*500STAFFORD, D.J., delivered the opinion of the court, in which SILER, J., joined. MOORE, J. (pp. 519-523) delivered a separate dissenting opinion.
OPINION
STAFFORD, District Judge.Appellant, Larry T. Tarwater (“Tarwa-ter”), appeals his conviction and sentence for making false statements to the Internal Revenue Service (“IRS”). We affirm.
I. THE EVIDENCE
In 1987, Tarwater, a certified public accountant, was retained by Jefferson Memorial Hospital (“JMH”) to perform its annual audit and to prepare its annual Medicare and Medicaid cost reports. At the time, JMH was using a consultant, Willie Davis, to review the hospital’s cost reports. Hired on a contingency fee basis, Davis was paid for his work if it resulted in additional Medicare and Medicaid reimbursements to the hospital. To obtain his fee, Davis submitted itemized invoices to JMH’s Chief Financial Officer, Karen Bradley Chambers (“Chambers”), explaining what amount of money the hospital would be receiving back from Medicare and/or Medicaid. The cost reports reviewed by Davis for the years after 1986 were prepared by Tarwater.
In 1988, Tarwater and Craig Peters (“Peters”) formed the Peters, Tarwater & Associates accounting partnership. The partnership maintained its only bank account at the Home Federal Bank in Knoxville, Tennessee, where the partners were supposed to deposit all business receipts. The Peters, Tarwater partnership lasted through 1991. Tarwater practiced accounting as a sole proprietor from January, 1992, until August 18, 1992. On August 19, 1992, Tarwater formed a corporation, Tarwater, Hines & Company, P.C. with another certified public accountant, Jenny Hines (“Hines”). The corporation maintained its business account at the Third National Bank where all business receipts were supposed to be deposited. Tarwater practiced with Hines until 1998.
In or about June of 1988, Barnett Bank of Florida notified Chambers that Davis had pledged his JMH fee receivables as security for a loan. Barnett Bank requested that any monies due Davis be made payable to both the bank and to Davis. Chambers agreed and thereafter wrote a check jointly to Davis and Barnett Bank in the amount of $26,852.75. Soon after she gave Davis the check, Chambers was notified by the bank that Davis had attempted — unsuccessfully—to cash the check. In fact, Davis had altered the check, removing Barnett Bank’s name as a payee. Angered by Davis’s action, and concerned that, if Davis would alter a check, he might do other unacceptable things as well, Chambers stopped payment on the check. She then told Robert Foster, the hospital’s administrator, about Davis’s conduct. Chambers explained to Foster that she was unwilling to work with Davis any longer, and she recommended that his contract •with the hospital be terminated.
Soon after her meeting with Foster, Chambers was advised that, while Davis’s contract was not being terminated, Davis would thereafter work through, and be paid through, Tarwater. Foster approved the Tarwater-to-Davis payment arrangement. Two checks totaling $26,852.75, the exact amount of the check from which Davis removed Barnett Bank’s name, were soon after made payable to Tarwater for Davis.
Bettye King (“King”), the JMH bookkeeper, prepared all checks for the hospital but had no signatory authority. Two administrative officers, usually Foster and Chambers, had to sign the checks. Tarwa-*501ter routinely gave King invoices to document his auditing and cost report work, and, based on those invoices, King prepared checks payable to Tarwater’s accounting firm. Beginning in August of 1988, King made the “Willie Davis” checks payable to Tarwater individually. Although Davis had previously submitted itemized invoices when JMH paid him directly for his work, no such invoices or statements were submitted after Tarwater became the conduit for payments to Davis. Initially, King wrote the “Willie Davis” checks to Tarwater at the direction of Chambers or Foster. Later, Tarwater simply told King what amounts were to be paid to him on behalf of Davis. According to King, she did not question the absence of documentation because Tarwater was the hospital’s auditor.
After learning about the Tarwater-to-Davis payment arrangement, Chambers attempted to institute an audit review process to determine the correctness and propriety of the hospital’s payments to Davis through Tarwater. Shortly after she started the process, however, she was instructed by Foster to cease the work and to accept the payment requests presented by Tarwater. Chambers complained about the absence of an audit trail, but to no avail. According to Chambers, Tarwater decided when, and for how much, checks were to be issued to him for Davis. Although it was her normal practice, as well as the hospital’s, to insist on documentation to support any payment of monies, Chambers signed the undocumented checks to Tarwater because “Tarwater was hired by the Board of Directors [and] he could tell [her] what to do.” J.A. at 375. Foster likewise signed the checks without insisting on documentation because he trusted Tarwater, knew that the checks were prepared under the direction of the chief financial officer, and had no reason to doubt that Davis was entitled to payment. On October 27, 1994, the JMH Board of Directors (the “Board”) held a meeting at which Tarwater was asked about Davis. Tarwater explained who Davis was, what he did for the hospital, and why monies intended for Davis were passed through Tarwater. As reflected in the minutes of the meeting, the Board learned that:
The reason these checks are made out to Mr. Tarwater is because Mr. Davis will call [Tarwater] from Florida and state[ ] he needs payment; so instead of [Tar-water] making a trip to Jefferson City, [Tarwater] will pay Mr. Davis’s firm [him]self and then get reimbursed from the hospital next time [he is] up here. If checks were made out to the Tarwa-ter firm for Mr. Davis’s services, then it would cost his firm 11% off the top for professional liability.
J.A. at 899. After expressing concern about the hospital’s failure to issue 1099 forms to either Tarwater or Davis for the amounts paid to Tarwater on Davis’s behalf, the Board decided to stop all payments to Davis pending the Board’s review of proper documentation, including proof of Medicaid/Medicare reimbursements. The Board also decided that, if any monies were thereafter owed to Davis, the hospital would pay Davis directly.
Following the October 27th Board meeting, Tarwater’s services to JMH were terminated and an investigation was begun. In November of 1994, the Board retained an accounting firm, Morgan, Newman & Davenport, P.C., to review all payments that were made by the hospital to outside consultants. As part of this review, Ralph Erwin Newman, Jr., CPA (“Newman”), interviewed Tarwater. Tarwater explained (1) that he did not make a nickel from his arrangement with Davis, that all monies intended for Davis were passed on to Davis; (2) that he could document all pay*502ments that went to Davis; (3) that he sometimes advanced Davis money out of his own funds, reimbursing himself when JMH issued a check; and (4) that he cashed checks for Davis — sending Davis either the cash, a wire transfer, or a cashier’s check — on the not-infrequent occasions when JMH issued him two checks at a time.
Beginning in 1995, the IRS. began an investigation of Tarwater’s tax returns for the years 1991 through 1994. When Tar-water both declined to discuss any tax matters with the revenue agent and also refused to turn over his personal and corporate records, a summons was issued to Tarwater’s bank and accounting firm. Over Tarwater’s motion to quash, the records were ultimately obtained by court order in the year 2000. ■ Review of those records resulted in Tarwater’s indictment on three counts of filing false tax returns — for the years 1992, 1993, and 1994 — in violation of 26 U.S.C. § 7206(1).
