“HUNTING FDR CUMMUN STOCKS E’Ul CHURCH PENSION FUNDS - AN EMPIRICAL EVALUATION Thesis for the Dome of Ph. 3. MICHIGAN STATE UNIVERSITY mm: mm HBRRIS, TR. 1911 —“" arr-“rt“: This is to certify that the thesis entitled ACCOUNTING FOR COMMON STOCKS FOR CHURCH PENSION FUNDS - AN EMPIRICAL EVALUATION presented by William John Morris, Jr. has been accepted towards fulfillment of the requirements for Ph. D . Accounting degreein étd ”3/6 C u' ‘— LIQ'((‘<" C—i hhfinpumuun Date ‘DC—Qi'noé~'y A5; /‘/‘-/0 0-7839 ABSTRACT ACCOUNTING FOR COMMON STOCKS FOR CHURCH PENSION FUNDS - AN EMPIRICAL EVALUATION by William John Morris, Jr. The general subject of this research effort is the valuation of equity securities held as a long term investment. An example would be securities held in a pension fund, where the objective is to pro- vide a specified retirement income amount at a distant future date. At what amount should the investment in equity securities be carried on the balance sheet in the published financial statements? The purpose of this study is to provide a useful answer to the question posed above for a specific situation, a church pension fund. Church pension funds issue published financial statements, giving rise to a need for valuation of common stocks. A research methodology was developed to provide a useful solution to this problem. This research methodology is summarized below: 1. Development of the accounting objectives based upon usefulness. 2. Development of specific criteria an accounting method should possess; the specific criteria being based upon the accounting objectives. 3. DeveloPment of a mathematical model to measure the effec— tiveness of accounting methods in meeting the criteria. 4. Testing of alternative accounting methods by use of actual William John Morris, Jr. data and by simulation. 5. Use of the model to rate the accounting methods, and selec- tion based upon this rating. The research has been conducted as proposed. The results can be summarized as follows: 1. Accounting objective: equitable allocation of earnings to participants. 2. Specific criteria: a) closeness to market value. b) stability of yield 3. Mathematical model: C2 = [w] C3 + c: ; where C3 is a mea- sure of closeness to market value, C is a measure of stability of 2 Y yield, and [w] is a weighting factor. 4. Test alternative accounting methods: book values and yields computed for twenty—one selected accounting methods for an actual church fund and for a fund simulated by the researcher. A high correlation of results between the funds was observed. 5. Rate accounting methods: six acceptable methods ranked in order; the other fifteen methods rated inferior. Each accounting method specifies a formula for computing the carrying value of the equity securities. The accounting methods recommended specify the valuation of equity securities which best meet the objec- tives of church pension funds. Historical Cost Method The study revealed that the Historical Cost Method of account— ing for common stocks is the least efficient method to achieve the William John Morris, Jr. objectives of church pension funds. It is recommended that the Histori- cal Cost Method of accounting be abandoned by all funds presently using this method. Current Market Value Method The study also revealed that the Current Market Value Method of accounting is very inefficient in achieving the objectives of church pension funds and is not an acceptable alternative to the Historical Cost Method. Any one of the six methods rated acceptable would be strongly preferred as an alternative to the Current Market Value Method. Recommended Methods of Accounting The conclusions of the study regarding recommended accounting methods are summarized below. The following three methods are highly recommended and ranked in the order listed: 1 and 2. Two Minimization Formula Methods developed by the researcher, equally ranked. 3. Moving Average Market Value Method, based upon an average of 5 years. The following method is considered acceptable but ranked much lower than the above methods: 4. 20% Write-up each Year of the Difference between Adjusted Book Value and Market Value. For those pension funds with high utility preferences for closeness to market value, two additional methods are considered acceptable. William John Morris, Jr. Donald J. Bevis stated in the lecture series sponsored by Michigan State University that the great problem of the Seventies is bringing the recognition of current values into financial statements. Perhaps the approach taken in this research study can be of assistance in seeking solutions to this problem. Donald J. Bevis, "Distinguished Accountants Videotape Series, Sidney Davidson and Donald J. Bevis" (East Lansing, Michigan: Michigan State University Lecture on August 3, 1970). ACCOUNTING FOR COMMON STOCKS FOR CHURCH PENSION FUNDS - AN EMPIRICAL EVALUATION by William John Morris, Jr. 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 1971 NJ (:> Copyright by WILLIAM JOHN MORRIS, JR. 1971 ACKNOWLEDGMENTS I would like to express my deep appreciation to the many people whose help and encouragement contributed to my ultimate success in the Ph.D. program. To Dr. James Don Edwards, Chairman of the Department of Accounting and Financial Administration, I express my gratitude for the advice and assistance that aided in my completion of the doctoral program. The consideration and guidance of Professor Floyd W. Windal (Chairman), Cary K. Stone, and Hal W. Hepler greatly facilitated the completion of this dissertation effort. The discussions and criticism of my colleagues Elba F. Baskin and Robert G. May were particularly helpful in getting the project started. The suggestions by Professor Herbert E. Miller concerning the early formulation of the research design were significant contributions to the continuation of the project. The editorial review by my colleague George W. Krull was greatly appre- ciated. The extraordinary effort and competence of Josephine McKenzie in expediting the completion of the dissertation was also appreciated. I express a special appreciation to B. J. Chenault, Treasurer of The Annuity Board of the Southern Baptist Convention for his assistance and encouragement throughout the study. For the honor of being selected as a fellowship recipient and for the financial assistance thus provided, I take this opportunity to thank Ernst & Ernst and the Earhart Foundation. To my wife, Mary, for her willingness to leave a comfortable life and undertake the relatively spartan existence of a graduate ii assistant, and for her love and encouragement throughout the program, I express my thanks and my love. To my children, Nancy, Marilyn, and John I eXpress my appreciation for their being my children. iii TABLE OF CONTENTS Page ACKNOWLEDGMENTS. . . . . . . . . . . . . . . . . . . . . . . . . ii LIST OF TABLES o o o o o o o o o o o o o o o o o o o o o o o o 0 Vi LIST OF FIGURES. o o o o o o o o o o O o o o o o c o o o o c o 0 1X Chapter I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . l A. Purpose B. Background C. Method D. Significance II. DEVELOPMENT OF CRITERIA. . . . . . . . . . . . . . . . 9 A Criteria Summarized B. Usefulness of the Information C. Users D Uses E. Alternative Methods of Allocation of Total Income F. Estimation III. ACCOUNTING METHODS .'. . . . . . . . . . . . . . . . . 26 A. Basis of Selection B. General Characteristics of Accounting Methods C. Discussion of each Accounting Method D. Summary of Methods Selected IV. RESEARCH DESIGN. . . . . . . . . . . . . . . . . . . . 60 A. The Model B. The Sample C. The Evaluation V. RESULTS — EVALUATION OF TESTS. . . . . . . . . . . . . 80 A. Reporting the Results B. Comparison of Funds C. Comparison of Time Periods D. Summary iv Chapter VI. RESULTS - PRELIMINARY EVALUATION OF ACCOUNTING METHODS. . . . . . . . . . . . . . A. Selection Criteria B. Selection of Better Accounting Methods C. Summary VII. RESULTS - FINAL EVALUATION OF ACCOUNTING METHODS A. Comparison on the Basis of each Factor B. Comparison on the Basis of 3 Sensitivity Analysis C. Comparison Based upon Unbiased Weights D. Evaluation of the Methods E. Summary VIII. SUMMARY, CONCLUSIONS AND EVALUATIONS . . . . . A. Summary B. Recommendations for Church Pension Funds C. Implications for Society BIBLIOGRAPHY . APPENDIX . . . Page 92 141 168 175 178 10. 11. 12. 13. 14. 15. 16. LIST OF TABLES Common stock data, facts assumed . . . . . . . . . . Rank of allocation methods . . . . . . . . . . . . . Values resulting from application of mathematical model to sample fund accounting results. . . . . . . Ordinal ranking of accounting methods ranked in inverse order by "C” . . . . . . . . . . . . . . . . Comparative statistics for sample funds. . . . . . . . Comparative ranking between sample funds . . . . . . . Coefficient of rank correlation between time periods Internal rate of return, 1946 - 1969 comparison with other data . . . . . . . . . . . . . Frequency distribution of percentage deviation from market value, Internal Rate of Return MQChOd, 1947 - 19690 0 o c o o o o o o o o o o o o 0 Comparison with other data, I. Historical Cost Method. . . . . . . . . . . . . . . . . Frequency distribution of percentage deviation from market value, 1. Historical Cost Method, 1947 - 1969. I o a o o o o o o o o o o 0 Frequency distribution of fluctuation in yield, 1. Historical Cost Method, 1947 - 1969 . . . Comparison with other data, II. Initial Cost with Formula Modification Methods. Number of years book value equaled historical cost value, C2 value and rank, II. Initial Cost with Formula Modification, 1947 - 1969. . . . . Frequency distribution of percentage deviations from market value, II. Initial Cost with Formula Modification, 1947 - 1969. Frequency distribution of fluctuation in yield, II. Initial Cost with Formula Modification, 1947 '- 19690 0 o o o o o o o o o o o o I o o o o o 0 vi Page 16 66 81 82 84 86 90 95 98 101 102 104 107 110 112 114 Table Page 17. Comparison with other data, IV. Current Market Value Method. . . . . . . . . . . . . . . . . . 118 18. Frequency distribution of fluctuation in yield, IV. Current Market Value Method, 1947 - 1969 . . . . . 119 19. Va. Market Value, Less a Reserve, Comparative "C” value data . . . . . . . . . . . . . . . . . . . . 122 20. Frequency distribution of percentage deviations from market value, Va. Market Value, Less a Reserve, 1947 - 1969 . . . . . . . . . . . . . . . . . 123 21. Frequency distribution of fluctuation in yield, Va. Market Value, Less a Reserve, 1947 - 1969 . . . . 125 22. V. Adjusted Market Value Methods, Comparative ”C" value data . . . . . . . . . . . . . . 127 23. Frequency distribution of percentage deviation from market value, V. Adjusted Market Value Methods, 1947 - 1969 . . . . . . . . . . . . . . 129 24. Frequency distribution of fluctuation in yield, V. Adjusted Market Value Methods, 1947 - 1969 . . . . 131 25. III. Modification based upon both Initial Cost and Current Market Value, comparative "C" value data . . . . . . . . . . . . . . . . . . . . 133 26. Frequency distribution of percentage deviations from market value, III. Modification based upon both Initial Cost and Current Market Value, 1947 - 1969 . . . . . . . . . . . . . . . . . . 136 27. Frequency distribution of fluctuation in yield, III. Modification based upon both Initial Cost and Current Market Value . . . . . . . . . . . . . . . 138 28. Frequency distribution of percentage deviations from market value, 1947 - 1969 . . . . . . . . . . . . 143 29. Frequency distribution of fluctuations in yield, 1947 - 1969 . . . . . . . . . . . . . . . . . . 145 30. AB Fund, sensitivity analysis, ranking of selected accounting methods for weights indicated. . . 149 31. Sensitivity analysis - AB Fund, ranking of selected accounting methods for weights indicated . . . . . . . 150 vii Table Page 32. Computation of average rank. . . . . . . . . . . . . . . 156 33. Correlation coefficient between average rank and weighted C2 values AB Fund. . . . . . . . . 158 viii LIST OF FIGURES Figure Page 1. Book value of common stock recorded by various allocation methods . . . . . . . . . . . . . . . . . . l8 2. Annual rate of return computed on book value of common stock recorded by various allocation methods . . . . . . . . . . . . . . . . . . 18 3. Least squares trend line of market value, data from Table l O O O O O O 0 O O O O I O O O O O O 56 ix CHAPTER I INTRODUCTION A. PURPOSE The general subject of this research effort is the valuation Of equity securities held as a long term investment. An example would be securities held in a pension fund, where the objective is to provide a specified amount of retirement income amount at a distant future date. The term equity security will be used interchangeably with the term common stock. "Common stock is defined as a stock which is sub- ordinate to all other stocks of the issuer."1 At what amount should the investment in equity securities be carried on the balance sheet in the published financial statements? The purpose of this study is to provide a useful answer to the question posed above for a specific situation, a church pension fund. Church pension funds issue published financial statements, giving rise to a need for valuation of common stocks. Since the funds are also sub- ject to annual audits, the valuation acceptable for audit purposes and for published financial statements should be in agreement. A signifi— cant problem in the determination of a valuation for Common stocks is the lack of a specific criterion to determine the method of valuation. 1Accounting Principles Board, APB Opinion No. 15: Earnings Per Share (New York: American Institute of Certified Public Accountants, May, 1969), p. 273. Many church pension plans are participatory plans. A partici- patory plan is a pension plan whereby the benefits paid are a function of the earnings of the pension fund. The amount credited to the par- ticipant on a periodic basis as a distribution of earnings determines the benefits to be paid. The method of valuation of common stocks will affect the periodic earnings credits and therefore the benefits paid to a participant. B. BACKGROUND General - Private Pension Funds A private pension fund is organized to administer specific funds for a group of employees. These employees have specific employment characteristics such as a common employer, common work tasks, or member- ship in a common union. The fund should Operate in accordance with instructions set out in a pension plan trust agreement. The principal relationships are those among employee, employer,. and pension fund management. The employee is the beneficiary covered by the pension plan trust agreement. The employer is the organization that employs the beneficiary, usually makes a substantial contribution towards payment of pension plan benefits, and is usually responsible for the liabilities imposed in the trust agreement. Pension fund management acts as a custodian of the pension fund and has varying responsibilities for investment policies as determined in the pension plan trust agreement. 1Joe J. Cramer, Indiana Business Information Bulletin 55: Accounting and Reporting Requirements of the Private Pension Trust, (Indiana University: Foundation for Economics and Business Studies: 1965), 6-8. The general purpose of the pension fund is to receive cash during an employee's work years, invest the funds to earn a return, and pay amounts to the employee during retirement or at other times under conditions specified in the trust agreement. The receiving and investing process for a specific employee may be continuous for 20 to 40 years before payment begins. This is a long term process. Long term goals and objectives should therefore be primary considerations of management policy,1 and should be given primary consideration in determining accounting and reporting policies. The investment function is a significant activity of the fund. A change of 1% in the average return for the fund assets over the work life of an employee can have a significant effect upon the amount available for retirement benefits and upon contributions required to fund the benefits. Assume contributions to an employees account in a retirement plan are $50 a month or $600 a year. Assume also that the employee participates in the plan for 40 years prior to retirement. The total contributions over the 40 year period are $24,000. If the pension fund earnings are credited to the participant's account at a 3% rate over the 40 years, the balance in the account at the end of the 40 years would be $45,919. If the credits to the account are at a 4% rate, the balance in the account at the end of 40 years would be $57,777. The balance in the account credited at 4% is in excess of 25% greater than the balance in the account credited at 3%. 