SUPPLEMENTAL OPINION
Sterrett, Judge:In its Memorandum Findings of Fact and Opinion (T.C. Memo. 1976-301), filed September 27,1976, this Court examined the acquisition in February 1964 by petitioner’s predecessor in interest of the K-D Lamp Division (hereinafter K-D) from the Duplan Corp. (hereinafter Duplan). K-D was involved in the manufacture and sale of automotive safety equipment. In our opinion, we sustained petitioner’s assertion that the negotiations leading to the sale were conducted in good faith and at arm’s length between unrelated parties. However, we found that the parties to the sale were not adverse in a tax sense, and we therefore refused to accept their allocation in the contract of sale of $1 of the purchase price to goodwill. In fact, we found that K-D lacked any goodwill that petitioner could have purchased in 1964. Nevertheless, we went on to find that petitioner acquired K-D as an ongoing business and that "the purchase price paid by petitioner for the various assets acquired in 1964 included substantial going-concern value which, as distinguished from goodwill, is the increase in the value of assets due to their existence as an integral part of an ongoing business.”1
Having found that going-concern value is nondepreciable (see Computing & Software, Inc. v. Commissioner, 64 T.C. 223, 232 (1975)), we proceeded to determine the proper depreciable basis for each asset. To do so, a portion of the total amount of nondepreciable intangible assets (of which going-concern value was the only one found to exist) had to be excluded from the amount of the purchase price attributable to each depreciable asset. Accordingly, we reduced the purchase price attributable to the buildings by 10 percent and the purchase price attributable to the other depreciable assets (the machinery and equipment, the tools, dies, jigs and fixtures, and the office equipment and furniture) by 20 percent. In so doing, we relied in part on the so-called Cohan v. Commissioner, 39 F.2d 540 (2d Cir. 1930), rule.
On appeal, the U.S. Court of Appeals for the Sixth Circuit affirmed our finding with respect to the presence of going-concern value. In doing so, that court agreed with our distinction between goodwill and going-concern value. However, it did not accept our use of the Cohan rule and remanded the case "for the Tax Court to explain its method of calculating the amount of going concern value” and "why it chose that method.” Concord Control, Inc. v. Commissioner, 615 F.2d 1153, 1156 (6th Cir. 1980). The Sixth Circuit court stated:
Though we realize that there are few guidelines for the Tax Court to follow in assessing the amount of going concern value and that the Tax Court may be compelled to make broad estimates, it must at least explain its method of valuation and its reasons for choosing that method. * * * [615 F.2d at 1156.]
Accordingly, we proceed to explain our method of determining the value of a business as a going concern.2
We note at the outset that there is no single, exclusive method for valuing intangible assets. "While various methods have been put forth to accomplish the measurement of going [concern] value, all are imperfect, and none has won any degree of acceptance.” R. Wixon, W. Kell & N. Bedford, Accountants’ Handbook 19.23 (5th ed. 1970). Each case must be considered on its own merits, and a method must be chosen based upon the particular facts presented. Watab Paper Co. v. Commissioner, 27 B.T.A. 488, 504 (1932).
Three methods of valuing intangible assets have been recognized by courts, and all three have been suggested for our use by the parties to this case. First, petitioner asks us to recognize the bargain of the parties as a valid measure of the value of intangibles. See 212 Corp. v. Commissioner, 70 T.C. 788, 800 (1978) (agreement with respect to value of property that was reached as a result of arm’s-length bargaining between parties with adverse legal interests was respected because the Court found no reason to question the bona fides of the transaction). It has long been established that "The Tax Court is not bound by the allocation of values made in the purchase contract, and is free to increase or decrease the amounts so allocated in accordance with the facts. See Hamlin’s Trust v. Commissioner, 10th Cir., 209 F.2d 761; Commissioner v. Court Holding Co., 324 U.S. 331.” Copperhead Coal Co. v. Commissioner, 272 F.2d 45, 48 (6th Cir. 1959), affg. a Memorandum Opinion of this Court.3
In this case, petitioner maintains that the parties bargained at arm’s length, had adverse tax interests, and agreed to an allocation of the purchase price that reflected economic reality. Suffice it to say that we already have determined that petitioner and Duplan were not adverse in a tax sense.4 Further, we have determined that no goodwill was transferred, but that a portion of the purchase price was attributable to the value of K-D as a going concern. As the parties themselves, in their contract of sale, did not attribute any of the purchase price to going-concern value, obviously we cannot find that use of the "bargain of the parties” method is a valid measurement of the going-concern value here at issue.