Tarwater’s case was tried before a jury for five days beginning on April 30, 2001. Through the testimony of two IRS agents, Mary Barton (“Barton”) and Karen Jackson (“Jackson”), the government presented evidence that Tarwater deposited the monies he received from JMH into four separate accounts at Third National Bank in Knoxville. The first account, the Peters, Tarwater & Associates Account, was used by Tarwater for his accounting business receipts during the early parts of 1992. The name of that account was changed in August, 1992, to the Tarwater, Hines & Company Account. The remaining three accounts were (1) the Larry T. Tarwater, CPA, Account; (2) the Larry T. or Janie C. Tarwater Account; and (4) the Larry T. or Janie C. Tarwater Construction Account.
In 1992, JMH issued Tarwater twelve checks for a total of $73,460 for work allegedly performed by Davis. Of those twelve checks, Tarwater received one check on each of two different dates, and he received two checks on each of five separate occasions. Of the total 1992 checks intended for Davis, Tarwater deposited $45,010 in his partnership accounts at Third National Bank. The remaining $28,450 was deposited into his Tarwater, CPA, Account. Contrary to what Tarwa-ter had told Newman, none of the twelve checks was cashed or endorsed over to Davis.
In Í993, JMH issued Tarwater fifteen checks for a total of $90,650 for Davis’s work. While seven of the checks were issued singly on seven different dates, eight of the checks were issued in pairs, two each on four separate occasions. Tar-water deposited $28,000 of the Davis checks in the Tarwater, Hines & Company Account, $14,900 in the Tarwater CPA, Account, and the balance — $47,750—in the Larry T. or Janie C. Tarwater Construction Account, an account used for the 1993 construction of Tarwater’s $385,000 home. Again, none of the checks was cashed or endorsed over to Davis.
In 1994, JMH issued Tarwater twenty-four checks for a total of $158,500 for work purportedly performed by Davis. The checks were issued two at a time on each of twelve occasions. Of the $158,500, $15,000 was deposited into the Tarwater, Hines & Company Account. The remaining $143,500 was deposited into the Larry T. or Janie C. Tarwater Construction Account.
During the years 1992 to 1994, Tarwater sent Davis a total of eleven checks, three drawn on the Tarwater, CPA, Account and eight drawn on the Larry T. or Janie C. Tarwater Construction Account. In 1992, he sent Davis three checks, each in the amount of $500.00. In 1993, he gave Davis four checks totaling $7,700, one each in the *503amounts of $200, $2000, $2,500 and $3,000. In the memo section on the $3000 check, Tarwater wrote the word “loan.” In 1994, Tarwater sent Davis four checks for a total of $16,000, one each in the amount of $2000, $3000, $5000, and $6000. In the memo section on the $2000 and $3000 checks, Tarwater wrote the word “loan.” On the $5000 check, he wrote the word “advance.” Also in 1994, Tarwater sent Davis six Western Union wire transfers totaling $6,555. The IRS found no other evidence of payments from Tarwater to Davis.
For each of the relevant tax years, Jackson reviewed both the monies deposited into as well as the monies drawn out of each of Tarwater’s bank accounts. Jackson found that, for each year, Tarwater deposited a great deal more of the monies allegedly intended for Davis than he paid out through checks written to Davis. Even when Jackson added Tarwater’s cash withdrawals and cash taken out of deposits to the checks written to Davis, giving Tar-water the benefit of an assumption that the cash was sent to Davis, Jackson still found that the monies taken in for Davis exceeded the monies sent out to Davis. According to Jackson, the excess of monies taken in for Davis over monies distributed out to Davis should have been retained in Tarwater’s accounts if those monies were, in fact, meant as income for Davis. Tar-water’s monthly ending bank balances demonstrated, however, that Tarwater did not retain the undistributed monies intended for Davis but, instead, spent those monies.
The government’s expert witness, Barton, opined that Tarwater did not state the true amount of either his gross receipts or his net income for the years 1992 through 1994. Specifically, as to income, she said that:. (1) in 1992, Tarwater understated his income by $52,233; (2) in 1993, he understated his income by $35,950; and (3) in 1994, he understated his income by $120,945. In 1992, Tarwater’s understatement of income was in part explained by his failure to report over $30,000 in gross receipts for the eight months that he operated as a sole proprietorship. Barton explained that a correct report of gross receipts and income is necessary to a correct computation of tax liability and that a false report of income is capable of influencing the IRS in the audit of tax returns.
Peters, Tarwater’s business partner during the first three and a half years of the JMH-to-Tarwater-to-Davis payment arrangement, testified that Tarwater never told him that he received money from JMH on behalf of Willie Davis. Hines, Tarwater’s business associate during the last years of the pass-through arrangement, said that Tarwater did not tell her about his arrangement with Davis until sometime in 1995, after JMH hired Newman to investigate and after JHM filed suit against Tarwater. According to Hines, Tarwater then explained to her that, years earlier, the hospital administrator had asked him to be the conduit for payments to Davis in order to help Davis avoid seizure of his assets by creditors.
Tarwater neither testified nor presented any expert testimony at trial. He did, however, call several lay witnesses.1 One of those witnesses was Carl Curtis (“Curtis”), the contractor who built Tarwater’s house. Curtis testified that Tarwater borrowed money from him on five or six occasions. According to Curtis, on each of two of those occasions, Tarwater borrowed $15,000 from him for Willie Davis. Curtis said that, although he did not know Davis, *504he was willing to lend Tarwater the money for Davis because he trusted Tarwater. The money, Curtis said, was repaid.
Tarwater also called his nephew, Michael Joe Tarwater (“Michael”), who testified that he worked part-time in his uncle’s office for about seven months while he was in school. Michael said that his uncle frequently asked him to wire money to Davis. Indeed, according to Michael, Tarwater would send Michael to wire Davis money a couple of times a week, each time giving him cash, or checks made out to Tarwater which Michael would cash, normally around $2000 at a time, although sometimes it would be as much as $4000 or $5000. Michael said that $112,000 would be a conservative estimate of the total amount he wired to Davis during the months — apparently in 1994 — that he worked for his uncle.
The jury convicted Tarwater on all three counts. At a sentencing hearing on July 12, 2001, the district court found that Tar-water was responsible for a tax loss exceeding $60,000, resulting in a base offense level of 13. To the base offense level, the court applied a two-level enhancement pursuant to U.S.S.G. § 3B1.3 for use of a special skill. Based on an adjusted offense level of 15, the court sentenced Tarwater to eighteen months imprisonment, one year of supervised release, and restitution in the amount of $45,116 to be paid to the IRS in a lump sum.
II. SUFFICIENCY OF THE EVIDENCE
Tarwater contends that the evidence was insufficient to convict him of the charged offenses. Tarwater preserved his right to appeal this issue by both moving for a judgment of acquittal at the conclusion of the government’s case as well as renewing the motion at the conclusion of all the evidence.
In reviewing a claim of insufficiency of the evidence, this court looks at all of the evidence 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 offense beyond a reasonable doubt. Jackson v. Virginia, 443, U.S. 307, 319, 443 U.S. 307, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979). We must view the evidence in the light most favorable to the prosecution, and “Circumstantial evidence alone, if substantial and competent, may support a verdict and need not remove every reasonable hypothesis except that of guilt.” United States v. Humphrey, 279 F.3d 372, 378 (6th Cir.2002).