1Ibid., p. 12, ”The long-run solvency of the pension trust, the crucial issue . . . ." 21bid., p. 77, 85. Church Pension Environment A church pension fund is a private pension fund set aside to provide retirement and related benefits for employees of a specific church group. The church group is usually a denomination such as Southern Baptist Convention, United Methodist Church or United Presby- terian Church in the USA. A church pension fund has at least two char- acteristics that distinguish it from many other private pension funds: 1) Many private pension funds have a single corporate entity responsible for the contributions to the fund. Such a corporate em- ployer can therefore specify the amount of risk of loss of principal it is willing to take in order to increase investment earnings and reduce its pension contributions. Most church pension funds do not have a single corporate entity that the fund can look to in case of a deficit of funds. A church pension fund cannot ordinarily afford high risks of loss of principal and expected earnings. The implications of this environment are that a church pension fund must specify a low risk investment policy and attempt to maximize return within this low risk. It would not seem unusual for average return to be lower for a church pension fund than for many corporate pension funds. 2) Church pension funds are virtually free of governmental control. There are presently no highly restrictive tax laws governing the amount of contribution the employer may make to the pension fund, since the employers are normally tax exempt institutions such as There are certain restrictions on the amount of the pension contribution provided by the employer. These restrictions are based upon the salary of the employee and affect the tax status of the em- ployee and not that of the employer. churches, educational institutions, hospitals, etc. The church pension funds are exempt from the major reporting requirements for private pen- sion funds imposed by the federal government under the Welfare and Pen- sion Plan Disclosure Act of 1958, subsequently amended in 1962.1 States do not generally regulate investments, benefit provisions or reporting policies for church pension funds as they do for insurance companies and bank trust departments. The limits of the regulations imposed upon the church pension funds are the legal requirement to meet the contrac- tual obligations of the trust agreement and the requirement to meet the general duties of a trustee as interpreted by the courts. The implica- tion of this freedom from governmental control is that investment deci- sions and reporting practices are unencumbered by many of the institu- tional constraints that restrict other private pension funds. Environmental Assumptions Since the purpose of this research effort is to provide a useful solution to a specific problem, the solution will be subjected to the following environmental constraints: 1) Present user needs for specific information will be accepted. For example, actuaries use a single rate of return to compute liabilities. No consideration will be given to the fact that a prob- ability distribution of rates of return might provide a better base to compute the liabilities. 2) The study will not be bound by present technicalities of 1President's Committee on Corporate Pension Funds and Other Pri- vate Retirement and Welfare Programs, Public Policy and Private Pension Programs, A Report to the President on Private Employee Retirement Plans, (Washington: U.S. Government Printing Office, January, 1965), p. 14. generally accepted accounting principles, but the philosophical base of present generally accepted accounting principles and reporting standards will be accepted. For example, the method of valuing equity securities should provide an objective measure, not necessarily historical cost, although some subjective estimate may be better according to some criteria. Additional environmental factors that will be excluded from con- sideration in this research are the effects of the Federal Income Tax laws and institutional regulation prescribed by the various governmental agencies. One of the major reasons for the selection of church pension funds is that these funds have relatively few constraints placed upon their accounting and their investment activity by governmental laws and regulations. C. METHOD There does not seem to be an explicit statement of purpose of financial reporting for church pension funds and thus no explicit state- ment of criteria to guide in selection of methods of valuation. There- fore, deveIOpment of criteria to provide a ranking of various accounting valuation methods will be a major part of the dissertation. The cri- teria will be the result of a theoretical development based on manage- ment and/or participant objectives for equity securities for church pension funds" A mathematical model will be developed incorporating the speci- fied criteria. Various alternative accounting methods, including some of those commonly used in current practice and some experimental, will be applied to the common stock portfolios of a theoretical pension fund and an actual pension fund. Annual yields and book values over a long period of time will be computed by each accounting method. The mathe- matical model, having the benefit of hindsight, will utilize the com- puted yields and book values to rate each accounting method. The most efficient methods1 will be selected and recommended for use. Other characteristics of the accounting methods will be observed and results reported. D. SIGNIFICANCE There have been many articles written concerning accounting for equity securities and studies have been made evaluating investment per- formance. Apparently there have been no studies made using an actual pension fund showing the effects on the financial statements of using alternative accounting methods.2 The major contribution of the proposed study is: a. The development of an explicit statement of criteria to judge accounting methods, and development of a model to incorporate these criteria. The ideas embodied in the model are not original. The explicit statement and model are original contributions. 1John E. Freund, Mathematical Statistics (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1962), pp. 218-219. An estimator is said to be a most efficient estimator if its mean square error (MSE) is at least as small as that of any other estimator. The mathematical model developed in the study has some of the mathematical properties of the MSE. 2Paul H. Jackson and James A. Hamilton, ”The Valuation of Pen- sion Fund Assets," Society of Actuaries - Transactions, XX (1969), 386-417. This related study was undertaken. This study used alterna- tive accounting methods applied to corporate pension funds to determine effect on the annual pension contribution of the corporation. This study did not evaluate the effects on the pension fund financial state- ments. b. The subjecting of the proposed methods of accounting to an actual case history and evaluating each accounting method on the basis of observed results. Historical cost is the present method in use by a large number of pension funds. Various other methods are also in use, including current market value. The study exposes to pension fund man- agement the effects of using the alternative accounting methods. This would provide the means of selection of accounting methods on a more informed basis than is presently available. The results of the research may provide the foundation for generalizability beyond church pension funds. Future research efforts could compare and distinguish between church pension funds and other institutional investors in equity securities to determine the extent the results of this research effort can be extended beyond church pension funds. CHAPTER II DEVELOPMENT OF CRITERIA A. CRITERIA SUMMARIZED Usefulness to eligible participants of the pension fund and the management of the fund will provide the bases for judging accounting methods. The primary use of financial reports (and valuation methods) is to compute annual income that equitably allocates earnings to par- ticipants. The critical theoretical question with regard to the valuation of common stock is the allocation of the difference between the pur- chase price and sales price to accounting periods. This is the amount represented by the gain or loss on sale of common stock when accounting by the Historical Cost Method. Allocation of this difference to provide a constant rate of return over the holding period is the method that equitably allocates earnings to participants and meets the other re- quired uses for information. Estimation of the rate of return for each common stock prior to sale is the major problem facing the accountant. Two characteristics of an increase in the value of common stock at a constant rate are (l) stability of yield and (2) closeness to market value. Therefore, the objective method of estimation, that has demonstrated its ability over long periods of time to provide the best combination of stable earnings and closeness to market value, is the appropriate method of 9 10 accounting for common stocks. B. USEFULNESS OF THE INFORMATION Usefulness will be adopted in this research effort as the basis for the search of a method of valuation of equity securities.1 "In establishing . . . standards, the all-inclusive criterion is the useful- ness of the information."2 What is meant by usefulness? The notion of usefulness implies that some person (or group) is thereby informed re: some purpose. That method of accounting for common stock investments for church pen- sion funds that meets the needs of users of the financial statements in a most efficient manner will be judged the better method. Users and their needs are the subject of the next sections. C. USERS The principal users of financial data for church pension funds are the employers, the employees and management of the fund. These are the principals that have a financial interest in the performance of the fund. There may be other distant users such as other pension funds or society in general, but these users are remote and will not be given consideration in this study. The basic philosophy embodied in our federal constitution of separation of church and state is one of the Elden S. Hendricksen, Accounting Theory (Homewood, Illinois: Richard D. Irwin, 1965), p. 98; Cramer, Private Pension Trust, p. 59. American Accounting Association, A Statement of Basic AccountinggTheory (Chicago, Illinois: American Accounting Association, 1966), p. 3. 11 major reasons that government has not acted as an interested party in the affairs of church pension funds. The term "participants" will be used to identify the employee- employer group. D. USES There are two basic types of pension plans that can be offered. These will be referred to as participatory and non-participatory. The participatory plan is a pension plan whereby the benefits paid are based upon the balance accumulated in the employees account upon retirement. The earnings credited to the employee's account annually are based upon the earnings of the pension fund. The amount credited to the employees account as a distribution of earnings deter- mine the benefits to be paid. Variable annuity plans are a sub-set of this classification. The non-participatory plan is a plan whereby benefits are a fixed contractual obligation of either the pension fund or the em- ployer. The current benefits paid are not a function of the current earnings of the pension fund. Benefits will generally be changed for a non-participatory plan through amendment of the contract as a result of a change in the long term rate Of return. Participants in the non- participatory plans have a financial interest in the method of com- puting earnings of the pension fund, although only indirectly. A pension fund can offer either type of plan or a combination of the plans. Where the information requirements differ for each type of plan, designation of the type of plan will be noted in the dis- cussion. 12 The uses are: l. Allocation of earnings to participants. 2. Other uses a. Stewardship b. Evaluation of management c. Computation of actuarial liability d. Amending pension plan benefits. Allocation of Earnings to Participants Many pension funds offer participatory plans whose benefits are based upon the amount in the employee's account upon retirement. For this type of pension plan, earnings credited to the employee's account on an annual basis directly affect the benefits received. The most important use for the publiShed accounting information is to provide a basis for allocation of amounts to the employees. The earnings from investments in common stocks are the algebraic sum of the cash flows. Proper allocation to each time period of these flows is necessary in order to give employees an equitable share of the earnings. The allocation method is frequently determined by an agreement between the participants and the managers of the fund. This method can be made explicitly in a written agreement or can be from a general understanding. In order to provide a flexible program for participants, some pension funds offer optional plans based upon the method of allocation of earnings to the participants of the fund. One type of plan, fre- quently referred to as a variable annuity, specifically requires that earnings be allocated to the participants on the basis of cash receipts 13 from dividends plus changes in market value of the investments for each time period. Contributions by participants for this type of plan are generally segregated into a separate fund. Other participatory plans usually provide for the current period earnings to be allocated on the basis of a rate of return on the participants investment in the fund. Sometimes these plans will guar- antee some minimum rate of return with participation in any excess earnings. If earnings are understated, benefits are transferred from present participants to future participants. If earnings are over- stated, excess benefits are given to present employees at the expense of future employees. If earnings credits fluctuate significantly, par- ticipants will be less able to project their own benefits, and the un- certainty of benefits will make the pension plan less desirable from the viewpoint of both the employee and employer. In those cases where the contract between the pension fund and the participant is explicit in its statement of the method of deter- mination of periodic earnings, then this specified method must be used. For participants in a variable annuity fund a method of allocation of earnings to time periods based upon market value changes is needed. If the contract between the pension fund and the participant is not explicit in defining the method of determining periodic earnings, then an equitable rate of return is needed. An equitable rate will be discussed in the next section. Other Uses It can be demonstrated that the method of valuation of common 14 stocks that provides an equitable allocation also meets the other specified uses. Since determination of earnings to provide an equit- able distribution to participants would in general take precedence over other uses,argument in support of the above statement is not con- sidered necessary. The stewardship function will be discussed since there are certain aspects of this use that any method must satisfy. Stewardship. An important function of reporting is management's report to the participants on its stewardship of the assets entrusted to the pension fund and on the ways in which the assets have been utilized. The outside auditor's Opinion covering the financial reports of the pension fund is an important aspect in discharging this stewardship function in reporting. Consequently, the financial reporting must meet standards acceptable to the independent CPA. Acceptable methods will be discussed in the next section. The method of valuatiOn should also be one that can be made understandable to a non-financial expert. This understanding is important in order to maintain confidence in management by the par- ticipants. Unintelligible methods could lead to the impression of manipulation by management. Since understanding differs in all people, management should have the option of selecting, from among several acceptable alternative methods, the method that its constitu- ents can most easily understand. Methods that become commonly accepted do develop a credibility because of their general use. Commonly used methods also become better understood because of the more widespread interest in them. Therefore, methods that are clearly inferior are not justified on the basis of simplicity alone. 