Estate of Gillet v. Comm'r

ESTATE OF CHARLES B. GILLET, DECEASED, SHERLOCK S. GILLET AND CHARLES C. FENWICK, CO-EXECUTORS, Petitioner v. COMMISSIONER OF INTERNAL REVENUE, Respondent Estate of Gillet v. Comm'r Docket No. 880-83. United States Tax Court T.C. Memo 1985-394; 1985 Tax Ct. Memo LEXIS 227; 50 T.C.M. (CCH) 636; T.C.M. (RIA) 85394; August 7, 1985. *227 Decedent died holding shares of common stock in a closely held water utility company. Held, for Federal estate tax purposes, the date-of-death fair market value of the shares of stock held by decedent was $125.25 per share. Stanard T. Klinefelter and Robert C. Young, for the petitioner. Robert A. Miller, for the respondent. STERRETT MEMORANDUM FINDINGS OF FACT AND OPINION STERRETT, Chief Judge: Respondent determined a deficiency, by notice dated*228 October 13, 1982, of $116,703.51 in the Federal estate tax of petitioner. The sole issue for decision is the date-of-death fair market value of shares of stock held by Charles B. Gillet in The Peoples Water Service Company. FINDINGS OF FACT Some of the facts have been stipulated and are so found. The stipulation of facts, together with the exhibits attached thereto, is incorporated herein by this reference. Charles B. Gillet (decedent) died a resident of Maryland on February 3, 1979. The Federal estate tax return of decedent listed as an asset 6,059 shares of stock of a closely held corporation, The Peoples Water Service Company (Peoples). Peoples was organized under the laws of the State of Maryland in 1929 and is a regulated public utility, the principal business of which is the collection, processing, and distribution of fresh water. The water is sold to domestic, commercial, and industrial consumers, and is also used for fire protection purposes. At one time Peoples served 29 communities located in 7 states. However, in February 1979 Peoples provided water service to a total of 22,301 customers located in 6 communities in 2 states, Florida and Louisiana. The largest*229 community served had 8,304 customers. Two of the communities served had customers of under 400. Peoples is affected adversely as a regulated industry in that rate increases lag behind increases in operating costs and fail to recognize adequately the substantial increases in replacement costs for property and plant facilities. Its capital investment required to replace existing property greatly exceeded depreciation in the years prior to decedent's death. The rates charged by Peoples for water service are subject to the approval of the regulatory bodies having jurisdiction over the communities served by Peoples. These regulatory bodies include the Board of County Commissioners of Escambia County, Florida, the Louisianna Public Service Commission, and Town Council. On February 3, 1979, Peoples had issued and outstanding 4,077 shares of 7 percent cumulative, $100 par value, preferred stock, 22,925 shares of common stock, and warrants to purchase 4,077 shares of common stock at $15 per share.These securities represented all of the equity capital of Peoples. 1 *230 At the time of his death, decedent owned 6,059 shares of common stock of Peoples. These shares represented 26.4 percent of the outstanding common stock. Exercise of the warrants would have increased the number of outstanding shares of common stock to 27,002 and would have decreased decedent's ownership of the outstanding common stock to 22.4 percent. Decedent's interest in Peoples did not represent voting control of the corporation. Peoples' "net income available for common stock" in the years ended August 31, 1974 through 1978 and in the 12 months ended January 31, 1979 was as follows: Net Income Available for Common Stock Year Ended Aug. 31 Total Per Share [1974] $211,986 9.25 [1975] 173,598 7.57 [1976] 325,656 14.21 [1977] 331,303 14.45 [1978] 416,760 18.18 Average 291,860 12.73 Twelve Months ended January 31, 1979 465,079 20.29 Peoples paid cash dividends on its common stock of $3 per share per year in 1974, 1975, and 1976, $3.75 in 1977, $4 in 1978, $5 in 1979, and $4 in 1980, 1981, and 1982. The balance sheet for Peoples on January 31, 1979 was as follows: Balance Sheet -- January 31, 1979 ASSETS Current Assets Cash $ 200,875 Accounts receivable, etc. 253,424 Materials and supplies 322,830 Securities portfolio, etc. 734,552 Cash surrender value of life insurance (net) 71,831 Total Current Assets 1,583,512 Plant and Property 9,316,059 Miscellaneous Investments 26,572 Goodwill $ 22,000 Unamortized Debt Discount 23,845 Deferred Charges and Prepaid Accounts 202,426 Total Assets $11,174,414 LIABILITIES & STOCKHOLDERS' EQUITY Current Liabilities Accounts payable $ 109,021 Dividends payable 14,269 Accrued liabilities 380,659 Total Current Liabilities 503,949 Long-Term Debt 1,165,000 Other Liabilities 385,341 Depreciation Reserve 2,804,996 Contributions for Extensions 444,921 Other Reserves 4,404 Stockholders' Equity 7% Cumulative Preferred Stock ($100 par) 407,700 Common Stock ($1 par) 22,925 Capital surplus 142,848 Earned surplus 5,292,331 Total Stockholders' Equity 5,865,804 Total Liabilities & Stockholders' Equity 2 $11,174,415 *231 Long-term debt of Peoples on February 3, 1979 was $1,135,000, which sum represented the then outstanding balance due Connecticut Mutual Life Insurance Company under a promissory note dated October 1, 1971. 3 The promissory note contained numerous restrictive covenants including, inter alia, covenants pertaining to the payment of dividends and the incurrence of additional debt. In the 5-year period prior to decedent's death, Peoples made capital expenditures of approximately $2,800,000, whereas the depreciation provision for the same 5-year period was approximately $1,000,000. Since no new long-term debt was incurred during this period, capital expenditures in excess of depreciation were made either out of earnings or liquidation of other assets. In decedent's estate tax return the 6,059 shares of common stock of Peoples was valued at $125.25 per share, for a total of $758,889.75. In his statutory notice of deficiency, respondent determined that said stock was worth $167.87*232 per share, for a total of $1,017,124.33. In its petition to this Court, petitioner alleged that each of the shares of Peoples had a value as of the date of decedent's death of $105 per share, for a total of $636,195, and claimed an