KROGER CO. v. COMMISSIONER

THE KROGER COMPANY AND SUBSIDIARIES, Petitioner v. COMMISSIONER OF INTERNAL REVENUE, Respondent KROGER CO. v. COMMISSIONER Docket No. 3358-94. United States Tax Court T.C. Memo 1997-2; 1997 Tax Ct. Memo LEXIS 7; 73 T.C.M. (CCH) 1637; January 2, 1997, Filed *7 Decision will be entered under Rule 155. P operated supermarkets and convenience 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 year's end. 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 year's end and made an accrual of the estimate. P calculated shrinkage accruals as a percentage of gross sales. Held: P's systems of maintaining book inventories (including the making of shrinkage accruals) conform to the best accounting practice and clearly reflect income. They are, thus, sound within the meaning of sec. 1.471-2(d), Income Tax Regs. Frederick H. Robinson, Craig D. Miller, Patricia M. Lacey, and Gary R. Vogel, for petitioner. Reid M. Huey, Nancy B. Herbert, Robert J. Kastl, Jennifer H. Decker, James E. Kagy, Timothy S. Sinnott, and Richard G. Goldman, for respondent. *8 HALPERN, Judge HALPERN MEMORANDUM FINDINGS OF FACT AND OPINION HALPERN, Judge: Respondent has determined deficiencies in petitioner's Federal income tax liabilities for the years 1984, 1985, and 1986 in the amounts of $ 7,152,527, $ 1,772,936, and $ 1,668,392, respectively. The parties*9 have reached agreement on certain issues, and the only 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 years 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 fact filed by the parties and the accompanying exhibits are incorporated herein by this reference. The parties have made approximately 450 separate stipulations of fact, occupying over 100 pages, and there are 143 accompanying 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. Kroger The Kroger Co. (Kroger) is an Ohio corporation, with its principal place of business in Cincinnati, Ohio. Kroger is the common parent corporation of an affiliated group of corporations making a consolidated return of*10 income. For itself, and as sole agent for each member of the affiliated group, Kroger filed the petition giving rise to this case. (In the papers filed in this case, the convention of the parties has been to use the term "petitioner" to refer to the affiliated group as a whole (as, from time to time, it was constituted). We will adopt that convention.) Petitioner's principal business activities are the operation of supermarkets and convenience stores and the distribution and sale of drug and general merchandise. During the years in issue, petitioner operated one of the nation's largest supermarket chains, measured by total sales, and one of the nation's largest drug store chains. Kroger, itself, was in the retail food business, operating numerous grocery product warehouses and supermarkets. Kroger generated over $ 11 billion in annual sales from its supermarkets during each of the years in issue. Superx, which operated a chain of drug and general merchandise stores throughout the United States, was a wholly owned subsidiary corporation of Kroger. Superx generated over $ 800 million in annual sales during each of the years in issue. Florida Choice, which operated a chain of supermarkets*11 in Florida, was a division of Superx. Florida Choice generated over $ 100 million in annual sales during each of the years in issue. (Hereafter, for convenience, we will refer to Kroger (but only with respect to its retail operations), Superx, and Florida Choice, collectively, as the retailers.) B. Accounting Practices Petitioner's annual accounting period and taxable year was a 52/53-week year ending on the Saturday closest to December 31. The retailers 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 year's end. 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. During the years in issue, the retailers used "cycle counting" to*12 conduct physical inventories of merchandise. Cycle counting is a method of conducting physical inventories at individual stores, in rotation, throughout the year. Most large retail companies, including grocery and drug retailers, 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. With few exceptions, the retailers took no physical inventories at the end of any of the years in issue. The retailers maintained "perpetual" or other book inventory records (without distinction, book inventory records) from which inventory could be determined without a physical count. Inventory determined from book inventory records often differs from inventory determined by physical count. When inventory is determined from book inventory records (computed without any accrual for estimated shrinkage), and the inventory so determined exceeds inventory determined*13 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". Shrinkage and overage (hereafter, generally, shrinkage) are attributable to a variety of factors, the total number of which cannot be quantified, including the following: 1. theft of merchandise (by employees, customers, and vendors); 2. unrecorded or improperly recorded losses of merchandise due to spoilage, breakage, and other damage; 3. unit discrepancies in goods received from and/or returned to vendors; 4. failure to ring or record the proper price upon sale of merchandise; 5. errors in recording retail prices (including price changes) on a taxpayer's perpetual record; 6. errors in marking and changing prices on merchandise; 7. failure to properly record returns by customers; 8. errors in conducting the physical inventory (including both unit errors and pricing errors); 9. errors in processing paper (including price-change documents, invoices, and merchandise transfers); and 10. errors in billing and other computer systems. The retailers experienced some or*14 all of the factors listed (shrinkage factors) during the years in issue. The occurrence of shrinkage factors is not limited to particular times during the year, but, 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. For each of the years in issue, the retailers estimated and accrued yearend shrinkage (that estimate and accrual hereafter being referred to as shrinkage accrual). Such shrinkage accruals were added to the other data constituting the retailers' book inventory records, which were used to determine yearend inventories. Shrinkage accruals reduced yearend inventories, which had the effect of increasing cost of goods sold*15 and, as a result, decreasing gross income. In determining yearend inventories, the retailers would, in addition to taking into account shrinkage as determined by physical count of inventory during the year (1) subtract shrinkage accrual as of that year's end and (2) add shrinkage accrual as of the prior year's end. Errors in estimating shrinkage accrual would be subject to correction in the subsequent year because of the addition of the prior year's shrinkage accrual to the subsequent year's ending inventory. The retailers calculated shrinkage accrual as a percentage of gross sales. 