Anthony Slaughter and Roy. Leonard were tried before a jury and convicted of conspiracy, to commit wire fraud and wire fraud in August, 1996. They appeal their convictions. We affirm the judgment of the district court.1
I.
On June 3, 1996, a federal grand jury returned an 11-count indictment charging Slaughter, Leonard, and Willie Stafford with conspiracy to commit wire fraud and wire fraud. See 18 U.S.C. §§ -371 and 1343. -The indictment charged Slaughter, Leonard, and Stafford2 with conspiring with others to defraud their employer, Ford Motor Company, by submitting' fraudulent overtime claims. According to the indictment, Howard McDaniels, a superintendent at the Ford plant in Claycomo, Missouri, submitted fraudulent overtime claims on behalf of Slaughter, Leonard, and others.
Trial commenced August 12, 1996. McDaniels, who pleaded guilty to an earlier indictmént concerning the same fraudulent scheme, testified at Slaughter’s and Leonard’s trial. According to McDaniels, he initiated the scheme in early 1993. He approached Ford employees and offered to adjust their overtime hours in return for cash kickbacks. As a Ford superintendent, McDaniels could enter the company’s computer system and adjust employee hours throughout the Ford plant." Using this scheme, false payroll information was transmitted by interstate wire from the Claycomo plant to Ford’s headquarters in Dear-born, Michigan. After a period of time, McDaniels asked Herman Moore, another Ford employee, to provide names and social security numbers of other' employees who would participate in the scheme. Moore did so, collecting kickbacks from the employees he recruited and giving the money to McDaniels.
McDaniels testified to entering fraudulent overtime for both Slaughter and Leonard. McDaniels stated he dealt directly with Leonard, while Moore recruited Slaughter. Evidence showed, that. Slaughter • knew McDaniels was inputting the false overtime claims. McDaniels testified Slaughter told him he knew McDaniels was putting money on his check, but “he wouldn’t tell on the scheme.”
During the trial, the government learned McDaniels had perjured himself. McDaniels falsely denied entering fraudulent overtime for two additional Ford employees. After discovering his false testimony, the government recalled McDaniels, who admitted his perjury. Defense counsel were then permitted to reopen McDaniels’ cross-examination.
Moore also testified at trial. He related how he recruited Slaughter to participate in the overtime scheme. Other witnesses corroborated Slaughter’s involvement. Ronald Sheppard, a Ford employee who participated in the overtime scheme, testified that Slaughter asked him about getting paid for overtime he had not worked. John Cartwright, another Ford employee- involved in the scheme, testified he asked Moore who else was participating. Moore gave him a number of names, including Slaughter’s.
In January, 1994, Ford began investigating the scheme. Investigator Scott Laing interviewed Slaughter on February 9 or 10, 1994, and interviewed Leonard on February 10, 1994. Slaughter told Laing he noticed receiving too much money on one check, but stated he reported this to his union committeeman. Slaughter also told Laing he had worked one weekend for .which he received overtime pay, but he denied having received overtime pay for another weekend when Ford’s records showed he received extra compensation. Leonard told Laing he had worked the weekends for which he received overtime pay.
Slaughter and Leonard both: testified at trial. Slaughter said he did not notice having been paid overtime for any week but one, and stated he reported , that overpayment to his union committeeman. Leonard stated he had also noticed receiving overtime pay for *627one weekend, but did not realize he received overtime pay for any other period.
During jury deliberations, the jury sent the court a question concerning the conspiracy instruction. Thé jury had been instructed that to find defendants guilty of conspiracy, it needed to find:
FIRST, that ... two or more persons reached an agreement or came to an understanding to commit wire fraud ...; SECOND, that [defendants] knowingly and intentionally joined in the agreement or understanding to commit wire fraud
THIRD, that at the time [defendants] joined in the agreement or understanding, [they] knew that the purpose of the agreement or understanding was to submit false overtime information with.the intent that Ford pay for the false overtime; and
FOURTH, that while the agreement or understanding was in effect, a person or persons may have joined the agreement and knowingly caused the false payroll information to be transmitted from the Ford plant at Clayeomo to Ford headquarters in Dearborn, Michigan.
The jury asked whether defendants, to be found guilty of conspiracy, needed to know that the falsified data was transmitted to Michigan by wire. The jury further asked whether defendants also needed to know that the scheme violated federal law.
