ABSTRACT AN APPLICATION OF A CURRENT MARKET VALUE ACCOUNTING MODEL BY James Charles McKeown In recent years accounting theorists have developed several models which include asset valuation rules using bases other than historical cost. As these models were develOped and discussed theoretically, disagreements arose concerning the applicability of these models to realistic situations. The settlement of these controversies can only be effected empirically. Unfortunately, this research is unlikely to originate with the practicing accountant, either internal or external. Therefore, these models must be implemented first by academic accountants who have a minimum of vested interest in maintaining the status quo and a maximum interest in improving the quality and utility of financial information. Prior research has already been performed concerning applicability of several of the models employing current cost of replacement as the basis for valuation of assets. Consequently, this study attempted to implement the model described by Raymond J. Chambers in Accounting, Evaluation, and Economic Behavior. This model basically values assets at their net realizable value and liabilities at discounted present value with residual equity being equal to total assets minus total liabilities. Income is then the change James Charles McKeown in residual equity (adjusted for changes in investment and general price level). A medium—sized road construction company was chosen as the subject company. The satisfactory application does not prove the general applicability of the model, but an unsatisfactory application would have provided very strong evidence of general impracticality because application of the model should be feasible for a company of this type if it is to be feasible for any type of firm. Two balance sheets and the intervening income state- ment were prepared in a form consistent with Chambers' model. Although all assets and liabilities were restated, the major test of the model came with the attempt to deter- mine the net realizable value of the plant assets. The primary measurement method for plant assets was multiple linear regression based upon auction prices. The standard error of estimate of the regression was compared to a dis— persion of the book values obtainable under application of alternative accounting methods for a particular asset. A further test was comparison of the diSpersions of measure- ments possible under generally accepted accounting princi— ples to the diSpersions of measurements determined at the direction of five independent measurers interpreting Chambers' model. These comparisons were aided by an index of accuracy developed in the appendix. The most difficult problem of the application related to the existence of a tax loss carryforward for the subject James Charles McKeown company. This type of problem was certainly not predicted by any of those who maintained that the model was imprac- tical. Most of these adverse predictors indicated the belief that the major problem would be the valuation of fixed assets. The results showed very clearly that measure- ments under the revised methods were more verifiable than the measurements under alternative methods acceptable under generally accepted accounting principles. All of the revised measurements showed acceptable diSpersions. The accuracy and verifiability of the measurements in the revised statements compared favorably with the measurements in the conventional statements and because of the marked difference in the amounts presented an informed reader of the revised statements would probably form a significantly different Opinion than he would if he had read the conven- tional statements. AN APPLICATION OF A CURRENT MARKET VALUE ACCOUNTING MODEL BY James Charles McKeown A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Accounting and Financial Administration 1969 Q. (Ia/SF! Z H45r70 ACKNOWLEDGMENTS The author is indebted to his committee, Professors R. F. Salmonson, Herbert E. Miller and Jan Kmenta for their guidance during both the research and writing of this thesis. Appreciation is also expressed for support from the Ford Foundation. The facts, Opinions, and conclusions presented herein are those of the author, not the Ford Foundation. ii TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . CHAPTER I. II. III. IV. INTRODUCTION . . . . . . . . The Model .. . . . . . . . . . MethOds O O o O O O O 0 o O O 0 THE BALANCE SHEET . . . Short-term Assets . . . . . . Cash . . . . . . . . . . Receivables . . Marketable Securities . Inventories . . . . . . Prepaid EXpenses . . . . Liabilities . . . . . Current Liabilities . . Notes Payable . . . . . .. Summary . . . . . . . . . . . PLANT ASSETS . . . . . . . Valuation by Regression . . Valuation by Reference to Published Market Values . . Valuation by Use of Indexed Calculations . . . . . . . Treatment of Tax Carryforwards The Residual Equity Section . The Full Revised Balance Sheet THE INCOME STATEMENT . . . . . Revenues O O O O O O O O 0 O 0 Costs . . . . . . . . . . . . Depreciation and Obsolescence The Complete Income Statement iii Page VI. iv DISPERSION OF DIFFERENT MEASURERS . Current Assets and Revenues . . . . Liabilities and Related Costs . . . Other Assets and Related Costs . . Machinery and Equipment . . . Additional Net Realizable Value Due to Tax Carryforwards . . Residual Equity and the Remainder of the Income Statement . . . . COST AND CONCLUSIONS . . . . . . . Cost 0 O O O O O O O O O O O O O 0 Conclusions . . . . . . . . . . . . BIBLIOGRAPHY . . . . . . . . . . . . . . APPENDIX. ACCURACY AND VERIFIABILITY . . Groups of Items . . . . . . . . . . 15. l6. 17. 18. 19. LIST OF TABLES Current Liability Summary . Notes Payable Summary . Partial Revised Balance Sheets Summary of Valuation by Regression Summary of Valuation by Regression Analysis of Unsuccessful Items . Direct Valuation by Reference to Published Sources Summary of Valuation by Indexed Calculations . . Summary of Valuation of Plant Assets Estimation of Accuracy of ANRV . Beginning. Ending . Conventional and Revised Balance Sheets Depreciation and Obsolescence . Comparison of Income Statements Estimation of DiSpersion of Balance Sheet Figures . Results of Measurement by Five Measurers Valuation by Regression (by Different Measurers) Summary of Valuation of Plant Assets by Five Measurers Depreciation and Obsolescence by Five Measurers Cost of Conversion V Page 26 33 35 A0 41 1+7 53 56 58 68 71 85 87 89 92 98 102 106 112 CHAPTER I INTRODUCTION One of the major criticisms of accountants in recent years has been their failure to present financial statements which have current relevance. This is somewhat puzzling since this deficiency was recognized more than fifty years ago by such writers as Montgomery, who believed that users "have the right to believe that the values stated are real values as of the date of the balance sheet,"1 and Dickinson who stated that ”a balance sheet is required to show the true financial position...".2 In 1939 MacNeal devoted an entire book to the subject, calling then current statements misleading and arguing for statements based on current values.3 As a result of these and other similar comments, several individuals and groups have published theoretical descripticns 1Robert H. Montgomery, Auditing Theory and Practice (New York: The Ronald Press Company, 1913), p. 10H, cited by He; eth MacNeal, Truth in Accounting (New York): The Ronald Press Company, 19§9T:‘pf'26. 2Arthur L. Dickinson, Accountinngractice and Procedure (New York: The Ronald Press Company, 191A), p. 93, cited by MacNeal,.gp. cit., pp. 27-28. 3 MacNeal, Truth in.Accounting. of accounting systems based either partly or wholly on some form of current value.LI This, however, has not completely solved the problem since little or no work has been done to investigate the feasibility and/or practical implications of these models. The need for attempts at application of these systems is shown by the following comments expressing doubt or dis- agreement with those who doubt: It is my opinion that realistic market prices are not nearly so widespread ag would be necessary if your theory were to be adopted. It appears to me, therefore, that either there are no markets for most of these goods [accounts receivable, raw materials, work in process, finished goods, and plant and equipment] or the firm is active on the ”Four of the best— —known, recent efforts: Edgar 0. Edwards and Philip W. Bell, The Theory and Measurement of Business Income (Berkeley. University of California Press, 1961); Robert T. Sprouse and Maurice Moonitz, "A Tentative Set of Broad Accounting Principles for Business Enterprises," Accounting Research Study Number 1 (New York: American In- stitute of Certified Public Accountants, 1962), pp. 1—59; Committee to Prepare a Statement of Basic Accounting Theory, A Statement of Basic Accountinngheory (Evanston: American Accounting Association, 1966), and Raymond J. Chambers, Ac- counting, Evaluation and Economic Behavior (Prentice- Hall, Inc. , 1966). 5Comments of William W. Werntz, on Robert T. Sprouse and Maurice Moonitz, "A Tentative Set of Broad Accounting Prin- ciples for Business Enterprises," Accountinngesearch Study Number 3 (New York: American Institute of Certified Public Accountants, 1962), p. 81. buying side of the market and really has no contact with the selling side.6 This must be a very limited per cent of-the total assets we are talking about [that have readily deter- minable market values]. It must be a fraction of one. per cent. I like market-value. I disagree with that one per cent. If industry would look around, they would discover a surprising-number of things for which an« accurate.market value could be determined. The problems areas [in determining current vglues for assets] cover a very minor part of the field. If Ross could really be convincing on this point [that the areas-are minor], it would go a long way to? ward persuading those.of us who can see the merit of current value statements, but doubt whether they can be achieved as easily as he [Ross] suggests. 0' My preference for current cost of replacement over sales prices is based in large measure on the belief the former is more readily determinable and more objective.11 6Discussion by Carl L. Nelson, on R. J. Chambers, "The Foundations of Financial Accounting," Berkeley Sympgsium 93 the Foundations g£_Financial Accounting (Berkeley, School of Business Administration, University of California, Berkeley, 1967), Pp. 51—52} 7TheMeasurement of Property, Plant, and Equipment in Financial Statements (Beston: Harvard University, Graduate School of Business Administration, 196A), p. 51. 81b1d. 9Howard I. Ross, "The Pursuit of Usefulness," Berkeley Symposium on the Foundations of Financial Accounting, p. . loDiscussion'byPaul Kircher, on Howard I. Ross, op, cit., p. 97. 11Discussion by Charles T. Zlatkovich, on R. J. Chambers, cit., p. “9- *3 v: The validity of these statements can only be determined by massive empirical.research. This call is sounded clearly by Zlatkovich as he says that the theoretical defeat, on paper, of_historical cost "has amounted to little more than academic exercise".12 Ross also sees this need as demonstrated by onecfi' his many calls:fin‘research: "Plenty of ideas have been batted around. It is time to find out which of them would prove serviceable in practice."13 Another important benefit from more innovation would be discovery of "the real problems of statement presentation instead of simply listening to ac- countants pontificating on what they suppose the problems might be."1" There are several reasons for the lack of innovation aimed at improvement of the relevance of published-financial statements. The public, investors, analysts and small credi- tors, do not have the direct power thatmanagement and large lenders have to demand more relevant statements. Without pressure, managements of corporations are unlikely to publish relevant statements since-there are.several reasons for mana— gers to shun statements based on current values: 1. The possibility, or even probability, of,a qualified audit opinion or objection by a regulatory agency to whom the 12Ibid., p. A8. 13Howard.I. Ross, The Elusive Art of Accounting (New York: The Ronald Press Company, 1955), p.-I3'2T_'w luIbid., p. 133. statements would be submitted. 2. Statements based on current values might increase the tax expense of the firm. 3. The expectation of additional expense required to prepare current-value statements. A. Fear of revealing information which will aid a competitor. 5. Better statements would mean that outsiders would be better able to judge the performance of managers.15 6. Many corporate managers may have motives which are in direct conflict with the objectives of current-value financial statements in the hands of owners and the general public. [Among these are:]...A vested interest in under- stated assets, thus reducing depreciation, overstating income or gain in the period of sale, as well as under- stating book value of investment for return on invest- ment computations [and manipulation of income through sales of particular assets (resulting in gain or 1088)]... may be a far more important influence on financial reports-than possible manipulation resulting from deliberfige errors in measuring current values of assets. 15HowardI. Ross, The Elusive Art of Accounting (New York; The Ronald Press Company, 1966), p. 198. 16Discussion by Paul E. Fertig, on Howard I. Ross, "The Pursuit of Usefulness," Berkelgy Symposium on the Foundationsgf Financial Accounting, pp. 92-9§. The author does not-intend to debate these points. They- are presented merely to point out the formidable barriers against initiation of the experimentation by corporate mana- gers. Corporate accountants have in large measure tended to concentrate on refining existing techniques rather than de— veloping basic new methods of presenting information.’ For these reasons the lead in determining the feasibility of the current—value—based models has fallen mainly to the academic accountant, who has-a minimum of vested interest in main- taining the status quo and a maximum interest in improving statement presentation. This study does not presume to deal conclusively and exhaustively with all of the opinions about practicality mentioned above. Instead the purpose is to attempt an application of the model proposed in R. J. Chambers' Account—' ing, Evaluation, and Economic Behavior toga medium-sized road construction company. If satisfactory, this application will not prove the general applicability of the model, but, if unsatisfactory, the attempt will provide a very strong evi— dence of general impracticality because the model should be feasible-for a company of this type if it is to be feasible for any-type of firm. In either case, the study will provide much needed evidence concerning the information available for the determination of market prices for various assets. The Model The Chambers model was chosen because it is based on market price. This approach has had the least amount of practical work17 and is favored by the author in preference to one using current cost of replacement as a basis for asset valuation. Chambers' definition of income is similar to that of J.R. Hicks: A man's income 35 BEES is the maximum amount which he can consume during a period and still expect to be as well off at the end of the period as he was at the beginning.18 Chambers' definition of income corresponds to the g5 post version of this definition. 19 "w:11 offn nes s" is deter ined 20 by the amount of capital held. Residual equity (capital) 17For examples of applications of replacement cost models, see Peter J. Dickerson, Business Income--A Critical Analysis (Berkeley: Institute of Business and Economic Re- search, University of California, Berkeley, 1965); and "Dis- closing Effects of Price-Level Changes," Appendix D in Accounting Research Study Number 6 (New York: American In— stitute of Certified Public Accountants, 1963), pp. 167—218. 18J. R. Hicks, Value and Capital (Oxford: Clarendon Press, 1946), p. 172. 19Raymond J. Chambers, Accounting, Evaluation and Economic Behavior, p. 116. 2OChambers accepts von Mises' definition of capital as "the sum of the money equivalent of all assets minus the sum of the money equivalent of all liabilities". Chambers, IE. cit., p. 114, citing Ludwig von Mises, Human Action ondon: William Hodge and Company,Itd.,19A97, p. ’262. is the sum of the monetary values of all assets minus the sum of the monetary values of all liabilities. Income is then the ending residual equity minus the beginning residual equity (adjusted for changes in capital investments anui general purchasing power).21 Assets are valued at current cash equivalent which is 22‘ This applies to all the realizable price from resale. assets except short—term inventories which are valued at the current cost of direct inputs.23‘ Liabilities are valued by. discounting the sum payable in the future using the rate of interest payable for the immediate use of the money necessary for immediate settlement.2u Methods The study began with restatement of two balance sheets into form consistent with Chambers' model. The income state— ment for the intervening year was then prepared based on the beginning and ending balance sheets. The date of preparation of revised statements was assumed to be two months after the ending balance sheet date. A comparison will be pre— sented between the revised statements and the original 21Chambers, op, cit., p. 122. 22Ibid., p. 10A, p. 92. 23Ibid., p. 265. 2uIbid., p. 107. statements, prepared according to generally accepted account- ing principles. The study will concentrate on determining the appli— cability of the model to this firm without specifically re— searching the usefulness of the data produced since the-need for a determination of feasibility is critical. Specifically, Chapter II will describe the adjustments needed to arrive at the revised balance sheet items other than» plant assets. Chapter III will describe the techniques used to value the plant assets. The conventional and revised balance sheets: will then be compared. The revised income statement will be developed and com— pared to the conventional statement in Chapter IV. Chapter V will compare the results obtained by the author with those obtained by following the instructions of- four_other persons familiar with the Chambers model. In Chapters III, IV, and V the major criterion for judgment of feasibility of restatement will be a comparison of the possible dispersion which could result from using different reasonable generally accepted accounting principles with the dispersion shown by the revised statements. The conclusiomswill be presented in Chapter VI. These will include estimates of the cost of conversion and the additional cost of maintaining the revised statements. CHAPTER II THE BALANCE SHEET Two revised balance sheets for X Company (the subject company) were prepared. The dates of these balance sheets are December 31, 1966 and December 31, 1967. The conver— sion process was performed with information which was available before March 1, 1968 since this would be the normal time of preparation of statements covering the calendar year 1967. As indicated in Chapter I, the Chambers balance sheet 1 reported most assets at realizable price. Liabilities are then reported "by discounting the sum payable in the future to a present sum using the rate of interest payable for the immediate use of the money necessary to enable 2 immediate settlement to be made." The difference be- tween the current cash equivalents of the assets and lia- bilities is then the current cash equivalent of the 3 residual equity. This chapter will report the valuation of the liabilities and the short-term assets.u lChambers, Accounting, Evaluation and Economic B3: havior, p. 104, p. 92. 