Rev. Proc. 72-36

Rev. Proc. 72-36

                          Table of Contents

The purpose of this Revenue Procedure is to prescribe guidelines relative to acceptable methods of estimating the volume of trading stamps to be redeemed at the end of any taxable year. They are to be used in conjunction with the rules under section 1.451-4 of the Income Tax Regulations./1/

Sec. 2. Background.

Section 1.451-4 of the regulations provides, in part, that, in determining the "estimated redemption percentage," referred to in section 1.451-4(c)(5) of the regulations (five-year rule), the growth factor referred to therein shall be as determined pursuant to guidelines published by the Commissioner. In order to implement these regulations these guidelines are being published. In addition, these guidelines also implement the regulations which concern themselves with other methods of determining estimated future redemptions. The word "year" as used in this Revenue Procedure means "taxable year."

Sec. 3. General.

.01 Except as provided in Section 8, the volume of stamps expected to be redeemed after the close of any taxable year may be estimated using any of the following four general methods.

1. A ratio method (See Section 4, below).

2. The probability sampling method described in Section 5, below.

3. A synthetic or reconstructive method (See Section 6, below).

4. Any actuarial, statistical or other mathematical method provided that the taxpayer can demonstrate to the satisfaction of the Commissioner of Internal Revenue (hereafter referred to as the Commissioner) that such method will produce a sound and acceptable measurement of the volume of stamps expected to be redeemed by the taxpayer after the close of any taxable year.

.02 The term "stamp" wherever used in this Revenue Procedure includes coupons, certificates, or any similar and appropriate devices qualifying for treatment under section 1.451-4 of the regulations.

Sec. 4. Ratio Method.

.01 The unadjusted ratio. For the taxable year, the taxpayer may compute the total stamps redeemed during the five year period up to and including such taxable year. For the same period he may compute the total stamps issued. The redemptions for such period divided by the issuances for such period will be the taxpayer's unadjusted ratio.

1. If the redemptions include any stamps issued by any other entity that the taxpayer has agreed to redeem, then such issuance must include at least an appropriate allowance for such other stamps. For example, Purple Company has a taxable year ending on March 31, 1973 and agrees to redeem Tan Company stamps, effective January 1, 1972. If Purple Company can establish to the satisfaction of the Commissioner the portion of the stamps issued by Tan Company that may be reasonably expected to be redeemed by Purple Company, then it may limit the increase in its denominator to such reasonable portion. Thus, if Tan Company has computed its reserve under this Revenue Procedure and established that it may reasonably expect to redeem 5,000 pads as of January 1, 1972, Purple Company may, with the approval of the Commissioner, satisfy the requirement of this Section by adding 5,000 pads (after adjustment for differences in the quantity of stamps per pad, if any) to its denominator of stamps issued through March 31, 1972, even though Tan Stamps are henceforth commingled with Purple Stamps for redemption purposes. For taxable years ending March 31, 1973 through 1976 Purple Company will continue to add 5,000 pads to its denominator for each such year. For taxable years after March 31, 1976, Purple Company need not add any Tan Stamps to its denominator even though some Tan Stamps, issued prior to January 1, 1972, are redeemed in such subsequent years.

2. If the taxpayer keeps separate records for stamps issued by such other entity, then taxpayer may exclude such stamps from both the numerator and denominator of its ratio. For example, Purple Company agrees to redeem Tan Company stamps, effective January 1, 1972. These stamps are of a distinctive color and Purple Company does not permit redeemers to commingle Tan Stamps and Purple Stamps in the same book. Further, Purple Company keeps separate records of the volume of Tan Stamps redeemed. In this case Purple Company may exclude Tan Stamps from both the numerator and the denominator of its ratio. Also, if Purple Company redeems partial or complete books of Tan Stamps by issuing new Purple Stamps (or certificates in lieu thereof, see Section 3.02, above) and includes the new Purple Stamps in its current issuance, then it will not be considered to have commingled its stamps with Tan Stamps by virtue of the redemption of such new Purple Stamps. If Purple Company elects, however, at any subsequent time to henceforth commingle the remaining Tan Stamps it must follow the procedure under paragraph 1, above, and for the year of commingling, include at least an appropriate allowance for the remaining Tan Company Stamps to be redeemed. For the four years following commingling, the Purple Company will continue to include the same allowance in its denominator of stamps issued but for subsequent years it need not make any allowance for Tan Stamps even though Tan Stamps issued prior to said agreement continue to appear among stamps redeemed. Thus if Purple Company redeems Tan Stamps from January 1, 1972 through March 31, 1972 but does not permit redeemers to commingle Purple Stamps and Tan Stamps and maintains separate records from January 1 through March 31, it will not include any Tan Stamps in either the redemptions or the issuances in computing its 1972 ratio under this Section. If Purple Company commingles Purple Stamps and Tan Stamps after March 31, 1972, and finds that the equivalent of 750 pads were redeemed between January 1, 1972 and March 31, 1972, it may subtract the 750 pads from the estimated January 1 reserve of 5,000 pads (see example under subsection 1, above) and add only 4,250 pads to its denominator for the taxable year ending March 31, 1973. For the 1974 through 1977 taxable years it will also add 4,250 pads to its denominator but for 1978 and subsequent years it need make no addition to its denominator even though Tan Stamps, issued prior to January 1, 1972, continue to be presented for redemption.

