach “overemphasizes earnings relative to dividends,” exceeded the “observed market price” of $7.50. At trial, however, Dr. Kenkel recalculated the intrinsic value to be $9.76, using *1373a 25% discount factor and, for future years’ earnings, the figure of $2.44, which is the average earnings for the years 1963 through 1967.
Lastly plaintiff’s expert performed a comparative price-earnings analysis of NPI stock. NPI’s five major competitors were Ex-Cell-O, Kennametal, Firth-Sterling, Avildsen, and Firth-Loach Metals (“FLM”). Dr. Kenkel concluded that, on the basis of sales revenues, FLM was most similar to NPI. After comparing earnings per share, dividends per share and number of shares outstanding of the two companies, Dr. Kenkel concluded that on the valuation date, NPI should sell for about one-third the price of FLM stock. Accordingly, dividing the average price of FLM stock in 1967 by 3, he obtained a value of $9.83 for a share of NPI stock.
Of his three estimates, Dr. Kenkel decided that $7.50 was the best, because it “is the market price at which the stock was actually sold.”
The IRS offered two experts in support of their $32.50 valuation. The first, John O’Farrell, a senior engineer with IRS, has a master’s degree in economics. His job involves valuing various properties primarily involved in litigation, more than half of which have been stocks in closely-held corporations.
Mr. O’Farrell accepted optimistic economic predictions set forth in NPI’s annual reports, including the 1968 annual report released several months after decedent’s death, which stated: “He [decedent] left us with a solid and secure base from which the company he founded shall continue to grow and prosper.” In addition to assuming that NPI’s growth would continue unabated after decedent’s death, Mr. O’Farrell considered the Greenleaf marketing agreement simply an “asset” to NPI and determined that it had no significant effect on valuation. Because earnings had grown more rapidly than sales, he thought that NPI was evidently well run and capable of running itself, and that future earnings would increase as they had for several years preceding decedent’s death. In sum, Mr. O’Farrell concluded that NPI “was a better than average growth enterprise in a growth industry in an expanding and growth period for American industry.”
Because NPI stock was not “freely traded in the market place,” Mr. O’Farrell decided that analytical methods were necessary to value the stock. He first plotted the ratio of price to book value against the ratio of earnings to book value for the following publicly-traded “comparable” companies that manufactured cemented tungsten carbide: UTD Corp., Kennametal, Inc., United-Greenfield Corp., Firth-Sterling, Inc., and Brown & Sharpe Mfg. Co. For earnings, he used in separate graphs 1) the average of the earnings for the 5 years preceding the valuation date, 2) the average of the earnings for the 3 years preceding the valuation date, and 3) the weighted (3-2-1) average of the earnings for the three years preceding the valuation date. By assuming that the points plotted lay on a straight line, which assumes that the price of stock varies directly as the company’s earnings, Mr. O’Farrell determined that NPI, if located on the same lines, would have a ratio of price to book value of 3.0 for all three graphs. NPI’s book value of $15.40 meant that its indicated public trading price was $46.20 per share. Correcting for NPI’s not being registered with the SEC yielded an 8.2% discount for the expense of registration, netting $42.40 per share, rounded, or a 24% discount for the more likely alternative of a private placement, netting $35.00 per share, rounded. Mr. O’Farrell concluded, accordingly, that the appropriate valuation of NPI stock was $35.00 per share.