21bid., p. 107. 3Ibid. “Short—term assets are the "cash already in hand, the short-term claims against debtors, the marketable securi— ties in possession, and the completed inventories of vendw ible products." Ibid., p. 191. 10 11 Short-term Assets The problem of determining the current cash equiva— lents of the short-term assets is merely a matter of appli~ cation of the principles deve10ped by Chambers with a few appr0priate assumptions. The conversions, assumptions and reasons therefore for the individual short-term assets will be explained below. Cash. No conversion necessary here. The current cash equivalent of cash held is the number of dollars held. Receivables. Short—term assets includes only the short- term claims against debtors,5 but the current discussion will apply to all receivables. The first problem of interpretation is that Chambers never defines "short-term." He implies a very short period when he says, "we may regard nominal amounts as adequate representation of the magnitude of short-term claims."6 This statement would indicate a period of a few months since at normal interest rates for a business of this size, the amount of distortion at three months is approaching two per cent. This interpretation would limit short-term receivables very severely; probably more severely than 5161a. 6Ibid., p. 196. 12 Chambers intended. Therefore, ”short-term" will be taken in the normal accounting sense (one year or the normal Operating cycle, whichever is longer). Under this assump- tion X Company has no long-term receivables since all receivables are tied to construction contracts and thus fall within the Operating cycle. The next problem is the determination of the discount rate. It is somewhat impractical to attempt to determine the rates of interest which apply to the borrowing of the money necessary for immediate settlement by the debtors. Thus, for practical reasons, the discount rate would be the effective interest rate on money borrowed by X Company. This appears to be the rate indicated theoretically also. The theoretical argument would be that discounting at the rate which X Company would have to pay would give the amount X Company could borrow at the balance sheet date and have the loan repaid entirely by the collections from the receivables (assuming that the amounts are received as predicted when the discounting calculation is per- formed).7 Early in 1967 X Company was granted a loan at 7For each collection of a eXpected mi periods from now the discounted present value at rate r per period is given by: a d i i (1) = (1+r) 1 Then the repayment amount L of a loan of amount d taken now to be repaid after mi periods with interest ra e of r will be given by: m i L1 = di(l+r) . (2) 13 a rate of 4.5% add-on. This is an effe tive rate of .626 per month or 7.7% per year. Early in 1968 a loan was being negotiated at the same rate. So the rate that was used for discounting of receivables was .6228 per cent compounded monthly. Having the amount and the discount rate, it was then only necessary to determine the due or eXpected date of receipt. This was not as simple as was implied by Chambersfi3 The method of payment of road construction contracts causes this difficulty. It is the practice to bid on a particular contract giving unit prices for all items in the contract. An estimate is made very two weeks on every job, to deter- mine the amount of work (number of units of each item in Substituting for di from (1) we get: a. m. 1,, = (——-1———) (1+r) 1 = m. (1+r) 1 L1 = a1 Thus, for each payment eXpected, the receipt of the pay- ment when expected will pay the principal and interest of a loan in the amount of the discounted present value (at balance sheet date) of the payment (as long as the inter- est rate on the loan and the rate used in discounting are equal). If this is true for each of N payments, we have the Conclusion stated in the text. 8"The amounts of obligation and their due dates being determinable,...." Ibid., p. 107. 11 the contract) completed to that point. Payment is then authorized for that amount less previous payment and a reserve to insure completion of the job by the contractor. Thus, at any point in time a certain amount is listed as receivable on a particular job, but this amount consists of the payment computed from the last biweekly estimate and the reserve held back from all eStimates. The per- centage held back is reduced at various stages of the con- tract, but the absolute amount of the reserve is not gen- erally reduced by a substantial amount until the contract is near completion. Even at completion a flat amount ($5,000 or $10,000) is held back until all details of the work are completed and the job is accepted by the buyer. This process can take from two weekstofour or five years. This problem was resolved by a first-in, first-out approach within jobs. This means that if $X was the total amount receivable from one job (including both the current esti- mate and the reserve amount), the first $X received or expected on that job in the next year were assumed to apply to the beginning balance. This applies to those jobs on which work was not completed and a terminal (flat amount) reserve had not been established. The terminal reserves were considered as expected at a time computed in the following way: All jobs com- pleted in the years 1961 through 1966 were filed accord- ing to time elapsed between completion of job and receipt of payment. Any job on which a terminal reserve had been 15 outstanding for n months was given an eXpected date of receipt computed from the jobs in the file which had re- serves outstanding more than n months.9 Using these dates for the construction receivables and the eXpected dates of receipt for the other receiv- ables, the amounts were discounted using a rate of in- terest of .6228 per cent per month compounded monthly. All amounts due or expected within one month were not discounted.lO This computation_resulted in a discount of $92,539 on the December 31, 1966 receivables.- The netr(or revised) receivable balance is $2,289,876 or 96.1% of the gross receivables, $2,382,Al5. 9Mathematically 2 a1 (mi - n) all m >n En = i if 2 ai # O 2 a1 all mi>n all mi>n where En is the expected date of receipt of terminal reserve outstanding for n months, a. is the amount of terminal reserve 1, m: is the time (in months) elapsed from completion to payment of terminal reserve i. En=° if ’3 ‘11:0 "all mj>n" This means that a terminal reserve remaining longer than any terminal reserve on the jobs in the sample is assumed to be uncollectible. (There was one account, $5,000, in this category). 0See footnote A. X Company Accounts Receivable December 31, 1966 Gross Discount Revised As shown by $2,057,203 $71,8u0 $1,985,363 engineers' estimates Other construc- 301,218 20,699 280,519 tion re- ceivables Other receivables 23,99A 0 233994L Total accounts receivable $2,382,415 $92,539 $2,289,876 The comparable results for the December 31, 1967 bal- ance sheet showed total discount to be $151,558 on $2,39A,982 gross receivables. The net amount of receivables was $2,2A3,A2A or 93.7% of the gross. The reason for the rela— tive increase in the discount (from 3.9% on December 31, 1966 to 6.3% on December 31, 1967) is that X Company com- pleted more contracts late in 1967. Thus, a larger portion than usual of the estimates receivable represented 11 reserves. 11Composition of estimates receivable were: December 31, 1966 December 31, 1967 Current $ 973,87A $ 886,292 Reserves 1,083,329 1,262,182 Percentage of reserves to total 52.7 58.7 1'7" X Company Accounts Receivable December 31, 1967 Gross Discount Revised As shown by $2,1A8,A7u $139,517 $2,008,957 engineers' estimates Other construc- 159,824 11,427. 148,397 tion re— ceivables Other 86,684 614 .86,070 receivables ""‘”_" Total accounts receivable $2,394,982 $151,558 $2,243,424 Marketable Securities. The securities were valued at the current cash equivalent as of the balance sheet date. Specifically this was done by determining the market values of the securities on the first trading day of the Succeed- ing year. The market value for securities listed on the major exchanges was taken as the average of the high and low quotations. For those securities traded over-the- counter, the market price was assumed to be the bid price reported. The current cash equivalent would seem to be the net realizable value to the company, not the market resale price. "What men wish to know, for the purpose of adapta- tion, is the numerosity of the money tokens which could be "12 substituted for particular objects... The net 12Ibid., p. 92. The example given on pp. 92-93 would also appear to support this conclusion. 18 realizable value of securities is the market price minus the commission on sale and the income tax effect of the sale (discounted from date payment is due to the date of sale).13 Since a gain on a sale of securities realized in early January would have to appear on a declaration of estimated tax filed by April 15, the tax would be due as follows: April 15 25% June 15 25% September 15 25% December 15 25% fl. 13Chambers does not Specifically state that the current cash equivalent is a net-of-tax measurement, but defining current cash equivalent otherwise would mean that an asset sold for an anticipated gain would result in a loss. For example, assume that at time 0 B Company holds as its only asset‘marketable securities which cost $6,000 but could be sold for $10,000, net of commission. If current cash equivalent is measured without considering the tax which must be paid if the asset is sold, the bal- anmesheet would be as follows: Marketable Securities $10,000 Residual equity $10,000 If the securities are sold at the anticipated price resulting in a liability for tax of $1,000 (25% of the gain), the following balance sheet will result: Cash $10,000 Tax liability $1,000 Residual equity , _2LQQQ Total ' . Total Liability Assets $10,000 and Residual Equity $10,000 The residual equity has decreased by $1,000 (from $10,000 to $9,000). Assuming no change in general price level, B Company would report a loss of $1,000 under this interpretation of current cash equivalent. If current cash equivalent is measured net-of-tax, the beginning residual equity is $9,000 and the income upon sale of the securities is $0. 19 Thus the average discounting period would be 219.5 days for the December 31, 1966 balance sheet and 220.5 days for the December 31, 1967 balance sheet.lLL The current cash equivalent of the securities will be computed by subtracting commissions and discounted taxes 15 from the market value. This computation results in marketable securities valued at $1,675,013 at December 31, 1966 and $1,859,538 at December 31, 1967.16 This is 353% 1” 1967 1968 Date Amount Due Date Date April 15 25%. 105 26.25 106 26.50 June 15 25% 166 41.50 167 41.75 September 15 25% December 15 25% 258 64.50 259 64.75 3A9 87.25 350 87.50 219.50 0. 0 >4><><>< 15X Company had a loss carryforward at each of the balance sheet dates. This complicates the analysis some- what, but because the current cash equivalent of an asset should be equal for different companies, current cash equivalent is computed net of taxes. Since the plant assets are also affected, this problem will be examined and discussed in more detail in Chapter III. 16 December 31, 1966 December 31, 1967 Market value $2,071,362 $2,309,062 Commissions* 19,451 21 017 Possible cash receipts $2,051,911 $ , , 5 Less: Cost 474,972 4921183 Popsible gain 6 86 all long term 1-57 932 1 7 2 2 Tax on gain (25%) $ 394,233 4%8,2I6 Discounted present value of tax payments at .6228 per cent per month Average term 219.5 days $ 376,898 Average term 220.5 days $ 428,507 Possible cash receipts $2,051,911 2,288,045 Discounted taxes payable 428 507 376 898 Net realizable value $Ij675f013 $1,859,538 *Commissions were computed based on the rates charged by New York Stock Exchange members assuming that sales were 20 of cost for 1966 and 382% of cost for 1967. The possible error is very small since at March 1, 1968 the market prices on January 2, 1967 and January 2, 1968 are known.17 Inventories. "...The current cash equivalent [of finished goods inventories] is the initial prices of the goods or services sacrificed in production, transformed to contemp- orary prices, and aggregated."18 This applies unless the prevailing price of the finished goods is less than the result obtained, in which case the price of the finished goods is the current cash~equivalent.197 This method also is to be applied to the raw materials and work—in-process inventories. "The pricing of raw materials inventories according to the same principle is relatively simple," and "the pricing of work-in-process may be carried out on the same principle...."20 In the case of X Company whose products are "sold" bi- weekly, the oldest inventories held were produced at most in round lots where possible. E.g., 220 shares of a security were assumed to be sold in two round lots plus an odd lot of twenty shares. 17The only possible difference between these figures and the amount which would have been realized by an im- mediate sale on the first trading day arises from the question of the time of sale. 18Ibid., p. 232. 19Ibid. 201bid., p. 233. 21 two weeks prior to the balance sheet date.21 No trans- formation of prices is needed for this short a period. Therefore the only adjustments necessary are the deletion of the non-direct costs and comparisons of the remainder to the contract price. The only inventory held by X Company at December 31, 1966 was $40,000 of raw materials purchased and received in late December for use in early 1967. Using the above interpretation of Chambers' position, the raw materials are valued at the initial price of the goods transformed to contemporary prices. For goods purchased in the last few weeks, this would be the amount paid, $40,000. This is lower than the selling price less costs to complete so the $40,000 was used for the balance sheet. On December 31, 1967, X Company again held raw mater- ials delivered in December at a cost of $40,000. By the same process the $40,000 is used for the December 31, 1967 balance. However at this date X Company also held work- in-process in the amount of $174,317. This amount in- cludes materials, supplies, performance, bond eXpense, taxes, wages, etc. directly related to the job. Also in- cluded is an allotted share of general corporation over- head and a rental charge for both owned equipment and equipment rented from outside sources. 21See pages 13-1h. I‘D D I Of the items included in the cost of the completed inventory, only the general factory overhead and the rental charge for equipment owned by X Company appear to be other than "goods and services sacrificed in production." All other items are so aggregated as to be directly related to the projects to which they are assigned. The general overhead, mainly expense of Operating the general office, is not directly related to production. The rental of owned equipment, however, contains deprecia— tion, repair costs, rental of yard Space, salaries of personnel directly charged with management of the equip- ment, etc. These costs would usually not be considered directly related to Specific jobs. Chambers does not directly indicate whether such costs would be part of short-term inventories. He does, however, imply that depreciation is to be accounted for separately.22 The remainder of the costs included in the rental of owned 11 ) 3 equipment would appear to be classifiable as joint costs. 22The income account lists separately as costs: "(i) current cash equivalent, at time of sale, of short—term inventories and durables" and ”(iii) depreciation and obsolescence." Ibid., p. 256. 23"A less clearcut group of sacrifices are those which vary in some way with the scale of production or trade but are not clearly identifiable with any particular product or group of products. These are joint costs." Ibid., p. 250. 23 Joint costs are to be treated as period cOStS.2u Thus none of the rental of owned equipment should be included in the current cash equivalent of short-term inventories. The current cash equivalent of X Company inventories was computed by removing an estimate of the general over— head and rental of owned equipment charges which were included. The estimate is made necessary because it is impractical to obtain an exact figure due to the way the records are currently kept. This problem of application would disappear if records were kept on a basis consistent with Chambers' model, i.e., the general overhead and rental charges would never be apportioned to jobs, and it would, therefore, not be necessary to extract them. The method of estimation used was simply the computa- tion of the percentage of these costs to total costs of jobs (per X Company records).25 This percentage was then applied to the total reported work-in-process inventory figure: 2L‘Ibicl. 25 General overhead $908,446. = = .055 Total cost of jobs $16,501,527. Rental of owned equipment $794,005. = = .048 Total cost of jobs $16,501,527. 24 Reported work-in-process $174,317. Less: General overhead, $9,596 Rental charges for owned equipment $8,388. 17,984 Revised work-in-process $156,333 The December 31, 1967 balance sheet will therefore show: Short-term inventories: Raw materials $ 40,000 Work-in—process 156,333 $196,333 Prepaid Expenses. "... amounts prepaid may be carried forward as monetary assets...."26 Thus the prepaid eXpenses which are actually prepaid do not need adjustment. (This does not apply to the item described as prepaid interest since it is properly an offset to the related Notes Payable account and will be treated as such.27 Therefore the only prepaid item is the $4,815 of Prepaid EXpense on the December 31, 1967 balance sheet. Liabilities Current Liabilities.l The current liabilities, except the current portion of long-term Notes Payable, are discussed in this section. The relevant measure for current liabili- ties is similar to the measure for receivables. The 26Ibid.,p. 250. 