Tarwater was convicted of three counts of violating 26 U.S.C. § 7206(1), which provides that “[a]ny person who ... willfully makes and subscribes any return, statement, or other document, which contains or is verified by a written declaration that it is made under the penalties of perjury, and which he does not believe to be true and correct as to every material matter ... shall be guilty of a felony.” Section 7206 is a perjury statute that criminalizes lying on any document filed with the IRS. It does not require the prosecution to prove the existence of a tax deficiency, exact amounts of unreported receipts or income, or an intent to evade taxes. See, e.g., United States v. Taylor, 574 F.2d 232, 234 (5th Cir.1978). Under the statute, the government need only prove that a defendant willfully made and subscribed a return, that the return contained a written declaration that it was made under penalties of perjury, and that the defendant did not believe the return to be true and correct as to every material matter. United States v. Bishop, 412 U.S. 346, 350, 93 S.Ct. 2008, 36 L.Ed.2d 941 (1973); United States v. Ristovski, 211 *505F.3d 1271, 2000 WL 491513, at *2 (6th Cir. Apr.18, 2000).
A matter is “material” if it has a natural tendency to influence, or is capable of influencing or affecting, the ability of the IRS to audit or verify the accuracy of a tax return. Neder v. United States, 527 U.S. 1, 16, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999) (quoting United States v. Gaudin, 515 U.S. 506, 509, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995)). In a prosecution under § 7206(1), “any failure to report income is material.” United States v. Holland, 880 F.2d 1091, 1096 (9th Cir.1989). Here, materiality was established by Barton’s testimony that Tarwater’s failure to report sizeable amounts of income was capable of influencing the IRS in the audit of Tarwater’s tax returns.
Tarwater does not dispute that he willfully made and subscribed a return containing a written declaration that it was made under penalties of perjury. He also does not dispute that a sizeable amount of the monies he received from JMH were not reported as gross income on his tax returns. What he does dispute is the government’s evidence, or lack thereof, that the “Willie Davis” monies constituted gross income that he should have reported on his tax return. He suggests, in other words, that he did not report the Willie Davis monies because he did not believe those monies constituted income to him. He thus challenges the jury’s finding that he did not believe his returns to be true and correct.
Tarwater attacks the testimony of the government’s expert witness, IRS Revenue Agent Barton, by arguing that Barton did not examine all of Tarwater’s ledgers and accounts, that she made mistakes in her computations, and that her opinion as to Tarwater’s understatement of income was unreliable because the opinion she gave at trial differed from the one she gave at a pre-trial hearing. Likewise, Tarwater attacks Agent Jackson’s testimony, arguing that, because her review of Tarwater’s financial records was incomplete, her conclusions were unreliable. At trial, however, defense counsel extensively cross-examined both agents, questioning the thoroughness of their review, their computations, and their conclusion that Tarwater understated his income by sizea-ble amounts in each of the relevant tax years. The jurors were able to assess the credibility of the agents, and — by their verdict — the jurors made clear that they believed the agents’ testimony. It is not for us to second-guess the jurors’ assessment of a witness’s credibility; nor is it for us to re-weigh any of the evidence.
Tarwater also argues that the evidence was insufficient because — he says— the government failed to prove that he did not make substantial cash payments to or on behalf of Davis. To be sure, the agents admitted that, if Tarwater made cash payments to or on behalf of Davis and if those payments were reasonably susceptible of being checked, those amounts would not be taxable to Tarwater. In fact, however, the agents said they found no evidence that Tarwater actually passed on the bulk of the JMH monies allegedly intended for Davis. Indeed, Tarwater’s bank records— with their trail of deposits, withdrawals, and ending balances — suggested that Tar-water did not pass on most of the “Willie Davis” monies but, instead, used those monies for his own purposes. In addition, although Tarwater told Newman that he cashed one check for Davis on each of the frequent occasions that he received two checks from the hospital on the same day, Tarwater’s bank records established that all such checks were instead deposited into one of Tarwater’s several bank accounts.
*506Moreover, Tarwater was a certified public accountant who knew very well the importance of documenting transactions and creating an audit trail. He nonetheless failed to provide the hospital with invoices for Davis’s work, failed to segregate the “Willie Davis” monies in a single account separate from his own personal and/or business accounts, failed to keep receipts for his purported cash payments to Davis, failed to advise his business partners about his arrangement with Davis, failed to keep receipts for most of the twice-weekly wire transfers about which his nephew testified, and otherwise failed to provide the IRS agents with the kind of documentation that accountants are known to handle on a daily basis, the kind of documentation that is reasonably susceptible of being checked.
Mindful that section 7206(1) is a perjury statute, requiring the government to prove that a defendant did not believe his or her tax return to be true and correct, several courts have determined that evidence of a defendant’s attempts to avoid making records, to conceal assets, or to mislead others is probative of the did-not-believe-the-return-to-be-true element of a section 7206(1) offense. For example, in United States v. Scott, 660 F.2d 1145, 1160 (7th Cir.1981), cert. denied, 455 U.S. 907, 102 S.Ct. 1252, 71 L.Ed.2d 445 (1982), the court determined that the jury had a sufficient basis from which to infer that the defendant did not believe his tax return to be true and correct where the evidence demonstrated (1) that the defendant was a lawyer and an experienced banker who typically invested most of his money derived from ordinary and legitimate sources in high yield interest bearing securities or certificates of deposit; (2) that the defendant secreted large amounts of cash in safe deposit boxes, which was very much out of character for a man who so carefully invested and earned interest on his other funds; (3) that the defendant failed to keep records of his living and travel expenses; and (4) that the defendant made statements to the Tax Division of the Department of Justice which “the jury could have believed ... to be false exculpatory statements, evidencing an intent to mislead or conceal.” Scott, 660 F.2d at 1160. See also United States v. Kaatz, 705 F.2d 1237, 1246 (10th Cir.1983) (explaining that the jury could infer willfulness from evidence that the defendants “handled their affairs so as to avoid making the records usual to the businesses which they operated, and they did not disclose to their accountant the receipts which they diverted”). In both Scott and Kaatz, the courts cited the Supreme Court’s decision in Spies v. United States, 317 U.S. 492, 499, 63 S.Ct. 364, 87 L.Ed. 418 (1943), a tax evasion case wherein the Court explained that, where a criminal tax statute makes “willfulness” an element of the offense, willfulness may be inferred “from conduct such as keeping a double set of books, making false entries or alterations, or false invoices or documents, destruction of books or records, concealment of assets or covering up sources of income, handling of one’s affairs to avoid making the records usual in transactions of the kind, and any conduct, the likely effect of which would be to mislead or to conceal.”
Here, the jury (1) heard two IRS agents testify that Tarwater understated his income by sizeable amounts; (2) heard several witnesses testify about Tarwater’s very unusual and virtually undocumented handling of the “Willie Davis” monies; (3) heard testimony revealing that Tarwater was a certified public accountant, one who by training understood the importance of documenting transactions, segregating funds, and maintaining an audit trail yet did none of those things in regard to the “Willie Davis” monies; and (4) heard testi*507mony demonstrating that Tarwater gave a false explanation to the accountant who began the initial investigation into Tarwa-ter’s handling of the “Willie Davis” monies. We think such testimony/evidence provided a sufficient basis from which the jury could infer that Tarwater knew very well that his tax returns for the years 1992 through 1994 were not true and correct as to every material matter.