3. If stamps are issued directly to prospective redeemers upon presentation of a certificate issued by a third party under a contract between taxpayer and the third party, then the stamps will be deemed to be issued in the taxable year in which the taxpayer issued the stamps to a prospective redeemer. If the certificate is redeemed for merchandise, cash or services, then the certificate is treated as issued in the same year as it is redeemed. The redemptions are included in the year in which the stamps are redeemed, or the certificates used directly for the purchase of goods, cash or services. For example, Purple Company has a contract with Steel Company that permits Steel Company to issue incentive award certificates for 10 books of Purple Stamps. These certificates may be presented to Purple Company by Steel Company employees and are honored by Purple Company. Purple Company then bills Steel Company in accordance with their contractual agreement. In this case, Purple Company will include the certificates in its count of equivalent stamps issued during the year in which the certificate is presented to Purple Company by the Steel Company employee (and for four years thereafter). The redemptions will be included in the year in which the certificates (or the Purple Stamps issued in lieu thereof) are actually redeemed (and for four years thereafter).

4. Example: Purple Company's issuances and redemptions for the period 1968-1972 and its unadjusted ratio for the taxable year ending March 31, 1972 are as follows:

 Taxable Year       Issuances      Redemptions

1. If some years are increases and some years are decreases, the sum required is the algebraic sum, i.e., a decrease is regarded as a negative increase.

2. If the growth percentage for any year exceeds 100%, then the growth percentage allowable for that year is 100%. Specifically, if no stamps are issued in a given year but some stamps are issued in the year following, then the growth percentage for the year following is 100%. Thus a new business automatically has 100% as the growth percentage for its first year of business.

3.--Table of Growth Factors for Use in Adjustment of "Buckeye Ratios" To Correct for Increases or Decreases in Volume of Stamps Issued

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5. If the algebraic addition (see subsection 1, above) results in a negative total, i.e., if there is a net decrease for the average of the five preceding years (as computed under the provisions of this subsection) then the multiplier is computed by subtracting the "average" percentage decrease from 100. For example, if the "average" net decrease is 10% the multiplier is .90 (100% - 10% = 90% = .9).

6. If the ratio computed under subsection .01, above, multiplied by the factor provided by this subsection exceeds 98%, then the adjusted ratio is 98%. 7. Example: Purple Company was organized in 1960 and issued its first stamps that year. Through 1965 its annual issuance was as follows:

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Sum of 5 growth percentages, 1960 through 1964 130 Above sum divided by 5: 26 Multiplier from Table (see subsection 3, above) 1.20

If the unadjusted multiplier computed for the years 1960-1964, as provided by subsection .01, above, is 80%, then 80% multiplied by a factor of 1.20 yields 96% and the adjusted ratio is 96%. This ratio will be used (see subsection .04, below) for the period 1960 through 1964 to establish the first measure of the volume of redemptions to be expected for stamps issued during this period that will be redeemed after 1964.

(b) For its 1965 adjustment, Purple Company computes--

Sum of 5 growth percentages, 1961 through 1965 -22 Above sum divided by 5 -4.4 Multiplier (see subsection 5, above): .956

If Purple Company's unadjusted ratio for the period 1961-1965 is 100%, then 100% multiplied by a factor of .956 yields 95.6% and the adjusted ratio for the year 1965 is 95.6%. Similarly, for all subsequent years the adjusted ratio will apply to only the last year of the period (in contrast to the ratio for the first five years, which is applied to the entire first five years of experience).

.03 Application of adjusted ratio to stamps issued and computation of expected number of stamps to be redeemed.

1. First four taxable years of experience. Since the adjusted ratio described under subsections .01 and .02, above, requires five years of experience, the taxpayer may compute his reserve based upon the experience of comparable firms for the first four years.

2. Fifth taxable year of experience. For a taxpayer using the method provided by this Section, the expected number of stamps that have been issued in the first five years and may be reasonably expected to be redeemed in the sixth and subsequent years may be estimated as follows:

(a) Add the total volume of stamps issued for the first five years to obtain the total issuance. This total may include an allowance for the issuances of other entities that the taxpayer has agreed to redeem, as described under subsection .011, above.

(b) Multiply the sum so obtained by the adjusted ratio for the first five years of experience, as provided by the procedure under subsection .02, above.

(c) Subtract total redemptions for the first five years from the product obtained as a result of step (b). If the difference is positive, this is the expected number of stamps issued during the first five years that the taxpayer may reasonably expect to redeem in the sixth and subsequent years. If this sum is negative or zero, then the allowance provided under this Section at the end of the five years is zero.

3. Sixth and subsequent taxable years.

(a) Multiply the stamps issued in the sixth or subsequent year by the adjusted ratio computed for such year as provided by subsection .02, above.

