Court Opinion

ID: 4596724
Source: CourtListenerOpinion
Date Created: 2020-11-20 19:17:41.134158+00
Date Added: 2024-06-11T07:51:39.892230
License: Public Domain

JOSTENS, INC., Petitioner v. COMMISSIONER OF INTERNAL REVENUE, RespondentJostens, Inc. v. CommissionerDocket No. 47611-86United States Tax CourtT.C. Memo 1989-656; 1989 Tax Ct. Memo LEXIS 643; 58 T.C.M. (CCH) 933; T.C.M. (RIA) 89656; December 13, 1989Sue Ann Nelson, for the petitioner. Genelle F. Forsberg, for the respondent.  WILLIAMSMEMORANDUM FINDINGS OF FACT AND OPINION WILLIAMS, Judge: The Commissioner determined deficiencies in petitioner's Federal income tax as follows: Taxable yearending:DeficiencyJune 30, 1980$ 181,403June 30, 1981474,729June 30, 1982132,640Petitioner has claimed overpayments for each of the years. After concessions, the issues remaining are: (1) whether respondent abused the discretion he exercised pursuant to section 471 1 by disallowing petitioner's write-down of inventory that petitioner considered "obsolete"; (2) whether respondent abused his discretion by disallowing part of petitioner's deduction for an addition to its bad debt reserve pursuant to section 166(c); (3) whether respondent correctly used the residual method to value intangible assets petitioner acquired from two corporations; and (4) whether petitioner may deduct prepaid royalty expenses.  *646  FINDINGS OF FACT Some of the facts have been stipulated and are so found.  Petitioner is a corporation with its principal place of business in Minneapolis, Minnesota at the time the petition was filed.  Petitioner's taxable year ends June 30, and petitioner prepares and files its Federal income tax returns using an accrual method of accounting. Petitioner manufactures high school and college class rings, yearbooks, graduation caps and gowns, and other related products.  Petitioner carries out its business activities through its three divisions: the Scholastic Division, which sells class rings, announcements, diplomas, and caps and gowns to high schools and colleges; the Recognition Division, which sells service and sales awards to Fortune 1,000 companies; and the Printing and Publishing Division (also known as the American Yearbook Company), which produces yearbooks for high schools and colleges. Stone Inventory IssueMany of petitioner's high school and college class rings contain synthetic stones. The stones are custom made to petitioner's exacting specifications by a West German manufacturer.  Petitioner offers a wide variety of styles, cuts, sizes, and colors*647  of stones for its class rings. Petitioner provides new stone selections every year in response to continually changing customer tastes and style preferences.  During the taxable years 1980 through 1982, petitioner introduced approximately 1,000 new stone styles, mostly synthetic. Petitioner offers a liberal lifetime warranty on its rings, including the stones. The warranty provides that petitioner will replace a defective or broken stone without charge except for stones broken as a result of obvious customer abuse.  Petitioner generally replaces the stones free of charge pursuant to the warranty. In a case of customer abuse, petitioner charges approximately $ 10 to replace the stone and bezel, and at least $ 20 to replace the ring. Petitioner has consistently used the lower of cost or market method for valuing its stone inventory for both financial accounting and income tax purposes.  Petitioner adjusts its stone inventory annually to reflect adjustments for what petitioner considers to be "obsolete" or "inactive" stones. The FIFO cost per stone was $ 3.23, $ 3.39, and $ 2.81 for taxable year 1980, 1981, and 1982, respectively. Petitioner kept the stones in stone cribs, sorted*648  by style or category.  Each year, petitioner counted the number of stones that had been used in each category and multiplied the result by three to project 3 years of usage. Petitioner identified as "inactive" the number of stones in each category that exceeded the projected 3 years' usage. Petitioner has developed a computer program which calculates the number of "inactive" stones for each taxable year. Petitioner counted the number of inactive stones in its outlying plants, rather than using the 3 years' usage method to identify "inactive" stones. The total stones identified as inactive in taxable years 1980, 1981, and 1982 from the computer report was 299,422, 301,415, and 303,001, respectively.  To these numbers, petitioner added the manually counted "inactive" stones from outlying plants in the amounts of 10,976 in taxable year 1980, 16,436 in taxable year 1981, and 18,127 in taxable year 1982.  Petitioner then adjusted the stone inventory to exclude from the category of inactive stones newly introduced stones and others that were not inactive. Although petitioner has no formal policy for the "manual" adjustments, it entrusted the determination to the judgment and discretion of*649  its personnel responsible for ordering stones. Petitioner reviews its computer analysis of the stone inventory and adjusts the computations to reflect exclusions and inclusions of various stones. The year-end stone inventory valuation included the total number of stones in the physical inventory less the number of "inactive" stones. In effect, the "inactive" stones were written down to zero in each taxable year. Petitioner determined for 1980, 1981, and 1982, quantities of inactive stones of 246,243, 277,560, and 286,711, respectively, and wrote them down to zero. Under petitioner's method, each stone style could have two classifications for inventory purposes with some stones valued at cost and some valued at zero.  The stones in each stone style, however, were identical and retained in inventory without segregation.  In addition, a stone style that petitioner had decided had inactive stones one year may not have had inactive stones in a subsequent year. 2 A stone style also could have inactive stones in one year, no inactive stones the following year, and inactive stones again the next year. 3*650 Petitioner's method can also result in a stone style with "obsolete" stones regardless of how many stones petitioner uses in that category during the year.  Moreover, having labelled a style as "obsolete," petitioner would nevertheless order additional stones of that style if the level of usage justified additional orders.  Despite some stones being labeled "inactive," petitioner continued to sell stones of that style and to use such stones for repairs and warranty. The only evidence in the record of the number of stones petitioner used in its warranty work is petitioner's partial analysis of 1981 stone usage. This report includes the number of stones used for sales, repair, and warranty in 1981 for each of the 135 stone styles that had more than 200 "inactive" stones. The total inventory of stones in these 135 styles was 48,421.  Of this amount, 46,960 stones were designated "obsolete." Petitioner used a total of 487 stones in these styles in 1981: 218 in sales, 31 in repairs, and 238 in warranty work.  Petitioner used from one to nine stones from each stone style. Petitioner offered 98 of the 135 stone styles described in the report for sale in its price book in 1981.  During*651  1981, the stones in any of the 135 styles that were still valued in inventory were more than sufficient to supply petitioner's business needs for those stone styles. Each stone style having had some stones categorized as "obsolete" is categorized in the chart below by "usage category," i.e., organized by how many stones petitioner used during the year of that style. For 1980 and 1982, the stones used may or may not have been classified as "inactive." For example, during 1980 the number of stones that petitioner used from stone styles having some stones designated "obsolete," from which petitioner actually used between 10 and 14 stones, was 2,068.  