overpayment of Federal estate tax. Respondent thereafter filed an Amendment to Answer asking for an increased deficiency in estate tax based on his determination that the per share value of the stock in question was actually $227.67, resulting in an additional deficiency of $152,895.02. At trial the Court received testimony with respect to the valuation of the stock from three experts, John G. Kovach, W. Edward Bard, and Frank J. Hanley. All three experts proceeded on the assumption that the outstanding warrants would be exercised and thus that decedent's shares in Peoples represented 22.4 percent of the outstanding common stock. Kovach Appraisal Following decedent's death, petitioner retained John G. Kovach, who at that time was a general partner in the investment banking firm of Alex. Brown & Sons, to determine the value of decedent's stock in Peoples. In his analysis, Kovach identified three positive factors. First, inasmuch as the water*233 distribution business involves a product that customers cannot do without, Peoples was assured of a rather steady stream of income. Second, inasmuch as Peoples did not have much debt opposite its net worth, there was a reduced risk of inability to service debt in the event of a decline in earnings. Third, Peoples appeared to be well managed. In contrast to the foregoing positive factors, Kovach identified five negative factors. First, the small size of Peoples subjected the corporation to a greater risk of inability to withstand sudden emergencies. Second, the family ownership and the small size of Peoples made it more difficult to raise additional capital. Kovach was aware from personal experience that the corporation had had difficulty in placing debt in 1971. Third, due to the fact that capital expenditures substantially exceeded the depreciation provisions, earnings needed to be committed to capital replacements, thereby limiting the expectation of possible increases in dividends in the future. Fourth, Peoples served only a small community. Fifth, between 1974 and 1979 there was a decline in the number of gallons of water sold by Peoples and a decline in the number of customers*234 that were being serviced by the corporation. Kovach's approach to placing a value on decedent's stock interest in Peoples consisted, in part, of placing a value on the operating segment of the corporation and adding thereto a value determined for the liquid non-operating assets not directly employed in the water service business. His approach also took into account the book value of the company. Kovach's valuation of the operating segment of the business was based on a comparison with ten publicly traded water service companies. Kovach determined that the price/earnings ratios for these companies for the most current 12 months prior to the valuation date ranged from 4.7 to 10.7 with the average being 8.1. The price/earnings ratios for the 5-year period prior to valuation date ranged from 5.7 to 9.4 with an average being 8.4. Kovach also examined the yields for the ten companies, finding a range from 7.4 percent to 10.4 percent and an average of 9.1 percent. He determined that the average payout of earnings as dividends for the ten companies was 75 percent. Finally, he determined that the market price as a percentage of book value for the ten companies ranged from 45 percent*235 to 150 percent with an average ratio of 84 percent. In Kovach's opinion, the company with a 150 percent price/book value ratio, Indianapolis Water, appeared to be an aberration due to outside interests. Excluding Indianapolis Water from the computation of the price/book ratio resulted in a range of 45 percent to 94 percent with an average of 77 percent. Kovach capitalized the net income of Peoples under the following procedures. He first determined the "net income available for common stock" after excluding therefrom investment income or loss net of income taxes as follows: Year ended Aug. 31 Total Per Share [1974] $192,706 $8.41 [1975] 261,459 11.40 [1976] 293,051 12.78 [1977] 286,608 12.50 [1978] 359,441 15.68 Average 278,653 12.15 12 months ended January 31, 1979 400,042 17.45 Kovach then averaged the income for the 12 months preceding the valuation date ($400,042) with the income for the 1978 fiscal year ($359,441) to obtain average water service income for the current period of $379,741. This figure was increased by estimated earnings ($3,058) on the proceeds from exercise of the warrants ($61,155) to a total of $382,799, or $14.18 per*236 share. Kovach capitalized the $14.18 per share by multiplying that figure by a price/earnings ratio of 7.5 and thereby arrived at a value of $106.35 per share. He then gave effect to the historical earnings of the five preceding fiscal years by first increasing the 5-year average ($278,653) by estimated earnings ($3,058) on the proceeds from the exercise of the warrants. Historical earnings were capitalized based on a price/earnings ratio of 8 to arrive at a per share value of $83.44. Finally, Kovach averaged the current per share value of $106.35 with the historical per share value of $83.44 to arrive at a value of $94.90 per share. Next, Kovach valued Peoples' investment portfolio on a closed end investment company basis. He valued the portfolio as of February 2, 1979 at $783,433 and discounted that value by 20 percent ($156,687) to reflect corporate ownership of the securities. The resultant value was $626,746 or $23.21 per share. Kovach added the per share value for the operating segment of the business ($94.90) to the per share value for the investment segment of the business ($23.21) to arrive at a value of $118.11 per share. Kovach determined book value on January 31, 1979 to*237 be $5,496,272, including receipt of insurance proceeds in excess of the carrying value ($38,168) of a life insurance policy on the life of decedent. He then increased such book value by $61,155 to reflect the proceeds from the exercise of the warrants and arrived at a total book value of $5,557,427 or $205.82 per share. The final step in Kovach's evaluation involved averaging the sum of the per share value for the operating and investment segments of the business and the book value, with a weight of two being assigned to the former value and weight of one being assigned to the latter value. The resultant value was $147.35, to which Kovach applied a