a test of the uniformity hypothesis

A Test of There is a large body of

ROBERT R. STERLING

the Uniformity Hypothesis literature on both sides of the debate over uniformity

versus flexibility. An entire issue, for example, of Law and Contemporary Prob- l e m was devoted to the subject.’ Although the opinions of the authors who write on this subject are varied, there is one recurrent theme presented by those who favour uniformity, namely,

1. dBerent methods or principles result in different accounting figures on the financial statements,

2. these different figures for like items are undesirable, 3. therefore, the methods or principles should be standardized or made uniform. The reason why different figures for like items are undesirable has not always

been explicit. There seems to have been a shift in emphasis from mere uniformity to comparability of the results of uniform practices.

One significant change in attitude took place almost imperceptibly. The arguments for a code of accounting principles changed between the first and second ‘boom’ in interest in statements of accounting principles. This change was not one that can be pinpointed to specific articles or even to a specific brief period (rather, a reader proceeding through the literature becomes increasingly conscious of it), but by the mid-’fifties accountants were talking about comparability of accounting statements rather than uniformity of accounting principles. The writers of the ’thirties had been vague about why ‘uniformity’ of accounting principles was desirable and were often wont to defend or condemn uniformity per se. In the post-war period, accountants were quite specific in identifying comparability of statements as the major factor requiring standardized principles, terminology, methods, etc.2

The present view therefore seems to be that different figures for like items are undesirable because they vitiate interfirm comparisons.

Although it is not often stated explicitly, one gets the clear impression that if the accounting principles or methods were uniform then the accounting figures for

1 . See also Reed K. Storey, The Search for Accounting Principles, AICPA, New York 1964, for further evidence of the amount of concern over this subject. He indicates that concern over uniformity, although waxing and waning, has preoccupied accountants for over 30 years. In one place he describes the problem as ‘a superabundance of accepted alternative practices’, p. 32. A request to Arthur Andersen & Co. for their file on this subject brought references to about 750 books and articles which were indexed under ‘Need for principles producing comparability’ and related titles. For a representative cross-section of this literature see the works cited by Storey and the articles in Law and Contemporary Problems, Autumn 1965. 2. Storey, Search, p. 38.

ROBERT R. STERLING is Professor of Business Administration in the University of Kansas. The author acknowledges the helpful comment and criticism of Richard Pollay and Raymond Radosevich.

37

A B A C U S

like items would be the same. For example, Bows3 calculates the different income and asset figures that could be presented by contrasting straight-lime with accelerated depreciation, lifo with fifo, etc. He deplores this situation and pleads for uniformity of method, presumably because uniformity of method would yield identical figures for identical situations.

A problem that has received little or no attention by those who favour uniformity is that the variation in accounting principles or methods is not the only cause of variation in the figures that appear on accounting reports. The situation is clearest in regard to depreciable assets.

The book value of a depreciable asset (and the related depreciation expense) is a function of three factors-capitalized cost (i.e., invoice price plus or minus adjustments for discounts, freight, etc.), life and salvage value. Obviously book values will vary if the estimates of those factors vary, i.e., if two accountants in different firms were to estimate merent lives for an identical asset, then different book values would be reported. In addition, the book value will vary as the functional form in which the factors are related varies. This functional form is the ‘depreciation method‘, and the ‘uniformity problem’ is that different methods are used for identical assets.

Thus, there are two sources of variation-ctifferent estimates of the facrurs and different methods of depreciation. The purpose of the research presented in this article was to test the variation in book values and the sources of that variation in respect of one depreciable asset. Hypotheses

one of the following ways: One might frame the uniformity hypothesis in regard to depreciable assets in

A. If the method of depreciation were standardized then identical book values would be reported for identical assets.

B. If the method of depreciation were standardized then the variations in reported book values would be negligible or immaterial.

C. The major cause of variations in reported book values for identical assets is that different depreciation methods are used.

The Study

follows: A questionnaire was designed in which a depreciable asset was described as

A CPA purchased a ten-key Monroe Printing Calculator on September 1, 1965. The calculator had a price tag of $900 but it was agreed that it could be bought for $100 down and $100 per month for seven months for a total of $800. The installment contract was accepted and no cash price was determined.