Also, in 1980 petitioner used 1,708 stones of those stone styles having "inactive" stones from which petitioner used at least 76 stones but no more than 100 stones. Number of Stones UsedUsageCategory6/30/806/30/816/30/8200001 to 39739109164 to 56426256176 to 91,1441,4091,44610 to 142,0681,9502,07715 to 201,9172,4052,71521 to 303,2463,3243,98431 to 403,2022,6022,75041 to 502,1752,0641,76951 to 753,4503,6032,93176 to 1001,7081,4911,579101 to 1501,5531,7741,063151 to 2001,016306349201 to 2502172150251 to 30002650301 to 350000351 to 400000401 to 45045000451 Plus000Total23,76122,94322,196Total AnnualUsage1,321,3301,349,7141,397,454(Stone Crib)*652 Petitioner's inventory records of obsolete stones show the number of "inactive" stones in each stone style on hand by the volume of usage in each style and are summarized in the following chart: STONE INVENTORY ANALYSIS6/30/806/30/816/30/82Total Stones - June 301,163,956 1,133,794 1,072,464 Physical Inventory"Obsolete" Stones(246,243)(277,560)(286,711)Stones Valued in Year-End Inventory917,713 856,234 785,753 Recap of "Obsolete"Stones by UsageCategories: Usage Category6/30/806/30/816/30/820         76,159 92,432 92,973 1 to 3    52,875 57,322 61,532 4 to 5    14,933 15,825 17,828 6 to 9    21,479 25,982 25,749 10 to 14  21,418 20,153 15,602 15 to 20  11,319 17,358 15,784 21 to 30  13,224 10,370 15,813 31 to 40  7,947 7,286 9,089 41 to 50  4,088 4,236 3,477 51 to 75  6,570 6,929 7,018 76 to 100 2,413 1,484 1,777 101 to 1502,672 2,531 1,915 151 to 200867 167 71 201 to 25036 207 0 251 to 3000 32 0 301 to 3500 0 0 351 to 4000 0 0 401 to 450115 0 0 451 Plus0 0 0 Total in Stone Crib236,115 262,314 268,628 "Obsolete" Stones atOutlying Plants10,976 16,436 18,127 Unlocated Difference(848)(1,189)(44)All "Obsolete" Stones246,243 277,561 286,711 *653  For example, in 1980, 76,159 "inactive" stones were in stone styles without any usage by petitioner and 36 "inactive" stones were in stone styles from which petitioner used between 201 and 250 stones. Respondent previously examined petitioner's method of adjusting the stone inventory during an audit of petitioner's 1976, 1977, and 1978 taxable years.  The revenue agent disallowed petitioner's write-down of the stone inventory for those years.  The parties then settled these years administratively at the appellate level.  In the settlement, respondent agreed to allow petitioner to deduct two-thirds of the obsolete stones even though he did not agree with petitioner's method.  Petitioner claimed an adjustment to its stone inventory on its income tax return for the taxable year 1982 consistent with the parties' settlement resolution of the stone inventory issue for the taxable years 1976, 1977, and 1978.Bad Debt Reserve IssueSometime in the mid-1970's, petitioner began assessing finance charges on customers' past due accounts receivable. The customer's purchase agreement, invoice, and monthly statement specified the due date for payment and that a monthly service charge*654  of 1.5 percent or the maximum allowed by local law would be assessed for late payment.  Finance charges, when assessed, were detailed on the statements sent to customers. Petitioner debited the assessed finance charges to accounts receivable and credited them to a finance charge income account.  The parties agree that the finance charges were legally enforceable obligations. The managers within each of petitioner's divisions had some authority to cancel the finance charges.  The division credit managers of Scholastic, Recognition, and American Yearbook Company ("AYC") had authority to cancel finance charges of up to $ 200, $ 1000, and $ 500, respectively.  Greater finance charges or charges over a certain number of days old were to be referred to the division controller. Petitioner's AYC Division seldom turned any school accounts over for collection because it believed it was not a good business practice, and it relied on repeat business.  AYC never turned a public school account over for collection.  Generally, when a customer paid the principal amount of the bill, AYC canceled the finance charges.  When finance charges were canceled, the amount of the canceled finance charge*655  was credited to accounts receivable and debited to finance charge income. The finance charges billed and the finance charges canceled for the taxable years 1976 through 1982 are as follows: Net FinanceChargeIncomeRatio:on AccrualCanceledFiscal YearBilledCanceled 4Basisto Billed1976Jostens *$  42,771$  26,791$  15,98063%AYC0001977Jostens *105,36062,77742,58360%AYC166,155128,31437,84177%1978Jostens *132,86194,11738,74471%AYC206,707171,31535,39283%1979Jostens *148,358118,77029,58880%AYC269,200203,89865,30276%1980Jostens *231,880184,90646,97480%AYC337,209323,07714,13296%1981Jostens *365,087283,92981,15878%AYC480,042360,150119,89275%1982Jostens *403,926374,18329,74393%AYC810,028577,184232,84471%Prior to and during the years in dispute, petitioner used the reserve method of accounting for bad debts for book and tax purposes. *656  In all relevant years, petitioner annually computed a bad debt reserve for Jostens which included its Scholastic and Recognition divisions and a separate bad debt reserve for the AYC division.  Petitioner's tax returns for taxable years 1976 through 1980, as originally filed, conformed to its books with respect to bad debt reserves and treatment of canceled finance charges. Respondent audited petitioner's returns for the taxable years 1976, 1977, and 1978, and adjusted its bad debt reserves and related bad debt deductions.  Petitioner agreed to the adjustments in December 1980.  With respect to the adjustments: a.  The Black Motor formula 5 was used in determining the reasonableness of the year-end bad debt reserves for each year under audit.  b.  In determining the outstanding receivables in the Black Motor calculation for the taxable years 1976, 1977, and 1978, receivables*657  arising both from credit sales and from finance charges assessed against customers with past-due accounts were included. c.  In determining the average of the debts actually charged off in the Black Motor calculation for the taxable years 1976, 1977, and 1978, the calculation included chargeoffs attributable to both receivables arising from credit sales and canceled finance charges. d.  The adjustments decreased petitioner's bad debt expense by $ 132,592 in taxable year 1976 and increased petitioner's bad debt expense by $ 22,400 in taxable year 1977 and $ 50,821 in taxable year 1978. Beginning with its return for taxable year 1981, petitioner reflected on Schedule M-1 deductions for additions to its reserve for bad debts for income tax purposes which were not deducted for book purposes.  Also, beginning with its taxable year 1981 return, petitioner based the additions to the bad debt reserve on a calculation of the Black Motor formula which included finance charges receivable in the ending receivable balances and canceled finance charges in the charge-offs. For taxable year 1980, petitioner claims additional bad debt expense deductions for Jostens and AYC totaling $ 61,487, *658  which were not deducted on its return.  