
    UNITED STATES of America, Plaintiff-Appellee, v. DYNALECTRIC COMPANY; Paxson Electric Company; G.W. Walther Ewalt; Wesley C. Paxson, Sr., Defendants-Appellants.
    No. 87-8451.
    United States Court of Appeals, Eleventh Circuit.
    Nov. 21, 1988.
    See also, D.C.Cir., 861 F.2d 730.
    
      John R. Lowery, Kutak Rock & Campbell, Atlanta, Ga., for Dynalectric and Ewalt.
    Emmet J. Bondurant, Bondurant, Mixson & Elmore, Atlanta, Ga., for Paxson.
    Rodney O. Thorson, Skadden, Arps, Slate, Meaher & Flom, Washington, D.C., for Dynalectric.
    John J. Powers, III, Dept, of Justice, Main Appellate Section, Andrea Limmer, Washington, D.C., for U.S.
    James H. Kelley, McGuire, Woods, Battle & Boothe, Washington, D.C., for appellants.
    Before RONEY, Chief Judge, and ANDERSON, Circuit Judges, and ALLGOOD , Senior District Judge.
    
      
       Honorable Clarence W. Allgood, Senior U.S. District Judge for the Northern District of Alabama, sitting by designation.
    
   ANDERSON, Circuit Judge:

Defendants Dynalectric Co., Paxson Electric Co., G.W. Walther Ewalt, and Wesley C. Paxson, Sr. appeal from their criminal antitrust and federal mail fraud convictions. Each defendant was convicted of one count of conspiring to violate Section 1 of the Sherman Act, 15 U.S.C. § 1, and two counts of violating the federal mail fraud statute, 18 U.S.C. § 1341. We affirm.

I. FACTS

The corporate defendants in this case, Dynalectric Co. (“Dynalectric”) and Paxson Electric Co. (“Paxson Electric”), are electrical contracting companies. The individual defendants, G.W. Walther Ewalt (“Ewalt”) and Wesley Paxson, Sr. (“Paxson”), are the presidents of Dynalectric and Paxson Electric, respectively. This case arises from an alleged conspiracy among the defendants and Fischbach & Moore, another electrical contracting company, to rig the bidding on the electrical subcontracting portion of a major construction project at the Snapfinger Creek Wastewater Treatment Plant in Dekalb County, Georgia. Dynalectric, Pax-son Electric, and Fischbach & Moore were the only electrical contractors who submitted bids on the Snapfinger project.

In 1982, the Justice Department empaneled several grand juries in the District of Columbia and began a wide-ranging investigation into allegations of bid rigging in the electrical contracting industry. Some records of the Snapfinger project were subpoenaed in 1982. In September, 1984, Pax-son testified before the grand jury pursuant to an immunity order. His testimony was that he had never participated in bid-rigging and specifically that the Snapfinger project was not rigged. Following Pax-son’s exculpatory testimony, the grand jury did not probe further into the Snap-finger contract until Bernard Trepte (“Trepte”), a Fischbach & Moore employee, testified extensively about the Snapfinger bidrigging before the grand jury in October 1985. Subsequently, the Justice Department revived its investigation of the Snap-finger project. As a result of this investigation, the defendants were indicted on September 19, 1986.

The gist of the conspiracy was that the conspirators agreed on their bid prices before they submitted their Snapfinger bids, thereby circumventing the competitive bidding process. The conspirators agreed that Paxson Electric would be the low bidder. Paxson Electric prepared its bid and then notified Dynalectric and Fischbach & Moore what their bids should be. In exchange for their cooperation, Paxson Electric agreed to forgive an $89,000 debt of Fischbach & Moore and to evenly divide the Snapfinger profits with Dynalectric. The defendants characterized the arrangement between Paxson Electric and Dynalectric as a silent joint venture.

The conspiracy was fleshed out when Ewalt, Paxson, and Trepte met in an Atlanta hotel room the evening before the Snap-finger bids were submitted. Trepte and Paxson first came to terms; Trepte originally had pushed for Fischbach & Moore to get the Snapfinger contract but eventually agreed to let Paxson Electric be the low bidder if Dynalectric also agreed to go along with the scheme. Trepte then left the hotel room and was told that if Paxson could convince Ewalt to participate in the bid rigging, he would receive a phone call notifying him of what Fischbach & Moore’s bid should be. Trepte received a call the next day informing him of the bid price. As a consequence of that call, he raised Fischbach & Moore’s bid by $500,000.

The bids were submitted on September 7, 1979. Paxson Electric was the low bidder for the electrical subcontracting portion of the Snapfinger project and was awarded the subcontract by the George Hyman Company (“Hyman”), the general contractor who was awarded the overall Snapfinger contract. On the $5 million dollar Snap-finger contract, Paxson Electric made a profit of approximately $1.7 million and paid half of this amount — $880,000—to Dy-nalectric pursuant to their alleged silent joint venture agreement. Evidence at trial established that Dynalectric did virtually no work on the Snapfinger project, yet received half of Paxson Electric’s profits. Paxson Electric made its final payment to Dynalectric in 1983 and received its final payment via mail from Hyman on January 24, 1985.

The defense at trial was that the joint venture was a legitimate one consummated in order to allow Paxson Electric to overcome anticipated minority representation problems in its dealings with Hyman. The defendants contended that the joint venture was not entered until several months after the Snapfinger bidding. They also denied that Ewalt, Paxson, and Trepte had met the evening before the bidding to discuss rigging the bids.

II. DISCUSSION

A. Statute of Limitations: Criminal Antitrust Conspiracy

The defendants first challenge the district court’s holding that the indictment was not barred by the five year statute of limitations for criminal conspiracies, 18 U.S.C. § 3282. We affirm.

Section 3282 provides that the statute of limitations runs for five years “after [the] offense shall have been committed.” The indictment was filed on September 16, 1986. The district court concluded that the antitrust conspiracy was not committed (i.e. completed) until Hyman' made the last payment to Paxson Electric in January 1985 and therefore that the indictment was filed well within the five year limitation period. The appellants argue that at the latest, the conspiracy was committed on January 14, 1980, the date on which the contract was entered after the bids were submitted in September 1979. They argue that the payoffs from Paxson Electric to Dynalectric (the last of which were in 1983) and the payments from Hyman to Paxson Electric (the last of which was in January 1985) were results — rather than objectives — of the conspiracy. The task before us is to decide whether the conspiracy to restrain trade was committed when the contract was awarded to Paxson Electric following the submission of rigged bids or whether the conspiracy continued either until Pax-son Electric received the last payments under the contract or until Paxson Electric made the last disbursement of the illicit profits to Dynalectric pursuant to the alleged joint venture agreement.

We agree with the district court. The case law, applied to the particular facts of this case, amply supports the district court’s conclusion that the payments from Hyman to Paxson Electric, pursuant to the Snapfinger subcontract, and the payments from Paxson Electric to Dynalectric, pursuant to the alleged joint venture agreement, were elements of a continuing conspiracy to restrain trade rather than merely the results of a completed conspiracy.

Our analysis of the relevant cases begins with United States v. Kissel, 218 U.S. 601, 31 S.Ct. 124, 54 L.Ed. 1168 (1910), the seminal Supreme Court case interpreting the criminal statute of limitations in the context of an antitrust conspiracy. Justice Holmes, writing for the Court, concluded that a conspiracy can have “continuance in time.” 218 U.S. at 610, 31 S.Ct. at 127. Holmes explained that a criminal conspiracy continues in time beyond the initial conspiratorial agreement until the objectives of the conspiracy either are abandoned or succeed. Id. Holmes also explained, however, that once the objects of the conspiracy succeed or are abandoned, “the mere continuance of the result of [the] crime does not continue the crime ... for purposes of the statute of limitations.” 218 U.S. at 607, 31 S.Ct. at 126.

To determine the extent to which a conspiracy continues over time, we must determine the objectives of the conspiracy. In any given case, the limits of a conspiracy to restrain trade depend on what the conspirators agreed to do. As the Supreme Court explained in Grunewald v. United States, 353 U.S. 391, 397, 77 S.Ct. 963, 970, 1 L.Ed.2d 931 (1957), “the crucial question in determining whether the statute of limitations has run is the scope of conspiratorial agreement for it is that which determines both the duration of the conspiracy and whether the act relied on as an overt act may properly be regarded as in further-anee of the conspiracy.” In short, Kissel and Grunewald teach that a conspiracy continues until the objectives of the conspiracy succeed or are abandoned and that to determine the objectives of any given conspiracy, the court must look to the conspiratorial agreement.

The relevant contours of a conspiratorial agreement in any given case are those charged in the indictment. United States v. Northern Improvement Co., 814 F.2d 540, 542 (8th Cir.), cert. denied, — U.S. -, 108 S.Ct. 141, 98 L.Ed.2d 98 (1987); United States v. Inryco, Inc., 642 F.2d 290, 293-94 (9th Cir.1981), cert. dismissed, 454 U.S. 1167, 102 S.Ct. 1045, 71 L.Ed.2d 324 (1982); United States v. Davis, 533 F.2d 921, 929 (5th Cir.1976) (“For purposes of the statute of limitations [18 U.S.C. § 3282] the overt acts alleged in the indictment and proved at trial mark the duration of the conspiracy.”); United States v. Helmich, 704 F.2d 547 (11th Cir.), cert. denied, 464 U.S. 939, 104 S.Ct. 353, 78 L.Ed.2d 317 (1983). Paragraph 18(d) of the indictment clearly alleges that two “substantial terms” of the “continuing agreement” among the conspirators were that Paxson Electric would earn profits on the rigged Snapfinger contract and that it would disburse fifty percent of those profits to Dy-nalectric in accordance with a silent joint venture agreement. In addition, Paragraph 17 of the indictment charged that the conspiracy continued through at least January 1985. Thus, it is clear from the indictment that the scope of the conspiratorial agreement specifically encompassed Pax-son Electric’s receipt of payments under the Snapfinger contract and Dynalectric’s receipt of a percentage of these profits in consideration for its participation in the conspiracy, and that the fulfillment of the objectives of the conspiracy continued through January 1985. The indictment, filed in September 1986, therefore was timely.

