DONALD RUSSELL, Circuit Judge:
This is a proceeding under 11 U.S.C. § 548(a)(2)(A) and (B) of the Bankruptcy [460]*460Code to void a transfer of corporate stock by the debtor to the defendant Ashley Communications, Inc. Section 548(a)(2)(A) and (B) provides that any transfer of property by a debtor while insolvent at any time within one year of the filing of his bankruptcy proceeding may be voided if the debtor has not received “reasonably equivalent value.” The bankruptcy judge found all requirements for voidance of the transfer in this case present except the receipt at the time of the transfer of “fair equivalent value,” as established by market value. He found expressly that the transfer was made in good faith “between a willing purchaser and a willing seller at a price upon which [the parties] agreed to at arm’s length.” However, he dismissed this fact because he said the parties to the transfer “were not well informed and not knowledgeable.” He hypothesized that had the parties been “knowledgeable,” they would have agreed that the “fair equivalent value” would have been “$50,000 at that time” (i. e., when the sale was made). He therefore declared that such amount ($50,000) represented the market value of the stock on the date of the sale (May 17,1984).1 He accordingly held that the transfer did not satisfy the requirement of “fair equivalent value” and held the transaction void. However, he directed under section 548(c) that the defendant should be repaid its purchase payment of $5,000 and allowed $20,000 for service in enhancing the value of the transferred property. The defendant challenges on appeal the conclusion that it did not give “fair equivalent value” at the time of the transaction and the Trustee cross-appeals the bankruptcy judge’s ruling under section 548(c). 75 B.R. 619 (Bankr.W.D.N.C. 1987). We reverse the avoidance of the transfer and remand for the entry of judgment in favor of the defendant.
I.
The debtor is Morris Communications, Inc., a North Carolina corporation organized in mid-1982 to conduct a paging and radio sales business in the Charlotte area of North Carolina. Its initial stockholders were Morris Communications, Inc., a South Carolina corporation (25%); an individual, James Berns (35%); and Viebeck, a Dutch holding company (40%). In the early days of the debtor, Horace Morris, who was the sole stockholder of the South Carolina Morris Communications corporation, was the active manager of the North Carolina corporation — until November 1983, when Frank Warlick took over. Among the assets acquired by the debtor was a 26% stock interest in C-PACT, a North Carolina corporation organized under the circumstances later discussed for the purposes of filing an application for a non-wireline cellular telephone license in the Charlotte-Gastonia area with the Federal Communications Commission (FCC). That stock interest is the subject of this suit. The sole issue in this case centers on the valuation of that stock in C-PACT at the time of the challenged transfer. The relevancy of that issue compels a determination of the value of C-PACT itself on May 17, 1984. C-PACT never had any asset other than its application for a cellular telephone license. The debtor’s stock represented a minority interest (26%) in that asset. In order to provide for any rational evaluation of the market price for a minority stock interest in a corporation whose value depends entirely on the value of the corporation’s cellular telephone license application, it is necessary to review briefly the development of the cellular telephone industry itself and the procedures whereby licenses for the operation of such a system are granted. We therefore divert at this point to examine those questions.
[461]*461The method of utilizing cellular telephone technology in order to provide mobile cellular telephone services contemplates the use of a multiple low-power transmitter operating within a specified limited geographic area plus a computerized switching facilities offering service beyond the limited geographic service area itself. The operation of such a system involves the use of the electromagnetic spectrum. Such use requires licensing by the FCC under the Communications Act of 1964. The FCC in 1968 issued a Notice of Inquiry to determine the advisability and method to be utilized, if found advisable, in licensing cellular telephone systems for commercial operation. Following this Inquiry, the FCC determined the development of such systems to be practical and promulgated in 1982 a plan for the division of the nation into specific geographic market areas, using for that purpose the 1980 Census for Standard Metropolitan Statistical Areas (SMSAs). The plan allocated to each such SMSA two licenses, one exclusively for existing telephone wire companies and the other for non-wireline applicants. It assumed that there would be a substantial number of applications for each type of license and that the competing applications would be dealt with under the normal administrative procedures of the Commission.
The FCC began the actual licensing process by opening thirty of the larger SMSAs for the receipt of applications for licenses. It was promptly inundated with a large number of competing applications in practically all the areas.2 Since the paging operations were somewhat similar to the cellular telephone systems, both being subject to licensing by the FCC, the operators of paging businesses were frequent applicants of cellular telephone licenses. In many instances, the same interests would have individual applications in several SMSAs or a partnership interest in a number of such applications. Thus, Elden Heinz, Jr., who was actively involved in the organization of C-PACT, had participations in a substantial number of applications in SMSAs other than the Charlotte-Gastonia SMSA.3 This mass of conflicting applications for licenses made it obvious that normal administrative proceedings would be too time-consuming, burdensome and expensive for the FCC with its limited staff. In an effort to meet this problem, the FCC published, in October 1983, a proposed new regulation under which licenses would no longer be awarded on a comparative hearing basis, but instead under a so-called “lottery” procedure. That regulation was formally approved by the FCC on April 11, 1984. As a result, any awards of licenses after that date were to be made under the new lottery procedure.
As we have said, Elden Heinz, Jr., was one of those who, with some engineering background, perceived the commercial possibilities of cellular technology. In January 1983, before there was any talk of changing the licensing process from an administrative hearing to a lottery, Heinz approached Horace A. (Jack) Morris, the then manager of the debtor, about filing an application for the non-wireline license assigned to the Charlotte-Gastonia SMSA. Morris himself had already shown an interest in filing for several licenses. The two agreed to coordinate their efforts in filing for a non-wireline application in the Charlotte-Gastonia SMSA. They approached the principals in T.A. Associates, a business entity, which often financed new growth ventures, for financial support. T. A. Associates agreed to provide the financial support for the venture. The three parties — the debtor, Heinz, and T.A. Associates — proceeded in late February 1983 to charter C-PACT as a North Carolina corporation in whose name the application was to be filed. The capital stock of the corporation was divided among the debtor Morris Communications (26%); Heinz (25%); [462]*462and T.A. Associates (49%)4 in the proportions indicated.5 The division of stock was arranged so that T. A. Associates would not have stock control of the corporation. Under the terms of incorporation, it was also provided that no stockholder could sell his stock without the consent of the other stockholders. Thus chartered, C-PACT, in March 1983, joined 21 other applicants in seeking the non-wireline license in the Charlotte-Gastonia SMSA.