Petitioner claims the increased deductions based on the Black Motor formula calculation described above. Respondent determined the reasonableness of petitioner's additions to the bad debt reserve for taxable years 1980, 1981, and 1982 by applying the Black Motor formula: the 6-year average of bad debt charge-offs, divided by the 6-year average of year-end accounts receivable, multiplied by the year-end balance of accounts receivable. Respondent included finance charges receivable in year-end accounts receivable but did not include canceled finance charges in bad debt charge-off figures. The following is a comparison of the difference between the bad debt reserve computed using the Black Motor formula with and without canceled finance charges in the numerator, with the amount of finance charge receivables included in total accounts receivable, as of June 30, 1982.  Petitioner is unable to identify the amount of finance charge receivables included in total accounts receivable prior to taxable year 1982. RESERVE UNDERBLACK MOTOR FORMULAINCLUDINGEXCLUDINGFINANCE CHARGESCANCELEDCANCELEDINCLUDED INFINANCEFINANCEYEAR-ENDCHARGESCHARGESRECEIVABLESJostens$ 381,202$ 123,181$ 176,118AYC545,742116,391471,709Total$ 926,944$ 239,572$ 647,827*659 Acquisition Issues1.  Durand On January 31, 1981, Joran, Inc. ("Joran"), a wholly owned subsidiary of petitioner, entered into a Purchase Agreement to acquire the assets of Durand Corporation ("Durand").  Durand manufactured and sold custom and stock loose-leaf ring binders with slant "D" rings. Joran agreed to pay $ 6,642,715 in cash and assume liabilities of $ 2,361,409 for a total purchase price of $ 9,004,124.  The transaction was between unrelated parties and resulted from bona fide arm's-length negotiations. The transaction resulting in Joran's acquisition of the Durand assets began in early 1979 as a discussion for the acquisition of the stock of Weldo Plastics, Ltd., a corporation formed under the laws of Canada ("Weldo Canada"), which in turn owned 75 percent of Weldo Plastics, Inc., a corporation formed under the laws of the state of New York ("Weldo").  Weldo owned 100 percent of the Durand stock (references to Weldo Canada, Weldo, and Durand collectively will be to the "Weldo Group").  The remaining 25 percent of the Weldo stock was owned by Loren Hulber, president of Durand.  Lewis Cohen was the president of Weldo Canada. In 1974, petitioner entered into*660  a Finder's Contract with Arthur H. Richland Co. ("Richland").  Between May of 1979 and January of 1981, petitioner negotiated first to purchase the stock of the Weldo Group, then to purchase the stock of Durand, and finally to purchase the assets of Durand.  The proposed purchase price over the negotiation period ranged from 7.5 times earnings to 8 or 9 times earnings. In June of 1980, during negotiations, petitioner's senior vice president wrote Richland that the Weldo Group would have to decide whether to sell Durand and set a price, and that any other approach would likely be a waste of effort. By letter dated January 9, 1981, petitioner agreed to purchase all of the assets and going business of Durand for (1) $ 6,022,000 cash, (2) an amount equal to any recapture taxes, and (3) an agreement to assume Durand's liabilities.  As a condition of the sale, Durand had to have, plus or minus 10 percent, net sales of $ 13 million, pretax earnings of $ 1.6 million, and a net worth of $ 3 million for the taxable year ended January 31, 1981. Petitioner purchased the assets and business of Durand as a going concern, including all of Durand's trade names, customer lists, designs, trademarks, *661  copyrights, trade secrets, patents, proprietary data, confidential information, and technical know-how and information.  Petitioner agreed to pay $ 6,642,715 in cash and to assume $ 2,361,409 in liabilities.  Pursuant to the purchase agreement, petitioner also acquired the exclusive right to purchase slant D-ring binder fittings from Weldo's supplier.  In addition, petitioner had the unilateral option to renew the purchase agreement for the binder fittings for subsequent years if it met minimum purchase requirements.  The parties agreed that in the event Weldo and Cohen received a patent for the binder mechanisms, they would grant petitioner an exclusive license to the patent for use within the United States as long as petitioner's agreement with Weldo's supplier was in effect.  The Weldo Group also executed a 7-year covenant not to compete with petitioner with regard to any products Durand sold. Before closing the transaction, petitioner conducted a due diligence investigation.  As part of the due diligence investigation, petitioner's assistant corporate controller reviewed Durand's operations for the taxable year ended January 31, 1981, in an internal memorandum dated February 24, 1981. *662  He found that Durand had sales of $ 13,137,000, pretax income of $ 1,741,000, net income of $ 917,000, and a return on investment of 38.9 percent.  He also estimated goodwill on the purchase as $ 1,633,000 using the residual method. This figure was again used internally in a preliminary report on the allocation of purchase price dated April 30, 1981.  Also, in the due diligence investigation, petitioner found that Durand's average annual growth in sales was 37 percent and estimated sales for taxable year 1982 at $ 16,000,000. Petitioner reported that although Durand did not have any long-range plans, Durand generally expected a 25 percent annual growth rate long-term.  Petitioner found that Durand's products were broadly distributed with 7,000 to 8,000 customers for its Weldo line and about 5,000 dealers for its Cardinal line.  No single customer represented over five percent of sales.  Petitioner found that customer relations, program selling, and service were key factors in Durand's business.  For Durand's Weldo line, about 50 percent of customers buying for the first time bought again the following year. Petitioner also found that Durand's programs and marketing strategies were*663  in good shape in taxable year 1981.  Petitioner believed that the key to Durand's future growth was expanding distribution using existing marketing programs, developing the college bookstore business, and adding retail outlets.  Petitioner believed it could use its position in college bookstores with Jostens class rings sales to market the binders. Durand's net sales, net income, and earnings per share for taxable years 1978 through 1981 were as follows: EarningsFiscal YearNet SalesNet Incomeper share1978 (19 mos.)$ 6,550,502$ 402,568 $ .8419797,053,249 497,920 1.04198010,355,969 664,139 1.40198113,136,891 927,149 1.93In June of 1981, petitioner valued Durand's intangible assets, goodwill, and going concern value at $ 682,000.  Petitioner thus determined that it paid a premium for the Durand assets equal to the excess of the purchase price over the value of the assets, $ 918,379.  Petitioner allocated the "premium" to all the acquired assets, tangible and intangible, on a pro rata basis. The parties agree that the fair market value of the tangible assets petitioner acquired from Durand was $ 7,403,745. *664  2.  MECA On August 15, 1980, J-Sportswear, Inc., a wholly owned subsidiary of petitioner, entered into a Purchase Agreement to acquire the assets of MECA Sportswear, Inc. ("MECA").  MECA manufactured and distributed sportswear, emblems, letters, and other insignia.  Pursuant to the Purchase Agreement, petitioner paid $ 1,490,348 in cash and assumed liabilities of $ 786,123 for a total purchase price of $ 2,276,471.  The transaction was between unrelated parties and resulted from bona fide arm's-length negotiations. Petitioner acquired all of the intangibles associated with MECA's business, including trade names, trademarks, copyrights, customer lists, contracts with customers and suppliers (other than some specified contracts), MECA's corporate name and the names of any subsidiaries, and any license agreements.  