non-marketability discount of 15 percent, which resulted in a final value of $125.25 per share. Hanley Appraisal Petitioner later sought a second valuation appraisal. This appraisal was performed by Frank J. Hanley, who is a senior vice president of Associated Utilities Services, Inc., an independent consulting firm providing services to investor-owned and publicly-owned utilities and to regulatory agencies. In his analysis, Hanley identified seven independent investor-owned water service companies that were publicly traded and*238 denominated these companies as a "barometer group" for purposes of comparison. Hanley's evaluation of Peoples led him to identify only one positive factor. He concluded that income before interest expenses and taxes, as it related to total capitalization, compared well with the average of this ratio for the barometer group. In contrast, Hanley identified ten negative factors. First, he viewed the small size of the company as a negative factor. Second, he noted that there was no market for the Peoples stock. Third, in Hanley's opinion there was an "above average" negative regulatory climate in that Peoples served six communities in two states and was subject to the regulation of three different bodies, making it threefold more difficult to obtain increases in revenues than would be the case with a typical water company operating intrastate. Fourth, Hanley viewed as a negative the high degree of capital intensity that requires water companies, in general, to make more dollars of investment to produce a dollar of revenue than nearly any other type of business. Fifth, Hanley noted that water companies, in general, for a number of years have sustained average market values significantly*239 lower than book values. Sixth, Hanley believed that inflation impacts more adversely on capital intensive utilities than on most unregulated enterprises. Seventh, Peoples had a low dividend payout ratio. Eighth, Peoples had a low dividend yield. Ninth, since decedent's stock interest lacked voting control, a purchaser's power to influence dividend policy was restricted. Tenth, Hanley observed that Peoples' non-utility income was very volatile. In the process of valuing Peoples' common stock, Hanley initially considered three overall valuation methodologies--the cost approach, the comparable sales approach, and the income approach. He concluded that the cost approach, which is normally associated with reproducing the cost of similar property in the public market, is an inappropriate methodology to use in valuing the common stock of a regulated public utility. Consequently, Hanley relied instead on the comparable sales and income approaches. Under the comparable sales approach, Hanley began by calculating a pro forma book value of $205.40 per share. He multiplied this value by the average percentage of the market price to book value for the barometer group of companies for*240 the period 1978 through 1982, 84.1 percent. 4 This calculation gave Hanley a per share value before discounts of $172.74. Hanley then applied a 15 percent discount for lack of liquidity and a 15 percent discount for low payout ratio. These computations produced a final per share value under the comparable sales approach of $120.92. Hanley next valued decedent's interest in Peoples under the income approach, which involves a capitalization of income. He performed this capitalization by use of the following formula: P = D/K-G P = current price or market value D = dividends per share K = investors' total required rate of return G = investors' expected rate of growth Viewing the historical record of cash dividends per share going back to 1973, Hanley concluded that it would be unreasonable for investors in early 1979 to anticipate an annual cash dividend in excess of $4 per share and accordingly, he assigned a $4 value to D in his formula. In so concluding, he noted that the dividend rate for 1978 was*241 $4. He acknowledged that, in retrospect, the dividend rate for 1979 was $5; however, the annual rate for 1980 through 1982 was $4. Hanley examined the financial data for the seven barometer companies before reaching a decision with respect to the appropriate percentage to be assigned to K in his formula. He found that the 5-year average earnings/price ratio for the barometer companies was 15 percent for 1978 through 1982, while it was 13.3 percent for 1974 through 1978. The 5-year compound average growth rates for the period ending with 1982 for the barometer group were 7.6 percent for earnings per share and 8 percent for dividends per share, and the 5-year average internal growth rate was 3.2 percent. 5 The average of all three measures of growth for 1978 through 1982 was 6.3 percent. 6 Because Hanley believed that the figures for the period 1978 through 1982 were the most meaningful for valuation purposes, he used an "adjusted earnings/price ratio indicated total cost rate of 15.9 percent (15 percent X 1.063 factor to reflect investors' expectation of growth)" for the K value. *242 After determining the D and K values, Hanley made a weighted comparison of the 5-year averages for the three previously discussed indicators of growth, earnings per share, dividends per share, and internal growth, using the actual figures experienced by Peoples. He found that the 5-year average growth rates for the period ending with 1982 for Peoples were 17.2 percent for earnings per share and 1.3 percent for dividends per share and that the 5-year average internal growth rate was 7 percent. 