The debtor itself, during the early fall of 1983, began experiencing financial reverses. In November 1983, Berns and Vie-beck, the owners of 75% of the stock of the debtor, sold their stock to Frank Warlick, who then assumed with the agreement of the other interested parties the management of the debtor. The debtor’s paging operations, like the proposed cellular telephone operations in which it was involved, were subject to the regulating and licensing authority of the FCC. In January 1984 the FCC charged that Warlick had violated FCC regulations in the paging operations of the debtor. It was feared by the stockholders in C-PACT that Warlick’s presence as a stockholder in C-PACT might prejudice C-PACT’s FCC application for a cellular telephone system. In any event, this financial difficulty of Warlick with the FCC contributed to a worsening in the financial condition of the debtor. The FCC fined the debtor for such violation.
Because the debtor’s financial condition was deteriorating, Warlick decided it was in the interest of the debtors to sell certain of the debtor’s assets to meet the problems caused by the financial reverses being experienced by the debtor. Ms. Martin, president of the defendant Ashley, had mutual business interests with Morris and Warlick, and through Morris she met and had talked to Heinz. At a meeting with Warlick on May 14,1984, Warlick first approached Ms. Martin with an offer to sell her the debtor’s paging business. Ms. Martin agreed to purchase such paging business. After this sale, Warlick broached with Ms. Martin the purchase of the debtor’s C-PACT stock. After some haggling, Warlick offered to sell such stock to Martin for $5,000. This was immediately after the FCC had established its lottery method for awarding cellular telephone licenses and when C-PACT’s application was merely a lottery “chance,” as the bankruptcy judge in his oral order characterized it.
Martin immediately sought advice from three parties on whether she should accept Warlick’s offer of the C-PACT stock. First, she called Betty Neisler, a well-known successful businesswoman from Atlanta, Georgia, with whom Martin had developed a friendship. Martin, after telling Neisler of Warlick’s offer, inquired whether she (Neisler) thought it was worth considering. Neisler told Martin she knew little about the cellular telephone business, but the whole thing seemed “iffy” and advised Ms. Martin only if she could afford to lose her investment should she consider such a chancy proposition. Martin next called Heinz and had an extended discussion with him.6 She told Heinz that War-lick had offered to sell her the debtor’s C-PACT stock. In the conversation, Heinz reviewed with her the development of the cellular telephone industry. Specifically, he told her that the debtor’s stock in C-PACT represented an investment of chance, which could be of no value or value of $500,000, dependent on whether C-PACT was granted the exclusive franchise as a non-wire operator in the Charlotte-Gastonia SMSA.7 This prophecy is in line [463]*463with the comment in The Wall Street Journal, September 16, 1989, Section C, pp. 1 and 2:
Because almost no cellular companies make a profit yet, the industry is valued on the basis of what companies might earn in the future. Cellular stock prices are valued on a very high level of future earnings, quoting one expert as declaring that “valuing cellular is largely guesswork; you can come up with any number you want for this industry.”
Heinz was indefinite whether Ms. Martin told him the price at which Warlick had offered to sell, though it is interesting that he did not testify that she had failed to tell him the price.8 Had he inquired, it can be assumed Martin would have told him since Martin told both Neisler and Morris the offering price and, if she freely told them the proposed price, there would appear to have been no reason for her not to have been as forthcoming with Heinz as she had been with Neisler and Morris. Moreover, Morris did tell both Heinz and Ware (who represented T.A. Associates) the price War-lick named to Martin.
Martin talked finally with Morris, whose interest in the debtor had not been acquired by Warlick. Morris expressed to Martin his delight that Warlick had offered to sell the debtor’s interest in C-PACT. The reason for his elation was his fear, shared by Heinz, that any continued connection of Warlick with the C-PACT application would be prejudicial to the success of C-PACT’s application before the FCC. This apprehension was prompted by the difficulties Warlick had earlier had with the FCC about his paging operation.9 Martin told Morris about the price she and Warlick had tentatively discussed. Morris proceeded to encourage Martin to proceed with the purchase, though he warned Martin that the success of C-PACT’s application was a “chance.” He expressed to Martin no interest in purchasing Warlick’s interest.
After her talk with these individuals, Martin finally decided to pay $5,000 for the C-PACT stock, conditioned, of course, upon the agreement of Heinz and Wade to her purchase in accordance with the conditions of C-PACT’s charter.10 Wade, however, [464]*464conditioned his agreement to Martin’s purchase on the latter’s agreement to sell him two of the twenty-six shares of C-PACT stock owned by the debtor. The price for the two shares was left for future discussion. On that basis, Wade joined Heinz in agreeing to Martin’s purchase. Martin thereupon completed the final purchase of the stock on May 17, 1984.
After the purchase was completed on May 17, 1984, Martin consulted Heinz about the price to be charged Wade for the two shares the latter wished. Both Martin and Heinz recognized that Wade’s interest in the purchase of only two shares would make him the controlling stockholder in C-PACT. Martin stated that neither she nor Heinz wished to see Wade obtain control of C-PACT. According to Martin, it was agreed that Martin should ask $10,000 for the two shares. Wade’s interest in the two shares was abandoned because he said the price was “ridiculous.” 11 Martin thus acquired, on May 17, 1984, the debtor’s C-PACT stock for a purchase price of $5,000.