Second, the parties propose to measure the value of intangible assets by use of the "residual” or "gap” method. Under the "residual” or "gap” method, going-concern value is determined by subtracting the value of the tangible assets from the total purchase price. See Jack Daniel Distillery v. United States, 180 Ct. Cl. 308, 379 F.2d 569 (1967); R. M. Smith, Inc. v. Commissioner, 69 T.C. 317, 320-323 (1977), affd. 591 F.2d 248 (3d Cir. 1979), cert. denied 444 U.S. 828 (1979). The use of such method is proper where the value of the tangible assets and the value of the business can be ascertained with reasonable certainty. Northern Natural Gas Co. v. United States, 470 F.2d 1107, 1110 (8th Cir. 1973), cert. denied 412 U.S. 939 (1973); Jack Daniel Distillery v. United States, supra.5
In the instant case, we have been presented with an appraisal of the tangible assets by an expert of petitioner and a different appraisal by respondent’s expert. The large discrepancy between the two appraisals indicates the difficulty in ascertaining the fair market values of the tangible assets and, therefore, the problem with using the "residual” method in the case at hand. Furthermore, in our earlier opinion in this case, we recognized that going-concern value is the additional element of value that attaches to property because of its existence as part of an ongoing business. It is due to "the ability of a business to continue to function and generate income without interruption as a consequence of [a] change in ownership.” VGS Corp. v. Commissioner, 68 T.C. 563, 592 (1977). As such, going-concern value arises because of the ability of the assets to continue to function together as an ongoing business after the sale of the entity. See Winn-Dixie Montgomery, Inc. v. United States, 444 F.2d 677, 685 n. 12 (5th Cir. 1971) (going-concern value defined as the ability of an acquired business to continue to generate sales without any interruption caused by change in ownership). Accordingly, we believe it is inappropriate, in this case, to derive the amount of going-concern value by directly relying upon the widely divergent appraisals of the value of individual tangible assets. Rather, going-concern value should attach to the business as a whole and not to the existence of specific assets.
Theoretically, under the third method for determining going-concern value, the capitalization method, going-concern value is determined based upon the total value of the assets operating together as an entity. The depreciable basis of each asset is determined only after ascertaining the total value of the business that is attributable to going-concern value.6 Application of the capitalization method requires us to calculate the annual earnings of the business and compare such earnings with an estimate of what is deemed to be a fair return on tangible assets alone.
In order to isolate and value the superior or differential layer of income, if such exists, there must be a determination of the amount of income absorbed in clothing the tangible resources employed with a reasonable rate of return. * * * [R. Wixon, W. Kell & N. Bradford, supra at 19.27-19.28 (5th ed. 1970).]
The excess earnings, which are attributed to intangible assets, are then capitalized to determine the value of intangible assets. See Forward Communications Corp. v. United States, 221 Ct. Cl. 582, 608 F.2d 485, 514 (1979); Dwight & Lloyd Sintering Co. v. Commissioner, 1 B.T.A. 179, 185 (1924).7
The capitalization of earnings approach to calculating going-concern value can be broken down into five discrete steps, as follows:
(1) Study past earnings record in order to estimate future earnings potential of the acquired business;
(2) Appraise tangible assets in order to measure the fair value of earnings that are attributable to tangible assets;
(3) Determine appropriate rate of return on tangible assets in the particular industry. Apply such rate of return on tangible assets to the appraised value of the tangibles;
(4) Determine differential in earnings attributable to intangible assets by subtracting expected return on tangible assets (step 3) from actual expected earnings (step 1); and
(5) Compute total value of intangible assets by capitalizing earnings attributable to intangibles (step 4).
See generally 10 J. Mertens, Law of Federal Income Taxation, secs. 59.30-59.35 (1976); L. Seidler & D. Carmichael, Accountants’ Handbook 23.34-23.35 (6th ed. 1981); W. Meigs, A. Mosich & C. Johnson, Intermediate Accounting 574-582 (4th ed. 1978); H. Simons, J. Smith & K. Skousen, Intermediate Accounting 361-366 (6th ed. 1977).
The following is an explanation of how we apply the capitalization formula to the facts of our case:
(1) We first calculate K-D’s average annual earnings over a 5-year period in order to estimate the future earnings potential that was acquired in the purchase of K-D.8
The net earnings of K-D Lamp Co., as determined in our original opinion, were as follows:
1960 . $458,550
1961 . 274,021
1962 . 299,594
1963 . 367,699
1964 . 9 285,531
Total .;. 1,685,395
Accordingly, the actual average annual earnings of K-D’s business over this period was $337,079. We find no evidence of extraordinary circumstances, such as the realization of extraordinary gains or losses, retirement of debt, or reorganization of the business structure, that requires us to adjust this amount.