(b) From the product obtained from step (a) of this subsection subtract the stamps redeemed during the same year.

(c) If the difference obtained from step (b) is positive, add the difference to the expectation obtained from step (c) for the preceding year (from this subsection for the seventh or any subsequent year, from subsection 2, above, if this is the sixth year). If the difference is zero, then the result of step (c) for the preceding year is the taxpayer's expectation for subsequent years. If the difference is negative, decrease the prior year's expectation by the difference (but the minimum expectation is zero).

.04 Conversion of expected number of stamps that may reasonably be expected to be redeemed into dollars. Multiply the number of stamps expected to be redeemed in subsequent years (obtained from subsections 2 or 3, above) by the average cost of merchandise as described in section 1.451-4(b)(1)(iii) of the regulations.

.05 Illustrative table--The table below illustrates the computation of the expected number of stamps to be redeemed by Tan Company through December 31, 1970.

     Ratio Method Applied to Tan Trading Stamp Company: Current

.01 Use of a probability sample. The percentage of stamps issued in a given taxable year and redeemed in the same and in subsequent taxable years may be estimated by determining the issuance year for each stamp included in a probability sample of stamps redeemed during the taxable year covered by the statistical study.

1. The approximate date of issue by the taxpayer and/or the approximate date of sale by the taxpayer must be readily determinable (e.g., by the use of letter codes or other devices).

2. Notwithstanding the date of issuance and/or sale requirements of subsection 1, preceding, stamps issued or sold prior to the effective date of this Revenue Procedure will be deemed eligible for statistical evaluation, as provided by this Section, if at least 90% of the stamps issued are so identifiable.

3. Stamps that were identifiable when issued are not disqualified merely because of mutilation by the redeemer, excessive wear or similar causes, provided the stamps when issued might reasonably be expected to be returned in legibile condition under ordinary circumstances.

.02 Acceptable sampling methods.

1. The taxpayer may use any sampling procedures that are in accord with generally accepted probability sampling techniques. The procedures used, however, must be documented and made available at the request of the District Director of Internal Revenue for the district in which the taxpayer's returns are filed. In these procedures the taxpayer must specify the steps taken to satisfy the requirements listed under subsection .03, below, titled "Standards of probability sampling."

2. Qualifications of sampling expert. While no specific requirements are established for the sampling expert responsible for the design of the study, it is recognized that probability sampling is a highly specialized field and that otherwise competent statisticians may not be qualified in the field of probability sampling. It is the taxpayer's responsibility to secure the services of a competent sampling expert. Where so requested by the District Director, the name, address and qualifications of the sampling expert, and the extent to which he is responsible for the study shall be supplied.

3. Use of recognized formulas and probability sampling methods. Any generally accepted methods may be used provided that they meet the requirements of subsection .03, below. When so requested by the District Director, the textbook, if any, used as a basis for the formulas and methods shall be identified by the taxpayer, including the edition, and the page number and formula number, if any, specified. Articles published in professional journals of statistics or mathematics may also be used. Creation of new formulas and methods or adaptations of existing formulas and methods are permitted, but the derivation of the new formula and the justification of the new method must be supplied to the District Director on request. Where the methods and formulas used by the taxpayer are invalid, whether published or not, then the taxpayer's results may be set aside and the District Director shall make a determination of the proper amounts allowable.

.03 Standards of probability sampling.

1. The sampling plan which is used must conform to the standards of the "Report of Committee on Standards of Probability Sampling for Legal Evidence--Admissibility of Data from Probability Samples," which was published by the Society of Business Advisory Professions, Inc., in cooperation with New York University. For convenience, this report is reproduced as an appendix.

2. In addition to satisfying the requirements of the above referenced report, the sampling plan must meet the following requirements:

(a) The procedures used and the records preserved must be such as to permit verification at a later date of the sample selection and the computations performed with sample accounts.

(b) The procedure used and the records preserved must be such as to permit verification that the frame from which sampling was done adequately covers the population at the time of sampling.

3. The population from which the sample is to be selected is all stamps redeemed during the taxable year. In creating a frame, the population may be partitioned, clustered, or otherwise organized in order to increase sampling efficiency.

4. Each sample stamp shall be classified as either--

(a) an allocable stamp, if its year of issue can be approximately determined, or

(b) a null if its year of issue cannot be approximately determined. 5. The tax year of issue for each stamp in the sample should be recorded in the format of Exhibit 1 and a copy attached to the tax return.

6. A statement of the sample design shall be attached to the tax return. This statement must include:

(a) Description of the frame or frames

(b) Definition of the sampling unit or units

(c) The procedure for drawing the sampling units

(d) Computations on which the decision of sample size was based (see subsection 7, below)

(e) The formula or procedure for calculating the relative sampling variability in the estimated proportion of stamps redeemed for each year of issue and for the combined proportion for stamps redeemed after a lag of 2 or more years.