7Hanley concluded that, in the case of the barometer companies, it was reasonable to assume that investors would have given equal weight to each of the three measures of growth; however, such an assumption would be unrealistic in the case of Peoples because of the low dividend payout ratio. He further concluded that, due to the excellent rate of growth in earnings per share, such growth would receive greater weight by investors. Accordingly, Hanley accorded weights of 60 percent to earnings, 20 percent to dividends, and 20 percent to internal growth. He assigned a percentage of 12 to G in his formula, which was derived as follows: Earnings per share growth of 17.2% X 60% = 10.32% Dividends per share growth of 1.3% X 20% = .26% Internal growth of 7.0% X 20% = 1.40% Weighted growth 11.98% Use 8 12.0% *243 Hanley applied the formula P = D/K-G to the variables determined for the period 1978 through 1982 and concluded that the value of decedent's shares under the income approach would be $102.56 per share, or an aggregate value of $621,411 for the 6,059 shares held by decedent. The formula was applied as follows: P = $4 / 15.9% - 12.0% P = $4 / 3.9% P = $102.56 Hanley reasoned that investors would give greater weight to the income approach than to the comparable sales approach because of today's emphasis on the time value of money. Accordingly, Hanley reached his final value by averaging the results of the two approaches, giving the income approach a weight of two and the comparable sales approach a weight of one. The weighted average resulted in a final per share value of $109, or an aggregate value of*244 $660,431 for decedent's entire stockholdings. Bard Appraisal W. Edward Bard, who is a financial analyst employed by the Internal Revenue Service, appraised the value of decedent's stock interest in Peoples on behalf of respondent. The method of valuation used by Bard was a statistical one involving a curvilinear regression analysis using an exponential curve with the formula, y = ae <bx> (a>0). Bard began his evaluation by gathering financial data on 10 to 12 publicly traded companies. He next selected eight of those companies as comparables. In comparing Peoples to the comparable companies, Bard examined the financial statements of Peoples for the years ended August 31, 1975, 1976, 1977, and 1978, as prepared by Snouffer & Company. Using Standard & Poor's summarized stock report sheets, Bard compared the financial reports of the comparable companies with the financial reports of Peoples and made the judgment that one of the principal criteria that could be used for comparative purposes was the concept of invested capital. Bard selected two ratios for the comparable companies, cash flow earnings to total invested capital and market price to total invested capital, and*245 plotted these on a graph. The plot of the variables appeared to present what Bard described as a "classic nonlinear relationship." Utilizing a sophisticated calculator, Bard then determined a mathematical relationship between these two sets of ratios and plotted Peoples on his graph. From his statistical analysis, Bard determined that the common stock of Peoples should be valued at 106.48 percent of total invested capital of $6,924,000, or $7,372,675. Bard then applied a 16.47 percent discount for lack of marketability to decedent's 22.4 percent interest in Peoples and arrived at a per share value of $227.67, or a total value of $1,379,480, for decedent's stock ownership in Peoples. Bard's use of a 16.47 percent discount was based on the S.E.C. Cost of Flotation of Registered Issues for 1971 through 1972. In calculating total invested capital for Peoples of $6,924,000, Bard added together long-term debt, capital stock, and surplus. Respondent has conceded on brief that the composite figures used by Bard from Standard & Poor's for total invested capital of the comparable companies contained items in addition to those considered by Bard in calculating Peoples' total invested capital.*246 9 After trial Bard performed a new curvilinear regression analysis using the items as listed in Standard & Poor's in the computation of Peoples' total invested capital. The resultant value, after a discount for lack of marketability, was $167.00 per share. Accordingly, respondent no longer is seeking an increased deficiency as set forth in his Amendment to Answer. OPINION At issue is the valuation for estate tax purposes of the stock of Peoples held by decedent on February 3, 1979, the date of decedent's death. As is typically true when valuing the stock of a closely held corporation, our task is a difficult and complex one. The value of the gross estate includes the value of all property at the time of the decedent's death in which the decedent had an interest. Section 2031(a), I.R.C. 1954. Section 2031(b) specifically provides that in the case of stock of a corporation, the value of which cannot be determined by reference to market*247 sales or bid or asked prices, the value should be determined by taking into consideration, along with all other relevant factors, the value of stock of similar corporations publicly traded. To get a few truisms out of the way, fair market value has long been defined as the price at which 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. Section 20.2031-1(b), Estate Tax Regs.; United States v. Cartwright,411 U.S. 546, 551 (1973). Valuation of stock is a question of fact, and the trier of fact has the duty to weigh all relevant evidence and to draw appropriate inferences therefrom. Hamm v. Commissioner,325 F.2d 934, 938 (8th Cir. 1963), affg. a Memorandum Opinion of this Court, cert. denied 377 U.S. 993 (1964). Section 20.2031-2(f), Estate Tax Regs., sets forth a laundry list of factors to be considered in the determination*248 of the value of stock in a closely held corporation. Those factors include the company's net worth, prospective earning power, dividend-paying capacity, and other relevant factors. "Other relevant factors" are stated to include-- [T]he goodwill 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; and the values of securities of corporations engaged in the same or similar lines of business which are listed on the stock exchange. However, the weight to be accorded such comparisons or any other evidentiary factors considered in the determination of a value depends upon the facts of each case. * * * In the abstract, both parties agree upon the validity of the above-referenced guildelines. However, the valuation methodologies used by the three experts differ widely; hence, considering that valuation is far from an exact science, the discrepancies in the contended values and the varying positions that the parties have taken are hardly surprising. As set forth in our findings of fact, petitioner originally valued decedent's*249 ownership of stock in Peoples at $125.25 per share. In his statutory notice of deficiency, respondent determined that the stock was worth $167.87 per share. In the petition, petitioner asserted that the stock was actually worth $105 per share. In an Amendment to Answer, respondent sought an increased deficiency based on his determination that the stock was actually