MECA executed a 5-year covenant not to compete with petitioner in the business of manufacturing, selling, or distributing sportswear, jackets, athletic letters, or other emblems. As a condition of the purchase, petitioner required that MECA's net income after taxes for taxable year ended June 30, 1980, be at least $ 170,000.  MECA's audited financial statements for*665  taxable year ended June 30, 1980, showed net income after tax of $ 179,727. Petitioner believed it could use its marketing and sales forces to expand MECA product sales from a regional market into the national market.  Petitioner valued MECA's goodwill at $ 87,000 using the "excess income" method of valuing intangibles with no independent appraisal.  It allocated the excess of the purchase price over the value of the assets to all assets on a pro rata basis. The parties agree that the fair market value of the acquired tangible assets was $ 1,868,258. Royalty Expense IssuePetitioner, through its wholly owned subsidiary, Artex Manufacturing Co., Inc., signed a royalty agreement ("1981 Agreement") with Volume Trading Corporation ("VTC") on March 1, 1981.  The agreement granted Artex the exclusive right to use the trade names, trademarks, service marks, and copyrights of the National Football League Players Association ("NFLPA") in the manufacture, distribution, and sale of certain sportswear in the United States.  VTC retained joint responsibility for sales of the licensed products, and authorized Artex to use its comprehensive sales promotion and support program.  VTC*666  reserved the right to authorize others to manufacture the same sportswear and to approve of the licensed products that Artex marketed. Artex agreed to pay VTC $ 75,000, $ 25,000 each in March, April, and May of 1981.  Artex also agreed to pay VTC commissions based on specified percentages of sales.  The $ 75,000 was nonrefundable but was creditable against the commissions due to VTC.  The initial term of the agreement was thirteen months, from March 1, 1981, through April 1, 1982.  The agreement provided Artex an option to renew if it paid VTC at least $ 100,000 in commissions, including the $ 75,000 initial payments.  The agreement contained a second option to renew for the following year if Artex paid VTC at least $ 200,000 in commissions in the first option year, and a third option for the succeeding year if Artex paid VTC at least $ 250,000 in commissions in the second option year.  The agreement also provided for good faith negotiation for an additional renewal period after the third option year. During the first year of the agreement, Artex' commissions to VTC based on sales were not great enough for renewal.  Artex and VTC amended the original agreement on March 16, 1982, however, *667  and extended it from April 1, 1982, through March 31, 1983.  Artex agreed to pay VTC the remaining $ 25,000 of the minimum renewal commissions for the first year on March 31, 1982, which would be offset by commissions due to VTC.  The amended agreement carried forward the portion of the prepaid royalty that petitioner had not recovered in the first year of the agreement. Petitioner debited the $ 100,000 royalty prepayment to a prepaid balance sheet account.  Petitioner was to eventually expense the payment as VTC earned the royalty. Sales during the taxable years 1981 and 1982 generated royalties to VTC in the respective amounts of $ 1,600 and $ 42,200.  Petitioner expensed these amounts in the respective years and reduced the prepaid royalty account accordingly.  In addition to the amounts expensed for generated royalties referred to above, petitioner expensed an additional $ 25,000 of the prepaid royalty account balance as of June 30, 1982.  This amount is the amount here in dispute.  On January 28, 1983, the parties extended the Agreement to March 31, 1984. 6*668  Total royalties VTC earned from March 1, 1981, through March 31, 1985, were as follows: Fiscal YearRoyalties Earned1981$  1,600198242,20019839,500198490019852,300$ 56,500Petitioner carried forward the prepaid royalty account each year.  Petitioner did not pay any commissions to VTC over the 5 years because commissions based on sales were less than $ 100,000 over the 5-year period.  Petitioner expensed the remaining balance in the prepaid royalty account of $ 18,500 ($ 100,000 less $ 56,500 total royalties earned less $ 25,000 written off in taxable year 1982) in taxable year 1985, after the Agreement terminated in March 1985. OPINION Stone InventoryThe first issue we must decide is whether respondent abused his discretion by disallowing petitioner's write-down of "obsolete" stone inventory pursuant to section 471.  Petitioner valued the stones in inventory using the "lower of cost or market" method.  Petitioner wrote down to zero the number of stones in any stone style that exceeded three times the current year's usage. Sections 446 and 471 govern inventory accounting.  Section 446(a) provides generally*669  that a taxpayer must compute taxable income under the method of accounting the taxpayer regularly uses to compute its income on the books.  "Method of accounting" includes the treatment of any material item such as inventory. Sec. 1.446-1(a)(1), Income Tax Regs. Section 446(b) provides that if the method the taxpayer uses "does not clearly reflect income, the computation of taxable income shall be made under such method as, in the opinion of the [Commissioner], does clearly reflect income." Each inventory method must also conform to the general rule for inventories in section 471: 7 (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 taxpayer's income.  Sec. 471; sec. 1.471-2(a), Income Tax Regs.*670 The "lower of cost or market" method of valuing an inventory meets the requirements of section 471.  Sec. 1.471-2(c), Income Tax Regs. "Under ordinary circumstances and for normal goods in an inventory, 'market' means the current bid price prevailing at the date of the inventory for the particular merchandise in the volume in which usually purchased by the taxpayer * * *." Sec. 1.471-4(a), Income Tax Regs. The "bid price" is the taxpayer's replacement cost.  Thor Power Tool Co. v. Commissioner, 439 U.S. 522">439 U.S. 522, 534 (1979). The regulations provide that where no open market exists, the taxpayer should use evidence of a fair market price to value inventory, such as specific purchases or sales, at the date of the inventory. Sec. 1.471-4(b), Income Tax Regs. Where the taxpayer offered the goods for sale at prices lower than the current price, the regulations also permit it to value its inventory at that lower price.  Sec. 1.471-4(b), Income Tax Regs.The regulations provide a valuation method for defective or subnormal goods: Any goods in an inventory which are unsalable at normal prices or unusable in the normal way because of damage, imperfections, shop wear, changes*671  of style, odd or broken lots, or other similar causes * * * should be valued at bona fide selling prices less direct cost of disposition, * * * or if such goods consist of raw materials * * * they shall be valued upon a reasonable basis, taking into consideration the usability and the condition of the goods, but in no case shall such value be less than the scrap value.  [Sec. 1.471-2(c), Income Tax Regs.] Tracking the regulations, petitioner argues that: (1) the "inactive" stones are not normal goods so it need not value them at current bid price (replacement cost); (2) no open market exists for the "inactive" stones, and because it did not offer the "inactive" stones for sale at less than the current price it cannot value the stones at that lower price; (3) the "inactive" stones were unsalable at normal prices because of changes in style; (4) although unsalable goods are usually valued at the bona fide selling prices, the "inactive" stones are raw materials, and, therefore, it properly valued the "inactive" stones "upon a reasonable basis." Respondent has broad discretion to determine whether a taxpayer's inventory method clearly reflects income.  