Every circuit that has addressed this issue has concluded that a criminal conspiracy to restrain trade by collusive, anti-competitive bidding continues for the purposes of the five year statute of limitations until either the final payments are received under the illegal contract or the final distribution of illicit profits among the conspirators occurs. See United States v. A-A-A Electrical Company, 788 F.2d 242 (4th Cir.1986); United States v. Northern Improvement Co., 814 F.2d 540 (8th Cir.1987); United States v. Inryco, Inc., 642 F.2d 290 (9th Cir.1981), cert. dismissed, 454 U.S. 1167, 102 S.Ct. 1045, 71 L.Ed.2d 324 (1982); and United States v. Evans & Associates Constr. Co., 839 F.2d 656 (10th Cir.1988). We find the reasoning in these cases persuasive, particularly the analyses of the Fourth Circuit in A-A-A and the Eighth Circuit in Northern Import.

In A-A-A, the appellants submitted collusive bids for an electrical construction project. A federal indictment charging appellants with violating § 1 of the Sherman Act was issued more than five years after the bids were submitted and the contract was awarded but less than five years after appellants received the final payments under the contract and made the final distribution of the illicit profits. Similar to the indictment in this case, the indictment in A-A-A charged “that the conspiracy by its terms included the rigging of a bid, the securing of an artificial price for the ... project, and payoffs to the coconspirators who helped secure the project.” 788 F.2d at 245.

The A-A-A appellants argued that the conspiracy was complete when they submitted the bids and that the payments received and the payoffs made did not restrain trade and thus were irrelevant for determining when the statute of limitations began to run. Id. at 244. The Fourth Circuit rejected both of these arguments. The court held that a criminal conspiracy to restrain trade should be treated the same as any other criminal conspiracy for purposes of determining the limitation period. Id. at 245. The court recognized that a § 1 Sherman Act violation can occur without any overt act, and hence that a party could suffer “legally cognizable harm” before any overt acts took place. However, the court emphasized that as with any criminal conspiracy, the relevant date in the statute of limitations analysis is the date on which the last overt act in furtherance of the conspiracy is made, not the date on which a party suffers “legally cognizable harm.” Id. Hence, although the payments and payoffs were not necessary elements of a criminal antitrust conspiracy to restrain trade, they constituted overt acts made in furtherance of the conspiracy.

The court also concluded that securing payments under the contract and making payoffs to fellow conspirators “were necessary to the successful consummation of the bid-rigging agreement,” id., i.e. were necessary objectives of the agreement, and that therefore under Kissel and Grüne-wald the statute of limitations did not begin to run until these objectives succeeded or were abandoned.

In Northern Improvement, the appellants submitted bids on several municipal improvement projects. Rather than agreeing that one of the appellants would submit the low bid on each of the three contracts and thereafter share the profits with the other conspirators, the appellants arranged the bids so that each conspirator was the low bidder on one project. Consequently, the conspirators did not divide the profits each made on its particular contract. The indictment was filed within five years after the appellants received the final payments under the contracts but more than five years after the bids were submitted and the contracts awarded.

The district court concluded that the conspiracy terminated when the bids were submitted, in part because “there was no sharing of spoils after the payments on the contracts_” 814 F.2d at 541. The Eighth Circuit reversed. After noting the indictment plainly charged that the appellants agreed to rig the bids “ ‘with the expectation that [the agreed upon] low bidder would be awarded the project and paid by the city awarding the project the Eighth Circuit reasoned that receipt of payments — in addition to rigging the bids— was a central purpose of the conspiracy to restrain trade. Id. at 542, quoting the indictment. The court also held that the unilateral receipt of payments under the contract was an overt act which furthered the conspiracy, regardless of the fact that there were no payoffs from the illicit profits. Id. at 543 n. 1.

We now turn to the specific arguments which appellants raise in this appeal, many of which were addressed and rejected by the four circuits that previously have considered this corner of the law.

Appellants primarily rely on City of El Paso v. Darbyshire Steel Co., 575 F.2d 521 (5th Cir.1978), cert. denied, 439 U.S. 1121, 99 S.Ct. 1033, 59 L.Ed.2d 82 (1979). Darbyshire is a civil antitrust case involving a virtually identical bid rigging conspiracy in which the court had to determine when the civil statute of limitations, 15 U.S.C. § 15b, began to run. The civil statute of limitations provides that a civil antitrust action must be brought within four years after the cause of action accrues. The Darby-shire court held that in a bid rigging case, a civil antitrust cause of action accrues when the contract is executed; at that point, the plaintiffs damages are fixed and ascertainable. Id. at 523.

The appellants assert that the requirement that damages must be ascertainable before the civil statute of limitations begins to run is a requirement above and beyond the criminal limitations requirement that the conspiracy must be completed. In other words, appellants contend that in a civil antitrust case, the conspiracy must be completed and the plaintiffs cause of action must have accrued before the statute of limitations begins to run. Therefore, they contend that the court’s holding in Darby-shire necessarily means that the conspiracy was completed when the contract was executed. Appellants offer no cases supporting their interpretation of Darbyshire, i.e., that a civil antitrust cause of action cannot accrue before the conspiracy is completed. We note that this interpretation directly conflicts with the Fourth Circuit’s decision in A-A-A that the criminal antitrust “statute of limitations begins to run, not from the date of the legally cognizable harm, but from the date of the last overt act.” 788 F.2d at 245; see discussion of A-A-A, supra.

We conclude that Darbyshire is not helpful in this case because it does not involve an interpretation of the appropriate statute of limitations. The requirement that a cause of action accrue in a civil antitrust case before the statute of limitations begins to run is separate and distinct from— not cumulative to — the requirement in a criminal antitrust case that the statute of limitations begins to run when the conspiracy is completed. As the Fourth Circuit explained in A-A-A:

We reach this conclusion [that a conspiracy to restrain trade encompasses receipt of payments for purposes of the criminal statute of limitations] mindful of the fact that the ... statute of limitations ... for civil antitrust actions begins to run at the time the antitrust cause of action accrues and that the continued receipt of payments may not constitute a continuing violation of the antitrust laws for civil statute of limitations purposes.... The present case, however, is ... [not controlled by the civil statute] but by an entirely different statute governing the limitations period for criminal conspiracies, including those of a continuing nature.

788 F.2d at 246 n. 4.

Moreover, nothing in Darbyshire addressed the duration of the conspiracy. The Darbyshire court did not hold that the cause of action accrued and the statute of limitations began to run because the conspiracy was complete nor did Darbyshire explicitly or implicitly hold that civil damages could not be ascertained before the conspiracy terminated. Thus, we agree with the government that accrual of a cause of action for civil statute of limitation purposes and completion of the conspiracy for criminal statute of limitations purposes are two entirely different and distinct issues.

The appellants also contend that the primary objective of a conspiracy to restrain trade in a § 1 Sherman Act case is the restraint of trade itself and that after the rigged bids are accepted, the restraint of trade ends. They argue that the payments received under the Snapfinger subcontract are results of the conspiracy, rather than objectives of the conspiracy.

We disagree. It is inconceivable to us that any business would conspire to restrain trade solely for the sake of restraining trade; the attendant battery of civil and criminal penalties for antitrust violations simply is too threatening to convince us that anybody would attempt to restrain trade without also having the further goal of financial self-enrichment by virtue of the restraint of trade. We believe that a central objective of a conspiracy to restrain trade is to garner illicit profits. We find persuasive the Eighth Circuit’s explanation of the objectives of a criminal conspiracy to restrain trade through collusive bidding:

We do not deal here with criminal behavior that is an end in itself. Common sense tells us that the conspirators’ purpose was to reap the benefit of the conspiracy: to be awarded public improvement contracts at anti-competitively high prices and to be paid for those contracts .... [T]he object and purpose of [the] illegal agreement [to collusively rig bids] was ‘illicit gain,’ the receipt of payments, and we conclude that the district court erred in holding that the purpose of the conspiracy terminated the moment the bids were submitted.

Northern Improvement, 814 F.2d at 542. See United States v. Rodgers, 624 F.2d 1303, 1310 (5th Cir.1980) (a bidrigging scheme “would have been meaningless, incomplete, and futile without final award and payment_”), cert. denied sub nom., Anthony J. Bertucci Constr. Co. v. United States, 450 U.S. 917, 101 S.Ct. 1360, 67 L.Ed.2d 342 (1981). Therefore, we reject the appellants’ argument that receiving payments under the contract or distributing illicit profits among the conspirators cannot as a matter of law be an objective of a conspiracy to restrain trade. The conspiracy continues so long as one or more of the conspirators continues to receive payments under a collusive contract — i.e. as long as they continue to realize a central and obvious objective of the conspiracy.

We also disagree with the appellants’ contention that the joint conspiratorial action necessary for a conspiracy ended when they submitted the rigged bids. The continued cooperation of Paxson Electric and Dynalectric was evident in two respects long after the bids were submitted in early 1980. Paxson Electric divided the illicit profits with Dynalectric pursuant to the joint venture agreement. The final payment to Dynalectric was made in 1983, well within the five-year limitation period. At least from Dynalectric’s perspective, these payments were a crucial element of the jointly conceived and executed conspiratorial plan; these payments would not have occurred if the parties had ceased to cooperate.

Continued cooperation tacitly was evidenced by Dynalectrie’s silence after it had received its final payoffs under the joint venture agreement. Dynalectric’s silence was necessary if the conspiracy was to be successfully carried to fruition, i.e., if Pax-son Electric was to receive all of its illicit profits via receipt of the subcontract payments from Hyman.

The appellants argue that the payments from Paxson Electric to Dynalectric and Dynalectric’s silence after it received the final payment under the joint venture agreement constitute efforts to conceal the completed crime. In Grunewald, the Supreme Court held that conspirators’ efforts to conceal their actions after they had accomplished the objectives of the conspiracy were not part of the overall conspiracy. 353 U.S. at 402, 77 S.Ct. at 972. The Supreme Court carefully limited its holding to cases involving concealment of the illegal activities after the main objectives of the conspiracy were accomplished. The court pointed out the difference between concealment done in furtherance of the objectives of the conspiracy, such as kidnappers hiding out until they receive the ransom or car thieves repainting a stolen car, and concealment done to cover up the crime itself, such as kidnappers covering their tracks after they had received the ransom. 353 U.S. at -, 77 S.Ct. at 974.

