GEE, Circuit Judge:

Defendant Bi-Co Pavers, Inc. was found guilty of one count of bid rigging in violation of 15 U.S.C. § 1 and three counts of mail fraud in violation of 18 U.S.C. § 1342. On appeal, Bi-Co argues that: (1) various errors of the trial court confused the jury, thereby depriving Bi-Co of due process of law, (2) the trial court erred in denying Bi-Co's motion for a new trial based on newly discovered evidence, (3) the trial court erred in admitting extrinsic offense evidence, and (4) the evidence was insufficient to support the conviction on the bid rigging count. Finding no merit in these contentions, we affirm the judgment of the trial court.

I. Facts

At the time of the actions alleged in the indictment, Bi-Co was a highway construction firm operating in Texas. Charles Lattimore was Bi-Co's president and primary stockholder. His cousin, John Lattimore, was sole owner and president of Lattimore Materials, Inc., a company that supplied highway construction materials to general contractors.

In 1976, Charles and John Lattimore formed Lattimore Industries: 55% of Lattimore Industries' stock was owned by Lattimore Materials and 45% was owned by Stringtown Materials, a wholly-owned subsidiary of Bi-Co. Because Lattimore Industries did not meet the statutory requirements to bid on highway contracts offered by the state of Texas, the two cousins agreed that Lattimore Industries would bid in Bi-Co's name. Consequently, Jack Carroll, an officer and employee of Bi-Co experienced in the highway construction business, became a salaried employee of Lattimore Industries so that he could sign bids for Lattimore Industries on Bi-Co's behalf.

In June 1977, the Texas State Department of Highways and Transportation put up for bid a project to repair a portion of a highway in Lamar County, Texas. One week before the bid letting, John Lattimore telephoned Gerald Ricks, president of another highway contracting firm, and told Ricks that he might need a "complementary bid" — an intentionally high bid "designed to deceive state officials into believing that the project had been bid competitively." United States v. Young Brothers, Inc., 728 F.2d 682, 685 (5th Cir. 1984), petition for cert. filed, 53 U.S.L.W. 3021 (July 17, 1984). Lattimore then asked Ricks to make out a bid proposal on the project.

The day before the bid letting, John Lattimore told Ricks that he was not sure whether a third company, Ashland-Warren, would bid or not and consequently asked Ricks to submit the complementary bid. He also asked Ricks to contact representatives of Ashland-Warren and convince them not to bid on the job. Ricks refused to speak with the Ashland-Warren representatives, but reiterated his willingness to submit a complementary bid. John Lattimore then supplied Ricks with the prices to bid so that Ricks' bid would not be too low.

II. Due Process

Bi-Co contends that due to various errors of the trial court the jury may have based its guilty verdict on lawful conduct, thus denying Bi-Co due process of law. We discuss these asserted errors individually.

A. Verdict based on legal acts

Bi-Co argues that not all of the overt acts alleged in Count One of the indictment (bid rigging) are illegal and that the jury could have based its guilty verdict on one of the legal acts. Bi-Co notes that "a general verdict must be set aside if the jury was instructed that it could rely on any of two or more independent grounds, and one of those grounds is insufficient, because the verdict may have rested exclusively on the insufficient ground." Zant v. Stephens, 462 U.S. 862, 103 S.Ct. 2733, 2745, 77 L.Ed.2d 235 (1983).

Here, some of the overt acts listed in the indictment are not illegal per se. Overt acts in furtherance of a conspiracy, however, need not be illegal. United States v. Jones, 642 F.2d 909, 914 (5th Cir. 1981). The acts listed here were performed for the purpose of forming or effectuating a conspiracy in restraint of trade and consequently constitute a violation of the antitrust laws. American Tobacco Co. v. United States, 328 U.S. 781, 809, 66 S.Ct. 1125, 1138, 90 L.Ed. 1575 (1946). This indictment, therefore, did not permit the jury to base its conviction on insufficient grounds.

B. Vagueness of indictment

Bi-Co argues that the trial court erred in refusing to grant its motion to dismiss the indictment for vagueness. An indictment is not vague if it alleges that the defendant committed each of the essential elements of the crime charged with sufficient clarity to enable the accused to prepare his defense and to invoke the double jeopardy clause in any subsequent proceeding for the same offense. United States v. Crippen, 579 F.2d 340, 342 (5th Cir. 1978), cert. denied, 439 U.S. 1069, 99 S.Ct. 837, 59 L.Ed.2d 34 (1979).

The indictment here is not vague. Paragraph 11 charges that Bi-Co and its coconspirators engaged in a conspiracy violating Section 1 of the Sherman Act. Paragraph 12 states that the conspiracy consisted of an agreement to submit collusive, noncompetitive, and rigged bids to the Texas State Department of Highways on the Lamar County project. Paragraph 13 lists some of the overt acts performed by the conspirators in furtherance of the conspiracy. This indictment surely put Bi-Co on notice of the offense charged, enabling it to prepare its defense and invoke the double jeopardy clause in a subsequent proceeding. Bi-Co's right to due process was not violated here.