This was the only asset that the accountant owned. He rented a furnished office and bought supplies in small quantities.

The questionnaire was mailed to 500 randomly selected CPAs in the United States and 134 provided usable responses. The respondents were asked to supply information on the depreciation method, capitalized cost, life and salvage value 3. Albert J, Bows, ‘The Urgent need for Accounting Reforms’, N.A.A. Bulletin, September 1960, p. 44.

38

A T E S T O F T H E U N I F O R M I T Y H Y P O T H E S I S

that they would use if they were accounting for this asset.4 The Results

Although there are several other acceptable depreciation methods, the respondents listed only the three that are most commonly used: 62%, 31%, and 7% selected straight-line, double-declining balance and sum of the year’s digits, respectively. The distribution of the factor estimates for all respondents is shown in Table I.

In response to another question some respondents indicated that an immediate write-off of the expenditure was an acceptable procedure. In effect they would have assigned a zero life to this asset. However, in answer to the direct question, What life would you use if you were accounting for this asset? there were no zeros given. Thus, there is an ambiguity in the lower end of the range of lives that would or could be used in accounting for this asset. Also at the upper end of the life range there were some non-specilk responses that could have been interpreted as an estimate of more than 20 years. It was decided that only sgecific figures given in response to the direct question would be used in these and the following calculations. TABLE I

Distribution Characteristics of the Factor Estimates for All Respondents Standard

High Low Mean deviation Capitalized cost 900 73 1 800 15.10 Salvage value 200 0 44 44.50 Life 20 3 8 2.24

Table I1 shows the book values that could have been obtained had the different depreciation methods been applied to the mean factor estimates.

TABLE I1 Variation in Book Values Due t o Different Depreciation Methods

with the Factor Estimates Held Constant a t their Mean Values

Straight- year’s declining Standard Year line digits balance Mean Range deviation

1 706 632 600 646 106 44.17 2 61 1 485 450 515 161 69.14 3 517 359 338 404 178 79.80 4 422 254 253 310 169 79.41 5 328 170 190 229 158 70.04 6 233 1 07 142 107 126 53.06 7 139 65 107 103 73 30.10 8 44 44 0 29 44 20.74

4. They were also asked to supply information on the minimum and maximum lives, salvage values and capitalized costs which they would ‘certify to’. That is, two types of questions were asked: (1) What life (salvage value, capitalized cost) would you use if you were accounting for this asset? (2) What minimum and maximum life (salvage value, capitalized cost) would you certify to if you were auditing this firm? The data used in this study were taken from Type (1) questions. Had the minimum and maximum figures from Type (2) questions been used the variations in factor estimates would have been larger. The data from Type ( 2 ) questions were used to test the verifiability of book values. See Robert R. Sterling and Raymond Radosevich, ‘A Valuation Experiment’, Journal of Accounting Research (Spring 1969) for the results of that test.

39

Sum of the Double-

A B A C U S

Table I11 shows the book values that could have been obtained had the depreciation method been held constant and the factors allowed to vary. In making the calculations in Table 111, all book values were calculated on the basis of an $800 capitalized cost. There were problems in handling the contents of the responses. First, it was impossible to determine exactly how the respondents would have treated the difference between the figure they set forth and the $800 outlay. Presumably they would have treated the difference as an income item. If so, the procedure used has the effect of understating the possible variations in total assets and expenses, as well as the possible variation in the particular asset. Second, one would expect, other things being equal, that the life and salvage value would vary inversely-the shorter the life estimate, the higher the salvage value estimate-but this was not the case. The life and salvage value estimates had a Pearson Product Moment correlation coefficient of -.149 which is not significantly different from zero at a .05 confidence level. Thus, the idea of calculating the possible variations by associating the highest salvage with the shortest life and the lowest salvage with the longest life was rejected. Instead, these two factors were taken in pairs as they were found on the responses.