The payments Paxson Electric made to Dynalectric were important objectives of the conspiracy, rather than “hush money” paid to conceal a completed crime. Thus, our conclusion that these payments continued the conspiracy is not at odds with Grunewald. An analogous case is United States v. Walker, 653 F.2d 1343 (9th Cir.1981), cert. denied, 455 U.S. 908, 102 S.Ct. 1253, 71 L.Ed.2d 446 (1982). In Walker, the defendant defrauded the government by submitting collusive bids and later splitting the illicit profits with the other conspirators, in violation of 18 U.S.C. § 371. The Ninth Circuit concluded:

We do not agree with [the defendant] that the acts of contract performance and division of profits are analogous to coverup activities and thus barred by Grünewald. However, even if we were to accept this tortured analogy and apply the Grünewald test, those acts formed part of the conspiracy because they did not follow the accomplishment of its central criminal objectives but rather were acts in furtherance of those aims, viz, obtaining and dividing the excess profits made on the timber. [Defendant’s] definition of the objective of the conspirators as limited to obtaining the award from the Forest Service is far too narrow.

Id. at 1348 (emphasis in original). The Walker court also noted that “[w]ithout the continuing cooperation of his co-conspirators, bought by the payoffs to them in various forms, the scheme would have fallen apart.” Id. at 1347.

We also believe that Dynalectric’s cooperative silence from 1983, when it received its final payment under the joint venture agreement, to 1985, when Paxson Electric received its final payment from Hyman, is akin to the kidnapper awaiting the ransom or the car thief repainting the car. In other words, Dynalectric’s continued tacit cooperation was necessary to the “successful accomplishment of the crime.” Grunewald, 353 U.S. at 405, 77 S.Ct. at 974; A-A-A, 788 F.2d at 245.

As a final matter, we note that if we were to adopt the appellants’ argument that the conspiracy concludes when the contract is awarded following the rigged bidding, we would effectively eliminate the difference that the Sherman Act explicitly makes between contracts and conspiracies in restraint of trade. We conclude that a conspiracy to restrain encompasses more than a contract in restraint of trade. The distinction between a contract in restraint of trade and a conspiracy in restraint of trade was explicitly noted by the Supreme Court in Kissel where Justice Holmes wrote that “[a] conspiracy in restraint of trade is different from and more than a contract in restraint of trade.” 218 U.S. at 608, 31 S.Ct. at 126. Therefore, we reject the appellants’ interpretation of the Sherman Act that makes its provisions redundant.

B. Mail Fraud Claims

We turn next to defendants’ challenges to their mail fraud convictions. Each defendant was convicted of two counts of mail fraud. The basis of each mail fraud count was a payment check mailed from Hyman to Paxson Electric.

1. McNally claim

First, defendants mount a challenge based on McNally v. United States, — U.S. -, 107 S.Ct. 2875, 97 L.Ed.2d 292 (1987). The federal mail fraud statute makes it illegal to use the mails to execute a scheme to defraud a person or entity of money or property. 18 U.S.C. § 1341. In McNally, the Supreme Court held that the mail fraud statute did not apply to schemes to defraud citizens of their intangible right to honest government. Subsequently, in Carpenter v. United States, — U.S. -, 108 S.Ct. 316, 98 L.Ed.2d 275 (1987), the Supreme Court clarified that the mail fraud statute did apply to schemes to defraud a victim of intangible property rights. See United States v. Italiano, 837 F.2d 1480 (11th Cir.1988) (extensive discussion of McNally and Carpenter and the ramifications of these cases on the application of the mail fraud statute).

The rule of law we discern from McNally and Carpenter is that the only fraudulent schemes exempt from the mail fraud statute are those involving intangible, non-property, non-monetary rights (hereinafter “McNally-type intangible” rights). Put another way, McNally and Carpenter teach that the mail fraud statute applies to any fraudulent scheme involving a monetary or property interest, whether that interest is tangible or intangible. See United States v. Asher, 854 F.2d 1483 (3d Cir.1988) (“Essentially, therefore, where rights are involved whose violation would lead to no concrete economic harm, and where those rights are the only rights involved in the case, McNally’s proscriptions would prevent upholding conviction on appeal. Where, on the other hand, a violation of the rights involved would result in depriving another of something of value, and the indictment, the proofs and the instructions are based on that fact, then the presence of intangible rights language will not prove fatal on appeal.”); United States v. Wellman, 830 F.2d 1453, 1462 (7th Cir.1987) (.McNally addressed “rights whose violation would ordinarily result in no concrete economic (or to use Justice Stevens’ term, ‘monetary’) harm.”); United States v. Baldinger, 838 F.2d 176, 179 (6th Cir.1988) (From McNally and Carpenter, the Sixth Circuit concluded that the Supreme Court “clearly intended to exclude from the reach of the mail fraud statute claims which did not involve a direct intention to deprive another of a recognized and traditional property right (tangible or intangible). ...”).

Defendants contend that a scheme to defraud the EPA and Dekalb County of their right to free and open competition falls within the bounds of McNally; hence, they assert their mail fraud convictions are infirm. In the plethora of post-McNally cases addressing challenges to pre-McNally mail fraud convictions, the courts uniformly have looked to the wording of the indictment and the jury instructions to determine if the convictions can stand. If the indictment and jury instructions were phrased in such a way that the jury could have convicted the defendant of scheming to defraud the victim of a McNally-type intangible right, the courts have reversed the convictions. Conversely, if the jury necessarily must have concluded that the defendant schemed to defraud the victim of a non -McNally type of right (i.e. a monetary or property right, whether tangible or intangible), then the convictions stand, even if the indictment charged and the jury was instructed on McNally-type intangible rights in addition to non-McNally rights. See United States v. Ochs, 842 F.2d 515, 522-24 (1st Cir.1988) and United States v. Asher, 854 F.2d 1483 (3d Cir.1988) (summarizing leading post-McNally mail fraud cases).

The defendants’ McNally claim only can succeed if the jury could have convicted them of scheming to defraud the EPA and Dekalb County of their right to open competition and if this intangible right to open competition falls within the scope of McNally. Based on the 'indictment and the jury instructions, we conclude that the jury must have convicted the defendants of scheming to defraud the victims of money, thus we reject their McNally claim.

a. Indictment

The indictment charged that:

23. Beginning in or about August 1979 and continuing thereafter until at least January 1985, the exact dates being unknown to the Grand Jury, the defendants and co-conspirators devised and intended to devise a scheme and artifice to defraud the County and the United States of America, through its agency, the EPA, of:
(a) money; and
(b) their right to free and open competition for the bidding on the electrical construction portion of the Snapfinger Creek project, such bidding to be conducted honestly, fairly and free from craft, trickery, deceit, corruption, dishonesty and fraud.
24. It was part of the aforesaid scheme and artifice to defraud that the defendants, and others, known and unknown to the Grand Jury, would and did submit collusive, artificially high and rigged bids in order to induce the general contractor selected to build the Snapfinger Creek project to award the subcontract for the electrical construction portion of the project to defendant Paxson Electric.

The plain language of the indictment charges the defendants with scheming to defraud the EPA and Dekalb County of money. While it also charges that the defendants schemed to defraud the victims of their right to open competition, the indictment is not worded in a way that would allow the jury to choose between the two theories. Rather, to convict the defendants in accordance with the indictment, the jury must have concluded that there was a scheme to defraud the victims of money and the right to open competition. See United States v. Perholtz, 836 F.2d 554, 559 (D.C.Cir.1988) (holding indictment was sufficient under McNally where it alleged defendants created a kickback scheme to defraud the victim of its “ ‘lawful right to conduct business and affairs free from kickbacks ...”’ and “also — not alternatively — one ‘to obtain money and property....”’ (quoting indictment) (emphasis in original)); United States v. Eckhardt, 843 F.2d 989, 996-97 (7th Cir.1988) (mail fraud conviction entered pursuant to plea agreement upheld where the indictment alleged a scheme to defraud the victim of intangible rights and “to obtain money and property by false and fraudulent pretenses.”).

In McNally, the indictment charged that defendants schemed to defraud the government and citizens of Kentucky of “their right to have the Commonwealth’s affairs conducted honestly_” — U.S. at - n. 4, 107 S.Ct. at 2878 n. 4. The indictment also charged that the defendants schemed to “obtain (directly and indirectly) money ...” but did not allege that they schemed to defraud the victims of money. Thus, the McNally indictment was substantially different from the one in this case.

b. Jury Instructions

The jury instructions also withstand a McNally challenge. We note that in reviewing the sufficiency of the jury instructions, we must examine the charge as a whole rather than isolating and examining the deficiencies of individual instructions. Italiano, 837 F.2d at 1487; United States v. Gordon, 817 F.2d 1538, 1542 (11th Cir.1987), vacated in part and rev’d in part, 836 F.2d 1312 (11th Cir.1988). Our review of the instructions as a whole convinces us that a reasonable jury must have concluded that the purpose of the scheme was to defraud the victims of money. The jury was instructed that to convict the defendants of mail fraud, the government had to prove beyond a reasonable doubt that, among other things, “the defendant knowingly and willfully devised a scheme to defraud_” (R. 24-3326). The judge instructed that a “scheme includes any plan or course of action intended to deceive others and to obtain by false or fraudulent pretenses money or property from the person so deceived.” Id. (emphasis added). This is directly contrary to McNally, where the court stated that “there was no charge and the jury was not required to find that the Commonwealth itself was defrauded on any money or property.” — U.S. at -, 107 S.Ct. at 2882.

Of equal importance is that the jury was not instructed on the intangible rights theory. No instruction was given that the scheme to defraud could include the right to open competition. This aspect of the scheme was implicit in the instruction that the government had to prove a scheme to defraud “substantially the same as the one alleged ...” in the indictment. (R. 24-3327). As discussed above, however, the scheme alleged in the indictment was one to defraud the victims of money and the right to open competition. Thus, the implicit reference to the right to open competition is not in violation of McNally. See Perholtz, 836 F.2d at 558 (where the indictment charged a scheme to defraud the government of money and its right to conduct its business free from kickbacks and the jury was instructed that to convict it had find a scheme “substantially the same as the one alleged in the indictment,” there was no McNally violation even though the judge explicitly charged the jury that the scheme to defraud included the deprivation of McNally-type intangible rights); United States v. Piccolo, 835 F.2d 517, 520 (3d Cir.1987) (defendant’s McNally claim rejected where the jury was charged that to convict it must find that defendant schemed to defraud the victim “ ‘of its right to the honest, faithful and loyal services of its employee, ... and further, to defraud [victims] of money.’ ” (emphasis in original)), cert, denied, — U.S. -, 108 S.Ct. 2014, 100 L.Ed.2d 602 (1988); United States v. Asher, 854 F.2d 1483 (3d Cir.1988) (although jury instructions made reference to a scheme to defraud of both tangible rights and McNally-type intangible rights, convictions affirmed where court was “unable to hypothesize a set of circumstances under which this jury could have found [defendant] guilty of depriving the citizens of the Commonwealth of their right to honest government ... without also having found that [defendant] was involved in a scheme, the sole purpose of which was to ensure that CTA obtained a no-bid ... contract at a substantially greater cost to the Commonwealth than a contract obtained through traditional competitive bidding.”).