In early 1984, a number of the Charlotte-Gastonia license applicants, apprehensive of awards made under a “chancy” lottery system, explored ways to avoid or reduce individually the odds of a lottery system. The method which seemed to have been taken by some of the applicants to reduce such odds was through the creation of partnerships in which all the applicants would have equal shares and to which all the applicants in the area would transfer their applications. By this procedure, there would be no contest over the award, since all the applicants had pooled their applications into a single entity which would then be the sole applicant for the award and the automatic licensee. This method was recognized by and acceptable to the FCC. The first action along this line among Charlotte-Gastonia applicants was represented in an agreement by nine of the twenty-two applicants to pool their applications under an agreement executed in February 1984. C-PACT was not a member of this group; it continued with its individual application. This was the situation when the defendant purchased the debtor’s 26% interest in C-PACT.
On September 28, 1984, all the non-wire-line applicants including C-PACT after extended negotiations finally agreed upon a partnership, merging all their applications, thereby creating a single applicant and assuring selection of the partnership as the non-wireline licensee in the Charlotte-Gas-tonia area. At that time, but only then, shares owned by the twenty-two former applicants (but not partial interests in an application such as that held by the defendant after its purchase from Warlick) began to be traded and sold at prices ranging from $200,000 to $300,000. Prior to this time there had been no market or trades involving applications or shares in applications in the Charlotte-Gastonia area.
In the last of October 1984, C-PACT’s V22 interest in the partnership became “the key piece in a bidding war between the Providence Journal and Metro-Mobile CTS” to determine control of the non-wireline license, to quote the opinion of the bankruptcy judge.12 The “war” finally ended with the Providence Journal offering $1,200,000 for C-PACT. That offer was accepted and, after paying expenses and debts, C-PACT was dissolved and $286,000 was allocated to the 26% which had been acquired by Ashley Communications. That $286,000 was, however, under an injunction issued by the bankruptcy court, placed in escrow to await the disposition of this action which had been previously filed to void the transfer from the debtor to the defendant of the [465]*465260 shares of C-PACT stock on May 17, 1984. The bankruptcy judge, after a trial, found the transfer void under the Bankruptcy Act.
II.
The bankruptcy judge’s conclusion that the transfer was void was premised on two findings of fact and conclusions of law: the first was made orally at the conclusion of the hearing; the second was in a written opinion filed some time after the trial and was more formal. In essence, however, the two findings and conclusions are similar. In both opinions, the bankruptcy judge concluded that the transfer of the C-PACT stock by the debtor to Ashley was void as a preference under the criteria declared in section 548. He based this conclusion entirely on his findings of fact. The first of such findings was that the transfer was “for less than reasonable equivalent value,” although in making that finding, he declared that the “transfer ... was between a willing purchaser and a willing seller at a price upon which they agreed to at arm’s length.” He discarded the fact that the transaction had been a voluntary one between two parties of mental competency trading at arm’s length without any fraud or improper. action by either party because he said that “the parties [to the transfer] were not well informed and not knowledgeable.” He accordingly concluded that “their [Warlick’s and Martin’s] conclusion as to value is not a fair valuation of what market value [was] at that point in time, to wit, when the May transfer occurred” but “that the value of the stock at the time of transfer ... [was] worth at least $50,000 and that a payment by a knowledgeable purchaser and a knowledgeable seller standing on equal footing, both willing to buy on one hand and willing to sell on the other, having knowledge would have come out at a figure of at least $50,-000.00 of that time_” He offered no explanation of how he arrived at the market valuation of either C-PACT or the debt- or’s C-PACT stock. The second finding made by the bankruptcy judge was that Ashley was a good faith purchaser. In arriving at this conclusion, the bankruptcy judge proffered his conclusion in his oral opinion that Ms. Martin, with limited information, agreed to venture $5,000
worth of capital on a chance. And the people who held that partial “chance” were willing to sell it for that. So as between these parties, I have no problem with that transaction. I’m convinced in my own mind from this evidence that neither of those two transaction parties in the transfer itself held knowledge or information which would put them in an advantaged position over the other; but that on the contrary, they were on about equal footing trading at arm’s length. And I can’t find any bad faith in that.
The bankruptcy judge expressed in his oral opinion some difficulty, on the basis of these two findings, in arriving at a proper disposition of the stock and its proceeds. He stated frankly that, if he had the power, he would split the proceeds between the Trustee of the debtor and the defendant Ashley Communications. But with clearly expressed reluctance he concluded he had no such equitable power. He did, however, provide for the return to the defendant of the $5,000 payment made by it in the May 17 purchase and did allow the sum of $20,-000 under section 550(d) of the Act for improvements made by the defendant to the property in dispute. Such “improvement” consisted of the various services contributed by the defendant in the protection and final sale of the property. These findings and conclusions were substantially repeated in the bankruptcy judge’s later written opinion.
III.
Ashley has appealed the decree of voi-dance of the transfer and the Trustee has cross-appealed the grant of $20,000 for costs incurred by the defendant in effectuating “improvements” within the meaning of section 550(d) and that as a consequence the value of the transferred C-PACT stock was increased by at least $20,000. We look first at the statute on which this action by the Trustee is founded and the decision relating to its application.