27See page 27. 25 current cash equivalent of current liabilities is computed by discounting the amount payable in the future using the rate of interest payable for the immediate use of the money necessary to enable immediate settlement to be made.28 The accounts payable to subcontractors based on engineers' estimates can be handled in exactly the same way as the receiVables based on engineers' estimates because the industry practice is that the prime contractor pays his Isubcontractor when he receives payments related to work which the subcontractor has completed. The other-aCCOunts payable were handled by discounting from theexpected date of payment at the same rate (.0062281 per month). All other current liabilities were eXpected to be paid in January and were not discounted. The revised sections of the balance sheets are shown in Table 1. Notes ngable. The Notes Payable account at December 31, 1967 contained three notes, two of which were aISO reported on the December 31, 1966 balance sheet. Two of these notes were forty-eight month notes being paid in monthly installments with an effective interest rate of .0062281 per month. These are the most recent 29 notes and this rate is the rate payable for any new loans. One note (Note One) is a $500,000 note with payments of gBIbid., p. 107. 29See pages 12—13. 26 Table 1. Current Liability Summary X Company Current Liabilities (except Notes Payable) December 31, 1966 Gross Discount Revised Accounts payable to subcontrac- tors based on engineers' estimates $851,137 $17,940 - $833,197 Materials, . supplies and other 720,329 14,527 705,802. Total accounts payable $1,571,466 $32,467 $1,538,999 Accrued payrolls 12,497 0 12,497 Accrued interest payable 40,141 0 40,141. Accrued taxes payable 61,918 0 61,918. Total $1,686,022 $32,467 $1,653,555. X Company Current Liabilities (except Notes Payable) December 31, 1967 Gross Discount Revised Accounts payable to subcontractors based on engineers' estimates $ 976,548 $ 71,354. $ 905,194. Materials, supplies and 'other 639,764. 41,691 598,073 Total accounts payable $1,616,312 $113,045, $1,503,267 Accrued payroll 5,499 0 5,499 Accrued interest payable 40,816 0 40,816 Accrued taxes Payable .__111112 .____12 34,442 Total $1,697,069 $113,045 $1,584,024 2/ $12,083 per month; the other (Note Two) $300,000, payments of $7,250. X Company had recorded each note at the total amount of the payments with prepaid interest being debited for the total interest charge for the note. The prepaid interest was being amortized on a straight line basis so that at each balance sheet date, the notes were shown as a liability for the total of the remaining payments and an asset ofthe unamortized portion of the interest. The revision was accomplished by discounting each payment from its due date back to the balance sheet date at the rate payable for new loans (.0062281 per month).30 The payments due within one month of the balance sheet date were not discounted.31 The third note (Note Three) invOlved in the Notes Payable account was a $2.3 million note with principal payable two years from each balance sheet date and interest payable quarterly at a rate of .0192 per quarter.32 Since this is a higher rate of interest than the .0062281 per month (which is .0188 per quarter), the discounted value 30The second note negotiated in July, 1967 evidences this rate on new loans after December 31, 1966. Another loan at the same rate was negotiated early in 1968. 31See page 15. 32At December 31, 1966, the principal was to be repaid December 31, 1968. The loan was extended for one year during 1967 so that at December 31, 1967, the term was still two years. of the note and quarterly interest paymegts is $2,307,503 ($7,503 greater than the principal). If the cost of new debt capital increases from .0188 per quarter to .0192 per quarter, the present value of Note Three will decrease to $2,300,000. The other liabilities and some of the assets (mainly accounts receivable) would also decrease. Since X Company is a net debtor, the liabilities would decrease by a greater amount than the decrease in assets.33 Therefore, X Company would show income, I, equal to the difference between the amount of the changes (ceteris paribus).34 X Company (or any net debtor) can cause net income to be reported merely by increasing its cost of debt capital. Conversely, a net debtor would report a loss due to a decrease in the cost of debt capital. This paradox results from Chambers' disqualification of goodwill 33This is generally true for net debtors although in certain cases the expected pattern of receipts and payments on receivables and liabilities could cause the change in receivables to be greater than the change in liabilities. Conversely, certain patterns could also make the change in liabilities greater than the change in receivables for a net creditor. The following discussion will use the term "net debtor" to refer to companies for which a change in cost of debt capital causes a greater change in present value of ltabilities than in present value of assets. 3“I = AA — AL (assuming no capital investment or disinvestment) where I income AA AL change in present value of assets (mainly receivables) change in present value of liabilities 29 as an asset.35 The following example should help to illustrate this point. Assume A Company has these assets, liability and residual equity at time 0: Cash $ 500,000 Bonds payable 1,000,000 Inventory $1,000,000 Residual equity 2,000,000 Plant assets 1,500,000 Total Liability ' ' ' ‘ and Residual Total Assets $3,000,000 Equity $3,550,000 where the assets are reported at their current cash equi- valents and the bonds payable are seven percent twenty- year bonds currently trading at their face value, i.e., to yield seven percent.36 The bonds are reported at the present value of future payments due discounted at the market rate of interest which is assumed to be equal to the cost of new debt. Goodwill is the difference between the investors' estimate of the value of the stockholders' equity and the reported residual equity: 35"Goodwill is not an asset of the firm, being neither severable nor measurable. It subsists in eXpectations of constituents, and is, therefore, capable of evaluation; such evaluations, being comparative, will vary from time to time." Ibid., p. 218. 36The same result (decrease in goodwill offsetting income) would be obtained if the assets were reported at historical cost or current replacement cost. 3O G = V — RE where G goodwill RE = reported residual equity V = value of stockholders' equity of A Company probably computed by use of a relationship such as: m I. v = z 1 i=1 (I+r5l where I. = income of A Company in period 1 i r = discount rate used by investors Therefore G0 = VO - $2,000,000 (1) If the cost of new borrowing changes to 8% at time 1, the following balance sheet will result (assuming no other changes): Cash $ 500,000 Bonds payable $ 901,036 Inventory 1,000,000 Residual equity Plant assets 1,500,000 at time 0 2,000,000 during period 0-1 98,964 * Total Liability ‘ ' and Residual Total Assets $3,000,000 Equity $3,000,000 Thus, income (or at least an increment to residual equity) of at least $98,964 results from the increase in cost of debt.37 But, V, the value of the stockholders' equity will certainly not increase. In fact, V will probably 37It is possible (even probable) that the current cash equivalent of plant assets will be increased because the discounted potential tax payments (deducted from market price to compute current cash equivalent) would be decreased because of the increase in the discount rate (assuming that the change in cOst if debt capital does not affect the market prices of th assets). . , 1 l 1 . ' : ' I 31 decrease as a result of one or both of the following effects: 1. If the projected incomes, Ii, had been computed assuming new borrowing at sevep percent, the change in cost of debt will decrease the projected incomes.38 2. The reason for the change in the cost of debt capital should be either the increase in the pure rate of interest or the increase in the risk premium required of A Company by lenders (i.e., a change in A Company's ' risk class). Either of these increases should be accom- panied by an increase in r, the rate used by investors to discount eXpected income. Therefore, V1 ,5 V6 (2) G1 = vl - $2,098,964 (3) (3)-(1) gives Gl-GO = vl - $2,098,964 - (VG-$2,000,000) Gl-GO = vl - VO - $98,964 (4) From (2) Vl-VO 5 0, therefore Gl-GO g,— $98,964, or Gl,g Go - $98,964, Or the decrease in goodwill at least offsets the income ($98,964).39 Reversing the whole process will cause a loss and offsetting increase in goodwill. ‘gl fl wv—v w—fivv— v v—v v' WrV— 38Assuming that investors believe the change will be in effect until some borrowing occurs or is foregone, due to the increased cost. 39It must be noted that A Company is in a better posi- tion financially than it would have been had management not secured the debt capital before the increase in cost. 32 Possibly foreseeing this difficulty, Chambers has made an exception to his normal meaSurement rule for obli- gations. For long-term liabilities the measurement will be "future payment discounted to present at contractual interest rate (generally equal to face value)."LLO This deviation from the usual market price standard is supported by the reasoning that until the company retires its liabilities, "the market price may be regarded only as indicating a possibility of gain."b'l Given this clearcut statement, Note Three was recomputed as the present value of the principal and interest payments discounted at the contractual rate (.0192 per quarter). The result of this computation was, of course, the face value of the note, $2,300,000. Notes One and Two were not recomputed since the contractual rate for these notes equals the market cost of debt capital which was the rate used in the original computation. The results of these computations are shown in Table 2. Summary Cash was not adjusted. The accounts receivable and current liabilities were discounted at the current cost of new debt capital. The long-term liabilities were V f 7m— 7 .vv fifi V V V v V—ffir w—fi uoIbid., p. 259. ulIbid., p. 290. w 33 Table 2. Notes Payable Summary X Company Notes Payable December 31, 1966 Gross Discount As Current Liabilities Note One $145,000 $ 4,836 As Long-term Liabilities Note One $. 362,500 $54,551 Note Three 2,300,000 0 Total Long-term Liabilities $2,662,500 $54,551 Total Notes Payable $2,807,500 $59,387 X Company Notes Payable December 31, 1967 Gross Discount As Current Liabilities Note One $ 145,000 $ 4,836 Note Two 87,000 2,901 Total Current Notes Payable $ 232,000 $ 7,737 As Long-Term Liabilities Note One $ 217,500 $25,895 Note Two 224,750 34,395 Note Three 2,300,000 0 Total Long-term Liabilities $g,742,250 $60,290 Total Notes Payable $2,974,250 $68,027 Revised $140,164 $ 307,949 2,300,000 $21748,113 Revised $ 140,164 84,099 $ 224,263 $ 191,605 190,355 2,309,000 $2,681,960 $§a9051223 34 discounted at the contractual rate. In all cases amounts eXpected to be paid within one month were not discounted. Marketable securities were computed at market value less commissions and taxes payable on gains (discounted from date due to balance sheet date). Short-term inventories were revised to the cost of goods and services sacrificed in production (or for raw materials, the cost), adjusted for price changes (none were necessary because of the short interval between incurrence of cost and the balance sheet date). Prepaid expenses were not adjusted. The partial balance sheets showing adjusted figures for the above items appear in Table 3. 35 Table 3. Partial Revised Balance Sheets X Company Partial Balance Sheets Current Assets Cash Marketable securities Accounts receivable Inventories Prepaid eXpenses Total Current Assets Liabilities Current Liabilities Accounts payable Notes payable - current Accrued payroll Accrued interest payable Accrued taxes payable Total Current Liabilities Long Term Liabilities Notes payable Total Liabilities December 31, 1966 $1,272,637 1,675,013 2,289,876 40,000 $5,277,526 $1,538,999 140,1 4 12,497 40,141 61,918 $1,793,719 $21607,949 $4,401,668 1967 $ 624,137 1,859,538 2,243,424 196,333 4,815 $4,928,247 $1,503,267 224,263 5,499 40,816 34,442 $1,808,287 $2,681,960 $4,490,247 ‘TEEJV |.' . ‘. ial- —._.:_. . CHAPTER III PLANT ASSETS The general measurement rules for assets as applied to marketable securities also apply to plant assets. This requires determination of the realizable price. The realizable price is again the market resale price less commissions and discounted tax payments necessitated by the sale. The major question is thus the determination of the market resale price. Two methods of accomplishing this objective were used. The first was the use of linear regression based on sales of similar assets. The second method was refererce to publications generally available which give resale prices of various assets at Specific points in time. Where both methods could be used the regression was used for reasons which will be eXplained later. If neither of these methods yielded a market resale price, the current cash equivalent was approximated by use of indexed calculations. Chambers indicates that this is an acceptable alternative, but that the ideal measure should be based on market resale prices.l 1R. J. Chambers, Accounting, Evaluation and Economic Behavior, p. 2M8. 36 37 Valuation by Regression The regression technique was used wherever possible because it was the only method of calculating current cash equivalent which yielded a diSpersion measure which could be compared to the diSpersion of measures obtain— able under alternative generally accepted accounting principles. This latter diSpersion was computed by first presenting many different depreciation methods to the Certified Public Accountant who audited X Company. He was asked, for each type of plant asset, to eliminate any methods which he would hesitate to accept if applied by X Company. For each asset the book value was computed as of each balance sheet date under each method accepted without hesitation by the C.P.A. The diSpersion of the measures obtained underthese different generally accepted accounting principleswas computed for each balance sheet date by computing the standard deviation of the book values at that date calculated under all acceptable depreciation methods.2’3 For each asset this figure 21f the purchase price of an item was unknown, it was treated as if it were zero. Therefore, the diSpersion under different depreciation methods for this item was zero. (The zero purchase price is implied by the omis- sion of this item from the conventional balance sheet.) 3As an example of the computation of this diSpersion, assume that the CPA indicated that straight line, sum-of- the-years' digits and double declining balance deprecia— tion methods with lives of three and four years and sal- vage value of zero were acceptable methods for reporting an asset which cost $10,000. If this asset had been 38 was compared to the standard error of estimate from the regression. The regression technique was used for most of the large items of equipment (cranes, crawler and wheel tractors, compacting equipment, graders, etc.). The observations used in the regression were taken from reports of actual sales at auctions throughout the year 1967 and throughout the country as reported by the largest firm handling auctions of this type of equipment.LL The dependent variable was, of course, the price for which purchased at the beginning of 1966, the possible book values at December 31, 1966 would be: Method Life 4 3 Straight line (SL) $6,666.67 $7,500.00 Sum of the years' digits (SYD) 5,000.00 6,000.00 Double declining balance (DDB) 3,333.33 5,000.00 Average book value 'x $5,583.33 Standard deviation 0 1,339.40 The standard deviation is more than thirteen percent of the cost and twenty-four percent of the average book value. At December 31, 1967 the average book value would be $2,953.70 and the standard deviation of book values would be $1,059.16 (35.9 percent of the average). “Blue Book 2§_Heavy Equipment Prices (Lincoln, NebraSEa: Forke Brothers Incorporated’ 1967). 39 the item of equipment was actually sold. The independent variables in most of the regressions were age, condition, list price new, list price of attachments, and month of sale. The combination of these variables which gave the best prediction for each class of equipment was used in the regression for that class. The input for a par- ticular regression was all items in that class for which both the dependent and independent variables were avail- able. The major source of the list price figures was the 5 Green Guide. This book gives prices for a wide variety of heavy equipment. Tables 4 and 5 report the application of the regres— sion technique at the two balance sheet dates. Although fewer than one-third of the items were valued by the regression, the value of these items constituted more than sixty percent of the value of the plant assets as of December 31, 1966 and more than fifty percent of the value of the plant assets as of December 31, 1967. Relative to the diSpersion criterion, the tables show that 86 of 115 items on the December 31, 1966 balance sheet and 87 of 117 items on the December 31, 1967 balance sheet had a lower standard error of estimate from the regression than the possible diSpersion in measures obtainable under generally accepted accounting principles 5Green Guide (Palo Alto, California: Equipment Guide- Book Company, I966, 1967, 1968). 