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 the virtually universal, practice; it is the best practice in that industry. Respondent disallowed the retailers' shrinkage accruals. That had the consequence of decreasing cost of goods sold and, as a result, increasing gross income. Respondent has proposed deficiencies based upon that increased income. II. KFS Division of Kroger A. General Operations Kroger managed its grocery products warehouses and supermarkets on a geographic*16 basis as Kroger Marketing Areas (KMAs). A KMA contained between 34 and 161 supermarkets. The KMAs were part of the Kroger Food Stores Division of Kroger (the KFS division). Altogether, the KFS division operated between 1,000 and 1,500 supermarkets between 1979 and 1992. Each KMA had its own management organization, which was part of the Kroger management structure. Management of each KMA reported to corporate management in Kroger's general office (the Kroger general office). The Kroger general office set the policies that governed the operation of the KMAs. After 1984, Florida Choice, although a division of Superx, was treated as a KMA for certain accounting purposes. B. Accounting Methods and Procedures The accounting methods and procedures used by each KMA were prescribed by the Kroger general office. Pertinent aspects of those methods and procedures for the years in issue were as follows. 1. Departments Store inventories were divided into departments and subdepartments. shrinkage accrual was made only for the grocery, drug/general merchandise, and cosmetics departments. 2. Retail Method of Inventory Valuation The retail method of valuing inventory was used by *17 the KFS division for store inventories in the grocery, drug/general merchandise, and cosmetics departments. Under the retail method, the cost of goods sold is estimated by multiplying sales revenue by the "cost complement". That technique translates the retail dollar value of the goods sold into its approximate cost dollar value. 3. LIFO Beginning with 1979, Kroger elected to use the last-in-first-out (LIFO) method of accounting. Kroger valued its inventories in stores and warehouses using the dollar value, link chain method of implementing LIFO. The KFS division also elected to use statistical sample techniques to determine the dollar value indexes. The KFS division initially used a single LIFO pool for all items in the grocery, drug/general merchandise, and cosmetics departments. Beginning with 1986, the KFS division allocated its single pool into nine pools. 4. Shrinkage Accruals The KFS division accounting policy for estimating shrinkage accrual was as follows: For each store in which no physical inventory is taken during a period, a shrinkage and spoilage loss will be accrued for each department: a. At the beginning of each year determine the KMA rate of *18 shrinkage and spoilage, at retail, for the previous year for each department. b. From this experience and evidence of trend, estimate the percentage (to the nearest hundredth of one percent) expected for the KMA for the current year for each department. c. Use the estimated percentages for all stores for the current year. If a change in rate appears desirable within the year request approval of a change from the Corporate Accounting Policy and Methods Department. No approval is required to change the percentages at the beginning of the year. C. Management of Shrinkage Minimization of shrinkage factors was a management goal common to all KMAs. Detailed records were maintained in the KMAs on the incidence (cost) of shrinkage factors. Records were maintained by store and by store manager. Control (minimization) of shrinkage factors was an important criterion in assessing the performance of a store manager. A store manager could be fired or might not be promoted for failure to minimize shrinkage factors. Programs were continually developed and implemented to control shrinkage factors. During the years in issue, the incidence of shrinkage factors varied among stores, among*19 departments within stores, and among KMAs. Overages were, on occasion, recorded by individual stores and, in some years, on a net basis by entire KMAs, but never for the KMAs together. No accrual was made to reflect an expectation of overage. From 1984 through 1987, in the face of recurring overages, the Michigan KMA did not make shrinkage accruals. The management of each KMA determined shrinkage accrual rates to be used throughout that KMA. Judgment played a large role in determining shrinkage accrual rates. Factors that would be taken into account included experience with shrinkage factors, store sizes, merchandising techniques, regional differences, and recent shrinkage trends. A separate percentage rate was determined for each department for which a shrinkage accrual was made. D. Physical Inventories From 1984 through 1992, the KFS division conducted an average of 2.3 physical inventories a year in each store. III. Florida Choice Florida Choice, although a division of Superx, was operated as if it were a part of the KFS division. During the years in issue, Florida Choice's chain of supermarkets grew from 22 to 30 stores. During the years in issue, Florida Choice*20 followed the same KFS division accounting methods and procedures utilized by the KMAs. Florida Choice followed the shrinkage accrual practices and procedures applicable to the KFS division to determine its shrinkage accrual rate as if it were a KMA. During 1984, Florida Choice conducted an average of three physical inventories a store. In 1985 and 1986, the average was two inventories a store. IV. Superx A. General Operations During the years in issue, Superx operated between 185 and 621 drug and general merchandise stores. Superx had its own management organization. Superx's management reported to corporate management in the Kroger general office. The Kroger general office set the policies that governed the general operations of Superx. B. Accounting Methods and Procedures 1. Booking Rate Calculations Inventory was reflected on Superx's inventory accounts at cost and not at retail. To calculate gross income of each store (and each department within a store) for the physical-to-yearend period, Superx multiplied sales during that period by a percentage known as the "booking rate". That process was similar to Kroger's retail method. Superx determined the booking*21 rate by calculating a company key rate from cost price data obtained from 80 selected stores. The booking rate represented the percentage of each dollar of sales that represented gross profit. Gross income was further reduced by shrinkage accrual. Cost of sales was computed by multiplying sales by the percentage equal to (1) 100 percent less (2) the applicable booking rate. That amount was used to reduce inventory. 