[466]*466Section 548(a)(2)(A) and (B), which is the statute on which the Trustee bases his action,13 enables the bankruptcy Trustee to avoid any transfer of property by the bankrupt within one year of the filing of the bankruptcy petition if the debtor received less than a “measurably equivalent value” and was insolvent on the date of such transfer or became insolvent as a result of such transfer. Butler v. Lomas & Nettleton Co., 862 F.2d 1015 (3d Cir. 1988); In re Roco Corp., 701 F.2d 978, 981 (1st Cir.1983). The burden of establishing these conditions rests on the trustee. Kiddie Skis Int’l v. Williams, 60 B.R. 808, 811 (W.D.Mo.1985); In re Hulm, 45 B.R. 523, 526 (Bankr.N.D.1984); Re: R. Purbeck & Associates, Ltd., 27 B.R. 953, 954-55 (Bankr. Conn.1983). It is stipulated that the transfer in this case was made within one year of the filing of the bankruptcy petition when the transferror-debtor was insolvent. The sole issue between the parties thus is whether the debtor-transferror received in exchange the reasonably “fair equivalent value” of the transferred property. The date for defining such reasonable equivalence is the date of the transfer (in this case, May 17, 1984). As Collier on Bankruptcy, § 548.09 at p. 116 (15th Ed. 1984), has put it:
The critical time is when the transfer is “made”. Neither subsequent depreciation in nor appreciation in value of the consideration affects the value question whether reasonable equivalent value was given.
The burden of establishing that the transfer was not made for fair equivalent value on the critical date of May 17, 1984, rested on the Trustee. In re Hulm, supra.
Section 548 provides no definition to guide the Court in the application of the term “reasonably equivalent value.” Congress left to the courts the obligation of marking the scope and meaning of such term. In discharging this responsibility, the courts have considered a number of standards to be applied. All of the cases seem to agree that reasonable equivalence is not wholly synonymous with market value, even though market value is an extremely important factor to be used in the Court’s assessment of reasonable equivalence.14 This is obvious in the various formulations of the standards for reasonable equivalence as stated in the cases. Some courts, for instance, have suggested the application of a mathematical formula as a benchmark for such determination. One of the standards known generally as the mathematical formula originated in the setting of a foreclosure sale in Durrett v. Washington Nat’l Ins. Co., 621 F.2d 201 (5th Cir.1980), and was followed in Madrid v. Lawyers Title Ins. Co., 21 B.R. 424 (Bankr. 9th Cir.1982), aff'd. on other grounds, 725 F.2d 1197 (9th Cir.), cert. denied, 469 U.S. 833, 105 S.Ct. 125, 83 L.Ed.2d 66 (1984). Under this standard, a consideration less than 70% of the fair market value will normally not qualify as “reasonably equivalent value.” Durrett, supra, at 201. The rules to be applied in defining reasonable equivalence, as adopted by the later cases, however, take a less rigid approach and are most accurately summarized in Bundles v. Baker, 856 F.2d 815, 823-24 (7th Cir.1988). That decision rejects any fixed mathematical formula for determining reasonable equivalence and [467]*467opts for the standard that “[Reasonable equivalence should depend on all the facts of each case,” an important element of which is market value. Such a rule “requires case-by-ease adjudication,” “as a starting point [for such review] the fair market value” of the property transferred. The bankruptcy judge in this case adopted this standard for determining reasonable equivalence. Drawing on his earlier decision in In re Smith, 24 B.R. 19 (Bankr.W. D.N.C.1982), and applying the rule that reasonable equivalence was to be determined by “an analysis of all the circumstances surrounding the suspect transfer,” he declared that:
Factors to be considered include the good faith of the transferee, the relation differences in the amount paid compared to the fair market value, and the percentage of the amount paid is of the fair market value.
Another factor said to be of “considerable importance” in assessing reasonable equivalence is whether the sale was “an arm’s length transaction between a willing buyer and a willing seller.” Bundles, supra, at 824. We accept the majority view on the meaning of reasonable equivalence in this context.
The bankruptcy court declared in its opinion there had not been reasonable equivalence in this transfer. In reviewing that decision, it is important to determine the standard for review of reasonable equivalence in a case. That standard depends on whether the bankruptcy judge’s rulings are to be treated as findings of fact or conclusions of law.
If the bankruptcy judge’s decision on reasonable equivalence represents a finding of fact in a bankruptcy proceeding, as here, that finding is reviewable under the clearly erroneous rule, see Bankruptcy Rule 8013. A finding is clearly erroneous when, although there is evidence to support it, the reviewing court on the entire record is left with the definite and firm conviction that a mistake has been made. United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 541, 92 L.Ed. 746 (1948). However, the purpose of the reviewing court is not so limited if the question of reasonable equivalence is to be considered a conclusion of law. Solomon v. Northwestern State Bank, 327 F.2d 720, 724 (8th Cir.1964). Whether a holding that a transfer was based on “reasonably equivalent value” is a finding of fact reviewable as such or a question of law requiring review de novo on the entire record by the court is a matter about which the authorities are in some confusion. Bundles, 856 F.2d at 821 (“If we take the statute at its face value, we must conclude that its unambiguous language requires the reviewing court to make an independent assessment of whether reasonable equivalence was given”); Durrett v. Washington Nat’l Ins. Co., 621 F.2d at 203; In re Roco Corp., 701 F.2d at 981-82; Klein v. Tabatchnick, 610 F.2d 1043, 1047-48 (2d Cir. 1979) (“Fairness of consideration is generally a question of fact”), and 4 Collier on Bankruptcy, Section 548.09 at 548-112 (15th ed.1990) (“Whether the transfer is for ‘reasonably equivalent value’ in every case is largely a question ... to the trier of the facts”). It is unnecessary, however, for us in this case to determine what standard of review to apply, since our conclusion would be the same under either standard. Applying these standards for review, we conclude that the decision below must be reversed. Our reasons for such conclusion follow.
IV.