40 Table 4. DECEMBER 31, 1966 Reported (a) Number of items valued by regression (b) Total number to be valued Percent valued by regression '(number) (a/b) (c) Valuation of items valued by regression $632.438 (d) Total valuation of all items $930,155 Average valuation of items in (a) (c/a) $5,499 Percent valued by regression ($) (c/d) 68.0 (e) DiSpersion of items in (a) $49,922 Average diSpersion (e/Rfa) $4,655 Accuracy * <2.00 x 10-5 (f) Number of items for which diSpersion of GAAP is lower (g) Number of items for which diSpersion of regression is lower Percent of (f) to total (a) (h) Valuation of items in (f) :0 Average value per item (h/f) 0 (1) Valuation of items in (g) $632,438 Average value per item (i/g) $7,354 Percent of valuation accounted for by successful items (i/c) 100.0 * As defined in Appendix. Summary of Valuation by Regression Beginning Revised 115 385 29.9 $631,244 $1,035,985 $5,489 60.9 2.26 x 10- -99 86 25.2 $6,465 $223 $624,779 $7,265 99.0 41 Table 5. Summary of Valuation by Regression Ending DECEMBER 31, 1967 Reported (a) Number of items valued by regression (b) Total number to be valued Percent valued by regression (number) (a/b) (c) Valuation of items valued ‘ by regression $500,778 (d) Total valuation of all items $926,808 Average valuation of items in (c) (c/a) $4,280 Percent valued by regression ($) (c/d) 54.0 (e) DiSpersion of items in (a $63,264 Average diSpersion (e/JFE) $5,849 Accuracy * <1.58 x 10'5 (f) Number of items for which diSpersion of GAAP is lower (g) Number of items for which diSpersion of regression is lower Percent of (f) to total (a) (h) Valuation of items in (f) $0 Average value per item (h/f) $0 (1) Valuation of items in (g) $500,778 Average value per item (i/g) $5,756 Percent of valuation accounted for by successful items (i/c) 100.0 * As defined in Appendix. Revised 117 436 26.8 $587,677 $1,122,918 $5,023 52.3 $4.396 $406 4 _) 2.27 x 10 30 5' 25. OWN $7,072 $236 $580,605 $6,674 98.8 42 (GAAP). These items can be classified as "successful" according to the diSpersion criterion. None of the other items (those for which the GAAP diSpersion was less than the standard error of estimate from regres- sion) had any book value. Not coincidentally the current cash equivalent of these itemsvws very small, averaging less than three percent of the average "successful" item. There are four basic eXplanations for these "unsuccess- ful" items. 1. Unknown purchase price. This automatically means that the item will be classed as unsuccessful. (The assumed cost of $0 causes book value to be $0 regardless of depreciation method. See note 2.) 2. Lack of arm's-length transaction at time of purchase resulting in unrealistically low cost. This lowers diSpersion of GAAP measures since the diSpersion 6,7 is almost directly prOportional to cost. 6The "almost" can be removed if the salvage value varies directly with the cost. 7Only straight-line, sum-of-the-years' digits, and double declining balance methods of depreciation were used. cost of asset 1 any constant depreciable life of assets 1 and 2 salvage value of asset 1 cost of asset 2 = KC ' salvage value of asset 2 = KS (see note 6.) age of assets 1 and 2 book value at straight-line depreciation of aSSét 1 .- ‘ bmemF‘p-qO U) 43 3. Extreme age. Some assets still in use were so old that none of the depreciation methods used resulted in a book value greater than zero. SL' = book value at straight-line depreciation of asset 2 ' similarly for SYD, SYD', DDB,.and DDB' representing sum-of-the years' digits and double declining balances SL = Q—i—S— (L - A) SL' = Eli—2(L _ A) KC - KS = -—-f—-—(L - A) = K(C£S) (L-A) = KSL (1) L-A L SYD = (C ‘ S) (12:1 i)/( 121 1) L-A L SYD'=(C'-S') (2 i)/(2 i) i=1 i=1 L-A L = K(C — S) (.2: i)/ (.2: l) 1: 1: = K SYD (2) DDB = C (1 - %)A DDB' = C' (1 — %)A = KC (1 — %)A II N U U 021 U.) 44 4. No adjustments of standard error of estimate for predictions close to or less than zero. If a prediction equaled zero, it could only be incorrect in one direction Thus, for each Xi in the distribution of book values for asset 1 there exists xi = Kxi (4) in the distribution of book values for asset 2. n '2 = ( 2 xi)/n = mean of book values of asset 1. i=1 n I x' = ( 2 xi)/n = mean of book values of asset 2. i=1 n = ( E Kxi)/n from (4) i=1 n =K(2 xi)/n i=1 = K? (5) 2 n —-2 o =.Z (xi - x) /n = variance of book values of 1:1 asset l :2 n l _l 2 0 =.Z (xi - x ) /n = variance of book values 1:1 of asset 2 n __ 2 . =i§l(Kxi -Kx) /n from (4) and (5) 2n -— 2 = K 2 x — x n i=1( 1 )/ = K2 02 (6) o = «[35, = standard deviation of book values of asset 1 I I o = o 2 = standard deviation of book values of asset 2 = ’K2 02 from (6) 45 (low) to be a relevant error. Thus the effective error of estimate for that item was approximately 71 percent of the standard error of the regression which generated the prediction.8 The possible adjustment is even greater for a prediction less than zero. Note that all four of these conditions are more :3 likely to occur in connection with a fully depreciated , 1 asset. Thus, the fact that the total book value of all "unsuccessful" items is zero is not a coincidence. The , regression technique is at a great comparative disadvantage for items of little value (either book or market). Thus the diSpersion varies directly with the cost of assets of equal depreciable lives and ages (if salvage value also varies directly with cost). ‘ 8The standard error of estimate is computed for the regression assuming all values of the dependent vari- able are relevant. This means that if the prediction is zero, the standard error of estimate is computed under the assumpt on that an observation of -a is possible and would add a to the sum of squared residuals. In this situation a negative net realizable value is adjusted to zero. Therefore the error is zero and the addition to the sug of the squared residuals should be zero rather than a . The effective standard error of estimate would be computed from the sum of squared residuals less the amounts included in that sum which relate to assumed possible negative observations. If the distribution of possible observations was symmetrical, the resulting effective sum of squared residuals would be one-half the ori inal. Thus, the effective standard error would be 1/ 2 times the original standard error (.7071 S). 46 A more complete analysis of the unsuccessful items is presented in Table 6. The total of the numbers of occurrence of the conditions will not check because several items had more than one of the four conditions present. This table indicates clearly that when the regression technique "fails," it does so on fairly trivial items. The measure of accuracy, A (as deve10ped in the r Appendix), of the regression for a particular item is equal to the inverse of the diSpersion measure (standard error of estimate, S) for that item. Thus, for the regression method Ar = é . The measure of accuracy, Ag, for the measures derived under alternative generally accepted accounting principles can not be determined (because the true measure of the attri- bute being measured can not be determined), but the upper limit of Ag can be determined and is equal to the measure of verifiability, vg (as defined in the Appendix).9 The inverse of verifiability for an item is equal to the standard deviation of the book values for that item, 0, C A < V = i. 10 8" g 0 0H4 or V = g 9V exists independently of the true measure of the attribute being measured. The Appendix demonstrates that the verifiability of a set of measurements is greater than or equal to the accuracy of that set of measurements. 10 l ._ A = where B = x — T E J42 B2 g g g o + g 'xg = the mean of all book values T = the true book value 8 47 Table 6. Analysis of Unsuccessful Items 1. Unknown purchase price 2. Lack of realistic purchase price 3. Extreme age 4. Negative prediction 5. None of the above Largest difference in diSpersion of items in 5. Average difference in diSpersion of items in 5. Largest difference in diSpersion of successful items (dis— persion GAAP > standard error of estimate of regression) Average difference in diSpersion of successful items (regres— sion better than GAAP) 1966 11 $98 $29 $19,441 $ 4,881 1967 12 10 $101 $39 $19,208 $ 6,314 48 If S < c, then Ar > V Z_A or Ar > A . Thus, 8 8 8 for all items where the diSpersion of the regression is less than the diSpersion of GAAP (S < a), the accuracy of the regression must be greater than the "accuracy" of the GAAP. If C < S, then Ag'fi V >.Ar. This tells nothing 8 about the relationship of A and Ar unless the assumption 8 is made that Ag = Vg. This would mean that Bg = O or that the mean book value was exactly equal to the true measure of the attribute being measured.11 This would seem to be an unsupportable assumption. Therefore the conclusion must be that for all items where S < a, the regression method is more accurate, but where a < 8, either method may be more accurate. This means the regression method was more accurate for three-fourths of the items measured by regression and may have been more accurate for the other fourth. A similar result is obtained for the accuracy, AR, of all items measured by the regression compared to the accuracy,A for the same items measured according to GAAP. g) From Tables 4 and 5: 1966 1967 AB 2.26 x 10’“ 2.27 x 10‘1‘L vG(z AG) 2.00 x 10'5 1.58 x 10'5 11This is the condition for equality of A and V as proven in the Appendix. ~" . on 44 u A Ir. '1. t“ 49 The regression technique in total has an accuracy measure more than ten times the "accuracy" measure of GAAP. The factor of ten indicates to some extent the extreme accuracy (and thereby verifiability since the accuracy measure includes verifiability) of the regres— sion technique relative to alternative GAAP.12 Valuation by Reference to Published Market Values If a market price could not be determined for an asset using the regression technique, an attempt was made to determine the market price by reference to published materials generally available which give market prices for many assets at Specific points in time.13 Unfortu- nately, the lack of data on market prices of individual items of a particular model prevented computation of measures of diSpersion and accuracy for this technique. f 12It is verifiability of which many accountants Speak when they discuss objectivity. Since objectivity is strictly a mental freedom from bias which cannot be mea- sured directly, verifiability (as defined in the Appendix) is generally accepted as evidence of objectivity. 13All assets which were valued by the regression tech- nique could have been valued by reference to published materials. The regression method was used instead mainly because it provided more data for purposes of comparison with alternative generally accepted accounting principles. 50 Automobiles owned by X Company were valued by refer“ ence to either of two publications. The one which was preferred was the Black Book which is published weekly and contains prices of cars sold at auction in a particu— lar state over the previous week.lLL These prices are averaged over the state for cars of a particular model, year, and condition. The auction price was used, not because X Company would sell directly at the auction, but because dealers, who can sell at the auction, will gener- ally be willing to pay (or allow on trade-in) a price which they feel they can recover at auction. 'The January 2, 1967 and January 1, 1968 issues were used because they are the issues to which the dealer would have referred to value an automobile the first week in January. The price re— ported for rough condition was used for automobiles used on construction jobs. The average price was chosen for the autos used by company officials. The automobiles which could not be priced using the _§lack Book were valued by use of the Red Book which is pub- lished every six weeks reporting average wholesale prices prevailing in the previous six—week period in a twenty-one 1”Black Book (Gainesville, Georgia: National Auto Research: Inc.,II967, 1968). 51 15’16 There state area for a particular model and year. was no gradation as to condition. Light trucks were valued where possible from the same publication. In this case the figure reported was "average finance value" which is the average amount for which a vehicle of this model and year could be financed. Since the average finance value for automobiles is reported at ninety per— cent of the reported average wholesale price, it was assumed that this ratio was also applicable to the truck market. Therefore, the wholesale price was obtained by multiplying the average finance value by 10/9. Those light trucks which could not be valued by use of the Red Book as well as the heavier trucks were priced 1? from the Truck Blue Book. This is published semi- annually and reports the average finance value prevailing in a twenty-one state region for a particular model and year as of the end of the previous six month period. Again no gradation as to condition is reported. The same 15One automobile of foreign manufacture could not be valued from either source and is included in the indexed calculations in the next section. 16Red Book, Official Used Car Valuations (Chicago: NationaI Market Reports, Inc., 1967, 1968). l7Truck Blue Book, Official Used Truck Valuations (Chicago: National Market Reports, Inc., 1967, 1968). 52 adjustment from average finance value to average whole- sale value (multiplying by 10/9) was used. All other assets which were valued by use of pub- lished materials were priced by use of the Green Guide, mentioned as a source of data in the previous section. This publication reports current average wholesale prices for various assets based upon their model and age. Average condition is all that is reported, but again there is no reason to believe that this is not a reason- able assumption. Over forty per cent of the plant assets were valued by use of the above methods, but the total value of this group was substantially less than forty percent for the December 31, 1966 balance sheet and slightly less than forty percent for the December 31, 1967 balance sheet. These and other data are reported in Table 7. No measure of diSpersion or verifiability was com- puted for the revised figures because any measurers follow- ing the method described would report the same figures. This will be discussed in more detail in Chapter V when the reports of five measurers will be presented. Valuation by Use of Indexed Calculations Chambers does not deal Specifically with the case of vendible assets when no market price can be determined. He makes the assumption that if there is a secondhand 53 "Table 7. Direct Valuation by Reference to Published Sources DECEMBER 31, 1966 Reported Revised (a Number of items valued 160 _b Total items to be valued 385 Percentage of total (by number) (a/b) 41.6 0 Valuation of items in (a) $197,356 $299,056 d Total valuation of all items $930,155 $1,035.985 Percentage of total ($ (c/d) 21.2 28.9 Average valuation of i ems in (a) (c/a) $1,233 $1,869 (e) DiSpersion $37,360 * Average diSpersion (e/Jfia) $2.954 * Verifiability 2.68 x 10'5 * DECEMBER 31, 1967 (f Number of items valued 188 g Total number to be valued (£30 Percentage of total (number) 43.1 (f/s) h Valuation of items in (f) $323,433 $427,197 1 Total valuation of all - items $926.808 $1,122 910 Percentage of total ($) (h/i) 34.9 30.0 Average valuation of items in (f) (h/f) $1,720 $2,272 (j) DiSpersion $38,447 * Average diSpersion (j/rf) $2,804 * Verifiability 2.60 :x 10‘5 * *Data were not available to compute the diSpersion or veri— fiability of the revised valuations. 54 market, the market prices of the durable assets can be ascertained.18 He then indicates that, theoretically, goods for which there is no secondhand market have no Opportunity cost,and therefore,no current cash equivalent should be assigned to them.19 He then outlines a possible method of approximation which can be used if it is desired to place a current cash equivalent on nonvendible assets.20 This method was used to value the remaining assets even though they do not fit the category "non- vendible." Briefly the method shown by Chambers can be described as adjusting the book value at a particular point in time for the change in Specific prices from date of purchase to the balance sheet date. Chambers indicates that the result of this computation stands in place of an ascer- tained market price.21 This must then be adjusted for tax effects. 18"... the case where there is a ready secondhand market, so that market prices of a durable inventory may be ascertained. Many firms, however, will acquire and hold some assets which are so highly Specialized that theri is no used goods market." Chambers, .gp. cit., p. 2 3. ___' l9Ioid. 20Ibid., pp. 245—249. ‘libid., p. 246. 55 For the actual computation the price index chosen was the construction machinery and equipment index avail; able monthly in the Survey of Current Business.22 The book value used was the book value of X Company at the 23 same balance sheet date. Using this method,llO items (29%) were valued for the December 31, 1966 balance sheet resulting in total net realizable value of $105,685 (Table 8). For December 31, 1967, 131 items (306) were valued at a total of $108,044. All items had a larger verifiability using the revised measurement method than under conventional methods.2u The average valuation for the items under both measurement Systems and for both years was under $1,000,and the total valuation of items valued by this technique was approximately ten percent 22Surve .2: Current Business, Vol. 4:, January, 1967, p. S-8. IT Business Statistics (Washington, D.C.: Office of Business Economics, 1963), p, 43. Business Statistics (Washington, D.C.: Office of Business Economics, 1965), p. 45. , Survey 2: Current Business, Vol. 46, January, 1966, p. 8-80 Survey of Current Business, Vol. 48, February, 1968, p. S—8. d3This means that the X Company estimates of life and depreciation methods were accepted. 2LLThe diSpersion for the revised technique is roughly 52% of the GAAP diSpersion, since the major cause of diSpersion using indexed calculations is the different possible depreciation methods. I ‘17‘TIOWIJS 56 Table 8. Summary of Valuation by Indexed Calculations DECEMBER 31, 1966 Reported Revised (a Number of items valued , 110 (b Total number to be valued 385 Percent valued (number) (a/b) 28.6 (c Valuation of items in (a) $100,361 $105,685 (d Total valuation of all items $930,155 $1,035,985 Percentage valued ($) (c/d) 10.8 10.2 Average valuation of items '111(a) (d/a) $912 $961 (e) DiSpersion $20,827 $11,981 Average diSpersion (e/J’a) $1,986 $1,142 Verifiability 4.80 x 10"5 8.34 x 10‘5 Number of items for which diSpersion of measures Obtainable under GAAP was lower 0 DECEMBER 31, 1967 Reported Revised f Number of items valued 131 g Total number to be valued 436 Percent valued (number) (f/g) 30.0 h Valuation of items in (f) $102,597 $108,044 1 Total valuation of all items $926,808 $1,122,91 Percentage valued ($) (h/i) 11.1 9.6 Average valuation of items 1J1(f)(h/f) $783 $825 (j) DiSpersion $20,784 $12,516 Average diSpersion (j/Jrf) $1,816 $1,094 Verifiability 4.8l.x 10'5 7.98 x 10"5 Number of items for which diSpersion of measures obtainable under GAAP 0 was lower 57 of the total valuation of all items. All of these figures indicate that the plant assets for which no market price could be determined were the relatively less significant items (smaller in value than items measured by use of regression or reference to published sources). This is further demonstrated by a comparison of the average valu- ation under each method (Table 9). Also reported in Table 9 are the summary results for all three methods of valuation. Here is emphasized the fact that whenever accuracy or verifiability could be determined for one of the revised methods, these measures were greater than the verifiability of generally accepted accounting prin- ciples. This means that the revised methods were more "objective" in terms of the normal connotation of observ- able objectivity. Also for each year only ten percent of the assets (by value) were not valued by direct valu- ation (either by regression or from published figures). Treatment of Tax Carryforwards As mentioned in Chapter II in the section dealing with marketable securities, X Company had an unallocated tax loss carryforward at both balance sheet dates. This carryforward amounted to $289,700 at December 31, 1966 and $1,067,858 at December 31, 1967. The existence of this loss means that the net of tax computations of 58 m-oa x mm.awzm-oH x om.av * man x mm.mv owm.ma mmm.aa . amm.mm oes.moa smm.oma omm.sma mae.ma mama mmm.aa o.ooH m.oa. m.Hm mma.omma Hmm.ooaa bmm.smaa * man x 3m.mv * * maa.aa * * Hmm.aaa * Hab.me Home aom.aa o.ooa m.oa m.mm www.mmo.aa www.moaa mmo.mmma o.ooH m.mm m.aa mmm oHH oma. 