(2) Second, it is necessary to compare K-D’s actual earnings with earnings that normally would be expected from a business with K-D’s amount of tangible assets. As such, a determination of the fair market value of K-D’s tangible assets, absent going-concern value, is required. After examining the appraisals proffered by the parties, and each party’s objections to the appraisal of the other, we cannot endorse either appraisal. Using our best judgment, we have taken the agreed value of the buildings ($572,800), the purchase contract valuation of accounts receivable ($592,693) and inventory ($1,100,446), and have taken an average of the two appraisals on the other assets.10 Accordingly, we conclude that the value of the tangible assets was $3,462,587.
(3) Third, we compare K-D’s actual average annual earnings with the earnings that could be expected in a business of comparable nature and size. If any excess was earned by K-D, such amount is attributable to going-concern value. In order to make such a comparison, we have determined that corporations in comparable types of business with comparable net sales had earnings of approximately 7.8 percent of net worth.11 Applying this rate to the value of petitioner’s tangible assets, we have determined that a business the nature and size of K-D could have expected annual earnings of $270,082.12
(4) Subtracting $270,082 from the amount determined, supra, to represent K-D’s actual average annual earnings ($337,079), we conclude that $66,997 of earnings is attributable to the only intangible asset possessed by K-D, going-concern value.
(5) In order to determine the total amount of going-concern value inherent in the purchase of K-D, earnings attributable to going-concern value, determined supra, must be capitalized. In choosing a discount factor, we note that K-D’s position in the industry was somewhat precarious because of its reliance on a single client for about 32 to 40 percent of its sales. In addition, the 5 major competitors and approximately 20 minor competitors in the industry jeopardized K-D’s position among the leaders of the industry. These factors would tend to support a high capitalization rate. However, we must balance this uncertainty and high risk with the fact that there are significant barriers to entering the automotive safety equipment business. A new entrant would have to invest in expensive, specialized capital equipment and would be forced to compete for employees and customers in a field already crowded with a large number of competitors. The large startup and development expenses that would be needed to achieve an ongoing operation on the scale of that of K-D would tend to require a low discount factor. In light of the conflicting considerations presented in this case, we conclude that a risk-adjusted discount rate would be proper for the capitalization of earnings attributable to K-D’s going-concern value. We determine this rate to be 20 percent.
Applying this rate, we divide the average excess earnings attributable to intangible assets ($66,997) by the capitalization factor for intangibles (20 percent), resulting in total going-concern value of $334,985.
Having satisfied the mandate of the U.S. Court of Appeals for the Sixth Circuit that we explain our method of calculating going-concern value, the reasons why we chose that method, and the amount of such intangible’s value, it remains only to determine the basis of the depreciable assets. Under sections 167(g) and 1012, the basis of depreciable assets is the cost of such assets. "Where the issue is to determine the cost basis of an aggregate of assets, including both depreciable and nonde-preciable items, it is essential to ascertain the fair market value of the items which are subject to depreciation.”13
"Fair market value” has been defined as the price at which a willing seller would sell to a willing buyer, neither being under any compulsion and both having knowledge of relevant facts. See, e.g., Elmhurst Cemetery Co. of Joliet v. Commissioner, 300 U.S. 37, 39 (1937), affg. a Memorandum Opinion of this Court; McShain v. Commissioner, 71 T.C. 998, 1004 (1979). In the instant case, we are concerned with determining the depreciable bases of the buildings, the machinery and equipment, the tools, dies, jigs and fixtures, and the office equipment and furniture. We have found that the contract for sale, which placed the purchase price of the assets at 89.5 percent of their value as determined in the Manufacturer’s Appraisal Co.’s (MAC) appraisal, was the product of arm’s-length, good-faith negotiations between unrelated parties and fairly reflected the intention of the parties thereto. We also have found that the MAC appraisal was a bona fide, independent appraisal. Accordingly, we find that the negotiated purchase prices represent the most accurate estimate available of the fair market values of each asset as part of an ongoing business.
In order to determine the depreciable bases of the four depreciable assets, we have allocated the total going-concern value, determined, supra ($334,985), among each depreciable asset in the same proportion that the purchase price of each asset bears to the total purchase price for the four assets. Our allocations are as follows:
Asset Percent of total purchase price attributable to each asset (purchase price of each asset Purchase divided by total price purchase price) Going-concern value ($334,985 X %) Depreciable basis (purchase price less attributable going-concern value)
Buildings $572,800 28.06 $93,997 $478,803
Machinery and equipment 695,132 34.04 114,029 581,103
Tools, dies, jigs and fixtures $661,006 32.38 $108,468 $552,538
Office equipment and furniture 112,694 5.52 18,491 94,203
Total 2,041,632 100.00 334,985
In view of the foregoing,
Decisions will be entered under Rule 155.
T.C. Memo. 1976-301. See also VGS Corp. v. Commissioner, 68 T.C. 563, 591 (1977); Conestoga Transportation Co. v. Commissioner, 17 T.C. 506, 514 (1951).