2. LIFO For its 1984 and 1985 years, Superx used the dollar value LIFO method of calculating its inventories, using five LIFO pools. It excluded optical centers, deli, restaurants, liquor, and inventories maintained by Florida Choice from its LIFO method. It discontinued the LIFO method for its 1986 tax year. 3. Shrinkage Accruals Superx made shrinkage accruals for all of its departments except its optical departments. Superx developed a single shrinkage accrual rate, which was expressed as a percentage of gross sales and used by all of Superx's drug stores (and applied uniformly, although yielding different shrinkage accruals depending on a store's sales). Superx's shrinkage accrual rate was determined at Superx headquarters. Superx management primarily examined*22 historical shrinkage experience and recent shrinkage trends at the company level in determining Superx's shrinkage accrual rate. Individual store managers could not use a different rate. Between 1981 and 1986, shrinkage accrual rates, as a percentage of gross sales, varied between 2.1 percent and 2.5 percent. C. Management of Shrinkage Controlling shrinkage factors was a significant concern of Superx management. Store managers could be fired, or their compensation reduced, for failure to control shrinkage factors. Superx maintained a risk management department, which performed field audits to see that procedures to reduce shrinkage factors were in place and performed analyses of shrinkage factors to aid in control of such factors. D. Physical Inventories During 1983 and 1984, Superx conducted an average of 1.7 physical inventories a year in each store. In 1985, the average was 1.6 inventories a store. OPINION I. Introduction Petitioner's principal business activities are the operation of supermarkets and convenience stores and the distribution and sale of drug and general merchandise. We are concerned here with (1) the Kroger Food Stores Division of Kroger (the*23 KFS division), (2) Florida Choice, a division of Superx, which operated a chain of supermarkets, and (3) Superx, a subsidiary corporation of Kroger, which operated a chain of drug and general merchandise stores (collectively, the retailers). During the years in issue, the retailers used cycle counting to conduct physical inventories of merchandise. Under the cycle counting method, physical inventories were taken in rotation, at the various stores, throughout the year. Also, the retailers maintained book inventory records from which inventories could be determined without a physical count. The retailers 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 retailers' shrinkage accruals, and we must determine whether that disallowance was 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 *24 necessary in 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. 1 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., *25 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 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. Dayton Hudson Corp. & Subs. v. Commissioner In Dayton Hudson Corp. & Subs. v. Commissioner, 101 T.C. 462 (1993), respondent determined a deficiency in the taxpayer's Federal income tax because, in computing its yearend book inventories, the taxpayer made a shrinkage accrual. In the Dayton Hudson case, which was before us on the Commissioner's motion for summary judgment, we held that section 1.471-2(d), Income Tax Regs., as a matter of law, does not prohibit making a shrinkage accrual in computing book inventories. *26 We acknowledged, however, that the Commissioner might yet argue that the taxpayer'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. Here, respondent acknowledges our holding in the Dayton Hudson case, but she does not agree that it is correct. We adhere to that holding. IV. Are the Retailers' Systems of Accounting for Inventories, Including the Use of Shrinkage Accruals, Sound? Because the retailers used cycle counting to conduct physical inventories of merchandise, and no count was taken at year's end, the retailers 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. The question of what constitutes a "sound accounting system" under section 1.471-2(d), Income Tax Regs., has not been answered by the courts. Section 1.471-2(a), Income Tax *27 Regs., however, provides two specific requirements with which acceptable inventory practices must conform. 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 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. Our inquiry, then, is, principally, whether the retailers' systems of maintaining book inventories (including the making of shrinkage accruals) conform to the best accounting practice and clearly reflect income. Indeed, the principal point relied on by respondent on brief is that "Petitioner's methods of estimating inventory shrinkage * * * failed to clearly reflect income." V. Best Accounting Practice The parties have stipulated that, for financial accounting purposes, *28 petitioner's financial statements for the years 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 retailers' systems of book inventories 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*29 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 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*30 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. 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)*31 (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 her to reject a taxpayer's method if it "does not clearly reflect income", and to substitute 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 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 that the Commissioner abused her discretion. E.g., Asphalt Products Co. v. Commissioner, 796 F.2d 843, 848 (6th Cir. 1986), affg. in part and revg. in*32 part Akers v. Commissioner, T.C. Memo. 1984-208, revd. per curiam on another issue 482 U.S. 117 (1987). An appeal in this case will likely lie in the Court of Appeals for the Sixth Circuit. That court has said: § 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 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);*33 Ansley-Sheppard-Burgess Co. v. Commissioner, 104 T.C. 367, 371 (1995); Hospital Corp. of America 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 California 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*34 clearly reflect income. See Asphalt Products Co. v. Commissioner, supra at 847. C. Retailers' Shrinkaqe Method The retailers 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 retailers' book inventory records under a method (the retailers' shrinkage method) involving three variables: (1) shrinkage verified by physical inventories during the taxable year, (2) shrinkage accrual for the taxable year, and (3) shrinkage accrual for the prior year. The retailers calculated shrinkage accruals as a percentage of sales. Shrinkage accrual rates for each department within a KMA and for Florida Choice were based on a combination of factors including experience with shrinkage factors, store sizes, merchandising techniques, regional differences, and recent shrinkage trends. Rates for Superx were primarily based on historical shrinkage experience and recent shrinkage trends at the company level. Prior year shrinkage accrual was subtracted from the amount of shrinkage determined by the first physical inventory of the taxable*35 year; that adjustment purported to calibrate shrinkage figures so as to provide an estimate of taxable year shrinkage. D. Petitioner's Expert Testimony 1. Introduction Petitioner relies on expert testimony to demonstrate that the retailers' shrinkage method clearly reflects income. In particular, petitioner relies on such testimony to demonstrate a strong correlation between sales and shrinkage, which correlation underlies the retailers' shrinkage accruals. Petitioner presents the expert testimony of Charles E. Bates, Ph.D. Dr. Bates is the director of economic litigation services for the Economic Consulting Services Group at KPMG Peat Marwick LLP. He is experienced in statistics, econometric modeling, and economic analysis. 