7. Number of stamps required for sample.

(a) During the first year a probability sampling system is used; the minimum number of stamps required is as follows:

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(c) Selection within books need not be uniform. If greater probabilities are assigned to certain pages of books, then correspondingly lesser weights must be assigned to stamps selected from such pages (e.g., if twice the probability is assigned to the first and last pages of each book, then the weight to be assigned stamps from the first and last pages shall be only half the weight assigned to stamps from the middle pages of the book). In such case a description of the method and the weights used is required under subsection 6(c), above.

(d) Provided that the test level of subsection 5.038, below, is met for the preceding year's sample, the following reduced sampling rates are permissible in lieu of the values shown in subsection (a), above:

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(g) A failure of the test provided by subsection 8 when sampling is conducted at the rate provided by subsection (a), above, will still permit the rates of subsection (a) to be applied.

(h) The minimum sample is 1,000 stamps per annum.

(i) Actual sampling rates should be computed on the basis of the preceding year's volume of stamps redeemed. Thus if the volume of stamps in the sample is below the minimums provided by subsections (a), (d), (e) and (h) because current year's redemptions are less than the previous year's redemptions, the number so obtained will be deemed adequate.

8. Test level required for reduction of sampling rate as provided by subsection 7, above.

(a) Unweighted replicate method. If the taxpayer uses an unweighted replicate method of sampling, then it may test the adequacy of its sampling plan as shown by Exhibit 3 of subsection .05, below. For 5 replicates, the method consists of determining the number of stamps in each replicate that corresponds to a lag in redemption of 2 or more years. For the specified lag, the number in the lowest replicate is subtracted from the number in the highest replicate and the difference is divided by the number of stamps with 2 or more years lag for all 5 replicates combined. If the result is less than the following test level, the sample has met the test of this subsection and the reduction in sample permitted by subsection 7 would apply:

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(c) Non-replicate method. The taxpayer is required to use the correct formula for its method (see subsection .036(e), above). He must demonstrate that the sampling and estimating procedure meets or exceeds the precision levels stipulated in subsection (a) of this subsection. The test levels specified in that subsection provide for a relative sampling variability in the estimated stamps with a lag in redemption of 2 or more years as a proportion of total stamps redeemed in the survey year (i.e., the coefficient of variation of the estimate expressed as a percentage).

.04 Exhibits

1. Exhibit 1, below, is shown for an unweighted replicated sample employing 5 replicates. If weights are required (see subsection .037(c), above), appropriate modification of Exhibit 1 would be necessary. If the sample is not replicated, then Exhibit 1 would consist, as a minimum, of the actual sample observations, classified by year, plus such other information derived from the sample as would be required for the computation of the sampling precision by formula (see subsections .036(e) and .038(c), above).

 Illustrative Exhibit 1.--Sample of 3,240 stamps redeemed from April

1200 stamps issued during 1973 ------------- = 800 million stamps 1.5 stamps per million

(1.5 stamps per million is a rate of .000 0015).

If non-uniform probabilities of selection are used, then appropriate modifications are made in the weight, as specified in subsection .037(c), above. The estimated redemptions (shown in column 3) are divided by the volume of stamps issued during the appropriate tax year, obtained from the regular accounting records of the taxpayer. Thus if the survey procedure indicates that an estimated 200 million stamps issued in 1971 were redeemed in 1973 and if the accounting records show that 2 billion stamps were issued in 1971, then it is estimated that 10% of the stamps issued in 1971 were redeemed in 1973. Column (6) shows the lag in years between issue and redemption, e.g., stamps redeemed in the year of issue (1973) are zero lag, stamps redeemed in 1973 but issued in 1971 are a lag of 2 years, and so on.

 Illustrative Exhibit 2.--Determination of percentage lag in stamp

(a) Exhibit 3.--Sampling variability for an unweighted, replicated sample:

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Line 1. Highest value: 121 stamps

Line 2. Lowest value: 79 stamps

Line 3. Range (Line 1 minus line 2) 42 stamps

Line 4. All subsamples combined: 540 stamps

Line 5. Relative sampling variability (Line 3 / Line 4) 7.8%

(c) Comments:

(1) Line 5 supplies part of the necessary data for the "test level" of subsection .038, above. The remainder is supplied by column (3) of Exhibit 2 (or from accounting records), i.e., the total stamps redeemed in tax year 1973 is 2.16 billion stamps. Referring to subsection .038, above, the test level is 20% if less than 3 billion stamps are redeemed during the survey year. Exhibit 3 passes the test and in this case the taxpayer is permitted to use a rate of 1 stamp per 3 million stamps redeemed for selecting next year's sample (see subsection .037(d), above). The preceding items will satisfy the requirements of subsection .036(d), above.

(2) If the provisions of subsection .037(c) are utilized, an appropriate modification would be made in Exhibit 3.

(3) If a non-replicate method is used, then Exhibit 3 would display the computations required by the formula for calculating the relative sampling variability in the estimated volume of stamps redeemed after a lag of 2 or more years as a proportion of all stamps redeemed. (See subsection .036(e), above.) The results of the computation would permit reduction in the sample size (see subsection .037, above) provided the equivalent requirements for "test level" are met (see subsection .038, above).