The other IRS expert testifying was Alexander O. Williams, who has a Ph.D. degree in finance and is presently an associate professor at the School of Business, University of Virginia. Dr. Williams concluded that no established market price was available because the shares of NPI were “not *1374widely traded.” After an extensive survey of the economic background and current position of NPI and the cemented carbide industry, in which he considered the effects of the Yiet Nam war, the NASA space program, the probable termination of the Greenleaf arrangement and the loss of the decedent as a key man to NPI, Dr. Williams concluded that the following assumptions, about the Viet Nam conflict, the NASA program and the economy were most appropriate:
“Assumption 2
—Conflict continues at high level for at least two more years and starts gradually winding down
—NASA’s Program continues at high gear until moon landing, 1969 and a gradual winding down until moon pro-, gram is complete
—Economy continues at high level until after Presidential election in 1969, when hard decisions can be made”
Based on these assumptions, and his opinions regarding internal factors, such as (1) James M. Praunholtz would effect NPI’s smooth transition following the decedent’s death, with only a “temporary slow down,” and (2) the termination of the Greenleaf arrangement in 1969 might cause a “slowdown in sales due to the learning period,” Dr. Williams concluded that NPI would encounter a 12% yearly growth rate for the two years following the valuation date, and an 8% rate thereafter.
With these projected growth rates, Dr. Williams determined NPI’s stock intrinsic value to be $33.25. In his computation, he used a 25% discount factor and a value of $4.89 for NPI’s initial yearly earnings as of the valuation date, which was NPI’s earnings reported for fiscal year 1966-67. For reasons unclear to us, however, Dr. Williams decided that if another of the three alternative assumptions regarding economic activity were used, the intrinsic value of NPI stock would deviate no more than 10 percent from the $33.25 value.
Dr. Williams also performed a comparative analysis of NPI stock. Considering firms competing with NPI in the cemented carbide industry, namely Ex-Cell-0 Corp., Kennametal, Firth-Sterling, Avildsen Tool and Machine, Inc. and Firth-Loach Metals, Inc. (“FLM”), Dr. Williams concluded on the basis of several factors that FLM was the company most comparable to NPI. This was the same conclusion reached by plaintiff’s expert witness, Dr. Kenkel. Because “the growth performance of NPI was more than two times that of FLM,” according to Dr. Williams, NPI’s price-earnings multiple would be between 1.5 and 2.0 times FLM’s 1967 price-earnings multiple of 4.2. Using instead a three-year average of FLM’s 1965-1967 earnings, which average is 3.90, produced an NPI price-earnings multiple range of 5.85 to 7.80, with the average value of 6.83. A price-earnings multiple of 6.83, when multiplied by NPI’s earnings per share of $4.89, corresponded to a price per share of NPI of $33.37. NPI’s price-earnings multiple based on the three-year average of FLM’s price-earning multiples, is biased on the low side, in Dr. William’s view, to reflect some concern for the “possible transitional slowdown” caused by the decedent’s death.
Using the “asset-value” approach, which he did not regard highly, Dr. Williams also calculated a market value of $26.90 per share.
Dr. Williams concluded that the intrinsic value method, resulting in a valuation of $33.25 per share, produced the best estimate.
Findings Regarding Experts' Analyses
In our view, plaintiff’s expert, Dr. Kenkel, was somewhat biased towards the plaintiff. His report tended to minimize NPI’s financial strengths and over-emphasize its financial weaknesses.
Dr. Kenkel relied too much on the actual sales transactions of NPI stock. The sales, however, were too remote in time and too small in quantity to lend more than minimum weight to the credibility of his conclu*1375sions. More importantly, however, no evidence was introduced to establish that the transactions were indicative of fair market value, i.e., that they took place between a willing buyer and a willing seller, neither of whom were under any compulsion to buy or sell and both having reasonaDÍe knowledge of relevant facts. See Treas.Reg. § 20.-2031-l(b).
Dr. Kenkel’s intrinsic value analysis is faulty in several respects. First, in his report, Dr. Kenkel incorrectly used the average of actual future earnings as an estimate of future earnings; at trial, however, he used an average of the years 1963 through 1967 for the estimate, offering no authority for not using the earnings for fiscal year 1966-1967 together with an assumed growth rate. Second, Dr. Kenkel erroneously assumed NPI would experience no growth. Third, Dr. Kenkel used a 30% discount factor in his report, which he inexplicably changed to a 25% discount factor at trial.
