Found guilty by a federal jury on two counts of transporting stolen computers across state lines in violation of 18 U.S.C. § 2314 and 18 U.S.C. § 2, the defendant was sentenced to imprisonment for a term of 33 months. He now appeals his conviction and sentence, contending, among other things, that he was the victim of prosecutorial misconduct and that the introduction of evidence of his refusal to talk with federal investigators violated his Fifth Amendment privilege against self-incrimination.
We conclude that there were occasions during the trial when the prosecutor overstepped the bounds of propriety, and we agree with the defendant that the prosecutor should not have elicited evidence, during the government’s case-in-chief, of the defendant’s unwillingness to speak to the investigators. In light of the record as a whole, however, and given the inherent improbability of the defendant’s contention that he did not realize the computers had been stolen, we conclude that the errors were harmless. Accordingly, and because we find no error in the district court’s calculation of the sentence under the sen*281tencing guidelines, we shall affirm the challenged judgment.
I
Christopher Banks, the defendant, is an attorney whose primary business is the operation of a lottery ticket store and U-Haul rental establishment in Cincinnati, Ohio. Mr. Banks was a social acquaintance of William Nieman, who worked as an inbound freight manager for a freight forwarder in Erlanger, Kentucky. Each month, six or seven truckloads of IBM Thinkpad laptop computers passed through the freight forwarder’s facilities; some of the computers arrived without proper documentation. Beginning in July of 1996, Mr. Nieman stole approximately 150 undocumented computers from six different IBM shipments.
Thanks to Mr. Banks, Mr. Nieman did not find it difficult to dispose of the stolen computers. Nieman initially offered to give Banks a laptop in satisfaction of a $500 gambling debt, according to Nieman’s account at trial. Nieman testified that he told Banks the computer had been stolen from the forwarder’s freight dock; that after inspecting the computer, Banks agreed to accept it as payment for the debt; and that Banks told Nieman to let him know if any more computers became available.
Mr. Nieman made four subsequent deliveries of stolen computers to the defendant. The final transaction occurred on Sunday, October 6, 1996, when Defendant Banks picked up 106 computers from the freight dock and drove them back to Cincinnati in a U-Haul. (All but six of these computers appear to have been in unopened boxes.) In total, Nieman sold Banks between 141 and 150 IBM Thinkpad computers for $52,500. Mr. Banks — to whom none of the computers was ever invoiced — resold the machines at prices reflecting large markups.
Mr. Nieman testified that he asked' Mr. Banks what Banks was telling his customers about the origin of the equipment. Banks allegedly replied that he told them he was liquidating the computers for a company called Tech Marketing, which was going out of business. There was no such company, of course.
The first person to whom Mr. Banks offered computers was Steve O’Bryan. It is uncontested that Steve O’Bryan was told that the computers belonged to “Tech Marketing” and that this company was liquidating its inventory. Agreeing to an initial purchase of 15 computers, Steve O’Bryan contacted his father, Tom O’Bryan, to arrange financing. Tom O’Bryan took some of the serial numbers and called IBM, he testified at trial, to make sure that the serial numbers were consistent with the model numbers and that the machines were configured as represented. IBM said nothing about the computers having been stolen. Steve O’Bryan subsequently paid Banks $12,000 for the 15 machines.
Early in September of 1996, Banks told Tom O’Bryan that he had seven more computers for sale. O’Bryan agreed to buy them for $6,700, paying with a check drawn to the order of Tech Marketing. He purchased another 20 computers a week later, again making the check payable to Tech Marketing. In October of 1996, Tom O’Bryan agreed to buy an additional 100 computers for $250,000. He picked up the computers from the defendant’s place of business in Cincinnati, but paid only $40,000 of the agreed price. The O’Bryans sold the computers to Computer Products Corporation at a price of $511,750, and that company resold them to users throughout the United States at prices totaling $697,135.
*282Meanwhile, the freight forwarder’s principal had reported as stolen 100 of the computers picked up by Mr. Banks on October 6, 1996. By tracing the serial numbers to Computer Products’ customers, the FBI followed the trail back to Messrs. Nieman and Banks. Mr. Nieman testified that while the FBI’s investigation was ongoing, he and Defendant Banks had numerous conversations about covering up Banks’ role in the affair. Tom O’Bryan cooperated in the government’s investigation, and he was promised that he would not be prosecuted.