The defendants contend that the jury instructions are invalid under McNally because they do not expressly limit the fraudulent scheme to the deprivation of money and do not expressly exclude a scheme based on the deprivation of the right to open competition. For example, the defendants argue that the charge defining the “scheme”, quoted above, is defective because it does not absolutely limit a mail fraud scheme to the deprivation of property but rather explains that a scheme includes a deprivation of tangible rights. Two other circuits have addressed McNally challenges to identical jury instructions defining “scheme”. The Tenth Circuit agreed with the defendants, concluding that “[although the above definition of ‘scheme’ states that it includes any plan by which the victim loses money or property, use of the open-ended word ‘includes’ does not require the jury to find such a loss.” United States v. Shelton, 848 F.2d 1485, 1496 (10th Cir.1988) (en banc) (emphasis in original).

The Sixth Circuit reached the opposite conclusion. It explained that the instruction defining “scheme” was acceptable because “[t]he clear emphasis on deprivation of money or property, combined with the absence of any instruction that the jury was free to convict Horton on the basis of the deprivation of Chrysler’s intangible right to conduct its business in an honest manner compels the conclusion that McNally does not control the disposition of the present case.” United States v. Horton, 847 F.2d 313, 320 (6th Cir.1988). Under the facts of this case, we agree with the Sixth Circuit that the definition of “scheme”, although somewhat open-ended, does not require a reversal of the mail fraud convictions. As in Horton, the jury here was not instructed on any intangible right theory. Moreover, it is clear to us that the focus of the jury charge, read as a whole, was on the deprivation of money and property, not on the deprivation of the right to free and open competition. Finally, in this case, the only mention of the open competition theory was in the indictment, and there it was clear that there must be a scheme to defraud of both money and open competition.

For these reasons, we reject defendants’ claim to the extent it is based on McNally.

2. Sufficiency of the Evidence

In reviewing a defendant’s challenge to the sufficiency of the evidence supporting his conviction, we must uphold the jury’s verdict if, “after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979). In addition, we must “make all reasonable inferences in support of the jury’s verdict.” United States v. Hewes, 729 F.2d 1302, 1320 (11th Cir.1984), cert. denied sub nom., Caldwell v. United States, 469 U.S. 1110, 105 S.Ct. 790, 83 L.Ed.2d 78 (1985).

a. Sufficient evidence of overcharge

The defendants challenge the sufficiency of the government’s proof with respect to several aspects of the mail fraud convictions. First, they contend there was insufficient evidence that the EPA and Dekalb County actually were overcharged because of the collusive bids. Defendants argue that there was no evidence that the bid price or profits were unreasonably high and thus no evidence of a scheme to defraud the EPA and Dekalb County of money. We conclude that there was sufficient evidence of a scheme to defraud the victims of money.

In her memorandum opinion, Judge Evans cited the following as evidence of overcharge. First, Trepte testified that he agreed to raise Fischbach and Moore’s bid $500,000 in exchange for Paxson Electric’s promise to forgive an $89,000 debt Fisch-bach allegedly owed to Paxson Electric. Trepte also testified that Paxson Electric never collected the $89,000 debt. R10-240-41. Second, there was testimony that Dy-nalectric received 50% of Paxson Electric’s Snapfinger profits (approximately $880,-000) in exchange for doing virtually no work on the Snapfinger project other than “periodic site inspections.” Third, Edward Baylin, the manager of Dynalectric’s Atlanta office who prepared the materials cost estimate for Dynalectric’s bid testified that he could not figure out how Dynalectric’s actual bid of $5.3 million was derived when the highest price he could come up with, using realistic (or somewhat higher) prices, was $4.7 million. R.ll-444-452. There also was testimony that the profit level (approx. 40% of the contract price) was unusually high relative to comparable projects. We conclude that a rational jury could conclude from this evidence, viewing all inferences favorably to the government, that the collusive bidding resulted in overcharges on the Snapfinger contract.

b. Sufficient evidence that overcharge passed on to EPA and Dekalb County

The defendants contend that even if there was sufficient evidence to establish that they overcharged Hyman, the general contractor, there is insufficient evidence to show that Hyman passed along these overcharges to the alleged victims of the scheme, the EPA and Dekalb County. Defendants rely primarily on the fact that Hyman had a negotiated lump sum contract, rather than a cost-plus contract, with the EPA and Dekalb County. However, the government presented testimony from a Hyman employee who worked on the Snapfinger bid indicating that Hyman’s bid price was a direct function of the various subcontract prices obtained from allegedly competitive bids from the subcontractors. We believe that a rational jury could infer from this testimony that at least some of the overcharge was passed on to the EPA and Dekalb County.

3. Jury Charge: No requirement that scheme to defraud actually succeed

The district court charged the jury that to convict the defendants of mail fraud, the jury did not have to find that the scheme to defraud actually succeeded. We hold that the substance of this charge was correct: conviction under the federal mail fraud statute only requires the government to prove a scheme to defraud; the success or failure of the scheme is irrelevant. Our conclusion is supported by the language of the statute and by the cases interpreting it. The mail fraud statute itself addresses the use of the mails to further a scheme to defraud a victim of money or property. McNally, — U.S. at -, 107 S.Ct. at 2881. The statutory language does not set forth a requirement that the scheme to defraud actually must succeed in defrauding its victim of money or property.

In addition, both pre- and post-McNally cases confirm our conclusion that Judge Evans correctly instructed the jury that the success of the scheme was irrelevant. See, e.g., United States v. Keane, 852 F.2d 199 (7th Cir.1988) (“[I]t may well be that none of this cost the City or anyone else one red cent_ But the mail fraud statute proscribes fraudulent schemes; it does not confine penalties to those whose schemes succeed in raking off cash, a point no less valid today than when emphasized on direct appeal [thirteen years ago].”); Ward v. United States, 845 F.2d 1459, 1462 (7th Cir.1988) (“[T]he mail fraud statute punishes the scheme to defraud, and does not require that the intended victim actually have been defrauded....”); United States v. Baldinger, 838 F.2d 176, 180 (6th Cir.1988) (mail fraud statute reaches schemes whose goal is “ ‘the transfer of something of economic value to the defendant.’ Comment, The Intangible Rights Doctrine and Political — Corruption Prosecutions Under the Mail Fraud Statute, 47 U.Chi.L. Rev. 562, 566 (1980)”); United States v. Asher, 854 F.2d 1483 (3d Cir.1988) (mail fraud convictions affirmed where scheme would have defrauded victim of money had it succeeded); United States v. Ochs, 842 F.2d 515, 523 (1st Cir.1988) (noting that post-McNally cases in which convictions were affirmed were those in which “the jury was in fact explicitly required to find that the fraudulent scheme was also intended to cause monetary harm.” (emphasis added)); United States v. Dial, 757 F.2d 163, 179 (7th Cir.) (mail fraud statute “punishes the scheme to defraud rather than the completed fraud itself.”), cert. denied, 474 U.S. 838, 106 S.Ct. 116, 88 L.Ed.2d 95 (1985).

Convictions in pre-McNally mail fraud cases involving bid rigging withstood sufficiency of evidence challenges absent an explicit showing that the victim actually lost money. For example, in United States v. Washita Construction Co., 789 F.2d 809, 818 (10th Cir.1986),

[t]he evidence adduced at trial indicated that the conspirators arranged to win highway contracts without submitting competitive bids. The scheme devised by the conspirators circumvented the state and federal competitive bidding procedures and allowed the contractors to virtually predetermine who would be awarded a contract. By arranging for complimentary bids to be submitted, the conspirators deceitfully created the illusion of competitive bidding and concealed their illegal collusion.

Significantly, the court did not indicate that any evidence of actual overcharge was adduced at trial, yet sustained the mail fraud convictions in the face of a sufficiency of evidence challenge. See also United States v. Young Bros., Inc., 728 F.2d 682, 689 (5th Cir.) (to withstand sufficiency challenge to mail fraud convictions, “the government was required to show that the mailings (relating to the billing and payment of the $10,001) were ‘in furtherance’ of the bidrigging scheme.”), cert. denied, 469 U.S. 881, 105 S.Ct. 246, 83 L.Ed.2d 184 (1984).

4. Other Challenges — Mail Fraud

The defendants’ remaining challenges to their mail fraud convictions warrant little discussion. They contend that there was an insufficient causal connection between the use of the mails and their participation in the bidding scheme. They point out that the two mailings which are the basis for the mail fraud counts occurred in 1984 and 1985, after Dynalectric received its final payment pursuant to the joint venture agreement in 1983 and well after the rigged bids were submitted in 1979. However, as we concluded in our discussion of the statute of limitations issue, the payments from Hyman to Paxson Electric were important aspects of the conspiracy. Thus, the payments which were mailed in 1984 and 1985 clearly were integral to the scheme to defraud. See United States v. Young Bros., Inc., 728 F.2d at 689 (court sustained mail fraud conviction in bid rigging context where defendant claimed that the mailings were not sufficiently closely related to the scheme to defraud; the court reasoned that mailing a payoff to a eoconspirator after the rigged bids were submitted was sufficient because “it reasonably can be inferred that [the defendant] would not have agreed to the scheme on behalf of his company without being paid.”); United States v. Rodgers, 624 F.2d at 1310 (mail fraud conviction upheld where victim mailed to defendants the final payment of a contract obtained by rigged bids; the court concluded that “[t]he scheme would have been meaningless, incomplete, and futile without final award and payment which were accomplished through the mail. Clearly, the mails were used ‘in furtherance’ of the scheme.”).