The comparative price-earnings analysis that Dr. Kenkel performed also is subject to question. Although his sole basis for similarity was the companies’ sales revenues, we cannot quarrel with his choice of FLM as a comparable company. But Dr. Kenkel assumed that after the decedent’s death, NPI earnings would level off and then decline, an assumption we view as unwarranted. The missing link in his analysis, however, is that he did not explain satisfactorily why NPI would sell for one-third the market price of FLM. For all the above reasons, we find that Dr. Kenkel’s valuation of NPI stock is too low.
The report of Mr. O’Farrell, an IRS expert, also contained serious flaws. Mr. O’Farrell accepted too readily the glowing economic predictions set forth in NPI annual reports. He underestimated the impact on NPI of the loss of the decedent and ignored the failing relations between NPI and Greenleaf Corporation. In addition, Mr. O’Farrell’s assumption that NPI’s growth would continue unabated into the future, in our view, is overly optimistic.
Mr. O’Farrell’s comparable approach was faulty. Whatever the soundness of the theory underlying his methodology, for which he cited no authority, we find that three of Mr. O’Farrell’s “comparable” companies, namely UTD, United Greenfield and Brown & Sharpe, do not manufacture cemented carbide tips and are not competitors of NPI. It is therefore inappropriate to use them as comparables.
Mr. O’Farrell, moreover, ignored FLM, the publicly-traded company most comparable to NPI. Both NPI and FLM sold cemented carbide tool inserts, not other carbide products or tools, drills or other machine cutting items. Both had a small share of the total market dominated by large producers such as Kennametal. Both had experienced a rise in earnings per share over the six-year period prior to the valuation date. Both were subject to the cycles of the metal cutting tool industry, which was controlled by defense and aero-space industries. Obviously, the opinion regarding FLM of investors on the public market is probative of the investor opinion that would have existed for Newcomer had it been publicly traded. We therefore conclude that his valuation is too high.
We are impressed with the thorough, thoughtful and seemingly objective analysis of the second IRS expert, Alexander O. Williams. He ignored, however, the factor that NPI’s competitive edge resulting from its reclamation process would be lost in the future, and he did not give sufficient weight to the loss of decedent, erroneously thinking that Mr. Fraunholtz was groomed to replace him. In addition, Dr. Williams’ economic assumptions regarding the Viet Nam war and the NASA program, and the resulting projected growth rates, although not unreasonable, were overly optimistic to some extent; we are not persuaded that his 10% adjustment is appropriate for alternative economic assumptions.
As a major concern regarding the marketability of the Newcomer estate’s *137642.4% holding of NPI stock, the plaintiff contends that (1) the holding’s minority position, (2) NPI’s poor dividend record and (3) the fact that NPI stock is not publicly-traded are factors which depress the value of the shares owned by the Newcomer estate. Plaintiff reasons that, to a prospective investor of this block of stock, the first and second factors would indicate that an investment in the stock would probably not produce income, and the first and third factors would indicate that the growth potential of the stock could not be realized readily for lack of an active market for the stock. We agree with this contention and conclude that both IRS experts should have made an appropriate adjustment to their valuation for these depressing factors. See, e. g., Estate of Kirkpatrick, T.C. Memo 1975-344, 34 CCH T.C. Memo 1490 (1975); Estate of Katz, T.C. Memo 1968-71,27 CCH T.C. Memo 825 (1968).
Conclusion and Finding of Ultimate Fact
Using Dr. Williams’ analysis as our fundamental approach, and making approximately a 34% adjustment for the factors we have found at odds with his assumptions, we conclude on the basis of all the evidence that a share of NPI stock had a value of $22.00 on July 6, 1967, the date of decedent’s death. Without attempting to specify the weight we accorded to specific factors, we note that we gave additional emphasis to NPI’s expected loss of a competitive advantage from its reclamation process, the effect on NPI of the loss of the decedent, the uncertainty in the economy, the minority holding to be valued, NPI’s poor dividend record and NPI’s not being publicly traded. Accordingly, plaintiff is entitled to a refund of the excess tax and interest paid, together with interest of all such sums paid from date of payment until refund at the appropriate rates for the periods involved.
An appropriate order will be entered.