2. Correlation Between Sales and Shrinkage Statistical correlation is a measure of the degree to which two variable quantities tend to change with respect to each other. Correlations are 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*36 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. Dr. Bates is of the opinion that the correlation between sales and shrinkage is strong. Dr. Bates is also of the opinion that the "business level" is the appropriate level to test the relationship of sales to shrinkage. Dr. Bates uses the term "business level" to refer, individually, to the aggregate operations of the KFS division, the aggregate operations of Florida Choice, and the aggregate operations of Superx. Dr. Bates acknowledges that correlation can be tested at other levels, e.g., the department level within a store, the store level, or, even, at the level of the "entire Kroger corporate entity". Dr. Bates believes that the business level is appropriate because that is the level at which taxable income is computed. Dr. Bates bases his opinions of strong correlation on the application of two methods to measure the correlation between sales and shrinkage at the business level. The first method derives the correlation between sales and shrinkage from aggregate data at the business level. *37 The second method derives the correlation between sales and shrinkage from individual inventory records at the store level. Dr. Bates is of the opinion that, for the years he examined, the correlation between sales and shrinkage is (1) at least 0.91 for the KFS division, (2) at least 0.89 for Florida Choice, and (3) at least 0.94 for Superx. 3. Yearend Shrinkage Dr. Bates is of the opinion that losses from shrinkage factors occur during the physical-to-yearend period. That proposition is not as simple to demonstrate as one might think. The problem, of course, is that, although losses on account of shrinkage factors will be demonstrated by physical count at the end of an accounting period, the lack of intervening physical counts makes it impossible to demonstrate the distribution of those losses within the period. Dr. Bates primarily derives his opinion by deduction from two premises: (1) sales occur during the physical-to-yearend period and (2) there exists a strong correlation between sales and shrinkage. In other words, he concludes that, because there are sales during the physical-to-yearend period, and there is a statistical relationship between sales and shrinkage, it *38 is likely that losses from shrinkage factors occur during, the physical-to-yearend period. He conducted two additional tests, however, which gave him more evidence to support his conclusion. First, he compared shrinkage among inventory cycles with physical-to-yearend periods of differing lengths. Second, he applied a conventional statistical analysis to test for the occurrence of yearend shrinkage. 4. Shrinkage Accrual Accuracy Analysis Dr. Bates is of the opinion that yearend shrinkage can reasonably be estimated by allocating a portion of the shrinkage revealed by the next physical count to the physical-to-yearend period. Dr. Bates has made such estimates in order to test the accuracy of the retailers' shrinkage accruals. He concludes that, for each of the retailers, annual losses, in the aggregate, claimed on account of shrinkage factors are within 5 percent of taxable year shrinkage based on an allocation of cross-year inventory shrinkage as a function of both sales and time. Dr. Bates knew the amount of losses from inventory cycles wholly within a taxable year. To that sum he added (1) an allocation of the shrinkage determined by the physical inventory first taken during*39 the taxable year and (2) an allocation of the shrinkage determined by the physical inventory first taken during the next taxable year. That calculation provided his estimate of taxable year shrinkage. Dr. Bates calculated taxable year shrinkage using sales to allocate shrinkage to the relevant portions of cross-year inventory cycles (sales-based taxable year shrinkage). To provide an alternative estimate of actual shrinkage, Dr. Bates calculated taxable year shrinkage using a time-based allocation method (time-based taxable year shrinkage). That approach allowed him to have a second way to test the accuracy of the losses from shrinkage factors that the retailers reported for tax purposes. Dr. Bates compared his estimates of taxable year shrinkage with the losses claimed by the retailers for Federal income tax purposes. He performed the same calculations to determine the accuracy of respondent's method of reflecting shrinkage factors, which would allow no shrinkage accrual, but would take account of shrinkage only in the year when demonstrated by physical count. Dr. Bates made these comparisons using estimates of taxable year shrinkage based on both sales and time. The results*40 of Dr. Bates' calculations and analyses are set forth in an appendix to this opinion. Dr. Bates determined that the accounting system utilized by the KFS division for Federal income tax purposes produced, in the aggregate, a net underestimate for the years 1984 through 1991 of 1.8 percent of sales-based taxable year shrinkage and 1.7 percent of time-based taxable year shrinkage. He determined that respondent's method produced a net underestimate of 4.4 percent of sales-based taxable year shrinkage and 4.3 percent of time-based taxable year shrinkage. In addition, Dr. Bates determined that the maximum error under respondent's method was 15.6 percent of sales-based taxable year shrinkage and 15.7 percent of time-based taxable year shrinkage (compared to 11.4 percent and 11.2 percent, respectively, under the system utilized by the KFS division). He concludes that respondent's method is less accurate than that used by the KFS division. Dr. Bates determined that the accounting system utilized by Florida Choice produced, in the aggregate, a net underestimate for the years 1984 through 1988 of 3.9 percent of sales-based taxable year shrinkage and 2.9 percent of time-based taxable year *41 shrinkage. He determined that respondent's method produced a net underestimate of 6.1 percent of sales-based taxable year shrinkage and 5.2 percent of time-based taxable year shrinkage. Dr. Bates determined that the maximum error under respondent's method was 20.2 percent of sales-based taxable year shrinkage and 20.5 percent of time-based taxable year shrinkage (compared to 12.3 percent and 14.0 percent, respectively, under the system utilized by Florida Choice). He concludes that respondent's method is less accurate than that used by Florida Choice. Dr. Bates determined that the accounting system utilized by Superx produced, in the aggregate, a net underestimate for the years 1983 through 1985 of 4.7 percent of sales-based taxable year shrinkage and 4.5 percent of time-based taxable year shrinkage. He determined that respondent's method produced a net underestimate of 7.1 percent of sales-based taxable year shrinkage and 6.8 percent of time-based taxable year shrinkage. Dr. Bates determined that the maximum error under respondent's