Dynalectric’s claim that there was insufficient evidence that it “caused” thé mails to be used is without merit. Paxson Electric, through its affiliate CCC Electric, caused the mails to be used by requisitioning the two payments from Hyman. Evidence was presented at trial that in the ordinary course of business, the general contractor (Hyman) mails the subcontractor its contract payments following the receipt and approval of the subcontractor’s payment requisition. Thus, we conclude that Paxson Electric reasonably could have anticipated that the mails would be used in the ordinary course of business to facilitate the transfer of contract payments to it (via CCC Electric) from Hyman pursuant to CCC Electric’s requisition for payment. United States v. Rodgers, 624 F.2d at 1310 n. 17. Moreover, because Dynalectric was a knowing participant in the scheme to defraud, the actions of coconspirator Paxson Electric which caused the mails to be used in furtherance of the scheme are sufficient to make Dynalectric legally liable for the use of the mails. United States v. Hewes, 729 F.2d at 1322 n. 24. As we explained in Hewes, “[t]he mere fact that [defendant’s] role in the scheme may have ended prior to the time the [mailings] occurred does not shield him from criminal liability.” Id. at 1324.

C. Kastigar Claim: Wesley Paxson

Wesley Paxson claims that the government improperly used grand jury testimony he gave in 1984 under a grant of use immunity to obtain the indictment and conviction in this case, in violation of Kastigar v. United States, 406 U.S. 441, 92 S.Ct. 1653, 32 L.Ed.2d 212 (1972). This court recently explained in United States v. Caporale, 806 F.2d 1487, 1518 (11th Cir.1986), cert. denied, — U.S. -, 107 S.Ct. 3265, 97 L.Ed.2d 763 (1987), that under Kastigar “the government bears the burden of proving that testimony that a defendant gave under a promise of use immunity was not directly or indirectly used in a subsequent prosecution against the defendant. To meet that burden, the government must show by a preponderance of the evidence that its evidence in the subsequent prosecution was derived from a legitimate independent source.” (Citing Kastigar, 406 U.S. at 460, 92 S.Ct. at 1665). However, the government does not have to “negate all abstract ‘possibility’ of taint.” United States v. Byrd, 765 F.2d 1524, 1529 (11th Cir.1985). A Kastigar claim involves factual determinations, therefore we must affirm the district court’s Kastigar decision unless it is clearly erroneous. Caporale, 806 F.2d at 1518; United States v. Hampton, 775 F.2d 1479, 1484 (11th Cir.1985).

Paxson’s Kastigar claim reaches this court with a substantial track record. In the proceedings below, the Kastigar issue was raised and briefed on three separate occasions. Prior to trial, both the magistrate and the district court issued written opinions denying Paxson’s Kastigar motions. These decisions were issued after the magistrate and the district court judge examined in camera transcripts of witnesses who appeared before the indicting grand jury, a transcript of Paxson’s immunized testimony, and fifty exhibits submitted by the government as evidence of legitimate independent sources. In addition, the government submitted the sixty-five page affidavit of Hayes Gorey, the lead government attorney for both the grand jury proceedings and Paxson’s trial. Gorey was present during Paxson’s immunized grand jury appearance. Gorey’s affidavit meticulously linked the independent sources of evidence (i.e., the 50 exhibits) to each piece of evidence presented to the indicting grand jury and to be adduced against Paxson at trial which conceivably was directly or indirectly revealed in Pax-son’s immunized testimony. Gorey also submitted a post-trial supplemental affidavit. At the conclusion of the trial, these exhibits and the affidavits were unsealed and Paxson was allowed to examine them. After reviewing this evidence, Paxson renewed his motion to dismiss the indictment on Kastigar grounds and in the same post-trial motion asked in the alternative for a judgment of acquittal or an evidentiary hearing on his Kastigar claim. The district court denied this motion in its memorandum opinion.

Paxson raises no new Kastigar issues on appeal, nor has he “come forward with any persuasive proof that the district court’s determination as to any questioned source was clearly erroneous.” Caporale, 806 F.2d at 1518. We have carefully reviewed the record and agree with the decisions of the district court and magistrate that the government has clearly demonstrated that it made no direct or indirect use of Paxson’s immunized testimony. The government convincingly demonstrated an independent source for all portions of the evidence adduced before the indicting grand jury and at trial against Paxson which conceivably had any relation to his immunized testimony. The government’s evidence showed that Paxson’s immunized testimony was not used as a direct eviden-tiary source or as a source of investigatory leads.

We note that much of Paxson’s immunized “testimony was self-serving and of no real value in the subsequent investigation.” Id. at 1518-19. Paxson claims that United States v. Hampton, 775 F.2d 1479 (11th Cir.1985), holds that the self-exonerating nature of immunized testimony is irrelevant to a Kastigar claim. Contrary to what Paxson urges, Hampton held that a defendant’s non-inculpatory testimony is relevant to a Kastigar claim if it yielded direct evidence or investigatory leads. In Hampton, it was undisputed that the defendant’s immunized testimony contained information about “several important matters and details” useful in the investigation for which no independent sources were established. Id. at 1486-87. In addition, in Hampton the government made no effort to systematically eslabjish independent sources for all evidence it introduced to the grand jury.

By contrast, in this case the government made a thorough and organized presentation that all of its evidence which conceivably could have been attributable to Paxson’s immunized testimony was derived from independent sources. More importantly, unlike Hampton, Paxson’s self-serving testimony provided no direct evidence or investigatory leads for which the government did not have a legitimate independent source. In fact, Paxson’s testimony apparently drew the Snapfinger investigation to a halt for thirteen months until Trepte’s grand jury testimony revealed substantial inconsistencies with Paxson’s immunized testimony about the Snapfinger project.

Paxson also claims that he was entitled to a full-blown post-trial evidentiary hearing on his Kastigar motion. The decision to grant an evidentiary hearing lies within the sound discretion of the trial court and we review the district court’s denial of the hearing only for an abuse of discretion. See United States v. Slocum, 708 F.2d 587, 600 (11th Cir.1983) (on appeal, district court’s decision not to hold an evidentiary hearing on Brady and newly discovered evidence allegations subject to abuse of discretion standard of review); United States v. Johnson, 596 F.2d 147, 148 (5th Cir.1979) (decision whether to hold eviden-tiary hearing on motion for new trial “is within the trial court’s sound discretion, subject to our review only for abuse”); United States v. Dicesare, 765 F.2d 890, 895 (9th Cir.1985); United States v. Cardarella, 588 F.2d 1204, 1205 (8th Cir.1978). We are cognizant of the fact that Kastigar motions generally are resolved following an adversary evidentiary hearing. Byrd, 765 F.2d at 1532. As this court stated in Byrd, the purpose of a Kastigar motion is to “ensur[e] that the government’s evidence has been obtained from legitimate, independent sources_” Id. at 1533. However, it is clear that an evidentiary hearing is not mandated for all Kastigar motions and that whether a hearing is necessary to properly resolve a Kastigar claim depends on the particular facts of the case. See, e.g., Byrd; United States v. Provenzano, 620 F.2d 985, 1006 (3d Cir.) (“If the Government’s documents conclusively demonstrate prior knowledge, we know of no reason why a hearing must be held.”), cert. denied, 449 U.S. 899, 101 S.Ct. 267, 66 L.Ed.2d 129 (1980); United States v. Lipkis, 770 F.2d 1447, 1451-52 (9th Cir.1985) (no evidentiary hearing necessary when defendant stipulated that there were only minimal differences between immunized testimony and non-immunized testimony given several months prior to the immunized testimony).

We conclude that under the facts of this case, the district court did not abuse its discretion in declining to grant Paxson’s post-trial motion for an evidentiary hearing. From their pre-trial examinations of the government’s Kastigar evidence, both the district court and the magistrate concluded that the government had exceeded its Kastigar burden by presenting ample and conclusive evidence of independent sources for all evidentiary and investigatory leads which Paxson’s testimony could have generated. After trial, the district court turned over all the government’s in camera evidence to Paxson. Despite his access to the government’s evidence, the only alleged Kastigar violations which Paxson could point out to the district court either were meritless or reiterated Kastigar claims raised pre-trial, which the district court already had rejected. Because of Paxson’s inability to demonstrate the need for a post-trial Kastigar hearing after he gained access to the in camera evidence, coupled with the district court’s in-depth familiarity with the government’s Kastigar evidence, the court’s first-hand knowledge of the evidence actually presented at trial, and the self-serving nature of Paxson’s immunized testimony, we conclude that the district court’s refusal to grant an evidentiary hearing was not an abuse of discretion.

In summary, we conclude that the district court was not clearly erroneous in dismissing Paxson’s Kastigar claim.

D. Other Issues

1. 404(b) Evidence

The defendants claim that the district court abused its discretion by admitting 404(b) evidence of other alleged bidrigging attempts despite the defendants’ offer to stipulate to the issue of intent. Federal Rule of Evidence 404(b) allows evidence of a defendant’s prior bad acts to be admitted if the evidence is relevant to an issue other than the defendant’s character (e.g., defendant’s criminal intent) and if the probative value of the evidence is not substantially outweighed by its prejudicial value. United States v. Bennett, 848 F.2d 1184, 1137 (11th Cir.1988). Judge Evans’ decision to admit the evidence cannot be overturned on appeal unless she abused the wide range of discretion afforded to district court judges on evidentiary matters. Id.

The disputed evidence pertained to three separate alleged bidrigging attempts by Dynalectric and Paxson Electric employees. The government contended, inter alia, that the evidence was relevant to the defendants’ intent to rig the Snapfinger bids. The defendants do not contest that the evidence was relevant to show intent, but contend that the district court improperly rejected their offer to stipulate to intent. Immediately prior to the testimony of the first 404(b) witness, the defendants offered the following written stipulation, which the government refused to accept and which the district court rejected: “If the jury finds that the defendants met and agreed to fix bids as alleged, intent to restrain trade shall be presumed.”

We conclude that the offer to stipulate was inadequate because it was a tautology. It is meaningless to offer to stipulate that if the defendants met and agreed to rig bids, they intended to restrain trade. Clearly, if they agreed to rig the bids, there is a strong inference that they intended to restrain trade. Thus, the proffered stipulation was inadequate and the district court did not abuse its discretion by rejecting it.

2. Anonymous Phone Call

Dynalectric claims that the district court erred by allowing Trepte, an employee of Fischbach & Moore who was intricately involved in the Snapfinger bidding process, to testify about a phone call he received from an unidentified caller on the morning the bids were submitted. Trepte testified that the caller told him what price he should use to bid on the Snapfinger job and that “there had been an arrangement that was satisfactory to the parties.” The district court admitted the statement pursuant to Fed.R.Evid. 801(d)(2)(E) and we can reverse the court’s decision on this issue only if it was clearly erroneous. United States v. Alexander, 850 F.2d 1500, 1505 (11th Cir.1988).

