opinion: David M. KEARNS and Janet Kearns, Petitioners-Appellants, v. COMMISSIONER OF INTERNAL REVENUE, Respondent-Appellee.
  No. 91-2228.
  United States Court of Appeals, Sixth Circuit.
  Argued Aug. 3, 1992.
  Decided Nov. 23, 1992.
  Kenneth Andrew Gamble, Theodore F. Claypoole (argued and briefed), Gamble, Hartshorn, Grace & Alden, Columbus, Ohio., for petitioners-appellants.
  Abraham N.M. Shashy, Jr., Chief Counsel, I.R.S., Office of Chief Counsel, Gary R. Allen, Acting Chief (briefed), Gilbert S. Rothenberg, William J. Patton (argued), U.S. Dept, of Justice, Appellate Section Tax Div., Washington, D.C., for respondent-ap-pellee.
  Before: MARTIN and SILER, Circuit Judges; and DOWD, District Judge.
  The Honorable David D. Dowd, Jr., United States District Judge for the Northern District of Ohio, sitting by designation.
  BOYCE F. MARTIN, JR., Circuit Judge.
  David and Janet Kearns appeal the United States Tax Court’s finding that they underreported their joint income for 1979, 1980, and 1981. David Kearns also appeals the court’s imposition of additional penalties based on his fraudulent underreporting of income on the federal tax forms.
  From 1979 through 1981, David Kearns owned and operated an automobile parts and service company. Janet Kearns, his wife, was the bookkeeper for the business. In their testimony before the Tax Court, they admitted that they conducted the vast majority of their automobile parts business in cash. During 1979 the Kearns reported an annual gross income of $19,512. The Tax Court determined that in 1979 and the following two years, the Kearns made bank deposits and cash expenditures of substantially larger amounts. It was proven that in mid-1979 the Kearns paid approximately $24,000 in cash for a purchase of land. The Kearns spent approximately $61,000 on materials and services to build a new house on the newly-acquired property, even though they reported an annual gross income of no more than $22,600 for those years.
  A tax audit was conducted and a deficiency was found for each of the tax years in question. Because the Kearns lacked accurate records, the Commissioner reconstructed the contested income by using the “bank deposits and cash expenditures” method. See 26 U.S.C. § 446(b) (1986); United States v. Abodeely, 801 F.2d 1020, 1023 (8th Cir.1986). In using the bank-deposits-and-cash-expenditures method, the government must “ ‘initially introduce evidence to show (1) that, during the tax years in question, the taxpayer was engaged in an income producing business or calling; (2) that he made regular deposits of funds into bank accounts; and (3) that an adequate and full investigation of those accounts was conducted in order to distinguish between income and non-income deposits.’ ” Abodeely, 801 F.2d at 1023-1024 (quoting United States v. Morse, 491 F.2d 149, 152 (1st Cir.1974)) (exhaustive explanation of the mechanics of the bank-deposits-and-cash-expenditures method).
  The bank-deposits-and-cash-expenditures method involves some simple mathematical calculations. It totals all bank deposits and deducts the non-taxable deposits and amounts on deposit prior to the tax years in question from this gross total. Abodeely at 1023-24. This subtotal is the net taxable bank deposits. Id. It then adds to this amount “any other income which the taxpayer received but did not deposit in any bank .account.” Id. The resulting figure is net unreported income. The government must also demonstrate that the net unreported income calculated by this method is derived from a taxable source. Id.
  Using this method of calculating income, the Commissioner found deficiencies in the Kearns’ federal income tax of $7,667 in 1979, $14,078 in 1980, and $6,705 in 1981. As a result, the Commissioner assessed civil penalties that totalled $14,225. The Kearns challenged the Commissioner’s determinations before the Tax Court. The Kearns explained that they had assembled a cash hoard of at least $90,000 in 1979 that was stored in a cash box. The Kearns claimed that they acquired the hoard from gifts, inheritances, loans, and nontaxable sales of equipment. The Kearns argued that their expenditures during 1979-1981 were drawn from this cash hoard, accounting for the discrepancy between their bank deposits, expenditures, and their tax returns. At trial, the Kearns testified that the cash hoard consisted of $60,000 in loans from David Kearns’ father, James Kearns; $15,000 from five Christmas gifts from James Kearns; a $6,500 award from a civil suit; $12,000 saved from per diem payments from David Kearns’ job with a mortgage company; and proceeds from the sale of automobiles, machinery, and tools.
  The Tax Court found that the Kearns' explanations about the existence and makeup of the cash hoard were internally contradictory and inconsistent, and it determined that the Kearns only possessed the $6,500 cash award from the civil suit. Specifically, the court found that James Kearns did not possess the financial means to make the alleged loans of $60,000 or the alleged Christmas gifts of $15,000. The court discounted, the $12,000 that David Kearns allegedly saved from the mortgage company per diem, finding that his various explanations concerning the payments were implausible and inconsistent. The court also found that the Kearns did not place funds from the sale of various cars, motorcycles, and equipment into the cash hoard.