In April of 1998 Mr. Nieman pleaded guilty to stealing the computers; he agreed to testify against Mr. Banks in exchange for a decreased sentence pursuant to U.S.S.G. § 5kl.l. On June 9, 1999, Mr. Banks was indicted by a federal grand jury on four counts of transporting stolen computers across state lines in violation of 18 U.S.C. § 2314 and 18 U.S.C. § 2, aided and abetted by William Nieman. On the government’s motion, the district court later dismissed the first two counts. Counts Three and Four were renumbered Counts One and Two, respectively, when the case went to trial.
Defendant Banks took the stand at trial, giving testimony that contradicted Nieman’s on key points. Mr. Banks testified that his first interaction with Mr. Nieman concerning computers occurred when Nieman asked him to repair an IBM Think-pad. Banks said that after making the repairs he offered to buy the computer for $1,000, paying $500 in cash and forgiving Nieman’s $500 gambling debt. Banks further testified that he asked where Nieman had got the computer and was told that it came from Tech Marketing, a company that was closing its offices and was returning computers to the freight forwarder.
In describing his subsequent transactions with Mr. Nieman, Mr. Banks claimed that the computers came in open boxes and were already registered to Tech Marketing. Mr. Banks also testified that he had his buyers make out checks to Tech Marketing for the reason that Nieman told him that his contact at Tech Marketing, Paul Keller, wanted to be paid in cash. Banks said that he gave these checks to Nieman, who would return several days later with the checks endorsed. The checks would then be cashed at Banks’ lottery store, with Banks taking his markup out of the proceeds and the rest of the cash being turned over to Nieman. Banks further testified that not until after the FBI began its investigation did Nieman tell him the computers had been stolen.
The jury ultimately found Banks guilty on both of the counts against him. The court sentenced him to imprisonment for a term of 33 months, to be followed by three years of supervised release. He was also ordered to make restitution in the amount of $205,000 and to pay a special assessment of $200. Mr. Banks has appealed his conviction and sentence, presenting six assignments of error.
II
A
When FBI investigators first approached Mr. Banks, he declined to speak with them. This fact came out at two points during the trial, and Banks argues that his Fifth Amendment privilege against self-incrimination was violated as a result.
During the government’s case-in-chief, sometime FBI Agent Dale Cannon testified about the investigation he conducted in December of 1996. In the course of his testimony Agent Cannon told the jury that he and Detective Bill Mark went to Banks’ *283home in order to speak with him. At this point the prosecutor, Ms. Laura Voorhees, asked Cannon the following question: “And what happened when you went to the door?” Cannon responded that Mr. Banks “advised that he didn’t want to talk to us, he wanted to talk to his attorney.” Defense counsel did not object, and the witness was immediately passed for cross-examination.
Defense counsel began his cross-examination by asking: “Former Agent Cannon, you have been around the block long enough to know that a person doesn’t have to talk to you just because you are an FBI agent, right?” Cannon replied in the affirmative.
The subject of the defendant’s silence was broached again while the defendant was being cross-examined after taking the stand in his own defense. Ms. Voorhees asked Mr. Banks why he had not cooperated with the government’s investigation in the beginning. He replied that he had cooperated by turning over all of the documents requested in a subpoena. Ms. Voorhees then asked, “But what I am talking about, sir, is that when Dale Cannon knocked on your door with Bill Park [sic], asked if you would talk to him, and you told him no — .” Defense counsel objected, and the court sustained the objection. The district judge thereafter gave the jury the following instruction:
“And the jury is advised that whenever an FBI agent came to Mr. Banks’ door and asked to talk to him, he didn’t have to talk to him, and that declining to talk with an FBI agent is not the same thing as declining to cooperate with either the FBI or with the Assistant United States Attorney. And, Ms. Voorhees, you are admonished not to make such an implication again.”