15 In summary, to perform the stewardship function, the common stocks must be valued in accordance with the standards of the account- ing profession. Summary of Information Requirements The information needed can be condensed to the following items: 1. Current earnings that equitably allocate earnings to participants. a. Current market changes or other specified method. b. Equitable rate of return on assets. 2. Valuation method not in violation with the standards of the accounting profession. E. ALTERNATIVE METHODS OF ALLOCATION OF TOTAL INCOME Earnings from investments in common stocks are the algebraic sum of the cash flows. The uses stated in the previous section require accountability by periods, and therefore, a major objective in account- ing for common stocks is to allocate these earnings to specific time periods. For purposes of this presentation, a distinction is drawn be- tween theoretical allocation methods and accounting methods. An under- standing of this distinction is essential to comprehend the remainder of the chapter. 1. Accounting methods are defined as methods capable of implementation in the actual world of uncertainty. These methods make no assumption of future knowledge. 2. Theoretical allocation methods are defined as the methods 16 of allocation of income assuming a knowledge of future income, sales price and date of sale for a given security at date of purchase. An illustration will be used to examine the theoretical basis for allocation of total income, as defined above, to specific time periods. The discussion in this section assumes a known total earnings, only methods of allocation being in question. The next section deals with the case of an uncertain future sale price for common stocks. Assume a stock was purchased December 31, 1965 for $100, no dividends will be paid and the stock will be sold for $146 on December 31, 1969. How should the $46 of earnings be allocated to time periods? See Table I for a display of the facts assumed. TABLE I COMMON STOCK DATA FACTS ASSUMED 12/31/65 12/31/66 12/31/67 12/31/68 12/31/69 Cost. . . . . . . . . $100.00 Sales price . . . . . $146.00 Market value. . . . . 100.00 $95.00 $120.00 $150.00 146.00 Dividends . . . . . . . . . . . . . . Earnings per share. . 6.00 7.00 10.00 10.00 Let us now review the possible bases for allocation of income and select the theoretical allocation method that satisfies the 17 information needs that have been established. This is a discussion of theoretical The I. II. III. IV. allocation methods and 22$ specific accounting applications. basic methods of allocation are: Allocate the entire amount ($46 in the example) in the period of sale (Historical Cost Method) or allocate to periods subsequent to sale. Allocate equal amounts ($11.50 per year in the example) (Equal Amounts Method) or some other arbitrary amount each year. Allocate based upon the reported earnings of the company in which the investment has been made (Earnings Method) or on the basis of some other indicator of economic progress of the company. Allocate based upon the market changes in each of the respective time periods (Current Market Value Method). Allocate amounts based upon a rate of return (10% per year in the example) that when applied to the purchase price of the investment, will generate an amount that will equal the sales price when the investment is sold (Constant Rate of Return Method). See Figures 1 and 2 for illustrations for the allocation methods. Use 1: Equitable Allocation of Earnings to Participants The primary use for valuation of common stocks is the determin- ation of an equitable allocation of earnings to participants. Alloca- tion of earnings must be in accordance with the provisions of the book value rate of return 150 140 130 120 110 100 50 40 30 20 10 -1O 18 1965 1966 1967 1968 1969 FIGURE 1 BOOK VALUE OF COMMON STOCK RECORDED BY VARIOUS ALLOCATION METHODS ll, ‘/ ./ 11“ / // \ / / \/ x”, ..-./ ...... ”g IL): __/.__...-—----'-"/" ‘\'-~ / ' \ / -/_ ........... \ / 1965 1966 1967 1968 1969 FIGURE 2 ANNUAL RATE OF RETURN COMPUTED ON BOOK VALUE OF COMMON STOCK RECORDED BY VARIOUS ALLOCATION METHODS I. = cost 11. °'°' = equal amount III. --°- = earnings IV. —-_- = market V. -—- = rate of return l9 pension plan. In those cases where the pension plan is specific with regards to the method of allocation of earnings, equitable allocation means allocation in accordance with the plan specifications. For a typical variable annuity plan, earnings must be determined on the basis of periodic market changes in the common stock investments. This is allo- cation method IV. This research study is not concerned with those cases where the allocation method is specified. For other plans, in which the method of determining the earn- ings of the pension fund are not specified, equitable allocation must be supported by the inherent equity of the allocation method. Each of the five methods of allocation described above will be examined by logical reasoning to determine the relative equity of the methods. This research study will be concerned only with plans in which the method of determining earnings are not specified in the pension plan. Method I. Historical Cost. A definite purpose in investing in equity securities is to achieve an increment in value of the investment through growth in the value of the assets of the company in which the investment is made. The participants in the fund whose cash is being used to make this investment should share in this growth. Therefore one attribute of an equitable method of allocation would be some system- atic method of allocation during the holding period of the asset. By this criterion, Method 1, Historical Cost or allocation of the income in a period subsequent to sale of the asset, is clearly less equitable (since the increment does not all occur, presumably, at sale date) than other methods that apportion the increment in value during the holding period for the common stock. 20 Method II. Equal Amount. Allocation of an equal dollar amount each year results in a declining annual rate of return. This is the result of an increasing investment base applied to a constant amount of earnings. See Figure 2 for an illustration of this declining rate. To allocate on the basis of equal amounts favors early participants over the later participants by awarding a higher rate of return without a significant reason for so doing. It would appear that all amounts of investment should be treated equally in the absence of some specific reason for not so doing. Therefore, to allocate equal dollar amounts each year would be clearly inferior to method V., allocation on the basis of a constant rate of return, which treats each dollar of invest- ment equally. Any arbitrary method of allocation of earnings to apportion in- come to participants would open management of the pension fund to criticism and possible lawsuit for being unfair. Therefore, any method of allocation should rely on its inherent equity and not be an arbi- trary method of allocation specified by management. Method II can be discarded as being inferior to other methods as an equitable method of allocation. Method III. Earning_. Economic factors such as earnings of the Company in which the investment is made, might be considered as the basis for an equitable method of allocation of income. However, the change in the value of the common stock from the date of purchase to the date of sale is the result of many factors of which "interim", i.e., annual earnings are only one factor. The market value at the date of sale (sales price) is the result of the market's appraisal of the future earnings of the company. 21 Past levels, stability and direction of earnings are important factors that are used in judging future earnings. However, it is the future earnings that are valued at that point in time, not past or current earnings. The market price is the result of a consensus evaluation of all economic factors (including earnings) affecting the company. Thus, it would appear that a change in market price would be a method of allocating income superior to the use of the underlying current earn— ings of the company or some other single economic factor. Method III can be discarded as inferior to Method IV as an equitable method of allocation of income. Methods IV and V. Current Market Value and Constant Rate of Return. At this point Method IV, allocation on the basis of market changes, and Method V, allocation on the basis of a constant rate of return have been judged superior to other methods of allocation as being equitable. The purpose and intention of management and the par- ticipants are important factors in determining an equitable method of allocation of income. In those cases where a church pension fund offers a variable annuity plan as an option, and the participant elects not to choose it, it is clear that the intention of the participant is to avoid the short term risks of annual market fluctuation. Therefore, to treat each dollar of investment equally and apportion earnings on the basis of constant rate of return is clearly the more equitable method of allo- cation of earnings. For other church pension funds where optional plans based upon current market changes are not available, treatment of each dollar of investment equally would be the more defensible position as an equitable 22 method of allocation of earnings, than to subject participant's annual earnings to the emotionalism and instability of annual market fluctu- ations. Method V, the Constant Rate of Return Method, which treats each dollar of investment equally, meets the requirement of equitable alloca- tion of earnings for pension plans where a method is not specified in the pension plan agreement. Use 2: Allocation by Methods Acceptable to the AccountingpProfggsion The method must not be in violation of generally accepted accounting principles. Pronouncements of the Accounting Principles Board (APB) and its predecessor are considered as specifying generally accepted accounting principles. The APB has not specifically dealt with the subject of valuation of common stocks for financial reporting purposes, although the Board in APB 8 gives indirect attention to the item in discussing the determination of the provision for pension cost for corporate entities with pension plans. The Board believes unrealized appreciation and depreciation should be recognized in the determination of the provision for pension cost on a rational and systematic basis that avoids giving undue weight to short-term market fluctuations.1 Items not specifically covered by pronouncements of the APB are subject to considerable latitude in their treatment. The general criteria applied to valuation of common stocks would include: 1. Measurement by an objective method. 2. A value that is reasonable in the judgment of the auditor. 1Accounting Principles Board, APB Opinion No. 8: Accounting for the Cost of Pension Plans (New York: American Institute of Certified Public Accountants, November, 1966), p. 80. See also discussion on pages 78-80. 23 Method V, the Constant Rate of Return Method, appears to provide a basis for accounting methods that are objective and reasonable. Method V recognizes unrealized appreciation and depreciation on a rational and systematic basis that avoids giving undue weight to short-term market fluctuations. Summary of Allocation Methods In general, allocation of the increment in market value of com- mon stock during the holding period best meets the needs of the users if allocation of income is on the basis of a constant rate of return over the holding period. It is concluded that Method V, the Constant Rate of Return Method, is the best theoretical method of allocation of income for investments in equity securities by church pension funds. This theoretical allocation method is applicable to all church pension plans where the earnings allocation method is not specified in the plan agreement. F. ESTIMATION The question has been answered concerning the most useful method of allocation of income to accounting periods. A Constant Rate of Return, Method V, has been determined the most useful method of allo- cation of appreciation or depreciation for equity securities. This determination was made on the assumption that the total income from an investment in a common stock is known ($46 in the example displayed in Table I). However, total incOme, including appreciation, is not known until after the investment has been sold. The problem of estimation of this amount prior to sale is the difficult problem facing the accountant. 24 Referring to theoretical allocation methods discussed in the preceding section, there are two characteristics of the constant rate of return method that can be observed from the example. 1. One characteristic is a stable earnings rate. That is, the earnings rate does not fluctuate from period to period. Therefore stability of yield is a characteristic of the constant rate of return method. 2. Another characteristic is that the sales price equals the computed value at the time of sale with no adjustment required. That is, equality of market price and a computed value at a specified time in the future for a specific equity security owned is a characteristic of the Constant Rate of Return Method. Since the specific time of sale is not known, closeness to market value at all times would pro- vide closeness to market value at the time of sale. Thus, two desirable characteristics of a method of estimation to approximate the constant rate of return method of allocation of in- come would be stability of yield and closeness to market value. Projecting a specific future expected rate of return for each particular stock would involve subjective estimates of such return. The success of such a method would depend upon the ability of the esti- mator. This ability is an unknown factor and would not provide a useful guide for accounting for common stocks. In addition, any subjective method of estimation is not readily capable of audit verification and would not likely meet criteria of objectivity as a method in accordance with generally accepted accounting principles. A more useful approach would be to select an objective method 25 (formula) that has performed as the most efficient method in the past. For accounting purposes, most acceptable methods of estimation are selected on the basis of past performance (bad debt expense computa- tions, rules for obsolescence, etc.). Therefore, a specific computa- tional method that has exhibited the characteristics of the Constant Rate of Return Method most efficiently over the past would be a logical method to select as a method for estimation for the future. It has been observed that two characteristics of the Constant Rate of Return Method of allocation of income are stability of yield and closeness to market value. Methods of estimation can be judged as reasonable methods based upon their past performance. Therefore, the accounting method that best meets the needs of church pension funds will be judged on the basis of its past performance over a long period of time. The criteria for judging will be closeness to market value and stability of yield. CHAPTER III ACCOUNTING METHODS These criteria for judging accounting methods have been estab- lished: (l) closeness to market value, and (2) stability of yield. Accounting methods will be judged by these criteria on the basis of their past performance over a long period of time. Various alternative accounting methods to be studied will now be selected. There are an infinite number of formulas that can be devised as methods of accounting for common stocks. Jackson and Hamilton list 37 methods in a single article. A. BASIS FOR SELECTION In order to reduce the many possibilities to a reasonable num— ber of methods for study, methods will be selected to the following bases: 1. Those methods presently in use. 2. Those methods that have a theoretical appeal in terms of the criteria specified in this study. The methods selected should include a representative cross—section of classes of alternative methods. The classification method developed by'Jackson and Hamilton in their study provide logical groupings and lJackson, ”Valuation of Assets," 412-415. 