.05 Use of estimates from probability sample

1. The estimates derived from a probability sample provide information about the lag in redemptions for stamps redeemed during the survey period. They do not provide direct information about stamps redeemed in years prior to the survey year or subsequent to the survey year. For example, the Tan Trading Stamp Company (see subsection 4.05, above) redeemed 150 stamp units during 1959, its initial taxable year of operations. During the same taxable year it issued 500 stamp units for a "zero lag" redemption rate of 30% for issuance year 1959. The 1960 taxable year redemptions consisted of 30% "zero lag" redemptions of 1960 issuance of 600 stamp units plus 40% "one year lag" redemptions of 1959 issuance. For 1961 redemptions, a "two year lag" redemption rate of 10% was used. Thus the Tan Company was constructed using a uniform redemption pattern applied to a uniformly increasing volume of stamp units issued. For an actual taxpayer, volume would not increase uniformly and the redemption pattern may vary from year to year. In particular, for the first year of issuance, the "zero lag" redemptions will usually be substantially less than the "zero lag" redemptions for the second and subsequent issuance years. Accordingly, if the "zero lag" redemptions for the survey period are 30% and the "zero lag" redemptions for the initial year of operations are only 10%, this in no way discredits the survey results.

2. The estimates derived from the survey year may be used:

(a) as the initial redemption pattern for the synthetic (or reconstructive) method described in Section 6, below, or

(b) as an input into an actuarial, statistical or other mathematical method (See Section 7, below).

Section 6. A Synthetic Method of Reconstructing Data for Prior Years

.01 The synthetic method may be used by the taxpayer to reconstruct data for taxable years before survey data become available. In this case, the prior year data are "synthesized" or "reconstructed" and the probability sampling method of Section 5, above, is used to obtain data for survey years.

.02 The synthetic method may also be used, where no survey data are available, to reconstruct prior taxable year data by using

1. an initial redemption pattern derived from the experience of another, similar company, or

2. the following arbitrary pattern:

redeemed in year of issue 35% redeemed with a one year lag 40 redeemed with a two year lag 11 redeemed with a three year lag 4 redeemed with a four year lag 2

3. a longer arbitrary pattern similar to the pattern of subsection 2, above, and derived from it by halving the percentage from the preceding year to obtain the percentage for each subsequent year. Thus for a 5 year lag the rate is 1%; for a 6 year lag, 0.5%; and so on.

4. any other pattern approved by the Commissioner.

.03 Annual redemptions assuming a constant redemption pattern.

1. For each taxable year since inception, the annual number of stamps issued by the taxpayer is multiplied by the redemption pattern determined in accordance with either subsection .01 or .02, above.

2. Illustrative Exhibit 6.1 displays the results of this computation for Tan Trading Stamp Company. The Tan Trading Stamp Company has elected to use the redemption pattern specified by subsection .022, above. It issued 500 stamp units in 1959 (its initial taxable year) and, if 35% are redeemed the first year, then 175 units were redeemed in that year. For 1960, 40% redemption of 1959 issuance implies 200 units redeemed (500 X .4 = 200). In addition 35% of the 1960 issuance of 600 units are redeemed in 1960, i.e., 210 units (600 X .35 = 210). Adding 210 to 200 yields a total of 410 units redeemed in 1960. In the same way, 1961 redemptions consist of 55 units from the 1959 issuance (11% of 500), 240 units from the 1960 issuance (40% of 600), and 245 units from the 1961 issuance (35% of 700), or a total of 540 units redeemed for taxable year 1961.

 Illustrative Exhibit 6.1.--Tan Trading Stamp Company: Estimated

Step 1. The totals obtained for each year's redemptions will not, in general, add to the total stamps redeemed each year according to accounting records. In order to constrain these totals to equal the accounting totals, each column requires a multiplier obtained by dividing the actual redemptions by the total obtained from subsection .03, above.

Step 2. Each entry in a table corresponding to Illustrative Exhibit 6.1, above, is multiplied by the value obtained for the appropriate column as a result of step 1, above. The results are posted in the form of Illustrative Exhibit 6.2, below.

Step 3. As a check on the accuracy of steps 1 and 2, above, a new total is obtained. If the new total does not match the accounting total used for step 1 (within reasonable rounding error) there is a mistake in arithmetic and steps 1 and 2 should be repeated to correct the mistake. For example, 1960 redemptions totaled 410 stamp units, as imputed by Illustrative Exhibit 6.1. If, in fact, the accounting totals show only 380 units were redeemed, then the components are both reduced proportionately to 185.37 for 1959 issuance and 194.63 for 1960 issuance. (380 / 410 = .926829 and 200 X .926829 = 185.37, 210 X .926829 = 194.63). Since 185.37 + 194.63 = 380, the allocation is correct. For 1961 redemptions, the total was imputed at 540 units but if only 500 were redeemed according to accounting records, the multiplier required is 500 / 540 = .925926. Thus

55 X .925926 = 50.93 240 X .925926 = 222.22 245 X .925926 = 226.85 ------ Total 500.00

 Illustrative Exhibit 6.2.--Tan Trading Stamp Company: Annual

for 1960 are 150 + 185.37 = 335.37,

for 1961 are 335.37 + 50.93 = 386.30,

for 1962 are 386.30 + 18.73 = 405.03, and so on.