III. JURY INSTRUCTIONS
A.
Tarwater contends that the district court impermissibly shifted the burden of proof when it instructed the jury that “the government is not required to prove the non-existence of alleged payments by [Tarwater] to or on behalf of Mr. Davis.” J.A. at 558. As Tarwater correctly suggests, the government carries the burden of proving each and every element of a criminal offense beyond a reasonable doubt, and any jury instruction that shifts that burden to a defendant constitutes a violation of due process. Carella v. California, 491 U.S. 263, 265, 109 S.Ct. 2419, 105 L.Ed.2d 218 (1989); Sandstrom v. Montana, 442 U.S. 510, 521, 99 S.Ct. 2450, 61 L.Ed.2d 39 (1979). Whether a jury instruction violates a defendant’s due process rights is reviewed de novo. United States v. Amparo, 68 F.3d 1222, 1224 (9th Cir.1995).
Tarwater does not suggest that the district court failed to accurately instruct the jury as to the elements of a section 7206(1) offense. Indeed, the district court instructed the jury that the government had the burden of proving, beyond a reasonable doubt, that Tarwater made and subscribed the three tax returns described in the indictment, that the returns contained a written declaration that they were made under penalty of perjury, that Tarwater knew the returns contained information that was material and false, and that Tar-water willfully filed the returns with the IRS. J.A. at 556. In defining the term “willfully,” the district court said that “[Tarwater] must have acted voluntarily and intentionally and with the specific intent to do something he knew the law prohibited, that is to say, with intent either to disobey or to disregard the law.” J.A. at 557. The district court also repeatedly instructed the jury that Tarwater had no obligation to present any evidence at all, that it was the government’s burden to prove beyond a reasonable doubt every element of the crime charged. In the district court’s words:
[Tarwater] starts out with a clean slate, with no evidence at all against him, and the law presumes that he is innocent. This presumption of innocence stays with him unless the government presents evidence here in court that overcomes that presumption, and convinces you beyond a reasonable doubt that he is guilty.
This means that [Tarwater] has no obligation to present any evidence at all, or to prove to you in any way that he is innocent. It is up to the government to prove that he is guilty, and this burden stays on the government from the start to the finish....
The government must prove every element of the crime charged beyond a reasonable doubt....
You are not to apply a different burden of proof in this case because [Tarwater] is an accountant. The government must prove to you beyond a reasonable doubt that [Tarwater] willfully failed to report income on his Internal Revenue Service Tax Return.
*508.... For each violation, you must decide whether the government has presented proof beyond a reasonable doubt that [Tarwater] is guilty of that particular violation.
While the government has the burden to prove beyond a reasonable doubt that the defendant understated the amount of gross receipts or total income reported on his 1992 Federal Income Tax Return and the amount of his total income reported on his 1993 and 1994 Federal Income Tax Returns, the government is not required to prove the non-existence of alleged payments by [Tarwater] to or on behalf of Mr. Davis.
.... Do not return a guilty verdict unless the government proves the crimes charged beyond a reasonable doubt.
J.A. at 552-560.
We do not agree that the district court impermissibly shifted the burden of proof when it instructed the jury that “the government is not required to prove the nonexistence of alleged payments by [Tarwa-ter] to or on behalf of Mr. Davis.” J.A. at 558. Indeed, our review of the relevant case law convinces us that the district court’s instruction was a correct statement of the law.
In United States v. Ballard, 535 F.2d 400 (8th Cir.), cert. denied, 429 U.S. 918, 97 S.Ct. 310, 50 L.Ed.2d 283 (1976), the Eighth Circuit considered the burden placed on the government in a section 7206(1) criminal prosecution. In that case, the government presented evidence of Ballard’s having deposited monies that were not reported as gross business receipts on his tax returns. Charged with willfully making and subscribing false income tax returns for two years, Ballard testified on his own behalf at trial, stating that fires had destroyed his business records, that he had — in fact — sustained a loss in his businesses during the two years in question, and that he had spent all of the cash he had received in operating his businesses. On appeal of his convictions, Ballard argued that the government could not establish its case by mere proof of gross receipts but was required to demonstrate Ballard’s receipt of income, measured by gross receipts less expenses. The Eighth Circuit disagreed, stating:
The Government’s burden [in a section 7206(1) ] case is less than in a tax evasion case. In the latter, the prosecution must show taxpayer’s receipt of taxable income... .The prosecution’s burden here is similar to that in a failure to file case in which evidence of unexplained receipts shifts to the taxpayer the burden of coming forward with the amount of offsetting expenses.... Thus, the evidence of unexplained receipts here established a prima facie case of taxpayer’s failure to disclose substantial amounts of gross income.
Ballard, 535 F.2d at 405. Other courts have similarly suggested that, while the government bears the burden of proof throughout any criminal tax case, the government is not required to negate every possible source of nontaxable income, to track down all possible expenses, or to prove the absence any off-setting costs or deductions. See Davis v. United States, 226 F.2d 331, 335-336 (6th Cir.1955) (explaining that “evidence of unexplained funds or property in the hands of a taxpayer establishes a prima facie case of understatement of income, and it is then incumbent on [the taxpayer] to overcome the logical inferences to be drawn from such proof’), cert. denied, 350 U.S. 965, 76 S.Ct. 432,100 L.Ed. 838 (1956); United States v. Orlowski, 808 F.2d 1283 (8th Cir.1986) (rejecting the defendant’s argument that, in a section 7206(1) case, the government was *509required to prove the nonexistence of alleged expenses), cert. denied, 482 U.S. 927, 107 S.Ct. 3210, 96 L.Ed.2d 697 (1987); United States v. Stein, 437 F.2d 775 (7th Cir.1971) (rejecting the defendant’s suggestion that, in a tax evasion case, the government was required to eliminate all non-income items from its bank deposit proof); Siravo v. United States, 377 F.2d 469, 473-474 (1st Cir.1967) (explaining that, in a section 7206(1) case, “evidence of unexplained receipts shifts to the taxpayer the burden of coming forward with evidence as to the amount of offsetting expenses, if any”).
In Holland v. United States, 348 U.S. 121, 135-136, 75 S.Ct. 127, 99 L.Ed. 150 (1954), the Supreme Court held that, in a net worth case, a case built “solely on the approximations and circumstantial inferences of a net worth computation,” the government makes out a prima facie case of tax evasion when it has proved the existence of a likely source of taxable income sufficient to account for a taxpayer’s net worth increases and has also investigated all “relevant leads furnished by the taxpayer — leads reasonably susceptible of being checked, which, if true, would establish the taxpayer’s innocence.” In so limiting the government’s investigative responsibilities, the Supreme Court stated:
Any other rule would burden the Government with investigating the many possible nontaxable sources of income, each of which is as unlikely as it is difficult to disprove. This is not to say that the Government may disregard explanations of the defendant reasonably susceptible of being cheeked. But where relevant leads are not forthcoming, the Government is not required to negate every possible source of nontaxable income, a matter peculiarly within the knowledge of the defendant.
Holland, 348 U.S. at 138, 75 S.Ct. 127; cf. United States v. Lawhon, 499 F.2d 352, 356-57 (5th Cir.1974)(explaining that in a case where the government bases its proof on specific items, the “leads doctrine” applicable in circumstantial evidence — or net worth — cases does not apply; in such a case, the government does not bear the burden of trying to discover and exclude all possible non-income items from its evidence of taxable income), cert. denied, 419 U.S. 1121, 95 S.Ct. 804, 42 L.Ed.2d 820 (1975).
