Dayton Hudson Corp. v. Commissioner

DAYTON HUDSON CORPORATION AND SUBSIDIARIES, Petitioner v. COMMISSIONER OF INTERNAL REVENUE, Respondent Dayton Hudson Corp. v. Commissioner Docket No. 21217-91 United States Tax Court T.C. Memo 1997-260; 1997 Tax Ct. Memo LEXIS 315; 73 T.C.M. (CCH) 2978; June 11, 1997, Filed *315 Decision will be entered for respondent. P operated department stores. P used "cycle counting" to conduct physical inventories of merchandise throughout the year. P maintained book inventory records from which inventory closing balances could be determined at yearend. P estimated losses from shrinkage factors (e.g., theft and errors in billing) occurring from the time of the last physical count of inventory to yearend and made an accrual of the estimate. P calculated shrinkage accruals as a percentage of sales. Held: P's systems of maintaining book inventories do not clearly reflect income. They are, thus, not sound within the meaning of sec. 1.471-2(d), Income Tax Regs. David R. Brennan and Walter A. Pickhardt, for petitioner. Reid M. Huey, John C. Schmittdiel, Robert J. Kastl, and Robin L. Herrell, for respondent. HALPERN HALPERN MEMORANDUM FINDINGS OF FACT AND OPINION HALPERN, Judge: Respondent has determined a deficiency in petitioner's Federal income tax for its 1984 taxable year in the amount of $ 17,384,314, and petitioner has claimed an overpayment of income tax for that taxable year in the amount of $ 180,375. 1*316 Previously, on respondent's motion for summary judgment, we addressed one of the issues presented in this case. In Dayton Hudson Corp. & Subs. v. Commissioner, 101 T.C. 462 (1993), we held that section 1.471-(2)(d), Income Tax Regs., as a matter of law, does not prohibit petitioner from making a shrinkage accrual in computing book inventories. The issue remaining for our consideration is the soundness of certain of petitioner's accounting systems that allow for the accrual of an estimate of losses from shrinkage factors (e.g., theft and errors in billing) in determining book inventories. Unless otherwise noted, all section references are to the Internal Revenue Code in effect for the year in issue, and all Rule references are to the Tax Court Rules of Practice and Procedure. FINDINGS OF FACT Some facts have been stipulated and are so found. The stipulations of facts filed by the parties, with accompanying exhibits, are incorporated herein by this reference. The parties have made approximately 180 separate stipulations of fact, occupying 50 pages, and there are 120 accompanying *317 exhibits. We will set forth only those stipulated facts that are necessary to understand our report, along with other facts that we find. I. Background A. Petitioner Petitioner is a Minnesota corporation with its principal office in Minneapolis, Minnesota. Petitioner makes its Federal income tax return on the basis of a fiscal year ending during January of each year (we shall refer to petitioner's taxable year ending within a year simply by referring to that year, e.g., "1984" for petitioner's taxable year ending January 28, 1984). During 1984, petitioner was a retailer operating 1,075 stores in 47 States, the District of Columbia, and Puerto Rico. Petitioner's operations included a rapidly growing low margin department store chain in 22 States called Target and a regional department store company called Dayton's. Target and Dayton's were divisions of petitioner. Target offered a merchandise mix of two-thirds convenience-oriented hardlines and one-third fashion softgoods. Target has had significant growth in the number of stores it has operated; in 1980, Target operated 80 stores, in 1984, it operated 205 stores, and, in 1993, it operated 506 stores. Dayton's included 13 stores, generally *318 referred to as department stores, and 3 "Home" stores specializing in furniture, carpeting, and draperies; all 16 stores were located in Minnesota, North Dakota, South Dakota, and Wisconsin. In 1984, Target had gross receipts of $ 3,098,325,882, and Dayton's had gross receipts of $ 488,375,001. B. Accounting Procedures Petitioner's annual accounting period and taxable year was a 52/53-week year ending on the Saturday closest to January 31. Petitioner used the accrual method of accounting for both Federal income tax and financial reporting purposes. Gross income was calculated using inventories to account for the purchase and sale of merchandise. Book inventories were maintained to determine closing inventories for taxable years for which no physical inventories were taken at the taxable yearend. Gross income, in a merchandising business, means gross receipts for the period in question less cost of goods sold, plus any income from investments and from incidental or outside sources. Cost of goods sold, slightly simplified, equals opening inventory plus inventory purchased during the period minus closing inventory. Both Target and Dayton's used the "cycle counting" method of conducting *319 physical inventories. Cycle counting is a method of conducting physical inventories at individual stores or departments within stores, in rotation, throughout the year. Most large retail companies do not perform a physical count of inventory on or near the last day of the annual accounting period. Large retailers prefer cycle counting to yearend counting because it is more accurate and less expensive and provides better inventory control. Cycle counting is also more efficient and practical in terms of the availability of internal resources and outside services to conduct physical inventories. Generally, petitioner did not conduct physical inventories on the last day of the taxable year in issue. During 1983 and 1984, and for a number of years prior thereto, petitioner maintained a "perpetual", or book, inventory system for its divisions and subsidiaries, including Target and Dayton's. Under its perpetual inventory system, petitioner debited its inventory or stock accounts with the cost of goods purchased and credited those accounts with the cost of goods sold. The perpetual inventory system also showed the sales proceeds from goods sold. During 1984, physical inventories were conducted *320 on a store-by-store basis within the Target division and on a departmental basis within the Dayton's division. Physical inventories were not taken in Target stores commencing operations during 1984. The results of a physical inventory often would indicate that inventory shrinkage had occurred. Inventory shrinkage is the difference between the amount of inventory the stock account shows as being on hand and the amount of inventory that is actually on hand. When inventory is determined from book inventory records (computed without any accrual for estimated shrinkage), and the inventory so determined exceeds inventory determined by physical count, the difference is termed "shrinkage". When book inventory so determined is exceeded by inventory determined by physical count, the difference is termed "overage". Factors that contribute to shrinkage and overage (hereafter, generally, shrinkage) include theft by employees, customers, and vendors, and paperwork, billing, and other systems errors. Both Target and Dayton's experienced some or all of the listed shrinkage factors during the year in issue. The occurrence of shrinkage factors is not limited to particular times during the year, but, *321 generally, each of the factors occurs throughout the year. C. Accounting for Shrinkage If inventory is not physically counted at the end of the annual accounting period (year), shrinkage (as defined above) cannot be determined for the period from the last physical count to the end of the year (the physical-to-yearend period). If cycle counting is used, and the cycle for a particular store does not end on the last day of the year, then losses from shrinkage factors for the physical-to-yearend period (yearend shrinkage) must be estimated if such yearend shrinkage is to be taken into account. Petitioner maintained a "Controller's Manual" containing a standard control procedure to set forth corporate policy for accounting for inventory shrinkage and for planning and reporting physical inventory results. That manual provided that all companies must take at least one complete physical inventory a year. It further provided that "each Operating Company Controller is responsible for accounting for inventory shrinkage in accordance with the accrual basis of accounting." The manual defined the term "inventory shrinkage accrual rate" as "the rate at which inventory is written off to cost of sales *322 to provide for inventory shrinkage. The rate is stated as a percentage of net sales." The manual further provided for the adjustment of physical inventory results as follows: When physical inventory shortage is less than the provision [i.e., the accrual] for inventory shrinkage, cost of sales should be reduced for the calculated difference between the physical inventory shortage and the provision for inventory shrinkage. When physical inventory shortage is more than the provision for inventory shrinkage, cost of sales should be increased for the calculated difference between the physical inventory shortage and the provision for inventory shrinkage. Petitioner estimated shrinkage factors for the periods between physical inventories and, on a monthly basis, accrued amounts on account thereof. At the time of each physical inventory, petitioner would take account of any difference between its accruals and the result of its physical inventory (accrual error). For each taxable year, petitioner's total adjustments for shrinkage factors would include (1) any accrual for the period from the start of the year until the physical inventory date, (2) any adjustment for an accrual error, and (3) *323 any accrual for yearend shrinkage (such accrual for yearend shrinkage hereafter being referred to as shrinkage accrual). Shrinkage accruals reduced yearend inventories, which had the effect of increasing cost of goods sold and, as a result, decreasing gross income. In the retail industry, the practice of making shrinkage accruals, and of calculating such accruals as a percentage of sales, is the prevalent, if not virtually universal practice; it is the best practice in that industry. Respondent disallowed petitioner's shrinkage accruals. That had the consequence of decreasing cost of goods sold and, as a result, increasing gross income. Respondent has proposed a deficiency based upon that increased income. II. Target A. Accounting Methods and Procedures 1. In General Target comprised 205 stores that were organized into 91 separate departments. Target maintained its inventory records by department and by store. 