An argument can be made that the government was entitled to attempt to impeach the defendant’s credibility by asking him on cross-examination about his refusal to speak with the investigators. See Combs v. Coyle, 205 F.3d 269, 281 (6th Cir.), cert. denied, 531 U.S. 1035, 121 S.Ct. 623, 148 L.Ed.2d 533 (2000), where we said (citing Jenkins v. Anderson, 447 U.S. 231, 236-238, 100 S.Ct. 2124, 65 L.Ed.2d 86 (1980)) that “permitting the impeachment use of a defendant’s prior silence does not unconstitutionally burden the exercise of Fifth Amendment rights.” See also Seymour v. Walker, 224 F.3d 542, 560 (6th Cir.2000) (when a defendant chose to testify in her own defense, “[t]he prosecutor ... had a legitimate interest in impeaching her testimony and in not allowing Seymour to use the Fifth Amendment as a sword rather than a shield”). The members of the panel are not of one mind as to the validity of this argument under the present circumstances. The panel is unanimous, however, in the view that by sustaining the objection to the prosecution’s question and instructing the jury as it did, the trial court cured any problem that may have been inherent in the cross-examination.
The panel is also unanimous in the view that the information about the defendant’s silence should not have been elicited during the government’s case-in-chief. The government argues that Agent Cannon’s testimony on direct examination was permissible because it was merely being used for impeachment purposes. The prosecution maintains that the defendant put his credibility at issue during his lawyer’s opening statement, when the jury was told that Mr. Banks would testify that he did not know the computers were stolen. Mr. Banks had not yet taken the stand when Agent Cannon testified, however, and the government’s anticipatory impeachment theory seems to have no support in the caselaw. The better view, we believe, is that the prosecution was at*284tempting to use Mr. Banks’ silence as substantive evidence of guilt. This the Constitution prohibits: “the use of a defendant’s prearrest silence as substantive evidence of guilt violates the Fifth Amendment’s privilege against self-incrimination.” Combs, 205 F.3d at 283.
Although Agent Cannon’s testimony was impermissible, it remains to be determined whether Mr. Banks is entitled to a new trial on this score. Since there was no objection, we must apply plain error analysis. See Fed.R.Crim.P. 52.1
To correct an error not raised at trial, there must be: (1) error, (2) that is plain and (3) that affects substantial rights. If these conditions are met, we may exercise our discretion to intervene if the error (4) “seriously affect[s] the fairness, integrity, or public reputation of judicial proceedings.” See United States v. Olano, 507 U.S. 725, 732, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993).
We shall assume, for purposes of analysis, that the error committed by the government during its case-in-chief qualifies as “plain” error. In order for us to set the conviction aside, under this hypothesis, it would still be necessary for us to conclude that the error affected the fairness or integrity of the proceedings. In other words, “the error must have been prejudicial: [i]t must have affected the outcome of the district court proceedings.” Olano, 507 U.S. at 734.
We find no reasonable likelihood of prejudice from Agent Cannon’s testimony. In light of the record, Mr. Banks’ contention that he was unaware the computers were stolen is wildly improbable. No reasonably prudent businessman-attorney could have thought it likely that the true owner (1) would deputize a freight forwarder’s employee to liquidate hundreds of thousands of dollars’ worth of computers on the fly, (2) would have him do so without issuing any documentation, and (3) would then have the employee pocket the proceeds in cash. It is true, as we shall see, that the jury initially encountered difficulty in reaching a unanimous verdict in this case, but the fact remains that the evidence against Mr. Banks was little short of overwhelming.
B
Mr. Banks contends that the prosecutor made a series of statements that constituted deliberate acts of misconduct and so tainted the trial that reversal by this court is warranted. Our review of this matter is de novo. United States v. Clark, 982 F.2d 965, 968 (6th Cir.1993).
Our first task in reviewing prosecutorial misconduct claims, not surprisingly, is to determine whether the prosecutor’s statements were in fact improper. United States v. Francis, 170 F.3d 546, 549 (6th Cir.1999). If the statements appear improper, we then look to see whether they were flagrant. Id. (citing United States v. Carroll, 26 F.3d 1380, 1388 (6th Cir.1994)). This court’s standard for flagrancy is: “(1) whether the statements tended to mislead the jury or prejudice the defendant; (2) whether the statements were isolated or among a series of improper statements; (3) whether the statements were deliberately or accidentally before the jury; and (4) the total strength of the evidence against the accused.” Id. at 549-550. To reverse a conviction on the basis *285of an improper, non-flagrant statement, we must determine that: “(1) the proof of the defendant’s guilt is not overwhelming; (2) the defense counsel objected; and (3) the trial court failed to cure the impropriety by failing to admonish the jury.” Id, at 550. Whether a prosecutor’s misbehavior was prejudicial must be decided in the context of the entire trial. See United States v. Young, 470 U.S. 1, 11, 105 S.Ct. 1038, 84 L.Ed.2d 1 (1985).