Third, there were no significant differences in the factor estimates of the respondents grouped by d8erent methods. That is, those who selected straight- l i e had about the same pattern of factor estimates as those who selected an accelerated method. Although differences in the number of respondents who selected each method made it difficult to be certain, it appears that factor estimates are independent of depreciation method selection. By a Kolmogorov-Smirnov test the factor estimates could be said to come from the same population at a .30 confidence level. In the author’s opinion the theoretical argument for independence is more important. In accounting theory one is supposed to select the best depreciation method and that selection has nothing to do with estimating the life of the asset. Critics of an earlier draft of this paper have suggested that the practising accountant may have a specific depreciation figure or pattern of figures in mind and then he selects the method and factors that will yield that figure or pattern of figures. Under this argument the factor estimates are not independent of the selected method. If this is the case then the depreciation calculation is redundant. That is, if it is possible to estimate directly the depreciation expense or book value then the estimation of the factors and the calculation is a ritual. It would be much simpler just to record the direct estimate. Nevertheless, the independence hypothesis is an interesting one and it should be tested more rigorously than the data of this study allow.

For these reasons, the entire sample of factor estimates was used in calculating the book values for each of the depreciation methods in Table 111.

40


Year 1 2 3 4 5 6 7 8

Year 1 2 3 4 5 6 7 8

Year 1 2 3 4 5 6 7 8

TABLE I11 Variations in Book Values Due to Differences

in Factor Estimate with the Depreciation Method Held Constant

(Assuming independence of method selection and factor estimates) A. Straight-line (n = 134)

High L O W Mean Range 760 720 680 640 600 560 520 480

High 720 648 583 524 472 425 383 343

High 724 65 1 583 518 457 400 347 297

550 704 210 300 613 320 50 523 630 0 434 640 0 347 600 0 27 1 560 0 207 520 0 147 480

B. Double-declining balance (n = 134) Low Mean Range 267 60 1 453

89 46 1 559 50 357 533 0 278 524 0 218 472 0 165 425 0 127 383 0 93 343

C. Sum of year’s digits (n = 134) Low Mean Range 425 634 299 175 497 476 50 381 533 0 286 518 0 21 1 457 0 150 400 0 108 347 0 78 297

Standard deviation 33.39 65.94 98.90

125.77 148.41 151.17 136.56 125.28

Standard deviation 69.38 95.78

101.85 100.41 95.01 94.72 84.33 78.85


102.35 107.32 100.03 93.59 77.92 63.88

Table N shows the book values calculated on the basis of the specific responses by each respondent. That is, the data were taken from the questionnaires in quadruples-method, capitalized cost, salvage value and life-and there was no interchange by method. Table IV could be interpreted as the actual range of book values that would have been reported by the respondents as opposed to the possible range of book values presented in Table 111. The small number of respondents who selected sum of year’s digits makes Table IV difficult to interpret and this is the reason for presenting the two tables calculated under different assumptions.

A comparison of Table I1 with Tables I11 and IV leads to a rejection of hypothesis A. Book values of identical assets are not necessarily identical even if the depreciation method is held constant. Acceptance or rejection of hypothesis B depends upon what one means by ‘materiality’. An attempt was made to make the respondents think that the book value of this asset was likely to be material

41

A B A C U S

Year 1

3 4 5 6 7 8

Year I 2 3 4 5 6 7 8

Year 1 2 3 4 5 6 7 8

7 I

TABLE IV Variations in Book Values Due to Differences in Factor Estimates

(Assuming factor estimates are not independent of method selection)

High 819 738 688 650 612 575 538 500

High 68 1 590 512 443 3 84 333 289 250

High 66 1 549 449 362 287 225 175 137

B.

A. Straight-line (n = 83) Low Mean Range 550 705 269 300 608 438 50 512 638 0 419 650 0 3 28 612 0 26 1 575

0 140 500 0 20 1 538

Double-declining balance (n = 42) Low Mean Range 480 616 20 1 288 477 302 173 370 339 104 289 339

0 222 384 0 173 333 0 135 289 0 83 250

Low Mean Range 533 612 128 320 456 229 160 3 26 289 53 222 309 0 144 287 0 92 225 0 58 175 0 37 137

C. Sum of year’s digits (n = 9)


108.93 131.48 149.63 130.39 106.34 89.89

Standard deviation 42.48 61.81 67.95 67.04 72.47 66.35 59.59 71.95


102.82 108.63 101.30 82.65 65.27 53.94

by indicating that this was the only asset owned by the firm. Nonetheless, the variations may still be considered immaterial if the revenue or cash balance were large. However, if one views materiality as the variations in book value relative to the mean book value, then hypothesis B would be rejected.