The court responded to the jury’s questions by submitting a new instruction, which stated:
FIRST, that ... two or more persons reached an agreement or came to an understanding to submit false overtime information to Ford with the intent that Ford pay for the false overtime ...;
SECOND, that [defendants] knowingly and intentionally joined in the agreement or understanding to submit false overtime information to Ford with the intent that Ford pay for the false overtime information ...;
THIRD, that at the time [defendants] joined in the agreement or understanding, [they] knew that the purpose of the agreement or understanding was to submit false overtime information with the intent that Ford pay for the false overtime;
FOURTH, in order to carry out the agreement or understanding, it is reasonably foreseeable by someone participating in the agreement that the false payroll information would be transmitted by electronic transmission from the Ford plant in Clayeomo to Ford headquarters in Dearborn, Michigan ...; and
FIFTH, that interstate wire communications were used in transmitting the false overtime information to Ford Motor Company to Dearborn, Michigan.
Defense counsel objected to the new instruction and suggested they would need to reargue the case to address the instruction, but made no formal motion for reargument.
On August 22, 1996, the jury returned its verdict, finding Slaughter guilty of three of four wire fraud counts and conspiracy to commit wire fraud. The jury found Leonard guilty of six of seven wire fraud counts and conspiracy to commit wire fraud.
II.
A.
Slaughter appeals his conviction. He argues: (1) the evidence was insufficient to support the jury’s verdict; (2) the court erred in submitting the amended conspiracy instruction; and (3) the indictment should have been dismissed for failure to plead materiality.
1.
Evidence is sufficient to .sustain a conviction if, when viewed in the light most favorable to the government, it offers substantial support for the verdict. Glasser v. United States, 315 U.S. 60, 80, 62 S.Ct. 457, 469, 86 L.Ed. 680 (1942); United States v. Mafin-Cifuentes, 866 F.2d 988, 992 (8th Cir. 1989). It is axiomatic that we do not “pass upon the credibility of witnesses or the weight to be given their testimony.” United States v. Witschner, 624 F.2d 840, 843 (8th Cir.1980) (citing Stanley v. Henderson, 597 F.2d 651, 653 (8th Cir.1979)).
*628Slaughter argues there was insufficient evidence from which to find he knowingly and intentionally participated in a scheme to defraud Ford Motor Company, or that he violated any known legal duty. , He points out that, because of his variable work schedule, his paychecks varied from week to week. Slaughter claims the only witnesses whose testimony tied him to the scheme were participants themselves. He challenges the credibility of these witnesses because they bargainéd with the government in exchange for their testimony. This argument was initially directed to the jury, which rejected it at trial. We" decline to revisit the jury’s credibility determination.
To prove a conspiracy, the government must show that two or more people agreed to commit an offense, and that at least one conspirator acted to achieve the agreement’s illegal purpose. United States v. Hoelscher, 764 F.2d 491, 494 (8th Cir. 1985). The government must prove, beyond a reasonable doubt, that the defendant knew the essential object of the conspiracy. Henderson v. United States, 815 F.2d 1189, 1191-92 (8th Cir.1987). To prove wire fraud, the government must show the defendant voluntarily joined a scheme to defraud another out of money, that he did so with intent to defraud, that it was reasonably foreseeable interstate wire communications would be used, and that interstate wire communications weré used. United States v. Proffit, 49 F.3d 404, 406 n. 1 (8th Cir.1995); Atlas Pile Driving Co. v. DiCon Fin. Co., 886 F.2d 986, 991 (8th Cir.1989).
Here, McDaniels testified that Slaughter told him he could be trusted not to “tell on the scheme.” Moore testified he recruited Slaughter into the scheme. Other conspirators related conversations with Slaughter showing Slaughter’s knowledge of, and parr ticipation in, the scheme. Ford’s investigator told of Slaughter’s claim that he reported an overpayment to his union committeeman, Tom Lawrenson. Lawrenson, however, denied having any such conversation. This evidence, viewed in the light most favorable to the government, shows Slaughter’s knowledge of the scheme and its purpose, and his agreement to participate.
In reaching its verdict, the jury clearly credited the.testimony of the government’s witnesses. That some of these witnesses were members of the scheme does not undermine the verdict. Witschner, 624 F.2d at 843; see also United States v. Cunningham, 83 F.3d 218, 222 (8th Cir.1996). Certainly, whether a witness has a plea agreement with the government, and whether a witness will receive a sentence reduction in exchange for his testimony, is relevant in assessing the witness’s credibility. United States v. Roan Eagle, 867 F.2d 436, 443-44 (8th Cir.1989). The jury, however, is always the ultimate arbiter of a witness’s credibility, and this Court will not disturb the jury’s findings in this regard. Witschner, 624 F.2d at 843. As such, we reject Slaughter’s claim of insufficient evidence.