worth $227.67 per share. At trial, petitioner presented two expert witnesses, one of whom expressed the opinion that the stock was worth $125.25 per share and the other of whom expressed the opinion that the stock was worth $109 per share. On brief, petitioner contends that the stock in question has a value somewhere in the range of $109 to $125 per share. Due to certain facts coming to light at trial, respondent to longer is seeking the increased deficiency set forth in his amended answer, and on brief, contends that the stock in question has a value of $167 per share. So much for the certitude of each party's position. Petitioner contends that respondent's position should be rejected because it is premised on Bard's appraisal, which is marred by its mathematical errors and distortions, its failure to consider all relevant*250 factors, and its dependence on narrow data and rigid formulas. For the reasons set forth below, we agree with petitioner that the appraisal is unreliable and conclude that petitioner has carried its burden of proving respondent's determination erroneous. The most striking fallacy we see in the approach taken by Bard is his failure to take seriously all relevant facts and circumstances into account as mandated by the regulations and the Code itself. To be sure, it considers a multitude of factors, such as the decline in joblessness, the increase in rail freight traffic and intercity truck tonnage, and the continued strength of the U.S. dollar in foreign exchange dealings, many of which factors we view as tangentially relevant, at best. Despite this superficial appearance of taking all facts and circumstnaces into account, when the dust settles it becomes readily apparent that Bard's appraisal is based on a narrow statistical comparison that takes into account only three aspects of the comparable companies, using data from an extremely isolated period of time--cash flow earnings for the year immediately preceding the valuation date, fair market value of the outstanding common stock*251 on the date of decedent's death, and total invested capital. He used these figures to devise two ratios--the ratio of cash flow earnings to total invested capital and the ratio of the market price of the common stock to total invested capital. Bard plotted these ratios on a graph, and by means of a regression statistical analysis, he determined the relationship of these variables and drew a curved estimating line on the chart. The ratio of Peoples' cash flow earnings to total invested capital was then plotted on the chart. This analysis (after giving effect to a discount for lack of marketability) formed the basis for Bard's valuation. In basing his valuation on the foregoing analysis, Bard failed to take into account certain factors that reasonably could have been expected to have been taken into account by a hypothetical willing buyer. For example, Bard gave no serious consideration to dividends paid or to asset value. Nor did Bard take into account the specific existence of loan restrictions or the fact that Peoples, as a closely held corporation, could not as easily generate debt capital as might a publicly traded company. While we are inclined to agree with respondent's*252 assessment that Peoples was cash heavy and could have afforded to pay more substantial dividends, we are satisfied from the record that at least part of the retention of corporate earnings was attributable to the regulatory difficulty of obtaining rate increases, the excess of replacement costs over depreciation, and the inherent difficulties of generating debt capital. As far as can be determined from the record Bard failed to give any recognition to the necessity of retaining a reasonable portion of profits in the company. Moreover, while common sense leads us to agree with respondent's abstract statements on brief that dividend-paying capacity, as opposed to actual dividends paid, is often a more reliable factor in valuation cases involving closely held corporations, it is unlikely that a hypothetical willing buyer of decedent's stock in Peoples would have ignored the low dividend payout rate. Decedent's stock interest in Peoples did not represent voting control; hence, from a theoretical viewpoint, there is no justification for assuming that the hypothetical willing buyer of that stock could alter dividend policies. Aside from its narrow perspective, Bard's appraisal was riddled*253 with errors in calculations. We believe these errors draw the credibility of the overall appraisal, even as revised by respondent on brief, into question. As previously stated, Bard used "total invested capital" as the denominators in the two ratios used by him in his statistical formula. Respondent has conceded on brief that the composite figures used by Bard from Standard & Poor's for total invested capital for the eight comparable companies took into account items in addition to those considered by Bard in calculating Peoples' total invested capital. His analysis in this respect was simply not fair. As petitioner points out, throughout extensive cross-examination on this point, Bard remained largely impassive to evidence of his errors. Another defect in Bard's analysis, which we find significant, is his failure to make any adjustments to account for the differences in the debt/equity mix among the comparable companies and Peoples. Although the denominator in the ratio of cash flow earnings to total invested capital included debt, the numerator included earnings after a deduction for interest expense for the debt included in the denominator. Obviously, if Bard wanted to*254 measure the return on invested capital including debt, he should have used earnings determined before any costs attributable to the debt that was included in the denominator of the ratio. In failing to adjust cash flow earnings by adding back interest costs on the debt included in total invested capital, Bard failed to construct a fair comparison of all the companies involved, including Peoples, which the parties agree was a low-debt corporation. In our view, Bard reasonably should have been put on notice of some of the errors inherent in his original appraisal. In this connection, Kovach commented on Bard's analysis as follows: The marketplace just does not reach price conclusions on such a narrow, limited and theoretical basis. Such