26 27 will be utilized to orderly present alternative methods of accouting. Methods Presently in Use In June, 1969, the Chase Manhattan Bank published the results of a survey of corporate pension funds.2 There were 502 funds that provided useable responses to their survey. This recent survey will be cited as the source for accounting methods presently in use by corpor— ate pension funds. It will be referred to as The CMB Study. Approximately 51% of the funds (255) use the historical cost method of accounting.3 The other 242 firms giving information on accounting methods use some type of write-up method.4 The CMB Study lists the following seven methods that over 80% of the 242 firms use: I. Long range appreciation method. II. Long range yield method. III. Write-up of some percent each year of the difference between adjusted book value and market value. IV. Use of an "earnings method” whereby book value is adjusted for the difference between common stock dividends and the actual per share earnings. V. Utilize a moving average market value based on the average of several years. VI. Assets are valued at full market value. lIbid., p. 389—390. 2Theodore G. Kane, Survey on Pension Fund Financing (New York: The Chase Manhattan Bank, N. A., June 1969). 3Ibid., Table 10a. 4lbid., Table 11. 28 VII. Write-up adjusted book value by amount required to equate with interest rate assumption. All of these methods will be tested in this study. The following methods with modification have been used by church pension funds in their financial reporting and/or to determine earnings available for credit to participants: 1. Historical cost. 2. Write-up of some percent each year of the difference between adjusted book value and market value. 3. Long range appreciation method. 4. Market value less a reserve. These methods with their respective modifications will be included in the Study. The accounting methods included in this study on the basis of present use are those methods cited above. Methods with Theoretical Appeal In the preceding chapter desirable characteristics of an accounting method were specified. They are: l. Closeness to market value. 2. Stability of yield. 3. Systematic allocation of appreciation (depreciation) during the holding period of the asset. 4. Objective method of valuation. l"Important Developments of the Year" as reported by the Administrative Office of each Board (The 1969 Church Pensions Con— ference); interviews with selected pension board personnel, 1970. 29 One of the criteria specified as a desirable characteristic for an accounting method was closeness to market value. In order for any method to bear some systematic relationship to market value, current market price must be included in the formula, either as a direct compu- tation or as a delimiting factor in the computation. Any method that does not include market value as specified above will be close to mar- ket value only by chance. Changes in economic conditions of the market and/or investment strategy could render such methods as inadequate, in terms of the criteria established in this paper. Therefore, a method with a theoretical appeal must include market value in the formula. Stability of yield is another desirable characteristic. One of the objections cited to the use of current market value as a method of accounting is the wide fluctuation in yield that results from its use. Any method that averages market values or specifically considers stability of earnings in the computation would tend to improve upon the current market value method in terms of stability of yield. There— fore, a method with theoretical appeal will use some form of averaging of market values or will specifically provide for stability of yield. Methods that defer recognition of gain or loss after date of sale of investments or give recognition of gain or loss before acquisi- tion of the asset would be rejected on the basis of not being equitable. A method with theoretical appeal must attempt a systematic allocation of appreciation (depreciation) during the holding period of the asset. Subjective methods will be rejected. A method that requires periodic review and revision of parameters based upon judgment is lCramer, Reporting Requirements, p. 80. 30 considered subjective. Methods that require projections of investment results to select current parameters will also be considered subjective since Opinions about future results are subjective. Methods with these characteristics do not meet the criteria of objectivity cited in the preceding chapter. Additional methods will be selected for testing on the basis of theoretical appeal. Methods with theoretical appeal will be obtained from suggestions proposed in the literature and will be deve10ped by the researcher. Frequently the methods suggested in the literature are the methods presently in use and classified in the CMB Study.1 Jackson and Hamilton in their study utilized a group of formulas in the adjusted market value classification worth further consideration.2 A repre- sentative method described in their article will be included in this study. This method will be labeled "Market value with variable adjustment". Two additional methods will be considered that were not given specific reference in the articles reviewed. One method is a modified market value method that averages market values and projects a value by use of a least squares trend line. The other method will be called a minimization formula. The method is a variable percentage write—up method. The percentage is changed each year to maximize stability of yield and closeness to market value in some predetermined ratio. 1Kane, Pension Fund Financing, Table 11. 2Jackson, "Valuation of Assets," p. 415. 31 Representative Cross-Sections of Types of Methods The classification developed by Jackson and Hamilton will serve as criteria to determine a representative cross—section of accounting methods.1 The assignment of a method to a specific classification is based upon this researcher's judgment. These classifications and the accounting methods to be included in this study are as follows: I. Initial cost. a. Historical Cost Method. II. Initial cost with formula modification. a. Long Range Yield Methods. b. Long Range Appreciation Methods. c. Write-up Adjusted Book Value by an Amount Required to Equate Earnings Yields with Interest Rate Assumption Methods (Minimum Yield). d. Earnings Methods. III. Modification based upon both initial cost and current market value. a. Write—up some Percent each Year of the Difference between Adjusted Book Value and Market Value Methods (Percentage Write-up). b. The Minimization Formula Methods. IV. Current market value. a. Current Market Value Method (Market Value). V. Adjusted market value methods. a. Market Value, Less a Reserve Method. 1Ibid., 389-390. 32 b. Moving Average Market Value Methods, based upon average of several years (Moving Average). c. Least Squares Trend Line Methods, based upon market value for several years (Trend Line). d. Market Value with Variable Adjustment Methods (Variable Adjustment). VI. Present value methods. 3. None. Methods of accounting representative of each class except Class VI have been included in this study. No Class VI, the present value methods, have been included. These methods are generally impractical. They require valuation of each common stock at the discounted value of future earnings. Future earnings are the algebraic sum of the future cash flows; these future cash flows are future dividends plus the future sale price. None are reported to be presently in use. They do not have the characteristics for theoretical appeal cited above. Cur— rent market value is not considered in the formula. They require highly subjective estimates of future cash flows. The methods give recognition to future market appreciation at date of purchase. B. GENERAL CHARACTERISTICS OF ACCOUNTING METHODS To obtain a better understanding of the description of each method there are several characteristics that are worthy of discussion. Individual and Aggregate Methods Formulas can be applied to each of the individual common stocks. They can also be used to adjust portfolio aggregate amounts by means of 33 a portfolio valuation reserve. These formulas value the individual stocks using one of the basic methods, initial cost or current market value. The portfolio valuation reserve is analogous to a reserve for bad debts which is applicable to all accounts receivable and not to a specific account. Certain of the formulas by their nature can be applied only to individual stocks. Other formulas are intended only for use as port- folio reserves. Some of the formulas can be applied either on an individual stock basis or on a portfolio reserve basis. The major advantages of the individual methods are: 1. Asset bases, earnings, yields, and gains on sale are mea- sured for each stock in the same way that portfolio amounts are mea— sured. This information can be useful in analyzing details of oper— ating results and current status of the investment accounts. 2. Gain or loss on sale of a specific stock can be deter— mined. Gain or loss on sale of a stock is not determinable with aggregate methods of accounting. Gains can be estimated by use of allocation methods. However, all allocation methods are somewhat arbitrary in nature. The major advantages of the aggregate methods of accounting are: 1. Relative simplicity in application. 2. Less fluctuation in the important variables than compu- tations based upon individual measures. The use of portfolio reserves may tend to provide a more stable yield measurement than methods applied to individual stocks. It is not the purpose of this paper to select a preference for 34 either the individual or aggregate methods of accounting. Both types will be tested. One method will be tested by both methods of applica- tion. The issues in the controversy are not critical in terms of the criteria developed earlier, with one exception. Provision must be made in the application of aggregate methods for non—deferral of gains or losses on sales of stocks after date of sale. Earnings and Asset Valuation Methods Accounting methods can vary in their approach to computing earnings and asset values. One group such as the long range yield method, computes earnings from the prescribed formula. Asset values at year end are the residual balances that result from computed earnings. Other methods, such as the write-up of percentage difference between adjusted book value and market value, compute asset values from the prescribed formula. Earnings for the year are the amounts that result from the change in asset values. This distinction is made for the pur- pose of understanding of each particular method and will be noted in the description of the accounting. Parameters, Constraints and Alternative Procedures The application of various methods involve selection of para- meters, constraints, and procedural alternatives. Examples of para— meters are (1) rates of yield or appreciation, (2) percentages for annual adjustment or reserve limits, or (3) number of years for aver- aging. An example of constraints are maximum or minimum values based upon current market value or historical cost value. An example of a procedural alternative is the optional treatment of a gain on sales. A gain can be included in current earnings or deducted from the 35 valuation reserve. The parameters selected for study will include those most fre— quently in use according to the CMB Study, those known to be in use by church pension funds, and other reasonable alternatives sufficient to provide a representative test of the accounting method. The constraints and procedural alternatives will be selected on a basis consistent with the criteria specified above. Many pro- cedural alternatives have little effect on yields and book values. In those cases where the researcher judges the alternatives would result in immaterial differences, selection will be based upon ease of appli— cation. In those cases where available alternative constraints or procedures are in accord with criteria specified for theoretical appeal, and significant differences may result, several modifications of the method will be included in the study. C. DISCUSSION OF EACH ACCOUNTING METHOD The following outline will be a guide in presenting a verbal description of each accounting method: 1. General purpose. 2. Description of the accounting. 3. Basis of selection. 4. Parameters, constraints, and alternative procedures. The methods will be presented in order according to the classi— fication listed previously. The mathematical formulas for each method are detailed in the APPENDIX. 36 I. Initial Cost a. Historical Cost Method General purpose. The Historical Cost Method is designed to meet the requirements for the stewardship function. All adjustments to the records are the direct result of transactions with independent organizations. The method provides " an internally consistent accounting system which enables the trustee to demonstrate that every dollar received has been properly held, invested, or applied to pay benefits, in accordance with the terms of the trust agreement." Description of the accounting. l. The Historical Cost Method is applied to each individual stock. 2. It is an asset valuation method. A common stock is valued at the purchase price until sold. 3. Earnings are the sum of dividends received plus the gains recorded for individual stocks. 4. Gains are recorded at the time of sale of shares of stock. The amount is the differential between the sales price and the purchase price of the stock. Basis of selection. 1. The basis of selection of the Historical Cost Method is its wide use by pension funds. Over 50% of the corporate pension 2 funds as well as many church pension funds use this method. 1Jackson, "Valuation of Assets," p. 396. Kane, Pension Fund Financing, Table 10a. 37 2. The method lacks theoretical appeal. Historical Cost Method does not use market value in its formula. Stability of yield is not inherent in the method, although by prOper timing of trans- actions stability of yield can be achieved. The method is an objec- tive method of valuation. It does not systematically allocate appre— ciation during the holding period. Parameters,gconstraints, and alternativegprocedures. 1. Parameters - none 2. Constraints - One possible constraint is the use of the lower of cost or market. Study of the Historical Cost Method is justified by its wide use. There is no reference to use of the lower of cost or market in the CMB Study and therefore the method will not be included in the study. 3. Alternative procedures - If there have been multiple pur— chases of an individual stock at different prices per share, there are alternative methods to compute cost of sales. These alternatives include: first-in, first-out; last-in, first-out; and average cost. For this study average cost will be used. It is not believed by the researcher that significant differences would result by use of other alternative procedures. 11. Initial Cost Methods with Formula Modifications All methods in this classification do not consider market value in the formula. Therefore, they are subject to this common criticism. They will in general be close to market value only by chance when applied consistently over a long period of time. Present use is the 38 basis of selection for methods in classification II. The choice of parameters will be those parameters most widely used. a. LongARange Yield Method General pugpose. The reporting of a stable yield is the pur- pose of the Long Range Yield Method. Annual earnings are computed by the estimated long run earnings rate. Description of the accounting. 1. The Long Range Yield Method is applied to aggregate port- folio amounts. The individual stocks are valued by the historical cost method of accounting. 2. It is an earnings method. Earnings are computed by appli- cation of the selected yield to the asset base of the portfolio. 3. The asset value of the portfolio is the aggregate value of the individual stocks valued by the Historical Cost Method plus a valuation reserve. The valuation reserve is cumulative. The periodic adjustment is the difference between earnings computed by the Histori- cal Cost Method and earnings specified above. Basis of selection. 1. Present use by pension funds is the basis for selection. 2. The method lacks theoretical appeal. All methods of this class do not use market value in the formula. Stability of yield is a characteristic of this method. Selection of the rate may be very subjective. If the appropriate rate is selected, appreciation is systematically allocated during the holding period. Otherwise, appre- ciation may be either anticipated or deferred. 39 Parameters, constraints and alternative procedures. l. Parameters - The rate of yield is the critical parameter to be selected. Both 6% and 7% are used by several firms.1 The literature frequently suggests 7%.2 A 7% yield will be tested. A study by Fisher and Lorie published in 1968 presented information indicating that a 9% return was reasonable for long term investments in common stock.3 While there is no objective basis for selection of 9% for a study simulating accounting results beginning in 1945, a 9% yield will be tested as a matter of interest. 