2. LIFO Retail Method Beginning in 1963 and continuing through 1984, petitioner elected to value Target's inventories using the LIFO Retail Method of inventory valuation pursuant to section 1.471-8, Income Tax Regs. Pursuant to sections 1.472-1(k) and 1.472-8(c), Income Tax Regs., *324 petitioner elected to use department store indexes prepared by the U.S. Bureau of Labor Statistics (BLS). Petitioner aggregated Target's departments into 17 LIFO pools that corresponded to merchandise groups as established by BLS. 3. Accrual Rate for Shrinkage Target accounted for its inventory shrinkage on the accrual method, by department and by store. Target accrued shrinkage as a percentage of sales using rates (accrual rates) that were set for each department in each store. The accruals were posted directly to the perpetual inventory system on a monthly basis, and adjustments were made to account for accrual errors. Target developed a companywide accrual rate for each taxable year by reviewing the inventory results for prior physical inventory periods. Target generally reviewed the most recent 3 to 5 years of store and company experience in arriving at a companywide rate. Target also considered a variety of other factors known to affect the rate of shrinkage (shrinkage rate), including demographics, crime levels, management problems, paperwork problems, measures to improve shrinkage, industry trends, performance of warehouses, and store acquisitions. The next step in the process *325 was the determination of accrual rates for each store. After considering store-specific information, Target would assign a preliminary accrual rate to each store. Target then adjusted those rates so that the sum of the individual store rates multiplied by each store's projected sales figures would equal the projected shrinkage dollars at the company level as determined from the companywide accrual rate. The adjustment for a specific store's accrual rate would not exceed 0.1 percent of its projected annual sales. Lastly, Target adjusted accrual rates at the department level within each store, based upon a 3-year average shrinkage rate for the department on a companywide basis. Those department rates were further adjusted to accord with the shrinkage rate for each store in proportion to each department's sales relative to the store's total sales during the most recent 12-month period. 4. Application of Accruals for Shrinkage Target used its accruals for shrinkage for the following purposes: (1) financial and tax reporting, (2) to determine the budget that would be available for the purchase of inventory in a particular department, (3) to set goals for and to evaluate the performance *326 of store managers and buyers, and (4) to determine the sources of shrinkage. B. Target's Physical Inventories 1. In General Target employed an outside inventory service to conduct physical inventories of stores generally during the period beginning with the first weekend in February and ending in mid-October. Each store had its own physical inventory period. Target attempted to conduct a physical inventory at each store every 8 to 16 months; however, in rare instances, as many as 18 months elapsed between physical inventories. Except for stores opened during the year, Target usually inventoried every store once each year. 2. New Stores Target generally did not conduct physical inventories of new stores in the year that they were opened because Target believed that such inventories produced meaningless results. Instead, Target conducted physical inventories of new stores in the year following the year of opening. In most cases, Target set accrual rates for new stores by considering the average shrinkage rate for the district in which the new store was being opened. Target also considered the demographics of that district, as well as the marketing plan of "sister stores"--stores that *327 are located in areas with similar demographics and have merchandise mixes similar to that anticipated for the new store--in setting accrual rates for new stores. 3. Warehouses During 1979 through 1984, physical inventories were performed at Target's distribution centers and metro warehouses (hereafter, collectively referred to as "warehouses") once each year prior to the close of the taxable year, during the months of December or January. The results of the physical inventories at the warehouses were taken into account in April of the subsequent taxable year on a departmental basis by the Target stores serviced by each particular warehouse. The amount of shrinkage was allocated to the Target stores based upon the store's use of a particular warehouse. That practice reflected the determination that the warehouses' shrinkage generally reflected billing errors to stores. C. Proposed Deficiencies With Respect to Target In the notice of deficiency, respondent disallowed shrinkage accruals for 1984. The LIFO cost adjustment was $ 36,339,217, which reflected a disallowance of shrinkage at retail for the post-physical inventory periods in the amount of $ 57,621,019. Target had sales for 1984 *328 in the amount of $ 3,045,802,000. During the periods between the dates of the physical inventories of Target's stores and the end of 1984, Target's sales were $ 2,370,786,576, or 77.8 percent of all sales for 1984. III. Dayton's A. Accounting Methods and Procedures 1. In General Dayton's comprised 16 stores, and each store had in excess of 400 departments. Dayton's maintained its inventory records by department. 2. LIFO Retail Method Petitioner elected to value the inventories of Dayton's using the LIFO Retail Method of inventory valuation pursuant to section 1.471-8, Income Tax Regs. Pursuant to sections 1.472-1(k) and 1.472-8(c), Income Tax Regs., petitioner elected to use department store indexes prepared by BLS. Petitioner aggregated the departments of Dayton's into 20 LIFO pools that corresponded to merchandise groups as established by BLS. 3. Accrual Rate for Shrinkage Dayton's accounted for its inventory shrinkage on the accrual method, by department. Dayton's accrued shrinkage as a percentage of sales using rates (accrual rates) that were set for each department for each taxable year. The accruals were posted directly to the perpetual inventory system on a monthly basis, and *329 adjustments were made to account for accrual errors. Dayton's established accrual rates as a percentage of sales on a departmental basis. The department rate was applied throughout the Dayton's division. In setting a department accrual rate, Dayton's considered numerous factors including the most recent shrinkage history and shrinkage trends of the particular department, the employment of new marketing strategies, changes in demographics, trends that were developing in related departments, changes in security procedures, and particular theft problems. Dayton's did not set a companywide accrual rate. The companywide accrual figure was simply the aggregate of the accruals for all of the departments. 4. Application of Accruals for Shrinkage Dayton's used its accruals for shrinkage for the following purposes: (1) financial and tax reporting, (2) to determine the budget that would be available for the purchase of inventory in a particular department, (3) to evaluate the performance of department heads, and (4) to determine the sources of shrinkage. B. Dayton's Physical Inventories Dayton's conducted its physical inventories of its departments by counting inventory on the same day at every *330 store that maintained a particular department. In conducting physical inventories, Dayton's used its own employees, and, at times, those employees were assisted by outside personnel. The physical inventories of the departments were performed at various times throughout the year, and, during the year in issue, they were performed as early as February 1983 and as late as January 1984. After a physical inventory was taken, the perpetual inventory system would be adjusted as necessary, and, generally, Dayton's adjusted the department accrual rate for the balance of the taxable year to reflect the most recent shrinkage experience. C. Proposed Deficiencies With Respect to Dayton's In the notice of deficiency, respondent disallowed shrinkage accruals for 1984. The LIFO cost adjustment was $ 2,440,127, which reflected a disallowance of shrinkage at retail for the post-physical inventory periods in the amount of $ 4,625,877. Dayton's had sales for 1984 in the amount of $ 415,467,423. During the periods between the dates of the