In Illustrative Exhibit 6.3, below, the 1959 and 1960 entries agree, but the 1961 entry is shown as 386.29 (the difference is ascribed to rounding error). Similarly, for 1962 the entry is shown as 405.02.

      Illustrative Exhibit 6.3.--Tan Trading Stamp Company: Cumulative

 Illustrative Exhibit 6.4.--Tan Trading Stamp Company: Cumulative

1. Example. Using the 12 year pattern permitted by subsection .023, above, yields the following Illustrative Exhibit 6.4a:

 Illustrative Exhibit 6.4a.--Tan Trading Stamp Company: Cumulative

.08 Extension to future years.

1. Direct extrapolation. When 5 or more years of redemption estimates are available for any given issuance year the cumulative percentages obtained from subsections .06 or .07, above, may be directly extrapolated to provide estimates of the amount to be redeemed in future years. A Gompertz curve

                            y = a * bcn

                        1 / y = a + b * cn

(a) If redemption is limited by company policy or any similar restriction, then redemptions may not be projected into a period in which redemptions are not permitted. For example, Tan Company stamps are marketed under a restriction that limits redemptions to five years. In this case no projection into the sixth or subsequent year is permitted. (See subsection .12, below, on expiration dates.)

(b) If the last three terms are equal, then no growth can be projected. For example, in Illustrative Exhibit 6.4, for issuance year 1959, and redemption years 1968 through 1970, the cumulative percentage redemption is 82.9046 for each year and no growth can be projected. For issuance year 1965, the cumulative redemption level is 87.1376 for 1968 and 89.0874 for 1969 and 1970. In this case a projection can be obtained using the entries for 1966, 1968 and 1970, even though the arbitrary pattern of subsection .022, above, provides for only 5 years of redemption. (See subsection (a), above, for a circumstance under which no growth is permissible.)

2. Imputed values. Where less than 5 years of redemption estimates are available for any given issuance year, it will be preferable to use the median net annual increase in estimated percentage redemption (see subsection .09, below) for the last 5 available years and construct an imputed redemption series before proceeding with the extrapolation, as above.

3. Other extrapolations. In lieu of the methods shown under subsections 1 and 2, above, the taxpayer may, with the consent of the Commissioner, extrapolate using any method that can be shown to be appropriate to his data.

.09 Use of net annual increase in estimated percentage redemption. The cumulative percentage redemption values of Exhibit 6.4a can be used to obtain the net annual increase in redemption for each issuance year. These values could also be obtained directly from Exhibit 6.2 using the annual issuances from Exhibits 6.1 or 6.3.

1. Example. Illustrative Exibit 6.5a demonstrates the computation of the net annual increase for Tan Company.

  Illustrative Exhibit 6.5a.--Tan Trading Stamp Company: Net Annual

(a) Tan Company's values for the issuance years 1965 through 1969 for redemptions with one year of lag ranged from 38.3404% to 38.4923%. The median for the five years is 38.4363. Similarly, for two years of lag, the values range from 10.5436 to 10.5854 (issuance years 1964 through 1968) with a median of 10.5700. For three years of lag, the median value of the last five entries is 3.84363 and, for four years of lag, the median is 1.92182.

(b) The median values obtained by application of subsection (a), above, may be assumed to be reasonable values to apply to redemptions in future years of stamps issued in 1970. Thus through 1971, the cumulative redemptions of 1970 issuance may be assumed to be 72.1171% (33.6808 + 38.4363 = 72.1171). Similarly, cumulative redemptions through 1972 may be assumed to be 82.6871% (72.1171 + 10.5700 = 82.6871); through 1973 the cumulative total may be assumed to be 86.53073%, and through 1974, 88.45255%. The table below shows the values for annual and cumulative redemptions for issuance years 1967 through 1970:

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.10 Iteration. The taxpayer may use the output redemption pattern derived from subsection .09, above, to generate a new input pattern to be used in lieu of the pattern provided by subsections .01 or .02, above. This process may be repeated without limit or restriction and terminated after any number of iterations.

1. Each new input pattern may be determined from a previous output in the form of Exhibit 6.5 by selecting the average value for each year of lag.

2. The taxpayer may elect to use either the median or the arithmetic mean in determining its "average values," but shall not change its election without the consent of the Commissioner.

3. In determining the average value for zero lag, the taxpayer should omit the first year of issue. (See subsection 5, below, for an illustration of this rule.)

4. Taxpayer may elect to follow any consistent rounding process subject to the following restrictions:

(a) For zero to five years' lag, input values must be stated in at least whole percentage points, e.g., 30%, 52%, 9%, and 1%.