2While this Court and others have undertaken to determine the value of goodwill (see, e.g., Forward Communications Corp. v. United States, 221 Ct. Cl. 582, 608 F.2d 485 (1979); Jack Daniel Distillery v. United States, 180 Ct. Cl. 308, 379 F.2d 569 (1967)), no case has clearly addressed the issue of how to determine the amount of going-concern value. See VGS Corp. v. Commissioner, 68 T.C. 563, 593-594 (1977); Black Industries, Inc. v. Commissioner, T.C. Memo. 1979-61. Accordingly, this appears to be a case of first impression with respect to a method for determining the amount of going-concern value. See generally the emerging literature on this issue, including Weiner, "Going Concern Value: Goodwill by Any Other Name?” 33 Tax Lawyer 183 (1980); Danzig & Robinson, "Going Concern Value Reexamined,” 11 Tax Adviser 32 (1980); Grigsby & Cotter, "Amortization of Certain Intangibles,” 30 U.S. Cal. Tax Inst. 543, 558-570 (1978).
See also Kunz v. Commissioner, T.C. Memo. 1962-276.
See also Black Industries, Inc. v. Commissioner, T.C. Memo. 1979-61 (bargain of parties not accepted because, while interests may have been adverse with respect to total value of consideration paid, interests were not adverse with respect to allocation to going-concern value; seller had no gain to recognize and any excess depreciation recapture would be offset by operating losses).
See also Black Industries, Inc. v. Commissioner, supra; R. M. Smith, Inc. v. Commissioner, T.C. Memo. 1977-23.
See Sanders v. Commissioner, T.C. Memo. 1973-75, wherein this Court accepted use of the capitalization method to determine amount of goodwill acquired on transfer of a business.
We note that respondent’s expert witness, Mr. George T. Williams, used a variation on the capitalization formula in making his appraisal. While we endorse the use of such formula in light of the facts presented here, we do not agree with the way the formula was applied by Mr. Williams or with the result that he reached.
In the Williams appraisal, the earnings for I960, 1961, and 1964 were excluded because Williams considered them abnormal. We disagree. The purpose of calculating past average annual earnings is to estimate the future earning power that has been acquired by the new owners as a result of their acquisition of an ongoing business. It is essential to use as long a period as possible in order to cover a fairly complete business cycle and to get a representative measure of business performance. We believe that the competitive nature of K-D’s business and the vicissitudes of the economic environment are reflected in the variations in the company’s earnings over the full 5-year period. Furthermore, use of an average of earnings over 5 years serves as a more accurate indicator of the future earning potential of the assets than does use of éamings for 1962 and 1963 only.
The net earnings for the 4 months ending Jan. 31,1964 ($95,177), have been annualized for the purposes of this calculation. To so annualize, we multiplied the net earnings figure by a factor of 3. We recognize that such a calculation may not take into account any seasonal variations in K-D’s business, but we take such liberty in order to give as accurate a portrayal as possible of the profitability of the business over as long a period as possible. See note 8 supra.
In ascertaining the value of the tangible assets to which going-concern value attaches, we did not consider two assets to which a portion of the purchase price was allocated: prepaid insurance ($13,341) and deposit premiums related to workmen’s compensation ($11,000).
In making our determination of appropriate rate of return, we referred to data from Statistics of Income — 1963, Corporate Income Tax Returns and Accounting Periods Ended July 1963-June 1964, U.S. Treasury Department, Internal Revenue Service Publication No. 16. We calculated the rate of return on net worth in three industry groups related to that of petitioner by looking at statistics of companies with net sales comparable to those of petitioner (about $5 million):
Size of firms Fabricated metal products Electrical machinery Motor vehicle equipment
(Net sales) $l-$5 Million $5-$10 Million $l-$5 $5-$10 Million Million $l-$5 $5-$10 Million Million
Number of returns examined 3,007 356 1,448 215 365 61
Total net earnings (in 000’s) $142,586 $64,249 $54,389 $39,984 $25,037 $10,466
Net worth (000’s) $1,815,393 $844,980 $776,346 $535,129 $248,057 $157,906
Net earnings as a percentage of net worth 7.9 7.6 7.0 7.5 10.1 6.6
On average, these related companies had net earnings of 7.8 percent of their net worth. The Williams appraisal refers to this amount as "fair return on net tangible assets.”
We have determined expected annual earnings by multiplying the value of the tangible assets ($3,462,587) by the expected rate of return on tangible assets (7.8 percent).
Philadelphia Steel & Iron Corp. v. Commissioner, T.C. Memo. 1964-93, affd. per curiam 344 F.2d 964 (3d Cir. 1965).