physical inventories of the departments of Dayton's and the end of 1984, sales for Dayton's were $ 254,488,635, or 61.3 percent of all sales for 1984. OPINION I. Introduction*331 Petitioner's principal business activities are the operation of department stores. We are concerned here with petitioner's Target division (Target) and its Dayton's division (Dayton's) (together, the Divisions). During the taxable year in issue, the Divisions used cycle counting to conduct physical inventories of merchandise. Under the cycle counting method, physical inventories were taken in rotation, at the various stores or departments within stores, throughout the year. Also, the Divisions maintained book inventory records from which inventories could be determined without a physical count. The Divisions estimated losses from shrinkage factors (e.g., theft and errors in billing) during the physical-to-yearend period (yearend shrinkage) and made an accrual of that estimate (shrinkage accrual). That practice had the effect of increasing cost of goods sold and decreasing gross income. Respondent disallowed the Divisions' shrinkage accruals, and we must determine whether that disallowance is an abuse of discretion. II. Statute and Principal Regulation Section 471(a) provides the following general rule: Whenever in the opinion of the Secretary the use of inventories is necessary in *332 order clearly to determine the income of any taxpayer, inventories shall be taken by such taxpayer on such basis as the Secretary may prescribe as conforming as nearly as may be to the best accounting practice in the trade or business and as most clearly reflecting the income. 2 As the regulations point out, section 471(a) establishes two distinct tests to which an inventory must conform: (1) It must conform as nearly as may be to the best accounting practice in the trade or business, and (2) It must clearly reflect the income. Sec. 1.471-2(a), Income Tax Regs. In accordance with the authority provided by section 471(a), the Secretary has promulgated rules for taxpayers maintaining a perpetual (book entry) system of keeping inventories. In pertinent part, section 1.471-2(d), Income Tax Regs., reads as follows: Where the taxpayer maintains book inventories in accordance with a sound accounting system in which the respective inventory accounts are charged with the actual cost of the goods purchased *333 or produced and credited with the value of goods used, transferred, or sold, calculated upon the basis of the actual cost of the goods acquired during the taxable year * * * the net value as shown by such inventory accounts will be deemed to be the cost of the goods on hand. The balances shown by such book inventories should be verified by physical inventories at reasonable intervals and adjusted to conform therewith. III. Prior Proceedings Previously, on respondent's motion for summary judgment, we addressed one of the issues presented in this case. In Dayton Hudson Corp. & Subs. v. Commissioner, 101 T.C. 462 (1993), we held that section 1.471-(2) (d), Income Tax Regs., as a matter of law, does not prohibit petitioner from making a shrinkage accrual in computing book inventories. We acknowledged, however, that respondent might yet argue that petitioner's accounting system, including the making of shrinkage accruals, is not "sound" within the meaning of the regulations, or fails to clearly reflect income. Id. at 468. Respondent acknowledges our holding in the earlier opinion, but does not agree that it is correct. We adhere to that holding. IV. Are the Divisions' Systems of Accounting *334 for Inventories, Including the Making of Shrinkage Accruals, Sound? Because the Divisions used cycle counting to conduct physical inventories of merchandise, and generally no count was taken at yearend, the Divisions necessarily had to maintain book inventory records to determine yearend inventories for purposes of computing cost of goods sold. Those book inventories included an entry for shrinkage accrual. We must determine whether those book inventories were maintained in accordance with a "sound accounting system". Sec. 1.471-(2)(d), Income Tax Regs. We have recently addressed the question of what constitutes a "sound accounting system" under section 1.471-(2)(d), Income Tax Regs. In Kroger Co. & Subs. v. Commissioner, T.C. Memo. 1997-2, we noted that section 1.471-(2)(a), Income Tax Regs., provides two specific requirements with which acceptable inventory practices must conform. We then stated: First, such practices must conform as nearly as may be to the best accounting practice in the industry. Second, the practices must clearly reflect the taxpayer's income. Section 1.471-2(b), Income Tax Regs., adds consistency of application from year to year as an important and explicit *335 element of inventory practices that clearly reflect income. The use of the adjective "sound" in section 1.471-2(d), Income Tax Regs., does not introduce an additional standard, but only incorporates the previously articulated standards, with the emphasis on the "system" or methodology employed to maintain book inventories. * * * [Id.] Therefore, our inquiry is, principally, whether the Divisions' systems of maintaining book inventories (including the making of shrinkage accruals) conform to the best accounting practice and clearly reflect income. V. Best Accounting Practice The parties have stipulated that, for financial accounting purposes, petitioner's financial statements for the taxable year in issue were consistent with generally accepted accounting principles (GAAP). In Thor Power Tool Co. v. Commissioner, 439 U.S. 522, 532 (1979), the Supreme Court stated that the phrase "best accounting practice", as it appears in section 471(a) (and section 1.471-2(a), Income Tax Regs.), is synonymous with GAAP. Petitioner followed the same accounting practices for both Federal income tax and financial reporting purposes. We find, therefore, that the Divisions' systems of maintaining book inventories *336 conform to the best accounting practice within the meaning of section 471(a) and section 1.471-2(a), Income Tax Regs. VI. Clear Reflection of Income A. Methods of Accounting and the Legal Requirement of Clear Reflection of Income The general rule for methods of accounting is set forth in section 446(a): Taxable income shall be computed under the method of accounting on the basis of which the taxpayer regularly computes his income in keeping his books. A taxpayer has latitude, however, in selecting a method of accounting. Section 1.446-1(a) (2), Income Tax Regs., provides: It is recognized that no uniform method of accounting can be prescribed for all taxpayers. Each taxpayer shall adopt such forms and systems as are, in his judgment, best suited to his needs. * * * The accrual method is a permissible method of accounting. Sec. 446(c). Section 1.446-1(c)(1)(ii)(A), Income Tax Regs., provides: Generally, under an accrual method, income is to be included for the taxable year when all the events have occurred that fix the right to receive the income and the amount of the income can be determined with reasonable accuracy. Under such a method, a liability is incurred, and generally is taken *337 into account for Federal income tax purposes, in the taxable year in which all the events have occurred that establish the fact of the liability, the amount of the liability can be determined with reasonable accuracy, and economic performance has occurred with respect to the liability. * * * The term "liability", as used in section 1.446-1(c)(1)(ii)(A), Income Tax Regs., is defined in section 1.446-1(c)(1)(ii)(B), Income Tax Regs., to include "a cost taken into account in computing cost of goods sold". Notwithstanding the latitude generally enjoyed by a taxpayer in selecting a method of accounting, where inventories are employed, accrual accounting is the general rule to account for purchases and sales: Where inventories are employed, purchases and sales must be computed on the accrual method (unless another method is authorized by the Commissioner) in order to avoid the distortion of income. Sec. 1.446-1(c)(2), Income Tax Regs.; Stoller v. United States, 162 Ct. Cl. 839, 845, 320 F.2d 340, 343 (1963). Molsen v. Commissioner, 85 T.C. 485, 499 (1985). In any event, a taxpayer's right to adopt a method of accounting is subject to the requirement that the method must clearly reflect income. *338 Section 446(b) states that, if the method adopted "does not clearly reflect income, the computation of taxable income shall be made under such method as, in the opinion of the Secretary, does clearly reflect income." See also sec. 1.446-1(c)(1)(ii)(C), Income Tax Regs. The term "clearly reflect income" is undefined in the Code. In most cases, generally accepted accounting principles, consistently applied, will pass muster for tax purposes. See, e.g., sec. 1.446-1(a)(2), (c)(1)(ii), Income Tax Regs. The Supreme Court has made clear, however, that GAAP does not enjoy a presumption of accuracy that must be rebutted by the Commissioner. Thor Power Tool Co. v. Commissioner, supra at 540. The Commissioner's supervisory power under section 446(b), permitting the rejection of a taxpayer's method if it "does not clearly reflect income", and its substitution with a method that, "in the opinion of the * * * [Commissioner], does clearly reflect income", was described by the Supreme Court in another case as leaving "much latitude for discretion", which "should not be interfered with [by the courts] unless clearly unlawful." Lucas v. American Code Co., 280 U.S. 445, 449 (1930) (quoted with