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There are several reasons for this procedure: 1. The additional net realizable value of assets, due to the loss carryforward, does not attach directly to any Specific assets since the total possible gain is greater than the loss carryforward. This means that, if this procedure were not followed, the order in which the assets were eXpected to be sold after the balance Sheet date would affect the carrying value of the assets. This is contrary to common sense and, more importantly in this context, contrary to Chambers' definition ofthe domain of accounting as excluding anticipatory calculations.26 2. The adjustment is not tied to the particular asset but rather is a result of previous misfortunes of the entity. Therefore both the asset and the loss carry- forward must exist for the additional net realizable value to exist. 1,. fifiv 25An adjustment is necessary because a tax was asses- sed on a prOSpective gain on the sale of an asset under the assumption that a tax would have to be paid on the gain. However, the gain would not be taxed if it were offset against the loss carryforward. Thus, the net realizable value of the asset would be equal to the pro- ceeds from the sale. 26"The domain of accounting is the range of retro- spective and contemporarg measurements and calculations." Chambers, pp, cit., p. 1 2. 61 3. If this procedure were not followed, the current cash equivalent of an asset would vary depending on the taxable income of the entity. This result seems neither reasonable nor useful eSpecially in light of 2. 4. The amount of the additional net realizable value (which is in some reSpects a valuation of the loss carry- forward) should be disclosed separately. If the two fig- ures were not reported, a reader would not know the valua- tion of the assets exclusive of the loss carryforward; i.e., the question, "How much of the net realizable value of the assets will remain after the loss carryforward is absorbed by profitable Operation?",can only be answered if the loss carryforward and assets are reported separ- ately. Even after making the decision to report the effect (on net realizable value of assets) of a loss carryfor- ward separately, the accountant will still be faced with a problem unless the loss carryforward is greater than or equal to the total of the prCSpective gains on sales of all assets. If this were the case,the effects of the carryforward would equal the disCounted value of the taxes which otherwise would be paid upon diSposal of all of the assets. The problem which arises undercmher circum- stances (total gains > loss carryforward) is that the loss carryforward offsets a certain amount of gains, thereby rendering the gains non-taxable. This, however, 62 does not determine the amount of tax which is saved by the existence of the carryforward because of the differ- ent tax rates applicable to long-term capital gains. For example, assume total eXpected gains from sale of assets are $2 million of which $1 million are eligible for Special long term capital gains tax rates. If the loss carryforward is $2 million or more, the additional net realizable value of assets due to the loss carry- forward is $730,000: $1,000,000 x .48 (ordinary income rate ) $480,000 $1,000,000 x .25 (long term capital gains rate) 250 000 matinee There is no problem here because the loss carryforward is large enough to offset all proSpective gains. The situation is not nearly so simple if the loss carryforward is less than-$2 million. If, for inStance, the loss carryforward is $1 million, the effect on net realizable value of assets may be $480,000 or $250,000 or anything between. If all assets whose gains do not qualify for the 25 percent rate are sold in the year fol- lowing the balance sheet, the taxes saved by the offset of'the losscarryforward will be $480,000. If all assets whose gains d3 qualify for the 25 percent rate are sold and no ordinary income is reported for the year, the tax savings due to the loss carryforward will be 63 $250,000.27 These are extreme examples, but they demon- strate that the tax savings (from the loss carryforward) on sale of assets can range from 25 to 48 percent of the carryforward.28 This problem was handled in an arbitrary but com- pletely reasonable manner. The expected gain on each asset was offset against that fraction (of the loss carry- forward) which equaled the fraction which is the expected gain on the asset divided by the total possible gain on all assets. This means that an asset whose gain is ten percent of the total possible gain would have its gain offset against ten percent of the loss carryforward. This procedure leads to the same result as dividing the loss carryforward by the total possible gains (yielding the fraction of possible gains which £2313 be offset) and offsetting that fraction of each asset's possible gains. The computation of this figure is easily accomplished by the following formula: _ T25% T48z ANRV—LC [(T) .25 + (T?) .48] 27An Operating profit during the period will in- crease benefits of the loss carryforward,but this is un- related to additional net realizable value of assets (and furthermore involves an anticipatory calculation). 28There is the Slight possibility of a 22 percent figure entering here if the total gains are less than $25,000. 64 where ANRV = additional net realizable value due to unabsorbed loss carryforward LC = unabsorbed loss carryforward T25$ = total possible gains which qualify for the 25% tax rate T48% = total possible gains taxable as ordinary income TG = total possible gain = T25% + T48%. For December 31, 1966: $289,700 [( i 647 E8 ) .25 + ( T76 ?99 ) .48 = $78,876 For December 31, 1967: $1,067,858 [( l 853 “83) .25 + < 3 $ 082) .48] = $310,021 These figures must then be discounted to the payment dates since the original deduction for taxes was handled that way. After this adjustment the figures will be: December 31, 1966 $75,404 December 31, 1967 $296,374 X Company has an additional potential benefit from its tax situation. At each balance sheet date, X Company had an investment credit carryforward which would take effect after the loss carryforward was absorbed. This type of carryforward directly reduces the tax so that there is no uncertainty as to applicable rates. The only adjustment necessary is discounting the future payment benefits back to the balance sheet dates. 65 December 31, 1966 1967 Investment credit carryforward $21,922 $39,047 Discounted investment credit carryforward $20,957 $37,373 Additional net realizable value of assets due to unabsorbed loss carry- forward 75,404 .296,374 Total additional net realizable value of assets due to tax carryforwards $96,361 $334,747 It is difficult to measure the accuracy of the addi- tional net realizable value mainly because of the in- ability to measure the accuracy of the measurement of fixed assets by either reference to published figures or indexed calculations. A further bar to measurement of accuracy is the necessity of an arbitrary formula for computation of the effects of the unabsorbed loss carry- forward. It might help, however, to point out the extreme possible values and the accuracy and separation of these. The lower limit at both balance sheet dates is 25 percent of the loss carryforward plus the investment credit carryforward (with zero diSpersion).29 The upper limit for each year is equal to the gross amount of the lower limit plus 23 percent of the prOSpective ordinary income 29Assuming that the true possible gain on sale of securities plus the long-term gain on sale of machinery and equipment is greater than or equal to the loss carry- forward. In order for this assumption to be incorrect, the true valuation of securities would have to be at least forty percent lower than the indicated market value (even more for December 31, 1966). -' 93w ‘7 . ' 'J |l‘! 66 from sale of assets.30 The diSpersion, S', of the maxi- mum can be computed as: S' = .23 E] 2 '[l di i]2 all 1 where ti=.48 (I-tip) , where S' = the diSpersion of the maximum benefit p = the discounting factor "”.95 d1 = the diSpersion of the revised measurement of asset 13 ti = marginal tax rate applicable to prOSpec- tive gain on asset i. 30 The maximum benefit of the loss carryforward occurs when as much ordinary income as possible is offset against the loss carryforward. In each case this means that all assets with prOSpective gains taxable at 48 percent are sold and the rest of the loss carryforward is offset against gains taxed at 25 percent, thus the maximum bene- fit, MB, is com uted as: MB = (.48) T48 + .25(LC - T48) MB (.48) T48 + .25 LC — .25 (T48) ME = (.48 - .25) $48 + .25LC MB = (.23) T48 + .25 LC The lower limit, mb, is computed as mb = .25 LC so MB = .23 T48 + mb. The benefit of the investment credit carryforward is not affected by the type of gain since this carryforward is applied directly to the tax. 31For assets valued by reference to published figures, the diSpersion u§ed was an estimate computed as RV i 2 2 1 ‘V/(gR + T;) R I where d1 = the estimated diSpersion of the RVi for asset i which was valued by reference to published figures RVi = the revised valuation of asset 1 TR = total revised valuation of those assets valued by regression" TI = total revised valuation of those assets valued by indexed calculations DR = total diSpersion of measurement by regreSSion DI = total diSpersion of measurement by indexed calculations 67 As shown in Table 10, the difference between the minimum and maximum benefit of the tax carryforward is $78,830 for December 31, 1966 and $86,631 for December 31, 1967 with diSpersions of the maximum of $5,598 and $6,300 reSpectively. Also shown are the diSpersions of the arbitrary measurements, $803 for December 31, 1966 and $2,472 for December 31, 1967.32 The Residual Equity Section The residual equity section of the balance sheet is divided into three sections: constituents contribu- tions (invested capital), retained earnings, and income 33 The invested for the immediately preceding period. capital is shown adjusted for changes in the dimension of the monetary unit from the date of investment. The retained earnings is adjusted in a similar fashion from the end of the period in which the income was earned. The income for the period just elapsed is equal to the ending residual equity minus the beginning residual equity (adjusted for general price change). When preparing the residual equity section of X Company's December 31, 1966 balance sheet, the income from the preceding period section was omitted mainly 32See note 31. 33Chambers, pp, cit., pp. 258-259. 68 Table 10. Estimation of Accuracy of ANRV December 31, 1966 (a) Minimum benefit $69,237 DiSpersion of minimum benefit $0 (b) Maximum benefit $108,067 DiSpersion of maximum benefit $5,598 Range of benefits (b-a) $38,830 Arbitrary measurement of benefit (by allocation) $96,361 DiSpersion of arbitrary measurement* $803 *See note 31. 1967 $255,213 $0 $341,844 $6.300 $86,631 $334,747 $2,472 69 because computation of this figure would have required preparation of the December 31, 1965 balance sheet, but also because segregation of this figure was not considered necessary. Separation of the other two components of residual equity can be accomplished without the apparently indicated computation of income for preceding years. The invested capital section was first computed by adjust- ing the investment to current dollars. The retained income amount is then the total residual equity minus the invested capital. (The total residual equity is computed by subtracting liabilities from assets.) Residual equity Invested capital $1,535,170 Retained income 473 034 Total Residual Equity $2:008f204 For December 31, 1967, the two amounts above were adjusted for the change in purchasing power between December 31, 1966 and December 31, 1967. This total was subtracted from the total residual equity (assets minus liabilities) of December 31, 1967 to determine income for the year. Residual equity Invested capital $1,584,692 Retained income 488,293 Income for the preceding period 177 320 Total Residual Equity $1,895,665 70 The Full Revised Balance Sheet The full revised balance sheets are shown and com- pared with the conventional balance sheets in Table 11. The major difference in each year is the change in cur- rent assets (which results in a change in Retained Earnings). The major change in current assets is due to the increase in Marketable Securities. Machinery and Equipment is also increased while a new asset, Additional Net Realizable Value Due to Tax Carryforwards, is created. This is really an additional increase in Marketable Securities and Machinery and Equipment. This makes the total increase in these two items about $1.4 million at December 31, 1966 and $1.8 million at December 31, 1967. Accounts Receivable and liabilities (and Inventories in 1967) are decreased. As far as accuracy is concerned the receivables and liabilities have an additional source of error as far as the estimate of payment date. In the case of liabili-~ ties this is determined by contract in some cases and company intentions in some others. The receivables and remaining payables are basically determined by the weather. The money will start changing hands shortly after work begins in the Spring. The error in this estimate is not likely to be more than one month so the error in discounting of receivables will be a maximum 71 Revised $1,272,637 1,675,013 2,289,876 40 000 $5,877,525 $1,035,985 96,361 Table 11. Conventional and Revised Balance Sheets X Company Balance Sheets December 31, 1966 Conventional ASSETS Current Assets Cash $1,272,637 Marketable securities 474,979 Accounts receivable 2,382,415 Inventories Total Current Assets $4,130,031 Deferred Charges Construction supplies $40,000 Prepaid interest 70,000 Total Deferred Charges $1I0,000 Total Current Assets and Deferred Charges $4,240,031 Other Assets Machinery and equipment $2,798,530 Less: Accumulated depreciation 1,868,375 Net machinery and equipment $930,155 Additional net realizable value of assets due to tax carryforwards Total Assets $5,170,186 LIABILITIES AND STOCKHOLDERS' EQUITY Current Liabilities Accounts payable Notes payable - current Accrued payroll Accrued interest payable Accrued taxes payable Total Current Liabilities Long-term Liabilities Notes payable Total Liabilities Stockholders' (Residual) Equity Paid in (invested) capital Retained earnings Total Stockholders' (Residual) Equity Total Liabilities and .Stockholders' Equity $1,571,466 145,000 12,497 40,141 61 918 $IztsEiREZ? $2 662 500 $H,E93,522 $1,200,000 (5233336) $676,664 $5,170,186 $62409>9ZE. $1,538,999 140,164 12.497 40,141 61 918 $1,793,719 $2.607,949 $4,401,668 $1,535,170 473,034 $2,008,294_ $6,409,812 72 Table 11 (cont'd) X Company Balance Sheets December 31, 1967 Conventional Revised ASSETS Current Assets ' Cash $624,137 $624,137 Marketable securities 495,183 1,859,538 Accounts receivable 2,394,982 2,243,424 Inventories 196,333 Prepaid eXpenses 4 815 Total Current Assets $3,514,302 $4,928,247 Deferred Charges Work in process 174,317 Lumber and supplies 40,000 Prepaid interest 93,000 Prepaid eXpenses 4 815 Total Deferred Charges $312,132 Total Current Assets and Deferred Charges $3,826,434 Other Assets Machinery and equipment 3,233,408 Less: Accumulated depreciation 2,306,600 Net machinery and equipment $926,808 $1,122,918 Additional net realizable value Of assets due to tax carryforward 334 747 Total Assets $4j753,242 $6,385,9L2 LIABILITIES AND STOCKHOLDERS' EQUITY Current Liabilities Accounts payable $1,616,312 $1,503,267 Notes payable - current 232,000 224,263 Accrued payroll 5,499 5,499 Accured interest payable 40,816 40,816 Accrued taxes payable 34,442 34 442 Total Current Liabilities $1,929,069 $1,808,287 Long-term Liabilities Notes payable 2,742,250 2 681 960 Total Liabilities 4,671,319 4,490,287 Stockholders' (Residual) Equity Paid in (invested) capital $1,200,000 $1,584,692 Retained earnings (1,118,077) 488,293 Income for past year ' (177,320) Total Stockholders' (Residua1)Equity $81,923 $1,895,665 Total Liabilities and I: Stockholders' Equity $4,753,242 $6,385,912 73 34 of about .58 per cent or about $13,000. The Inven- tory amount is as good as the records supporting it. The Marketable Securities only source of error is the different prices prevailing on one trading day. The average should be very close with over fifty issues involved.35 The measurement of Machinery and Equipment has al- ready been shown to be more accurate than conventional methods for the items measured by regression and indexed calculations. Using the diSpersion estimating procedure described in footnote 31 of this chapter, the total dis- persion for those items measured by reference to pub- lished sources was computed. The complete comparison of diSpersions as shown on the following page. 3“If there is a necessity for estimating bad receiv— ables, the net receivables would be affected by a smaller amount than the gross receivables. 35NO holding of any security is a significant frac- tion of the issue. 