1. Nieman’s Handwriting Exemplar
One of the issues at trial was whether it was Defendant Banks or his friend Mr. Nieman who endorsed the checks made out to Tech Marketing. Banks testified that Nieman eventually told him that he, Nieman, had signed “Tech MKT” on the backs of the checks. Nieman denied having said this and denied having made the endorsements. As part of the investigation, the government obtained a handwriting exemplar from Banks but not from Nieman. No handwriting expert testified at trial as to whether Mr. Banks’ handwriting matched the endorsements.
During the rebuttal portion of her closing argument, the prosecutor said this:
“Mr. Banks through his attorney wants you to believe that we were at fault or did something wrong by not getting a handwriting exemplar from Mr. Nieman. Why should we have done that, ladies and gentlemen? In the beginning he told us that that was his handwriting, he told us that there’s no basis for us to get a handwriting exemplar. We believed what he told us. It was only later when he told us that that wasn’t his handwriting, it was Mr. Banks’ handwriting.”
The prosecutor’s statement was untrue; Nieman never told the government that he had endorsed the checks, nor was any such evidence presented at trial. In a subsequent filing with the district court, the prosecutor admitted that she had been mistaken. The defendant argues that Ms. Voorhees’ false statement constitutes serious prosecutorial misconduct that requires reversal.
Since defense counsel did not contemporaneously object to what Ms. Voorhees said in closing argument, we can only reverse on the basis of the misstatement if we find it tainted by the requisite flagrancy. See Francis, 170 F.3d at 550. We do not believe it was so tainted. What Ms. Voorhees said was certainly misleading, but we do not think it was particularly prejudicial. Because it detracted from Nieman’s credibility, the statement may even have bolstered Mi’. Banks’ position. Although Ms. Voorhees obviously should have been more familiar with the facts of her case than she appears to have been, moreover, we cannot say that her lapse was deliberate. And although this was not her only lapse, it came in the context of a very strong government case — a case which, if properly presented, should have posed no particular problem for the prosecution.
2. Handwriting Comparisons
The government elected not to call a handwriting expert and to let Mr. Banks’ handwriting exemplar and the endorsed cheeks speak for themselves. The defense contends that Ms. Voorhees attempted to make up for the absence of expert testimony by repeatedly making the jury aware of her personal opinion that Mr. Banks’ handwriting matched the endorsements on the checks.
During cross-examination of Mr. Banks, the following colloquy occurred:
Q. “Would you agree with me that your block printing on this handwritten note looks very similar to what appears on the back of all of these checks?
*286A. No, I won’t. I mean it’s somewhat similar but it’s not myit’s not my underwriting.
Q. You could understand why I might think it was, couldn’t you?
A. You are entitled to have your own opinion.”
No objection was made. Later, during her rebuttal closing argument, Ms. Voorhees said this:
“But when you look at that handwriting exemplar and you compare it to the endorsement on the backs of those checks, I submit that that shows that those endorsements are virtually identical. And it is that fact alone that destroys the defendant’s defense. Bill Nieman did that or Paul Keller or somebody acting on Mr. Nieman’s behalf. Those are in fact his endorsements, and it is the way Mr. Nieman told you it occurred, that Mr. Banks was the one that thought up this scheme, came up with the plan of Tech Marketing. He’s the one with all the knowledge about Tech Marketing. And I submit to you that Mr. Nieman’s testimony was accurate, that this was Mr. Banks’ idea, thereby establishing to you ladies and gentlemen that he knew these computers were stolen .... ”
As to the cross-examination, Ms. Voorhees’ use of the phrases “agree with me” and “I might think” may have come close to the improper expression of a personal opinion. It probably did not cross the line, however, and if there was any impropriety in the form of the questions, it was far from flagrant.