Statements by a eoconspirator of a party made during the course of and in furtherance of a conspiracy are admissible, non-hearsay evidence under Fed.R.Evid. 801(d)(2)(E). Dynalectric claims that because the caller was unidentified, the statements could not be characterized as statements of a coconspirator; thus, Trepte’s testimony about the call was inadmissible hearsay outside the scope of Rule 801.

To be admissible under Rule 801(d)(2)(E), the party offering the testimony must prove by a preponderance of the evidence “that there was a conspiracy involving the declarant and the nonoffering party, and that the statement was made ‘in the course of and in furtherance of the conspiracy.’ ” Bourjaily v. United States, — U.S. -, 107 S.Ct. 2775, 2778, 97 L.Ed.2d 144 (1987). In making its eviden-tiary assessment, the district court may look both to the alleged hearsay statement itself and to independent outside evidence. Id. 107 S.Ct. at 2781-82; United States v. Chestang, 849 F.2d 528, 531 (11th Cir.1988), Alexander, 850 F.2d at 1505.

Based on the record before us, we conclude that the district court did not err in admitting the testimony about the phone call as a statement of a coconspirator made in furtherance of the conspiracy. There was independent evidence of a conspiracy and of Trepte’s participation in it. Trepte testified that he met with Paxson the night before he received the phone call and they agreed that he would go along with the proposed bidrig if Paxson and Ewalt could reach some sort of agreement later that evening. When Trepte left the meeting with Paxson that evening, he testified that he was told he “would get a phone call to let [him] know whether they had come to terms.” R. 9-188. There also is evidence that Trepte’s employer, Fischbach & Moore, did in fact participate in the bid-rigging scheme by raising its Snapfinger bid by $500,000. This is sufficient to establish the conspiracy without reference to the phone call. In other words, the fact that Trepte agreed to rig the bids if Ewalt also so agreed and the fact that Trepte later actually rigged Fischbach & Moore’s bid after he received the phone call establishes a conspiracy. The substance of the telephone call simply bolsters this conclusion.

With respect to the relative anonymity of the caller, although Trepte did not know precisely who it was that called him, it is clear from the testimony and the context that the caller was associated either with Dynalectric or Paxson Electric. Similarly, it is clear from the context and Trepte’s testimony that the call was made in furtherance of the conspiracy. We therefore conclude that the evidence of the phone call was properly admitted.

3. Juror’s Introduction of Extrinsic Evidence

During an overnight recess in the jury’s deliberations, one of the jurors reviewed notes she had taken during a health law class, jotted down three phrases from these notes on a bookmark, and took the bookmark and read these phrases to her fellow jurors the following morning. The phrases, which the juror informed her fellow jurors were “principles of the jury process,” were:

(1) Innocent until proven guilty; (2) All evidence and testimony is presumed truthful until proven otherwise; and (3) In dealing with conflicting evidence merely decide which has the greatest probability of being true or simply, what is the most reasonable and sensible.

Shortly thereafter, pursuant to a request made just before court had recessed the preceding day, the jury was reinstructed on the proper consideration of circumstantial evidence. Later that day the jury returned its verdicts.

Upon learning that the juror had brought her notes into the jury room, the district judge held an evidentiary hearing during which she questioned each juror about the incident. Based on the jurors’ responses and the substance of the alleged extrinsic evidence, Judge Evans concluded that the juror’s conduct had not created a reasonable possibility of prejudice.

Although defendants correctly state that a jury’s verdict cannot stand if there is a reasonable possibility that the verdict was prejudiced by the introduction of improper extrinsic evidence, see United States v. Perkins, 748 F.2d 1519, 1533 (11th Cir.1984), we agree with the district court that the juror’s notes on her bookmark did not create a reasonable probability of prejudice. We assume, arguendo, that the notes the juror brought into the jury room during deliberations constituted improper extrinsic evidence and that all members of the jury heard and remembered her comments. We conclude, however, that the substance of the notes was not dramatically different from what the judge actually charged the jury. Thus, we conclude that the district court correctly held that the jury’s decision was not tainted by improper extrinsic evidence.

III. CONCLUSION

In summary, we conclude that the district court correctly held that the indictment, filed on September 19, 1986, was brought within the five-year statute of limitations for criminal antitrust actions. We also affirm the mail fraud convictions. The jury instructions and the indictment were such that the jury could not have convicted the defendant solely on a theory of the McNally-type intangible rights. There also was sufficient evidence to support the mail fraud convictions. Also, the jury was properly instructed that the scheme to defraud did not have to succeed in order to convict defendants of mail fraud. We also conclude that the district court did not err in admitting the 404(b) evidence or the testimony about the anonymous phone call, nor was the jury tainted by extrinsic evidence. Finally, no improper use was made of Wesley Paxson’s immunized grand jury testimony.

For the foregoing reasons, the judgment of the district court is

AFFIRMED. 
      
      . Fischbach & Moore was named in the same indictment as the defendants but opted to enter a guilty plea prior to trial.
     
      
      . See note 28, infra.
      
     
      
      . The subcontract actually was awarded to CCC Electric Co., a minority business enterprise (“MBE”) in which Paxson Electric had a 49% ownership interest. However, all the bid preparation work and the submission of the bids was handled by Paxson Electric. Hyman, the general contractor, required the use of an MBE to meet the requirements of the EPA and Dekalb County, who paid for the Snapfinger construction. For convenience in this opinion, we shall refer to Paxson Electric as the company which was awarded the subcontract.
     
      
      . 18 U.S.C. § 3282 provides that:
      Except as otherwise expressly provided by law, no person shall be prosecuted, tried, or punished for any offense, not capital, unless the indictment is found or the information is instituted within five years next after such offense shall have been committed.
     
      
      . This case was decided prior to the close of business on September 30, 1981, and is binding precedent under Bonner v. City of Prichard, 661 F.2d 1206, 1209 (11th Cir.1981).
     
      
      . The appellants contend that the charges raised in the indictment and the evidence presented at trial are irrelevant to a determination of when a Sherman Act conspiracy is completed for purposes of the statute of limitations. They contend that the extent of an antitrust conspiracy is strictly a matter of statutory interpretation of § 1 of the Sherman Act. Section 1 prohibits "every contract, combination, ... or conspiracy, in restraint of trade or commerce.”
      We agree that to determine when the limitations period begins to run, it is necessary to interpret the statute which allegedly was violated. However, the purpose of this exercise is to determine whether the conspiracy offense requires an overt act. If an overt act is necessary, then the indictment must charge and the evidence at trial must show that an overt act in furtherance of the conspiracy was made in the limitation period. If an overt act is not required, then the indictment suffices if it charges that the conspiracy continued into the limitations period. As this court explained in United States v. Coia, 719 F.2d 1120, 1124 (11th Cir.1983), cert. denied, 466 U.S. 973, 104 S.Ct. 2349, 80 L.Ed.2d 822 (1984):
      [A] conspiracy requiring an overt act is deemed complete for the statute of limitations purposes at the time of completion of the last overt act. This is a rule of statutory construction, rather than a factual determination of whether a conspiracy existed at a particular point in time. With respect to conspiracy statutes that do not require proof of an overt act, the indictment satisfies the requirements of the statute of limitations if the conspiracy is alleged to have continued into the limitations period. The conspiracy may be deemed to continue as long as its purposes have neither been abandoned nor accomplished.
      We note that an overt act is not required for a § 1 Sherman Act conspiracy violation. United States v. A-A-A Electrical Co., 788 F.2d 242, 245 (4th Cir.1986). The instant indictment clearly charged and the evidence presented at trial showed that the receipt of payments under the contract and the sharing of these payments pursuant to the joint venture agreement were objectives of the conspiracy and that the appellants pursued at least some of these objectives until January 1985. Thus, the indictment sets forth a conspiracy that was completed well within the limitations period. Even assuming arguendo that an antitrust conspiracy requires overt acts, the payments and payoffs would constitute overt acts made in furtherance of the conspiracy within the limitations period.
     
      
      .Paragraph 18 of the indictment charged:
      18. The aforesaid combination and conspiracy consisted of a continuing agreement, understanding and concert of action among the defendants and coconspirators, the substantial terms of which were that:
      (a) defendant Paxson Electric would submit the lowest bid to Hyman and other general contractors for the electrical construction portion of the Snapfinger Creek project;
      (b) the defendant companies would submit collusive, artificially high and rigged bids to Hyman and other general contractors for the electrical construction portion of the Snap-finger Creek project;
      (c) in return for defendant Fischbach and Moore’s participation in the conspiracy, defendant Paxson Electric would forgive a preexisting debt of $89,330.06; and
      (d) in return for defendant Dynalectric’s participation in the conspiracy, defendant Paxson Electric would form a silent joint venture with defendant Dynalectric pursuant to which defendant Dynalectric would receive 50 percent of the profits earned from the performance of the electrical construction portion of the Snapfinger Creek project.
     
      
      . Paragraph 17 of the indictment charged:
      17. Beginning in or about August 1979 and continuing thereafter until at least January 1985, the exact dates being unknown to the Grand Jury, the defendants and others, known and unknown, engaged in a combination and conspiracy in unreasonable restraint of the aforesaid interstate trade and commerce in violation of Title 15, United States Code, Section 1.
     