approval *339 in Thor Power Tool Co. v. Commissioner, supra at 532). B. Standard of Review When the Commissioner determines that a taxpayer's method of accounting does not clearly reflect income, the taxpayer has a heavy burden to show an abuse of discretion. E.g., Asphalt Prods. Co. v. Commissioner, 796 F.2d 843, 848 (6th Cir. 1986), affg. in part and revg. in part Akers v. Commissioner, T.C. Memo. 1984-208, revd. per curiam on another issue 482 U.S. 117 (1987). The Court of Appeals for the Sixth Circuit has stated: § 446 gives the Commissioner discretion with respect to two determinations. The Commissioner first determines whether the accounting method chosen by a taxpayer clearly reflects income. If the Commissioner concludes that the taxpayer's chosen method does not meet this standard, he has the further discretion to require that computations be made under the method which, in his opinion, does clearly reflect income. It would be difficult to describe administrative discretion in broader terms. Id. at 847. Notwithstanding the authority conferred under section 446(b), the Commissioner cannot require a taxpayer to change to another method where the taxpayer's method of accounting does clearly *340 reflect income, even if the method proposed by the Commissioner more clearly reflects income. Ford Motor Co. v. Commissioner, 71 F.3d 209, 213 (6th Cir. 1995), affg. 102 T.C. 87 (1994); Ansley-Sheppard-Burgess Co. v. Commissioner, 104 T.C. 367, 371 (1995); Hospital Corp. of Am. v. Commissioner, T.C. Memo. 1996-105. Nor will the courts approve the Commissioner's change of a taxpayer's accounting method from an incorrect method to another incorrect method. Harden v. Commissioner, 223 F.2d 418, 421 (10th Cir. 1955), revg. 21 T.C. 781 (1954); Prabel v. Commissioner, 91 T.C. 1101, 1112 (1988), affd. 882 F.2d 820 (3d Cir. 1989); see also Southern Cal. Sav. & Loan v. Commissioner, 95 T.C. 35, 44 (1990) (Wells, J., concurring) ("Section 446(b) authorizes respondent to require accounting changes that produce clearer reflections of income, not greater distortions of income"). Therefore, in order to prevail in a case where the Commissioner determines that a taxpayer's method of accounting does not clearly reflect income, the taxpayer must demonstrate either that his method of accounting clearly reflects income or that the Commissioner's method does not clearly reflect income. See Asphalt Prods. Co. v. Commissioner, supra at 847; *341 Kroger Co. & Subs. v. Commissioner, T.C. Memo. 1997-2. C. The Divisions' Shrinkage Methods The Divisions maintained book inventory records from which yearend inventories could be determined. Losses for the taxable year occasioned by shrinkage factors (taxable year shrinkage) were reflected in the Divisions' book inventory records under methods (individually, Target's shrinkage method and Dayton's shrinkage method; together, when no distinction is intended, the Divisions' shrinkage methods) that essentially involved three variables: (1) an estimate of losses from shrinkage factors for the portion of the taxable year preceding the date of the physical inventory (preinventory accrual), (2) the accrual error (a measure of error in both the prior year's shrinkage accrual and the preinventory accrual), and (3) the shrinkage accrual for the taxable year. Target accounted for shrinkage as a percentage of sales using rates (accrual rates) that were set for each department in each store for each taxable year. Those rates were derived from a companywide accrual rate that was based on a combination of factors including historical shrinkage experience, demographics, crime levels, management problems, *342 measures to improve shrinkage, industry trends, performance of warehouses, and store acquisitions. Except for stores opened during the year, Target generally conducted a complete physical inventory of an entire store on a particular day once each year. Dayton's accounted for shrinkage as a percentage of sales using rates (accrual rates) that were set for each department for each taxable year. Companywide, department accrual rates were based on a combination of factors including the most recent shrinkage history and shrinkage trends of the particular department, the employment of new marketing strategies, changes in demographics, trends that were developing in related departments, changes in security procedures, and particular theft problems. Dayton's conducted its physical inventories of its departments by counting inventory on the same day at every store that maintained a particular department. The physical inventories of the departments were performed at various times throughout the year, and, during the year in issue, they were performed in as early as February 1983 and as late as January 1984. In sum, both Target and Dayton's estimated losses from shrinkage factors as a percentage *343 of sales, using methods that essentially reflected (1) verified shrinkage for the preinventory period, (2) an estimate of yearend shrinkage (shrinkage accruals), and (3) accrual error attributable to the shrinkage accrual for the prior taxable year. D. Respondent's Method Respondent would permit the Divisions to account for losses from shrinkage factors only when such losses are verified by physical inventories (respondent's method). Respondent claims that that "method is nothing more than application of the principle that taxpayers may not reduce income by unverified losses or expenditures, or unreliable estimates". Upon closer analysis, we conclude that respondent's method essentially estimates yearend shrinkage for the taxable year based on yearend shrinkage for the prior taxable year. Respondent's method would adjust the Divisions' book inventories by disallowing any shrinkage accrual. The Divisions' cost of goods sold, as determined by book inventories, would essentially include shrinkage for inventory cycles beginning in the prior taxable year and ending in the taxable year and not any portion of the shrinkage determined for inventory cycles beginning within the taxable year *344 and ending in the next taxable year (i.e., yearend shrinkage). In sum, the Divisions' cost of goods sold for a taxable year that included cross-year inventory cycles would include shrinkage accurately measured (i.e., verifiable) for some period other than that taxable year (i.e., an inventory year). If it is assumed that there is yearend shrinkage, then, unless the amount of yearend shrinkage for the taxable year is identical to the amount of yearend shrinkage for the previous year, respondent's method would produce only an estimate of the loss from shrinkage factors for the taxable year. The facts underlying that conclusion can be illustrated by the following diagram, in which it is assumed that a physical inventory is taken semiannually, on March 31 and September 30, and that the taxpayer is a calendar year taxpayer. 1995 Taxable Year 1996 Taxable Year 1997 Taxable Year Dec. 31 Dec. 31 Dec. 31 1995 Inventory Year 1996 Inventory Year 1997 Inventory Year Sept. 30 Mar. 31 Sept. 30 Mar. 31 Sept. 30 Mar. 31 Sept. 30 Under respondent's method, the taxpayer's cost of goods sold for a taxable year would be computed by including shrinkage for the taxpayer's inventory year ending September 30. Shrinkage for *345 the inventory year might equal taxable year shrinkage, but the occurrence of that remote possibility is impossible to verify. What is likely (almost a certainty) is that the taxpayer, computing his cost of goods sold under respondent's method, would be making that computation using some figure for taxable year shrinkage that was not the actual taxable year shrinkage. In other words, the taxpayer would be forced to use what is almost certainly no more than an estimate of taxable year shrinkage in computing cost of goods sold. Respondent does not seriously claim that losses from shrinkage factors in a cross-year inventory cycle occur only in the latter year. Nor does respondent claim that losses from shrinkage factors do not occur generally throughout an inventory cycle. On the record before us, we have no doubt that, on a regular basis, the Divisions experienced losses from theft, billing errors, and other shrinkage factors. We also have no doubt that some of those losses were experienced during the physical-to-yearend period and gave rise to yearend shrinkage. Therefore, the principal difference between the Divisions' shrinkage methods and respondent's method is that respondent, without *346 admitting it, accepts an estimate of yearend shrinkage while the Divisions, by making shrinkage accruals, consciously attempt to estimate that shrinkage. 3*347 E. Petitioner's Expert Testimony 1. introduction Petitioner relies on expert testimony to demonstrate that (1) the Divisions' shrinkage methods clearly reflect income, (2) respondent's method does not clearly reflect income, or (3) the Divisions' shrinkage methods more clearly reflect income when compared to respondent's method. In particular, petitioner relies on such testimony to demonstrate a strong correlation between sales and shrinkage, which correlation underlies the Divisions' shrinkage accruals and petitioner's contention that respondent's method does not clearly reflect income. Petitioner presents principally the expert testimony of W. Eugene Seago, Ph.D. Dr. Seago is a certified public accountant and a professor of accounting at Virginia Polytechnic Institute and State University. 