method was 9.4 percent of sales-based taxable year shrinkage and 9.8 percent of time-based taxable year shrinkage (compared to 6.1 percent and 5.4 percent, *42 respectively, under the system utilized by Superx). Dr. Bates concludes that respondent's method is less accurate than that used by Superx. E. Respondent's Expert Testimony Respondent offered rebuttal expert testimony of Donald M. Roberts, Ph.D., a professor of decision and information sciences at the University of Illinois. Dr. Roberts had been asked to examine the statistical basis of Dr. Bates' conclusion that the correlation between sales and shrinkage for the KFS division for the period 1984 through 1992 was 0.91. Dr. Roberts confirmed that the correlation was 0.91. In his rebuttal report, Dr. Roberts does not offer any criticism of Dr. Bates' opinion that losses from shrinkage factors occur during the physical-to-yearend period or undermine Dr. Bates' shrinkage accrual accuracy analysis. Dr. Roberts' own opinion is that the correlation between sales and shrinkage is generally low and that sales do not provide a reasonable basis for estimating inventory shrinkage. Dr. Roberts had been asked to examine sales and shrinkage only for the KFS division. He examined data at the department level within stores in the KMAs. He computed correlations for each department for the years*43 1984, 1985, and 1986. He also computed correlations for each department within each KMA for the period 1984 through 1992. Petitioner offered additional expert testimony of Dr. Bates in rebuttal to Dr. Roberts' opinion that the correlation between sales and shrinkage is generally low and that sales do not provide a reasonable basis for estimating inventory shrinkage. Dr. Bates' principal criticism of Dr. Roberts' conclusion is that Dr. Roberts' correlations are not relevant to analyzing the accuracy of the KFS division shrinkage accruals because Dr. Roberts' correlations measure the tendency of shrinkage to vary in proportion to sales from inventory to inventory and store to store within each department and KMA rather than the tendency of annual shrinkage for the business to vary in proportion to annual sales for the business. Dr. Bates is of the opinion that it is correlation of year-to-year changes in business level shrinkage and sales that is relevant to determining the accuracy of shrinkage accruals. Dr. Bates states: "[Dr. Roberts'] more restricted conclusion is technically correct, but irrelevant for assessing the propriety of accruing shrinkage as a percentage of sales for *44 tax purposes." In his oral testimony, Dr. Roberts made clear to us the limitations of any conclusions to be drawn from a consideration of statistical correlation. A strong correlation between two variables (e.g., shrinkage and sales) does not necessarily mean that one can predict the value of one variable (e.g., shrinkage) based on the value of the other (e.g., sales). To say that there is a strong correlation between two variables means only that there is a strong linear relationship between the two. Neither Dr. Bates nor Dr. Roberts finds the other's computation of correlation inconsistent with his own. That is explained by the fact that they chose to correlate different variables. Each, however, has gone another step (beyond correlation) and ventures an opinion as to the predictability of shrinkage based on sales. Not surprisingly, they have reached different opinions. While we cannot fully reconcile those different opinions, Dr. Bates, principally by way of his rebuttal report, has persuaded us that the low correlations found by Dr. Roberts are not inconsistent with Dr. Bates' opinion as to the accuracy of sales as a predictor of shrinkage at the business level. More importantly, *45 Dr. Roberts has not persuaded us that the low department level correlations found by him are determinative of the question of clear reflection of taxable income. Moreover, Dr. Roberts has failed to rebut Dr. Bates' opinion that losses from shrinkage factors occur during the physical-to-yearend period or to undermine Dr. Bates' shrinkage accrual accuracy analysis. At this point, it is sufficient to say that we attach credence to Dr. Bates' analysis and are convinced that, at the business level, sales have value as a predictor of shrinkage. We will consider the weight to be accorded to Dr. Bates' conclusions infra. F. Shrinkage Accruals and LIFO The shrinkage accruals made by the retailers were only estimates, and because they were estimates, they were subject to error. We have found that errors in estimating shrinkage accruals were subject to correction in the subsequent year because of the addition of the prior year's shrinkage accrual to the subsequent year's ending inventory. Respondent argues, however, that the additional demands associated with the retailers' use of LIFO "compounds" the errors inherent in making shrinkage accruals. Respondent presents the expert testimony*46 of David W. LaRue, Ph.D., an associate professor of commerce at the University of Virginia, who testified to, among other things, the "tax effects" resulting from the accrual of erroneous estimates of undetected shrinkage for the KFS division. Dr. LaRue examined the KFS division's practice of making shrinkage accruals. He designed simulation models to analyze shrinkage estimation errors under the retail dollar value LIFO method used by the KFS division. He concluded that the process of making subsequent year corrections was inadequate because of changes in factors such as LIFO inflation adjustment factors and retail method cost complement factors. Respondent also presented the report and testimony of William R. Sutherland, Esq., an attorney and accountant. Mr. Sutherland came to essentially the same conclusions for Superx that Dr. LaRue came to for the KFS division. Both Dr. LaRue and Mr. Sutherland concede, however, that respondent's adjustments -- which disallow the retailers' shrinkage accruals -- would produce exactly the same types of errors if there were undetected yearend shrinkage. Indeed, the magnitude of such errors under respondent's method might well be greater because*47 of respondent's failure to account for trends or other factors applicable to the taxable year. In any event, respondent's proposed adjustments will not eliminate the flaws perceived by respondent's experts. It appears that only the practice of yearend physical inventories at all stores 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. G. Retailers' Shrinkage Method Compared to Respondent's Method Respondent's method would permit the retailers to account for losses from shrinkage factors only when such losses are verified by physical inventories. Respondent claims that her "method is nothing more than the application of the principle that taxpayers may not reduce income by unverified losses or expenditures, or unreliable estimates." Respondent states that "any alternative method of estimating shrinkage imposed by Respondent would have been wholly arbitrary since it would not clearly reflect income." 