This contentious dispute — spanning almost two decades, two bankruptcy filings, and countless appeals and counter-appeals — revolves around the sale of a business called Lake Cumberland State Dock, Inc. ("LCSDI") in 1985 by L. Coleman Coffey and his son, Robert Bruce Coffey (together, the "Coffeys"), to Kool, Mann, Coffee & Co., Inc. ("Kool Mann"), which is principally owned by Thomas O. Moore ("Moore"). The substantive claims asserted by the parties are actually relatively simple: the Coffeys claim that Kool Mann owes them the balance remaining of the $5 million purchase price from the sale of LCSDI, while Kool Mann contends that it is entitled to a number of set-offs against that balance because of alleged misrepresentations by the Coffeys as well as certain other deductions. It is the tortured procedural history of this matter which makes this appeal exceedingly — and unnecessarily — complex.

Since litigation began in 1986, this dispute has gone before, inter alia, the United States District Court for the Eastern District of Kentucky and the Sixth Circuit, twice before the Bankruptcy Court of the Virgin Islands (which issued numerous orders and opinions), twice before the District Court of the Virgin Islands, and once before us, the Third Circuit. We summarize the procedural history of this matter in more detail below. Suffice it to say that it has been 17 years since Kool Mann agreed to purchase LCSDI.

For our purposes here, we have detailed only those facts that bear on our current disposition.1 In light of the protracted nature of this litigation and the length of time and judicial resources it has consumed, we have taken it upon ourselves to determine the value of the Coffeys' proof of claim in bankruptcy to be $238,280.78. We have done so even though under normal circumstances we might have been inclined to remand to the District Court for a remand to the Bankruptcy Court to recalculate the damage figures. In the interests of both judicial efficiency and fairness — and to terminate what has appeared to be interminable litigation — we will affirm the District Court's affirmance of the Bankruptcy Court's findings of fact of fraud and, for the reasons set forth in this opinion, conclude with the ruling that the amount owed by Kool Mann to the Coffeys in this proceeding is $238,280.78. We do so despite the fact that we will be affirming in part and reversing in part the District Court's October 2, 2001 judgment. However, in an effort to conclude this long standing controversy, we will not remand any portion of this appeal, even that segment we are reversing, but will rather decide the relevant value of the Coffeys' claim in this opinion and direct that that value be entered by the Bankruptcy Court.

LCSDI was a family-owned marina and houseboat rental business owned by the Coffeys on Lake Cumberland, Kentucky. It owned and operated an extensive system of docks and slips, a number of pontoon boats, and other boats which it rented to customers for use on Lake Cumberland. The boats were leased by LCSDI from Vacation Cruises ("VC"), a partnership also owned by the Coffeys. In 1986, VC owed about $700,000 to three regional banks in connection with the boats it owned.

Kool Mann is an exceedingly complex leasing business.2 Primarily, Kool Mann's business consisted of purchasing certain equipment (such as computers, telephones, trailers, and construction equipment) and leasing them to various customers known as users. In turn, Kool Mann would assign the lease payments as security against financing which was used to purchase the equipment in the first place. Under this arrangement, Kool Mann's investors were purportedly enabled to utilize certain income tax incentives and investment tax credits, take depreciation on the equipment, and sell the equipment at the expiration of the lease for a profit. Kool Mann operated this arrangement successfully for a number of years.

In the fall of 1985, Moore, the principal owner of Kool Mann, approached the Coffeys about purchasing LCSDI and VC. On December 11, 1985, Moore agreed that Kool Mann would pay a total of $5 million to the Coffeys for the outstanding stock of LCSDI.3 A first payment of $200,000 was due at closing, and an additional $800,000 (plus interest at a 10% per annum rate) was payable three months later (together, the "down payment"). The remaining principal balance was to be paid pursuant to an installment promissory note, which contemplated five annual installments of $150,000 principal and a final balloon principal payment for the remaining $3,250,000 due on September 30, 1991. The note also provided for interest to be paid with the installment payments at 0.5% above the prime interest rate. The Coffeys were provided with a security interest in the assets of LCSDI and a personal guaranty by Moore. The closing was scheduled to take place on December 31, 1985.

The Coffeys provided Kool Mann with unaudited September 30, 1985 and November 30, 1985 financial statements (together, the "financial statements"). After realizing that transactions concerning certain houseboats were not accurately described on the financial statements, L. Coleman Coffey wrote a letter to Moore on December 20, 1985 (the "December 1985 Letter") stating that "[t]he financial statements are reasonally [sic] accurate except for the houseboat transactions. These amounts will wash-out and show a small profit for the corporation."

The sale was finalized on December 31, 1985 pursuant to a Purchase and Sale Agreement dated December 31, 1985 (the "Purchase Agreement"). The representations and warranties in the Purchase Agreement were modified to reflect the existence of the December 1985 Letter, stating

(e) The financial statements as of November 30, 1985 ... are complete and correct and fairly represent the financial condition of the Corporation ... except as noted, discussed and agreed by the parties and evidenced by a letter to Tom Moore of December 20, 1985, which is hereto attached and herein incorporated.

Moreover, the parties entered into a side letter dated December 31, 1985, whereby the Coffeys agreed that any favorable tax savings they received due to the capital gains treatment of the disposition of the houseboats (the "Tax Savings") would serve to reduce the final balloon payment to be paid by Kool Mann on September 30, 1991 (the "Tax Savings Side Letter").

Shortly after the sale, a dispute arose as to which party would assume certain pre-existing debts of LCSDI, totaling approximately $1.213 million for the houseboat fleet it owned (including the $700,000 debt originally held by VC). In the fall of 1986, Kool Mann filed suit in federal court in Kentucky seeking declaratory relief as to the assumption of debt issue and also sought a set-off against the purchase price of LCSDI for alleged misrepresentations and accounting fraud by the Coffeys. The Coffeys counterclaimed for judgment on the $ 4 million balance due on the purchase price. The Coffeys also filed suit in state court against Moore, individually, under his personal guaranty. That action was removed to federal court and both were consolidated before the Honorable Karl S. Forester, U.S. District Court Judge for the Eastern District of Kentucky.

The Kentucky federal court bifurcated the assumption of debt issue from the misrepresentation and fraud issue. After a six-day trial, Judge Forester ruled on January 31, 1990 that Kool Mann had agreed to assume the company's debt when it agreed to pay $5 million for LCSDI, and that therefore Kool Mann was not entitled to set-off the amount of the assumed debt against the money it owed. See Moore, Owen, Thomas v. Coffey, 1991 WL 519627, slip op. at ¶¶ 6, 8, 10, 14.I (E.D. Ky. Jan. 31 1990). That ruling was not appealed.

On December 20, 1990, while the fraud issue was still pending before the district court in Kentucky, Kool Mann filed for bankruptcy protection in the Virgin Islands, where it purportedly maintained certain offices. Recognizing that he could not rule against Kool Mann due to its pending bankruptcy, Judge Forester entered summary judgment against Moore on October 11, 1991, rejecting Kool Mann's charge of fraud and holding that Moore was responsible for the balance owed to the Coffeys.

The Sixth Circuit reversed, finding a material issue of fact concerning the alleged misrepresentations. That court also held that the obligation of Moore on his personal guaranty could not be determined until the amount due from Kool Mann was first ascertained, and ruled that if fraud on the part of the Coffeys were to be found, Moore's personal liability under the guaranty would be discharged. See Moore, Owen, Thomas & Co. v. Coffey, 992 F.2d 1439, 1448-50 (6th Cir.1993).

As noted, Kool Mann filed for bankruptcy protection on December 20, 1990. The filing was made in the Virgin Islands, and the proceedings were assigned to the Honorable William Gindin, U.S. Bankruptcy Court Judge, sitting by designation in the Virgin Islands.