2. Constraints - In order to insure that realized gains are included in income, a constraint will be included. The method will be modified so that the portfolio asset value will not be less than the valuation based upon historical cost measurements. 3. Alternative procedures - none. b. Long RanggpAppreciation Methods General purpose. The reporting of a stable rate of appreci- ation is the purpose of the Long Range Appreciation Method. Annual appreciation recognized as earnings are computed by the estimated long run appreciation rate. 11bid., Table 12b. 2Jackson, "Valuation of Assets,‘ p. 413; Cramer, Reporting Requirements, p. 82; Frederick P. Sloat, "Valuation of Equities Held in Retirement Plan Trust Funds," The Lybrand Journal, Vol. 45, No. 4 (1964), p. 44; Thomas Gainer and Walton Kingbury, "Pension Plans ... A Survey and Commentary based on 163 Actual Plans," The Price Water- house Review (Autumn, 1966), p. 17. 3Lawrence Fisher and James H. Lorie, "Rates of Return on Investments in Common Stock: The Year-by-year Record, 1926-65," Journal of Business, XXXX, No. 3 (July, 1968), p. 296. 40 Description of the accounting. 1. The Long Range Appreciation Method is applied to aggregate portfolio amounts. The individual stocks are valued by the Historical Cost Method of accounting. 2. It is an earnings method. Earnings are the sum of the dividends received plus an amount computed by application of the selected appreciation rate to the asset base of the portfolio. 3. The asset value of the portfolio is the aggregate value of the individual stocks valued by the Historical Cost Method plus a valuation reserve. The valuation reserve is cumulative. The periodic adjustment is the difference between earnings computed by the Histori- cal Cost Method and earnings specified above. This adjustment is the difference between realized gains recorded by the Historical Cost Method and the appreciation computed above. Basis of selection. 1. Present use by pension funds is the basis for selection. 2. The comments concerning theoretical appeal for the Long Range Yield Method are equally applicable to the Long Range Appreci- ation Method. It lacks theoretical appeal. Parameters,_constraints and alternative procedures. 1. Parameters - The rate of appreciation is the critical para- meter to be selected. Over 70 percent of those reporting percentages in the CMB Study use 3% appreciation.1 The average rate of appreci- ation for the Standard & Poor's price index for 500 common stocks for Kane, Pension Fund Financing, Table 123. 41 the period from 1918 to 1960 was 3.84%1 Three percent is suggested in the literature.2 One church pension fund uses 6% appreciation as the basis for earnings credits available to the participants. Both 3% and 6% appreciation will be selected to test this method. 2. Constraints - In accordance with the reasoning set forth in the discussion of the Long Range Yield Method, this method will be modified so that the portfolio asset value will not be less than the valuation based upon historical cost measurements. 3. Alternative procedures - One church pension fund imposes as additional constraint. The annual addition to earnings for appre- ciation is eliminated when the fund value is equal to or exceeds 80% of market value. This modification will be tested. c. Write-up Adjusted Book Value by an Amount Required to Equate Earnings Yields with the Interest Rate Assumption Method (Minimum Yield) General purpose. Sufficient earnings each year to meet the actuarial interest requirements are reported by use of the Minimum Yield Method. Description of the accountipg. 1. The Minimum Yield Method is applied to aggregate portfolio amounts. The individual stocks are valued by the Historical Cost Method. 1Harold C. Fraine, Valuation of Securities Holdings of Life Insurance Companies (Homewood, Illinois: Richard D. Irwin, Inc.), p. 98. 2Jackson, "Valuation of Assets," p. 413; Cramer, Reporting Requirements, p. 82; Sloat, ”Valuation of Equities," p. 43; Gainer, "Survey and Comentary," p. 17. 42 2. It is an earnings method. Subject to certain constraints, earnings are the greater of the dividends received or an amount suffi- cient to provide a yield equal to the actuarial rate of interest. 3. The asset value of the portfolio is the aggregate value of the individual stocks valued by the Historical Cost Method plus a valu- ation reserve. The valuation reserve is cumulative. The periodic adjustment is the difference between earnings computed by the Histori- cal Cost Method and earnings specified above. Basis of selection. 1. Present use is the basis for selection. 2. The comments concerning theoretical appeal for the Long Range Yield Method are equally applicable to the Minimum Yield Method. It lacks theoretical appeal. Parameters; constraints and alternative procedures. 1. Parameters - The actuarial interest rate is the critical parameter to be selected. Of the 12 firms in the CMB Study using this method, 4 use 6% actuarial interest rate.1 All others use a lesser rate. Six percent will be utilized to test this method. Yields for dividends based upon the Historical Cost Method would probably equal or exceed 6%, and, therefore, it would be redundant to test the method at lower rates of return. 2. Constraints - In accordance with the reasoning set forth in.the discussion of the Long Range Yield Method, the Minimum Yield Method will be modified so that the portfolio asset value will not be ‘ 1Kane, Pension Fund Financing, Table 14. 43 less than the valuation based upon the historical cost measurements. 3. Alternative procedures - none. d. Earnings Methods General purpose. Use of the Earnings Method assumes that a change in the intrinsic value of the common stock has a one to one relationship with undistributed earnings. The purpose is to assign to the value of the stock that portion of earnings not paid to the investor in dividends. Description of the accounting. l. The Earnings Method is applied to each individual stock. 2. It is an earnings method. Earnings recorded by the pen- sion fund are the sum of that portion of the earnings reported by the industrial firm applicable to the shares owned by the fund plus gains on sales of individual stocks. 3. A common stock is valued at the initial cost plus cumula- tive earnings less dividends received. 4. The amount of gain on sales is the difference between the sales price and the asset value computed above. Base of selection. 1. Present use by pension funds is the primary basis of selection. 2. The method does not meet all of the criteria for theoretical appeal. Market value is not included in the formula. Similar to the Historical Cost Method, stability of yield is not inherent in the method, although by proper timing of transactions stability of yield 44 can be achieved. The method is an objective method of valuation and systematically allocates portions of the appreciation during the holding period. Parameters,iconstraints and alternative_procedures. 1. Parameters - none 2. Constraints - none 3. Alternative procedures - There are alternative procedures to compute cost of sales under certain conditions. Average cost will be used to test the Earnings Method. See the Historical Cost Method for discussion. III. Modification Based upon Both Initial Cost and Current Market Value 3. Writeup some Percent each Year of the Difference between Adjusted Book Value and Market Value Method (Percentage Write-up) Generalppurpose. Smoothing of the adjustment to market value by taking only a portion of the difference between book value and cur- rent market value periodically is the purpose for use of the Percentage Write-up Method. Description of the accounting. 1. The Percentage Write-up Method is applied to aggregate portfolio amounts. The individual stocks are valued by the Historical (Zost Method of accounting. 2. It is an asset valuation method. The asset value of the 13C>rtfolio is the aggregate value of the individual stocks valued by tifle Historical Cost Method plus a valuation reserve. The valuation 45 reserve is cumulative. Realized gains recorded by the Historical Cost Method are deducted from the valuation reserve. The specified per- centage of the difference between the current market value and the adjusted book value, after deduction for realized gains, is added to the valuation reserve. 3. Earnings are the sum of the dividends received plus the adjustment to the valuation reserve computed above. Basis of selection. 1. Present use is a basis for selection. According to the CMB Study, this method is the most widely used, write-up method of . 1 . accounting. 2. The method also meets all of the criteria for theoretical appeal. The method considers market value in the formula. It smooths the adjustment to market value and therefore specifically provides for stability of yield. Selection of the percentage adjustment would depend upon the pension fund's weighting of the two factors above, not a projection of future values, and therefore the method is objective. The formula attempts to systematically allocate appreciation during the holding period of the asset. Parameters, constraints and alternative procedures. 1. Parameters - The percentage to be applied to the difference between current market price and adjusted book value to obtain the Periodic adjustment is the parameter to be selected. Ten and twenty IDer cent are the most frequently used percentages according to the \ 11bid., Table 11. 46 CMB Study.1 One church pension fund uses a 50% write-up. All three percentages will be used to test this method. They should provide a representative test. 2. Constraints - This method will be modified so that the portfolio asset value will not be less than the valuation based upon historical cost measurements. See the Long Range Yield Method for discussion. 3. Alternative procedures - There are alternative ways to treat realized gains on sales of stocks. However, these are generally impractical refinements of the method described above and are not recommended for use. b. Minimization Formula Methods General purpose. The Minimization Formula Methods are designed to optimize the recorded asset values in terms of specified criteria. The factors to consider in this study are reported yields and current market values. The purpose for the use of the minimization is to com- pute annual book values considering both current market values and stability of yield. Description of the accounting. 1. The minimization formulas can be applied to each individual stock or to aggregate portfolio amounts. The aggregate method will be discussed in this section. The individual stocks are valued by the Historical Cost Method of accounting. lIbid., Table 12c. 47 2. It is an asset valuation method. The asset value of the portfolio is obtained from a formula. The formula was derived to mini- mize both the change in yield from the preceding period and the devi- ation from current market value according to a specified relationship. The derivation of the formula is shown in the APPENDIX. The valuation reserve is the total value obtained above less the aggregate value of the individual stocks valued by the Historical Cost Method plus the change in the valuation reserve computed above. Basis of selection. 1. The method is not reported to be presently in use. 2. The method was selected for its theoretical appeal. It was designed specifically to meet the criteria of consideration of market value and stability of yield. The method is objective in terms of its application and attempts to systematically allocate appreciation during the holding period of the asset. Parameters, constraints and alternative procedures. 1. Parameters - The relative weight given to each factor is the parameter to be selected. In the absence of any evidence to do otherwise, equal weight will be assigned to the factors to give a representative test of the method. 2. Constraints - none 3. Alternative procedures a. The method can be modified to consider additional factors, such as conservatism. This study will be restricted to the use of the two primary factors developed in Chapter II. b. The method can be applied to individual stocks as 48 well as portfolio totals. Because of the theoretical appeal of this method it will be tested on individual stocks and portfolio totals. IV. Current Market Value Method. General purpose. The Current Market Value Method is designed to equate accounting measures with the objective of measuring invest- l ment performance. Market value changes are recorded as they occur. Periodic earnings are the result of market value changes. Description of the accounting. l. The current market value is applied to each individual stock. 2. It is an asset valuation method. A common stock is valued at the current market value. 3. Earnings are the sum of the dividends plus the gains recorded for individual stocks. 4. Gains represent, (a) the market appreciation during the period for stocks held at the end of the period, and (b) the difference between the sales price and market value at the beginning of the period for stocks sold during the period. Basis of selection. 1. Present use is a basis for selection. Its use is not extensive. Only 18 of the 497 firms in the CMB Study specified using the Current Market Value Method. The method ranked fifth out of eight Peter O. Dietz, ”Measuring Pension Fund Performance," Financial Executive, XXXVII (November, 1969), 20-21. 49 methods specified in that study.1 2. The method lacks theoretical appeal because of the fluctu- ating yields that result from its use. The method is discussed widely in the literature2 and therefore deserves to be included in the study on that basis alone. Parameters,ficonstraints and alternative procedures. 1. Parameters - none 2. Constraints - none 3. Alternative procedures - none V. Adjusted Market Value Methods a. Market Valuej_Less a Reserve General purpose. The Market Value, Less 8 Reserve Methods are designed to recognize market appreciation but on a conservative basis. Conservatism with regards to current market value is the gen- eral purpose of these methods. Description of the accounting. 1. The Market Value, Less a Reserve Methods are usually applied to aggregate portfolio amounts. The individual stocks are valued by the Current Market Value Method. 2. It is an asset valuation method. The asset value of the Kane, Pension Fund Financing, Table 11. 9 ”Fraine, Life Insurance Companies, p. 10; Jackson, "Valuation of Assets," p. 392; Cramer, Reporting Requirements, 80-81; Sloat, "Valuation of Equities," 38-41; Gainer, "Survey and Commentary," p. 16. 50 portfolio is the aggregate value of the individual stocks valued by the Current Market Value Method less a valuation reserve. The valuation reserve is the lesser of (l) a percentage of the current market value, (2) an amount computed by any one of many formulas. The most commonly recommended formula is the difference between the current market value and the historical cost valuation. When this formula is applied the portfolio is valued at the greater of the Historical Cost Method or a percentage of current market value. 3. Earnings are the sum of the earnings computed by the Current Market Value Method plus the change in the valuation reserve. Basis of selection. 1. Present use by a church pension fund is the basis of selection. 2. The method has limited theoretical appeal by the criteria established in this study, since conservatism is the primary objective. Parameters, constraints and alternative procedures. 1. Parameters - The percentage to be applied to current market value to obtain the reserve is the parameter to be selected. Ten, twenty, and thirty-three percent should provide a representative test of the accounting method and will be selected for testing. The church pension fund uses a 20% reserve. 2. Constraints a. Since conservatism is the objective and market value is the maximum value logically permitted, this constraint will be observed. b. The reserve percentage is in reality a constraint 51 and represents the minimum value for the portfolio. 