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*48 method would adjust the retailers' book inventories by disallowing any shrinkage accrual. If we were to sustain respondent's disallowance, the retailers would compute book inventories much as they do now, except that they would neither add to shrinkage as determined by physical count during the year any shrinkage accrual for the physical-to-yearend period of that year nor subtract from such shrinkage the shrinkage accrual for the prior year's physical-to-yearend period. See sec. I.C. (Findings of Fact), supra. The retailers' cost of goods sold, as determined by book inventories, would, therefore, include shrinkage for all inventory cycles beginning and ending in the taxable year, plus shrinkage for inventory cycles beginning in the prior taxable year and ending in the taxable year, but not any portion of the shrinkage determined for the inventory cycle beginning within the taxable year and ending in the next taxable year (i.e., yearend shrinkage). In sum, the retailers' 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 *49 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 the inventory year might equal taxable year shrinkage, but the occurrence of this remote possibility is impossible to verify. What is likely (almost a certainty) is that the taxpayer, computing his cost of goods *50 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 retailers 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 retailers' shrinkage method and respondent's method is that respondent, without admitting it, accepts an estimate of yearend shrinkage while the retailers, by making a shrinkage accrual, consciously attempt to estimate that shrinkage. H. Annual Accounting It is well settled that *51 the Federal income tax system is based on annual accounting. E.g., Heiner v. Mellon, 304 U.S. 271, 275 (1938). "Inventories are intended to insure a clear reflection of the year's income by matching sales during the taxable year with the costs attributable to those sales". Rotolo v. Commissioner, 88 T.C. 1500, 1515 (1987). Respondent's method, in effect, substitutes yearend shrinkage of the prior year for yearend shrinkage of the taxable year. Sales during the taxable year are matched with losses verified to be both losses for that year and losses for the end of the prior year. On its face, respondent's method violates the principle of annual accounting. Of course, under the retailers' shrinkage method, the retailers' estimates of shrinkage accruals are also based on information gathered from prior years, since the retailers' shrinkage rates are dependent, in part, on historical data. The distinction, however, is that the retailers' shrinkage method utilizes prior year information as a factor in calculating the current year's shrinkage rate, whereas respondent's method plainly substitutes yearend shrinkage of the prior year*52 for yearend shrinkage of the taxable year. If physical inventories were required to be taken at year's end, 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 year's end. Sec. 1.471-2(d), Income Tax Regs. Once the Secretary decided not to require physical inventories at year's end, 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 retailers' shrinkage method) or substitution (respondent's method). Respondent recognizes that fact. Respondent's position, however, is that, unless a taxpayer can demonstrate the accuracy of his calculation of yearend shrinkage, the taxpayer must choose between yearend physical inventories and respondent's substitution method of accounting for yearend shrinkage. Respondent also recognizes, however, that, under the logic*53 of Dayton Hudson, if petitioner demonstrates the accuracy of the retailers' shrinkage method, that method does clearly reflect income. On brief, respondent states: The crucial issue in determining whether Petitioner's methods of estimating shrinkage clearly reflected income is whether the methods were designed to produce accurate results. Clear reflection of income means that income should be reflected with as much accuracy as standard methods of accounting practice permit. [Citing Caldwell v. Commissioner, 202 F.2d 112, 115 (2d Cir. 1953).] We must determine the accuracy of the retailers' shrinkage method to determine whether it clearly reflects income. I. Accuracy Absolute accuracy is not required. Indeed, respondent as much as concedes that absolute accuracy is not required by stating that clear reflection means reflection with as much accuracy as standard methods of accounting practice permit. Also, absolute accuracy is not the standard demanded of book inventories by section 1.471-2(d), Income Tax Regs. That section explicitly states that balances shown by book inventories "should be verified by physical inventories*54 at reasonable intervals and adjusted to conform therewith." (Emphasis added.) Both verification and adjustment would be unnecessary if only absolute accuracy were acceptable. Finally, section 1.446-1(c) (1) (ii) (A), Income Tax Regs., which specifies when a liability is incurred for purposes of the accrual method of accounting, requires only reasonable accuracy in determining the amount of an established liability. As noted previously, the term "liability" specifically includes a cost taken into account in computing cost of goods sold. Sec. 1.446-1(c) (1) (ii) (B), Income Tax Regs. The accuracy of the retailers' shrinkage method presents a question of fact. Petitioner bears the burden of proving that fact. Rule 142(a). Since, under the cycle method of counting used by the retailers, yearend inventories are not ordinarily taken, the accuracy of the retailers' shrinkage method is not a fact that petitioner can prove simply by comparing the retailers' estimates (shrinkage accruals) to actual yearend shrinkage figures. Petitioner must rely on an indirect method of proof. That is why petitioner relies on the expert testimony of Dr. Bates, whose expertise is in statistics, *55 econometric modeling, and economic analysis. Dr. Bates was given the retailers' estimates of yearend shrinkage based on sales. He hypothesized that he could prove the accuracy of those estimates by showing that they did not differ, or differed by only a small percentage, from amounts determined on the basis of a sales-based allocation of the actual shrinkage for the relevant inventory cycles. Dr. Bates' conclusion is that, for each of the retailers, annual losses, in the aggregate, claimed on account of shrinkage factors are within 5 percent of sales-based taxable year shrinkage. Dr. Bates performed a similar analysis to determine the accuracy of respondent's method of accounting for losses from shrinkage factors. He concluded that respondent's method is less accurate than the retailers' shrinkage method and is subject to a greater range of error. Dr. Bates performed a second accuracy analysis, which was independent of the correlation between sales and shrinkage and apportioned actual shrinkage evenly over each inventory cycle without regard to sales or any factor other than the passage of time (i.e., a time-based allocation). For each of the retailers, he found a level of *56 accuracy similar to what he found using a sales-based allocation. Applying a time-based allocation to respondent's method, he again concluded that respondent's method is less accurate than the retailers' shrinkage method and is subject to a greater range of error. Dr. Bates