We preface this discussion with a restatement of the findings and conclusions of the bankruptcy judge which were adopted by the district judge as his findings and conclusions. In reaching his dis-positive conclusion that the defendant did not give reasonable equivalence for the transfer, the bankruptcy judge stated that “[t]he word ‘value,’ in the [statutory] phrase ‘reasonably equivalent value’ means ‘fair market value,’ that is, what a willing purchaser with full knowledge would pay and what a willing seller would accept,” determinable as of the date of the transfer (ie., May 17, 1984). The bankruptcy judge then declared “that on 17 May 1984 the fair [468]*468market value of C-P ACT’s cellular application in the Charlotte-Gastonia SMSA was at least $192,307, twenty-six (26%) percent of which is $50,000,” and that “a payment of $5,000 (which was the consideration given by the buyer in this case) was only 10% of, and was $45,000 less than, the fair market value of the transferred stock.” There is no clear explanation of how the bankruptcy judge arrived at his figure of $192,307 in which he rested his findings of a market value of $50,000 for the debtor’s C-PACT stock on May 17, 1984. The only basis given for the bankruptcy’s judge’s finding that the debtor’s C-PACT stock was worth $50,000 on May 17 was: “After receiving the more than two days of oral and documentary evidence in this case, including the testimony of four disinterested value witnesses, this court concludes that the value of the transferred C-PACT stock at the time of the transfer was at least $50,000.” 15 As we have said, he dismissed as irrelevant on the issue of reasonable equivalence the price for the stock as arrived at between Warlick and Martin in fair, arm’s length bargaining because, as he said, neither was “truly knowledgeable” of the market value of the stock and, had they been, they would have agreed upon a price of $50,000. Any review and analysis of the correctness of these findings and conclusions must begin with a clear understanding of the asset being evaluated.
The challenged transfer involved a sale of approximately a one-fourth stock interest in the corporation C-PACT. The only asset which the corporation C-PACT had was its application for a cellular telephone license; the record establishes C-PACT had no liabilities of any consequence. Accordingly, the reasonable market value of the transferred stock depended on, or, as the bankruptcy judge put it, was “directly related to the fair market value of C-PACT’s sole asset,” i.e., its license application, determinable as of the date of the transfer itself. At the time of the transfer, C-P ACT’s cellular application’s value represented nothing of present value; it was merely a right to participate along with 21 other applicants in the award of the non-wireline cellular license for the Charlotte-Gastonia SMSA through the “rolling of the dice” in a lottery and not on the basis of an administrative hearing on the merits of the various applications.
As we have said, at least ten of the competing applicants for the Charlotte-Gastonia non-wireline license as of late April 1984, discouraged at the prospect of having their applications decided by chance in a “rolling of the dice” in a lottery, had pooled their applications through the creation of what was spoken of as the “Grand Alliance,” with each applicant having a one-tenth interest in the “pooled” right to a license. C-PACT was not a part of this combination. The bankruptcy judge assumed that “[bjecause the partial settlement group would have as many chances to prevail as it had applications, partial settlement increased an applicant’s odds of obtaining a share of one of the two licenses which would be issued in that SMSA.” We assume this statement was added to the findings of the bankruptcy judge for the purpose of showing that later in May 1984 the value of C-PACT’s “odds” in the lottery was substantially increased with the pooling arrangement represented by the “Grand Alliance,” and that such increase in its “odds” gave enhanced value to C-PACT’s license application. If this is the [469]*469purport of the bankruptcy judge’s finding, we find the finding incorrect. The pooling of their applications by ten of the twenty-two applicants did not increase or enhance in the slightest the “odds” of C-PACT being a winner in the lottery. The pooling arrangement meant simply that the ten participants could pool all their applications jointly and, if any one of such pooling applicants won, then its winning award of the license would be divided among the ten members of the pool. It could be said that the ten participants had enhanced to some extent the likelihood in the lottery of their obtaining a one-tenth interest in the license. But such an arrangement did not increase the “odds” in the lottery for any non-pooling applicant such as C-PACT; there would still be twenty-two “chances” in the lottery, though one party in the lottery participation (not C-PACT) would hold ten chances. On May 17, 1984, C-PACT thus still had just one chance out of twenty-two for success in the lottery; its “chances” were not enhanced at all by the April partial settlement by ten of the other applicants.
Also, since we will be repeatedly referring to “full settlement” in our discussion of the value of C-PACT and the debtor’s interest therein, it seems appropriate at this time to state what a “full settlement” is, as distinguished from a lottery chance such as C-PACT had on May 17, 1984. The bankruptcy judge correctly described the term “full settlement” as follows:
If the SMSA became “fully settled,” that meant all applicants for either the non-wireline or wireline had pooled their respective applications. Since there were then no longer any competing applicants, a full market settlement assured the settlement group that it would be issued either the non-wireline or wireline license, whichever was applicable.
There is accordingly, as the witness DePri-est said, no real distinction between “a full market settlement and an actual construction permit [or license].” It follows that a “full settlement” converts each application into a proportionate interest in the license. As one of the Trustee’s witnesses testified without contradiction, there is obviously “a very big difference between the value of the application and the value of the license (or of a full settlement) because you’ve got to allow for the probability of winning the lottery.” Since on the critical date of May 17 all that C-PACT had was a lottery chance and no more, what we are concerned with is not the market value of a “full settlement” (which was the equivalent of a license), but the value of a lottery chance — along with twenty-one other applicants — to obtain a cellular license.