The Coffeys filed a $6 million Proof of Claim in the bankruptcy proceedings, seeking the balance of the purchase price, interest, and attorneys' fees. In response, Kool Mann objected to the amount of the Coffeys' claim in the Bankruptcy Court (the "claim objection"), and also filed a separate complaint against the Coffeys, alleging fraud, misrepresentation and set-off against any claim the Coffeys may have had against Kool Mann, including attorneys' fees and punitive damages (the "adversary proceeding"). Moore joined Kool Mann as a plaintiff in the adversary proceeding seeking to void his personal guaranty on the ground of fraudulent inducement.

A motion for estimation of the Coffey's Proof of Claim was filed under 11 U.S.C. § 502(c) (the "Estimation Hearing").4 The object of such a proceeding is to establish the estimated value of a creditor's claim for purposes of formulating a reorganization plan. The Bankruptcy Court conducted several days of hearings in 1992, but suspended them because of the intervening bankruptcy filing of Robert Coffey, in the Western District of Kentucky before the Honorable Wendell Roberts.

Judges Roberts, Gindin and Forester conferred and agreed that the most efficacious way to proceed would be to resolve all issues (including those still unresolved in the Kentucky litigation) in one forum, before Judge Gindin. Counsel for the parties agreed, and the hearings continued before Judge Gindin in 1992. On June 9, 1993, Judge Gindin issued his findings (the "June 1993 Findings").

There, Judge Gindin decided that the Coffey's ultimate claim was $26,915.78. First, he gave credence to Kool Mann's claim that it had relied upon the fraudulent misrepresentations of the financial statements presented by the Coffeys during the negotiation of the sale of LCSDI. Crediting Kool Mann's valuation expert, the Bankruptcy Court valued LCSDI's "true" worth in 1985 absent misrepresentations at $2,549,482, roughly $2.45 million less than the negotiated purchase price. Second, the Bankruptcy Court credited Kool Mann with $236,566.22 pursuant to the Tax Savings Side Letter. Third, the Bankruptcy Court further reduced the Coffey's claim by the number of principal payments that Kool Mann had made prior to the dispute. Finally, Judge Gindin credited Kool Mann with the debt payments (the assumed indebtedness of $1.213 million) it had made on behalf of LCSDI after the sale. Accordingly, the Bankruptcy Court held that the Coffeys' total claim after all the credits and deductions totaled $26,915.78.

In September 1993, the Bankruptcy Court entered a declaratory judgment in the adversary proceeding on the basis of its June 1993 Findings, and released Moore from his personal guaranty as a result of the Coffeys' fraudulent inducements.

The Coffeys appealed to the District Court of the Virgin Islands. In an Opinion dated July 17, 1995 (the "July 1995 Opinion"), the Honorable John Fullam, United States District Court Judge, sitting by designation from the Eastern District of Pennsylvania, reversed the Bankruptcy Court and remanded the case to that court for further proceedings. Noting that an Estimation Hearing has no legal effect other than establishing the approximate amount of the claim that will be recognized in a reorganization, Judge Fullam held that inadequate notice had been afforded to the Coffeys that the results of the Estimation Hearing would also be binding in the adversary proceeding. Accordingly, the case was remanded to the Bankruptcy Court for a reestimation of the Coffeys' claim and a trial of the adversary complaint on its merits.

However, Judge Fullam did not stop there. He noted that "[i]nasmuch as further proceedings will be required in any event, it is appropriate to address what appear to be significant errors in the bankruptcy judge's analysis." In re Kool, Mann, 233 B.R. 291, 1999 WL 249423, slip op. at 7 (1995). Judge Fullam stated that the Bankruptcy Court did not adequately consider the effect of the time pressure on the parties' negotiations, and that the Bankruptcy Court had put too much emphasis on the fact that the senior Coffey was an accountant. He also cautioned that the Bankruptcy Court paid too little attention to the findings made by Judge Forester in Kentucky and the views expressed by the Sixth Circuit.

A "more serious error," according to Judge Fullam, was the complete absence of a "causal relationship between the alleged fraudulent misrepresentations and inaccurate financial records, on the one hand, and damage to the debtor on the other." Id. at 9. He expressed concern about the methodology used by Kool Mann's expert because it was "based upon hypothetical cash flow projections bearing little or no relationship to the actual facts pertaining to this particular business." Id. at 10. The court therefore concluded that "[o]n this record, the evidence is insufficient to establish the amount of damages attributable to the Coffey's misrepresentations." Id. at 10-11.

Moreover, Judge Fullam noted that the Bankruptcy Court should not have credited Kool Mann with the assumed indebtedness and that Kool Mann was not entitled to the Tax Savings credit because the Tax Savings Side Letter contemplated that the credit would occur only when the Coffeys first realized their tax saving. "Since the debtor has not yet paid the purchase price, there has been no tax saving, and the debtor is not yet entitled to the credit." Id. at 12.

The parties appealed Judge Fullam's decision. On February 29, 1996, a panel of this Court summarily affirmed Judge Fullam's decision in its entirety, without opinion. See In re Kool, Mann, 79 F.3d 1138 (3d Cir.1996).

On remand, the parties proceeded in the Bankruptcy Court to reestimate the Coffeys' claim, agreeing to present additional evidence to supplement the pre-existing record. An order was issued by Judge Gindin on June 24, 1996 setting forth the procedure to be followed and stating that the Bankruptcy Court would "adjudicate and determine the Coffeys' claim and the debtor's objection thereto thereby making an estimation of the claim" unnecessary. In re Kool, Mann, No. 390-00017, order at 1 (Bankr.D.V.I. Jun. 24, 1996). A motion for an immediate trial on the adversary proceeding, however, was denied.

Over the next several years, the Bankruptcy Court issued three decisions relevant to this appeal.

1. The Bankruptcy Court's March 1999 Findings

Judge Gindin issued his new findings with regard to the value of the Coffeys' claim in a March 1999 Opinion (the "March 1999 Findings"). See In re Kool, Mann, 233 B.R. 291 (1999). Once again finding that the Coffeys had committed fraud, Gindin listed seven specific instances of fraud and their related dollar amounts:

1. The overvaluation of 33 houseboats for a total of $330,000;

2. In the November 30, 1985 financials, the listing of the value of houseboats as $429,607 in inventory when those boats did not exist;

3. In the November 30, 1985 financials, the listing of the value of motors in inventory as $40,190 when they did not exist;

4. In the November 30, 1985 financials, the overstating of profits by $100,000 as a result of incorrectly recording the sale and purchase of motors;

5. Representation by the Coffeys that the purchase of new houseboats and sale of old houseboats would "wash" or show a little profit, when the transaction actually resulted in a loss of $168,500;

6. Disclosure in a report submitted by Coffeys' expert, James Graves (the "Graves Report"), that costs of sales of boat motors in the amount of $58,000 were omitted from the financials; and

7. L. Coleman Coffey's testimony that he represented that cash flow was over $500,000 per year, when it was only $188,848.

In re Kool, Mann, 233 B.R. at 301. According to the Bankruptcy Court, the aggregate dollar amount of these misrepresentations totaled roughly $1.487 million. Id. at 305 n. 10. The Bankruptcy Court also found 7 additional instances of fraud which did not result in corresponding exact dollar amounts:

1. Coffey's representation that the financial statements were kept in accordance with GAAP, when they were not kept in accordance with GAAP;

2. Violation in the November 30, 1985 financials of GAAP Financial Accounting Standard No. 57 because no disclosure was made of certain intercompany transactions between VC and LCSDI;

3. In the November 30, 1985 financials, improper crediting to the account of "Notes Receivables" when the transaction was actually a sale of substantial assets;

4. Overstatement of assets of business due to the reporting of sale of houseboats under the asset side of the balance sheet, without a corresponding reduction on the liability side; 5. Breach of the representation that there were no changes in the methodology of maintaining LCSDI's financial statements, despite Coffey's testimony that he changed the way LCSDI recorded houseboat transactions from the September 30, 1985 financials to the November 30, 1985 financials;

6. Coffey's admission that he breached the representation that the financial statements did not include any non-recurring income or special items of income; and

7. Coffey's testimony that all of the information concerning the overstatements, errors and changes in accounting methodology was available to him prior to closing.