C. Failure to give joint venture instruction

Bi-Co contends that the trial court erred in failing to give its proposed instruction 17 stating that joint venture bidding on Texas state highway projects is legal and that discussions among contractors concerning joint ventures are not in themselves illegal under the antitrust laws.

We note first that counsel for Bi-Co did not object to the failure to give this instruction until after the jury began deliberating. Such an objection is not timely. Kanatser v. Chrysler Corp., 199 F.2d 610, 620 (10th Cir. 1952), cert. denied, 344 U.S. 921, 73 S.Ct. 388, 97 L.Ed. 710 (1953). Rule 30, Fed.R.Crim.P., clearly states that "[n]o party may assign as error any portion of the charge or omission therefrom unless he objects thereto before the jury retires to consider its verdict, stating distinctly the matter to which he objects and the grounds of his objection." (Emphasis added). Even so, we will consider the objection under Rule 52(b), Fed.R.Crim.P., if it constitutes plain error; that is, error "so obvious that our failure to notice it would seriously affect the fairness, integrity, or public reputation of [the] judicial proceedings and result in a miscarriage of justice." United States v. Howton, 688 F.2d 272, 278 (5th Cir. 1982).

Bi-Co has not demonstrated plain error. The trial court's refusal to give the requested instruction did not prevent Bi-Co from presenting its defense to the jury. In closing argument, Bi-Co's counsel asserted that Lattimore had merely intended to form a joint venture with Ricks. Then, arguing from the trial court's instruction that it is not unlawful for a bidder to learn from another bidder the amount he proposes to bid, counsel for Bi-Co explained to the jury that joint venture bidding is legal. Because defense counsel was able to focus the jury's attention through final argument on the correct legal standard for joint venture bidding, we cannot hold that failure to give a joint venture instruction seriously affected "the fairness, integrity, or public reputation" of these proceedings. See United States v. Amaral, 488 F.2d 1148, 1151 (9th Cir. 1973); United States v. Shelvy, 458 F.2d 823, 824 (D.C. Cir. 1972). We find no plain error here.

D. Jury confusion

During deliberations, the jury sent several notes to the trial judge asking for clarification on various issues of law. Bi-Co contends that this demonstrates jury confusion about what the evidence needed to show and, consequently, that the jury convicted Bi-Co of activities that were not illegal.

Here, the persistent questioning of the judge by the jury did not indicate juror confusion, but rather suggested that the jury was conscientiously pursuing its duty. Cf. United States v. Dono, 428 F.2d 204, 209 (2d Cir.), cert. denied sub nom. Bonaguro v. United States, 400 U.S. 829, 91 S.Ct. 57, 27 L.Ed.2d 59 (1970). Such questioning does not demonstrate a denial of due process.

III. Newly Discovered Evidence

Bi-Co alleges that the government failed to turn over to it a letter sent to the government by Peter Chantilis, Bi-Co's civil counsel. Bi-Co's criminal counsel was not informed of this letter until after the completion of the trial. Bi-Co thus argues that this letter constitutes newly discovered evidence warranting a new trial.

Chantilis wrote this letter in reference to an answer given in an affidavit submitted by Bi-Co's accountant to the grand jury on behalf of Bi-Co. The answer in the affidavit stated that John Lattimore was an employee of Bi-Co with responsibility for bidding state highway projects. Shortly after the affidavit was submitted, Chantilis called the government's counsel to explain that the answer was incorrect — that Lattimore was not an employee of Bi-Co. The letter at issue confirmed this phone conversation. The government did not turn over this letter to Bi-Co.

The district court denied Bi-Co's motion for a new trial based on newly discovered evidence. We reverse the denial of such a motion only when the following factors are shown:

(1) the evidence must be discovered following trial;

(2) the movant must show due diligence to discover the evidence,

(3) the evidence must not be merely cumulative or impeaching,

(4) the evidence must be material to the issues before the court, and

(5) the evidence must be of such a nature that a new trial would probably produce a new result.

United States v. Mesa, 660 F.2d 1070, 1077 (5th Cir. 1981).

Bi-Co has not demonstrated the existence of all five factors. First, due diligence would require that Bi-Co's criminal attorney investigate what was known by Chantilis, Bi-Co's civil attorney. Second, the letter was cumulative of other evidence: John Lattimore, Shaw Skinner and Charles Lattimore each testified that John Lattimore was not an officer or employee of Bi-Co. We therefore hold that the district court did not abuse its discretion in denying the motion for new trial.