      
      . One of appellants’ arguments is that a continuing conspiracy to violate the Sherman Act does not exist unless there is a continuing substantive antitrust violation. In other words, appellants argue that to be a part of a continuing conspiracy, the payments themselves must be illegal acts, i.e., in restraint of trade. If the payments themselves are not in restraint of trade then appellants conclude that the conspiracy to restrain trade ends when the contract is awarded.
      We accept arguendo — but explicitly do not decide — appellants’ argument that the restraint of trade ended when the contract was awarded. However, we do not believe that the conspiracy is as narrowly circumscribed. The indictment clearly alleged that the appellants conspired and agreed to submit collusive bids on the Snapfinger project, to receive payments from Hyman pursuant to the contract, and to divide the pay-merits under the alleged joint venture agreement. The cases are clear that all acts which are part of an illegal conspiracy do not themselves have to be illegal.
      For example, in United States v. Helmich, 704 F.2d 547 (11th Cir.), cert. denied, 464 U.S. 939, 104 S.Ct. 353, 78 L.Ed.2d 317 (1983), the defendant was convicted of conspiracy to commit espionage. He transmitted classified information in 1964 to the Soviet Union and attempted to collect his compensation from the Soviets in 1980. He was indicted in 1981. Helmich argued that the indictment was barred by the five-year statute of limitations for criminal conspiracies because the transmittal of defense information was the only substantive crime under the espionage statute. He argued that getting paid for his efforts was not illegal, thus the 1980 collection attempt could not be the subject of a prosecution for conspiracy to commit espionage. Id. at 549. The court rejected this argument, explaining that "the legal as well as the illegal aspects of an agreement are all part of a conspiracy to commit an illegal act for statute of limitations purposes." Id.; see abo United States v. Mennuti, 679 F.2d 1032, 1035-36 (2d Cir.1982) (Conspiracy to commit mail fraud continued until the conspirators received their payoffs, even though the payoffs themselves were not illegal under the mail fraud statute. Thus, the five-year statute of limitations was not violated when the substantive mail fraud offense was committed in December 1975, the payoff was received in July 1976, and the indictment was returned in February 1981.); United States v. Walker, 653 F.2d 1343, 1348-50 (9th Cir.1981), cert. denied, 455 U.S. 908, 102 S.Ct. 1253, 71 L.Ed.2d 446 (1982) (In a § 371 prosecution for conspiracy to defraud the government by bid rigging a timber sale, the conspiracy continued for statute of limitations purposes until the profits were received and divided among the conspirators, even though the contract was awarded outside the statute of limitations.); Koury v. United States, 217 F.2d 387, 388 (6th Cir.1954) ("A conspiracy is not ended by the illegal transportation of a stolen car when the fruits of the transportation are yet to be obtained and divided by the conspirators.”); United States v. Xheka, 704 F.2d 974, 987 (7th Cir.), cert. denied, 464 U.S. 993, 104 S.Ct. 486, 78 L.Ed.2d 682 (1983) (18 U.S.C. § 371 conspiracy to destroy building with explosives continued after the building was destroyed until conspirators either received the economic benefits (insurance proceeds) that motivated the crime or abandoned their claim).
      The Helmich court distinguished Grünewald on the same basis as we do in this opinion: the concealment efforts in Grünewald were not an objective of the conspiratorial agreement, whereas the compensation Helmich received from the Soviets clearly was part of a conspiratorial agreement to commit espionage, even though the payments were not received until sixteen years after he actually spied for the Soviets. Analogously in this case, even if we assume that the contract payments and the payments made pursuant to the joint venture agreement were not in restraint of trade, they clearly were objectives of the conspiracy to restrain trade. Thus, the statute of limitations did not begin to run until these objectives were achieved or abandoned.
     
      
      . 15 U.S.C. § 15b provides in pertinent part:
      Any action to enforce any cause of action under sections 15, 15a or 15c of this title shall be forever barred unless commenced within four years after the cause of action accrued ....
     
      
      . 18 U.S.C. § 1341 provides in pertinent part:
      Whoever, having devised or intending to devise any scheme or artifice to defraud, or for obtaining money or property by means of false or fraudulent pretenses, representations, or promises, ... for the purpose of executing such scheme or artifice or attempting so to do ... [uses the mails or causes them to be used,] shall be fined ... or imprisoned ... or both.
     
      
      . In our discussion of the applicability of the mail fraud statute to schemes to defraud various types of rights (i.e., monetary or non-monetary, property or non-property, tangible or intangible), we recognize that in all cases the government also must prove an appropriate use of the mails to obtain a conviction under the mail fraud statute.
     
      
      . See United States v. Alexander, 850 F.2d 1500, 1503 (11th Cir.1988) (jury was instructed that the alleged fraudulent scheme had three objectives, one of which was ‘"to fraudulently deprive the citizens of a county of their right to have the county's business conducted honestly ..” and that to convict the defendants of mail fraud, " ‘you [the jury] need only to find that the scheme sought to achieve only one of these objectives_’ ” (quoting the jury instructions)); United States v. Conover, 845 F.2d 266, 268-71 (11th Cir.1988) (In the context of a kickback scheme, mail fraud convictions were reversed where the indictment did not charge nor did the instructions require the jury to find that the defendants schemed to defraud the victim of money or property.); United States v. Italiano, 837 F.2d 1480, 1487 (11th Cir.1988) (mail fraud conviction vacated where the indictment failed to allege a scheme to defraud the victim of money or property and where “the jury instructions served only to exacerbate, rather than ameliorate, the infirmities which permeated the indictment.”); United States v. Covino, 837 F.2d 65, 71-72 (2d Cir.1988) (government’s theory of mail fraud, as alleged in the indictment and charged to the jury, was that the defendant employee breached a fiduciary duty to his employer by accepting kickbacks and by failing to inform the employer of the kickbacks. The court reversed the convictions, explaining that "the indictment and charge in the instant matter neither alleged nor asked the jury to find that [the victim] was defrauded of money or property.”); United States v. Baldinger, 838 F.2d 176 (6th Cir.1988) (where defendant challenged his mail fraud conviction solely on the sufficiency of the indictment, the court found a McNally violation where the indictment alleged solely that the defendant devised a scheme to defraud the victims of "their right to conduct business free of false, fictitious and fraudulent informa-tion_”); United States v. Holzer, 840 F.2d 1343, 1345-46 (7th Cir.) (conviction reversed where indictment alleged defendant judge’s receipt of bribes from lawyers appearing before him was a scheme to defraud Illinois and its citizens of "the right to the administration of justice by an honest judge” and the jury was instructed that it needed to find a plan to deprive the victims of something of value and that ”[t]he thing of value that the Government says was lost here is what the lawyers call intangible rights.”), cert. denied, — U.S. -, 108 S.Ct. 2022, 100 L.Ed.2d 608 (1988); Ingber v. Enzor, 841 F.2d 450 (2d Cir.1988) (conviction overturned where jury was charged on the alternative grounds that defendants devised a scheme to defraud the victims of money or property or to defraud them of their right to a fair and free election); United States v. Murphy, 836 F.2d 248, 250-54 (6th Cir.1988) (although the jury was instructed that it could convict the defendants of mail fraud if they concluded that the defendants devised a scheme to defraud the victims of money, the convictions were reversed because the jury instructions improperly broadened the allegations of the indictment, which only alleged a scheme to defraud the victims of McNally-type intangible rights); United States v. Ochs, 842 F.2d 515 (1st Cir.1988) (Although the indictment alleged that the defendants schemed to defraud the victims of both tangible and intangible rights, the conviction was reversed because the jury was explicitly instructed that " “You do not have to find that the City actually lost money because of this scheme. It is sufficient if you find that the scheme did defraud or deprive the public of an intangible or political or civil right, such as the right to honest government_’”); United States v. Shelton, 848 F.2d 1485 (10th Cir.1988) (en banc) (convictions reversed either because the indictment expressly charged only a violation of McNally-type intangible rights or, where the indictment charged a deprivation of both tangible and McNally-type intangible rights, the instructions did not require the jury to base a guilty verdict in whole or in part on the tangible rights theory); United States v. Stack, 853 F.2d 436 (6th Cir.1988) (although indictment charged a scheme to defraud victim of "‘right to have business conducted honestly ... and to obtain money by ... false and fraudulent pretenses mail fraud convictions were reversed because jury was instructed that " ‘[a]ny actions designed to deprive an employer of his right to have his business conducted honestly ... may constitute a fraud within the meaning of the mail fraud statute and thus could have convicted defendants solely on a McNally-type intangible rights theory, (emphasis added)).
     
      
      . See United States v. Eckhardt, 843 F.2d 989 (7th Cir.1988); United States v. Fagan, 821 F.2d 1002 (5th Cir.1987), cert. denied, — U.S. -, 108 S.Ct. 697, 98 L.Ed.2d 649 (1988); New York v. Hendrickson Brothers, Inc., 840 F.2d 1065, 1082 (2d Cir.1988) (holding in bid rigging context that mail fraud conviction withstood McNally); United States v. Horton, 847 F.2d 313 (6th Cir.1988); United States v. Lance, 848 F.2d 1497 (10th Cir.1988) (en banc); United States v. Perholtz, 836 F.2d 554 (D.C.Cir.1987); United States v. Piccolo, 835 F.2d 517 (3d Cir.1987); United States v. Richerson, 833 F.2d 1147 (5th Cir.1987); United States v. Runnels, 833 F.2d 1183 (6th Cir.1987); United States v. Wellman, 830 F.2d 1453 (7th Cir.1987); United States v. Asher, 854 F.2d 1483 (3d Cir.1988).
     
      
      . Because we hold that this jury must have found that the defendants schemed to defraud the EPA and Dekalb County of money, we explicitly do not decide whether the intangible right to free and open competition is a McNally-type intangible right. We also do not reach the question of whether the intangible right to open competition is "inextricably intertwined” with tangible monetary interests and therefore outside the scope of McNally. See, e.g., United States v. Lance, 848 F.2d 1497, 1501 (10th Cir.1988) (en banc) (where the government presented adequate evidence of "split deal” scheme in which the defendant billed his employer for nonexistent purchases and pocketed the payment, the court concluded that the alleged deprivation of the employer’s intangible right to good government was “inextricably intertwined” with a tangible monetary loss and affirmed mail fraud conviction); United States v. Wellman, 830 F.2d 1453, 1463 (7th Cir.1987) (court looked to "the nature of the scheme,” as established by the proof presented at trial, to determine if there was a McNally violation); United States v. Washita Construction Co., 789 F.2d 809, 818 (10th Cir.1986) (in pre-McNally mail fraud case involving bid-rigging, the Tenth Circuit concluded that a collusive bidding scheme was the valid basis for a mail fraud conviction because it “deprived taxpayers of the monetary advantage of competitive bidding_”).
     
      
      . Our conclusion comports with the result in State of New York v. Hendrickson Bros., Inc., 840 F.2d 1065 (2d Cir.1988), which is the only case we are aware of in which a court addressed a McNally challenge to a mail fraud conviction. In Hendrickson Bros., the Second Circuit concluded that McNally was not pertinent to mail fraud convictions stemming from bid-rigging scheme because "the indictments alleged that the scheme was to defraud the agencies, not to corrupt them, and the jury was instructed accordingly.” Id. at 1082.
     