In this case, the district court correctly instructed the jury that Tarwater had no obligation to present any evidence at all, that he was presumed innocent unless and until the government proved, beyond a reasonable doubt, the elements of the section 7206(1) charges against Tarwa-ter. The court correctly defined those elements and cautioned the jury that government had the burden of proving every element of the crimes charged beyond a reasonable doubt. As suggested in numerous cases, including Ballard, Davis, Orlowski, and Holland, the government was not required to prove the absence of pass-through payments to Davis, particularly where, as here, Tarwater provided the government no help in identifying the form or source of those payments. We accordingly conclude that the district court in no way shifted the burden of proof when it instructed the jury that “the government is not required to prove the non-existence of alleged payments by [Tarwater] to or on behalf of Mr. Davis.” J.A. at 558. The district court correctly stated the law, and there was no violation of Tarwater’s due process rights.
B.
Tarwater also argues that the district court erred by not giving a good faith instruction and by not giving Tarwa-*510ter’s proposed instruction that “a transfer- or of funds does not have any reporting requirements under the Internal Revenue Code.” J.A. at 274. We review for abuse of discretion the district court’s choice of instructions. United States v. Prince, 214 F.3d 740, 760-761 (6th Cir.2000). We must consider the instructions as a whole to determine whether they fairly and adequately submitted the issues and applicable law to the jury. United States v. Khalil, 279 F.3d 358, 364 (6th Cir.2002). Generally, a defendant is entitled to an instruction on defense theories that are supported by law and raised by the evidence presented. United States v. Duncan, 850 F.2d 1104, 1118 (6th Cir.1988). However, we will reverse a district court’s refusal to give a requested instruction only when (1) the requested instruction is a correct statement of the law; (2) the requested instruction is not substantially covered by other instructions actually delivered; and (3) the failure to give the requested instruction impairs the defendant’s theory of the case. United States v. Chesney, 86 F.3d 564, 573 (6th Cir.1996).
Initially, we question whether Tarwater presented any evidence to support his good faith defense. Assuming arguendo that he did, however, we nonetheless find that the instructions, viewed as a whole, adequately encompassed his theory of defense. The district court instructed the jury on the specific intent required for a conviction for filing false tax returns by stating:
The word “willfully,” as used in this statute, means a voluntary, intentional violation of a known legal duty. In other words, the defendant must have acted voluntarily and intentionally and with the specific intent to do something he knew the law prohibited, that is to say, with intent either to disobey or to disregard the law. Negligent conduct is not sufficient to constitute willfulness.
J.A. at 557. The jury’s conclusion that Tarwater acted willfully would necessarily negate any possibility of “good faith” in filing false tax returns. See United States v. Pomponio, 429 U.S. 10, 12-13, 97 S.Ct. 22, 50 L.Ed.2d 12 (1976) (explaining that where a district court instructs the jury that the term “willful” as used in section 7206 means “a voluntary, intentional violation of a known legal duty, ... [a]n additional instruction on good faith [i]s unnecessary”); United States v. Ervasti, 201 F.3d 1029, 1041 (8th Cir.2000) (holding that the district court did not abuse its discretion in refusing the defendant’s request for a good faith instruction where the court instructed the jury that “[a]n act is done willfully if it is done voluntarily and intentionally with the purpose of violating a known legal duty”).
In support of his proposed trans-feror instruction, Tarwater cites Marlar, Inc. v. United States, 151 F.3d 962 (9th Cir.1998). In Marlar, the court held that a club which transferred monies from its customers to the club’s dancers did not make “payments” triggering a Form 1099 reporting requirement on the part of the club. We are unconvinced that Marlar supports Tarwater’s argument that the district court abused its discretion in refusing to instruct the jury in this section 7206(1) case that “a transferor of funds does not have any reporting requirements under the Internal Revenue Code.” Indeed, we find no such abuse.
TV. PROSECUTORIAL MISCONDUCT
Tarwater contends that the district court erred by denying his motion for a mistrial based on improper statements made by the government’s counsel during closing arguments. Whether the government’s closing argument constitutes *511prosecutorial misconduct presents a mixed question of law and fact that we review de novo. United States v. Emuegbunam, 268 F.3d 377, 394 (6th Cir.2001), cert. denied, — U.S. -, 122 S.Ct. 1450, 152 L.Ed.2d 392 (2002); United States v. Clark, 982 F.2d 965, 968 (6th Cir.1993). When reviewing claims of prosecutorial misconduct, we determine first whether the statements were improper. United States v. Krebs, 788 F.2d 1166, 1177 (6th Cir.1986). If they appear improper, we then look to see if they were flagrant and warrant reversal. United States v. Carroll, 26 F.3d 1380, 1388 (6th Cir.1994). To determine flagrancy, we consider: 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. United States v. Monus, 128 F.3d 376, 394 (6th Cir.1997) (citing United States v. Cobleigh, 75 F.3d 242, 247 (6th Cir.1996)).
Tarwater contends that, during closing arguments, the prosecutor improperly commented on Tarwater’s post-Mircrocfa right to silence. Specifically, Tarwater complains about four statements, two made by AUSA Weddle and two made by AUSA Baxter in their rebuttal closing. Weddle said: (1) “Mr. Tarwater declined to discuss any tax matters with the Revenue Agent;” and (2) “No one in the courtroom knows whether money went to Willie Davis; well, maybe there is one other person in this courtroom who knows.” J.A. at 541, 543. Baxter said: (1) “[Defense counsel] could have brought Willie Davis before this jury just like the government;” and (2) “Now, from a criminal defense point of view, justice means one thing. It means: ‘Acquit my client.’ I mean, there is no other explanation or definition for justice for a criminal defense lawyer.” J.A. at 544-546. Defense counsel objected to each of these statements, albeit without elaboration. According to Tarwater, because Miranda warnings had been given to him before he exercised his right to silence when he was questioned by the IRS agent, the prosecutors violated his rights under Miranda by referring to his silence or failure to call witnesses.
The Fifth Amendment states: “No person ... shall be compelled in any criminal case to be a witness against himself. ...” U.S. Const, amend. V. The Supreme Court, in Miranda v. Arizona, stated that “it is impermissible to penalize an individual for exercising his Fifth Amendment privilege when he is under police custodial interrogation. The prosecution may not, therefore, use at trial the fact that [the defendant] stood mute or claimed his privilege in the face of accusation.” Miranda v. Arizona, 384 U.S. 436, 468 n. 37, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966). Consistent with Miranda, prosecutors may not comment on a defendant’s post-arrest silence in their case in chief, on cross-examination, or in closing arguments. Doyle v. Ohio, 426 U.S. 610, 619-20, 96 S.Ct. 2240, 49 L.Ed.2d 91 (1976). Such proscription, however, does not extend to a defendant’s failure to call a witness or to otherwise present exculpatory evidence so long as the prosecutor does not tax the exercise of the defendant’s right to remain silent. See, e.g., United States v. Cabrera, 201 F.3d 1243, 1250 (9th Cir.2000); United States v. Sblendorio, 830 F.2d 1382, 1391 (7th Cir. Ordinarily, we review prosecuto-rial comments about a defendant’s post-Miranda silence under a harmless error standard.) See, e.g., United States v. Moreno, 185 F.3d 465, 472 (5th Cir.1999).