2. Correlation Between Sales and Shrinkage Statistical correlation (R) is a measure of the degree *348 to which two variable quantities tend to change with respect to each other. R is expressed in a range between positive one and negative one. A correlation of positive one indicates that the two quantities change in exact proportion and in the same direction, whether up or down. A correlation of zero indicates that the two quantities change without reference to each other. A correlation of negative one indicates that the two quantities change in exact proportion, but in opposite directions: When one goes up, the other goes down. In addition, the square of the correlation coefficient is termed the coefficient of determination (R<2>). Generally, R<2> measures the predictive power of one variable with respect to another variable. The principal experts in this case do not limit their use of the term "correlation" to represent R in the technical sense, but rather, use that term to signify R<2> at times and also to signify the general relationship between two variables. We shall conform, for purposes of this report, to the experts' broad usage of the term "correlation". Dr. Seago states in his rebuttal report that "the purpose of ascertaining whether shrinkage correlates to sales is to test *349 whether Target's use of sales to estimate shrinkage is appropriate." Dr. Seago acknowledges that testing the correlation of sales and shrinkage at the LIFO pool level for Target would be highly relevant because tax effects occur at that level, but, since data to test that correlation does not exist, he concludes that the "next best thing" is to examine correlation at the aggregate division level. Dr. Seago is of the opinion that the correlation between sales and shrinkage at the aggregate Target-wide level is strong. Dr. Seago conducted a regression analysis of the relationship between sales and shrinkage at the aggregate Target-wide level during the years 1979 through 1988 (the 10-year correlation analysis). For each Target store, he paired actual sales figures between inventory dates with verified shrinkage figures for the same period. Dr. Seago then aggregated the data according to the taxable year in which the closing inventory was taken. He is of the opinion that, for the years examined, "the change in sales each year explained over 97% of the change in shrinkage." Dr. Seago concludes that, "according to the statistical evidence, sales is a nearly perfect predictor of the loss *350 from shrinkage." He did not conduct a similar analysis with respect to Dayton's. To compensate for the absence of data to test correlation at the LIFO pool level, Dr. Seago randomly placed individual Target stores into 21 "surrogate pools" and examined the correlation between sales and shrinkage for the fiscal years 1979 through 1988. Dr. Seago concludes that the correlation between sales and shrinkage at the surrogate pool level is strong and that "comparable results would be achieved if sales and shrinkage for the actual LIFO pools were available." 3. Shrinkage Accrual Accuracy Analysis Dr. Seago believes that the 10-year correlation analysis demonstrating a correlation between sales and shrinkage with respect to Target leads to the conclusion that the Divisions' shrinkage methods 4 are theoretically correct methods. Dr. Seago acknowledges, however, that the next step is to determine whether those methods were properly applied. He recognizes that a comparison of the shrinkage verified by physical count with the shrinkage claimed by petitioner for the taxable year is of limited significance because the comparison would be of figures for two different periods. In an attempt to analyze *351 the accuracy of the Divisions' shrinkage methods and to compare those methods with respondent's method, Dr. Seago developed a model to determine taxable year shrinkage. He applied that model to data for Target during the taxable years that ended in 1983 through 1986. Dr. Seago believes that, when a physical inventory is taken at the close of a period that includes portions of 2 taxable years, and an accrual error is detected, some portion of that error is attributable to each of the taxable years. With support from the results of the 10-year correlation analysis, Dr. Seago assumed that sales and shrinkage were perfectly correlated throughout the year and, thus, determined that any accrual error should be allocated according to the relative sales between the two relevant taxable *352 years to arrive at a figure for taxable year shrinkage. Dr. Seago examined Target's sales figures for the taxable years ending in 1984, 1985, and 1986, and determined that approximately 75 percent of sales between physical inventory dates are allocable to the taxable year prior to the taxable year in which the physical inventory is taken. As a result, Dr. Seago allocated 75 percent of the applicable accrual error to the taxable year prior to the taxable year in which the physical inventory was taken and 25 percent to the taxable year in which the physical inventory was taken. Dr. Seago compared his resulting figures for taxable year shrinkage (sales-allocated taxable year shrinkage) with the shrinkage claimed by Target for tax purposes and the shrinkage that would be allowed under respondent's method. Dr. Seago's analysis produced the following results: 5 TARGET'S SHRINKAGE METHOD Target Book Taxable Sales- Shrinkage Minus Difference as Year Target Allocated Sales-Allocated Percent of Ending Book Taxable Year Taxable Year Sales-Allocated In Shrinkage Shrinkage Shrinkage Shrinkage [1983] $ 54,175,800 $ 48,257,951 $ 5,917,849 12.26% [1984] 63,773,400 63,217,484 555,916 0.88% [1985] 66,205,504 73,483,645 -7,278,141 -9.90% [1986] 82,227,200 81,441,206 785,994 0.97% 1983- 266,381,904 266,400,286 -18,382 -0.01% [1986] RESPONDENT'S METHOD - TARGET DIVISION Verified Taxable Loss Sales- Loss Minus Difference as Year Verified by Allocated Sales-Allocated Percent of Ending Physical Taxable Year Taxable Year Sales-Allocated In Inventory Shrinkage Shrinkage Shrinkage [1983] $ 41,733,212 $ 48,257,951 -$ 6,524,739 -13.52% [1984] 51,323,565 63,217,484 -11,893,929 -18.81% [1985] 65,194,206 73,483,645 -8,289,439 -11.28% [1986] 80,248,800 81,441,206 -1,192,406 -1.46% 1983- 238,499,783 266,400,286 -27,630,152 -10.37% [1986] *353 Dr. Seago determined that Target's estimates of taxable year shrinkage produced, in the aggregate, a net underestimate in the amount of $ 18,382 for the taxable years ending in 1983 through 1986 when compared to sales-allocated taxable year shrinkage. He also determined that the maximum error under Target's shrinkage method was 12.26 percent of sales-allocated taxable year shrinkage. From that analysis, Dr. Seago concludes that the Divisions' shrinkage methods produced "a reasonably accurate measure of the loss" occasioned by shrinkage factors. Dr. Seago notes that, in contrast, respondent's method yields a cumulative overstatement of income in the amount of $ 27,630,152. Dr. Seago concludes that respondent's method "contains a systematic bias towards the understatement of losses during periods when sales are increasing." 4. Sales Percentage Shrinkage Analyses To further examine the accuracy of Target's shrinkage method, Dr. Seago computed for each Target store during the taxable years ending in 1980 through 1989 (1) the *354 verified shrinkage between physical inventory dates as a percentage of sales for that period (actual shrinkage), (2) the shrinkage estimates accrued in book inventory as a percentage of sales for the same period (estimated shrinkage), and (3) the difference between (1) and (2). Dr. Seago hypothesized that, if Target could accurately predict shrinkage between physical inventory dates, i.e., the difference between actual and estimated shrinkage is small, Target should likewise accurately predict shrinkage for the taxable year. Dr. Seago's calculations revealed that, over the period examined, the simple average difference between actual and estimated shrinkage was 0.12 percent of sales and the weighted average (weighted by sales) difference was 0.16 percent of sales. That difference represents approximately 7 percent of actual shrinkage. In addition, Dr. Seago performed a regression analysis comparing sales and shrinkage for each Target store during the taxable years ending in 1980 through 1989. 6 He determined an R<2> of 0.367. Dr. Seago explains that finding by stating, "while an accrual based solely on the historical relationship between sales and shrinkage would result in substantial *355 errors in predictions * * *, Target personnel are able to significantly reduce the error by adjusting the accrual factor to take into account factors known to contribute to shrinkage in the particular store." Dr. Seago asserts that the demonstrated success of Target in predicting store shrinkage suggests that Target likewise accurately predicts shrinkage at the department level. Dr. Seago also presents a sales percentage shrinkage analysis for Target at the aggregate division level. He states that, from 1979 through 1988, verified shrinkage has averaged 2.102 percent of sales, with a range of 1.90 percent to 2.30 percent. Dr. Seago states that Target's estimates of shrinkage as a percentage of sales, when compared to the verified percentage, showed that the estimates deviated from the actual figures by no more than 25 percent. 