Id. at 301-02. The court rejected the Coffeys' contention that the December 1985 Letter remedied each of these misrepresentations. Engaging in a "multiple cash flow analysis" advanced by Kool Mann's expert,5 the Bankruptcy Court determined that the combined net effect of all of these misrepresentations caused more than a mere dollar-for-dollar reduction to the value of LCSDI. The court concluded that the inaccuracies amounted to valuing the company at $2,288,167. That value resulted in more than a $2.7 million reduction from the $5 million purchase price.

The Bankruptcy Court then addressed a number of what it deemed to be "procedural" issues. As an initial matter, the court rejected the Coffeys' complaint that it improperly conducted a trial on the merits instead of an "Estimation Hearing," ruling that a bankruptcy judge has wide discretion in deciding how an estimation hearing may be conducted.

Next, Judge Gindin found that most of Judge Fullam's July 1995 Opinion did not bind him as it merely expressed several areas of "concern" regarding the fraud evidence and testimony. According to the Bankruptcy Court, Judge Fullam in his District Court opinion made three rulings which were affirmed by this Court in 1996, and which Judge Gindin was accordingly obliged to follow: (1) that the Coffeys were afforded inadequate notice that the findings of the Estimation Hearing would be binding on the adversary proceeding, (2) that Kool Mann was not entitled to a credit for the pre-existing indebtedness of LCSDI (assumption of the $1.213 million debt), and (3) that Kool Mann was not entitled to a Tax Savings credit because the Coffeys had not yet received any tax benefit.

As to the "substantive" issues, the Bankruptcy Court applied Kentucky law and ruled that Kool Mann satisfied each of the elements supporting its fraud case against the Coffeys. Judge Gindin, among other things, then rejected Kool Mann's request for punitive damages and rejected the Coffeys' request for pre-petition interest.

Accordingly, the Bankruptcy Court held that due to the Coffeys' fraud, the value of LCSDI at the time of the sale and after all elements of fraud and misrepresentation had been discounted, was actually $2,288,167. From this amount, the court deducted $1 million, the downpayment previously made by Kool Mann, and ruled that the value of the Coffeys' claim in the bankruptcy proceeding was $1.288 million. An Order was filed on April 20, 1999, reflecting the foregoing as well as relieving Moore from his individual obligations under his personal guaranty because of the Coffeys' fraud as it would be held under Kentucky law. See, e.g., Moore, Owen, Thomas & Co., 992 F.2d 1439, 1448 (6th Cir.1993).

2. The Bankruptcy Court's November 1999 Opinion

Shortly after the Bankruptcy Court issued its findings in connection with the value of the Coffeys' claim, Kool Mann and Moore filed a motion for summary judgment in the related adversary proceeding, which the court granted on November 8, 1999 (the "November 1999 Opinion"). There, Judge Gindin ruled that the claims raised in the adversary proceeding were identical to those raised in valuing the Coffeys' claim, and that, therefore, the findings made in the March 1999 Findings had preclusive effect on the claims in the adversary proceeding under the doctrine of res judicata. See In re Kool, Mann, No. 390-00017, slip op. at 14 (Bankr.D.V.I. Nov. 8, 1999). Moreover, Judge Gindin ruled that although Moore was not technically a party when the earlier March 1999 Findings were made, all claims involving Moore were also precluded by reason of res judicata since his interests were identical to those of Kool Mann. See id. at 10-13.

Judgment was entered in the adversary proceeding in favor of Kool Mann and Moore.

3. The Bankruptcy Court's October 10, 2000 Opinion

On October 10, 2000, the Bankruptcy Court ruled on Kool Mann's motion to amend the court's March 1999 Findings (the "October 2000 Opinion"). There, Judge Gindin ruled that Kool Mann was entitled to an additional credit of $528,350.22.

There were two grounds for the court's ruling. First, in light of the court's prior rejection of the Coffeys' request for pre-petition interest, Judge Gindin ruled that prior interest payments made by Kool Mann in 1986 in the amount of $291,784 should be recharacterized as principal payments.

Second, the Bankruptcy Court ruled that because the Coffeys received a depreciation recapture in 1986, they had, indeed, realized the Tax Savings contemplated under the Tax Savings Side Letter. Accordingly, Judge Gindin ruled that Kool Mann was entitled to a Tax Savings credit of $236,566.22 pursuant to that agreement.6

The Bankruptcy Court, however, rejected Kool Mann's arguments that it was entitled to a credit for the pre-existing indebtedness of LCSDI and also rejected its contention that it was entitled to attorneys' fees.

Judgment was entered on October 24, 2000 reflecting an additional credit to Kool Mann in the amounts of $291,784 and $236,566.22. Consequently, the value of the Coffeys' claim in bankruptcy was reduced to $759,816.78.

The parties again cross-appealed the various orders of Judge Gindin to the District Court of the Virgin Islands. On October 2, 2001, the Honorable Stanley Brotman, U.S. District Court Judge of the District of New Jersey, sitting by designation, issued an opinion affirming in part and reversing in part Judge Gindin's orders (the "October 2001 Opinion").

Approving of most of the Bankruptcy Court's decision, Judge Brotman agreed with the Bankruptcy Court that the bulk of Judge Fullam's July 1995 Opinion was dicta, and that it merely vacated the Bankruptcy Court's initial findings on procedural grounds (i.e., inadequate notice) with only two additional substantive holdings: (1) that Kool Mann was not entitled to a set-off for payments made on assumed indebtedness of LCSDI; and (2) that Kool Mann was not entitled to a set-off for Tax Savings. Judge Brotman then found that in any event, "the Bankruptcy Court adequately responded on remand to Judge Fullam's comments." In re Kool, Mann, Nos. 99-00058, 99-00204, 00-00230, slip op. at 14 (D.V.I. Oct. 2, 2001). However, Judge Brotman ruled that the Bankruptcy Court erred with respect to his granting of the Tax Savings issue and denied that credit to Kool Mann.

Judge Brotman's rulings are set forth in the District Court's judgment issued on October 2, 2001, and can be succinctly summarized as follows:

1. Bankruptcy Court's decision to combine the Estimation Hearing and the adjudication of Kool Mann's claim is AFFIRMED;

2. Bankruptcy Court's finding of fraud by the Coffeys, and calculating the actual value of LCSDI as a result of that fraud at $2,288,167 is AFFIRMED;

3. Bankruptcy Court's grant of credit to Kool Mann for the $1 million downpayment is AFFIRMED;

4. Bankruptcy Court's release of Moore of his obligations under the personal guaranty is AFFIRMED;

5. Bankruptcy Court's denial of Coffeys' request for pre-petition interest is AFFIRMED;

6. Bankruptcy Court's denial of credit to Kool Mann for assumed indebtedness in the amount of $1.213 million is AFFIRMED;

7. Bankruptcy Court's denial of punitive damages to Kool Mann is AFFIRMED;

8. Bankruptcy Court's grant of summary judgment in favor of Moore in the adversary proceeding is AFFIRMED on basis of collateral estoppel, not res judicata;7

9. Bankruptcy Court's grant of credit to Kool Mann in the amount of $236,566.22 in tax savings is REVERSED;

10. Bankruptcy Court's grant of credit to Kool Mann of $291,784 due to recharacterization of interest payments to principal payments is AFFIRMED.

See In re Kool, Mann, Nos. 99-00058, 99-00204, 00-00203, judgment at 2-4 (D.V.I. Oct. 2, 2001). Consequently, Judge Brotman ruled that the total balance due and owing to the Coffeys by Kool Mann was $1,051,600.78.8

In this appeal, the Coffeys claim that the District Court erred in the following respects: (1) that the Bankruptcy Court's rulings on remand concerning fraud, the calculation of fraud damages and its decision to forgo an Estimation Hearing violated our mandate affirming Judge Fullam's July 1995 Opinion; (2) that the Bankruptcy Court's findings of fraud were not supported in the record; (3) that the Bankruptcy Court's calculation of damages was erroneous; and (4) that the Bankruptcy Court improperly recharacterized the 1986 interest payments as principal.