Before the prosecutors made the challenged statements in their rebuttal ar*512guments, defense counsel argued to the jury:
You haven’t heard why Willie Davis isn’t before this jury. You haven’t heard that, have you? No. Where is Willie Davis? The government didn’t call Willie Davis; [the IRS agent] didn’t talk to Mr. Willie Davis, and the government has the burden of proof.
J.A. at 539-540. AUSA Baxter responded to this argument by saying: “[[D]efense counsel] could have brought Willie Davis before this jury just like the government.” J.A. at 544. Baxter’s comment was proper and did not run afoul of Tarwater’s Fifth Amendment rights.
To the extent, if any, AUSA Wed-dle improperly commented about Tarwa-ter’s failure to discuss any tax matters with the revenue agents, we find his comments harmless. As Weddle himself pointed out to the jury, Tarwater himself put into evidence an exhibit which twice stated that Tarwater declined to discuss any tax matters with the revenue agent. J.A. at 541, 1038.
Finally, we do not find Baxter’s comment about defense counsel’s view of justice so flagrant as to warrant reversal.
V. EVIDENTIARY ISSUES
A.
Tarwater argues that the district court should not have admitted Agent Barton’s expert opinion testimony that Tarwa-ter under-reported his income. According to Tarwater, Barton’s opinion was unreliable “because it was based upon facts or assumptions about which she had no knowledge, let alone the ‘specialized knowledge’ required by Rule 702.” Def.’s Br. at 41. Tarwater suggests that the magistrate judge who conducted the Dau-bert hearing “focused on Barton’s qualifications and expressly abandoned the gate keeping function of Daubert.” Id. We review a district court’s decision to admit expert testimony for abuse of discretion. United States v. Langan, 263 F.3d 613, 620 (6th Cir.2001).
The magistrate judge held a Daubert hearing on January 18, 2001. Based on the evidence and argument presented, the judge ruled that Barton’s testimony was “both relevant and reliable pursuant to Rule 702, Federal Rules of Evidence, and should be admissible at trial.” J.A. at 187. In particular, the magistrate judge found that it was “clear from the evidence presented during the Daubert hearing that Ms. Barton is qualified to express an expert opinion on whether defendant understated his taxable income for the years 1991-1994.” J.A. at 179. In concluding its twenty-five page memorandum and order, the court wrote:
Ms. Barton is a qualified expert in her field who possesses technical knowledge that will assist the trier of fact to understand and determine the issues in this case. Her testimony is based upon sufficient facts and/or data, the testimony is the product of reliable principles and methods, and it appears that Ms. Barton has applied the principles and methods reliably to the facts of this case.
J.A. at 187. After reviewing the magistrate judge’s memorandum and order, the transcript of the Daubert hearing, and the pleadings filed by the parties, the district court overruled Tarwater’s objections and appeal of the magistrate judge’s ruling on the admissibility of Barton’s opinions. J.A. at 210-213.
In Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993), the Supreme Court held that Federal Rule of Evidence 702 requires district courts to ensure that an expert’s scientific testimony “both rests *513on a reliable foundation and is relevant to the task at hand.” Daubert, 509 U.S. at 597, 113 S.Ct. 2786. The Court suggested a non-exclusive list of factors for courts to consider when deciding whether proposed scientific expert testimony is sufficiently “reliable.” Such factors include: (1) whether a theory or technique has been or can be tested; (2) whether the theory or technique has been subjected to peer review and publication; (3) the known or potential rate of error; and (4) whether the technique has been accepted by a relevant scientific community. Daubert, 509 U.S. at 593-594,113 S.Ct. 2786.
In Kumho Tire Co. v. Carmichael, 526 U.S. 137, 119 S.Ct. 1167, 143 L.Ed.2d 238 (1999), the Court extended Daubert to include any expert testimony based on “technical” and “other specialized knowledge.” Kumho Tire Co., 526 U.S. at 152, 119 S.Ct. 1167. With respect to the individual factors enumerated in Daubert, the Kumho Court held that, while trial courts may consider such factors when assessing the reliability of all types of expert testimony, “Daubert’s list of specific factors neither necessarily nor exclusively applies to all experts or in every case.” Kumho, 526 U.S. at 141, 119 S.Ct. 1167. “[Wjhether Daubert’s specific factors are, or are not, reasonable measures of reliability in a particular case is a matter-that the law grants the trial judge broad latitude to determine.” Kumho, 526 U.S. at 153, 119 S.Ct. 1167.
After reviewing Barton’s trial testimony, we cannot say that the district court abused its discretion by allowing her to testify as an expert witness. We find no merit to Tarwater’s argument that the district court abandoned its Daubert gate-keeping function by failing to consider the Daubert factors. To be sure, the court concluded — and we agree — that the Dau-bert factors were of limited value here, but the court nonetheless carefully considered whether Barton’s testimony was reliable and relevant. The court summarized its findings as follows:
Ms. Barton’s testimony is the product of well-established principles of bookkeeping and accounting as those areas of expertise are applied to the Internal Revenue Code. Ms. Barton demonstrated an understanding of the rules and regulations of the IRS Code that require the reporting of all taxable income. The methods employed by Ms. Barton in reaching her expert opinion were the application of her education, training, knowledge and experience to analyze defendant’s tax returns and business records to determine whether the defendant complied with the requirements of the Internal Revenue Code to report all his income.
J.A. at 182. Given such findings, we are confident that the district court had an adequate basis for concluding that Barton’s testimony was both reliable and relevant.
Moreover, we reject Tarwater’s assertion that Barton’s testimony was unreliable because “based upon facts or assumptions about which she had no knowledge.” Def.’s Br. at 41. Indeed, the record refutes any such assertion. As stated by the district court:
Ms. Barton testified that her computations were based upon Defendant’s bank records and business records, and her expert opinion that Defendant under reported his income is based upon her examination of Defendant’s record, her ability to trace the flow of income and the disbursement of same as viewed by a Revenue Agent with twenty-five years of experience and training, and from her analysis of Defendant’s bank records and business records. It appears to the Court that Ms. Barton has applied the *514principles and methods of her technical expertise to the facts of this ease.
J.A. at 183. At trial, Barton reiterated that her opinions were based upon her review of Tarwater’s records — books, bank statements, and checks — and tax returns. Tarwater’s suggestion that Barton’s opinion involved a determination of the credibility of two non-testifying taxpayers is without merit.
B.
As an expert witness, Agent Barton was permitted to testify — over Tarwa-ter’s objection — regarding her opinion that Tarwater understated his income for the years 1992-1994. On direct examination, the government elicited testimony from Barton regarding her review of the documentary evidence, including Tarwater’s personal and business financial records, income tax returns, bank records, and JMH records. On cross-examination, defense counsel asked Barton whether she had talked with Willie Davis (she had not), whether she knew if Tarwater had made any cash payments to Willie Davis (she knew only what was recorded in the books and records), and whether she did or did not answer “yes” when she was asked in the earlier Daubert hearing if she would want to talk with Willie Davis to determine whether cash payments were made to him (she answered “yes”). Tarwater contends that, by opining that Tarwater understated his income, Barton necessarily communicated her opinion that Tarwater did not make sufficient payments to or on behalf of Willie Davis. He contends that Barton thus improperly “vouched” for the credibility of Davis’s alleged out-of-court statement to the effect that he had not received any cash payments from Tarwater.