Bi-Co also argues that the government's failure to provide a copy of the letter to its counsel violated the requirements of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). Brady requires that the government disclose material evidence favorable to the defendant; suppression of that evidence by the prosecution will result in a reversal of the conviction. United States v. Brown, 628 F.2d 471, 473 (5th Cir. 1980). The government is not obliged, however, to furnish a defendant with information he could have obtained with any reasonable diligence. United States v. Prior, 546 F.2d 1254, 1259 (5th Cir. 1977). As noted above, the letter here could have been obtained by Bi-Co with reasonable diligence, and, therefore, no Brady violation has occurred.

IV. Extrinsic Offense Evidence

The government introduced evidence at trial that John Lattimore had attempted to rig bids in Bi-Co's name on several other occasions and that Charles Lattimore and Jack Carroll tried to get competitors to refrain from bidding on a particular project. Bi-Co argues that this evidence is inadmissible under Rule 404(b), Fed.R.Evid., which states: "[e]vidence of other crimes, wrongs, or acts is not admissible to prove the character of a person in order to show that he acted in conformity therewith."

Extrinsic offense evidence is admissible if it is relevant to an issue other than defendant's character, and if its probative value is not substantially outweighed by its undue prejudice. United States v. Lemaire, 712 F.2d 944, 946 (5th Cir.), cert. denied, ___ U.S. ___, 104 S.Ct. 535, 78 L.Ed.2d 716 (1983). Here, the trial court instructed the jury to limit the use of this evidence to the issue of the state of mind or authority with which John Lattimore performed the acts charged in the indictment. The evidence was clearly relevant to show that Lattimore acted with the intent to rig bids (rather than to enter into a joint venture) and that he acted under Bi-Co's authority. The evidence was not used to prove Lattimore's or Bi-Co's character and is admissible.

Bi-Co also maintains that the government did not lay a factual predicate for the extrinsic acts. These extrinsic acts must be proven by "sufficient evidence for a jury to conclude that the defendant committed the extrinsic act[s]." Id. at 947. The undisputed testimony of John Lattimore and John McKinsey sufficiently demonstrates that Charles Lattimore and Jack Carroll attempted to rig a bid with McKinsey and that John Lattimore, on several occasions, rigged bids with Ricks.

V. Sufficiency of the Evidence

Bi-Co maintains that the evidence was insufficient to sustain its conviction for bidrigging. In determining the sufficiency of the evidence, we must view the evidence and all reasonable inferences which may be drawn from it in the light most favorable to the government. United States v. Shaw, 701 F.2d 367, 392 (5th Cir. 1983), cert. denied, ___ U.S. ___, 104 S.Ct. 1419, 79 L.Ed.2d 744 (1974). We reverse only if no rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.

Specifically, Bi-Co contends that the evidence does not sufficiently show that John Lattimore agreed to rig bids with Ricks. Ricks testified, however, that Lattimore asked him to turn in an intentionally high bid and supplied the prices for such a bid. The jury was entitled to credit this testimony. United States v. Mack, 695 F.2d 820, 822 (5th Cir. 1983). Ricks' testimony is not "so unbelievable on its face that it defies physical laws," id., and so we must accept the jury's credibility determination and find the evidence sufficient to show that Lattimore attempted to rig bids with Ricks.

Bi-Co also argues that the evidence does not show that John Lattimore had authority to bind Bi-Co. It is clear that a corporation is criminally liable for the unlawful acts of its agents, provided that such conduct is within the scope of the agent's authority, actual or apparent. United States v. Hilton Hotels Corp., 467 F.2d 1000, 1004-07 (9th Cir. 1972), cert. denied, 409 U.S. 1125, 93 S.Ct. 938, 35 L.Ed.2d 256 (1973); Continental Baking Co. v. United States, 281 F.2d 137, 149-51 (6th Cir. 1960). Apparent authority is the authority which outsiders would normally assume the agent to have, judging from his position with the company and the circumstances surrounding his past conduct. Continental Baking Co., 281 F.2d at 151.

The evidence here amply supports the jury's finding of apparent authority. Charles and John Lattimore both testified that Lattimore Industries bid for highway contracts in Bi-Co's name. John Lattimore signed contracts on behalf of Bi-Co to obtain construction materials for the Lamar County project. Jack Carroll, a Bi-Co officer, knew that John Lattimore was rigging bids to be made in Bi-Co's name and did not object to the practice. Finally, Bi-Co's accountant filed an affidavit with the grand jury identifying John Lattimore as an employee of Bi-Co with the authority to bid on highway projects. Such evidence demonstrates John Lattimore's authority to act for Bi-Co.

Finding no merit in any of appellant's contentions on appeal, we affirm the judgment of the trial court.

AFFIRMED.

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Q. Who besides yourself attended these bid lettings when this occurred?

A. Well, most of the time it was Jack Carroll and myself.

Q. Did Mr. Carroll ever tell you not to do this as far as giving an intentionally high bid and receiving an intentionally high bid?

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Q. These bids that were submitted where there was intentionally high bidding going on back and forth between you and Mr. Ricks, in whose name did you submit the bid?