As to the closing argument, we see no impropriety. With or without expert testimony, juries are allowed to make their own comparisons of handwriting in documents admitted in evidence. See United States v. Woodson, 526 F.2d 550, 551 (9th Cir.1975); see also United States v. Sivils, 960 F.2d 587, 592-593 (6th Cir.1992). It was not impermissible for Ms. Voorhees to “submit” to the jury that the comparison favored the government and that Nieman’s testimony was accurate. As we explained in United States v. Stulga, 584 F.2d 142, 147 (6th Cir.1978), the phrase “I submit” is not the equivalent of expressing a personal opinion; rather, it should be interpreted to mean “I submit that upon the facts as shown by the evidence.” (Internal quotations omitted.)
3. Bolstering of Tom O’Bryan’s Credibility
In rebuttal closing argument, Ms. Voorhees said the following:
“There wasn’t sufficient evidence to prosecute Mr. O’Bryan and he was simply told that he wasn’t going to be prosecuted. That was long after he had given evidence regarding his specific conversations with Mr. Banks. There was no motivation for him at that point to make up those stories such as Mr. Banks would like to have you believe occurred. He simply was told that he wasn’t going to be prosecuted.”
No objection was made by defense counsel.
The record did not show that there was insufficient evidence to prosecute Mr. O’Bryan. Several factors, however, lead us to conclude that there was no flagrant impropriety in this connection. First, Ms. Voorhees’ argument is generally consistent with Mr. O’Bryan’s testimony at trial. Second, the accuracy of O’Bryan’s testimony had already been admitted, defense counsel having said this during his closing argument:
“the government gave Mr. O’Bryan a free pass, told him that he would not be prosecuted. But, you know, I heard Mr. O’Bryan testify and I thought he was *287quite candid. I thought the things he said were not hurtful to Chris.”
Third, the district court gave the jury two cautionary instructions. The morning after O’Bryan’s testimony, the court reminded the jury that the government had promised not to prosecute him. The court then went on to say this:
“It is permissible for the government to make such promises, but you should consider Mr. Nieman’s and Mr. O’Bryan’s testimony with more caution than the testimony of other witnesses. Consider whether their testimony may have been influenced by the government’s promise.”
This instruction was repeated in the court’s general charge, further minimizing any risk of prejudice.
4. IRS Record-Keeping Comments
In his final allegation of prosecutorial misconduct, the defendant submits that during cross-examination and closing argument the prosecutor made references to the IRS that were improper because no evidence was presented as to IRS record-keeping requirements; the prosecutor’s statements, it is claimed, reflected nothing more than her personal opinion.
In her closing, the prosecutor made this argument:
“And the IRS is going to believe him based on what he claimed. It doesn’t matter what’s in his books or on the account or something like that. It’s really what he claims to the IRS that matters. That, ladies and gentlemen, is absolutely incredible.”
No objection was made. The prosecutor later made the following observation:
“Any person, the IRS or anybody else that wanted to find out what had happened, they couldn’t tell at all by looking at those bank statements and seeing the bank statements what Mr. Banks would have in his hands to show or try to represent to people that he didn’t receive this money.”
At this point defense counsel objected to the numerous references to the IRS. In response, the district judge cautioned the jury as follows: “Members of the jury, you’re instructed that no charge in this ease relates to the IRS. The only charges are knowing transportation, knowing interstate transportation of stolen goods.”
We do not consider the IRS references to have been improper expressions of personal opinion. The prosecutor was attempting to demonstrate that Mr. Banks’ poor record-keeping strengthened the conclusion that he knew the computers were stolen. Most people know that the IRS requires businesses to keep adequate financial records, and there was ample reason to question whether the defendant had done so here. In any event, the district judge’s cautionary instruction minimized whatever potential problem there may have been in this regard.
C
Next, Mr. Banks contends that the district court erred in its handling of a situation that arose after the jury retired to deliberate.