has persuaded us that, assuming either a sales-based or time-based allocation of losses from shrinkage factors, the retailers' shrinkage method is more accurate than respondent's method, and we so find. J. Consistency of Retailers' Inventory Practices As stated in section IV, supra, section 1.471-2(b), Income Tax Regs., makes consistency of application from year to year an important and explicit element in determining whether the inventory practices of a taxpayer clearly reflect income. Respondent argues that there are certain technical flaws in the retailers' shrinkage accrual practices. We assume that respondent wishes us to conclude that those flaws make the practices inconsistent and, thus, inaccurate. Respondent cites the failure of the Michigan KMA to accrue shrinkage for the grocery or drug/general merchandise departments for the period 1984 through 1987 despite the general corporate policy of *57 shrinkage accrual. Respondent also cites the fact that one KMA did not follow the standard procedure that, when a store was transferred from one KMA to another, it was to use a combination of the two KMAs' shrinkage accrual rates during the year of transfer. One KMA permitted the stores transferred to its area to continue to use the prior KMA's shrinkage rate during the year of the transfer. We have considered those and other incidents cited by respondent, and we cannot conclude that the retailers' inventory practices were applied inconsistently from year to year. Each of the retailers adopted accounting practices that were to be applied uniformly and consistently. The scope of the retailers' operations was enormous. The KFS division alone operated between 1,000 and 1,500 supermarkets, with annual sales in excess of $ 11 billion. Given the scope of the retailers' operations, and the minor flaws cited by respondent, we believe that there was consistency of application in inventory practices from year to year, and we so find. K. Did Respondent Abuse Her Discretion in Determining That the Retailers' Shrinkage Method Does Not Clearly Reflect Income and That Respondent's Method Does *58 Clearly Reflect Income? We have found that the retailers' shrinkage method was applied consistently from year to year. We have also found that, assuming either a sales-based or time-based allocation of losses from shrinkage factors, the retailers' shrinkage method is more accurate than respondent's method. We consider whether respondent abused her discretion in determining that the retailers' shrinkage method does not clearly reflect income in light of section 1.471-2(d), Income Tax Regs., which allows for book inventories whose balances are verified by physical inventories conducted at reasonable intervals. Respondent has not challenged the intervals at which the retailers verified their book inventories by physical count. Indeed, during each of the years in question, the KFS division and Florida Choice conducted an average of 2 or more physical inventories a store, and Superx conducted an average of 1.5 or more physical inventories a store. The retailers used cycle counting to take physical inventories. Throughout the year, cycles ended and physical inventories were taken. On average, the physical-to-yearend period was no more than 3 months for both the KFS division and Florida*59 Choice. For Superx, the average length of the physical-to-yearend period was 4 months. Of course, since estimates were involved, there were bound to be errors in the shrinkage accruals for those physical-to-yearend periods. Those errors, however, were subject to correction within the next taxable year and would, on average, involve no more than 3 or 4 months of possible overestimates. The limited potential for deferral is significant to us in deciding whether income was clearly reflected. 2 *60 Respondent abused her discretion in determining that the retailers' shrinkage method does not clearly reflect income and that her method does clearly reflect income. Taxable income must be reflected with as much accuracy as standard methods of accounting practice permit. Caldwell v. Commissioner, 202 F.2d at 115. Because the retailers did not generally take physical inventories at year's end, no accounting method can state with certainty either yearend shrinkage or the year's taxable income. In order to determine the accuracy of the retailers' shrinkage method, we must, therefore, hypothesize the taxable income for each of the years in question. 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. The assumption underlying Dr. Bates' time-based accuracy analysis, on the other hand, is independent of any correlation between sales and shrinkage. Indeed, it is independent of *61 the correlation between shrinkage and any particular factor. Moreover, respondent has not argued that shrinkage is a function of any particular factor. Thus, the hypothesis that taxable income reflects a ratable allocation within cross-year inventory cycles of shrinkage determined for those cycles provides a neutral guideline to judge not only the accuracy of the retailers' shrinkage method but also the relative accuracy of that method compared to respondent's method. Based on Dr. Bates' time-based comparison of the retailers' shrinkage method with respondent's method, utilizing KFS division, Florida Choice, and Superx data for various years between 1983 and 1991, see sec. VI.D.4., supra, we are convinced that respondent's method of estimating losses from shrinkage factors is less accurate than the retailers' shrinkage method and is subject to a greater range of error. Respondent abused her discretion because petitioner has convinced us that the retailers' shrinkage method was more accurate in reflecting taxable income than was respondent's method. If, indeed, shrinkage is a function of sales, our conclusion would not change, because, on that basis also, the retailers' shrinkage*62 method is more accurate than respondent's method. In sum, we conclude that respondent abused her discretion in determining that the retailers' shrinkage method does not clearly reflect income because the retailers' shrinkage method more clearly reflects income when compared to respondent's method based on an allocation of cross-year inventory shrinkage losses as a function of time. In addition, the frequency of the retailers' physical inventories and the uniform and consistent application of the retailers' shrinkage method insured correction of overestimates on a regular basis and promoted the clear reflection of income. VII. Conclusion The retailers' systems of maintaining book inventories (including the making of shrinkage accruals) conform to the best accounting practice and clearly reflect income. They are, thus, sound within the meaning of section 1.471-2(d), Income Tax Regs. To reflect the foregoing, and to give effect to agreements reached by the parties, Decision will be entered under Rule 155. Appendix 3 *63 Sales-Based Accuracy Analysis for the KFS Division KFS DIVISION - RETAILERS' METHOD Sales- Allocated Difference Annual As Shrinkage Percent Minus Of Sales- Actual Annual Allocated Actual KFS KFS Annual Sales- Annual Annual Tax Tax Allocated Year Shrinkage Shrinkage Shrinkage Shrinkage [1984] $ 16,730,176 $ 16,152,686 $ 577,491 3.5% [1985] 