Hypothesis C is more difficult. If one accepts the ranges of book values as an appropriate test, then hypothesis C would be rejected since the ranges in Table I11 and IV are greater in all years than the ranges in Table 11. If one accepts the standard deviation as an appropriate test, similar conclusions would be drawn. The standard deviations in Table 11, Part A are greater than those in Table 11 in six of the eight years. In Parts B and C of Table I11 the standard deviations are greater in all years than those in Table IT. Comparison of Parts A and C of Table IV with Table I1 yields similar conclusions. Part B of Table IV does not permit the conclusion since the standard deviations in the first four years due to factor differences are less than the standard deviations due to different methods. However, it does seem safe to say that the differences in factor estimates causes

42


at least as much variation in book values as do the differences in methods, and therefore hypothesis C should be rejected.

The Importance of the Life Estimate Analysing the factor estimates individually reveals that the life estimate is the

most important factor in that it causes more variation in book values than the other factors. This is due to the functional form of the depreciation equations and the size of the salvage value relative to the capitalized cost. The salvage value estimates varied most, having a coefficient of variation of 101%.5 The coefficient of variation for life estimates was much smaller--28%-but it caused much more variation in book values. This can be illustrated by the same method used to calculate standard cost deviations. Using the maximum and minimum lives and salvage values shown in Table I and assuming a straight-lime method, the first year’s depreciation expense can be analysed as follows:

Capitalized Salvage First Life cost value depreciation expense

3 $800 $200 $200.00 20 800 0 40.00

Difference 17 $ 0 $200 $160.00

Depreciation variance due to difference in life estimates $ ( 170.00) Depreciation variance due to difference in salvage value estimates 66.66 Depreciation variance due to the joint effect (56.66)

Net $ 160.00

- - -

- - -

Of course, after three years the difference in depreciation expense drops to $40 but that difference is due entirely to the difference in life estimates. Under double- declining balance the first year depreciation expense is even greater ($453.33) and that difference is also due entirely to the difference in life estimates. Thus. the factor that caused the greatest variation in the book values was the difference in life estimates. The second greatest cause was the differences in salvage value estimates and the factor that caused minimal variation was the capitalized cost.

Limitations of the Results It would not be proper to attempt to generalize these findings. It may be that

other kinds of assets would yield smaller differences in factor estimates. These differences might be small enough to make the variations in accounting figures due to factor estimates significantly less than the variations due to depreciation methods. Whether or not this is the case will have to await further research. However, it should be noted that the asset selected for this study is one that almost all accounting firms own and therefore one with which all respondents are likely to be familiar. One would expect that variations in factor estimates 5. Capitalized cost varied least with a coefficient of variation of less than 2%. This had little effect on book values and was another reason for making all calculations on the basis of $800 in Table 111.

43

A B A C U S

concerning this asset would be less than variations concerning an asset with which the accountants were less familiar. To put it negatively: had a manufacturing machine been selected it is likely that extreme estimates would have been received from respondents who had specialized in banking or retailing. Thus, one might reasonably assume that a different asset would have resulted in greater differences in factor estimates6

There are, of course, many other limitations on the generality of the results of this test even if the above supposition is correct. For example, this test concerned only one asset. Perhaps there is an offsetting effect in the life estimates of multiple assets. If so, the different depreciation methods may cause more variation in total assets than the different life estimates. Another obvious limitation is that this was a (singular) test of the uniformity hypothesis in regard to a depreciable asset. Tests of inventory variations, for example, are likely to reveal that the different methods contribute more to the variation than differences in the count. In short, the test reported is only one data point and many other tests must be conducted before any general conclusions can be drawn. This test was intended to suggest the existence of a problem; it was not intended to be a definitive test of the general problem of uniformity. Conclusions

If the above results are representative, the implications for accounting research are vast. Taking the amount of literature devoted to the subject as evidence, it appears that accountants think that the existence of different depreciation methods is a problem of major proportions and they do not recognize that differences in factor estimates exist or they think that such differences are negligible. If the objective is to represent identical items with identical book values, then the results of this test would indicate that much more effort should be directed toward finding a method for estimating factors, particularly life, than toward eliminating different depreciation methods.