Kool Mann opposes the Coffeys' contentions and argues further that, as a threshold matter, the Coffeys are precluded from making any of their arguments on appeal because they failed to challenge properly the Bankruptcy Court's November 1999 judgment in the adversary proceeding. Moreover, Kool Mann cross-appeals the District Court's ruling that affirmed the Bankruptcy Court's denial of credit for payments made by Kool Mann on assumed indebtedness of LCSDI, and the District Court's reversal of the Bankruptcy Court's decision to permit the Tax Savings credit.

As the District Court sat as an appellate court in this matter, our review of the District Court's determination is plenary. See Fellheimer, Eichen & Braverman, P.C. v. Charter Technologies, Inc., 57 F.3d 1215, 1223 (3d Cir.1995). "In reviewing the bankruptcy court's determinations, we exercise the same standard of review as the district court." Id. (citing Brown v. Pennsylvania State Employees Credit Union, 851 F.2d 81, 84 (3d Cir. 1988)). The Bankruptcy Court's factual findings may not be set aside unless they are clearly erroneous. Bankruptcy Rule 8013; Brown, 851 F.2d at 84 (citation omitted). "It is the responsibility of an appellate court to accept the ultimate factual determination of the fact-finder unless that determination either is completely devoid of minimum evidentiary support displaying some hue of credibility or bears no rational relationship to the supportive evidentiary data." Hoots v. Pennsylvania, 703 F.2d 722, 725 (3d Cir.1983) (citation omitted). "Furthermore, in reviewing the bankruptcy court's factual findings we are to give due regard to the opportunity of that court to judge first-hand the credibility of witnesses." Fellheimer, 57 F.3d at 1223 (citing Bankruptcy Rule 8013) (internal quotation marks omitted). The Bankruptcy Court's legal determinations are reviewed under a plenary standard, and its exercises of discretion for abuse thereof. In re Engel, 124 F.3d 567, 571 (3d Cir.1997).

Kool Mann contends that in this appeal the Coffeys raise issues relating only to the findings made by the Bankruptcy Court with respect to the value of their claim, and fail to challenge the Bankruptcy Court's November 1999 judgment in the adversary proceeding. It reasons that this failure means that any objection to the judgment in the adversary proceeding has been waived, and that therefore, the judgment in the adversary proceeding, in turn, has preclusive effect on the findings of fraud underlying the value of the Coffeys' claim. Consequently, Kool Mann concludes that the Coffeys are estopped from advancing the arguments they make in this appeal since these arguments urge a result in the claim valuation inconsistent with the judgment entered in the adversary proceeding.

We disagree. As an initial matter, we conclude that the Coffeys did not fail to challenge the judgment rendered by the Bankruptcy Court in the adversary proceeding. A number of the issues raised by the Coffeys in their opening brief directly challenge various findings made by the Bankruptcy Court which form the very underpinning of both the value of their claim and the merits of Kool Mann's adversary proceeding. For instance, by arguing that the lower court's findings of fraud were clearly erroneous, we interpret such a challenge to mean that the Coffeys believed that the findings of fraud supporting both judgments — the one made pursuant to the claim valuation and the one made pursuant to the adversary proceeding — were clearly erroneous. While the Coffeys could have made their intentions more explicit, the context of their arguments makes it reasonably clear that they challenged the merits of both judgments.

Moreover, in advancing its argument, Kool Mann confuses the failure of the Coffeys to challenge the preclusive effect of the March 1999 Findings on the adversary proceeding with the failure to challenge the judgment in the adversary proceeding itself. It is true that the Coffeys cannot — and do not — argue in this appeal that preclusion principles do not apply between the findings made in connection with their claim valuation and the merits underlying the adversary proceedings. The issues involved in both proceedings are, in fact, one and the same, and the Coffeys' opening brief does not question the res judicata analysis conducted by the Bankruptcy Court. See Nagle v. Alspach, 8 F.3d 141, 143 (3d Cir.1993) ("When an issue is either not set forth in the statement of issues presented or not pursued in the argument section of the brief, the appellant has abandoned and waived that issue on appeal"). However, the fact that the Coffeys have abandoned their right to challenge the binding effect of one judgment upon another, does not mean that they have lost the ability to challenge the merits of both judgments.

Accordingly, we reject this argument and turn to the remaining claims in this appeal.

The Coffeys contend that the Bankruptcy Court's findings on remand violated the "law of the case" doctrine by ignoring our 1996 mandate affirming Judge Fullam's July 1995 Opinion. See Bankers Trust v. Bethlehem Steel Corp., 761 F.2d 943, 949 (3d Cir.1985) ("[On remand, the] trial court must proceed in accordance with the mandate and the law of the case as established on appeal."). First, they argue that the Bankruptcy Court's findings of fraud and calculation of fraud damages in its March 1999 Findings contradicted the holdings made by Judge Fullam when he noted that the evidence was insufficient to support a finding of fraud and when he criticized the methodology used by Kool Mann's expert in valuing LCSDI. Second, they contend that the Bankruptcy Court violated Judge Fullam's instruction by failing to conduct a separate Estimation Hearing on remand.

A. The Bankruptcy Court's Findings of Fraud and Calculation of Fraud Damages on Remand

Upon careful examination of the District Court's July 1995 Opinion, we conclude that Judge Fullam's sole mandate (and therefore our sole 1996 mandate) was to vacate Judge Gindin's June 1993 Findings on procedural grounds and to order a new trial on the merits. Consequently, the views expressed by Judge Fullam in his 1995 opinion concerning the findings of fraud and calculation of damages should be read merely as dicta. In the July 1995 Opinion, Judge Fullam held only that the Coffeys did not receive adequate notice that the Estimation Hearing was to be combined with the adversary proceeding, and he therefore vacated the Bankruptcy Court's initial June 1993 Findings. The Bankruptcy Court was directed to:

reconsider and reestablish an estimated value of the Coffey's claim, on the basis of the present evidentiary record together with such additional evidence as the parties may present. The adversary proceeding will be remanded for trial on the merits (or such other disposition as the parties may consent to).

In re Kool, Mann, No. 390-00017, slip op. at 12 (D.V.I. Jul. 17, 1995). Once Judge Fullam decided that notice to the Coffeys' was inadequate, he offered a number of observations and comments on the evidence and other matters before Judge Gindin.

Inasmuch as further proceedings will be required in any event, it is appropriate to address what appear to be significant errors in the bankruptcy judge's analysis.

Id. at 7 (emphasis added).

Each of Judge Fullam's comments about the merits of the case was simply precatory and was not necessary to the actual holding of the case. Accordingly, these statements are properly considered dicta, and are not binding. See Government of the Virgin Islands v. Marsham, 293 F.3d 114, 2002 WL 1204957, at *4 (3d Cir.2002) ("That statement, however, is dictum and is not binding on this, or any other, panel of this Court."); Calhoun v. Yamaha Motor Corp., 216 F.3d 338, 344 n. 9 (3d Cir. 2000) ("Insofar as this determination was not necessary to either court's ultimate holding, however, it properly is classified as dictum. It therefore does not possess a binding effect on us pursuant to the `law of the case' doctrine."). Therefore, the "significant errors" deemed to have been made by the Bankruptcy Court concerning the sufficiency of the evidence of fraud, causation, and damages — as well as Judge Fullam's belief that Kool Mann was not entitled to an assumed indebtedness credit or a Tax Savings credit — were not binding on remand.