The determination of the dispositive issue of “market value” of C-PACT on May 17, 1984, is dependent on the method to be used in arriving at that value. There are various methods for arriving at a market value for any asset. It has been often declared by the courts that the method of “comparable sales” in the relevant time frame is “more appropriate than any other method in determining market value of the property taken.” United States v. 100 Acres, 468 F.2d 1261, 1265 (9th Cir.1972),16 cert. denied, 414 U.S. 822, 94 S.Ct. 119, 38 L.Ed.2d 54 (1973). The bankruptcy judge appears to have adopted this comparable sales method for arriving at the “market value” or “reasonable equivalent value” of the C-PACT stock of the debtor. The Trustee, accepting this method of evaluating the debtor’s C-PACT stock, produced three witnesses to provide evidence of such “market value.” Primarily, these witnesses did this by attempting first to evaluate C-PACT itself and then by arriving at the value of the debtor’s C-PACT as approximately one-fourth of the C-PACT value. The difficulty of applying such a formula for ascertaining value in this case is identification of comparable sales which could provide guidance for valuing the asset being valued. The Trustee sought to meet this problem by the testimony of his three value witnesses. These witnesses initially identified the sale of ACTS in the Washington-Baltimore SMSA which was agreed on in late 1983 but finalized in 1984 as the [470]*470appropriate sale to be used as a “benchmark” for valuing the debtor’s stock on May 17, 1984, under the “comparable sales” method of valuation. However, it developed conclusively that ACTS was not a sale of a mere license application such as C-PACT had on May 17, 1984; it was the sale of a fully licensed, operating cellular telephone system. Actually, ACTS had been licensed as an experimental operation as early as 1977 and by late 1983 was operating as a commercial system. It consequently represented a sale both of a license and of an operating system. Obviously, it was not comparable to the sale here, which was a sale of a mere application. And, so far as the record shows, no one had ever used in an actual transaction relating to a sale of a mere license application this “benchmark” established by the ACTS sale. In fact, as we later point out, there is in the record no sale similar to the one here. It follows that ACTS provides no guidance to the market value of C-PACT on May 17.
Reference was also made by the Trustee’s value witnesses to a transaction involving transfers of some cellular applications of Knight-Ridder. Again, this effort to find a comparable sale in such transaction was flawed because the transactions by Knight-Ridder represented an exchange of license applications and not a sale. And the witnesses so conceded. One witness, in another effort to identify a comparable sale, pointed to some sales/purchases by Belting-Hemingway which he said were comparable to the sale of the debtor’s stock on May 17. However, as the witness later admitted, these sales were made only after full settlement, when the applications had matured into actual shares in a license. All the witnesses testified that there was a “very big” difference between a sale of a mere license and a sale of such license after “full settlement.” These transactions had no relevancy to our inquiry here. Finally, one of the value witnesses testified that John Kluge had purchased, prior to May 1984, a number of paging systems which also had pending applications. The witness, however, did not consider that such transactions were similar to the sale here, because these were actually purchases of paging systems.
The fact of the matter is simply that there is no evidence of any sales similar to the sale by Warlick to Martin of the C-PACT stock in the same time frame. This is evident from the testimony of the Trustee’s value witnesses. These witnesses were executive officers of two of the most active participants in the cellular telephone industry. Both companies were interested in extending their investments. DePriest and Richards were the president and vice-president/general counsel, respectively, of the Charisma Corporation, and Witze was the president of Metro-Mobile CTS. According to their testimony, their companies had never bought a license application before there had been a full settlement by all the applicants in the relevant SMSA. Before the full settlement, they remained, as did other parties interested in cellular licenses,17 on the sideline. They had not the slightest interest in purchasing a lottery chance, which was all C-PACT had on May 17. But when a full settlement was agreed on by all the applicants for the non-wireline license in the Charlotte-Gastonia SMSA on September 28, 1984, both of these companies immediately became active, aggressive bidders for C-PACT and similar interests. That seems to have been their policy. It was the full settlement which was the catalyst for changing C-PACT from an asset for which there were no bidders to one which, as a result of the full settlement, represented a partial interest in a license. We are not concerned with the value of C-PACT after that value had been enhanced by the full settlement agreement of September 28; for us in this case the “critical” question, as Collier, quoted above, states, is value on May 17, before the enhancing event represented by the full settlement executed about four and a half months later.
Another fact which evidences the disinterest of anyone in bidding for C-PACT on [471]*471May 17 is the attitude taken by Heinz and Wade when they heard of Warliek’s offer to sell the debtor’s C-PACT stock to Martin. There can be no question that Heinz, Morris and Wade were fully knowledgeable about C-PACT and its value. Heinz and Morris had been the founders of C-PACT. Heinz had also been the party who interested Wade, described by Heinz as a “sophisticated investor” in the cellular field, in becoming a stockholder in and financier of C-PACT. As the other parties interested in C-PACT, Heinz, Morris and Wade were the three individuals who would have most likely had an interest in buying the debtor’s stock and who were in a superior position to evaluate the worth and market value of both C-PACT and a stock interest in CPA'CT. Moreover, they were in a favored position to make such an offer. Under C-PACT’s articles of incorporation any sale of stock by any stockholder required for validity the consent of all the other stockholders. Heinz and Wade thus had to consent to any sale by Warlick to Martin (Ashley Communications).18 Martin had told both Morris and Heinz about Warliek’s offer of the stock. Morris and Wade knew the price at which Warlick had offered the stock to Wade. Heinz was indefinite as to his own knowledge.19 Certainly Martin had not sought to conceal any of the details. She freely told Morris all the details and she had every reason to assume that Morris talked with Heinz about the matter and the record shows that he did. Both Heinz and Wade, as C-PACT stockholders, had the power of stymieing any sale by Warlick of the stock simply by refusing under the corporation’s articles to consent to any sale until they had an opportunity to make their own bid for the stock. Neither used this right to refuse consent in order to force Warlick to offer the stock to “them” or to compel Martin to “cut them in” on the purchase. They both readily agreed. Wade, however, conditioned his agreement of consent on Martin’s agreeing to sell him two percent of the stock at, according to him, the same proportionate price Martin had paid for the 26% block, but, according to Martin, at a price to be later agreed upon. Later events suggest that Martin’s version of the price to be paid for the two percent block was correct, as Wade subsequently acquiesced in her statement of the agreement.20 It is also manifest that Heinz never made any real effort to locate War-lick or to buy the stock himself. According to his testimony, he had participated in some 200 license applications in various SMSA’s. He excused his indifference to pursuing Warlick by his preoccupation with all his other applications. See note 3, supra. Morris, Heinz and Wade encouraged Martin to buy the stock in question and made no real effort to buy the stock themselves, even though they had an effective leverage to force Warlick to deal with them before he could sell the stock to Martin. This conduct demonstrates that, though they were more knowledgeable than anyone else on the worth of the debtor’s C-PACT stock, they made no effort to buy the stock on May 17, 1984. This indifference substantiates the conclusion that there was no evidence of a market value for the Trustee’s C-PACT stock on May 17. Not only were there no comparable sales, there were no interested bidders for such stock.