74 December 31, 1966 December 31, 1967 Conventional Revised Conventional Revised Regression $49,922 $4,427 $63,264 $4,395 Price reference $37,360 8,137 38,447 9,521 Indexed cal- culation $20,827 $11,982 $20,784 $12,516 Total machinery and equipment $65,740 $15,143 $76,893 $16,329 DiSpersion of addi- tional net reali- zable value due to tax carry- forwards $803 $2,472 Total diSpersion of additional net realizable value of marketable securities and machinery and equipment $15,166 $16,515 The diSpersion of the revised figures is smaller for each group in each year. The total diSpersion for Machin- ery and Equipment is less than one-fourth of the diSpersion of the conventional measurements. This holds true even after the diSpersion of the Additional Net Realizable Value is added. The conclusion must be that the accuracy of the re- vised balance sheets compares favorably with the accuracy Of the conventional balance sheets and that the figures reported are substantially different. In fact, they are different enough that the prediction might be made that a reader Of the revised balance sheets might form a signifi- cantly different Opinion than he would if he had read the conventional balance sheets. CHAPTER IV THE INCOME STATEMENT Chambers gives a sample income statement on page 256: Revenues: from sales of short—term inventory from sales of durables Total revenues Costs: (i) current cash equivalent, at time of sale, of short—term inventories and durables (ii) price adjustments to short-term inventories and durables (Cr. if prices have risen) (iii) depreciation and obsolescence (iv) purchase prices Of services not assigned to short—term inventory (v) capital maintenance adjustment Total costs Business income: Total Revenues minus Total Costs Windfalls: Total Income: Business Income plus Windfalls 1 This sample statement is a starting point and employs interesting terminology, but several adjustments in wording and concept are necessary before the actual statement will either make sense or report the same income as was shown on the ending balance sheet. These adjustments will be introduced and explained together with the appropriate section of the income statement. A lR.J. Chambers, Accounting, Evaluation and Economic Behavior, p. 256. I 75 76 Revenues Revenues are "receipts of money or claims to money."2 This includes payment for all goods sold and services render— ed by X Company. Chambers mentions specifically only re— venues resulting from sales of short—term inventory and dur- ables. Revenue from sales of short—term inventory is the construction revenue, but X Company a1SO‘earns and receives interest revenue both from its security holdings and from accepting deferred payment for goods and services. This ad- dition is the first necessary adjustment of the sample state- ment. Similarly we must add dividend revenue. The revenue from sales of durables would be receipts upon sales Of machinery and equipment. This does not in- clude revenue from sales of marketable securities (which are short—term assets). Therefore we must add a section for revenue from sales of marketable securities. The resulting revenue sections of the income statements are: Conventional Revised Construction revenue $15,826,951 $15,243,065 Interest revenue 8,413 ' 533,279 Dividend revenue 82,212 82,212 Proceeds from sale of machinery and equipment 15,994 19,724 Proceeds from sale Of securities 539 736 Total Revenues $15,934,109 $15,879,017 2 Ibid., p. 257. 77 Construction revenue is discounted by use of the same procedure used for receivables in Chapter II. That is, the amounts summed are the current cash equivalents of the claims to money at the time of sale. Thus the gross revenue Of $15,826,951 becomes $15,243,065. Interest revenue is computed as the beginning re— ceivables discount plus the discounts of construction revenue during the period, less the ending receivables discount. To this result is added the amount of interest earned on secur— ities held. Discount on beginning receivables $ 32,332 Discount of construction revenue. ,5 3 * $ 6703424 Less: Discount on ending receivables 151,558 Total interest earned through acceptance. , of deferred payments $ 52“,§66 Interest revenue on bonds 8,413 Total Interest Revenue $ 533,279 One further comment on construction and interest re— venue as far as the revision is concerned: The-sum of con— struction and interest revenue is entirely independent Of the discount computed on the construction revenue. It depends entirely upon the gross construction revenue and the beginning and ending discounts on receivables.3 3In succeeding years, a record of the divergence of management's discount expectations and results might be deemed useful. In this case the construction revenue plus the interest revenue plus the divergence would be inde- pendent Of the discount of the construction revenue. 78 The point is that an error in estimation of the discount on construction receivables will result in an error in classi- fication of revenue only and-will not affect net income. The other revenue items are simply the amounts received. The conventional figures for sales of equipment and securities are different because current practice is to show only the gain on the disposal of a non-inventory item. Costs Costs iS’a rather misleadingtitle for this section of. the income statement. A more.descriptive title might be something like "Deductions from revenue" or "Charges against- revenue." Section (1) of the costs must be augmented-by the current cash equivalent of the securities sold, plus the amount of the additional net realizable value due to tax carryforwards which was used to avoid taxes on disposal of equipment and.marketabhe securities.u‘ Section (ii) must be almost cempletely rede— fined since it excludes price adjustments to marketable securities and additional net realizable value. Further, section (iii includes price adjustments to durables which for most durables are properly included under section (iii). T ”Again-marketable securities.and additional net realizable value are neither shorthterm inventories nor durables. 79 Sections (iii), (iv) and (v) need only one adjustment. The capital maintenance adjustment [section (v)] must be re— duced by the amount-of the adjustment for general price level change included in depreciation and obsolescence [section (111)].5 The cost sections of the income statement which result are: Conventional Revised Costs: (1) Current cash equivalent Of jobs sold $16,327,210 $14, 273,353 Current cash equivalent of equipment sold 15,119 Current cash equivalent Of securities sold 607 Amount of ANRV used in sales of equipment and securities 4,734 (ii) Price adjustment of marketable securities (CR.) (164,732) Price adjustment to ANRV (CR.) (243,120) (iii) Depreciation and Obsolescence 467,000 (iv) General and administrative expense. 1 V178, 48? Interest expense 201,640 534 813 (v) Capital maintenance adjustment 64,781 Less: Adjustment included in (111) (443705) Total Costs $16,528,850 $16,056,337 5In other words, Chambers' formulation of the income statement double counts part Of the capital maintenance adjust- ment. The adjustment included in sections (iii) and (v) could easily be more than twice.the proper adjustment. (The pri— mary discussion and several later comments on depreciation and Obsolescence, Chambers, Op, Cit., pp. 209, 218, 242, 265, clearly include general price level adjustments as part of depreciation and obsolescence. However, the section concern- ing entries to be made for implementation, Ibid. , pp. 254— 256, could be inconsistent on this point, if Chambers does not in— tend to include general price level effects upon durables as part of depreciation, there is no double counting.) 80 The current cash equivalent of jobs sold was computed by deducting from the gross cost of jobs ($16,501,528) the in— direct costs, the discount on the direct costs and the direct cost of the ending inventory.6 Gross cost 7 $16,501,528 Less: Indirect costs 1 702 451 Direct Costs $14,799,077 Less: Discount on direct costs 369,391 Direct costs of short-term inventory $14,429,686 Less: Direct cost Of ending inventory ' 156,333 Current Cash Equivalent Of Jobs Sold $14,273,353 The current cash equivalents of the equipment and securities sold are simply the proceeds less the discount— ed tax payments. The use of the additional net realizable value (ANRV) results from the fact that the tax payments need not be made. The price adjustment to marketable securities is simply the change in current cash equivalent of securities adjusted for disposals and additions. 6The direct costs were discounted by the same pro— cedure.used in Chapter II to discount Accounts Payable. 7Includes both general and administrative expenses and rent for owned equipment. (The "profit" or "loss" on the equipment yard is closed to general and adminis- trative expense.) 81 Marketable securities—December 31, 1967 $1,859,538 Current cash equivalent Of securities sold 607 $1,860,145 Less: Additional investment in securities 20,400 $1,839,745 Less: Marketable securities—December 31, 1966 1,675,013 Price Adjustment to Marketable Securities $ 164,732 (credit since prices have risen) The price adjustment to additional net realizable value due to unabsorbed tax carryforwards (ANRV) was computed in a similar manner. ANRV-December 31, 1967 $ 334,747 ANRV used to reduce tax.payments on sale Of equipment and securities 4,734 $ 339,481 ANRV—December 31, 1966 6 61 Price Adjustment to ANRV $ 3,120 (credit since prices have risen) The computation of depreciation and obsolescence will be covered in the next section since it is a major test of the revised income statement. The general and administrative expense was the total of the general and administrative expense and the rental of own- ed equipment exclusive Of depreciation on machinery and equip— ment since the depreciation was entered in section (iii) under Costs. General and administrative expense $908,446 Rental of owned equipment $794,005 Less: Depreciation of machinery and equipment 523,964 210,041 General and Administrative Expense $1,17 , 7 The interest expense consists of the interest actually paid on the notes payable plus a computation involving dis- counts on Accounts Payable and direct costs of jobs similar 82 to the computation Of interest revenue which involved dis— counts on Accounts Receivable and construction revenue. Discount on beginning Accounts Payable $ 32,467 Discount on direct cost Of jobs 363 391 $401,858 Less: Discount on ending Accounts Payable '7 113,045 Total amount of value received from suppliers and subcontractors through their willingness to accept deferred payment $288,813 Interest expense on Notes Payable Note One $28,656 Note Two 10,704 Note Three 176,640 Total interest expense on Notes Payable 216 000 Total Interest Expense $504,813 \ The capital maintenance adjustment is that amount by which residual equity would have had to increase if X Company were to exactly maintain its purchasing power. Chambers has indicated that his choice of index (of the general level of prices) for use in computation is the consumer price index.9 The consumer price index at December 31, 1966 was computed as the average of the December, 1966 and January, 1967 indices or 114.7 (1957—1959 =100).lo The comparable figure for Dec—, ember 31, 1967 was 118.4.11 The total capital maintenance adjustment was then computed as the product of the beginning For Notes One and Two the interest was computed simply as the reduction in discount, but this is valid only when the effective rate of interest does nOt change. 9Chambers, 2p. cit., p. 229. p S :OSurvefi 9: Current Business, VOl- 48: February, 1968’ 11Survey pf Current Business, Vol. 48, March, 1968, p. s-7. 83 residual equity, $2,008,204, and the fraction (118.4 - 114.7)/ll4.7 yielding as a result $64,781. Of this amount $44,705 was included in the depreciation and.obsolescence total so that the net adjustment in section (v) was $20,076. Depreciation and Obsolescence Chambers indicates that there are two separate components of depreciation and Obsolescence, change in measurement due to relative price change and change due to wear, tear and technical obsolescence.l2 He then states that these two com- ponents need not be shown separately.13 Thus the deprecia— tion and obsolescence of an asset is equal to the beginning current cash equivalent, adjusted for general price change, minus the ending current cash equivalent.lu For equipment held the entire year, this figure is equal to the decrease in current cash equivalent plus the increase indollars necessary to maintain the amount of purchasing power im- plicitly refused when the asset was not sold at the beginning of the year. Using this formula, the depreciation and obsolescence for l2Chambers, 9p, cit., pp. 239—240. 13Ibid., p. 242. 1“It is possible that "negative depreciation" might re— sult from relative price changes offsetting wear, tear, and technical Obsolescence. 84 X Company was $467,000 Of which $44,705 was adjustment for change in the general price level. This amount must be deducted from the capital maintenance adjustment section [section (v) of the income statement] to avoid double count— ing the adjustment for general price level change. The accuracy and tabulation of "unsuccessful" items are shown in Table 12. The same conclusion must be drawn. from this measurement as was drawn from the original mea— surement of current cash equivalent: The revised methods only fail on the least significant items. These unsuccessful items again have a total book value of $0. The majority (16 of 23) result from one Of the four disadvantage situations listed in Chapter III. The Complete Income Statement The complete revised income statement, its dispersions, and the conventional income statement appear in Table 13. The dispersion of revised net income is less than the dis- persion of the GAAP depreciation alone. Thus the accuracy Of revised net income is more than four times a generous estimate of the verifiability of conventional net income. The dispersion of the sum of construction revenue and interest revenue is computed directly from estimated dis- persions of the beginning and ending accounts receivable since the sum is independent Of the discount of construction revenue during the year. The dispersions of the accounts receivable were estimated assuming the true measure had equal probability 85 mloa x om.m mmmnmzm *310H x mm.HV *mmm «Ea ooo wmzw 0.004 em: Hmooe 0s + o + ma0a x omem mu0a 2 H0.: 000.0Ha mas.0ma :10H x 0H.mv *:-0H s mm.mv moansa *mom.ma 00m :09 muzamsam m.mm a.z: Hma m0m mmmmm coaoooaaoom mocoommaomoo pom sompmfiooaooo 0a mm 010H x.m0.m s0m.mma :10H x sm.0 m00.aa 0m0.mmma m.wm HNH soammoswmm .NH OHQmB o>oom on» mo osoz .m 000a .Hm soosoooo on psoam>advo ammo psossso mo soapoaooao o>fiummoz .owm osoauxm moaaa.mmmnopso .oapwfiamos mo x084 . momma commando ssocxco . macaw dogmmooosms: you msommom MN m:- osam>.xoon Hmpoe sozoa mos m¢tv Am<om Aamnsdov owmpsoosom msopfi mo sooszz 86 Aezaco mampou mo confismasoo mom ma x CH posOfipoos soaposapmo 029V pmpmo unofioammsmsH+ .Aopmo sampamo m on ucoam>advo nmmO anemone mo omopmcfi new» one son soapmfioosooo so Comma ohm chHmthmHo pom mpswfioz on» page poooxov HHH souomco no mm opospoom sH confisomoo 003905 on» an ,oopmeflpmo mosswfim.oo£maaoom Op mooosommp an oosam> mama“ no soamaoomfimx mam.me coamsoonao ommso>m sfi.oososoMMHQ s0:.aaa lasso soampoamHOVCOfimmoswmm sofimaoomfiov soawhoomdo CH monopoMMHo snowman mmsmufi Hammmmoozm Hmw soamaoomfio owmso>m CH mososoMMHo aoaw coamaoomfio ofi.oocmsoMMfio pmowsmq coflmmmswom AU.onoV NH mHDmE 87 Table 13. Comparison of Income Statements X Company Income Statement for the Year Ended December 31, 1967 DiSpersion Conventional Revised of Revised REVENUES: a Construction revenue $15,826,951 $15,243,065 $11,096 Interest revenue 8,413 533,280 a Dividend revenue 82,212 82,212 0 Proceeds from sale of equipment 15,994 19,724 0 Proceeds from sale of , securities 539 736 - 0 Total Revenues $15,934,109 $15,879,017 $11,096 COSTS: Cost of jobs $16,327,210 $14,273,353 $ 7,204b Current cash equiv— alent of equipment sold 15,119 0 Current cash equiv- alent of securities sold 607 0 Current cash equiv- ' alent of ANRV used 4,734 0 Price adjustment to securities (164,732) A“'0 Price adjustment to ANRV (243,120) 2,599 Depreciation and Obsolescence 467,000 6,399 General and adminis— trative expense 1,178,487 0 Interest expense 201,640 504,813 b Capital maintenance adjustment (net) 20,076 510 Total Costs $16,528,850 $16,056,337 $9,993 Total Income (Loss) ($594,74lg (177,320% $10,072 Accuracy of total income <2.36 x 10 c 9.93 x 10 a. The dispersion of the sum of construction revenue and in- terest revenue is shown opposite construction revenue. b. The dispersion of the sum of the cost Of jobs and inter- est expense is shown opposite cost of jobs. c. The figure opposite accuracy Of total income for conven— tional is the verifiability of depreciation under GAAP. 88 of being any amount within the error range (: .58 perv cent).15 The measures of beginning and ending receivables were assumed to be independent. A similar procedure was followed for the computation of the dispersion of the sum of cost of jobs and interest expense. The dispersion of the adjustment to additional net realizable value was derived assuming that the beginning and ending measurements were independent.16 The dispersion of depreciation and obsolescence was computed directly and reported in Table 12. The dispersion of the capital maintenance adjustment is the adjusting fraction (.03226) times the dispersion Of the beginning residual equity (estimated in Table 14). In Tables 13 and 14 all items whose dispersions are $0 result either from counts or legal liabilities whose date of pay- ment is specified by contract. The rectangular distri— bution is assumed for all other obligations. The dis- persion of residual equity is computed assuming all items except estimates receivable and estimates payable to sub— contractors are independent. The estimates receivable 15This assumption of a rectangular distribution prob— ably gives an overly generous estimate since if a normal distribution is assumed with the probability of the error exceeding .58 per cent being less than .05,the dispersion would decrease 13.4 per cent. 16This assumption is not valid, but is again a gener- ous estimate of dispersion. 