5. Dr. Seago's Criticism of Respondent's Method Dr. Seago states that the shortcomings of respondent's method are that (1) the loss for the taxable year is dependent on the date *356 of the physical inventories and (2) losses actually attributable to a prior taxable year are included in the loss for the current year and losses attributable to the current taxable year are deducted in the following taxable year. Dr. Seago asserts that respondent's method contains a systematic bias towards understating losses when sales are increasing. F. Respondent's Expert Testimony 1. Introduction Respondent presents the testimony of two experts, Dennis J. Gaffney, Ph.D., a professor of accounting at the University of Toledo, and David W. LaRue, Ph.D., an associate professor of commerce at the University of Virginia. 2. Dr. Gaffney Dr. Gaffney was requested to render an opinion as to whether the Divisions' shrinkage methods were appropriate for financial accounting and reporting purposes and, if so, the degree of error in estimating shrinkage that could be tolerated for those purposes. Although Dr. Gaffney's opinions on those issues are not relevant with respect to the issue of clear reflection of income for tax purposes, we believe that Dr. Gaffney's comparison of Target's verified and accrued shrinkage in retail sales figures for inventory periods that ended in taxable years *357 ending in 1980 through 1993, nevertheless, provides an important perspective on sales and shrinkage data for Target. That comparison produced the following results: TARGET - COMPARISON OF VERIFIED AND ACCRUED SHRINKAGE FOR INVENTORY PERIODS 7*358 Verified Shrinkage Accrued Shrinkage Accrued Minus Verified TYE in $ 000 %Sales $ 000 %Sales $ 000 %Sales %Difference [1980] 17,513 1.94 20,689 2.29 3,175 0.35 18.04 [1981] 25,608 2.25 25,763 2.27 [156] 0.02 0.89 [1982] 37,186 2.21 36,605 2.18 -580 -0.03 -1.36 [1983] 41,733 2.15 43,983 2.26 2,250 0.11 5.12 [1984] 51,324 2.02 61,464 2.42 10,141 0.40 19.80 [1985] 65,194 2.00 76,076 2.33 10,882 0.33 16.50 [1986] 80,249 2.20 81,370 2.23 1,121 0.03 1.36 [1987] 91,512 2.30 85,749 2.15 -5,763 -0.15 -6.52 [1988] 87,816 2.05 91,068 2.12 3,252 0.07 3.41 [1989] 115,560 1.90 145,048 2.38 29,488 0.48 25.26 [1990] 97,610 1.57 147,806 2.37 50,196 0.80 50.96 [1991] 148,717 1.92 169,731 2.19 21,014 0.27 14.06 [1992] 130,260 1.59 163,944 2.00 33,683 0.41 25.79 [1993] 162,692 1.70 188,526 1.98 25,834 0.28 16.47 Dr. Gaffney observed that out of the 14 years considered by him, an overaccrual of shrinkage was made in 12 of those years. 3. Dr. LaRue Dr. LaRue testified to, among other things, the "tax effects" resulting from the accrual of erroneous estimates of unverified shrinkage (shrinkage estimation errors). He designed simulation models to analyze shrinkage estimation errors that result from the use of cycle counting in conjunction with the LIFO Retail Method. Dr. LaRue believes that the LIFO Retail Method imposes certain additional demands on any method of shrinkage estimation. To better appreciate Dr. LaRue's assertion, we must acquire a basic understanding of the LIFO Retail Method. See secs. 1.471-8, 1.472-1(k), 1.472-8(c), Income Tax Regs. The LIFO Retail Method is a method of inventory valuation designed to meet the special needs of high volume retailers dealing in a wide variety of merchandise. In general terms, the sales at retail for an accounting period are subtracted from the retail value of goods *359 available for sale during that period to produce a figure for the retail value of ending inventory. That figure for the retail value of ending inventory must be converted into a figure for cost of ending inventory, which can be subtracted from cost of goods available for sale during that period to produce a figure for cost of goods sold. In simplified terms, the process of converting the current year retail value of ending inventory to cost of ending inventory involves dividing the current year retail value of ending inventory by the current retail price index (which, for retailers using U.S. Bureau of Labor Statistics (BLS) indexes, is the current BLS price index for the particular inventory pool divided by the BLS price index for the year in which that pool was adopted (base year)) to yield a figure for current year retail value of ending inventory expressed in base year dollars. Comparing that result to a similar figure computed as of the end of the immediately preceding accounting period reveals whether an increment or decrement in the quantity of goods has occurred as of the end of the period, as opposed to mere changes in retail price levels. If there has been no decrement in *360 the quantity of goods as of the end of the period, cost of ending inventory is the sum of the prior year's cost of ending inventory plus the cost of the quantity of inventory in the current increment (if any). The retail value of the increment expressed in base year dollars is multiplied by the current year's retail price index and then multiplied by the cost complement 8 to arrive at the cost of the increment in the quantity of goods. In the event of a decrement, the decrease is subtracted from the annual layers of the period's beginning inventory in reverse chronological order. Those procedures are applied to each LIFO pool, which generally maintains its own set of BLS indexes, cost complement, layer structure, and other pool attributes. Having acquired a basic understanding of the LIFO Retail Method, we can better analyze Dr. LaRue's criticism of the Divisions' shrinkage methods. Dr. LaRue believes that the process of making corrections to shrinkage estimates in the subsequent year is inadequate because changes in LIFO pool *361 attributes, such as BLS indexes and cost complements, prevent corrections from accurately offsetting previous shrinkage estimation errors in the earlier year. In addition, Dr. LaRue asserts that the varying tax effects of shrinkage estimation errors among LIFO pools, which is a product of differing pool attributes, even undermines the validity of a methodology that, in the aggregate, produces an accurate estimate of taxable year shrinkage. In sum, Dr. LaRue believes that cycle counting and the LIFO Retail Method impose "significant additional demands on the design and implementation of a methodology that might be considered capable of producing sound accruals of shrinkage losses." In addition, Dr. LaRue considered Target's shrinkage method and concluded as follows: In my opinion, the "methodology" employed by Target to forecast its shrinkage experience and to then allocate that forecast to each of the departments in each of its stores for the purpose of accruing these losses in its books and records fails to evidence the objectivity and verifiability required to establish the overall process as a sound method that can be expected to clearly reflect its income. That opinion, according *362 to Dr. LaRue, is based on Target's failure to "directly" consider a department's actual shrinkage experience in setting that particular department's shrinkage rate coupled with the inability of "a disinterested party with full knowledge of all relevant data * * * to independently reconstruct the forecasted shrinkage derived" by Target's shrinkage method. Dr. LaRue disagrees with Dr. Seago's conclusion that the Divisions' shrinkage methods produce reasonably accurate estimates of losses from shrinkage factors. Dr. LaRue believes that the tax effects of shrinkage estimation errors are not the result of errors at the aggregate level because shrinkage is accrued at the store and department levels, and, therefore, minimal errors at the aggregate level are misleading. Dr. LaRue states: I think he [Dr. Seago] is looking at the wrong phenomena. I think it doesn't matter a whole lot. It matters, but it doesn't matter a whole lot whether our shrinkage estimation methodology produces very small or very large errors at the aggregate level. Shrinkage is not accrued at the aggregate level. Dr. LaRue believes that, notwithstanding a net figure of zero at the aggregate level, the fact that retail dollars *363 of shrinkage have to be converted into cost dollars among the various LIFO pools, which pools utilize diverse conversion processes (i.e., differing BLS indexes and cost complements), undermines the significance of Dr. Seago's shrinkage accrual accuracy analysis. Dr. LaRue acknowledges, however, that a finding of low shrinkage estimation error at the aggregate level is not irrelevant. Indeed, he believes that such a finding creates a presumption of a "pretty good model". In addition, Dr. LaRue, although in agreement with Dr. Seago's mathematics, questioned the significance of the high correlation between sales and shrinkage derived from the 10-year correlation analysis. Dr. LaRue conducted his own analysis of Target data and concludes that the correlation between sales and shrinkage disintegrates as the level of analysis moves from the Target-wide level to the department and store levels. G. Evaluation of Expert Testimony 1. Origin of Shrinkage Estimation Errors An inquiry into the origin of shrinkage estimation errors provides the proper perspective to evaluate Dr. LaRue's criticism that the Divisions' shrinkage methods are inherently flawed because the additional demands of the LIFO *364 Retail Method prevent accurate, subsequent year corrections of shrinkage estimation errors. If physical inventories were required to be taken at yearend, taxable year shrinkage would be known with certainty, and no estimate of yearend shrinkage would be necessary. Physical inventories, however, are not required to be taken at yearend. Sec. 1.471-2(d), Income Tax Regs. Once the Secretary decided not to require physical inventories at yearend, see Dayton Hudson Corp. & Subs. v. Commissioner, 101 T.C. at 467; sec. 1.471-2(d), Income Tax Regs., and taxpayers began to exercise the privilege of computing yearend inventories from book inventory records, estimations of yearend shrinkage became inescapable, whether the method of estimating yearend shrinkage involves calculation (the Divisions' shrinkage methods) or substitution (respondent's method). The realization that estimates of yearend shrinkage are an inescapable byproduct of cycle counting reveals that Dr. LaRue's criticisms are, in fact, a condemnation of cycle counting by means of highlighting the additional demands of the LIFO Retail Method, which are just as applicable to respondent's method. In other words, errors resulting from *365 respondent's method of substituting yearend shrinkage for the taxable year with yearend shrinkage for the prior taxable year are subject to the same problems of varying tax effects arising from changing LIFO pool attributes and dissimilar pool attributes among pools. Respondent's proposed adjustments will not eliminate the flaws perceived by Dr. LaRue. It appears that only the practice of yearend physical inventories at all stores or departments could eliminate such errors. That, however, would not be practical, nor is it required by the regulations. See sec. 1.471-2(d), Income Tax Regs. In sum, we consider Dr. LaRue's objection as an inherent component of all estimates of yearend shrinkage. 