(b) For six to nine years' lag, values other than zero must be expressed to at least one-tenth of a percentage point, e.g., 1.2, 0.9, and 0.1.

(c) In lieu of rules (a) and (b), above, taxpayer may round each input value to a fixed number of significant digits (but not less than 2), e.g., 12, 1.2, .12, .012, .0012, .00012 and so on.

(d) All rounding is to be to the nearest number satisfying the required number of digits, as provided by this subsection. Where two such digits are equally near, the taxpayer may consistently follow any one of the following rules:

(1) addition of an extra digit, e.g., exactly 1.0125 is equally near to 1.012 and 1.013 and may be left unrounded as 1.0125. (But note that 1.01251 is closer to 1.013 and, if the taxpayer has elected to follow rule (c) and is determining input values to four significant digits, then the input value would be rounded to 1.013.)

(2) rounding to the next larger number (bank rounding), e.g., exactly 1.0125 may be rounded to 1.013 (but 1.012499 would be nearer 1.012 and, if taxpayer is rounding to four significant digits, would be rounded to 1.012).

(3) alternate rounding (bookkeeping rounding) follows bank rounding (see (2), above) for the first applicable entry but the next applicable entry is rounded down and subsequent applicable entries would be rounded alternately up and then down. E.g., if the first applicable entry is exactly 31.05, which is to be rounded to three significant figures, this would be rounded up to 31.1; if the second applicable entry is exactly 21.95, this would be rounded down to 21.9 and if the third applicable entry is exactly 11.15, this would be rounded up to 11.2, and so on.

(4) rounding to the nearest even number (statistical rounding), e.g., if the entry is exactly 10.1245, this would be rounded to five significant digits as 10.124, but exactly 10.1255 would be rounded to 10.126.

(5) Where taxpayer uses a computer that follows a standardized rounding system, that system is also acceptable for this subsection.

(6) Any other rounding rule may be used, provided the Commissioner agrees that such rule would be reasonable and proper.

(e) The taxpayer shall not change its rounding rules without securing the consent of the Commissioner, except that if the taxpayer's rounding rules are determined by a computer system, then a change from one computer system or one computer service to another where the rounding rule is not readily determinable by the taxpayer, or a change from a manual system to a computer system, or vice-versa, shall not require the consent of the Commissioner.

5. As an illustration of the use of iteration, Tan Company elects to iterate once, using the median. For zero lag, the median value (excluding the value for the first year of issuance, i.e., 30) is 33.487, which will be found in Illustrative Exhibit 6.5a on the line for issuance year 1965. For one year lag, the median value is 38.2709 (including the first year of issuance). For a lag of two years, the median is conventionally determined as midway between the two middle terms or 10.5390 (1/2 of (10.5245 + 10.5436)). The complete set of medians to six significant digits is shown in the table below:

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.11 Illustrative use of sample data.

1. After several years of experience, Tan Company decides to use a sample (see Section 5, above) to obtain better estimates of its redemption pattern during a survey year. As a result of the sample investigation Tan Company discovers that its redemption pattern during the survey year is as follows:

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  Illustrative Exhibit 6.4b.--Tan Trading Stamp Company: Cumulative

1. Where redemption is limited to a specified period or otherwise restricted as to date of redemption, no allowance may be made for redemption after such specified date. (See subsection .081(a) for an illustration of the effect of this restriction.)

2. If the preceding restriction is later withdrawn by the taxpayer and such stamps are, in fact, redeemable, then an allowance may be made for such post-expiration date redemption, provided the Commissioner concurs with the taxpayer's method of estimating such allowance. For example: Corporation X encloses a coupon in each package of cigarettes sold but initially limited redemptions to a three year period. During the fourth year, Corporation X discovered that taxpayers presented expired coupons for redemption along with more recent coupons. Corporation X reviewed its policy in this regard and decided to honor such coupons without regard to expiration date and so informed its customers. Further, Corporation X was able to establish to the satisfaction of the Commissioner that redemptions of such expired coupons were about half of the rate that would otherwise be appropriate for a coupon four or more years after issue date. In this case, Corporation X would be allowed to project such redemptions of expired coupons at one-half the normal rates.

Section 7. Actuarial, Statistical And Other Mathematical Methods

The taxpayer may use any actuarial, statistical or other mathematical method, provided that it can demonstrate to the satisfaction of the Commissioner that its method is sound and will produce an acceptable measure of the volume of stamps to be redeemed by the taxpayer after the close of any taxable year.

Sec. 8. Appropriateness of Method

The taxpayer is required to choose a method that is appropriate to his experience and circumstances. If the District Director is not satisfied that the taxpayer's method is appropriate or that the results obtained are reasonably accurate and reliable considering all the circumstances, the taxpayer shall recompute its estimate of the volume of stamps to be redeemed at the end of any taxable year, or make appropriate adjustments to its original computations in a manner satisfactory to the District Director. Situations in which such changes may be necessary are indicated below.