an approach may be one of the means used by investors to determine if they have an interest in a particular security, but it would not be the sole means of determining a price at which they would buy or sell a security. The weakness of this dependance [sic] on but a single determinant of the price is evidenced by the application of a number of tests that one should make to check the reasonableness of his conclusion. First, the point on the X*255 axis of the chart for Peoples Water is quite some distance to the right from the cluster of points for the comparable companies. It appears to be isolated and if one were using Peoples Water as a guide for valuing another company, you would probably be tempted to treat it as an aberration and to ignore it. It does not necessarily have to fall within or close to the cluster, but when it appears at such distance from the cluster, it should be viewed with suspicion. Secondly, and very importantly, the conclusion as to value produced by this statistical approach must be tested against other accepted valuation approaches in the marketplace, such as yield, price/earnings ratio and the ratio of market price to book value. The valuation produced by the Bard formula was $273.04 per share before discount for lack of marketability.Based on this valuation, the price/earnings ratio for Peoples Water would be 17.6 times, which is more than 50% higher than the high end of the range of 4.7 to 10.9 for the comparable companies, shown in Bard's report. The yield on the Peoples Water stock based on the $5 dividend would be only 1.8%, which compares with the range of Bard's comparable companies of*256 7.5% to 9.2%. The Bard value would represent 133% of book value while the range of his comparable companies was 33% to 92.3% of book value. The above market tests indicate either that the valuation approach is defective or Peoples Water had some very unusual characteristics which would justify such high premiums over the comparable, alternative investment opportunities. There were no unusual characteristics present at Peoples Water to justify such high premiums. On the contrary, the small size of Peoples Water and the few small communities served by it would dictate a discount rather than a premium when viewed against the large companies in the comparable company group. The Bard conclusion, thus, does not stand the market test, and when investors view his price for the stock versus the other market opportunities, they would turn away from Peoples Water stock at such a price. No useful purpose would be served by further dissecting Bard's analysis. Suffice it to say that we reject such analysis under the facts of this case and hold that petitioner has carried its burden of proving in error respondent's determination, which was premised on Bard's analysis. We do not intend to*257 imply herein that a statistical analysis such as that employed by Bard would never be considered as indicative of fair market value. It may well be that the facts and circumstances of a particular valuation case would justify the use of such an analysis. However, petitioner herein has satisfied us that this is not that case. Of course, our rejection of respondent's position does not resolve the valuation issue presented. We are left with the alternatives of accepting the value placed on the stock by one of petitioner's two experts or substituting our independent judgment, based on our deductions from the evidence presented, for that of all three experts. In this endeavor we turn first to Hanley's appraisal. To recapitulate briefly, Hanley used a weighted average of two approaches in making his valuation appraisal. The first approach he used was denominated the "comparable sales approach." Under this approach, Hanley took the pro forma book value of Peoples as of February 1979 and multiplied it by the actual average market to book ratio of seven publicly traded barometer companies for the years 1978 through 1982. He then took a 15 percent discount for lack of liquidity and a*258 15 percent discount for the low payout ratio to arrive at a per share value of $120.92 under his comparable sales approach. The second approach used by Hanley was denominated the "income approach" and involved a discounted cash flow analysis. Under this approach, Hanley used a formula of P = D/K-G, where P = market value, D = dividends per share, K = investors' total required rate of return, and G = investors' total required rate of growth. In applying the formula, Hanley used a value of $4 for D, which represented the annual rate of dividends for 1980 through 1982 and also represented the rate for 1978. For K, he used the actual average earnings/price ratio for the barometer companies for 1978 through 1982, times 1.063, a factor intended to represent investors' expectation of growth. This 1.063 factor, in turn, consisted of the average of three measures of growth experienced by the barometer companies for 1978 through 1982, specifically, earnings per share, dividends per share, and internal growth rate. For G, Hanley used a weighted average of actual figures experienced by Peoples for the years 1978 through 1982 of earnings per share (given a 60-percent weight), dividends per*259 share (given a 20-percent weight), and internal growth rate (given a 20-percent weight). Using the variables so arrived at, Hanley's formula yielded a value of $102.56 per share. Finally, Hanley took a weighted average of the values determined under the comparable sales and income approaches, giving the former value a weight of one and the latter value a weight of two, and determined that the per share value of the stock was $109. As readily can be seen from examining Hanley's valuation methodology, his ultimate conclusion rests largely on the application of formulas using values and percentages that did not exist as of the relevant valuation date, February 3, 1979, the date of decedent's death. Respondent's primary attack on Hanley's appraisal is focused on the use of such post-death values. It has long been recognized that the use of hindsight is not permissible in making vluations. Ithaca Trust Co. v. United States,279 U.S. 151 (1929); Estate of Tully v. United States, an unreported case ( Ct.Cl. 1978, 41 AFTR2d 78-1477, 78-1 USTC par. 13,228).