Secs. 446, 471; Thor Power Tool Co. v. Commissioner, supra at 532;*672 United States v. Catto, 384 U.S. 102">384 U.S. 102, 114 (1966); Thomas v. Commissioner, 92 T.C. 206">92 T.C. 206, 220 (1989); Sam Goldberger, Inc. v. Commissioner, 88 T.C. 1532">88 T.C. 1532, 1550 (1987). We will not disturb respondent's determination unless it is "clearly unlawful," Lucas v. American Code Co., 280 U.S. 445">280 U.S. 445, 449 (1930), or "plainly arbitrary," Lucas v. Kansas City Structural Steel Co., 281 U.S. 264">281 U.S. 264 (1930). The taxpayer, therefore, has a heavy burden of proof to overcome respondent's disallowance of an inventory accounting method.  Thor Power Tool Co. v. Commissioner, supra at 532. We hold that petitioner in this case has not carried its heavy burden of proof. We believe the authority most apposite to this case is Thor Power Tool Co. v. Comimissioner, supra. The taxpayer in Thor Power used the "lower of cost or market" method to value parts for the tools it manufactured.  Thor produced large quantities of each part because predicting future demand for the parts at the time of manufacture was difficult.  The taxpayer later adjusted its inventory for "excess" inventory, i.e., inventory held*673  in excess of any "reasonably foreseeable future demand." It wrote the "excess" down to its "net realizable value," usually its scrap value.  Thor Power Tool Co. v. Commissioner, supra.Thor used two methods to write down the "excess" inventory. First, Thor predicted future demand based on the current year's usage if current data permitted.  It assumed future demand for the parts would remain the same as the current year, and valued an amount equal to one year's demand at cost.  Any amount greater than 2 years' demand was written off and amounts for more than 1 year but less than 2 years were written down by 50 to 75 percent.  Thor did not have any statistical evidence, such as evidence of actual sales, to support these percentages or the time frame for the write-downs.  Thor Power Tool Co. v. Commissioner, supra at 527-528. Instead, Thor's employee used his business experience to determine the write-down percentages.  If the current year's data was not sufficient to predict future demand,Thor's second method for writing down "excess" inventory was a flat percentage write-down of 5, 10, and 50 percent based on Thor's best estimate of future demand.  Thor*674  did not scrap the parts it wrote down nor did it sell these parts at reduced prices.  439 U.S. at 529. Instead, Thor physically retained the parts in its inventory and continued to sell them at the original prices. The Supreme Court sustained respondent's exercise of discretion in Thor Power because the write-down was "plainly inconsistent with the governing Regulations." Thor Power Tool Co. v. Commissioner, supra at 533. The Court found that the taxpayer had in effect taken a current deduction for an estimated future loss.  439 U.S. at 542. The Court reasoned that a taxpayer who uses the "lower of cost or market" method may value its inventory at something other than the market or bid price in two situations: (1) if the taxpayer offered the goods for sale at less than replacement cost, and (2) if the goods were defective.  439 U.S. at 534-535. The taxpayer must prove that it falls within an exception by objective evidence.  439 U.S. at 535. Thor did not fall within an exception: an active market existed for the parts; Thor sold the inventory at the original prices; the "excess" inventory was indistinguishable*675  from and intermingled with the inventory that was not written down; and Thor produced no evidence that the "excess" inventory had the "market value" Thor gave it.  439 U.S. at 535-536. We believe petitioner also has attempted to take a current deduction for an estimated future loss.  Petitioner, like the taxpayer in Thor Power, used current year's usage to predict future demand.  Petitioner did not show that its formula reflected actual future use.  Petitioner's computer printouts of inventory set forth only a physical count of the inventory. The computerized records do not reflect any actual sales to support the write-downs. Petitioner used some stones for warranty and repair, but the record contains inconclusive evidence of the number of stones used.  The only evidence of sales, repair, and warranty use is an analysis for 1981 of the 135 stone styles having more than 200 "inactive" stones. The total number of stones in the 135 styles was 48,421.  Of these, 46,960 were "obsolete." Petitioner used 487 stones, all still valued in inventory, as follows: 218 in sales, 31 for repairs, and 138 in warranty. Nevertheless, petitioner offered 98 of the 135 styles in its*676  price book in 1981.  Furthermore, this evidence is limited by category (activity in the more than 200 "inactive" stones categories) and is restricted to one year.  With these limitations, the evidence does not support general inferences that petitioner's "inactive" stones were worthless. This is especially clear in comparing the number of "inactive" stones analyzed, viz, 48,421 with the total claimed to be inactive in 1981, viz, 277,560. Moreover, there were inactive stones used for sales, and these were sold at the same prices as "active" stones of the same style. Petitioner did not offer the stones for sale at less than replacement cost.  Petitioner, therefore, does not come within the first exception to valuing inventories at other than market or bid price. Petitioner points out that it did not use any stones at all from some inactive styles. For example, in 1981, 92,432 of the total 277,560 "obsolete" stones were in styles with zero usage. These were not, however, the only stones petitioner wrote down.  Petitioner used 450 stones in one stone style with "obsolete" stones. Furthermore, a stone style could have "inactive" stones regardless of how many stones petitioner used.*677  It is also important to observe that a stone style with inactive stones in one year could have no inactive stones the following year.  In 1980, 1981, and 1982, petitioner used 23,716, 22,943, and 22,196 stones, respectively, from styles with "inactive" stones. Petitioner's "inactive" stones were indistinguishable from and commingled with stones in inventory that were not written down.  Many of the stones styles with some "inactive" stones were listed in petitioner's price book.  As in Thor Power, these excess stones do not fit the description of subnormal inventory which are "unsalable at normal prices or unusable in the normal way because of damage, imperfections, shop wear, changes of style, odd or broken lots, or other similar causes," sec. 1.471-2(c), Income Tax Regs. These terms describe differences in inventory which would distinguish the subnormal units of inventory from other units of inventory. What this Court observed about Thor's inventory can be said with equal force about petitioner's, Thor Power Tool Co. v. Commissioner, 64 T.C. 154">64 T.C. 154, 171 (1975): "Excess inventory is not so distinguishable.  