[472]*472Frustrated in his efforts to discover a market for a license application such as C-PACT prior to full settlement, the Trustee sought through his three witnesses to create an entirely hypothetical and unorthodox market. These witnesses testified in depositions held in 1988 that each would have paid approximately $50,000 for the debtor’s C-PACT stock in May 1984 had the stock been offered to them. Such testimony is necessarily suspect and lacks credibility. Testifying as to what he would have done four years earlier under conditions existent at that time but did not do at the time the event occurred is to engage in an excursion in dreamland. In the four or five years which intervened between the sale in May 1984 and the testimony of these witnesses in 1988, there had been drastic changes in C-PACT and in its value. C-PACT had evolved from a mere chance in a lottery scheme on May 17, 1984, into an actual absolute interest in a cellular telephone license by reason of the execution of a full settlement on September 28, 1984. While C-PACT was an asset for which there were no bidders on May 17, it had become with the full settlement of September 28 an asset for which the bankruptcy judge found that there was an active market at a beginning price of $200,-000 for C-PACT, or presumably a price of $50,000 for the one-fourth interest in C-PACT which the debtor had owned. Beyond that, by a kind fortune, C-PACT had become the key item in a stock battle for control of the license itself in late October 1984, because of which C-PACT’s market value had increased to $1,200,000, giving the debtor’s interest (had it retained it) a value of approximately $300,000. Knowing all that, it was easy for these witnesses to opine that, if they had had a chance in May 1984, they would have paid approximately $50,000 for the debtor’s C-PACT stock and thereby received $300,000 as their share of the sale of C-PACT in late October. But the fact is that the companies for which these witnesses worked, sophisticated investors in cellular properties as they all were, did not make a bid at any time for a lottery chance in the award of a non-wire-line cellular license but delayed any bid on their part until there had been a full settlement. In short, the Trustee’s value witnesses were unable, as we have seen, to point to any specific sale by any one of or even of an interest in a mere license application prior to full settlement. It is also interesting that these witnesses had never bid for or bought a license application or an interest in such an application either before or after a full settlement.21
It may be said that these witnesses had prefaced their statements of what they would have paid for the C-PACT stock on May 17, 1984, with the qualification “if it [the C-PACT stock] had been offered us.” The record shows that whenever they were interested in purchasing an application after “full settlement,” these companies did not sit motionless on a log; they began actively to make offers to purchase and they actually made purchases. After full settlement in the award of the non-wireline license in the Charlotte-Gastonia area on September 28, both Charisma and Metro-Mobile rushed in as eager, avid bidders. It is crystal clear that neither these companies nor, it would seem, any other like investor was interested in bidding for or in purchasing any property such as C-PACT was on May 17, 1984. Careful investors simply weren’t interested in bidding for a lottery ticket which was all C-PACT was on May 17. Only someone who was willing to make a payment for a mere chance, such as Martin, was a likely purchaser on May 17, 1984, and for such a chance, only a small purchase price could reasonably be expected. In summary, there was neither [473]*473an actual nor a hypothetical market for property such as C-PACT.
Perhaps the oddest thing about the testimony of the Trustee’s value witnesses and of Heinz is that the amount each said he would have paid for the debtor’s C-PACT stock on May 17 (when C-PACT was still no more than a chance in the lottery), and the amount at which it could have bought that same stock interest in either C-PACT or in any one of the other non-wireline applicants after the full settlement on September 28, 1984, was precisely the same.22 This is plainly illogical under the evidence, since as Witze testified, there was a “big difference” in the value of C-PACT as a mere applicant (which was all it was on May 17) and its status after a full settlement on September 28. This is simple common sense. The Trustee and his witnesses recognized the egregious inconsistency in their position to the contrary and sought to counter it with the intimation that at all times after the introduction of the lottery system of awarding the cellular license full settlement by all applicants in all markets was assured. Full settlement was not inevitable or assured. Thus, Witze identified a number of markets where full settlements were never achieved. Even a partial settlement such as resulted from the creation of the so-called Grand Alliance was arrived at only after what DePriest, the architect of such Alliance, called “meetings for a several-month period anywhere from two to six meetings per day virtually every day during the period ... during February, March, April ... right up through the mid part of the year.” Witze further testified that “[o]n the wireline side, I believe more than half were full settlement, more than half ... in the non-wireline side ... it may have been as high as three-quarters.” Moreover, if full settlement was inevitable, why did the Charisma and Metro-Mobile companies, whose managers were the Trustee’s witnesses, make no effort to buy interests such as C-PACT until there had been a full settlement on September 28? Their actions belie any testimony of these witnesses that they knew that full settlement was so certain. And the bankruptcy judge perceived this for he found that “[f]ull settlements had by no means here arrived on 17 May 1984, although some non-wireline applicants believed in May, 1984 that full market settlements among all non-wireline applicants would have to occur because too much investment of time and money was at stake to risk losing.” This finding should dispose of that contention.
Some reference is made by the Trustee to the fact that Martin priced two percent of the twenty-six percent she bought from Warlick at $10,000, indicating thereby that she placed a high value on the stock purchased. This argument disregards the circumstances under which this price was established. What Wade wanted — and all he wanted — was just enough additional stock to give him control of C-PACT. Before stating to Wade a price for the two percent, Martin consulted Heinz. According to Martin, neither Heinz nor Martin was anxious to see Wade secure control of C-PACT. Heinz denied this but the record unquestionably supports Martin’s views. At the outset, Morris and Heinz had limited Wade to a no-control position. There was still no desire on Heinz’s and Martin’s part to see him acquire control in May 1984. The price of $10,000 which Martin demanded for the two percent was suggested and fixed by Heinz, not Martin, for the control stock. Heinz’s testimony on this point was:
Q. Was there any way that you and Lynn [Martin] could have had a conversation and that she could have gotten her figure from you before she wrote the letter to Jim Wade asking about it?