3. Alternative procedures 3. Since the method specifies upper and lower con- straints, any other method of accounting can be used in combination with this method. Use of these constraints are particularly appro- priate for methods in Classification I and II that do not consider market value in the formula. However, testing of this method will be restricted to use with the Historical Cost Method and the method dis- cussed below. b. One church pension fund is using the following modifi- cation to compute earnings when there is less than a maximum size re- serve: One percent of the total current market value is deducted from earnings and added to the reserve. Earnings are dividends received less this 1% charge. b. Moving Average Market Value based upon the average of several years (Moving Average) General purpose. Stability of yield in the use of market value is the general purpose of the Moving Average Method. Description of the accountipg. 1. The Moving Average Method is applied to each individual Stock. 2. It is an asset valuation method. Each stock is valued at the average market value computed over a specified number of years. 3. Earnings are the sum of the dividends received plus the gains recorded for the individual stocks. 4. Gains recorded are (a) the changes in value during the 52 period as computed above for stocks held at the end of the year and (b) the difference between the sales price and the average value at the beginning of the year for stocks sold during the year. Basis of selection. 1. Present use is a basis for selection. This is one of the methods cited in the CMB Study.1 2. The method also meets all of the criteria for theoretical appeal. It considers market value and smooths the adjustment to mar- ket value by averaging values. The method is objective. The formula with proper modification attempts to systematically allocate apprecia- tion during the holding period of the asset. Parameters, constraints and alternative procedures. 1. Parameters a. The number of years to average market value is the critical parameter to select. Since the method attempts to smooth earnings by averaging market value, the time period is somewhat related to business cycles. In discussing the length of time to average, Fraine cites that the arithmetic mean length of business cycles from 1854 to 1958 to be 4-1/6 years. The conclusion is that a 5 year moving average is a desirable length of time.2 Of the 27 funds using the method, 23 selected 5 years as the length of time.3 Although 3 years is sometimes mentioned in the literature, 5 years is most 1Kane, Pension Fund Financing, Table ll. ’7 ‘Fraine, Life Insurance Companies, p. 115. 3 Kane, Pension Fund Financing, Table 12d. 53 frequently suggested.1 Therefore, a 5 year moving average was selected. A single parameter for number of years is considered suffi- cient to adequately test the method. b. Other parameters that can be considered are the respective weights given to each year in averaging values. In the absence of specific reasons for considering a specific alternative, equal weighting will be applied to each year in this study. 2. Constraints - A strict application of a 5 year moving average market value would imply valuing purchases at an amount other than the price paid on the date of purchase. In order to systemati- cally allocate appreciation during the holding period only market values on and subsequent to the date of purchase will be considered in computing the average market value. 3. Alternative procedures a. There are several possible methods to modify the Moving Average Method to consider only values subsequent to the date of purchase. The following method will be used by this researcher: (1) Purchase price at date of purchase will be considered the initial market value. (2) If the number of time periods subsequent to the date of pur- chase is less than 5, purchase price will be weighted sufficiently to bring the total number of time periods to 5. (3) If the number of time periods is greater than or equal to 5, purchase price will be disregarded in computing the moving average. 1 Jackson, "Valuation of Assets;' Requirements, p. 81. [L 414; Cramer, Reporting 54 It is the opinion of this researcher that other alternatives would not significantly alter the evaluation of the Moving Average Method. b. In a manner similar to the Historical Cost Method, the Moving Average Method offers alternative procedures to compute cost of sales. Average cost will be used in this study. c. Least Squares Trend Line based upon market value for several years,(Trend Line) General purpose. Stability of yield in the use of market value is the general purpose of the Trend Line Method. Closeness to market value is also a purpose of the method as it projects a current average value. Description of the accounting. l. The Trend Line Method is applied to each individual stock. 2. It is an asset valuation method. Each stock is valued at the projected value. The projected value is computed by use of a trend line based upon the market values for a specified number of years. The least squares method is used to compute the trend line. 3. Earnings are the sum of the dividends received plus the gains recorded for the individual stocks. 4. Gains recorded are (a) the changes in value during the period as computed above for stocks held at the end of the year and (b) the difference between the sales price and the average value at the beginning of the year for stocks sold during the year. Basis of selection. 1. The method is not reported to be presently in use. 2. The method was selected for its theoretical appeal. It 55 is a modification of the Moving Average Method that should be closer to market value than the Moving Average Method. It considers market value and average market value to obtain some stability of yield. The method is objective. The formula with prOper modification attempts to systematically allocate appreciation during the holding period. Parameter§,,constraints and alternative procedures. 1. Parameters. a. The number of years to average market value is the critical parameter to select. Five years will be selected. The rea- sons discussed for the Moving Average Method apply to the Trend Line Method. b. Various weights can be assigned to each year in com- puting the trend line. In the absence of specific reasons for con- sidering a specific alternative, equal weights will be applied to each year. 2. Constraints - Only market values on or subsequent to the date of purchase will be considered in computing the projected value. See the Moving Average Method for discussion of this constraint. 3. Alternative procedures. a. The procedures described for the Moving Average Method will be used for the Trend Line Method to adjust for stocks owned less than 5 years. b. The shapes of the trend line are alternative pro- cedures that can be applied to the Trend Line Method. Examples of alternatives are linear, quadratic, exponential and logarithmic. For purposes of this research the linear trend line will be tested. 56 The discussion concerning refinements of the method beyond a linear trend line is similar to the discussion for weighting. c. Another alternative procedure is to project a value for year 4 instead of year 5, that is for year t-l. This alternative would provide a compromise between the Moving Average Method and the projected value for the Trend Line Method. See Figure 3 for an illus- tration. Using the hypothetical data from Table l in Chapter II, the 150 \\*<; 1401 // 13d /4/ 120' / 1101 * x 100 *§\¥\// 90 1565 1966 1967 1968 1969 FIGURE 3 LEAST SQUARES TREND LINE OF MARKET VALUE DATA FROM TABLE 1 5 year Moving Average Method would provide a book value of $122.20 which is the value on the trend line for 1967. The book value for Trend Line Method would be $151.60 which is the value on the trend line for 1969. The value for year t—l, 1968, would be $136.90 which is the mid—point value between the Trend Line Method and the Moving Average Method. This alternative need not be tested to represent the 57 respective methods. d. Market Value with a Variable Adjustment Methods (Variable Adjustment) General purpose. In this study, methods with the designation "Market Value with Variable Adjustment" refer to a specific group of methods suggested by Jackson and Hamilton.1 The authors consider mar— ket value as the apprOpriate method of value portfolios but believe un- reasonable fluctuation should be screened from annual valuations. The objectives of the methods are to achieve some stability of yield around the actuarial rate of return in the use of market values for valuation and to achieve an element of conservatism in the valuation. Description of the accounting. 1. These Variable Adjustment Methods are applied to aggregate portfolio amounts. The individual stocks are valued by the Current Market Value Method. 2. These are earnings methods. The earnings are functions of the actuarial rate of interest, the change in market value during the period, dividend income and the ratio of the book value of the fund to the market value of the fund. The functional relationships for the alternative selected for testing are specified in the APPENDIX. 3. The asset value of the portfolio is the aggregate value of the individual stocks valued by the Current Market Value Method less a valuation reserve. The reserve is cumulative. The periodic adjustment lJackson, "Valuation of Assets," 393—395. 58 is the difference between earnings computed by the Current Market Value Method and earnings specified above. Basis of selection. 1. The methods are not reported to be presently in use. 2. The methods were recommended in the literature and generally meet the criteria for theoretical appeal. The methods consider market value in the formula, specifically provide for stability of yield and attempt to systematically allocate appreciation during the holding period of the asset. The use of the actuarial rate of interest may be considered subjective, however the method generally fits the notion of an objective method of valuation. Parameters, constraints and alternative procedures. 1. Alternative procedures - There are seven modifications sug- gested in the Jackson and Hamilton article.1 The alternative proce- dures must be specified before selection of parameters. The various alternatives specify the amounts to be added or deducted from the valu— ation reserve based upon the amount of deviation in earnings from some mean yield. The actuarial rate of interest is recommended as an alter- native to a mean yield. The modification selected for study appeared representative of methods suggested. Except for the actuarial rate of interest, the parameters and constraints are specified in the article. 2. Parameters - The actuarial rate of return is the critical parameter to be selected. A 4% actuarial interest rate will be used to test this method. Approximately 40% of the corporate pension funds 1Ibid., p. 415. 59 included in the CMB Study1 use 4% for actuarial purposes. The mean percentage for those church pension funds reporting to the December, 1969 Church Pensions Conference was 3.9%2 3. Constraints a. Current market value is the maximum value of the portfolio. b. The annual earnings will not be less than the actuarial rate of return, subject to the above constraint. c. The annual earnings will not exceed an amount based upon the actuarial interest rate, plus 10%, plus an amount based upon the valuation reserve at the beginning of the year. D. SUMMARY OF METHODS SELECTED Twelve methods have been selected for study. With the various alternative parameters, constraints and procedures the total methods have been expanded to twenty one. Nine of the twelve methods are presently in use. Five meet all of the criteria for theoretical appeal. lKane, Pension Fund Financing, Table 6. 2Kenneth H. Ross, "Notes on Annual Statistical Reports of Participating Pension Funds" (paper presented at the 55th annual meeting of the Church Pensions Conference, New York, December 4 and 5, 1969). p. 9. mmFERIV RESEARCH DESIGN A mathematical model will be developed incorporating the cri- teria specified in Chapter II. The accounting methods selected in Chapter III will be applied to the common stock portfolios of a theo- retical pension fund and an actual pension fund. Annual yields and book values over a long period of time will be computed by each account- ing method. The mathematical model, having the benefit of hindsight, will utilize the computed yields and book values to rate each account- ing method. The most efficient methods will be selected and recommended for use. Other characteristics of the accounting methods will be ob- served and results reported. A. THE MODEL Formulation of the Model The criteria for judging accounting methods has been determined to be, (a) closeness to market value, and (b) stability of yield. These are the characteristics to be measured by the model. The accounting method with the smallest aggregate deviation from a measure of these characteristics is the optimal method. Let Cv = a measure of closeness to market value; coefficient of vari- ation between book value (as determined by the specific accounting method) and current market value. 60 61 a measure of stability of yield; coefficient of variation Let C between yield (as determined by the specific accounting method) for time (t) and time (t-l). 2 _ 2 2 Let C - Cv + Cy o _ 2 2 o o C — Cv+cy lThis is the basic model. The C, Cv and Cy values are the amounts to be determined. Evaluation of results will be based upon resultant values of these variables. The accounting method with the smallest C or C2 value is the optimal method. Formal statistical methods will not be used to reach conclu- sions. However, the notion of relative variance as described in classical statistics is the basis for the measures developed in this study.1 C2 . The coefficient of variation between book value and market v value, CV, will be defined in the formula below. It is a measure of the percentage deviation of book value from the corresponding current market value. It is stated as follows: Cv = Coefficient of variation 2 between book value and N Bjt - Mt market value CZ 1 E Bjt= Boo: pain; fir acc02n§ing = _ met 0 j a time t V N t=1 Mt Mt = Market value at time (t) N = Number of years 1Taro Yamane, Elementary_Sampling Theory (Englewood Cliffs, N. J.: Prentice-Hall, Inc., 1967), 33-37. 62 The formula is derived as follows: IBjt -Mt 2 Cy The absolute value of the difference between the computed book value for accounting method (j) and the market value. This is the closeness to market value for time period (t). The percentage difference between com- puted book value for accounting method (j) and the market value. This is the relative closeness to market value for time period (t). The sguared percentage deviation between the computed book value for accounting method (j) and the market value. The sum of the squared deviations over all time periods. The average variation over all time periods. Dividing by N is not necessary unless comparisons over unequal time periods are made. The coefficient of variation between yield for time (t) and time (t-l), will be defined in the formula below. It is a measure of the relative change in earnings. It is stated as follows: 63 C = Coefficient of variation be- tween yield for time (t) and th = YiEId for time (t) based upon the accounting method (j). Yj(t-l) = Yield for time (t-l). The formula is derived as follows: Squared deviations. The absolute value of the difference between the yield for accounting method (j) from time (t-l) to time (t). A stable yield has a small change in yield from period to period. Yield is a ratio. This difference represents the relative change in earnings. The squared deviation between yield for time (t) and time (t-l) for accounting Inethod (j). The sum of the squared deviations over all time periods. The average variation over all time periods. Dividing by N is not neces- sary unless comparisons over unequal time periods are made. The squared deviations have been selected rather than the absolute deviations. The mathematical property of 64 squared deviations to magnify large amounts in relationship to many small amounts is the reason for this choice. Small differences between book value and market value are of little consequence. Likewise, small fluctuations in yield from period to period are not significant. A single large deviation that results from the use of a particular accounting method will result in a large C or C2 computed value. As a result such an accounting method will be assigned a low ranking. 