We are not persuaded by Tarwater’s “vouching” argument. Barton was asked by the government to review the documentary evidence, and she rendered an opinion about the accuracy of Tarwater’s tax returns based on that evidence. The jury was capable of determining that, if Tarwa-ter failed to document the alleged cash transfers to Davis, those cash transfers would not be reflected in Barton’s calculations. That she did not consider undocumented transfers in no way suggests that she “vouched” for an alleged out-of-court statement by Davis that he did not receive any cash payments from Tarwater.
C.
On September 15, 2000, approximately seven months before trial, the government provided Tarwater with a written summary of Agent Barton’s proposed testimony. As required by Federal Rule of Criminal Procedure 16(a)(1)(E), the summary described Barton’s opinions, the bases and reasons for those opinions, and Barton’s qualifications. The summary also disclosed that Barton’s opinions were based on her examination of Tarwater’s income tax returns, bank records, business records, and records from JMH. J.A. at 73-75. The government supplemented Barton’s summary on September 20, 2000, disclosing to Tarwater that Barton would also testify that a taxpayer’s failure to include all income on a tax return can influence the correct computation of tax liability and can impede the IRS’s verification and/or audit of the tax return. J.A. at 79-80.
On October 3, 2000, in response to Tar-water’s motion to strike Barton’s testimony, the government again supplemented Barton’s summary, disclosing to Tarwater the specific details of Barton’s computations. J.A. at 110-120. The magistrate judge denied Tarwater’s motion to strike Barton’s testimony on January 4, 2001, ruling that the government’s disclosures were sufficient and did not constitute a violation of Rule 16(a)(1)(E).
*515On January 18, 2001, at the Daubert hearing, Barton testified as to Tarwater’s understatement of income for the years 1991 through 1994, giving complete details of her computations. Following the Dau-bert hearing, the magistrate denied Tarwa-ter’s renewed motion to strike Barton’s testimony, again ruling that the government had complied with Rule 16(a)(1)(E). The court stated:
The “summary” required by Rule 16(a)(1)(E) is only required to describe the witness’ opinions, the bases and the reasons for those opinions, and the witness’ qualifications. It does not require the expert to set forth a detailed justification for her expert opinion. That is an area which may be explored by counsel on cross-examination at trial.
J.A. at 185.
The evening before Barton was scheduled to testify at trial, the government produced a report entitled “Explanation of Items.” Prepared by Barton, the report revealed that, at an early stage in her investigation, Barton estimated that Tar-water was entitled to credits of $3,276.00 per year for payments to rental car companies on behalf of Davis. Barton later eliminated those credits from her computations.
Also the evening before Barton was scheduled to testify, the government produced a copy of Barton’s revised computations of Tarwater’s understatement of income. Interestingly, the revisions in Barton’s computations represented a net effect of approximately $18,000 in Tarwa-ter’s favor.
Based on the government’s last minute production of Barton’s “Explanation of Items” and revised reports, Tarwater moved to strike Barton’s testimony. Claiming Brady and Rule 16(a)(1)(E) violations, Tarwater also moved to dismiss or to continue trial. The district court denied Tarwater’s motions.
Tarwater now contends that the district court erred by denying Tarwa-ter’s motions to strike and/or to dismiss. This court reviews a district court’s rulings on Rule 16(a)(1)(E) issues for abuse of discretion. United States v. Azad, 809 F.2d 291, 294 (6th Cir.1986), cert. denied, 481 U.S. 1004, 107 S.Ct. 1626, 95 L.Ed.2d 200 (1987). We reviéw de novo the issue of whether evidence withheld by the prosecution constitutes Brady material. United States v. Phillip, 948 F.2d 241, 250 (6th Cir.1991). A district court’s denial of a Brady claim is reviewed by this court de novo, to determine whether the suppressed Brady evidence undermines confidence in the outcome of the defendant’s trial. United States v. Miller, 161 F.3d 977, 987 (6th Cir.1998).
To establish a violation under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), a defendant has the burden of establishing that the prosecutor suppressed evidence that was unknown to the defendant. See United States v. Agurs, 427 U.S. 97, 103, 96 S.Ct. 2392, 2397, 49 L.Ed.2d 342 (1976) (explaining that the Brady rule applies to “the discovery, after trial, of information which had been known to the prosecution but unknown to the defense”); United States v. Mullins, 22 F.3d 1365, 1371 (6th Cir.1994) (explaining that “Brady is concerned only with cases in which the government possesses information which the defendant does not”); Coe v. Bell, 161 F.3d 320, 344 (6th Cir.1998) (explaining that there is no Brady violation if. the defendant knew or should have known the essential facts permitting him to take advantage of the information in question-, or it the information was available to him from another source).
Tarwater claims that the government violated Brady when it disclosed — before *516Barton testified—that Barton at one time gave him credit for car rental payments that Tarwater himself supposedly made on behalf of Davis. Obviously, Tarwater knew whether he did or did not make such payments on behalf of Davis. Because the information about which he complains was not unknown to him, and because the information was disclosed to him before Barton testified, permitting him to take advantage of the information during his cross-examination of Barton, we find no Brady violation whatsoever.
Furthermore, we find that the district court did not abuse its discretion when it denied Tarwater’s motion to dismiss and/or strike on the grounds that the government violated Rule 16(a)(1)(E) by producing Barton’s revised reports the day before Barton testified. Tarwater’s counsel was able to review the revised reports before extensively cross-examining Barton about the changes reflected in those reports. As explained by Barton at trial, the changes were necessitated by information that Barton acquired from Tarwater’s own records not long before trial. The changes, moreover, were largely in Tarwa-ter’s favor. For example, the revised reports reflected no change in the understatement of income for 1992, a $19,000 reduction in the understatement of income for 1993, and an $810 increase in the understatement of income for 1994. Because Tarwater did not suffer any surprise and because he does not suggest how the outcome of the case would have been different if he had learned about Barton’s revised computations earlier, we will not disturb the decision of the district court.
D.
Tarwater contends that the district court abused its discretion by permitting the government to use summary charts at trial that were not disclosed to him in advance of trial. The charts, however, were not admitted into evidence, were not submitted to the jury during deliberations, and were not used in lieu of the bank records upon which the summary charts were based. In contrast, Tarwa-ter’s bank records were admitted into evidence, were disclosed to Tarwater long before trial, and were given to the jury to review during their deliberations. Moreover, the district court instructed the jury that the summary charts were not evidence and should be disregarded if they did not correctly reflect the facts or figures shown by the evidence. Under the circumstances, we find Tarwater’s claim regarding the summary charts to be frivolous.
E.