Another example of this same situation occurs in the tax allocation dispute. If one used these data to calculate the income effects of allocation and non- allocation relative to the income effect of different life estimates, the allocation effect would be miniscule relative to the life effect. However, the amount of literature devoted to the two subjects would lead one to believe that the exact opposite is true. If the objective is to make income statements more comparable, then narrowing life estimates is a much more pressing problem that the existence of different methods of treating taxes.

In short, accountants have been addressing themselves to only a partial cause of the variation in accounting figures. It appears that there would be less variation in accounting figures if the factor estimates were standardized than there would 6. Along the same lines one might expect that different kinds of accountants would have had different patterns of estimates. This was tested by grouping the respondents in various ways, e.g., public v. industrial accountants, members of national firms v. members of local firms, partners of firms v. their juniors. We were unable to discover any significant differences in factor estimates among the groups.

44


be if the methods or principles were made uniform. Thus, at least a portion of future research on uniformity or comparability should be directed toward narrowing the differences in factor estimates.

The Problem in Perspective Despite the fact that this test was concerned with one depreciable asset and

therefore the conclusions must be restricted to that asset, the problem of making factor estimates or measurements can be generalized. Accounting values can be generally characterized as a function of some underlying factors. The value of inventory is a function of the quantity of units purchased, the quantity of cash expended, the date of purchase, and the quantity sold. The book value of a depreciable (or depletable) asset is a function of the quantity of service life or output purchased, the quantity of cash expended, the date of purchase, the present date or the quantity of output used. And so forth for each asset or expense. Thus, in general an accounting value, Vi, is a function of some specific quantity, qi.

( 1 ) v1 = f(q1, q2, * *

Some people argue that a particular value ought to be calculated in a different way. (2) vj = g(q1, q2, * - 1

Thus, two different accountants or two different firms could report either Vi or Vj as a description of the same object or event. This is the uniformity problem. In addition, two different accountants or two different firms could estimate different 9’s.

We now have four possible accounting values-Vi, Vj, V;, V,’-that could be used to describe the same object or event.

From a structural point of view it is obvious that possible differences in the q’s are just as important as the differences in the functions. In this one test the differences in the q’s are also equally as important from an empirical point of view. That is, in the case tested the range from V,’ to Vi or from V,’ to Vj was greater than the range from V, to Vj. Whether or not the differences in the q’s are empirically important in other cases will have to await further research. Regardless of the empirical importance of the differences in the q’s, they will remain quite an important problem from a structural point of view. Note that the functional form is a method of calculating a figure but the determination of the q’s is an empirical operation-either an estimation or a measurement. Now the calculation of a magnitude is quite a different process from the measurement of a magnitude. Among other things the arguments concerning the two take different forms and the resolution of the arguments require

g(ql, q2, . . . ) is the ‘best method‘ is different in kind from the argument over whether qi or 9,’ is ‘more accurate’.

Note also that highlighting the fact that factor estimates are required may be helpful in analysing some of the current disputes. For example, it is now considered to be theoretically correct to capitalize only the discounted value of the

45

( 3 ) VI’ = f(q1’, qz’, . . - )

different operations. That is, the argument over whether f(ql, q2, . . . or

A B A C U S

payments on an instalment contract and treat the discount as interest expense. Finney and Miller7 present that argument but conclude that ‘ . . . this is rarely done-partly because of the necessity of arbitrarily deciding on an interest rate’. This test confirms the rarity of the procedures and the debriefing of a sub-set of the respondents to the pre-test confirms the reasons given by Finney and Miller. The respondents did not discount because they said they did not know what interest rate to use. The interesting point is to compare the difficulty of determining what interest rate to use with difficulty of determining the life or salvage value of the asset. It is not immediately apparent that the life or salvage value is any less arbitrary or difficult to determine than the interest rate. Yet all of the respondents were willing to estimate a life and salvage value while less than 2% indicated that they would discount and less than 3% specified a rate. As one other example, one might want to compare the difficulty of determining the life or salvage value of the asset with the difficulty of determining its replacement cost or current cash equivalent. It is not immediately apparent that the life and, particularly, the salvage value are that much easier to determine.