After about four hours of deliberations, the jury foreperson sent the district judge a note asking for help because the jury was deadlocked as a result of two or three jurors holding out for a verdict of not guilty. The judge asked if further deliberations would be helpful. The foreperson responded that two jurors had said that further deliberations would not change their vote for acquittal. Defense counsel then moved for a mistrial on the grounds that this response violated an instruction against disclosing a vote split during delib*288erations. The court denied the motion but cautioned the jury not to do it again.
Ultimately, following the denial of a request by the jury to review Tom O’Bryan’s testimony and without objection by the defendant, the court gave a standard-form Allen charge.2 After giving the charge, the district judge commented to the jury that “as I indicated I hope you are able to reach a unanimous agreement. You may be able to, you may not be able to .... ”
This court reviews the denial of a motion for a mistrial for abuse of discretion. United States v. Atisha, 804 F.2d 920, 926 (6th Cir.1986). Here we see no abuse of discretion in the denial of the motion for a mistrial after the jury’s numerical split was disclosed. The district judge did not know which two jurors were in the minority and could not single them out for coercive pressure.
Given the absence of a timely objection, we find no reversible error in the court’s delivery of the Allen charge. As we explained in United States v. Lash, 937 F.2d 1077, 1086 (6th Cir.1991) (citations omitted), Allen charges have generally been upheld where the jury has disclosed a split sua sponte and the instructions have not targeted the minority. In the case at bar the jury revealed its split spontaneously, with no solicitation from the court, and the instruction directed both the majority and the minority to reconsider their positions. The instruction was not aimed solely at the minority, and was thus not coercive.
Furthermore, “we traditionally have found an Allen charge coercive when the instructions themselves contained errors or omissions, not when a defendant alleges that the circumstances surrounding an otherwise correct charge created coercion.” Frost, 125 F.3d at 375. The Allen charge given here closely followed Sixth Circuit Pattern Criminal Jury Instruction 9.04 and contained no errors or omissions. The defendant contends that the judge’s expression of hope for a unanimous verdict rendered the charge coercive, but we do not find the contention persuasive. The judge’s comment came in the context of an explanation that it would be perfectly acceptable for the jurors not to reach a unanimous verdict and that they should deliberate at their own pace.
D
In his fourth assignment of error, the defendant claims that the government presented insufficient evidence to sustain his conviction because there was no proof that he caused the transportation of the goods in interstate commerce. We review sufficiency of the evidence claims only to determine “whether, 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.” United States v. Martin, 920 F.2d 345, 348 (6th Cir.1990) (citations omitted). We believe a rational jury could have decided that Mr. Banks was causally responsible for the interstate transportation of the computers referred to in both counts of the amended indictment.
Count One dealt with 17 computers delivered to the defendant by Mr. Nieman. Nieman testified that he transported the computers from the freight forwarder’s *289dock in Kentucky to Mr. Banks’ place of business in Cincinnati, Ohio. The defendant argues that there was no proof that he caused Nieman to bring the computers across the state line. The argument leaves us unconvinced. As the Second Circuit explained in United States v. Scandifia, 390 F.2d 244, 248 (2d Cir.1968), reversed and vacated on other grounds, 394 U.S. 310, 89 S.Ct. 1163, 22 L.Ed.2d 297 (1969), “[t]here can be no doubt that a defendant may be found to be a ‘cause’ if the result which the law forbids was reasonably foreseeable.” The jury was entitled to find Mr. Banks the cause-in-fact of the computers having moved in interstate commerce because it was reasonably foreseeable that when Banks agreed to buy the computers from Nieman the latter would transport them across the state line. The jury could have also inferred that defendant directed Nieman to deliver the computers from Kentucky to Ohio to complete the sale.
As to the 106 computers dealt with in Count Two, Mr. Banks himself testified that he picked up the computers in question from the freight forwarder’s facility in Kentucky on a Sunday, put them in storage, and did not look at them again until they were turned over to Mr. O’Bryan the following Friday. O’Bryan testified that he took possession of the computers in Cincinnati. From this testimony, we believe a jury could reasonably have inferred that defendant transported the computers from Kentucky and placed them in storage in Cincinnati, Ohio.