Tarwater complains that the trial court abused its discretion in admitting evidence of crimes for which he was not on trial—namely Medicare and Medicaid fraud—in violation of Rule 404(b). In particular, Tarwater contends that the district court abused its discretion when it refused to exclude testimony concerning the circumstances surrounding his receipt of the “Willie Davis” checks. For example, the court refused to exclude evidence about whether the hospital received invoices for the checks written to Tarwater personally, whether the hospital verified Medicare or Medicaid receipts before signing checks to Tarwater, whether Chambers was instructed to cease work on a review of the correctness and propriety of making payments to Davis and Tarwater, and whether it was a customary practice in Tarwater’s and Peters’ accounting practices to send invoices to clients for payment. Tarwater contends that this testimony may have suggested to the jury that he received funds unlawfully or fraudulently from JMH.
*517In denying Tarwater’s pre-trial motion to exclude this evidence, the district court found that, because the challenged evidence was inextricably intertwined with evidence of the crimes charged, Rule 404(b) was not implicated. See United States v. Everett, 270 F.3d 986, 992 (6th Cir.2001) (explaining that “Rule 404(b) is not applicable where the challenged evidence is ‘inextricably intertwined’ with evidence of the crime charged”). We agree that the challenged evidence was inextricably intertwined with the evidence of the crimes charged, and we accordingly find no abuse of discretion on the part of the district court in refusing to exclude the evidence.
VI. SENTENCING ISSUES
A.
Tarwater first challenges the constitutionality of the United States Sentencing Guidelines (“Guidelines”). He contends that, contrary to what the Guidelines permit, a jury should decide, beyond a reasonable doubt, all facts that are used to increase a defendant’s Guidelines sentencing range. In this case, a tax case, the Guidelines provide a base offense level of 6, with a corresponding sentencing range of zero to six months. Tarwater argues that, by permitting the court to adjust his offense level above a level of 6 based upon the court’s preponderance-of-the-evidence factual findings, the Guidelines unconstitutionally removed from the jury the assessment of facts that increased the prescribed range of penalties for his offense. We review constitutional challenges de novo. United States v. Beavers, 206 F.3d 706, 708 (6th Cir.2000). We also review questions of law concerning the application of the Guidelines de novo. United States v. Canestraro, 282 F.3d 427, 431 (6th Cir.2002).
In Apprendi v. New Jersey, 530 U.S. 466, 490, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000), the Supreme Court held that “[o]ther than the fact of a prior conviction, any fact that increases the penalty for a crime beyond the prescribed statutory maximum must be submitted to a jury, and proved beyond a reasonable doubt.” Recently, in Harris v. United States, — U.S. -, 122 S.Ct. 2406, 153 L.Ed.2d 524 (2002), five members of the Court agreed that facts increasing the range of punishment below the statutory maximum may be determined by the judge and need not be found beyond a reasonable doubt by a jury. Among other things, the Harris Court recognized the continuing vitality of McMillan v. Pennsylvania, 477 U.S. 79, 106 S.Ct. 2411, 91 L.Ed.2d 67 (1986), a case wherein the Court held constitutional a state statute that permitted a sentencing court, rather than a jury, to find facts that raised the mandatory minimum sentence. McMillan, 477 U.S. at 88, 106 S.Ct. 2411. Together, Harris, Apprendi, and McMillan foreclose Tarwater’s constitutional challenge to the Guidelines.
Tarwater was convicted of violating 26 U.S.C. § 7206(1), which provides that any person convicted of violating that statute “shall be fined not more than $100,000 ... or imprisoned not more than 3 years, or both.” Tarwater was sentenced to eighteen (18) months imprisonment, well below the statutory maximum. Because no factual determinations made at Tarwater’s sentencing increased his penalty beyond the statutory maximum, we find no merit to his argument that his sentence was constitutionally infirm.
B.
Tarwater contends that the district court did not make independent factual findings for each contested matter in the presentence report in violation of *518Federal Rule of Criminal Procedure 32(c)(1). Such rule provides that “[a]t the sentencing hearing ... [f]or each matter controverted, the court must make either a finding on the allegation or a determination that no finding is necessary because the controverted matter will not be taken into account in, or will not affect, sentencing.” Fed. R. Cr. P. 32(c)(1). Because the purpose of the rule is to ensure that sentencing is based on reliable facts found by the court itself after deliberation, a court may not merely summarily adopt the factual findings in the presentence report or simply declare that the facts are supported by a preponderance of the evidence. United States v. Corrado, 227 F.3d 528, 540 (6th Cir.2000); United States v. Tackett, 113 F.3d 603, 613 (6th Cir.1997). We require “literal compliance” with Rule 32(c)(1) because it “helps to ensure that defendants are sentenced on the basis of accurate information and provides a clear record for appellate courts, prison officials, and administrative agencies who may later be involved in the case.” Tackett, 113 F.3d at 613-614.
Tarwater made three factual objections to the presentence report. Specifically, he objected to: (1) the amount of the tax loss and restitution; (2) the adjustment for illegal activity pursuant to U.S.S.G. § 2Tl.l(b)(l); and (3) the adjustment for abuse of a position of trust pursuant to U.S.S.G. § 3B1.3. The district court held a lengthy sentencing hearing on July 12, 2001, at which time the lawyers presented evidence and argument concerning Tarwa-ter’s objections.
From the partial transcript included in the record before us, it appears that the court first considered Tarwater’s objection to the amount of the tax loss. On page eight of the transcript, defense counsel stated: “[A]t this time, we would take up the calculation of the amount of the tax loss and the related issue, of course, of the calculation of restitution.” J.A. at 676. On page twenty-nine of the transcript, the next page to be included in the record, the court stated:
What the defense is trying to suggest to the court is that anything that the government could not prove that he should receive a credit for, the defendant should receive credit. As I understand the burden of proof for the government in this case, is the government had to show that the defendant received “X” dollars in funds and that of those funds he failed to report it on his income tax return.
The government was able to show and trace most of these funds to the defendant’s checking account, various checking accounts, and from that I think the proof was clear beyond a reasonable doubt that these funds were used for his benefit. The jury was so convinced and I am so convinced.
J.A. at 677. On page forty-six of the transcript, the next page to be included in the record, the district court agreed to reduce the probation officer’s estimate of Tarwa-ter’s 1994 understatement of income by $48,000. J.A. at 678. On page sixty-seven of the transcript, the court stated: “[Concerning the amount, I have calculated the amount, which is now $218,936, multiplied by 28%, will give a tax loss of $61,302.08.” J.A. at 680. Although we cannot determine what the district court may have said or heard on the missing pages of the transcript, the few pages that we have reviewed clearly reveal that the district court did not merely summarily adopt the amount of loss presented in the presen-tence report.
That the district court understood its responsibility to make independent factual findings was made crystal clear when the judge stated at the sentencing hearing: *519“The Sixth Circuit has held that the district court must make specific findings of fact, as required by Rule 32(c)(1) of the Federal Rules of Criminal Procedure, and must not rely on the presentence report.” J.A. at 681. After making this statement, the district court set out its independent factual findings as to Tarwater’s remaining two objections, those regarding the adjustments for illegal activity and for abuse of a position of trust. J.A. at 680-684. These findings, along with what we know about the district court’s treatment of the amount of loss, satisfy the requirements of Rule 32(c)(1).
VII. CONCLUSION
Having found no merit to any of Tarwa-ter’s arguments on appeal, we AFFIRM.
. Both the government and Tarwater subpoenaed Davis — who was present in the witness room throughout the trial — -but neither elected to call him to testify.