In summary, the process of accounting for something may be broken down into three parts :

(1) a particular functional form is selected from a set of generally accepted

(2) the factors that go into the selected function are determined, (3) the accounting figure is calculated.

functional forms,

A good deal of effort has been expended on Part ( l ) , and Part (2) has been neglected. From a structural, and perhaps from an empirical, point of view Part (2) is as important as Part (1). Arguments about Part (1) are different in kind from arguments about Part (2) and they will require different kinds of research to resolve them. Comparing the determinations required in Part (2) to some suggested determinations raises some questions about the justifications given in the literature.

Critics of an earlier draft of this paper have objected to the above general- ization of the problem. Some of them objected to the specific test. The grounds for objection were that it was not the accountant’s duty to determine the factors. Instead it was alleged that this was management’s duty and therefore the questionnaire should have been mailed to managers, not accountants. The argument presented above, that the familiarity of the asset was likely to lessen the variation in factor estimates, was countered on similar grounds. It was alleged that, if a completely unfamiliar asset had been selected for the test, then the variation in life estimates would have been small because the respondents would have gone to the income tax guidelines and used whatever life they found there. Perhaps the critics are correct. It may be that it is not the accountant’s duty to determine the factors, However, the consequences of this view are most disturbing. If one

7. H. A. Finney and Herbert E. Miller, Principles of Accounting Intermediate, Englewood Cliffs, N.J. 1958, p. 335.

46


accepts the above three-part view of the process of accounting then it will be noted that Part (1) is supposed to be performed by management because the ‘ . . . responsibility for financial statements of corporations (a) rests primarily on management, who has the duty to employ [select] methods of accounting best suited to the needs and purposes of the corporation, . . . ’.8 The critics are claim- ing that Part (2) also ought to be performed by management or by the taxing authority. This leaves only Part (3)-the calculation-to be performed by the accountant.

Perhaps these considerations are the most important findings of this simple little test. It appears that a significant number of accountants view accounting as exclusively a calculational process. The literature lends some support to this view. In the textbooks the students are taught how to calculate depreciation, work-in- process, etc., but they are not taught how to determine the service life or the number of equivalent units. Journals are full of discussions about which way one ought to calculate depreciation, cost of goods sold, etc., but seldom does one find a discussion of how one determines the salvage value or the number of units in the inventory. If this conjecture is true-that accounting is viewed as a calculational process with the factors supplied by somebody else-it would partially explain why some suggestions have become accepted accounting practices and others have not. It would also permit some predictions as to which suggestions will become accepted and which will not. For example, price-level adjusted historical costs will become an accepted accounting practice because one can calculate those figures and the index used for the calculation is supplied by somebody else. Non-cost valuation proposals will not become accepted accounting practices because one cannot normally calculate replacement costs or current cash equivalents.

This conjecture seems to fall under the more general point made by Alexander? Another very powerful factor operating on the development of accounting methods has been the attempt to reduce the accountant’s responsibility for the human judgments which must be made in passing from a consideration of the accounts to the conduct of business affairs. This attempted avoidance of responsibility has led accountants to set up two requirements for sound accounting that somewhat limit the choice of methods. These are the requirements of objectivity and conservatism. To the extent that accountants have achieved objectivity and conservatism they have transformed the measurement of income into a safer activity but one which yields a result that only partially achieves the end sought.

Calculation is a much safer activity than determination of the factors. To let management or the taxing authority make the determinations is a good way to avoid responsibility. However, if we continue to define the accounting process so as to make it safe and so as to avoid responsibility, we may define it so narrowly that it withers and dies. 8 . Paul Grady, Inventory of Generally Accepted Accounting Principles for Business Enter- prises, AICPA, New York 1965, p. 31. 9. Sidney S. Alexander, ‘Income Measurement in a Dynamic Economy’ in Five Monographs on Business Income, The Study Group on Business Income of the American Institute of Accountants, New York 1950, p. 2.

47

a test of the uniformity hypothesis

Documents