2.
Both Slaughter and Leonard challenge the district court’s amended conspiracy instruction. They claim the instruction constructively amended the indictment. In particular, they claim the instruction improperly converted the case into one of conspiracy to submit false information, while the indictment charged conspiracy to commit wire fraud. We disagree.
A jury Instruction constructively amends the indictment if the instruction “modif[ies] the essential elements of the offense charged so that a substantial likelihood exists that the defendant was convicted of an offense other than that charged in the indictment.” United States v. Johnson, 934 F.2d 936, 941 (8th Cir.1991). We find no such constructive amendment in this case, because the revised instruction did not modify the essential elements of the crime charged in the indictment.
The district court’s revised instruction required a finding that two or more people agreed' to submit false overtime information to Ford, intending that Ford pay money based on the false information. A finding that two or more people agreed to submit false. overtime information necessitates a finding that two or more people agreed to defraud Ford. The jury was told it must find *629defendants knowingly and intentionally joined this agreement, knowing its purpose. This requires a finding that defendants joined the agreement knowing its purpose was to defraud Ford. Finally, the instruction told the jury it must find this false information was transferred by interstate wire, and that the use of this communication method was reasonably foreseeable. We find the district court’s instruction fairly tracks the elements of the indictment’s charges of conspiracy to commit wire fraud.
Slaughter further argues the revised instruction misstates Eighth Circuit law, because it required the jury to find it reasonably foreseeable that interstate wire communications would be used to effectuate the conspiracy. Slaughter asserts the conspiracy must have contemplated the use of interstate wire. As we set out above, the government needed to show only that the use of interstate wire was reasonably foreseeable. See Proffit, 49 F.3d at 406 n. 1; Atlas Pile Driving Co., 886 F.2d at 991.
Slaughter also argues the district court denied reargument following the court’s reply to the jury, thus prejudicing his defense and violating Rule 30 of the Federal Rules of Criminal Procedure. His argument necessarily fails; as we have determined above, the instruction neither amended nor added a new element to the indictment’s charge. As such, reargument was not required. See United States v. Fontenot, 14 F.3d 1364, 1368 (9th Cir.1994) (“A supplemental instruction which merely clarifies an existing theory does not mandate additional arguments.”).
Finally, Slaughter argues the district court’s response to the jury was premature. We disagree. A district court is afforded broad discretion in responding to a jury’s requests for supplemental instruction. United States v. Felici, 54 F.3d 504, 507 (8th Cir.1995), cert. denied, — U.S. -, 116 S.Ct. 251, 133 L.Ed.2d 176 (1995). The district court’s reply fell well within its broad discretion. We find no error in the instruction or its timing.
’ 3.
Finally, Slaughter argues that the district court erred in denying his motion to dismiss the indictment for failure to plead materiality. This argument is without merit. We join our sister court.in the Tenth Circuit in finding that “materiality is not a separate essential element of wire fraud.” United States v. Daily, 921 F.2d 994, 1006 (10th Cir.1990); cf. United Healthcare Corp. v. American Trade Ins. Co., 88 F.3d 563, 571 n. 5 (8th Cir.1996) (“[I]t is well settled that ... a showing [of detrimental reliance] is not required to prove ... wire fraud.”). The district court correctly denied Slaughter’s motion to dismiss.
B.
Leonard also appeals his conviction. He argues: (1) the indictment alleged a single conspiracy, when the trial evidence proved multiple conspiracies; (2) the government knew, or should have known, McDaniels’ testimony was perjured; (3) the court erred in its reply to the jury’s question concerning the conspiracy instruction; and (4) cumulative errors at trial denied him his right to a fair trial and due process.
1.
Leonard contends the evidence at trial proved multiple conspiracies, rather than the single conspiracy with which he was charged. He argues this caused a variance and urges that the variance is fatal to the verdict. Leonard’s argument, however, is unavailing.
It is a question of fact for the jury whether the government has shown a single conspiracy or multiple conspiracies. United States v. Morales, 113 F.3d 116, 118-19 (8th Cir.1997); see also 2 Devitt, Blackmar and O’Malley, Federal Jury Practice and Instructions § 28.09, at 179-BO (4th ed.1990) (instruction on single or multiple conspiracies). Notably, neither defendant requested a multiple ' conspiracy instruction, nor . did they object to the initial conspiracy instruction. Under these circumstances, it is problematic whether this issue is properly before us. United States v. Merritt, 982 F.2d *630305, 306-07 (8th Cir.1992) (“This court will not consider an issue raised for the first time on appeal absent a showing of plain error resulting in a miscarriage of justice.”); see also Fed.R.Crim.P. 52(b). Here, we find there was no plain error because the evidence revealed only a single conspiracy.