E
Mr. Banks argues next that the district court committed reversible error in giving the jury the following “deliberate ignorance” instruction, an instruction based on Sixth Circuit Pattern Jury Instructions 2.09:
“No one can avoid responsibility for a crime by deliberately ignoring the obvious. If you are convinced that the defendant deliberately ignored a high probability that the computers he received from Bill Nieman were stolen, then you may find that he knew the computers had been stolen.
But to find this, you must be convinced beyond a reasonable doubt that the defendant was aware of a high probability that the computers had been stolen, and that the defendant deliberately closed his eyes to what was obvious. Carelessness, negligence, or foolishness on his part is not the same as knowledge, and is not enough to convict .... ”
We review a district court’s choice of jury instructions for abuse of discretion, and we reverse only when the jury charge fails accurately to reflect the law. See United States v. Beaty, 245 F.3d 617, 621 (6th Cir.2001) (citations omitted).
Mr. Banks contends that the deliberate ignorance instruction given here was improper in light of the government’s proof that he had actual knowledge the computers were stolen. The contention is without merit. In United States v. Mari, 47 F.3d 782, 786 (6th Cir.1995), we held that when a district court gives a deliberate ignorance instruction that does not misstate the law but is unsupported by the evidence, the error is ipso facto harmless. We do not think that the court erred in giving the deliberate ignorance instruction here, but if we are wrong in this it is clear, under Mary that any error was harmless.
Relying on a Second Circuit case, Mr. Banks further argues that the instruction was defective because it failed to include a proviso informing the jury that it could not find deliberate ignorance if it concluded that the defendant actually believed the goods were not stolen. See *290United States v. Sicignano, 78 F.3d 69, 71 (2d Cir.1996). Such a proviso is required by Second Circuit precedent, and both parties in Sicignano asked that the instruction include it. Id. There is no corresponding Sixth Circuit precedent, and as far as the record reveals defense counsel never requested inclusion of the proviso here. Mr. Bank’s argument is thus unpersuasive.
F
Finally, Mr. Banks argues that the district court erred in its calculation of the amount of the loss attributable to his conduct under U.S.S.G. § 2B1.1 and failed to make specific findings in this regard, as required by Fed.R.Crim.P. 32(c)(1). See Monus, 128 F.3d at 396. We review the district court’s calculation of loss for clear error, and we give due deference to the court’s application of the guidelines to the facts. United States v. Jackson, 25 F.3d 327, 330 (6th Cir.1994).
At Mr. Bank’s sentencing hearing, the district judge explicitly found the amount of the loss to be $684,800 (rounding from $684,833), based on the testimony of IBM Security Investigator Chris Ferracane. At trial, Ferracane testified that IBM had sold the computers in Count One for $65,433 and the computers in Count Two for $619,400. The sum of these two amounts is $684,833, which shows that contrary to a suggestion by Mr. Banks, the district court did not include the value of computers from the dismissed counts.
Mr. Banks further maintains that the district court should have used wholesale prices to determine the amount of loss rather than retail prices. But as Application Note 2 to U.S.S.G. § 2B1.1 explains, ‘“Loss’ means the value of the property taken, damaged or destroyed. Ordinarily, when property is taken or destroyed the loss is the fair market value of the particular property at issue.” The standard test for determining the market value of stolen property is “the price a willing buyer would pay a willing seller at the time and place the property was stolen.” United States v. Warshawsky, 20 F.3d 204, 213 (6th Cir.1994) (citations omitted). The district court was able to put the fair market value of the stolen computers at $684,833 because IBM had already sold the computers for that price by the time they were stolen. Accordingly, we find no error in the court’s calculation of the loss.
The judgment of conviction and sentence is AFFIRMED.
. Rule 52 provides as follows:
"(a) Harmless Error. Any error, defect, irregularity or variance which does not affect substantial rights shall be disregarded.
(b) Plain Error. Plain errors or defects affecting substantial rights may be noticed although they were not brought to the attention of the court.”
. An Allen charge is a "supplemental instruction designed to encourage the jury to reach a verdict by requesting each juror to reconsider his or her respective position during continued deliberations. The name comes from Allen v. United. States, 164 U.S. 492, 17 S.Ct. 154, 41 L.Ed. 528 (1896), where the Supreme Court approved such an instruction.” United States v. Frost, 125 F.3d 346, 373 (6th Cir.1997).