A. I’m certain she got the figures from me before she wrote the letter to Jim Wade [pricing the two percent stock interest].23
Both Heinz and Martin recognized, as did Wade, that the figure was “ridiculous.” C-PACT at the time was mainly a holder of a lottery ticket, as Morris characterized it, giving the holder a “chance” to win in the [474]*474lottery. But the stock being offered was the control stock in the corporation. That control stock commands a significantly higher price than ordinary stock shares is demonstrated by the fact that Providence Journal paid approximately $1,200,000 for C-PACT’s control interest in the final license membership, even though other like interests were selling in a “free market” at a figure of $200,000. Providence Journal thus paid six times as much for control stock as it would have had to pay for the same interest if it had not represented control. It is difficult to believe that Wade would not have preferred to pay the $10,-000 for the control stock if at the time he had thought that the license award was certain. Clearly, in his mind, the C-PACT status as a winner of the license or of a share in the license was still “chancy.” And the bankruptcy judge understood this, for he dismissed the suggestion — that the size of this price asked by Martin of Wade for the two percent indicated that she thought that she had something of “added value” — with the blanket statement that such assumptions “don’t stand alone because the transfer of that two percent to the right entity would give that entity control and that makes that two percent worth something.” We agree with the bankruptcy judge and dismiss the offer to Wade as credible of the value of the full stock interest of the debtor in C-PACT on May 17.
Finally, we would take note of the bankruptcy judge’s denial of any evidentiary value in the issue of reasonable equivalence in the price Warlick and Martin arrived at after full and fair arm’s length negotiations of a reasonable price for the debtor’s C-PACT stock as of May 17. The bankruptcy judge discounted the value of their agreement price as evidence of the current market value of the stock on May 17 because he said the two trading parties were not knowledgeable. However, he found that “[throughout the fall and winter of 1983 and into spring of 1984” War-lick, Morris and Heinz “had various meetings, telephone conferences and correspondence regarding mutual interests. On occasion the parties discussed developments in the cellular industry generally and the importance and value of C-P ACT’s cellular application.” 24 (Emphasis added.) In fact, Heinz and Warlick had discussed filing an application in other areas. After being fully advised by Heinz, it would appear improper to say that Warlick was not “knowledgeable” about the value of C-PACT. Similarly, after receiving Warlick’s offer, Martin requested advice from Heinz. There was no one in a better position to advise Martin on the value of C-PACT or an interest in it than Heinz. Heinz accurately told Martin that if C-PACT obtained the license, the debtor’s C-PACT stock would have real value but that if it didn’t prevail the license application of C-PACT would be worthless; in essence, he counseled Martin that, if she bought the stock, she would be acquiring a chance but no more than a chance. That was accurate advice. Under the circumstances, it was all the advice that could be given a prospective purchaser about the prospect for a non-wireline license application in the Charlotte-Gastonia area. As the commentator in the Wall Street Journal of September 16, 1989, Section C, pp. 1 and 2, supra, had • said, absent evidence of profit or cash, flow experiences, “valuing cellular is largely guesswork; you can come up with any number you want for this industry.” Martin had at the time the best “guesswork” in value that was available. Under these circumstances, it was improper for the bankruptcy judge to dismiss the sale price agreed upon between Martin and Warlick as irrelevant because the parties to such negotiations were not “fully knowledgeable.”
V.
In summary, we are of the opinion that the bankruptcy judge was clearly erroneous in finding that the record supported by credible evidence a finding of $50,000 as the value of the debtor’s C-PACT stock on May 17, 1984; nor did the Trustee sustain his burden of proof that the price paid by [475]*475the defendant for the debtor’s C-PACT stock did not represent reasonable equivalence at the time of the transfer. In reaching a contrary conclusion, the bankruptcy judge relied basically on the general opinion testimony of three witnesses proferred by the Trustee. He specified nothing else of substance. None of these witnesses had ever purchased or participated in the purchase of a cellular telephone license such • as was represented in C-PACT on May 17, 1984. Nor had any company with which they had been connected participated in such a purchase. Their experience was confined to purchases after full settlement, something entirely different from the application itself when it was just a lottery chance, a fact recognized in all the evidence. Such testimony, given four or more years after the sale and after there had been a great change in the value of the transferred property by parties who had not only never participated in a purchase such as was involved here but were unable to identify a single sale of similar property, does not provide credible evidence to sustain a finding of a fraudulent conveyance under the statute. We repeat: when the defendant purchased the debtor’s stock, there was no market for such stock, representing as it did mainly a lottery chance. Even the Trustee’s witnesses testified that those entrepreneurs most sophisticated in the cellular field were unwilling to risk money or time in lottery chances. The other stockholders in C-PACT, individuals with knowledge in the cellular field, evidenced no desire to compete with the defendant in purchasing the debtor’s stock; indeed, they were anxious for the defendant to buy the stock. Only long after fortuitous events occurred, substantially enhancing the stock, did any of the witnesses suddenly declare that, if the stock had been offered to them on May 17, 1984, they would have paid $50,000, which was how much the stock’s price was enhanced by the September 28, 1984, full settlement. The defendant on May 17, 1984, took a chance none of the expert witnesses or Heinz was willing to take — or for that matter, that anyone else that engaged in the cellular industry was taking. Because the stock later appreciated substantially is no ground for invalidating the sale. The critical time for judging the propriety of the sale was the time of the sale, and the Trustee has not proved the seller did not receive reasonable equivalence at that time. The Trustee has failed entirely to meet his burden.
The judgment below is accordingly reversed and the cause is remanded to the district court with direction to enter judgment in favor of the defendant.
REVERSED AND REMANDED.