Accordingly, the Bankruptcy Court was free to consider "those issues not expressly or implicitly disposed of by the appellate decision," and was "thereby free to make any order or direction in further progress of the case, not inconsistent with the decision of the appellate court, as to any question not settled by the decision." Bankers Trust, 761 F.2d at 950 ("upon a reversal and remand for further consistent proceedings, the case goes back to the trial court and there stands for a new determination of the issues presented as though they had not been determined before, pursuant to the principles of law enunciated in the appellate opinion") (emphasis added). Therefore, we conclude that the Bankruptcy Court did not violate our 1996 mandate affirming Judge Fullam's 1995 order when it again found fraud by the Coffeys and entered a calculation of claim damages in its March 1999 Findings.

The Coffeys also contend that the Bankruptcy Court violated Judge Fullam's mandate by forgoing the Estimation Hearing on remand, and by effectively combining the Estimation Hearing, claim objection, and the adversary proceeding into one proceeding. We disagree.

After Judge Fullam's decision was issued, the Bankruptcy Court held numerous telephone conferences with counsel to decide the best procedure for determining the value of the Coffeys' claim in bankruptcy and to determine the merits of the adversary proceeding. Kool Mann filed a motion to consolidate all issues into one proceeding, or alternatively, to set a hearing only on Kool Mann's claim objection, or alternatively, to set the adversary proceeding for immediate trial.

The Bankruptcy Court ruled on the motion to consolidate pursuant to its Case Management Order, dated June 24, 1996. There, the Court determined to go forward with the claim objection, stating that

[t]he debtor's objection to the Coffeys' proof of claim in this matter will be consolidated with the remanded estimation proceeding pursuant to Rule 42(a) Fed.R.Civ.P. and determined in accordance with 11 U.S.C. § 502(b)9 and Bankruptcy Rule 3007;10 as a result of this consolidation the Court will adjudicate and determine the Coffeys' claim and the debtor's objection thereto thereby making an estimation of the claim under § 502(c) unnecessary.

In re Kool, Mann, No. 390-00017, order at 1 (Bankr.D.V.I. Jun. 24, 1996). With regard to the valuation of the Coffeys' claim, the parties agreed to a trial on the papers and were permitted to present additional evidence through briefs and affidavits to supplement the already existing 1992 record. The parties waived the right to present further live testimony and accordingly waived the right to further cross-examine witnesses in this matter.

This procedure did not violate Judge Fullam's mandate. In remanding the case to the Bankruptcy Court, Judge Fullam required that the Bankruptcy Court do two things: (1) reconsider the value of the Coffeys' claim and (2) remand the adversary proceeding for trial.

As to Judge Fullam's first requirement (determination of the Coffeys' claim), there was no requirement that a particular kind of procedure be employed in estimating the value of the Coffeys' claim. In Bittner v. Borne, 691 F.2d 134 (3d Cir.1982), we noted that the Bankruptcy Code was silent "as to the manner in which contingent or unliquidated claims are to be estimated," and that under the authority of the Bankruptcy Court to estimate the value of claims under 11 U.S.C. § 502(c), "[t]he bankruptcy court ha[d] exclusive jurisdiction to direct the manner and the time in which such a claim is to be liquidated or estimated as to its amount, and its decision should be subject to review only on the ground of abuse of discretion." Id. at 138. There, we rejected the stockholder's argument that the bankruptcy court had erred because it assessed the ultimate merits rather than estimating their claims, substantially similar to the argument presented here by the Coffeys. Accordingly, we wrote that

we are persuaded that Congress intended the [Estimation Hearing] procedure to be undertaken initially by the bankruptcy judge, using whatever method is best suited to the particular contingencies at issue.... In reviewing the method by which a bankruptcy court has ascertained the value of a claim under Section 502(c)(1), an appellate court may only reverse if the bankruptcy court has abused its discretion. The appellate court must defer to the congressional intent to accord wide latitude to the decisions of the [bankruptcy court].

Id. at 135 (emphasis added). Indeed, we further noted that "[i]t is conceivable that in rare and unusual cases arbitration or even a jury trial on all or some of the issues may be necessary to obtain a reasonably accurate evaluation of the claims." Id.

Judge Gindin's decision to conduct a trial on the papers in connection with the claim objection and dispense with an Estimation Hearing was not an abuse of discretion. From a judicial economy standpoint, the Bankruptcy Court's decision to forgo an extraneous Estimation Hearing under § 502(c) makes practical sense since there would be no need to estimate the Coffeys' claim once the claims were actually adjudicated and valued under § 502(b).

As to Judge Fullam's second requirement (that the adversary proceeding be remanded for trial), the Coffeys contend that the Bankruptcy Court violated this mandate by combining the trial on the adversary proceeding with the claim objection proceeding. However, the adversary proceeding was never actually combined with the adjudication of the value of the Coffeys' claim. Indeed, the Case Management Order of June 24, 1996 setting forth the procedure of the claim objection denied the motion to set a date for the adversary proceeding to go to immediate trial, suggesting that the claim objection and the adversary proceeding were to be treated separately.

Rather, the Bankruptcy Court waited until the proceeding on the claim objection was completed, and then entertained summary judgment motion papers on the adversary proceeding to determine whether — as in all summary judgment motions — a trial on the merits was warranted. In a separate November 1999 Opinion, the Bankruptcy Court determined that the principles of res judicata prevented it from entering a result in the adversary proceeding that was different than that of the claim objection,11 and therefore the Bankruptcy Court entered summary judgment in favor of Kool Mann and Moore.

Accordingly, we conclude that the Bankruptcy Court did not violate Judge Fullam's mandate by dispensing with the Estimation Hearing and deciding the adversary proceeding in a summary judgment proceeding.

Since Judge Fullam's comments in 1995 are not binding as to the facts of this case, the only issue concerning the Bankruptcy Court's findings of fraudulent behavior by the Coffeys on remand was whether they were clearly erroneous. As described below, we are satisfied that the findings of fraud made by the Bankruptcy Court and affirmed by the District Court are correct and amply supported by the record.12

The parties do not contest the application of Kentucky law to the merits of this action. They also do not dispute that, under Kentucky law, the party alleging fraud must prove five elements: (1) a material misrepresentation that is false; (2) is known to be false or made recklessly; (3) made with inducement to be acted upon; (4) which is relied upon; and (5) causes injury. See Moore, Owen Thomas & Co. v. Coffey, 992 F.2d 1439, 1444 (6th Cir.1993).

As previously noted, the Bankruptcy Court found numerous instances of misrepresentations made by the Coffeys during the negotiation of the sale of LCSDI, especially with respect to financial information that was provided to Kool Mann as part of its due diligence concerning the company. In some cases, the value of the particular misrepresentations could be quantified, such as: (1) the value of houseboats as $429,607 when they did not exist; (2) the value of motors in inventory as $40,190 when they did not exist; (3) the overstatement of profits by $100,000 by incorrectly recording the sale and purchase of motors; (4) omission of costs of boat motor sales by $58,000; and (5) improper credits to "Notes Receivables." The aggregate total amount of these quantifiable misrepresentations was at least $1.4 million. See In re Kool, Mann, 233 B.R. at 305 n. 10. The affidavit testimony adduced in the bankruptcy proceedings combined with the financial statements presented by the Coffeys to Kool Mann amply support a conclusion that these items were inaccurately reported prior to sale.

Moreover, the record supported Judge Gindin's finding that a number of false statements were made about the financial statements by the Coffeys, many of which were unquantifiable. For example, although the Purchase Agreement warranted that the financial statements were prepared in accordance with Generally Accepted Accounting Principles ("GAAP"), L. Coleman Coffey conceded in a deposition that the financial statements were not kept in accordance with GAAP. See Purchase Agreement at ¶ 5(e). In addition, the record supports the finding that prior to closing, the Coffeys represented that there were no changes made in the methodology of maintaining LCSDI's financial statements, despite L. Coleman Coffey's own testimony conceding that he changed the way LCSDI recorded certain houseboat transactions from the September 30, 1985 financials to the November 30, 1985 financials. Moreover, L. Coleman Coffey conceded that he breached the representation made in ¶ 5(e) of the Purchase Agreement that the financial statements did not include any non-recurring or special items of income.