It is commingled with the other inventory and it is excessive*678  not because of its physical characteristics but because of management's view as to future demand for it." See also Thor Power Tool Co. v. Commissioner, 439 U.S. at 536. Petitioner continued to sell stones from categories with "inactive" stones. It did not scrap the excess stones or sell them at reduced prices, but it continued to need and use them for current business. Petitioner believes Thor Power is distinguishable on the grounds that petitioner's stones are raw materials.  Raw materials can be valued "upon a reasonable basis." Sec. 1.471-2(c), Income Tax Regs. We do not agree that the stones are raw materials.  They have been processed for use in petitioner's rings. They are manufactured according to specification.  Perhaps the stones' only use is in petitioner's rings, but this limited utility does not suggest the stones' characterization as raw material.  They are finely tooled for a specific purpose.  Consequently, the "reasonable basis" method of inventory valuation is unavailable to petitioner for its stones. Petitioner has not shown that respondent's disallowance of its inventory accounting method was an abuse of discretion.Bad Debt Reserve*679  Beginning with its taxable year 1981 return, petitioner used the Black Motor formula to calculate the additions to its bad debt reserve. Petitioner included finance charges receivable in the ending receivable balances and included canceled finance charges in bad debt charge-offs. Respondent contends that petitioner should include finance charges receivable in year-end accounts receivable but should exclude canceled finance charges from the bad debt charge-offs. Respondent argues that petitioner did not write off the finance charges because they were worthless and, therefore, they cannot be said to have been bad debts. Generally, petitioner has the burden of proof.  Rule 142(a), Tax Court Rules of Practice and Procedure.  Petitioner argues in its reply brief, however, that respondent did not raise the "worthlessness" issue in his notice of deficiency and, therefore, he has the burden of proof on this issue.  Petitioner believes that respondent disallowed additions to the bad debt reserve on other grounds aside from failure to show worthlessness, i.e., that petitioner was on the specific charge-off method. In his notice of deficiency, respondent determined petitioner's bad debt*680  reserve. The notice stated: It is determined that your deductions for bad debts were overstated by $ 269,934 for the year ended June 30, 1981 and $ 240,490 for the year ended June 30, 1982 because you have claimed amounts that exceeded reasonable additions to your reserve for bad debts.  In addition, you may not claim deductions for additions to your reserve for bad debts relating to receivables for which bad debts are deducted on the specific charge off method.  [Emphasis added.] It appears that the "charge-off method" argument was raised in addition to a general statement that petitioner's increases in its bad debt reserves exceeded reasonable additions.  Implicit in this general language is the failure to qualify for the addition to reserves on several grounds, including (1) that there was no additional debt or (2) that the debts claimed to be worthless were not worthless but were collectible.  Moreover, respondent may rely on a theory that is consistent with a broadly worded notice of deficiency; a consistent theory is not a new matter.  Zmuda v. Commissioner, 79 T.C. 714">79 T.C. 714, 722 n.19 (1982), affd.  731 F.2d 1417">731 F.2d 1417 (9th Cir. 1984). Respondent's*681  theory that petitioner's canceled finance charges were not worthless is entirely consistent with the explanation that petitioner "claimed amounts that exceeded reasonable additions to [its] reserve for bad debts." The addition to the reserve for bad debts depends on the "amount of debts that have become wholly or partially worthless * * *." Sec. 1.166-4(c)(3), Income Tax Regs. Petitioner, therefore, has the burden of proof on this issue. Section 166(a) 8 allows a deduction for any debt that becomes worthless. Section 166(c) 9 authorizes a reserve for bad debts in lieu of the deduction pursuant to section 166(a).  An addition to a reserve for bad debts is an estimate of expected future losses attributable to current transactions.  Ehlen v. United States, 323 F.2d 535">323 F.2d 535, 542 (Ct. Cl. 1963); Massachusetts Business Development Corp. v. Commissioner, 52 T.C. 946">52 T.C. 946, 951 (1969). *682 A reserve allows a taxpayer to anticipate a future expense, but there must be specific statutory authorization to establish a reserve.  Brown v. Helvering, 291 U.S. 193">291 U.S. 193 (1934); Quality Chevrolet Co. v. Commissioner, 50 T.C. 458">50 T.C. 458, 463 (1968), affd.  415 F.2d 116">415 F.2d 116 (10th Cir. 1969), cert. denied 397 U.S. 908">397 U.S. 908 (1970). Petitioner was on the reserve method of accounting for bad debts during the years at issue. The authorization for the reserve for bad debts is explicitly conditioned on the approval of the Secretary.  Sec. 166(c).  Petitioner, therefore, must show not only that his claimed addition to the reserve is reasonable but also that respondent abused his discretion in disallowing the claimed additions to the reserve.  Massachusetts Business Development Corp. v. Commissioner, supra at 951; Roanoke Vending Exchange, Inc. v. Commissioner, 40 T.C. 735">40 T.C. 735, 741 (1963). The parties agree that the finance charges were debts owed petitioner.  Petitioner, therefore, properly accrued the finance charges in income at the time it billed the charges.  The issue is whether the canceled finance charges*683  are worthless debts that "may be anticipated for tax purposes by the establishment of a reserve." Quality Chevrolet Co. v. Commissioner, supra at 461. A bad debt for purposes of establishing a reserve pursuant to section 166(c) must be a "bad debt" within the meaning of section 166(a).  See Quality Chevrolet Co. v. Commissioner, supra at 464. That is, the reserve is for anticipated bad debts.  Sec. 166.  We must determine, therefore, whether the finance charges were canceled due to worthlessness. A debt is not worthless within the meaning of section 166 if a taxpayer voluntarily cancels the debt.  Roth Steel Tube Co. v. Commissioner, 620 F.2d 1176">620 F.2d 1176, 1181 (6th Cir. 1980), affg.  68 T.C. 213">68 T.C. 213, 221 (1977). A taxpayer, therefore, may not by his own act make a debt worthless. Liggett's Estate v. Commissioner, 216 F.2d 548">216 F.2d 548 (10th Cir. 1954), affg. a Memorandum Opinion of this Court; O'Bryan Bros. v. Commissioner, 127 F.2d 645">127 F.2d 645, 646 (6th Cir. 1942), affg.  42 B.T.A. 18">42 B.T.A. 18 (1940), cert. denied 317 U.S. 647">317 U.S. 647 (1942). The majority of the canceled finance charges*684  were those of AYC.  AYC rarely turned its school accounts over for collection because in its judgment it was not a good business practice.  When a customer paid the principal amount of a bill, AYC generally canceled the finance charges.  The record contains no evidence that any of AYC's customers were financially unable to pay or refused to pay the finance charges.  Apparently, some customers would ignore the finance charges and pay only the principal amount due.  AYC would send one more statement to these customers billing the unpaid finance charges.  AYC took no other steps to collect the unpaid finance charges.  We believe that AYC voluntarily canceled the finance charges. We do not question that it may have been a sound business practice to cancel the finance charges.  As respondent concedes, the cancellation of the finance charges may give rise to a deduction under some other provision of the Code in the year they are canceled. Petitioner did not introduce any evidence of the nature of the canceled finance charges in its other divisions.  The record shows only that division managers had some authority to cancel the finance charges.  