      
      . The indictment further charged that:
      25. On or about the dates of mailing set forth below, for the purpose of executing and carrying out the scheme and artifice to defraud, and attempting to do so, the defendants and others did knowingly cause the two checks listed below to be delivered by mail by the United States Postal Service according to the directions thereon, to an address within the Northern District of Georgia, each such use of the mails constituting a separate count of this indictment and a separate violation of Title 18, United States Code, Section 1341....
      The two mailings which were the basis for the two mail fraud counts were payments mailed from Hyman, the general contractor, to CCC Electric Co., the MBE subcontractor affiliated with Paxson in response to bids mailed from CCC Electric Co. to Hyman. The payments were mailed on May 24, 1984, and January 24, 1985.
     
      
      . The defendants do not challenge the sufficiency of the evidence which establishes the existence of the fraudulent scheme and our independent review of the record confirms that there was ample evidence that the defendants rigged the bids on the electrical contracting portion of the Snapfinger Creek project.
     
      
      . The defendants also argue that the trial court erred in excluding economic evidence of instability in the economy and in various raw materials markets at the time the bids were submitted. The defendants offered this evidence as relevant to explain the seemingly high prices and profits on the Snapfinger subcontract. Defendants argued that because of the volatile economic environment, the bids had to be higher to account for potential price rises and that the profits turned out to be relatively high because the anticipated price fluctuations for raw materials did not occur to the extent provided for in the bid prices.
      Judge Evans excluded the evidence because there was no evidence that any of the people who actually prepared the bid relied on the purported volatility in assimilating the bid price. After a review of the record, we conclude that Judge Evans was well within the broad discretionary bounds given to trial judges on evidentiary matters.
      In United States v. Goodman, 850 F.2d 1473 (11th Cir.1988), decided after oral arguments were heard in this case, the Eleventh Circuit held that where the government introduced evidence of anti-competitively high prices to prove the existence of a criminal antitrust conspiracy, the district court’s exclusion of defendant’s evidence that the prices were reasonable was reversible error. Goodman is distinguishable from this case for three reasons.
      
        First, Judge Evans made it clear throughout the trial that she would not allow the government to prove the existence of an antitrust conspiracy with evidence that the Snapfinger bid prices and profits were unreasonably high. Judge Evans conducted the trial on the correct assumption that because collusive bidding is a per se antitrust violation, proof of unreasonably high prices or profits was not necessary to convict defendants of conspiracy to violate the antitrust laws. Thus, in contrast to Goodman, Judge Evans did not allow the government to prove the requisite agreement to restrain trade through evidence of unreasonably high prices or profits. Rather, she limited the government to presenting direct evidence of the agreement (e.g., the evidence of the meeting between the defendants the evening before the bids were submitted and the resultant phone call to Trepte the following morning). Cf. Goodman, 850 F.2d at 1478 ("Although pricing is not an actual element of customer allocation, ... once the government used that evidence in attempting to prove the existence of the customer allocation agreement, the door was open for the appellants to rebut the same.”).
      Second, even if Judge Evans had allowed the government to argue the existence of the conspiracy from evidence that the profits and prices were unreasonably high, it was not error to exclude the defendants’ proffered economic evidence because this evidence did not explain why the Snapfinger prices and profits were seemingly high. For example, in Goodman, the defendants wanted to introduce evidence that their business costs increased to explain why they charged their customers more; they also wanted to introduce evidence of their competitors’ profit and loss statements to show that the competitors’ prices, although lower than the defendant’s prices, were not commercially reasonable because they were below cost. In the first instance, evidence of actual higher operating costs would be a legitimate explanation of why the defendant raised the price they charged their customers. In the second instance, evidence that the competitors’ prices were unreasonably low would tend to show that the defendant’s prices, although higher, were not commercially unreasonable.
      In this case, however, the defendants did not seek to explain their prices and profits by offering evidence that the actual raw material prices used to carry out the Snapfinger contract actually increased and that these prices were passed onto their customers. Instead, they attempted to use expert evidence of the alleged volatility in the raw material markets to support an argument that their bid prices reflected anticipated jumps in the cost of necessary materials and that the profits were relatively high because the materials prices in fact were not as volatile as expected when the bids were prepared. As explained above, the proffered evidence is irrelevant absent evidence that defendants actually relied on this information in preparing their bids. Because the defendants failed to prove that they relied on alleged volatility in making their bids, the proffered evidence was properly excluded, even if the government had been allowed to argue that the high prices and profits evidenced a conspiracy.
      Third, the type of evidence defendants sought to introduce in this case was very different from the evidence excluded in Goodman. In Goodman, the trial court erroneously excluded the profit and loss statements of a competitor of the defendants. This evidence was directly related to the specific events and actors under scrutiny in the trial. In this case, however, the evidence was not connected to any of the actual events in the case.
     
      
      . The defendants’ reliance on Illinois Brick Co. v. Illinois, 431 U.S. 720, 97 S.Ct. 2061, 52 L.Ed.2d 707 (1977), is misplaced. The defendants assert that Illinois Brick precludes use of the pass-on theory where cost-plus contracts are not involved. The issue addressed by the Supreme Court in Illinois Brick was whether indirect purchasers of a product which the direct purchaser bought pursuant to rigged bids could collect actual and treble damages from the collusive bidders in a civil antitrust case. The court declined to allow the indirect purchasers to collect the damages, citing the difficulties inherent in proving the precise amount of overcharge passed on from the direct purchasers to the indirect purchasers. However, the Court did not hold nor imply that the absence of a cost-plus contract precludes an inference that some portion of the overcharge was passed along. Moreover, because our case does not require a calculation of actual damages, Illinois Brick is not controlling.
     
      
      . Judge Evans instructed the jury that “[i]t is not necessary that the government prove all of the details alleged in the indictment concerning the precise nature or purpose of the scheme or that the material mailed was itself false or fraudulent, or that the alleged scheme actually succeeded in defrauding anyone_” R 24-3327.
     
      
      . We note that there are several post -McNally cases whose language might be interpreted to require proof of actual loss (i.e., proof that the scheme to defraud actually succeeded) to support a mail fraud conviction. See, e.g., United States v. Evans, 844 F.2d 36, 39 (2d Cir.1988) (“If a scheme to defraud must involve the deceptive obtaining of property, the conclusion seems logical that the deceived party must lose some money or property.”); United States v. Runnels, 833 F.2d 1183, 1185 (6th Cir.1987) ("Decisions permitting convictions despite the absence of economic loss still required that the defendant deprive the victim of some economic benefit.”). This circuit’s decision in United States v. Conover, 845 F.2d 266 (11th Cir.1988) has ambiguous language which similarly might be interpreted as requiring that the scheme to defraud must succeed. See Conover, 845 F.2d at 271 ("On the basis of McNally, it is inferable that to sustain the convictions in this case, the Government would have to offer proof and the jury would have to be instructed that [the victim] would have paid less_”).
      However, neither Conover nor any of the other cases cited above address the distinction between a successful and an unsuccessful scheme to defraud the victim of money or property. These cases do not address the issue of whether a mail fraud conviction can stand where there is sufficient evidence that the defendants schemed and intended to defraud the victims of money or property, but failed to cause the victims any actual loss. Thus none of these cases are apposite.
     
      
      . Paxson was granted immunity pursuant to 18 U.S.C. § 6002.
     
      
      . See Record on Appeal, vol. 2-26 (Paxson’s Motion to Dismiss); 2-40 (Government’s Opposition to Motion to Dismiss); 3-55 (Paxson's Reply to Government’s Opposition to Motion to Dismiss); 3-59-22-33 (Magistrate’s Report and Recommendation); 3-61 (Paxson’s Objections to Magistrate's Report and Recommendation); 3-64-5-9 (Government’s Opposition to Paxson’s Objections to Magistrate’s Report and Recommendation); 3-74-7-10 (District Court Order Denying Motion to Dismiss on Kastigar Grounds); 6-152 (Paxson’s Renewed Motion to Dismiss); 6-158 (Government's Answer to Motion to Dismiss); 7-164 (Paxson’s Reply to Government’s Opposition); 7-174-28-33 (District Court Memorandum Opinion Denying Motion to Dismiss).
     
      
      .The pre-trial in camera examination of grand jury materials was proper. See Byrd, 765 F.2d at 1532-34.
     
      
      . In Byrd, we issued a strong warning that it is "unwise” to permit an attorney who is familiar with the immunized testimony to participate in the prosecution. Nevertheless, in Caporale, we rejected a Kastigar claim on facts very similar to the instant case. Although the prosecutor in Caporale had read the immunized testimony, the government, as in this case, met its burden of showing an independent source for each piece of evidence. Also like this case, the prior immunized testimony was self-serving and of no real value in the subsequent investigation.
     
      
      . To establish legitimate independent sources, the government had to show that all evidence presented to the grand jury and at trial either was in the possession of the government prior to Paxson’s immunized grand jury appearance or was derived from a source independent of Paxson’s testimony (i.e., that Paxson’s testimony provided neither new direct evidence nor investigatory leads). United States v. Byrd, 765 F.2d 1524, 1531 (11th Cir.1985).
     
      
      .In Caporale, the court noted that “the chief government prosecutor went so far as to state that he believed that [the defendant’s] earlier testimony was untruthful.” 806 F.2d at 1519 n. 34. Evidence of the self-serving nature of Paxson’s immunized testimony is even stronger in this case. Paxson was convicted of perjury and obstruction of justice for his immunized grand jury testimony by the District Court for the District of Columbia. The conviction currently is on appeal to the D.C. Circuit.
     
      
      . In a post-trial motion, Paxson requested alternative remedies of dismissing the indictment on a judgment of acquittal because of a Kastigar violation or, at a minimum, an evidentiary hearing on his Kastigar motion. R. 6-152-22.
     
      
      . See United States v. Bi-Co Pavers, Inc., 741 F.2d 730, 737 (5th Cir.1984) (In a criminal antitrust prosecution of bidrigging, 404(b) evidence of defendant’s other attempts to rig bids is admissible because it is "clearly relevant to show that [defendant] acted with the intent to rig bids (rather than to enter into a joint venture)_”).
     
      
      . Because we conclude that the defendants’ offer to stipulate was inadequate, we do not reach the issue of whether an adequate offer to stipulate to intent that is not agreed to by the government is sufficient to prevent 404(b) evidence relevant to intent from being admitted. See United States v. Williford, 764 F.2d 1493, 1498 (11th Cir.1985).
      The defendants’ other 404(b) arguments are without merit and warrant no discussion.
     
      
      . All other issues raised by defendants on appeal are without merit and warrant no discussion.
     