Finally, in connection with cash flow, L. Coleman Coffey also conceded that he had told Moore prior to closing that cash flow was around $500,000 to $600,000 per year. Both Kool Mann and the Coffeys introduced evidence — in the form of expert and lay testimony — that LCSDI's cash flow was, in fact, far less than $500,000 in 1985.

Accordingly, the findings of material misrepresentations by the Bankruptcy Court were well supported in the record.

There is also sufficient evidence to support Judge Gindin's finding that the Coffeys knew of their fraud. L. Coleman Coffey testified that he had access to all of the correct information prior to the closing date, and his formal training as a certified public accountant has not been disputed. Moreover, Judge Gindin made various credibility determinations regarding L. Coleman Coffey's testimony, and determined, as the fact finder is entitled to do, that his testimony was not credible in many respects, and that Coffey was aware of the misrepresentations that were being made prior to closing. Scully v. U.S. WATS, Inc., 238 F.3d 497, 506 (3d Cir. 2001) ("credibility determinations are the unique province of a fact finder").

Judge Gindin was entitled to find, as he did, that the Coffeys intended that Kool Mann rely upon many inaccuracies presented during negotiations. The testimony adduced at trial supported the view that L. Coleman Coffey knew that in order to obtain a $5 million purchase price, he had to show a cash flow of over $500,000. The evidence also showed that Coffey conveniently provided a cash flow figure in that range, and that he knowingly provided the inaccurate financial statements which supported his cash flow range. As discussed above, the Bankruptcy Court was entitled to find that Coffey knew of the numerous misrepresentations and inaccuracies prior to providing the information to Kool Mann. Accordingly, it was not clearly erroneous for the Bankruptcy Court to have found that Coffey intended for Kool Mann to rely upon his misrepresentations.

Judge Gindin was also entitled to find that Kool Mann did, in fact, rely upon the misrepresentations when it agreed to purchase LCSDI. The evidence demonstrates that Kool Mann calculated its purchase price on values and figures presented on the financial statements provided to Kool Mann. Moore testified that he needed a cash flow of over $500,000 to be able to service the debt he would incur as a result of the purchase of LCSDI and that he would not have entered into the transaction had he known that cash flow was not over $500,000. This evidence is sufficient to establish reliance on the part of Kool Mann.

Finally, there is little doubt that the record supports the existence of damages to Kool Mann caused by the misrepresentations discussed above. Moore testified that his calculation of the purchase price was based upon the financial statements provided to him by L. Coleman Coffey. Moreover, the record is replete with references to the amount and magnitude of various misrepresentations, and their respective effects on asset valuation and cash flow.

Accordingly, we will affirm the Bankruptcy Court's finding of fraud by the Coffeys.

The Coffeys challenge the method of calculation of fraud damages employed by the Bankruptcy Court in 1999, contending that its method used to value LCSDI without fraud was incorrect. To determine the magnitude of the injury to Kool Mann as a result of the Coffeys' fraud, the Bankruptcy Court sought to establish the "true value" of LCSDI at the time of sale. See Sowell v. Butcher, 926 F.2d 289, 297 (3d Cir.1991) ("under ... common law fraud actions, a plaintiff's damages are most commonly calculated as the difference between the price paid for the security and the security's `true value.'"). This "true value" represented the real worth of LCSDI at the time of the sale in 1985 without any inaccuracies, and thereby subsumed all of the fraudulent conduct by the Coffeys.

In order to ascertain LCSDI's "true value," the Bankruptcy Court utilized a multiple of cash flow analysis by calculating LCSDI's actual 1985 cash flow without the misrepresentations and projecting it over 15 years at a pre-determined 7.5% growth rate and an 18.5% present value discount factor. This calculation purportedly yielded a value of $2,288,167. For the reasons set forth below, while we approve of the methodology employed by the Bankruptcy Court in arriving at LCSDI's "true value," we conclude that the value of LCSDI, after taking into account all of the fraud found by the Bankruptcy Court, should be corrected to reflect a value of $1,766,631, not $2,288,167.

Both the Coffeys and Kool Mann submitted expert testimony on LCSDI's actual 1985 cash flow. The Coffeys' expert, James Graves, determined that free cash flow in 1985 was $352,585. See Graves Report at 2. In reaching this figure, Graves noted that he made two additional downward adjustments which had not yet been disclosed at that time: (1) a cost of sale increase of $29,000 due to sale of a 46 foot boat in 1985; and (2) understatement of the cost of motors sold in 1985 by $58,000.

Judge Gindin noted that Graves' figure was artificially inflated because it included proceeds from net long-term debt in the amount of $173,000. In other words, Graves added the difference between the proceeds LCSDI borrowed from creditors in 1985 minus the amount LCSDI was required to pay back to those creditors in 1985 (which netted to $173,000). Agreeing with one of Kool Mann's experts, Thomas Millon, that net debt proceeds do not belong in cash flow figures, see Affidavit of Thomas Millon dated June 27, 1996 at ¶ 18, the Bankruptcy Court reduced Mr. Graves' figure further by $173,000 to arrive at $179,585.

The Bankruptcy Court also analyzed the testimony and exhibits of Kool Mann's cash flow expert, Robert Malinowski. Piggybacking from Malinowski's cash flow analysis presented at the Estimation Hearing in 1992 (at which time he calculated LCSDI's actual cash flow to be $246,848), Malinowski deducted from his original amount of $246,848 the $58,000 cost of motors item disclosed on the Graves report to arrive at a cash flow of $188,848. See Affidavit of Robert Malinowski dated June 27, 1996 at ¶¶ 5-7. Noting that both experts arrived at nearly the same cash flow amount (after deducting long-term debt proceeds from Graves' figure), and also observing that the Coffeys did not dispute the accuracy of Malinowski's cash flow analysis, Judge Gindin applied the $188,848 amount as LCSDI's 1985 actual cash flow.13

The Coffeys raise two objections to the Bankruptcy Court's calculation of cash flow. First, they complain that the reduction of $173,000 in cash flow due to the inclusion of net long-term debt proceeds is, at worst, a disagreement among experts, and therefore cannot have been proximately caused by the Coffeys' fraud. Accordingly, they argue that the cash flow value used by Judge Gindin should be increased by $173,000.

We are not persuaded. The Bankruptcy Court, as finder of fact, was entitled to exclude net debt proceeds from LCSDI's cash flow. Hoots, 703 F.2d at 725 ("It is the responsibility of an appellate court to accept the ultimate factual determination of the fact-finder unless that determination either is completely devoid of minimum evidentiary support displaying some hue of credibility or bears no rational relationship to the supportive evidentiary data."). As an initial matter, it is important to remember that the Coffeys represented prior to closing that LCSDI's cash flow was around $500,000 to $600,000. On this record, the Bankruptcy Court could have found that this representation was unqualified and unconditioned — that is, the representation that cash flow was above $500,000 was not conditioned upon the need to borrow more money in order to reach that amount. See Affidavit of Thomas Millon at ¶ 18 ("the free cash flow is artificially inflated as a result of the business borrowing $173,000 more each year than it repays"). Accordingly, we conclude that finding that this inflation of cash flow is a result of fraud is not clearly erroneous on the state of this record.

Second, the Coffeys contend that the $58,000 reduction in cash flow for understated costs related to motors sold in 1985 was an improper deduction because this "understatement" had been disclosed prior to closing. As proof, the Coffeys refer to a schedule attached to the 1985 Purchase Agreement listing a number of motors with "not paid" written next to some of them, representing motors in LCSDI's inventory which were ultimately sold to Kool Mann and which were not fully paid off. According to the Coffeys, these motors were the very motors related to the $58,000 cost. Kool Mann, in turn, claims that these motors are different from those that were the subject of the $58,000 reduction, arguing that an understated "cost of motors sold" in 1985 could not be the same thing as motors remaining in LCSDI's inventory at the end of 1985.