We hold that petitioner has not shown that*685  respondent abused his discretion in disallowing additions to the bad debt reserve. Petitioner further argues that the canceled finance charges are includable in the bad debt charge-off portion of the Black Motor formula because: (1) the parties agree that the finance charges were legally enforceable debts, (2) both parties include finance charges in the receivables component of the Black Motor formula, and (3) in a prior audit, respondent allowed petitioner to include canceled finance charges in the numerator of the Black Motor formula. We are not persuaded.  First, the fact that the finance charges are legally enforceable debts means only that petitioner accrues them in income when billed.  This has no bearing on whether the canceled finance charges are bad debts to be included in the numerator of the Black Motor formula. Second, the receivables component of the formula contains all receivables, not just the receivables that petitioner believes may someday become bad debts. Certainly if any finance charges were bad debts, i.e., canceled due to worthlessness, they would be included in the numerator of the formula. Third, respondent is not bound by the results of an earlier audit. *686  Even if respondent had specifically approved the inclusion of canceled finance charges in bad debt charge-offs in the prior audit, respondent may change petitioner's method of accounting for bad debts if petitioner's method does not clearly reflect income.  Thomas v. Commissioner, 92 T.C. 206">92 T.C. 206, 223-224 (1989). Allowing an addition to a bad debt reserve for amounts that are not bad debts would not clearly reflect income. Acquisition of Durand and MECAWe next must decide the value of intangible assets petitioner acquired when it purchased the assets of two corporations, Durand and MECA.  The parties agree to the value of the tangible assets. Petitioner argues that it paid a premium for the assets, and that it properly allocated the total purchase price among all of the assets it acquired, tangible and intangible.  Petitioner in effect argues that the fair market value of all the assets was less than the amount it paid for them.  Respondent contends that he correctly valued the intangibles using the residual method and that petitioner did not pay a premium for the assets.  We agree. Petitioner and respondent each presented one expert witness at trial who valued*687  the intangible assets in Durand.  Respondent's expert also valued MECA's intangible assets. Respondent's expert witness, John P. Huffman, used the residual method to value the intangible assets of Durand and MECA.  Huffman concluded that the amount of the purchase price in excess of the agreed value of the tangible assets equals the value of the goodwill, going concern, and other nondepreciable intangibles.  Huffman found that for Durand, this value was $ 1,600,379, and for MECA, this value was $ 408,213. Petitioner's expert witness, Gerald Gray, used the "excess earnings" method expressed in Rev. Rul. 68-609, 2 C.B. 327">1968-2 C.B. 327, to calculate the value of the Durand intangibles.  See also Concord Control, Inc. v. Commissioner, 78 T.C. 742">78 T.C. 742 (1982). Pursuant to this method, Gray estimated the return on all assets and then deducted a "normal" return on the appraised tangible assets, 18 percent for working capital, 25 percent for fixed assets.  He described the difference as excess earnings attributable to goodwill.  Gray then capitalized the excess earnings at an "appropriate" rate, 50 percent, to estimate the value of goodwill.  Gray determined that petitioner*688  paid more than fair market value for the assets acquired.  He valued the intangibles for Durand at $ 682,000. When a combination of depreciable and nondepreciable property is acquired for a lump sum, the purchase price is allocated to the properties in proportion to the fair market values. Sec. 1.167(a)-5, Income Tax Regs. The parties have agreed to the value of the tangible assets; the only issue, therefore, is how to value the intangible assets. Pursuant to the residual method, the value of the intangible assets equals the difference between the purchase price and the value of the tangible assets. Banc One Corp. v. Commissioner, 84 T.C. 476">84 T.C. 476 (1985), affd.  815 F.2d 75">815 F.2d 75 (6th Cir. 1987). This method is appropriate if the purchase price for all of the assets is the fair market value. The "fair market value of property is the price at which the property would change hands between a willing buyer and a willing seller, neither being under any compulsion to buy or sell and both reasonably informed as to all relevant facts." VGS Corp. v. Commissioner, 68 T.C. 563">68 T.C. 563, 588-589 (1977). The best evidence of fair market value is a sale between unrelated*689  parties at arm's length. Banc One Corp. v. Commissioner, supra at 502; Florida Publishing Co. v. Commissioner, 64 T.C. 269">64 T.C. 269, 279-280 (1975), affd. without published opinion 552 F.2d 367">552 F.2d 367 (5th Cir. 1977). The purchase price is presumed to be the fair market value of acquired assets. Banc One Corp. v. Commissioner, supra at 503. When the purchase price is negotiated at arm's length and the value of the tangible assets is agreed, "the case represents the paradigm for application of the residual method." Banc One Corp. v. Commissioner, supra at 502. Either party, however, may introduce evidence to rebut the appropriateness of applying the residual method. R.M. Smith, Inc. v. Commissioner, 591 F.2d 248">591 F.2d 248 (3d Cir. 1979), affg.  69 T.C. 317">69 T.C. 317 (1977), cert. denied 444 U.S. 828">444 U.S. 828 (1979). Petitioner negotiated the purchase of the Durand and MECA assets at arm's length with unrelated sellers.  The purchase prices, therefore, are the best evidence of fair market value. Petitioner introduced expert testimony that it paid a premium for the Durand assets, but we are*690  not persuaded that its valuation method is appropriate. Petitioner's expert relied on Rev. Rul. 68-609, supra.  This ruling, however, qualifies its "formula" approach with the caveat that it should be used only if there is not a better method available to determine the value of intangible assets. Rev. Rul. 68-609, supra at 328.  This caveat in consistent with the case law.  Banc One Corp. v. Commissioner, supra.The residual method, if available, is superior to the excess earnings method for valuing intangible assets. The excess earnings method requires acceptance of "difficult and uncertain" assumptions and judgments that invite speculation rather than sound analysis.  Compare UFE, Inc. v. Commissioner, 92 T.C. 1314">92 T.C. 1314, 1326-1328 (1989); Banc One Corp. v. Commissioner, supra at 506. In addition, Gray used rates of return on tangible assets and for capitalization of excess earnings (50 percent) that appeared to surpass the high end of acceptable rates.  Gray did not convince us that the rates he used were appropriate. Petitioner argued that its valuation was correct because it valued the assets*691  at the time of the transaction.  Petitioner argues that because it used the excess earnings method to value the assets at the time of the purchase, the method is correct.  Contemporaneous use does not, however, imbue an inappropriate method with correctness.  Moreover, we note that an internal memorandum dated February 24, 1981, on petitioner's due diligence investigation reported that petitioner was acquiring from Durand goodwill of $ 1,633,000.  