*260 Events occurring subsequent to the valuation date should not be considered in determining fair market value except to the extent that they were reasonably foreseeable on that date. Estate of Tully v. United States,supra; Couzens v. Commissioner,11 B.T.A. 1040, 1165 (1928). In support of his use of post-valuation date market data, Hanley indicated that investors, by means of financial journals, would have had a reasonable basis for projecting future earnings per share. He testified as follows: [I]nvestors clearly, * * * while they may not have had any actual specific detail forecasts going out, certainly had a perception of from what they could read in the newspapers, from various financial journals, and periodicals, and so on, projections of what the economic and financial conditions were going to be like throughout 1979, and indeed even into and perhaps through 1980. In our view neither the foregoing testimony nor anything else in the record establishes that the plug figures for the variables used in Hanley's formulas, which figures were derived from knwn data for the period 1978 through 1982, were foreseeable as of the valuation date. Thus, Hanley's*261 use of actual figures derived from events post-dating the valuation date is inappropriate. Obviously, if such a technique were accepted, there would be little need to resort to the courts in valuation cases. The mere passage of time, together with the accumulation of post-valuation date data, would convert the valuation process from an inexact science to an exact science. For that reason, without further delving into the methodology employed by Hanley, we reject his appraisal. 10 *262 We now turn to Kovach's appraisal. Stated in summary fashion, Kovach's valuation consisted of a weighted average of three components--his valuation of the operating segment of Peoples, his valuation of the liquid, non-operating assets of the corporation, and book value. In valuing the operating segment of the corporation, Kovach proceeded as follows. He determined the net income from the operating segment of Peoples available for common stock for the fiscal years 1974 through 1978 and for the 12 months ended January 31, 1979. He averaged such income for the 12 months ended January 31, 1979 with the income for the 1978 fiscal year and capitalized the income so determined at a price/earnings ratio of 7.5. He then averaged such income for the 5-year fiscal period from 1974 through 1978 and capitalized the income so determined at a price/earnings ratio of 8.0. He then averaged the two capitalized values to arrive at his valuation figure of $94.90 per share for the operating segment of the corporation. In valuing the liquid, non-operating segment of the corporation, Kovach valued the investment portfolio at market value as of February 2, 1979, and then discounted the resultant*263 figure by 20 percent. For this segment of the business, he valued the stock at $23.21 per share. The final component of Kovach's valuation of Peoples was the book value of the company, increased by the proceeds that would be derived from exercise of the warrants and increased by the excess of the proceeds from a life insurance policy on the life of decedent over the carrying value of such policy. Kovach determined a book value per share of $205.82. Kovach assigned a weight of two to the sum of the value of the stock based on the value of the operating segment of the business and the value of the stock based on the value of the non-operating segment of the business. He assigned a weight of one to book value per share. He then computed the weighted average of the two figures to arrive at a per share value. From this value, he took a 15 percent discount for lack of marketability to reach his final valuation conclusion that the stock held by decedent was worth $125.25 per share. In our discussion of Kovach's valuation approach, we begin by noting that the instant case appears to present a proper scenario for segregating the corporation whose stock is to be valued into its operating*264 and non-operating segments. Generally, primary consideration should be accorded to earnings when valuing stock of an operating company. On the other hand, the greatest weight should be given to the value of the underlying assets when valuing the stock of an investment company. 11 In the instant case, although Peoples is an operating company, it held a rather substantial investment portfolio. We have already stated our agreement with respondent that the corporation was cash-heavy and, while the evidence satisfies us that part of the corporation's earnings was retained for working capital needs, it is evident that a fair portion of the retained earnings could have been distributed as dividends without jeopardizing the corporation's working capital needs. In our view, Peoples had an investment fund in excess of its operational needs and separable from them. The segregated approach to valuation has been accepted by the courts where the evidence establishes that there was an accumulation by the corporation of assets*265 in excess of business needs that would require separate evaluation. See Schlegel v. United States,71 F.Supp. 495, 497 (W.D.N.Y. 1947), affd. 164 F.2d 276 (2d Cir. 1947) (accepting the segregated approach where the evidence demonstrated that there was no need for the large reserve represented by investments of an operating company); cf. Worthen v. United States,192 F.Supp. 727, 730-732 (D.Mass. 1961) (rejecting the segregated approach where the evidence established that there was no accumulation of assets in excess of business needs). Not surprisingly, respondent does not question the use of a segregated approach to valuation in the instant case. Respondent objects to Kovach's appraisal on a number of grounds. He questions Kovach's selection of the rates used to capitalize net earnings from the operating segment of the business. It is true, as respondent points out, that Kovach's report simply states that "[n]et income of the water service business was capitalized at the appropriate rates." However, Kovach, whom we found to be a credible witness and who had had some prior unrelated dealings with the corporation and was thus*266 familiar with its history, testified that his choice of price/earnings ratios, which roughly fell in line with the average price/earnings ratios for the comparable companies, was based on his study of the ratios of the