  The court also found that the Commissioner proved that the underpayments were due to fraud. After adding a fraud penalty to the assessment of David Kearns, the court found that the period of assessment remained open for both David and Janet Kearns. Because Janet Kearns significantly benefitted from the underreporting, the court did not award her the innocent spouse relief under section 6013(e) of the Internal Revenue Code. In reviewing the findings of the Commissioner, the Tax Court adjusted the deficiencies and penalties in favor of the Kearns to account for eight cash expenditures items.
  Here the Kearns argue that the Tax Court' erred in assessing their deficiencies and in finding that the - Commissioner proved that David Kearns fraudulently un-derreported nis income. The Kearns argue that the Tax Court erred by not shifting the burden of proof to the Commissioner when the Tax Court adjusted some of the Commissioner’s findings concerning the Kearns’ deficiency. The Kearns also argue that the Tax Court erred by ignoring alleged misrepresentation by an Internal Revenue agent assigned to investigate the Kearns.
  The Commissioner’s determination of a tax deficiency is generally presumptively correct and the taxpayer has the burden of proving that- the determination is erroneous or arbitrary. United States v. Janis, 428 U.S. 433, 440, 96 S.Ct. 3021, 3025, 49 L.Ed.2d 1046 (1976). See also Rule 142(a), Rules of Practice and Procedure of the United States Tax Court (Jan. 16, 1984). We generally review the Tax Court’s findings of fact on the clearly erroneous standard. Rose v. Commissioner, 868 F.2d 851, 853 (6th Cir.1989). We have generally followed the rule that factual determinations are not clearly erroneous unless we are left with a definite and firm conviction that a mistake has been made. Anderson v. City of Bessemer City, 470 U.S. 564, 573, 105 S.Ct. 1504, 1511, 84 L.Ed.2d 518 (1985). We review .the Tax Court’s application of the law using the de novo standard. Rose, 868 F.2d at 853. See also Humana Inc. v. Commissioner, 881 F.2d 247, 251 (6th Cir.1989).
  In the present case, the Tax Court heard the Kearns’ evidence concerning the existence of a cash hoard and found that the Kearns had deficiencies for the years in question. It is the Tax Court’s role to find the facts and it is our role to review those findings of fact and apply the clearly erroneous standard to them. See Rose, 868 F.2d at 853; Humana, 881 F.2d at 251. The Tax Court’s determination of a deficiency, utilizing and adjusting the Commissioner's determination, was a finding of fact and therefore is subject to the clearly erroneous standard of review. The Ta,x Court found that the Commissioner’s determinations were substantially correct. After hearing the evidence, including the Kearns’ rebuttal of the Commissioner’s evidence, the Tax Court found against the Kearns. In light of the court’s fact-finding and considering the evidence the Tax Court had before it, the Kearns’ argument concerning burden shifting is without merit. The finding that there was no cash hoard of $90,000 was not clearly erroneous. We also reject the Kearns’ argument that the Tax Court erred in finding that David Kearns committed fraud in underreporting income. The facts certainly establish that David Kearns committed fraud and accordingly the Tax Court’s finding of fraud was not clearly erroneous.
  The Kearns’ final argument is that the Internal Revenue agent who conducted the audit acted fraudulently by intimidating witnesses and fabricating evidence. This contention involves credibility and is relevant to the legal question of how much did the Kearns owe. David Kearns claims that two cash expenditures on the Commissioner’s notice of deficiency were fabricated by the IRS agent. The disputed items are an expenditure of $800 to David Evans for backhoe work and an expenditure of $4,000 to Paul Edwards for paving a driveway. At trial, David Evans testified that he did not do any backhoe work and that Kearns did not pay him $800. Evans also testified that Cremeens, the IRS agent in question, intimidated Evans by threatening an audit. Paul Edwards testified that Keariis only paid him $3,800 in cash for the driveway work. Edwards also stated that Cremeens took a blank invoice. The blank invoice was later filled in with $4,000 and Edwards’ signature, ostensibly by Cremeens.
  The Tax Court properly examined Kearns’ assertions in determining the taxes and penalties owed by the Kearns. Concerning the $800 and $4,000 invoices, the government conceded the Kearns’ position on the two expenditures at trial. By that time, Cremeens no longer worked for the IRS and could not be found in order to testify. Moreover, Kearns admitted spending $3,800 on paving a driveway during one of the tax years in question and thus got the benefit of the government’s conclusion. Kearns did not present evidence that established that the Tax Court erred in computing the amount due. Consequently, sufficient evidence existed to support the determination by the Tax Court that Kearns owed $14,225 in civil penalties.
  For the reasons stated above, we affirm the judgment of the Tax Court.-