Again, such an argument may be proper before the finder of fact, but it is not for us — a reviewing court — to decide. The Bankruptcy Court's decision to believe Kool Mann's explanation over the Coffeys' explanation, and to ascribe fraud to the Coffeys, is supported by this record and is therefore not clearly erroneous. Indeed, there is nothing in the record to show that the disclosed debt on certain "unpaid" motors is the same "cost" of motors sold which was unreported and which resulted in overinflated revenues by $58,000.

Accordingly, we find that Judge Gindin did not err in concluding that LCSDI's actual cash flow was $188,848.

Once LCSDI's 1985 cash flow was ascertained, the Bankruptcy Court applied the cash flow to certain growth rates and discounts projected by Kool Mann's methodology expert, Thomas Millon, who the Bankruptcy Court found to be credible. The Bankruptcy Court purported to use the cash flow amount of $188,848 and to apply to it a number of factors, including an annualized growth rate of 7.5% and a present value discount of 18.5% over 15 years. According to Kool Mann's expert, the rates and time frame utilized were industry standards in valuing a company like LCSDI, an assertion which was not disputed by the Coffeys' expert. Using this methodology, the Bankruptcy Court concluded that the actual value of LCSDI — after discounting for all of the Coffeys' fraud — was $2,288,167 in 1985, a reduction in value of $2,711,833 from the $5 million purchase price. See In re Kool, Mann, 233 B.R. at 307-08.14

The Coffeys argue that the cash flow methodology used by the Bankruptcy Court is objectionable in that it is the same methodology that was criticized by Judge Fullam in his July 1995 Opinion. However, since we have already concluded that that portion of Judge Fullam's decision was dictum, see Section V.A., supra, we reject the Coffeys' objection to the Bankruptcy Court's damage calculation.

In any event, we are satisfied that the Bankruptcy Court did not err in its use of the cash flow methodology in this particular case. A number of courts have commented on the propriety of the discounted cash flow methodology for certain valuation situations, particularly where valuing stock and other securities of a company. See In re Valley-Vulcan Mold Co., 2001 WL 224066, No. 99-4129 (6th Cir. Feb. 26, 2001) (noting, with approval, that expert's "valuations were based on discounted cash-flow valuation, a well-recognized methodology for determining a business's going concern values."); In the Matter of Genesis Health Ventures, Inc., 266 B.R. 591, 613 (2001) (noting the use of the discounted cash flow method as one method to support value of an enterprise); In re Grant Broadcasting of Philadelphia, Inc., 75 B.R. 819, 824 (E.D.Pa.1987) ("the Debtors' expert used a valuation method, the multiple of cash flow method, which both parties' experts agreed was the most frequently used in the broadcast industry to determine the value of stations."); see also Wilson v. Great American Industries, Inc., 979 F.2d 924, 933 (2d Cir.1992) (approving of "capitalization of earnings method"); Burlington Northern Railroad Co. v. Bair, 815 F. Supp. 1223, 1229 (N.D.Iowa 1993) (approving the discounted cash flow methodology as one of several available "methods of arriving at true market value").

Other courts have criticized the use of cash flow valuations in valuing companies, complaining of the imprecision of such a methodology. But even those courts have recognized its value in certain limited situations. See, e.g., Metlyn Realty Corp. v. Esmark, Inc., 763 F.2d 826, 835-36 (7th Cir.1985) (noting that "[s]uch valuations are highly sensitive to assumptions about the firm's costs and rate of growth," and that cash flow studies may not be "the best way" to value a business, but "may be necessary when there is no other way to find value"). Indeed, this Circuit has stated previously that "the law does not command mathematical preciseness from the evidence in finding damages," and that "all that is required is that sufficient facts ... be introduced so that a court can arrive at an intelligent estimate without speculation or conjecture." Scully v. U.S. WATS, Inc., 238 F.3d 497, 515 (3d Cir.2001) (internal quotations omitted); see also Jones & Laughlin Steel Corp. v. Pfeifer, 462 U.S. 523, 552, 103 S. Ct. 2541, 76 L. Ed. 2d 768 (1983) ("We do not suggest that the trial judge should embark on a search for "delusive exactness." It is perfectly obvious that the most detailed inquiry can at best produce an approximate result.... But we are satisfied that whatever rate the District Court may choose to discount the estimated stream of future earnings, it must make a deliberate choice, rather than assuming that it is bound by a rule of state law.").

The particular facts of this case, which involve the extremely difficult task of valuing the stock of a company which is privately owned and not traded on a public exchange, favor the use of such methods which take into account the expected value of the company's future performance. Indeed, the record shows that if cash flow had been, in fact, somewhere in the $500,000 to $600,000 range (as the Coffeys' represented it was), the cash flow methodology used by the Bankruptcy Court would have valued LCSDI somewhere between $4,816,318 to $5,404,088, consistent with the $5 million agreed upon by the parties. See Millon Aff. at ¶ 6. This fact only further supports Judge Gindin's decision to accept the Millon methodology as a valid way to value LCSDI in 1985.

As already noted, the Bankruptcy Court concluded that the "true value" of LCSDI was $2,288,167 in 1985. However, a close examination of the record shows that the application of the methodology employed by the Bankruptcy Court should have yielded a value of LCSDI as $1,766,631, as demonstrated by Exhibit D to Millon's affidavit.

In the normal course, given this discrepancy, we would have returned this discrete issue to the District Court for remand to the Bankruptcy Court for recalculation. However, in light of the fact that we are convinced this litigation should be brought to a halt, we have scrupulously analyzed the manner in which the damages figures were reached by Judge Gindin (and affirmed by Judge Brotman) and conclude that the Bankruptcy Court, in fact, intended to apply the $1,766,631 figure.

In rough summary, Exhibit D starts with an Adjusted Cash Flow of $188,848 on a 7.5% adjusted annual growth rate and an 18.5% present value factor, each consistent with Judge Gindin's analysis. Had the Bankruptcy Court followed through with the Exhibit D figures, it would have reached a total present value of $1,766,631 for LCSDI. Indeed, this exhibit reveals that for the year 1986, the starting figure of cash flow on a 15 year analysis was the $188,848 value, giving rise to a present value of $173,482.

On the other hand, Exhibit C of Millon's affidavit, which has a bottom line figure of $2,288,168, was adopted by the Bankruptcy Court although the details giving rise to this present value were disclaimed, and not used in its analysis, by the Bankruptcy Court. For instance, Exhibit C commences with a cash flow figure of $215,018 (not $188,848) which was derived from Exhibit A.I. attached to Mr. Millon's affidavit (appearing on page 437 of the Joint Appendix). However, in its opinion, the Bankruptcy Court expressly declined to use the hypothetical projections endemic in the analysis contained in Exhibit A.I., and decided instead to use the historical data supplied by the cash flow analysis in Exhibit D. See In re Kool, Mann, 233 B.R. at 305. Indeed, the cash flow figures used in Mr. Millon's Exhibit C appear to be derived from the very analyses that Judge Fullam criticized as being too speculative in his July 1995 Opinion. In re Kool, Mann, No. 390-00017, slip op. at 10-11 (D.V.I. Jul. 17, 1995).

The details underlying the analysis in Exhibit D — concluding that the value of LCSDI after all misrepresentations and fraudulent matters had been deducted was $1,766,631 — reflects that the Bankruptcy Court relied on these various percentages and present value rates, but accepted the bottom line valuation not of Exhibit D, but of Exhibit C. With the record in this posture, we are confident that the Bankruptcy Court and the District Court would readily agree that the value of LCSDI had to stem from an Exhibit D analysis and chart, and should have been recorded as $1,766,631. This being so, and reading the respective opinions as we believe the authors intended them to be read, we conclude that the value of the stock purchased by Kool Mann was $1,766,631, and it is that figure which we have utilized in determining the ultimate obligation of Kool Mann to the Coffeys.