89 Table 14. Estimation Of Dispersion of Balance Sheet Figures December 31, 1966 1967 Cash $0 $0 Marketable securities »»0 "'0 Accounts receivable 668 7,512 Inventories O O Prepaid expense 0 0 Machinery and equipment 15,145 16,329 Additional net realizable value 803 2,472 Accounts payable 5,154 5,034 Other liabilities O 0 Residual equity 15,826 17,229 Accuracy Of residual equity 6.32 x 10-'5 5.80 x 10-5 90 and payable to subcontractors are not independent since X Company acts as collection agent for the subcontractor. Therefore, any error in measurement of a receivable which will be paid to a subcontractor is offset (in the computation of residual equity) by an equal error in the measurement of the corresponding liability. This adjustment is also made for the computation of the dispersion of revised net income. The figures labeled "accuracy" for net income in Table 13 and residual equity in Table 14 are not quite estimates of ac— curacy because the dispersion measure for machinery and equipment valued by use of price indices yields only the verifiability measure. These figures have been labeled "accuracy" because that is their only component which is not an estimate of dispersion from the true figure. The conclusion must again be that in accuracy and verifiability the revised income statement compares favorably with the conventional statement and that an informed reader might form significantly different Opinions concerning the statements. CHAPTER V DISPERSION OF DIFFERENT MEASURERS In order to test empirically the diSpersion Of measurements according to the Chambers model, four doc- toral candidates at Michigan State University were asked to give measurement rules. These four students were selected because they were familiar with the Chambers model. The results may be biased by the fact that all four were attending the same graduate school. This ten— dency toward bias would probably be mitigated by the fact that they attended four different undergraduate schools. Each of the four subjects was interviewed independ— ently and informed of the type and quantity of data avail- able. He was then asked to place himself in the position of the controller of X Company and give instructions for the preparation of financial statements based on the data available. The resulting four sets of statements and the author's statements (shown in the previous chapter) were compared and diSpersions and averages computed. These averages and diSpersions are presented in Table 15. Current Assets and Revenues In all cases cash was simply accepted as the count shown in the records and therefore has no diSpersion. 91 92 Table 15. Results of Measurement by Five Measurers X Company Balance Sheet December 31, 1966 Average (A) Standard Deviation (SD)'IK SD xlOO Assets Current Assets: CaSh $1,272,637 Marketable securities 1,675,013 Accounts receivable 2,294,238 Inventories 40,000 Total Current Assets $5,281,888 Other Assets: Machinery and equipment 1,024,977 Additional net realizable value 95 750 Total Assets $6:402:6I5 $ Liabilities and Residual Equity Current LiabilitieS: Accounts payable $1,541,577 Notes payable-current 140,164 Accrued payroll 12,497 Accrued interest payable 40,141 Accrued taxes payable 61,918 Total Current Liabilities $1,796,297 Long-term Liabilities: Notes payable - non-current 2,607,949 Total Liabilities $ , O ,2 Residual Equity: Invested capital 1,535,170 Retained earnings 463,199 Total Residual Equity 11998.369 Total Liabilities and Residual Equity $6,402,615 0 0 2,187 0 2,187 7,825 370 6,906 .10 .04 076 .39 .ll .14 .12 .05 1.44 .33 .11 93 Table 15 (cont'd) X Company Balance Sheet December 31, 1967 Standard SD x100 Average (A)_ Deviation ($91-17 Assets Current Assets: Cash $ 624,137 $ 0 Marketable securities 1,859,538 0 Accounts receivable 2,245,908 2,103 .09 Inventories 196,333 0 Prepaid eXpenses 4,815 0 Total Current ' Assets $4,930,731 2,103 .04 Other Assets: Machinery and equipment 1,110,292 9,159 .82 Additional net realizable value 332 004 1,579 .48 Total Assets $6,373,027 8,623 .14 Liabilities and Residual Equity Current Liabilities: Accounts payable $1,502,265 818 .05 Notes payable-current 224,263 0 Accrued payroll 5,499 O Accrued interest payable 40,816 0 Accrued taxes payable 34,442 0 Total Current Liabilities $1,807,285 818 .04 Long-term Liabilities: Notes payable - non-current 2 681 960 0 Total Liabilities $4,489,245 818 .02 Residual Equity: Invested capital 1,584,692 0 Retained earnings 478,141 6,907 1.44 Income for prior year (179,051) 4,196 2.34 Total Residual Equity $1,883,782 8,676 .46 Total Liabilities and Residual Equity $6,373,027 8,623 .14 Table 15 (cont'd.) .Income Statement For the Year Ended December 31, 1967 Revenues: Construction revenue Interest revenue Dividend revenue From sales of equipment From sales of securities Total Revenues Costs: Current cash equiva- lent Of jobs sold Current cash equiva- lent Of equipment sold Current cash equiva- lent Of securities sold Current cash equiva- lent of ANRV used Price adjustment to securities Price adjustment to additional net realizable value Depreciation and obsolescence General and adminis- trative eXpense Interest eXpense Adjustment for change in general price level Less: Adjustment included in depreciation Total Costs Income (Loss) for the Year Current Cash Equivalent of Jobs Sold + Interest Expense 94 X Company Standard x 10 O Average(Al_ Deviation (SD) 7r' $15,237 695 $3.152 .02 536,771 3,902 73 82, 212 0 19,724 0 736 0 $15,877,I38 2,065 .01 $14,290,439 13,951 .10 15,119 0 607 0 4.734 0 (164,732) 0 (240,987) 1,248 .52 468,269 3,368 .72 1,178, 487 0 484,146 16,875 3.48 64,463 216 .34 44 356) 252 .57 _2 4‘ 5,813 .03 ($179,051) 4,196 2.35 $14,775,855 2,881 .02 95 All measurers saw no need to adjust inventories for price changes, and all chose the same method for removing in~ direct costs from ending work-in-process inventory. There- fore, these items had no diSpersion. Marketable securities show no diSpersion since all measurenscomputed the market price in the same manner and used the same procedure for arriving at net of tax from a given market price.1 Similarly no diSpersion appears in the price adjust- ment to securities or the current cash equivalent of securities sold. The accounts receivable and construction revenue were discounted using instructions from the measurers. Four used the same rates but different minimum periods for discount or methods of computing the discount. The fifth measurer used a rate, 2 per cent per quarter, which was slightly higher than X Company's cost of debt capital, .62281 per cent per month. Number Five also had a lOne measurer directed that the effects of tax carry— forwards be added directly to the assets involved, but his method of computation yielded the same total for marketable securities plus machinery and equipment plus additional net realizable value. The means and standard deviations were computed using the results which would have been ob- tained if the additional net realizable value had been reported separately. This procedure does not affect total assets, residual equity or net income. 96 different minimum discount period. Obviously these dif- ferent instructions yielded different measurements of accounts receivable and construction revenue. These in turncaused a diSpersion in interest revenue. These stan- dard deviations, ranging from $2,100 to $3,900 (or .02 per cent to .73 per cent of the corresponding average), must be considered acceptable to all but the penny- hunters.2 Prepaid eXpense, and the other revenues were accepted by all measurers at the amounts shown in the conventional books. Since no adjustments were made, the diSpersions are zero. The diSpersion of total current assets was less than $2,200 and .04 per cent for each year. Liabilities and Related Costs Four of the measurers gave the same instructions for discounting liabilities as they had given for discounting receivables. The fifth measurer changed the rate to be used for discounting. This means that all measurers used the same discount rate but different periods. These dif— ferent periods caused diSpersions in accounts payable, cost Of jobs, and interest eXpense ranging from $818 to $16,875 or .05 per cent to 3.48 per cent. Note that as 2Note also that the standard deviation of the sum Of construction revenue and interest revenue is less than .02 per cent of the average sum. 97 far as effect on income is concerned the diSpersion Of the sum of cost of jobs and interest eXpense is $2,881 or .02 per cent. The five measurers all discounted the notes payable (current and long-term) in the same fashion so there is no diSpersion for the notes payable. The other current liabilities were all due within one month of the balance sheet date which meant that none of them were discounted by any of the measurers. The diSpersions Of total liabilities were $2,111 and $818 for the two balance sheets. The percentage diSpersions were .05 per cent and .02 per cent reSpectively. Other Assets and Related Costs Machinery and Equipment. All measurers chose regres- sion as their primary valuation procedure. This did not produce common results since different regression pro- cedures were Specified by different measurers. As Table 16 shows, the diSpersion of the five measurers is less than one-tenth the diSpersion of the measures obtained from application of generally accepted accounting principles in total. The percentage of unSuccessful items is slightly over ten percent for each balance sheet date, but again these items are among the least valuable items Table 16. 98 Valuation by Regression (by Different Measurers) December 31, 1966 Reported Revised (Averagp) (a) Number of items valued by regression 115 (b) Total number to be valued 385 Percent valued by regression (number) (a/b) 29.9 (c; Valuation of items in (a) $632,438 $620,236 d Total valuation of all items $930,155 $1,024,977 Average valuation of items in (a) (C/a) $5,499 $5,393 Percent valued by regression ($) (c/d) 68.0 60.5 (e) DiSpersion of items in (a) $49,922 $3,913 Average diSpersion (e/‘[5) $4,655 $36 Verifiability * 2.00 x 10-5 2.56 x 10- (f) Number of items for which diSpersion of GAAP was lower 12 (g) Number of items for which diSpersion of five measurers was lower 103 Percent of (f) to total (a) 10.4 (h) Valuation of items in (a) $0 $4,217 Average value per item (h/f) 0 $351 (i) Valuation Of items in (b) $632,438 $616,019 Average value per item (i/g) $6,140 $5,981 Percent of valuation accounted for by suc- cessful items (i/c) 100.0 99.3 * As defined in Appendix. 99 Table 16 (cont'd.) December 31, 1967 (j) Number of items valued by regression (k) Total number to be valued Percent valued by regression (number) (j/k) (m) Valuation of items in (d) n Total valuation of all items Average valuation of items in (d) (m/J) Percent valued by regression ($) (m/n) (p) DiSpersion Of items in (j) Average diSpersion (P/fg) Verifiability * (q) Number of items for which diSpersion of GAAP was lower (r) Number of items for which diSpersion of five measurers was lower Percent of (q) to total (j) (5) Valuation of items in (q) Average valuation per item (s/q) (t) Valuation of items in (r) Average valuation per item (t/r) Percent of valuation accounted Reported $500,778 $926,808 $4,280 54.0 $63,264 $5,849 1.58 x lO-5 $1,806 $129 $498,972 $4,844 for by successful items (t/m) 99.6 -)(- As defined in Appendix. Revised (Average) is 26.8 $575,050 $1,110,292 $4,915 51.8 $4,391 $40 2.28 x 10‘ 14 103 12.0 $5,674 $405 $569,376 $5,528 99.0 100 Table 16 (cont'd.) ANALYSIS OF UNSUCCESSFUL ITEMS 1966 1967 1. Unknown purchase price 6 4 2. Extreme age 3 3 3. None of the above 3 7 Largest difference in diSpersion of items in 3. $39 $32 Difference in average diSpersion of items in 3. $20 $9 Largest difference in diSpersion of successful items $19,984 $18,574 Difference in average dispersion of successful items $4,505 $5,802 101 in this group.“ Further the difference in average dis- persions and largest difference in diSpersion (favoring GAAP) of the unsuccessful items are insignificant com- pared to the same figures for the successful items (favoring revised figures). The verifiability of the five measurements was greater than 2.25 x 10-4 compared to the verifiability of the GAAP measurements which was less than or equal to 2.00 x 10-5. The five measurenschose reference to published fig- ures as their second measurement method. All instructions yielded the same results as were shown in Table 7 (Chapter III, p. 53). These results are also presented in Table 17. The uniformity Of results means that the verifiability measure is not defined.5 This verifiability, however, is greater than the verifiability of any set of measurements with a positive standard deviation. All measurers directed,the same procedure for val— uing items which could not be valued directly by either of the above methods. . 'L v “This can be seen by comparing the average valuations (book value or revised) of the successful items with the average of the unsuccessful items. 5The measure of verifiability derived in the Appen- dix yields 6.which is not a valid number. ' 102 ammo 0 0 ammo sam.:a 0 0 sam.ea 0% 0 0 on ma 0 0 ma 0-0Huamm.s 0-0a x 00.: 0-0a x mo.m 0-0a x 00.m 00m.m0 mmm.aa amm.ma mmoqao oes.mma www.0ma oom.sma www.mea mas.me mama mmm.aa 003.0% 0.00s m.0H m.Hm o.m0 . 004.0mma Hom.0oaa 00m.smaa mma.mm0a 0-0H x m.s 0-0H x 0m.w + -0H s 0m.m memo mea.sa 0W ems aoo.maa Hmm.asa 0 mam.m% www.ma Home 00m.sa m0m.m 0.00s m.0H m.0m m.00 ssm.am0.aa mmo.moaa 000.00ma 0mm.0m0o 0.00s 0.mm 0.H0 0.0m 0mm >44 00H was Hmpoe *xoocH Cowpmowfioza COHmmosmom mumszmmoz o>Hm an mpomm< pooam no GOHpoSHm> no msmsssm mmma .Hm sooeoooo Aoomw>mmv Amv CH msopw mo soflpmsam> owwso>< Amy CH msopa mo oon> ooma>mm Amv CH msopw mo moam> xoom smsoa mos m< soflmsoomflo ommso>< Cowmsommfim ozam> xooo owoso>< AosHo> xooov owmpcoosom moao> moom nm< ooflmsoamflo ommso>< coamsoomfim cowpmoam> owmso>< ACOHPmSHm> oomw>osv ommpooosom soapmsHm> “QMmH>mm Asoosoov owopooosom msopfi Mo gonadz .SH canoe 103 mm «so>ozom .Osou coop sopmosw we cowmnmamwo moon: psosmsomoms has mo apflawnowmwso> one sonv hopmoaw.wH szHHomHmwsm>.onp .ouon m0 cowmhoomao one .ouon ma soamsoamac ozp sons penance #0: ma thHaQoHMHAo> mo assumes o£B+ .ss:HOO wasp CH cow: was mosao> soon mo scamsoamao oopmsnom one oasoonom :oapowoonaoo msapmwxo so no owov Iso>om onp o>oson op nacho :H owns 0 0 mafia aso.m% 0 0 use mm 00m.H 0 0 oom.a as 0 0 0H cowmhmmmac m-0H x 0m.H 0-0H x Hm.a 0-04 x oo.m muoH x mm.a amonma cummaa somnme osmnmo m00.0so 40s one see 0mm son moo owe me mwse 0ms.aa omm.eo 0.00H H.HH 0.3m 0.0m mom.mmma smm.moaa mm:.mmma ms».00ma muoa x mm.s 0-0H x mm.s + auoa x mm.m mmow emonaa 0% 003% own man 040 was 0 Ham 0% 0:0.mo mama www.ma mam.e 0.00s s.m m.wm m.Hm mmm.0aa.aa 0:0.mosa sma.smew 0m0.msmo 0.00s 0.0m H.m: m.0m 0m: Hma was was Hopoe *xoooH COHPoOHHoom cowmmoswom hwma «Hm nonsmoom A.o.osoov as 04000 .pHdmmm memo map oopaowh mHoHSmooE an oocwavso woonvos HH<* Acoma>omv Any :0 maovw mo coauodao> owouo>< ADV CH macaw mo osao> oomw>om ADV :H msopa mo osao> xoom hosoa mos m<¢u mo Evans you macaw mo nonssz ADV "MSHBH qpmmmmUoDmZD spaaaoouuano> sowmhommwo owoho>< soamnoowan ooam> moon owoho>< Aosao> xoonv owopsoonom coam> xoom um< coamnommao owmso>< soawnommwn sowposao> owono>< AsowposHo>V omopCoOhom :OHposHo> "QHmH>Hm Ascendsv owopcoonom mace“ mo sonaoz 104 The method and results are the same as those des- cribed in Chapter 111 (pp. 52-55) and reported in Table 8 (Chapter III, p. 56). The results are also summarized 'in Table 17. Although the actual diSpersion is zero, the diSpersions shown are those which would result if the indexed calculations were performed using all reasonable depreciation methods. This was done because the measurers directed that the existing depreciation methods be used. If these depreciation methods had not already been in use for these particular assets, the measurers would have had to choose from the set of ”reasonable" depreciation methods (acceptable to the CPA). ‘The resulting diSpersion would probably have approximated the adjusted diSpersion of book values (Chapter III, pp. 55-57). The indicated diSpersion thus puts the revised methods on the same basis as GAAP as far as choosing a depreciation method.6 Table 17 shows that the total GAAP diSpersion for Machinery and Equipment is at least five times the dis— persion of the revised measures at each balance sheet date. In other words, the verifiability of the revised measures is five times as great as the verifiability of the GAAP measurements. 6Note that this is the only method which requires a choice of depreciation procedures. The other revision methods do not require the accountant to exercise judgment in the choice of depreciation procedures. Thus an ele- ment of subjectivity is removed. The removal of this ele- ment of subjectivity accounts for a large part of the difference in diSpersion of the conventional and revised valuation methods. 105 The measurers gave equivalent directions for computa- tion of depreciation and obsolescence and ending current cash equivalents. Thus the diSpersions of items measured by reference to published sources or indexed calculations were zero. These were adjusted upward in the case of the items measured by indexed calculations for the reasons mentioned above. The diSpersions for items measured by regression are a direct result of the diSpersions in current cash equivalents at the balance sheet dates. The total of these diSpersions is $3,226 for the revised and $35,297 for GAAP giving the revised measurement a verifiability more than ten times the verifiability of the GAAP measure- ments. There were only ten unsuccessful items out of 121 with six of these items having a zero diSpersion for GAAP due to unknown purchase prices and one item which had an unrealistically low purchase price. The difference in average diSpersion for the other three items of $17 indicates that when the diSpersion of GAAP was lower, it was not lower by very much (largest difference in dis- persion was $37). (See Table 18.) Additional Net Realizable Value Due 32 Tax Carryforwards. Four measurers gave instructions which resulted in the same values for Additional Net Realizable Value Due to Tax 106 4H .so>ozom «moosoomm .Osom ooze sopoosw m4 o04msoam4e moons pomeossmmme mom mo mp444o048446> one cons sopmosw m4 mp444o04w4sm> map .Oson ma CO4msoomHU one .Osom m4 COHmsmamflo one some omsammo poo m4 mPHHHomHmaso> mo osommos 058+ .CESHOO m4£p SH mom: was mosam> xooo mo Cowmsoamao oopmsnom 039 on op sooso SH m. 0 0 amen 0% on e4a 0 04 ems 0a 0a m 0 0 4 0 0 m o o 04 0 0 m-04040m.m m-O4mem.m 0-04 x m.4 mmm.mza 00m.044 mas.0ma 4-04 x s.4 -04 s 4.m + mms.m% 0a.:a 0o 040M4 004a 4004 00a 0044 000 sea one 0s4a 0.004 m.mm 4.44 am: 4m4 mom 4oooe *xooc4 co4ooo44oom whosommoz o>4m an mocoOmmHOmoo pom ss0.ma s40.o44 4. sass s44 ems \Or—lm m-04 x mm.m smm.mma 4-04 x 4.m www.mo mmm.4a mm0.4mma S.mm Hma Cowmmoswmm COHpmHOosmom .pHSmms meow ocp pooaowz moosSmmoE ho oocHHPSO moocpoe HH<* COHmsmmmHo omoso>o :4 oooosoMMHm ACO4msomm40 m<o 24 somehoMMHQ m s4 meoPH mo oOHmsoom40 :4 oooosmMMHo pmomsmq o>ooo one mo ocoz .m oOHsQ ommnosoa OHQmHHmoa no good .m moans commends ozosxob .4 msopfi HSMmmoooswss you msomoom sozoa we: m< Amaaov :o4msoom4o sp444oo444so> Apom4>osv CO4msoom4m .mwmsm>< mocoOmmHOmoo pom ooHpoHOosmoo ooma>mm owmpooosom meop4 mo someoz .m4 o4ooe 107 Carryforwards and its price adjustment. The fifth measurer instructed that the additional net realizable value be disclosed,not separately, but as a part of the current cash equivalent of the assets involved. The method of computation yielded the same total result for ANRV as would be the case if computed in total under instructions from one of the other measurers. Therefore, for compara- bility, the ANRV for this measurer was shown separately and adjusted separately on the income statement.7 The effect of this was to alter for this measurer the values reported for marketable securities, machinery and equipment and ANRV, but not total assets. Items affected on the income statement were current cash equivalents of equip- ment and securities sold, current cash equivalent of ANRV used, price adjustment to securities and ANRV and depreci- ation and obsolescence. Neither total costs nor net income was affected. With this change in instructions, the computations of the ANRV were performed in the manner described in Chapter III (pp. 63—65). The diSpersion of prOSpective gains inherent in the diSpersion Of current cash equiva- lents of equipment caused diSpersions of $370 and $1,579 in the ANRV at December 31, 1966 and December 31, 1967 reSpectively. Both of these diSpersions were less than 7This was the only case where the measurers' instruc— tions were not followed. ' 108 one-half of one percent of the average ANRV, $95,750 and $332,004 reSpectively. The diSpersion of the price adjustment to ANRV was $1,248 or about one-half of one percent of the average adjustment, $240,987.8 Residual Equity and the Remainder of the Income Statement The total residual equity is simply the difference between total assets and total liabilities. Since total assets and total liabilities have diSpersions, residual equity also has a diSpersion on each balance sheet. This diSpersion is in each case less than one-half of one per- cent of the average residual equity. Within residual equity, invested capital has no diSpersion since all measurers directed identical general price level adjustments of prior investments using the same index. The retained earnings at December 31, 1966 (total residual equity minus invested capital) thus shows all of the diSpersions of residual equity.9 At December 31, 1967, the diSpersion of total residual equity has two sources, retained earn- ings and prior year's income. At this date, diSpersion of residual equity $8,676, is still less than one-half of one percent of average residual equity but the diSpersion 8 The diSpersions of the current cash equivalents of equipment sold and ANRV used are zero since the market value is observed not estimated. 