This figure was again used by petitioner in a preliminary report dated April 30, 1981, on allocating the purchase price. This figure was determined by applying the residual method. Petitioner next argues that it paid a premium because the price resulted from extensive negotiations, price considerations of the seller, and the "synergistic elements of the acquisition." That the price was the result of extensive negotiations supports the conclusion that the price was the fair market value. Petitioner did not explain how "price considerations of the seller" (e.g., paying for tax on recapture items) forced it into paying a premium above fair market value. We believe that petitioner's "synergy" in this case is the normal result of a well-thought-out*692  business strategy.  See Florida Publishing Co. v. Commissioner, supra.Petitioner bought a corporation that it believed would be successful under petitioner's ownership and management. We believe the purchase prices for Durand and MECA were the fair market values of the assets purchased.  Durand was a very successful corporation.  Durand's sales and net income were growing.  Both Durand and MECA met petitioner's minimum income requirements for the transactions.  The transactions were between willing buyers and willing sellers under no compulsion to buy or sell, all reasonably informed of the relevant facts.  The residual method used by respondent, therefore, produces the correct value of the intangible assets. Petitioner has not rebutted the presumption that the purchase price is the fair market value. RoyaltyThe next issue we must decide is whether petitioner is entitled to deduct $ 25,000 in taxable year 1982 for prepaid royalty expenses.  VTC licensed various intangible assets of the NFLPA to petitioner.  In taxable year 1981 petitioner prepaid $ 75,000 in royalties pursuant to the 1981 Agreement, and in taxable year 1982, petitioner prepaid $ *693  25,000 in royalties pursuant to an amendment to the 1981 Agreement.  As commissions were credited against prepaid royalties, petitioner deducted the credited amounts.  Petitioner, however, currently deducted the $ 25,000 of prepaid royalties for taxable year 1982. Petitioner argues that deducting the $ 75,000 prepaid royalties as royalties came due and were credited was erroneous.  It believes the $ 75,000 payment was attributable to the 13-month period, March 1, 1981, through April 1, 1982, and should be deductible when paid.  Likewise, petitioner argues the $ 25,000 payment was attributable to the 12-month period beginning April 1, 1982, and should be deductible when paid.  Petitioner alternatively argues that the portion of these payments for use of trademarks and trade names was a single noncontingent license payment deductible ratably over the period of the 1981 Agreement pursuant to section 1253(d)(2)(A).  To the extent not attributable to trademarks and trade names, petitioner argues that the payments are deductible ratably over the period of the 1981 Agreement pursuant to section 162(a)(3). Respondent argues that (1) because the payments were contingent payments pursuant*694  to section 1253(d)(1), section 162(a) controls, and (2) because the all events test was satisfied only as prepayments became creditable, petitioner should deduct royalties incurred as sales were made. In large part petitioner's argument turns on a conclusion that the 1981 Agreement was for a limited 13-month term and that subsequent renewals of the Agreement were independent agreements for separate terms.  We believe to the contrary that at the time petitioner and VTC entered into the 1981 Agreement, they reasonably anticipated future renewal of the contract for 5 years.  Cf.  Toledo TV Cable Co. v. Commissioner, 55 T.C. 1107">55 T.C. 1107 (1971), affd.  483 F.2d 1398">483 F.2d 1398 (9th Cir. 1973). The 1981 Agreement provided for successive renewals of the contract over a 5-year period.  Petitioner had a right to renew only by achieving a certain level of sales of the licensed products.  Nevertheless, petitioner and VTC amended the 1981 Agreement in 1982 to extend the Agreement for another year despite petitioner's failure to generate enough sales.  Instead, petitioner paid an additional $ 25,000 in prepaid royalties. After petitioner had failed to generate royalties that exceeded*695  prepaid amounts in 1981 or 1982, petitioner and VTC renewed the Agreement for three more years without additional payments by petitioner.  Moreover, the amended Agreement gave petitioner the right to credit the remaining balance of uncredited $ 75,000 prepaid royalties against royalties incurred on future sales through the end of the fifth year of the Agreement as amended.  Throughout the 5 years of the Agreement, petitioner incurred less royalties than the prepaid amounts.  In each successive year of the Agreement, petitioner could credit the remaining prepaid royalty amounts against royalties incurred.  The 1981 Agreement was effectively for a term of 5 years. Petitioner argued that the $ 100,000 in prepaid royalties is deductible pursuant to either section 1253 or section 162 ratably over the terms of two separate agreements.  We have decided, however, that the term of the 1981 Agreement was 5 years.  On this finding, respondent's position allows petitioner a greater deduction than the amount allowable pursuant to petitioner's theory.  Moreover, we believe that respondent's method clearly reflects petitioner's income.  Sec. 446(b).  He allowed petitioner to deduct $ 42,200 in*696  1982, the amount of royalties that petitioner incurred and against which petitioner credited prepaid royalties. Respondent's method matches income from sales of the licensed products with the royalty expense associated with producing gross receipts on those items.  We sustain respondent's determination on this issue. Because of concessions, Decision will be entered under Rule 155.  Footnotes1. All section references are to the Internal Revenue Code of 1954 as in effect for the years in issue, unless otherwise indicated.↩2. See, e.g., stone style #3163 on Exhibits 8, 9, and 10.  ↩3. See, e.g., stone style #1740 on Exhibits 8, 9, and 10.↩4. The canceled charges may or may not have been billed in the same year.  * Includes Scholastic and Recognition divisions.↩5. Black Motor Co. v. Commissioner, 41 B.T.A. 300 (1940), affd. on other grounds 125 F.2d 977">125 F.2d 977↩ (6th Cir. 1942). The Black Motor formula is used to determine the allowable bad debt reserve based on a six-year average ratio of bad debt charge-offs to year-end accounts receivable.6. We note the inconsistency between the term of the final extended agreement, viz, through March 31, 1984, and the final year VTC earned royalties pursuant to the agreements, viz, through March 31, 1985.  The parties stipulated to the years VTC earned royalties and that the agreement terminated in March 1985.↩7. SEC. 471.  GENERAL RULE FOR INVENTORIES. (a) GENERAL RULE. --Whenever in the opinion of the Secretary the use of inventories is 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.↩8. Sec. 166 BAD DEBTS. (a) GENERAL RULE. -- (1) WHOLLY WORTHLESS DEBTS. -- There shall be allowed as a deduction any debt which becomes worthless within the taxable year. (2) PARTIALLY WORTHLESS DEBTS. -- When satisfied that a debt is recoverable only in part, the Secretary may allow such debt, in an amount not in excess of the part charged off within the taxable year, as a deduction.  ↩9. (c) RESERVE FOR BAD DEBTS. -- In lieu of any deduction under subsection (a), there shall be allowed (in the discretion of the Secretary) a deduction for a reasonable addition to a reserve for bad debts. [Section 166(c) was repealed by the Tax Reform Act of 1986, Pub. L. 99-514, sec. 805(a), 100 Stat. 2361.]↩