.01 The ratio method, as explained in Section 4, above, can be expected to yield appropriate results, except where the taxpayer's volume of stamps issued (or redeemed) fluctuates erratically from year to year. For example, in each of the situations described below, the District Director may find it necessary for the taxpayer to recompute its estimate using the synthetic method described in Section 6, above.

1. Unusual decrease in volume of stamps issued. If for any taxable year in the last five, an unusual decrease occurs in the volume of stamps issued while redemptions remain constant or continue to increase, the volume of stamps redeemed during the year may substantially exceed the stamps issued during that year. Under these circumstances the ratio method may provide erroneous estimates of the volume of stamps to be redeemed. For example, Taxpayer A had the following experience:

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2. Unusual increase in the volume of stamps issued. A sudden, substantial increase in the volume of stamps issued may make the ratio method unreliable. For example, Taxpayer B had the following experience:

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3. Wide fluctuations in volume of stamps issued. If the taxpayer's volume of stamps issued shows both substantial increases and substantial decreases (as opposed to normal growth over several years followed by a leveling off of volume for several years and then a gradual decline), the ratio method may be unreliable. For example, Taxpayer C had the following experience:

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.02 Sampling method. While properly designed samples, carefully executed in strict conformance to the sample design, can be relied upon to produce valid redemption information for the year actually investigated, prior experience and results of similar surveys for this taxpayer or for similar taxpayers may provide a basis for modification or rejection of sample data.

1. Internal evidence.

(a) For most taxpayers the bulk of the redemptions during the survey year will have been issued during the survey year or the preceding year. If the estimated redemptions for either of these years (expressed as a percentage of the stamps issued during the year) is more than double the percentage for the other year, the taxpayer should be prepared to substantiate the validity of his result. For example, Taxpayer D used a sample in 1972 with the following results (in units of X pads):

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(b) The third year should be about one-fourth of the average value for the first two years. For example, Taxpayer D found the third year to be about 10%. A value of only 5% would have been questionable. If the value had exceeded 20%, additional supporting evidence may be desirable.

(c) The fourth and subsequent years should bear a reasonable relationship to the third year. In general it would be expected that for redemptions during the survey year, the percentages related to earlier issuance years would continue to decrease as the issuance years become more remote. Taxpayer E found that for these earlier issuance years the percentages were 5, 2, 0.5, 0.2, and so on. These results were reasonable. On the other hand, Taxpayer F discovered that its redemptions during the survey year were distributed as percentages of each of several consecutively more remote issuance years as follows: 1, 1, 1, 2, 1. Further inquiry made it apparent that the survey plan had not been properly executed and as a consequence the taxpayer found it necessary to modify or reject the sample data and used the synthetic method described in Section 6, above.

2. Conflicting results for two or more survey years. Where two or more survey years apparently yield contradictory results, further evidence may be required to resolve the problem. For example, Taxpayer G found its pattern to be the following percentages for 1972 and 1973 survey years:

 PERCENT REDEMPTION BY YEARS OF LAG FOR 1972 AND 1973 SURVEY YEARS

.03 Synthetic method. The synthetic method starts with the assumption that an approximate redemption pattern is known (e.g., from a sample survey of a later year or of a similar taxpayer) or may be described by any other pattern permitted by subsection 6.02, above. This Rev. Proc. provides latitude to make suitable modifications in the pattern as required to discover a plausible pattern that is appropriate to the taxpayer's own experience. These modifications are illustrated by the following examples:

1. Taxpayer H used the pattern described in subsection 6.022, above, and found that for one or more issuance years the cumulative redemptions exceeded 100%. Since there seemed to be no physical explanation for excessive redemption of such issuance year, Taxpayer H used the iterative method described in subsection 6.10, above. As a result, it found that the following pattern provided a more plausible redemption experience: 30%, 50%, 6%, 4%, and 2%. Alternatively, the District Director may find it necessary for the taxpayer to use a more appropriate initial redemption pattern.

2. Taxpayer I used a sample survey to determine its redemption pattern for a later year and found that when it tested its results against earlier year redemptions and issuances, using the synthetic method of Sec. 6, that for one or more years the cumlative redemptions exceeded 100%. Since there seemed to be no physical explanation for such excessive redemption, Taxpayer I secured the services of an authority on sampling methods who recommended changes in the sample design for subsequent years and suggested appropriate modifications in the sample results for the first study. The modified pattern was found to be consistent with Taxpayer I's accounting data as to the annual volume of stamps issued and redeemed since the inception of the business.

3. Taxpayer J considered that it was similar to Taxpayer K and made use of a redemption pattern that had been found suitable for Taxpayer K. Upon investigation, the District Director concluded that the similarity between Taxpayer J and Taxpayer K was limited to factors unrelated to redemption experience. The District Director determined that (1) the initial redemption pattern used by Taxpayer J was inappropriate to its accounting data as to the annual volume of stamps issued and redeemed and (2) a modified initial redemption pattern was, in fact, appropriate to Taxpayer J's accounting data.

1 The references to section 1.451-4 of the Income Tax Regulations are to the proposed regulations under this section published in the Federal Register on May 6, 1972 (37 F.R. 9287-89).