As the parties' agreement provided, and as we have related, Kool Mann had agreed that interest would be paid on the remaining balance due on the purchase price of LCSDI. In October and November of 1986, Kool Mann made interest payments of $330,000, of which $38,216 was returned by the Coffeys as overpayment (for a total interest payment of $291,784). These payments were continuously characterized as interest payments until the Bankruptcy Court's October 2000 Opinion. At that time, the Bankruptcy Court — on a motion for reconsideration — recharacterized those payments as principal payments. The Bankruptcy Court did so on the ground that the fraud committed by the Coffeys resulted in a reduction in the amount owed by Kool Mann. Thus, the principal amount due the Coffeys was not quantified or known and could only be classed as an unliquidated sum. While prejudgment interest is allowed on a liquidated sum, prejudgment interest on an unliquidated sum is, under Kentucky law, permitted only at the discretion of the court. See Brown v. Fulton, 817 S.W.2d 899, 901-02 (Ky.App.1991). The upshot of this recharacterization of interest to principal was to reduce the Coffeys' claim in bankruptcy by an additional $291,784.

We will affirm the Bankruptcy Court's recharacterization of interest payments into principal payments. In the absence of any fraud, it is undisputed that Kool Mann would have been contractually obligated to pay the $291,784 in interest payments, which was based upon the remaining principal amount. The difficulty is that in light of the fraud and corresponding revaluation of the value of LCSDI, the amount of interest due cannot now be calculated the same way, as the principal amount has become uncertain. Indeed, the only true way to calculate contractual interest would have been to re-amortize the installment payments of principal and interest, recalculated to take into account the far smaller principal due from Kool Mann after deductions for fraud had been made.

To the extent some portion of the $291,784 could be considered payment of contractual interest, we note that the Coffeys — and Kool Mann, for that matter — have not demonstrated how we would determine what portion, if any, of the $291,784 could be considered contractual interest based on a reconstituted principal amount in light of the Coffeys' fraud. We also conclude that Kentucky law would permit a judge to reject such interest where the contract at issue has been permeated with fraud. Cf. Middleton v. Middleton, 287 Ky. 1, 152 S.W.2d 266, 268 (1941) ("in the case of an unliquidated claim, the allowance of interest rests in the discretion of the jury or the court trying the case").

In this way, a much smaller portion of the $291,784 would have been contractually obligated to have been paid as interest. To the extent any remaining amount could be considered prejudgment interest, the Bankruptcy Court was well within its discretion to deny such interest in toto, in light of the many findings of fraud on the part of the Coffeys. See Church & Mullins Corp. v. Bethlehem, 887 S.W.2d 321, 325 (Ky.1992) ("the determination as to whether or not to award prejudgment interest [on an unliquidated sum] is based upon the foundation of equity and justice.").

Moreover, the Coffeys could not expect interest on the ultimate amount we have settled on as being due to them from Kool Mann's estate in bankruptcy inasmuch as any such award would, in effect, constitute post-petition interest which is not generally available. See 7 Collier on Bankruptcy, ¶ 1129.04[4][b][i][C], pp. 1129-97-98 (rev. 15th ed. 1999) ("[U]nless the debtor is solvent, or the creditor is oversecured, post-petition interest is not part of a creditor's allowed claim.").

Accordingly, we will affirm the Bankruptcy Court's recharacterization of interest payments into principal payments, thereby reducing the Coffeys' claim in bankruptcy by an additional $291,784.

Kool Mann cross-appeals the District Court's affirmance of the Bankruptcy Court's refusal to grant a credit for payments made in connection with certain pre-existing houseboat debt of LCSDI in the amount of $1,213,000. Both the Bankruptcy Court and the District Court relied in part upon the decisions of the Kentucky litigation and Judge Fullam's June 1995 Opinion to conclude that Kool Mann was not entitled to this credit. While Judge Fullam's comments on this matter were dicta and therefore not binding (see Section V.A., supra), the decision rendered by Judge Forester on the assumption of debt issue in 1990, which was never appealed, must be considered final.

In the Kentucky litigation, Judge Forester ruled that Kool Mann was not entitled to a set-off against the purchase price for indebtedness it assumed as part of the business. Moore, Owen v. Coffey, No. 87-64, slip op. at ¶ 25 (E.D.Ky. Jan. 31, 1990). Indeed, by purchasing LCSDI's stock, and not just its assets, Kool Mann agreed to pay a particular price for LCSDI as a whole — its assets and liabilities. To credit Kool Mann with the payments it made against this indebtedness now would conflict with the Kentucky court's decision. Accordingly, we will not permit the indebtedness credit.

Kool Mann also cross-appeals the District Court's ruling which reversed the Bankruptcy Court's grant of a Tax Savings credit to Kool Mann pursuant to the Tax Savings Side Letter. While the parties do not dispute that the Coffeys have received a tax benefit of $236,566.22 and both the Coffeys and Kool Mann had agreed on the amount of the savings, the District Court refused to credit Kool Mann with this amount because Kool Mann had not yet made a final "balloon payment" as contemplated by the Tax Savings Side Letter.15

As noted, the parties agreed to pay the remaining balance of the purchase price over five annual installment payments of $150,000 plus a final balloon payment on September 30, 1991 of $3,250,000 ($5 million price minus $1 million down payment minus $750,000 in installment payments). Had there been no fraud, the $236,566.22 would have been deducted on September 30, 1991 from the remaining $3,250,000 payment pursuant to the Tax Savings Side Letter. The problem now, however, is that due to the fraud and decades-long litigation, there can be no final balloon payment against which the Tax Savings can be offset, other than the amount determined in bankruptcy as the amount which Kool Mann now owes the Coffeys.

To determine that figure, we have accepted $1,766,631 as the value of the company after fraud from which we have thus far deducted the $1 million down payment, $291,784 principal payments after interest was recharacterized, no installment payments (since they were not made), and no payments for assumed indebtedness of $1.213 million (because of the decisions rendered in the Kentucky litigation). These deductions leave $474,847 owed to the Coffeys by Kool Mann in bankruptcy. We conclude that this figure now represents the final "balloon payment" to be made by Kool Mann to the Coffeys after the fraud and above referenced deductions have been properly accounted for. As a result, the Tax Savings credit of $236,566.22 must now also be subtracted from the after-fraud value, resulting in Kool Mann owing the Coffeys $238,280.78 in bankruptcy.

For the foregoing reasons, we will affirm the District Court's October 2, 2001 judgment, other than with respect to the calculation of the Coffeys' claim and Kool Mann's obligation. In that connection, as we have explained, we hold as follows: LCSDI must be valued as $1,766,631 as a result of the Coffeys' fraud, not $2,288,167 as the Bankruptcy Court and the District Court held. In addition, we will reverse the District Court's order which had reversed the Bankruptcy Court on the Tax Savings issue and we will reinstate the Bankruptcy Court's ruling thereby granting Kool Mann an additional credit in the amount of $236,566.22. As discussed in Section VIII, supra, Kool Mann is also entitled to a credit based on the recharacterization of interest as principal in the amount of $291,784.

Accordingly, the value of the Coffeys' claim in the Kool Mann bankruptcy will be calculated as follows:

•   Value of LCSDI after fraud:                                        $1,766,631

•   Credit for down payment made to the Coffeys
      by Kool Mann:                                - $1,000,000

•   Credit for recharacterization of interest as
     principal                                     - $  291,784

•   Credit for payments on assumed indebtedness
      of LCSDI:                                     - $       0

•   Credit for Tax Savings:                         - $ 236,566.22
                                                    --------------
    Total amount of deductions                                       - $1,528,350.22
                                                                     ---------------
Value of Coffeys claim in Bankruptcy:                                  $  238,280.78

We will therefore direct the District Court to remand this matter to the Bankruptcy Court with the direction that the Bankruptcy Court record the value of the Coffeys' claim in the Kool Mann bankruptcy to be $238,280.78.