2. Dr. Seago As a preliminary matter, Dr. Seago, in his report and in his testimony at trial, made clear that his opinions regarding clear reflection of income were made in the context of financial accounting principles and not tax accounting principles. In addition, Dr. Seago, at trial, acknowledged that he had not reviewed directly any taxpayer's method of accounting for inventory shrinkage other than the Divisions' shrinkage methods. Although we consider Dr. Seago's concessions in evaluating *366 the weight of his testimony, this Court will focus on the substance of his analyses. We first consider Dr. Seago's shrinkage accrual accuracy analysis. Under the cycle method of counting used by the Divisions, yearend inventories are not ordinarily taken, and, thus, whether the Divisions' shrinkage methods clearly reflect income is not a fact that petitioner can prove simply by comparing the shrinkage claimed by Target and by Dayton's for the taxable year to actual taxable year shrinkage figures. Petitioner must rely on an indirect method of proof. That is why petitioner relies on the expert testimony of Dr. Seago. Dr. Seago developed a model for determining taxable year shrinkage. First, Dr. Seago assumed that sales and shrinkage are "perfectly correlated", based on his findings in the 10-year correlation analysis, supra section VI.E.2. As we have stated, Dr. Seago allocated 75 percent of any accrual error to the taxable year prior to the taxable year in which the physical inventory was taken and 25 percent to the taxable year in which the physical inventory was taken. That allocation of the accrual error in conjunction with the aggregate of monthly accruals for shrinkage for the *367 relevant taxable years yielded, in Dr. Seago's opinion, the best estimate of taxable year shrinkage (i.e., sales-allocated taxable year shrinkage). Dr. LaRue criticizes Dr. Seago for aggregating sales and shrinkage figures at the Target-wide level. Dr. LaRue believes that variances in LIFO pool attributes and discontinuities in the timing of the physical inventories throughout the taxable year render the aggregate data virtually meaningless. Although we appreciate Dr. LaRue's criticism, we believe that an analysis of divisionwide or companywide data is not necessarily without merit, especially when an analysis of such data exposes relative differences between methods at the aggregate level. See Kroger Co. & Subs. v. Commissioner, T.C. Memo. 1997-2 (accepting the taxpayer's presentation of an aggregate analysis, which compared the taxpayer's method with the Commissioner's method based on an allocation of cross-year inventory shrinkage as a function of time; this Court found the aggregate analysis dispositive of whether there was an abuse of discretion by the Commissioner). Taxable year shrinkage estimates derived by a taxpayer's shrinkage method and by the Commissioner's method must *368 be subjected to the same indexes and cost complements when converting from retail to cost, and, thus, relative differences between two methods at the aggregate level may be significant. This Court, however, agrees with Dr. LaRue when aggregate data is used for other purposes. In particular, we have difficulty accepting the significance of Dr. Seago's 10-year correlation analysis, which found a strong correlation between sales and shrinkage for Target during the years 1979 through 1988, and which underlies Dr. Seago's shrinkage accrual accuracy analysis. At the most basic level, it appears that changes in the Divisions' LIFO pool attributes from year to year, differences in attributes among pools, and discontinuities in the timing of physical inventories from year to year combine to produce sales and shrinkage figures that represent different variables from year to year. We understand correlation, for present purposes, as a measure of the degree to which two variable, but consistently constituted, quantities tend to change with respect to each other and not as a measure of the degree to which two inconsistently constituted quantities change with respect to each other. Essentially, Dr. *369 Seago has not persuaded this Court that the strong correlation between sales and shrinkage derived from the 10-year correlation analysis is the product of the true relationship between sales and shrinkage and not the product of the confluence of varying LIFO pool attributes. Dr. Seago has failed to explain that apparently fundamental flaw in the 10-year correlation analysis. That is not to say that we would never accept statistical analyses demonstrating a correlation between sales and shrinkage; that is only to say that Dr. Seago, in this case, has simply failed to prove the significance of the correlation derived from the 10-year correlation analysis. 9 Dr. Seago recognizes that an analysis of the correlation between sales and shrinkage at the LIFO pool level would produce a more meaningful correlation and attempts to examine that correlation by the creation of surrogate pools in the absence of such data. We are not convinced by Dr. Seago's analysis of hypothetical pools of data derived from randomly placing individual Target stores into 21 pools because that approach divorces particular sales and shrinkage figures for each actual pool from the corresponding pool attributes; the *370 preservation of that relationship is precisely the purpose of analyzing sales and shrinkage data at the LIFO pool level. Because we are reluctant to accept Dr. Seago's 10-year correlation analysis, his shrinkage accrual accuracy analysis does not persuade us that Target's shrinkage method clearly reflects income, that respondent's method does not clearly reflect income, or that Target's shrinkage method more clearly reflects income when compared to respondent's method. Dr. Seago allocated accrual *371 errors under the assumption, which was derived from the 10-year correlation analysis, that sales and shrinkage are perfectly correlated. In addition, Target's monthly accruals for shrinkage were made as a percentage of sales. Therefore, Dr. Seago's estimate of the actual taxable year shrinkage--sales-allocated taxable year shrinkage--relies entirely on the critical assumption that sales and shrinkage are sufficiently correlated so that the sum of aggregate monthly shrinkage accrued as a percentage of sales for the taxable year, adjusted for an allocation of any accrual error based on a ratio of relative sales between the relevant taxable years, yields a figure for taxable year shrinkage that would clearly reflect income. 10*372 Although we believe that sales have some value as a predictor of shrinkage at the Target-wide level, we simply cannot accept the critical assumption that underlies Dr. Seago's shrinkage accrual accuracy analysis. Dr. Seago did not conduct an analysis of the correlation between sales and shrinkage or a shrinkage accrual accuracy analysis for data derived from the operations of Dayton's. We assume that petitioner wishes that we infer both a strong correlation between sales and shrinkage and a favorable shrinkage accrual accuracy analysis for Dayton's based on the analyses of Target data. Even if this Court were to engage in that type of speculation, our rejection of the analyses *373 with respect to Target renders that method of proof ineffectual. In addition, petitioner presents evidence demonstrating that the aggregate estimated shrinkage rates of Dayton's for inventory periods spanning the taxable year in issue are less than the verified rates of shrinkage for the same periods. That evidence, without more, does not provide a basis to evaluate clear reflection of income for the taxable year in issue for the reasons set forth in our discussion that follows of Dr. Seago's sales percentage shrinkage analyses based on Target data. Dr. Seago presents analyses that compare actual and estimated shrinkage rates as a percentage of sales for physical inventory periods (sales percentage shrinkage analyses). See supra sec. VI.E.4. Those analyses were conducted at both the store and Target-wide levels. Not only are we unimpressed by Dr. Seago's results, we have reservations about his assumptions. Dr. Seago's analyses compare results for inventory periods and not the taxable year or any other taxable year. An identity of results between actual and estimated shrinkage rates as a percentage of sales for inventory periods does not tell us anything about the relative distribution *374 of losses from shrinkage factors within those inventory periods. Thus, unless sales and shrinkage are correlated, evidence of an identity between actual and estimated shrinkage rates for an inventory period is no evidence that the shrinkage estimation rate for the inventory period is accurate for that portion of a taxable year that falls within (but is not identical to) the inventory period. 