9Translation of a distribution does not affect its standard deviation. 109 of prior year's income, $4,196, is 2.35 percent of the average prior year's income. This is the highest ratio of diSpersion to average for any attribute reported in Table 15 (except interest eXpense which acts in conjunc- tion with cost of jobs sold to produce a much smaller effect on total costs). The adjustment for change in general price level showed a diSpersion due to the diSpersion in beginning residual equity. This can be checked by multiplying the diSpersion of beginning residual equity, $6,691, times P —P _1 0 118.4 - 114.7 . PO <' 114.7 to verify diSpersion of the price level adjustment, $216. The ratio the adjustment factor of the standard deviations to the averages were equal as a result of this relationship. The diSpersion of the portion of the general price level adjustment included in depreciation and obsolescence results mainly from the diSpersion in valuation of Machinery and Equipment held at December 31, 1966.10 General and administrative expense was accepted without adjustment by all measurers due to the short period of time between receipt of services and payment for those services. 10The absolute value of adjustment for change in general price level included in depreciation and obsoles- cence varies almost directly with the weighted average investment in assets during the period. 110 Total costs averaged $16,055,947 with a standard deviation of $5,413 (.03 percent Of the average). This deviation certainly must be classified as acceptable. The deviation of net income (resulting from the diSper— sions of total revenues and total costs) was $4,196 coma pared to the average loss of $179,051. This should also be considered as acceptable eSpecially in light of the diSpersion of depreciation measures possible under alter— native generally accepted accounting principles, $42,355. The diSpersions of measurements as directed by five 3 independent measurers and reported in Table 15 were in each case less than the estimated diSpersions Of revised measurements presented in Tables8 and 14 (ChaptersIII, IV, pp. 56, 89). The results Of this test then should further reinforce the results and conclusions of Chapters III and IV, namely, that the revised statements report the finan- cial position and the results Of Operations of X Company with more verifiability than conventional statements. Further the reader of the revised statements would prob- ably form a significantly different conclusion regardirg X Company if he were presented with the revised rather than the conventional statements. CHAPTER VI COST AND CONCLUSIONS Cost. One property of any application of a new accounting r- technique or system, which should be determined, is the cost. I In this case the cost was computed as the additional ex— penditure necessary to restate the two conventional balance Sheets and one income statement. This will basically be the L cost of the Operations described in Chapters II, III, and IV. The total cost of conversion was $1,975 as detailed in' Table 19. The times shown are actual hours of each type of l The hourly rates are the rates at labor or computer use. which X Company was being charged at that time for that class of labor. The hourly rate for the computer usage was the rate chargeable for the computer on which the conversion was actually performed (a CDC 3600) rather than the rate for the machine X Company used at the time (an IBM 1401). Clerical work included cOding of regression observa— tions, coding Of parameters of actual equipment, lThe keypunch-verify time, the actual time, is generous since the operators were not as skilled as the Operators who would have been used by X Company. The computer time is, to some extent, an estimate because the actual runs computed and compared dispersions and did the computations for Chapter V as well as the work necessary for the preparation Of one set of statements. This adjustment did not effect the amount charged for regression, which was the major part of the computer usage. 111 112 Table 19. Cost of Conversion Total Conversion Costs Function Rate Hours CIerIcaI $4.007hr. 137.48 Keypunch—verification $10.50/hr. 15.03 Programming $10.00/hr. 5.00 Computer $245.00/hr. 4.97 Total Conversion Costs Regression Costs Clerical $4.00/hr. 17.48 Keypunch—verification $10.50/hr. 11.66 Programming $10.00/hr. 3.00 Computer $245.00/hr. 4.87 Total Regression Costs Conversion costs not using regression One—Time Costs* Clerical $4.00/hr. 115.00 Keypunch—verification $10.50/hr. 2.38 Programming $10.00/hr. 4.00 Computer $245.00/hr. .05 Conversion costs after first year *Assuming no savings on regression after first year. Total 4550 158 50 $1 217 $1,975 $70 123 30 $1 192 $If415 $560 $460 25 40 12 $537 $1,438 113 valuing equipment by price reference, and coding (for discount- ing) intervals between incurrence and payment of obligations. The keypunch and verify work transferred the coded data to cards. The programming and computer time performed the re— gressions, discounted the receivables and payables, applied the regressions to the equipment parameters to determine es— timated-current cash equivalents, performed the indexed calcu— lations, and used the previously determined beginning and end- ing current cash equivalents to determine depreciation and Obsolescence. The major part Of the cost of conversion was the cost associated with the regressions, $1,415. Thus if the re— gression method Of valuation were deemed unnecessary, the cost Of conversion would be $560.2 Another side of the cost picture is the amount of costs which would only be incurred at the time of initial conversion. These are the costs associated with the discounting procedure. These costs would be avoided after the initial conversion be— cause the records would be kept showing expenses and revenues at net rather than-gross amounts. The discounting costs avoided in later years (one-time costs) totaled $537 making the recur- ring_costs $1,438 (assuming the regression technique was used in these years). This is probably an overestimate since the 2Remember that the published figures were available for all items valued by regression. 114 knowledge gained from the regressions run it initial con- version would probably reduce the costs of regression in later years. The question of the advisibility Of.incurring this $2,000 of additional cost must be answered by comparing this cost to the benefits of the conversion. The benefits will not be measured here, but with $16 million plus Of costs any improvement in management due to the information provided by the revised statements would be almost certain to exceed $2,000. Conclusions. All of the evidence in Chapters 11 - V indicates that, in this situation, the revised measurements show dis— persion\which should be acceptable to statement users. The dispersion of revised net income was about five percent when estimated in Chapter IV.3 The actual dispersiOn of five measurements Of net income was 2.35 percent. Most of the adverse predictions in Chapter I indicated the belief that the major problem would be the valuation of fixed assets.5 The results showed very clearly that the 3Table 13, p. 87. ”Table 15, p. 92. 5Pp. 2-3. 115 revised methods were more objective (verifiable) than the methods acceptable under generally accepted accounting principles. The regression technique provided the greatest amount of comparative data. Under this method, the accuracy was ten times greater than the accuracy of generally accepted accounting principles.6 Unsuccessful items (those for which the dispersion of methods acceptable under GAAP was less than the dispersion of the regression) had a total book value of zero and total revised value of about one percent of the revised value of the items valued by regression.7 The com— ; parison of dispersions of depreciation emphatically support the conclusion that regression was able to measure these assets more objectively than conventional depreciation methods. Further, seventy percent of the items were valued directly with their total value (book or revised) equalling approximately ninety percent Of the value of fixed assets. This figure would probably be increased if the Chambers model was widely used since increased demand for sale data. and published-resale prices would cause increased and more diversified supply. The conclusions stated above do not prove.that the Chambers model is generally applicable in all situations. 6Tables 4 and 5, pp. 40-41. 7Ibid. 8Table 12, p.85. and Table 13, p. 87. 116 They indicate that the model was practical in this particular situation. The further statement could.be made that the model would probably be applicable to companies similar to X Company. The one overriding general conclusion is that a large scale study should investigate.a wider sample.of companies (possibly over a longer period of time) to deter- 4 ' '. —’¢ U: mine the extent of the situations.in which the model is practical. BIBLIOGRAPHY BIBLIOGRAPY Accounting Research Division, American Institute of Certi- fied Public Accountants. "Disclosing Effects Of Price-Level Changes." Appendix D in Accounting Research Study Number 6. New York: AmerICan Insti- tute Of Certified PublIc Accountants, 1963. Pp. 167-218. Black Book. Gainesville, Georgia: National Auto Research, Inc., 1967, 196 . ' Blue Book pf Heavy Equipment Prices. Lincoln, Nebraska: Forke BrOthers Inc., 1967. Business Statistics. Washington, D.C.: Office of Business Economics, 1963, 1965. Chambers, Raymond J. Accounting, Evaluation and Economic Behavior. New York: Prentice—Hall, Inc., 1966. Committee to Prepare a Statement of Basic Accounting Theory. A Statement pf Basic Accounting Theor . Evanston: American Accounting Association, 1966. Dickerson, Peter J. Business Income-~A Critical Analysis. Berkeley: Institute of Business afidTEconomic Research, University of California, Berkeley, 1965. Dickinson, Arthur L. Accountinngractice and Procedure. New York: The Ronald Press, 1914, cited by Kenneth, MacNeal, Truth in Accounting, New York: The Ronald Press, 1939. —_' Edwards, Edgar and Philip Bell,. The Theory and Measure- ment pf Business Income. BerkeIey: University of California Press,“l96l. Fertig, Paul E. on Howard Ross._ "The Pursuit of Useful- ness," Berkeley Symposium on the FOundations of Financial Accounting. BerkEIey: SEEDOI Of BusIfiess Administration, University Of California, Berkeley, 1967. Pp 0 90‘93 a Green Guide. Palo Alto, California: Equipment Guide- BOOk Company, 1966, 1967, 1968. Hicks, gé R. Value and Capital. Oxford: Clarendon Press, 19 . 117 118 Ijiri, Yuji and Robert Jaedicke. "Reliability and Objec- tivity in Accounting Measurements," The Accounting Review, July, 1966, 474-483. Kircher, Paul, on Howard Ross. "The Pursuit of Useful- ness,” Berkeley Symposium on the Foundations of Financial Accounting. BerEEley:766hool of BuSIness Administfation, University of California, Berkeley, 1967. Pp. 94-97. The Measurement of PrOperty, Plant, and quipment in “7 FinanciaI’SfEtemenES. Boston: Harvard UniverEIty, Graduate SchoOl of Business Administration, 1964. MacNeal, Kenneth. Truth 1p.Accounting. New York: The Ronald Press, 9 9. Montgomery, Robert H. Auditing Theory and Practice. New York: The Ronald Press, 1913, cited by Kenneth MacNeal, Truth in Accpunting. New York: The Ronald Press, 1939. '7' Nelson, Carl, on R. J. Chambers. "The Foundations of Financial Accounting," Berkelgy Symposium on the Foundations of FinanciaIIAccounting. BerkEIeyT—School of Business AdministratIOn, University of Cali- fornia, Berkeley, 1967. Pp. 50—54. Red Book, Official Used Car Valuations. Chicago: National Market Reports, Inc., 1967, 1968} Ross, Howard 1. The Elusive Art 2£_Accounting. New York: The Ronald Press, 1966. . "The Pursuit of Usefulness," Berkeley Symposium on the Foundations of Financial Accounting, Berkeley: SEhoOl of Business Administration, University of California, Berkeley, 1967. Pp. 76-89. Sprouse, Robert and Maurice Moonitz. ”A Tentative Set Of Broad Accounting Principles for Business Enter- prises," Accounting Research Study Number 3. New York: American Inefitute of Certified PublIc Accountants, 1962. Pp. 1-59. Survey Of Current Business, January,l966, p. S-8; February, 1968, pp. S-7, S-8; March, 1968, p. S-8. Truck Blue Book, Official Used Truck Valuations. Chicago: National Market Reports, Inc., 1967, I968. 119 von Mises, Ludwig. Human Action. London: William Hodge and Company, Ltd., I939, cIted by R. J. Chambers. Accounting, Evaluation and Economic Behavior. New York: Prentice-HaII,_I9667 'T Werntz, William, on Robert Sprouse and Maurice Moonitz. "A Tentative Set of Broad Accounting Principles for Business Enterprises," Accounting Research Stud Number 3. New York: American Institute 6? er fied Public Accountants, 1962. Pp. 79-82. Zlatkovitch, Charles T., on R. J. Chambers. "The Founda- tions of Financial Accounting," Berkeley_S osium on the Foundations of Financial ACcounting. Berkeley: SEhEEI'6?:Business Administration *UnIVersity of California, Berkeley, 1967. Pp. £5-49. APPENDIX APPENDIX ACCURACY AND VERIFIABILITY Ijiri and Jaedicke have defined a measure they call reliability.l Unfortunately, this measure requires that the decision maker's predictive function be known. This means that the measure of reliability depends upon the decision-maker. For this study (and probably other pur- poses), it is more useful to define a measure of accuracy which is independent of the decision-maker and his predic- tive function.2 Thus accuracy, A, is defined by (l) where the x are a set of n measurements of the same attribute of a particular item or entity. ' T is he true measure of the attribute. lYuji Ijiri and Robert K. Jaedicke, "Reliability and Objectivity of Accountin Measurements," The Accounting Review, July, 1966, pp. ETA-483. f 2The reliability measure combines two factors, veri- fiabilityemm.accuracy of predictive function. If the predictive function chosen is poor, the set of measurements is automatically very low irl reliability regardless of the susceptibility to measurement of the attribute being measured and the precision of the methods used. Since this study is concerned with the susceptibility to measure- ment of certain attributes of a firm and the precision of the methods which can be employed to measure these attri- butes, the reliability measure must be rejected. 120 12l The concept of accuracy can also be related to the accountant's concept of objectivity. Because objectivity is a state of mind (freedom from bias), it cannot be measured directly. This does not present a problem since the aver- age accountant considers a measurement to be objective if many different accountants, measuring the same attribute, would give the Same or similar measures as their result. The concept might more prOperly be called verifiability and could be defined as: V“2 = 5H4 HP15 —-2 . (Xi ' X) (2) 1 l where: the Xi are a set of n measurements of the same attribute of a particular item or entity n 'f =-£ 2 x. = the mean of the measurements. n 1 i=1 n - or V: n _, =51. 2 (X. - X) 1 i=1 from (1) A‘2 = %- Q (xi - T)2 i=1 n A"2 = %. 1:1 [(xl - x) + (x - T)]2 n A-2 =5}: 1:1 [(xi _ 36)2 + 2(xi—35)(§ — T) + (“ - in?) A'2 =—l_ :21 (x.—3'c')2 +3 £31 [(x -33\(§-T)] n i=1 n i=1 1 n +% :(X-T)2] (3) l22 -n2+fi-TF (m A-2 = V"2 + (E - T)2 or, A'2 = v'2 + 52 (5) where B = x - T = bias (6) 2 Since B a O, A'2 2. v'2 or 1 l — > _ A2 " v2 inverting A2 s V2 taking positive square root A S V (7). Therefore the measure of accuracy, A, is less than or equal to the verifiability, V, of the same set of measurements. The condition for equality of (7) is that B (from (6)) = O. This would be the case where the mean of the measurements was equal to the true measure of the attribute, i.e., where bias is zero. Otherwise A < V. 123 Groups of Items The measure of accuracy AS of the sum of a group of n items which were independently measured will be defined as: 1 n n '7’ - = 2 Are 8 ¥ S i=1 1 ( ) Similarly the verifiability of such a sum is: § —1 n .2 .‘i v = 2: V. (9) -— S i=1 1 ' from (7) Ai E—Vi for each i, i = l,2,...,n. Since each element in the sum in (8) is less than or equal to each element of the sum in (9), SV (10) A s S n The condition for equality in (10) is the 2 B. = O, or that the mean of the measures for each item in the group must be exactly equal to the true measure of that item. If this seemingly rather improbable condition does not exist, the more likely relationship is AS < Vs’