A single conspiracy involves individuals “sharing common purposes or objectives under one general agreement.” Morales, 113 F.3d at 118-19 (quotations omitted). Thus, if the evidence shows “one overall agreement to commit an illegal act,” the evidence reveals a single conspiracy. Id. at 119 (quoting United States v. Regan; 940 F.2d 1134, 1135 (8th Cir.1991)). A jury may find ah overall agreement when the participants in the conspiracy share a common aim or purpose, and enjoy mutual dependence and assistance. Id.
If the indictment charges a single conspiracy, but the evidence shows multiple conspiracies, a variance exists. Id. To determine whether a variance exists, “we consider the totality of the circumstances, including the nature of the activities, the location and time frame in which the activities were performed, and the participants involved.” Id.
Viewing the evidence in the light most favorable to the verdict, we find this was a single, “hub and spokes” conspiracy. In such a conspiracy, “the hub constitutes] the central , figure,.- the spokes form[ ] its various branches and ramifications, and all [are] held together by the rim, which represents the agreement.” Hayes v. United States, 329 F.2d 209, 214 (8th Cir.1964) (quotations omitted). Here, McDaniels was the conspiracy’s hüb, and its spokes wére the employees who benéfitted' from the false overtime submissions, and thereafter divided their ill-gotten overtime payments with McDaniels or his agent, Moore.
Neither the law, nor logic, requires that all of the conspirators know each other or the full extent of the conspiracy’s reach. See id. at 213 (“To unite [conspirators] in a single conspiracy it is only necessary that the activities of each individual or group be directed toward accomplishing a single criminal objective.”) (quotations omitted). Indeed, a single conspiracy exists even where the members .of the conspiracy undertake to commit several crimes, so long as there is a single agreement. See id. (“If there is but one agreement, there is but one conspiracy.”).
Even adopting Leonard’s view that the evidence revealed multiple conspiracies, a view we decline to adopt, his argument fails. We need not reverse a conviction merely because of a variance. “Rather, we must reverse [for variance] only when a ‘spillover’ of evidence from one conspiracy to another has prejudiced a defendant’s substantial rights.” Morales, 113 F.3d at 119. Here, Leonard has not shown or argued any “spillover” occurred, nor have we found any which could have acted to his prejudice.
The government did not allege or attempt to show Leonard was connected to any other conspiracy. See id. No one suggested Leonard acted to further anyone’s interests beyond his own. The conspiratorial events were straightforward: McDaniels entered fraudulent overtime hours for a limited number of Ford employees. See United States v. Jones, 880 F.2d 55, 66 (8th Cir.1989) (“[T]his case did not involve so many conspirators and conspiracies that a jury could not be expected to give separate and individual consideration to the evidence against each defendant.”). The government presented sufficient evidence against Leonard to leave us no concern that the jury’s verdict was based on evidence of unrelated conspiracies.3 See Morales, 113 F.3d at 120. Accordingly, we reject Leonard’s variance claim.
2.
Leonard’s second argument, that he was prejudiced by McDaniels’ perjured testimony, is without merit. To prevail on this claim, Leonard must show the government used perjured testimony that it knew or should have known was perjured. United States v. Perkins, 94 F.3d 429, 432-33 (8th Cir.1996), cert. denied, — U.S. -, -117 *631S.Ct. 1004,136 L.Ed.2d 882 (1997). Leonard must further show a “reasonable likelihood” that the perjured testimony could have affected the jury’s judgment. Id.
Here, we need not even examine whether the government knew or should have known the testimony at issue was perjured, as we find no likelihood it could have affected the jury’s judgment. McDaniels’ testimony that he did not enter fraudulent overtime for two unindicted Ford employees had no bearing on whether he entered fraudulent overtime for Leonard, among others. On discovering the perjury, the government immediately and properly advised the court and defense counsel. McDaniels was recalled, admitted his falsehoods, and was subjected to cross-examination concerning his willingness to give false testimony under oath. The jury knew full well that. McDaniels had lied. We cannot fathom how Leonard could have been prejudiced by having the government’s star witness shown as a self-confessed perjurer. Accordingly, we reject this claim.
3.
Our discussion concerning the propriety of the revised conspiracy instruction disposes of Leonard’s claims in this regard. See supra § 11(A)(2).
4.
Finally, based on our prior determinations, we reject Leonard’s claim that cumulative errors denied him a fair trial or due process.
III.
The judgment of the district court is affirmed.