2 Weighting. The relative weighting assigned to the C3 or Cy factor depends upon the relative importance of each factor to each pension fund. This is a matter of individual choice. There does not appear to be any theoretical grounds for assigning a particular set of weights as being the universal set of correct weights. For purposes of this study, equal weights will be assigned the factors for the initial evaluation of accounting methods. Computation of yield. Yield will be computed as follows: Y3: = Ejt / (Bj(c-1> + Pt ' Sjt) Ejt = Earnings for time (t) by accounting method (j). Bj(t-l) = Book value for time (t-l) by accounting method (j). PC = Purchases at cost for time (t), adjusted for part year holdings. Sjt = Cost of sales for time (t) by accounting method (j), adjusted for part year holdings. The alternative methods to compute yields are to, (1) base the yield on the accounting method being tested as per above, or (2) base 65 the yield on some universal amount such as current market value. The formula for the latter method is as follows: th = Ejt / (M(t_1) + Pt - st) M(t-l) = Market value for time (t-l). St = Sales for time (t) priced at market value for time (t-l), adjusted for part year holdings. 2 y value among the various For method (1) the relative change in the C accounting methods is a function of two variables, the earnings and the book value. For method (2) the relative change in the Ci value among the various accounting methods is a function of one variable, the earn- ings. The denominator is a constant over all accounting methods. A more consistent yield measure among the accounting methods is the major argument for use of the constant base. The effects of the varying earnings can be isolated. However, this argument is not relevant to the purpose of this study. The purpose is to judge the accounting methods. The relevant yield computation to be tested should be the one that produces the value that would be reported for the accounting method when in use. One of the variables in the yield computation is cost of sales. For aggregate methods of accounting, no specific cost of sales is determined for the individual stocks sold. When aggregate methods of accounting are used, the individual stocks are valued by the Historical Cost or Current Market Value Methods. A valuation reserve is computed which is applicable to the portfolio, but not assigned to individual stocks. (See Chapter III, General Characteristics of Accounting Methods, for review of aggregate methods.) For purposes of computing 66 yield an estimate for cost of sales will be computed as follows: 1. As specified in Chapter III, cost of sales will be computed for the individual stocks by the Historical Cost or Current Market Value Methods, whichever method is used to value the individual stocks. 2. The cost of sales amount for time (C) will be adjusted by the ratio of the valuation reserve to the book value of the portfolio for time (t-l). Characteristics of the Model Example. An example will be used to explain some of the char- acteristics of the model. Table 2 illustrates how the model ranks the theoretical allocation methods discussed in Chapter II, assuming the facts given in Table l in that chapter. This is hypothetical and is not necessarily representative of the results that would be obtained Eran the study. The yields and book values are graphed in Figures 1 and 2 of Chapter II. TABLE 2 RANK OF ALLOCATION METHODS Method Rank C2 = 0‘2, + (2)2, I. Historical cost 5 10.59 3.54 7.05 11. Equal allocation 2 1.06 1.05 .01 III. Earnings 3 1.51 1.17 .34 IV. Current market value 4 7.12 - 7.12 V. Constant rate of return 1 0.95 0.95 - NOTE: The ranking is based upon information assumed in Table 1, Chapter II. 67 Ranking. The use of the model provides a means of assignment of an ordinal ranking of the accounting methods. The rankings are assigned in inverse order by C2 value. This ranking provides the initial judgment about accounting methods. In this illustration the constant rate of return theoretical allocation method has the lowest C2 value, 0.95, and therefore would be ranked number one. The histori- cal cost method has the highest C2 value, 10.59, and would be ranked as the poorest method. A review of the C2 values reveals that the value for the equal allocation method is very close to the value for the constant rate of return method, 1.06 to 0.95. Based upon the closeness of these numbers, it would be difficult to support a recommendation of the superiority of the constant rate of return method without additional evidence. From a review of the numbers it can be judged that both methods are superior to the historical cost and current market value methods. It becomes clear that an ordinal ranking from this single test does not give sufficient evidence for final recommendations. Additional judgments including 'consideration of the cardinal values of the numbers are required in order to draw conclusions from the use of the model. Closeness to market value. The C3 value measures closeness to market value for each allocation. As noted in Table 2, the C3 amount for the current market value method equals zero. This method is by definition the optimal method in terms of closeness to market value. The data from Table l is for a relatively short period of time. All methods in the illustration converge on market value at the end of the sample time period. As a result the example does not illustrate clearly the effects on closeness to market value of those methods 68 that do not consider market value in the formula. For those two theo- retical allocation methods that require execution of a sale to converge . . 2 . on market value, adjustment in the Cv amount excluding the effect of the sale is as follows: 2 Cv amount Method Table II Adjusted 1. Historical cost 3.54 5.92 III. Earnings 1.17 1.37 Without convergence at the terminal period, both methods have a larger Ci value than the other methods illustrated and give some indication of a trend of higher deviations from market value. Conclusions about the specific methods cannot be drawn from the illustrated results. The example does demonstrate how the model evaluates closeness to market value and should rate higher those methods that consider market value in the formula. Stabiligy of yield. The CS value measures stability of yield for each allocation method. If it were possible to have a crystal ball and use the constant rate of return method as in the example, then the 0: value for this method equals zero. This method is by definition the optimal method in terms of stability of yield. In constrast, the current market value method, illustrating fluctuating values and resulting yields that range from large positive amounts to negative amounts has a 0; value that is very large. Even though the current market value method shows a C3 = 0, this method ranks a poor fourth out of five methods when ranking the methods on the C2 value. 69 Large changes in yield will give an accounting method a low rank. Any method, such as the historical cost method, subject to large gains or losses when sales occur should rank in a low position. In this illustration the historical cost method had no fluctuation in earnings during the first three periods and a large gain in the final period. As a result the Ci amount for the historical cost method almost equaled the C3 amount for the current market value method with its highly fluctuating earnings, 7.05 to 7.12. Again conclusions about the methods cannot be drawn from the illustrated results. The example does demonstrate how the model evalu- ates fluctuating yields. Those methods that systematically allocate appreciation during the holding period, Methods II, III and V, rated higher than the methods that did not. Combined effects. The C2 value measures the combined effects of closeness to market value and stability of yield. In the illustra- tion the constant rate of return method ranked first in overall results. The criteria for the model was based upon an analysis of this theoretical method and therefore, would be expected to rank first when considering a single investment. Although a set of facts could be for- mulated where some other method would outrank method V, this would be unusual. The methods that, (a) consider market value in the formula, and (b) average market appreciation over time to smooth the effects of changes in market value or specifically provide for stability of yield, would be expected to have relatively low C2 values and rank as the best methods. Methods II, IV and V consider market value in the formula. Method II, equal allocation, averages appreciation over time. Method V, 7O constant rate of return, specifically provides for stability of yield. Methods 11 and V ranked as the best methods in the illustration. B. THE SAMPLE The accounting methods selected for evaluation will be tested with a sample of two funds over a specific time period. These sample funds will be an actual church pension fund and a theoretical pension fund. The Actual Pension Fund Description of the fund. The church pension fund selected for testing will be referred to as the AB Fund. The AB Fund is a member of the Church Pensions Conference.1 It is one of the largest pension funds submitting information to this Cenference with total assets in excess of $200,000,000. The AB Fund provides retirement benefits on a voluntary basis for all personnel working for a church or agency affiliated with the church group represented by this fund. It has been in existence since 1918. The investments in common stocks have ranged from 15% to 25% of the total assets of the fund. Over $50,000,000 are currently invested in common stocks.2 1The Church Pensions Conference represents a group of 29 Church and other non profit pension boards that meet annually to exchange in- formation and attend seminars on current developments in the pension field. Included as a presentation of the Fifty-Fifth Annual Meeting in 1969 was the report by Kenneth H. Ross, "Notes on Annual Statistical Reports of Participating Pension Funds", p. 5 which indicated total assets for this group of $1,992 million. 9 Information on the AB Fund has been obtained from published annual reports and internal information furnished by management of the fund. 71 Over the period to be tested the AB Fund averaged 66 stocks in its common stock portfolio. It had an average rate of increase in investment of approximately 20%. This represents a fairly high rate of sustained growth. The AB Fund had an average annual turnover in its common stock portfolio of approximately 10%. A 10% turnover would be representative of a buy and hold type of investment philosophy. There were seven years in which the turnover was less than one percent and three years in which the turnover was greater than 252. These three years of high turnover indicate a non-consistent application of the buy and hold philosophy. This non-consistency along with the general tendency of holding stocks a long period of time should provide an interesting test of accounting methods. With changing leadership and with dynamic attitudes concerning investment goals and the relative worth of types of investment, invest- ment policies towards common stocks have undergone many changes during the life of the AB Fund. Therefore, tests over a long period of time utilizing this pension fund would test the composite of several invest- ment strategies, mixed with the various economic and psychological conditions of the market. While no one fund can be called typical of all church pension funds, the AB Fund is of sufficient size and age to provide a representa- tive test of accounting methods for the church pension funds. Description of the accounting. The data gathering and applica- tion of accounting methods to this fund is the major empirical effort of this dissertation. For the period covered in the study, the detailed transactions 72 for each common stock have been obtained. These are the purchases, sales and stock splits. The number of shares, amount and year and month of the transaction have been recorded. If there are multiple transactions of one type for a common stock in the same year, the transactions have been combined into a single transaction. An average month for the transaction has been estimated and recorded. Additionally, the cash dividends received during each year and the market value at December 31 of each year have been recorded for each stock owned. Advantgges. The chief advantage for the use of an actual pen- sion fund as opposed to purely simulation is that actual investment decisions are tested under actual market conditions. Disadvantages. There are two principal disadvantages to the use of one actual pension fund: 1. One disadvantage is the use of a single fund. The fund selected may not be representative. The investment results for the AB Fund when evaluated against the model, may reach conclusions that would be different for the average of the other church pension funds. This is an inherent disadvantage with a small sample. This disadvantage is exaggerated by the use of one fund. 2. Another disadvantage results from the use of actual pension funds. Accounting methods and investment decisions are not independent. Management is sometimes influenced in its investment decisions by the effects these decisions have on reported results. Management can be influenced in another manner. Any accounting method in use over a suf— ficient length of time establishes some credibility. In spite of 73 initial knowledge of the biases of specific accounting methods, manage- ment tends to believe the reported results and act accordingly. For these reasons, the use of differing accounting methods may result in alternative investment decisions and lead to differing investment results. Therefore, research conducted studying the effects of the use of alternative accounting methods for an actual pension fund suffer from some unknown amount of inaccuracy, since changing accounting methods may also change portfolio results. The results from any empirical research that is conducted with this type of limitation must be treated with some reservations unless a test is performed to overcome this bias. The Theoretical Pension Fund Description of the fund. A theoretical fund has been simulated. The Dow Jones Industrial Index, The Index, has been used to provide the basic information. The theoretical fund will be referred to as the Dow Fund. Quarterly earnings, dividends and quoted prices have been ob- tained from The Dow Jones Investor's Handbook.1 Shares of The Index have been purchased and sold at the price currently quoted in The Index. All transactions take place at the end of a calendar quarter. The simu- lated activity for the Dow Fund takes place concurrently with the time period selected for study for the AB Fund. The investment strategy has been specified. The initial invest- ment is 100 shares. Ten shares of The Index have been purchased annu- ally. Twenty shares of The Index have been sold every five years. They 1Maurice L. Farrell, ed., The Dow Jones Industrial Handbook, 1970 (Princeton, New Jersey: Dow Jones Books, 1970), 24-26. 74 were sold in blocks of ten shares. This results in a net growth of 30 shares every five years. Shares were selected rather than specific dollar amounts because of the ease of implementation. The results should not be materially affected by the fonn of specification. The general trend of The Index since the Great Depression has been increas- ing over time. Selection of a constant number of shares results in an increasing dollar amount of purchases over the period of the study. St0ck selection and timing of transactions were by random choice. Each year's purchases were designated as a separate stock. The quarter in which the purchase was made was selected at random. The year and quarter for each sale of 20 shares was selected at random. The division of shares sold into blocks of 10 shares is for the purpose of assigning a specific stock sold. The determination of the stock sold was by random selection. The Dow Fund averaged 9 stocks in its portfolio. It had an average rate of increase in investment of approximately 8%. This repre- sents a modest rate of sustained growth. The Dow Fund had an average rate of turnover of approximately 3%. This is a very low turnover. Since stock sales and purchases were on a very systematic basis, the Fund should provide a contrast with the non-consistencies of the AB Fund. Description of the accountigg. Each year's purchases have been accounted for as a separate stock. Where applicable, the accounting was the same as for the AB Fund. Advantaggs. Independence between investment strategy and accounting methods is one of the principal advantages of the use of a simulated fund. The stock selection is not influenced by the accounting 75 method in use. Disadvantages. The major disadvantage of the use of simulation is that replication of actual investment decisions cannot be duplicated on an economically feasible basis by methods presently known. See the study by Clarkson for an example of the complex nature of the simulation . . l of investment dec131ons. Time Period A historical time period will be selected for study. One objec- tion to the use of past time periods is that there is no guarantee that what occurred in the past will repeat itself. The general use of the historical approach to select acceptable accounting methods is one argu- ment in favor of the use of historical time periods. While this may be sufficient, a stronger argument can be presented for use of historical time periods. The purpose of the study is to determine the accounting method that best meets the criteria established in this paper. An ac- counting method that has been tested under many economic conditions, various psychological statesof the stock market, and changes in the in- vestment strategies; and has demonstrated its superiority would continue to rate highest in accordance with the established criteria under new factual situations. The time period covered should be of sufficient length to in- clude a variety of economic conditions and investment opportunities. The researcher believes that the twenty five years ended in 1969 pro- vide a time period of sufficient length and variety to provide a fair 1Geoffrey P. E. Clarkson, Portfolio Selection: A Simulation of'TIrust Investment (Englewood Cliffs, New Jersey: Prentice-Hall, Inc-, 1962). 