11*375 We rejected above a general correlation between sales and shrinkage based on the 10-year correlation analysis. In addition, Dr. Seago derived only an R<2> of 0.367 from his disaggregated analysis of Target stores during the taxable years ending in 1980 through 1989. In sum, we cannot accept Dr. Seago's assumption of a strong correlation between sales and shrinkage, and, therefore, Dr. Seago's sales percentage shrinkage analyses do not persuade us that the Divisions' shrinkage methods clearly reflect income. Lastly, Dr. Seago criticizes respondent's method as containing a systematic bias towards understating losses when sales are increasing. The validity of that assertion also relies on a strong correlation between sales and shrinkage. Although respondent's method is merely another method of estimating losses from shrinkage factors for the taxable year, see supra section VI.D., *376 Dr. Seago's unproven assertion, however, does not convince us that respondent's method does not clearly reflect income. H. Is Respondent's Determination That the Divisions' Shrinkage Methods Do Not Clearly Reflect Income and That Respondent's Method Does Clearly Reflect Income an Abuse of Discretion? Petitioner has a heavy burden to prove that respondent's determination that Target's shrinkage method and Dayton's shrinkage method do not clearly reflect income and that respondent's method does clearly reflect income is an abuse of discretion. See supra sec. VI.B. We find no such abuse of discretion here. But cf. Kroger Co. & Subs. v. Commissioner, T.C. Memo. 1997-2 (finding an abuse of discretion); Wal-Mart Stores, Inc. v. Commissioner, T.C. Memo. 1997-1 (same). Petitioner relies on the testimony of Dr. Seago who asserts that both Target's shrinkage method and Dayton's shrinkage method produce reasonably accurate shrinkage accruals and that those methods clearly reflect income. Dr. Seago also asserts that respondent's method does not clearly reflect income. The critical assumption upon which all of Dr. Seago's conclusions rely is the existence of a strong correlation between sales and *377 shrinkage derived from the 10-year correlation analysis. We cannot take the inferential leap that is required to accept that assumption. In light of respondent's broad discretion to determine clear reflection of income, this Court cannot accept the significance of Dr. Seago's 10-year correlation analysis because we cannot overlook the fact that aggregate sales and shrinkage data at the Target-wide level consist of sales and shrinkage figures from numerous LIFO pools, which each have different pool attributes that vary from year to year. In addition, we are not persuaded by any of the other evidence presented by petitioner in this case. Therefore, respondent's determination that the Divisions' shrinkage methods do not clearly reflect income and that respondent's method does clearly reflect income is not an abuse of discretion. VII. Conclusion The Divisions' systems of maintaining book inventories do not clearly reflect income. They are, thus, not sound within the meaning of section 1.471-2(d), Income Tax Regs. To reflect the foregoing, Decision will be entered for respondent. Footnotes 1. The claim for overpayment contests the disallowance of shrinkage accruals in computing the tax consequences of a prior settlement between the parties for the taxable year in issue. 2. The Tax Reform Act of 1986, Pub. L. 99-514, sec. 803(b)(4), 100 Stat. 2356, designated the quoted language as sec. 471(a). Before amendment, the quoted language was the entirety of sec. 471↩. 3. Petitioner attempts to distort our understanding of respondent's method by stating that, for Target, "respondent allows shrinkage at retail of $ 6,152,381 or 0.202 percent of sales." Petitioner also states that "respondent has not even allowed the shrinkage verified by physical inventories during the year of $ 51,323,565." That characterization of respondent's method is misleading because it fails to recognize that respondent's adjustments for the year in issue are not isolated determinations, but, rather, reflect a method change. Indeed, in the petition, petitioner alleges, alternatively, that a sec. 481 adjustment would be required in the event that respondent's adjustments are sustained. At trial, however, petitioner's counsel acknowledged that no evidence was submitted on that issue and that petitioner intended to rely on defeating respondent's determination of deficiency. On brief, petitioner's counsel cites respondent's failure to make an adjustment to opening inventory as evidence of the arbitrariness of respondent's method. Adjustments to opening inventory are the province of sec. 481; petitioner having abandoned its sec. 481 argument, we believe that it cannot show arbitrariness based on respondent's failure to make an adjustment to opening inventory, and we reject petitioner's attempt to distort respondent's method. 4. It should be noted that Dr. Seago refers to both Target's shrinkage method and Dayton's shrinkage method as Dayton Hudson's method, without distinction. Although there are many significant similarities between the two methods, this Court will evaluate the two methods independently and refer to the two methods as the Divisions' shrinkage methods only for convenience and when there are no relevant distinctions.↩ 5. These tables contain a few minor computational errors, and we have taken the liberty of calculating the aggregate percentage difference using Dr. Seago's numbers.↩ 6. That analysis of the relationship between sales and shrinkage at the individual store level appears in Dr. Seago's rebuttal report and is distinct from the 10-year correlation analysis.↩ 7. Dr. Gaffney notes that the columns "may not foot and crossfoot due to rounding." In addition, he notes that the data for 1981, which was provided by petitioner, do not appear mathematically correct, and the 1993 data include warehouse shrinkage that was computed separately in that year. Lastly, we have taken the liberty of deleting Dr. Gaffney's aggregate calculations because those calculations did not take into account the adjustment to book inventories following physical inventories. 8. Generally, the cost complement is the weighted average relationship between the cost of current year purchases and the retail value assigned to those purchases.↩ 9. It should be noted that, in Kroger Co. & Subs. v. Commissioner, T.C. Memo. 1997-2, we stated: Although we accept Dr. Bates' opinion as to the correlation between sales and shrinkage at the business level, and we are impressed by Dr. Bates' sales-based accuracy analysis, we are hesitant to rest our conclusion as to the accuracy of the retailers' shrinkage method on a correlation whose significance we may not fully appreciate. * * *↩ Similarly, in this case, although we accept Dr. Seago's opinion that the data he examined in the 10-year correlation analysis revealed a strong correlation, Dr. Seago has not demonstrated the significance of that finding to the issue of clear reflection of income. 10. In addition, this Court has difficulty with Dr. Seago's shrinkage accrual accuracy analysis for other reasons. Target's shrinkage method results in the accrual of shrinkage based on a rate set at the beginning of the taxable year for each department within each store. Thus, conceivably, a department within a store could accrue shrinkage at two different rates during the cross-year inventory period, e.g., 2 percent of sales during the taxable year's physical-to-yearend period and 2.5 percent of sales during the period prior to the physical inventory in the next taxable year. An allocation of any accrual error only↩, as opposed to an allocation of total verified shrinkage, is inconsistent with the underlying assumption that sales and shrinkage are perfectly correlated. In the same vein, Dr. Seago allocates accrual error based on a 75/25 ratio that is an approximation of the relative sales between the relevant taxable years and not the actual cross-year sales percentages. 11. The requirement of the assumption that sales and shrinkage are correlated is illustrated by the following example. Assume that X Co. (1) is a calendar year taxpayer; (2) has an inventory period from Apr. 1 to Mar. 31; (3) has no sales from Jan. 1, 1990, to Mar. 31, 1990, and $ 1 of shrinkage for that period; (4) has $ 100 of sales from Apr. 1, 1990, to Dec. 31, 1990, and no shrinkage for that period; (5) has no sales from Jan. 1, 1991, to Mar. 31, 1991, and $ 2 of shrinkage for that period; and (6) accrued shrinkage at a rate of 2 percent of sales for all relevant periods. Upon the physical inventory on Mar. 31, 1991, X Co.'s records would indicate $ 100 of sales and $ 2 of shrinkage during the inventory period. Thus, verified shrinkage of 2 percent of sales would correspond to accrued shrinkage of 2 percent of sales. The identity of results for the inventory period does not correspond to an identity of results for the taxable year because actual shrinkage for the taxable year was 1 percent of sales. That discrepancy exists because the example did not assume that sales and shrinkage are correlated.