comparable companies and on his considered judgment that the selected ratios were the appropriate ones to be used in capitalizing Peoples' earnings. When questioned about his choice of the price/earnings ratio used to capitalize current income, Kovach testified as follows: As I looked at the comparable companies and their records, and their territories, their size, and where they were trading in the market place and then look at The Peoples' Water Service Company and then take into account the size of it, * * * it is a judgment call at this point coming from my experience in the securities markets, and having to price securities for public issues and so on, means that you get a feel for just about where * * * this particular security would be selling out there in the market place. And out of that work, I concluded that, in my judgment, this company would command a price earnings ratio on those current earnings of about 7.5 times. The valuation process necessarily*267 involves some judgment calls. We are satisfied from the overall record that Kovach was qualified to exercise that judgment in selecting the appropriate price/earnings ratio to be used in capitalizing Peoples' operating income. Respondent also objects to Kovach's discount of 20 percent for the marketable securities owned by Peoples on the basis that the discount was not supported by market data. Kovach testified that his selection of a 20-percent discount was based on his analysis of the market price of publicly owned closed end investment companies. Respondent offered no evidence whatsoever to cause ut to question the particular discount chosen. The theory underlying the use of a discount such as the one in question is premised on the recognition that minority shareholders in a corporation have no right to receive their pro rata share of net asset value and on the recognition that the ownership interest in the entity holding those assets is being valued and not the underlying assets themselves. See Harwood v. Commissioner,82 T.C. 239, 267 (1984); F. Burke, Jr., Valuation and Valuation Planning for Closely Held Businesses, 128 (1981). Nothing in the record*268 casts doubt on Kovach's selection of a 20-percent discount, and we believe that Kovach was qualified to make a judgment on this matter. Finally, respondent asserts that Kovach gave little, if any, consideration to the dividend paying capacity of Peoples and placed primary emphasis on the actual dividends paid. Respondent is simply in error in this assertion.Kovach's basic approach was to capitalize earnings, not dividends. In capitalizing earnings, Kovach fully accounted for the dividend paying capacity of Peoples. In fact, if anything, it could be argued that by capitalizing earnings and separately valuing Peoples' investment portfolio, Kovach might be guilty of overstating dividend-paying capacity, without considering the necessity of retaining a certain amount of earnings for operational needs. Kovach may have erred too far in one direction or another with respect to one or even several of the various steps in his analysis. However, on balance, having weighed all of the evidence in the record and bearing in mind that valuation involves approximation, we are satisfied, and so hold, that the value placed on the stock by Kovach, that is, $125.25 per share, represented the fair*269 market value of the stock held by decedent on the date of death. Because of other adjustments made in the notice of deficiency and not at issue herein, Decision will be entered under Rule 155. Footnotes 1. The preferred stock was not convertible into common stock and was non-voting except during periods when two or more semiannual dividends were unpaid and was redeemable at $107.50 per share plus accrued unpaid dividends. The common stock was entitled to one vote per share.↩ 2. The discrepancy between the Total Assets figure and the Total Liabilities & Stockholders' Equity figure is presumably attributable to a "rounding off" process.↩ 3. As stipulated by the parties.↩ 4. Hanley found that the average percentage of the market price to book value for the barometer group of companies for the period 1974 through 1978 was 84.7 percent.↩ 5. Comparable figures for the 5-year period ending in 1978 were 1.2 percent for earnings per share, 7.7 percent for dividends per share, and 3.6 percent internal growth. ↩ 6. The average of all three measures of growth for 1974 through 1978 was 4.2 percent.↩ 7. Hanley found that the 5-year average growth rates for the period ending with 1978 for Peoples were 17.5 percent for earnings per share and 5.9 percent for dividends per share and that the 5-year average internal growth rate was 4.5 percent. ↩ 8. Hanley noted that a similar weighing for the period 1974 through 1978 resulted in a weighted growth rate of 12.6 percent.↩ 9. These items included "contributions in aid of construction," "deferred income taxes," and "deferred income tax credits."↩ 10. on brief, both parties attempt to apply Hanley's methodology using the financial data he found applicable to the period 1974 through 1978. However, the parties are unable to agree on the variables to be plugged into the formulas, and as a result, petitioner arrives at a per share value of $121; whereas, respondent arrives at a per share value of $212.43. The major point of disagreement revolves around the percentage to be assigned to the K variable (investor's total required return rate), in the formula, P = D/K-G. Stated simply, respondent would look solely at historical data in assigning a percentage figure to the K variable. Petitioner, on the other hand, views the K variable as requiring a prospective analysis in light of the financial and economic climate existing on the date of valuation, and for that reason contends that the K variable cannot be based solely on historical operating results. While we are inclined to agree with petitioner that an investor's total required rate of return cannot be based solely on historical data, petitioner's recomputation again commits the error of deriving the K variable from actual post-valuation date data without any showing of a tie-in between that data and an investor's expectations as of the valuation date.↩ 11. See generally F. Burke, Jr., Valuation and Valuation Planning for Closely Held Businesses 33-39 (1981); see also Rev. Rul. 59-60, 1959-1 C.B. 237↩.