12,480,853 13,803,649 -1,322,796 -10.6% [1986] 18,828,725 16,674,582 2,154,143 11.4% [1987] 14,965,650 15,920,349 -954,699 -6.4% [1988] 11,573,159 10,415,192 1,157,967 10.0% [1989] 18,949,137 17,067,966 1,881,170 9.9% [1990] 23,781,623 24,735,994 -954,371 -4.0% [1991] 28,082,463 28,014,682 67,781 0.2% 1984- 145,391,786 142,785,100 2,606,686 1.8% [1991] KFS DIVISION - RESPONDENT'S METHOD Sales- Allocated Difference Annual As Shrinkage Percent Minus Of Sales- Shrinkage Annual Allocated Based on Sales- Annual IRS IRS Allocated Year Shrinkage Method Method Shrinkage [1984] $ 16,730,176 $ 16,719,232 $ 10,944 0.1% [1985] 12,480,853 13,166,875 -686,022 -5.5% [1986] 18,828,725 16,541,601 2,287,124 12.1% [1987] 14,965,650 15,066,016 -100,366 -0.7% [1988] 11,573,159 9,763,096 1,810,063 15.6% [1989] 18,949,137 16,497,880 2,451,257 12.9% [1990] 23,781,623 24,409,148 -627,526 -2.6% [1991] 28,082,463 26,868,966 1,213,498 4.3% 1984- 145,391,786 139,032,814 6,358,972 4.4% [1991] Time-Based Accuracy Analysis for the KFS Division KFS DIVISION - RETAILERS' METHOD Time- allocated Difference Annual As Shrinkage Percent Minus Of Time- Actual Annual Allocated Actual KFS KFS Annual Time- Annual Annual Tax Tax Allocated Year Shrinkage Shrinkage Shrinkage Shrinkage [1984] $ 16,804,512 $ 16,152,686 $ 651,826 3.9% [1985] 12,417,480 13,803,649 -1,386,170 -11.2% [1986] 18,667,248 16,674,582 1,992,666 10.7% [1987] 15,153,369 15,920,349 -766,980 -5.1% [1988] 11,585,858 10,415,192 1,170,666 10.1% [1989] 18,930,812 17,067,966 1,862,846 9.8% [1990] 23,843,933 24,735,994 -892,061 -3.7% [1991] 27,847,797 28,014,682 -166,885 -0.6% 1984- 145,251,008 142,785,100 2,465,908 1.7% [1991] KFS DIVISION - RESPONDENT'S METHOD Time- Allocated Difference Annual As Shrinkage Percent Minus Of Time- Shrinkage Annual Allocated Based on Time- Annual IRS IRS Allocated Year Shrinkage Method Method Shrinkage [1984] $ 16,804,512 $ 16,719,232 $ 85,280 0.5% [1985] 12,417,480 13,166,875 -749,396 -6.0% [1986] 18,667,248 16,541,601 2,125,647 11.4% [1987] 15,153,369 15,066,016 87,353 0.6% [1988] 11,585,858 9,763,096 1,822,762 15.7% [1989] 18,930,812 16,497,880 2,432,932 12.9% [1990] 23,843,933 24,409,148 -565,215 -2.4% [1991] 27,847,797 26,868,966 978,831 3.5% 1984- 145,251,008 139,032,814 6,218,194 4.3% [1991] Sales-Based Accuracy Analysis for Florida Choice FLORIDA CHOICE - RETAILERS' METHOD Sales- Allocated Difference Annual As Shrinkage Percent Actual Minus Actual Of Sales- Florida Florida Annual Allocated Choice Florida Sales- Annual Annual Tax Annual Allocated Year Shrinkage Shrinkage Shrinkage Shrinkage [1984] $ 1,285,541 $ 1,189,507 $ 96,034 7.5% [1985] 1,465,206 1,575,637 -110,430 -7.5% [1986] 1,283,771 1,441,437 -157,666 -12.3% [1987] 3,191,210 2,843,037 348,172 10.9% [1988] 3,150,351 2,923,998 226,353 7.2% 1984- 10,376,079 9,973,616 402,463 3.9% [1988] FLORIDA CHOICE - RESPONDENT'S METHOD Sales- Allocated Difference Annual As Shrinkage Percent Minus Of Sales- Shrinkage Annual Allocated KFS Based on Sales- Annual IRS IRS Allocated Year Shrinkage Method Method Shrinkage [1984] $ 1,285,541 $ 1,025,390 $ 260,151 20.2% [1985] 1,465,206 1,360,463 104,744 7.1% [1986] 1,283,771 1,382,411 -98,640 -7.7% [1987] 3,191,210 2,572,824 618,386 19.4% [1988] 3,150,351 3,400,035 -249,684 -7.9% 1984- 10,376,079 9,741,123 634,956 6.1% [1988] Time-Based Accuracy Analysis for Florida Choice FLORIDA CHOICE - RETAILERS' METHOD Time- Allocated Difference Annual As Shrinkage Percent Actual Minus Actual Of Time- Florida Florida Annual Allocated Choice Choice Time- Annual Annual Tax Annual Allocated Year Shrinkage Shrinkage Shrinkage Shrinkage [1984] $ 1,289,498 $ 1,189,507 $ 99,991 7.8% [1985] 1,471,431 1,575,637 -104,206 -7.1% [1986] 1,264,544 1,441,437 -176,893 -14.0% [1987] 3,171,919 2,843,037 328,881 10.4% [1988] 3,076,645 2,923,998 152,647 5.0% 1984- 10,274,037 9,973,616 300,420 2.9% [1988] FLORIDA CHOICE - RESPONDENT'S METHOD Time- Allocated Difference Annual As Shrinkage Percent Minus Of Time- Shrinkage Annual Allocated Based on Time- Annual IRS IRS Allocated Year Shrinkage Method Method Shrinkage [1984] $ 1,289,498 $ 1,025,390 $ 264,108 20.5% [1985] 1,471,431 1,360,463 110,968 7.5% [1986] 1,264,544 1,382,411 -117,867 -9.3% [1987] 3,171,919 2,572,824 599,095 18.9% [1988] 3,076,645 3,400,035 -323,390 -10.5% 1984- 10,274,037 9,741,123 532,914 5.2% [1988] Sales-Based Accuracy Analysis for Superx SUPERX DIVISION - RETAILERS' METHOD Sales- Difference Allocated As Annual Percent Shrinkage Of Sales- Actual Minus Actual Annual Allocated Superx Superx Sales- Annual Annual Tax Annual Tax Allocated Year Shrinkage Shrinkage Shrinkage Shrinkage [1983] $ 15,786,221 $ 14,822,148 $ 964,073 6.1% [1984] 19,940,756 19,004,471 936,285 4.7% [1985] 23,163,483 22,272,344 891,139 3.8% 1983- 58,890,459 56,098,963 2,791,497 4.7% [1985] SUPERX DIVISION - RESPONDENT'S METHOD Sales- Allocated Difference Annual As Shrinkage Percent Minus Of Sales- Shrinkage Annual Allocated Superx Superx Time- Annual Annual Tax Annual Tax Allocated Year Shrinkage Method Method Shrinkage [1983] $ 15,786,221 $ 14,498,732 $ 1,287,489 8.2% [1984] 19,940,756 18,062,925 1,877,831 9.4% [1985] 23,163,483 22,155,386 1,008,097 4.4% 1983- 58,890,459 54,717,043 4,173,416 7.1% [1985] Time-Based Accuracy Analysis for Superx SUPERX DIVISION - RETAILERS' METHOD Time - Difference Allocated As Annual Percent Shrinkage Of Time- Actual Minus Actual Annual Allocated Superx Superx Time - Annual Annual Tax Annual Tax Allocated Year Shrinkage Shrinkage Shrinkage Shrinkage [1983] $ 15,665,951 $ 14,822,148 $ 843,803 5.4% [1984] 20,020,109 19,004,471 1,015,638 5.1% [1985] 23,050,060 22,272,344 777,716 3.4% 1983- 58,736,119 56,098,963 2,637,157 4.5% [1985] SUPERX DIVISION - RESPONDENT'S METHOD Time- Allocated Difference Annual As Shrinkage Percent Minus Of Time- Shrinkage Annual Allocated Based on Time- Annual IRS IRS Allocated Year Shrinkage Method Method Shrinkage [1983] $ 15,665,951 $ 14,498,732 $ 1,167,219 7.5% [1984] 20,020,109 18,062,925 1,957,184 9.8% [1985] 23,050,060 22,155,386 894,674 3.9% 1983- 58,736,119 54,717,043 4,019,076 6.8% [1985] *64 Footnotes 1. 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↩. 2. Shrinkage accruals are no more than estimates, and because there are tax incentives for maximizing shrinkage accruals, the potential for tax avoidance exists. That is so notwithstanding that minimization of shrinkage factors was a management goal for each of the retailers. Essentially, the determination of shrinkage accrual rates by the management of each KMA (the analysis is the same for Florida Choice and Superx) is not dependent entirely on shrinkage factors, which individual store and department managers have an incentive to minimize. The potential for tax avoidance is one of respondent's objections to shrinkage accruals. On the record before us, however, we are unconvinced that there was a significant potential for tax avoidance or that, indeed, there was any tax avoidance. Any potential overestimates were subject to correction within the following taxable year and would, on average, involve no more than 3 or 4 months of excess shrinkage accruals. We see no pattern of overaccruals for tax avoidance purposes.↩ 3. These tables contain a few immaterial computational errors.↩