76 test of the accounting methods. This time period includes the immediate post war period with its boom and recession. The Korean War with its rapid economic expansion and economic controls followed. During the 1950's there was generally a steady economic expansion interrupted by mild recessions in 1954, 1958 and 1960. During the early 1960's there was steady economic expansion, full employment, and a relatively stable monetary unit.1 With the entry into Viet Nam in 1965 the economic balance was upset by rapid expansion into war production and an infla- tionary cycle began. The period ended in 1969 with a recession in process. During the period investor attitudes underwent several changes. . . . In the late 1940's, in spite of considerable postwar pros- perity, you could buy the best-known and most highly regarded com- mon stocks at seven or eight times their annual earnings per share. Most people were still anticipating the big postwar depression that was often predicted but never arrived. Then in the decade of the 1950's the mood gradually changed to one of optimism, and stock prices rose as investors came more and more to expect further increases in earnings and dividends per share. By the late 1950's the rise in market prices had far outrun increases in earnings and dividends, as stock buyers estimated optimistically future improvement in the financial abilities of business corporations. Despite occasional recessions, this period of favorable estimates continued into the 1960's. . . . The 1Harry Sauvain, Investment Management (Englewood Cliffs, NQMI Jersey: Prentice-Hall, Inc., 1967, 3d ed.), 140-142, 192-194. 77 long-term upward trend in the average price-earnings ratio is an excellent measure of the change in investors' attitudes from fear of the worst to hope for the best. During the 1960's a cyclical market was experienced with peaks in 1961, 1965 and 1968 followed by sharp declines in the market. The market peak in 1965 reflected by the Dow Jones Industrial Index was not reached again in the remainder of the decade.2 The price earnings ratio for The Index dropped from 24.2 in 1961 to 13.6 in 1969.3 The time period selected for study in the 25 years ended in 1969 and should provide a rigorous test for the accounting methods. C. THE EVALUATION The accounting methods described in Chapter III will be applied to the sample funds described above over the 25 year period from 1945 through 1969. The annual yields based upon each accounting method will be computed. The yields, book values and market values will be used to 2 2 compute the values required in the model, Cv , C and C2. These values y will be used to evaluate the accounting methods. Initial Evaluation The initial evaluation will be based upon equal weighted factors for the 25-year time period. The methods will be ranked in inverse order by aggregate C2 value for each of the funds. lIbid., 140-141. 2Farrell, Investor's Handbook, p. 24. 31bid. 78 Comparison of funds. The respective ranking of the accounting methods by each fund will be compared for the degree of correlation. The results will be analyzed and significant differences explained. Should there remain unexplained significant differences, the sample will be enlarged to include additional simulation models. Should the results demonstrate that the AB Fund is not representative, the sample will be expanded to include additional pension funds. The results will be evaluated as follows: 1. A very high degree of correlation would indicate universal applicability of results. 2. Mixed results, with high correlation among certain pairs of funds and low correlation among other pairs would require analysis to determine factors that affect general applicability of results. 3. A low correlation among funds after expansion of the sample would indicate a unique solution for each fund. Comparison of accounting methods. The ordinal ranking and rela- tive values for each method will be reviewed. From this evaluation a group of acceptable methods will be determined. In addition, paired comparisons will be made to determine those methods that are clearly better than other specific methods. Expanded Tests and Evaluation Additional tests will be performed upon the sample funds in order to obtain additional information about the effects of varying Certain factors in the model. Sensitivigy analysis. The original model utilized equal 79 weighting for the C3 and C; factors. A sensitivity analysis will be performed by varying the weights to the factors. The results of this analysis should determine the range in which certain methods demonstrate their advantages. The C: factor, deviations from market value, will be weighted over the range from 0.01 to 20.0. This weighting should pro- vide a reasonable range. Weighting beyond the end points would be equivalent to evaluating a single factor and omitting the effects of a two-factor model. Time period analysis. As one additional test, the time periods will be shortened to determine whether certain methods performed dif- ferently during Specific time periods. Overlapping periods of 10 years will be tested. Summary of the Evaluation Process. The ordinal ranking of the accounting methods will be the pri- mary basis for judging and selection of the best accounting method. This judgment will be modified by a study of the respective "C" values. The results will be amplified by use of sensitivity analysis and vari- able time period analysis. A group of accounting methods that are acceptable for use as judged on the basis of the criteria established in this paper will be selected. For those acceptable methods the characteristics that would make a particular method more desirable under alternative sets of conditions and more desirable under alternative sets of utility prefer- ences will be set forth. CHAPTER V RESULTS - EVALUATION OF TESTS Annual yields and book values have been computed over the time period from 1945 through 1969 for each sample fund by the account- ing methods specified in Chapter III. The internal rate of return for each fund has been computed. 2 2 The CV, Cy and C2 values indicated in the mathematical model have been computed. The results will be reported. These results will be evaluated in this chapter to determine the extent of general appli- cability of the results among pension funds and across time periods. A. REPORTING OF RESULTS The results are displayed in Table 3 and 4. They are based upon equal weighted factors for the 25 year time period of the study. The formula is, C2 = (1.0) C5 + (1.0) C3, in which Cv and Cy are de- fined in Chapter IV. The 25 year time period resulted in 23 "C" values. The initial balance at the end of 1945 is utilized to compute yield for 1946. Since 1946 was the initial year for yield information, 1947 is the first year for which a Cy value was available. The values dis- IDlayed in the tables are the sum of the ”C" values for each time period. 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Ho.N mm.N 0N. wH.H ¢¢.H ammz Hm.H Hm.H mw.m Nw.N uwoo HmoHHOumHz um 03Hm> .UHGH I m M H no. mm.m oo.m «H. mo.m mm.N umoo HNUHHOumHm 03Hm> % > % > ND ND No ND ND ND Gme 309 azah m¢ nomHmZ_Hmoo Hmp moaH NS New aoflmcae =55an qu NHm :oHumH>mv CmHUoZ mm .. 2 NH aafi $3 MN I MN Nam. ou NH mm I mm n.\eoH Ou o\om mm m HN nNON ou o\eoH ON I NH Non ou NON ON m NH New Ou Non NH m N Non ou Noq ¢H «H N Now um>o whom» «0 .oz mummy whom? mo .02 mummw osHm> ummeS m>HuwHDESU mo .02 w>HumHDESU mo .02 50pm :oHumH>m© nzum 309 Ozam m < owmucmouoa %Hpmmw aomH I mqu MBA/3 Hmmmg momma: Hmoo 133.558 mH: 20mm ZOHHMQ mogzmommm mo ZOHHDmHEmHQ HH mama? .H wozgommm 103 As noted in Table 11, the median deviation for the AB Fund was 31% and for the Dow Fund was 54%. These large differences illus- trate one of the major objections to the Historical Cost Method of accounting. The higher C3 amount for the Dow Fund illustrates the effect of long holding periods and low turnovers on the Historical Cost Method of accounting. A comparison of the C3 values for the Historical Cost Method with the I R R.Method illustrate the effect on the ranking of this method because of the use of the historical cost valuation as a con- straint on certain accounting methods. Application of a 9.9% rate of return unconstrained by historical cost valuations resulted in a C3 amount, 2.82, which is in excess of the G: amount for the Historical Cost Method, 2.63. This will be cited further in the discussion of methods where selection of an earnings parameter is required of the accounting method. Stability of yield. The Historical Cost Method ranked thir- teenth for the AB Fund and tenth for the Dow Fund by ranking of the G: values. The C: values had little effect upon the overall ranking. If the C: values were zero, the Historical Cost Method could have im- proved its ranking from twenty-first to nineteenth. As noted in Table 12 the median annual change in yield for the AB Fund is .03 and for the Dow Fund is .02. These represent small average changes in yield. However, the rankings for the method were not exceptional. The C; values were .14 for the AB Fund and .07 for the Dow Fund. It should be noted that the maximum change in yield is .24 for the AB Fund and .17 for the Dow Fund. Investigation of these maxi- mums provides an explanation for these rankings. The AB Fund sold a 104 mH. «N. mwamno adamez No. no. «mango smHUmz MN m MN m Ho. ca 00. mH 0H ON NH mo. ou Ho. m m w 0 OH. ou mo. N N N I ON. ou OH. 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H H N N on. ou OO. mummy mo .02 mummy mummy mo .02 mummw mummy No .02 mummy meme» mo .oz mane» m>HuMHsado No .02 m>HuwHaa=O mo .02 m>HomHaa=O No .02 m>HumH385O mo .02 NON NOO NON NOH OHme aH o o o o mOcm was OmHOHOoz OO H ca OZDN O < OOOH I NOOH OOOONON a OOOH .NOH<> emxm QHmHW zH ZOHH OOHa maHm> Omxumz NH N N OH N N OOHH Osaka ON N O N O O N O mOmwm>m OcH>oE HO O H NH NH H OH OH Omxpaa Om .OHaH I O O H OH HN HN NH HN HN Omoa HmOHOoOmHO HN H m HN H w mDHm> umxumfi quHHDU mxcmm ON. NO. NO.H ON. ON. OO. .HOO Oa> OOHs maHa> Omxpmz NN. OO. ON. HN. NO. ON. mcHH Oamuu ON O NO. NO. NO. OO. NN. HO. mwapm>m NOH>oe ON O NO. ON. ON.H OH. OO. NH.H OOHOmz NN. HO.N NN.N ON. OH.H OO.H saw: I NO.H NO.H I NO.N OO.N Omesme Om .OHOH I N O H NO. ON.N OO.N OH. NO.N NN.N Omou HOOHOOOOH: NN.H I NN.H HO.H I HO.H maHa> smegma OOOHOOO mmHHHHw> NO >O O NO >O O N N N N N N BEN 38 NEE Na <53 MOH<> :O: EHHEEHOU OQOEHMZ mDH<> mem NN mHmwO OOOH NON NO NNN OOHOOH>OO asamez NNH NO NO OOHOOH>OO,OOHOOO NN N NN N NN H NH cans OOOH ON N HN OH NN O NO as NH NH N N N NH O NOH cu NO NH O .. . HH N NON oO NOH N N O O NON oO NON Noq cu NOO 129 NOO cu Noq Now Hm>o mono» mo .02 mummy mummy mo .02 meme» mummy mo .02 mummy m>HudeadO mo .02 o>HOmHDESO mo .oz m>HOmHssdo mo .02 m: m> um HOE ucoaumafiv¢ mHOmHHm> mcHH OcmHH mwmpm>< wdH>oz EouH coaowa>m OOH: ummw m “mew m w . . O OOmOcoouma NHummw msHm> waumz QZDN m < OOOH I NqOH moomHmZ MDH<> Hmmm mDH<> memMQ m0Homaaasu mo .02 o>flumasaso mo .02 o>Humaseau mo .02 ucmsuwsfio< manmwpm> mafia oomph owmum>< wcfi>oz oamww Cw mwcmsu Hmocc< nuflz one» m new» m msam> uwxumz ozpm m < moma I mama moomhmz m24<> Hm¥m<2 QmHmDfiad .> quHw zH ZOHHeocH NH q a a e a mummmtmw< nocume cofiumNHEHcHz «a m o ma m q Now Ha OH 0 OH m c NON N «a NH m NH m NOH bonuoe aoIooHuz owmucoouom H ma ma H ma «H uoxuoe om .uwcw I m m H OH HN HN ma HN HN omoo HmoHMOuwH: HN a m HN a w moam> omxpme oCouusu mwdumm NH. ca. mm. OH. ON. ON. Hmsow>flocH ma. ma. om. do. oH. ma. oumwouwm< mH58p0m GOHuMNHENcfl: mN. «H. mm. NN. oo. am. Now No. om. mm. OH. we. mm. NON oo. om.H om.H oH. NO.N NN.H NOH bosuoe dolooHHB mwmucoouom no. ow. om.a oH. Om. wH.H sowed: Nm. HO.N mm.N 0N. wH.H qq.a :mmz I mo.a mo.H I mo.N oo.N uoxume um .ueCH I m m H No. mm.m oo.m «a. mo.N NN.N umoo Hmoeuoumwz mN.H I mN.H HO.H I HO.H msam> uoxuma ucwuuau moaam> so >o u so >o o N N N N N N 023m 309 ozmm m< :U: m>HH Hmmmwv coma Nqa Nqa Nma Nmm mom COHumfl>mw Eseflxmz mm Ne Nm NHH Nma coaumfl>ov cmflwmz .m H mm H mm c mm N mm 1 NH cu No mm OH mm Ha ma w Hm m mm c wm cu “a NH 0 Ha c AH m ma m ma N NOH 0o Nm m m m m N N ma n ma m wow cu NOH o 0 OH 0 Nom cu New q q Noe cu Nom Now on Noe mom uo>o memo» mummy memo» mummy mumow mummy memo» memo» memo» memo» mo .02 m0 mo .02 mo mo .02 wo mo .02 wo mo .02 mo m>wuma .oz m>wuma .oz o>fluma .oz m>fiuma .oz o>fluma .oz osam> umxumz Isasu 3:850 Isado 128:0 1:830 mnefi>aeaH mumwupmm< «om vow woa sons coaame>ma a . . o o . mwmucouumm maumm» mHDEpom.GOHumNHEHcHz mslmuwu3 mwmucwoumm QZDm m < moma I nqma mDA<> mem memmQ muwuma .oz m>wuma .oz m>wuma .cz m>wowa .cz o>wuma .oz mama? cfl IDESU IsEzu I:E:U 1:530 33530 vmcmcq Hmscc< Hmaea>flecN oamwusmme Non woN NOH . . mHSEpom cowummfieflcflz - awnvuwpz owmucwouom gene a < maa<> smemUzmaommw 139 highest methods. They rank significantly better than the Historical Cost Method. With the exception of the 10% Write-up Method, they rank significantly better than the Current Market Value Method. The Minimi- zation Formula Methods ranked first and second. With the exception of the 10% Write-up Method, Classification III methods had very high rankings in the measurement of closeness to market value. They had only average rankings in the measurement of stability of yield. All of the methods meet the criteria for theoretical appeal defined in Chapter III. The 50% Write-up Method and the Minimization Formula Methods ranked high, third, fourth and fifth, in closeness to market value. In general all of the methods can be considered as better methods and considered for further analysis. The 10% Write-up Method was considerably outranked by the other methods in Classification III. he Ci value, the measure of closeness to market value, was considerably higher than for any other method, 1.03 for the AB Fund and 1.83 for the Dow Fund. The method with the . 2 . . 2 next highest Cv values, the 204 Write-up Method, had Cv amounts of .48 and .84 respectiVely. Since the lO% Write-up Method demonstrated no improvement over the 20% Write-up Method in the measurement of stability of yield, the lOX Write-up Method will be excluded from further consid- eration as a recommended method. All other methods in Classification III will be included in the extended analysis. C. SUMMARY In this chapter each accounting method that was selected for testing has been evaluated. The methods have been evaluated on the basis indicated at the beginning of this chapter. The methods judged 140 inferior have been discarded from further consideration. Seven methods including the alternative parameters have been selected for further consideration. They are: II b. Long Range Appreciation Method, 6% appreciation. III a. Write-up Some Percent Each Year of the Difference between Adjusted Book Value and Market Value, 20% and 50%. III b. Minimization Formula Methods, applied on both aggregate and individual common stock basis. . V b. Moving Average Market Value Methods, based upon an average of 5 years. V c. Least Squares Trend Line Method, based upon market values for 5 years. CHAPTER VII RESULTS - FINAL EVALUATION OF ACCOUNTING METHODS The twenty-one accounting methods selected for study have been evaluated against the criteria developed in this study. The major criteria were: closeness to market value, and stability of yield. Fourteen of the methods have been discarded as inferior. The following seven methods have been selected for further analysis: II b. Long Range Appreciation Method, 6% Appreciation. III a. Write-up Some Percent Each Year of the Difference between Adjusted Book Value and Market Value, 20% and 50% Write-up. III b. Minimization Formula Methods, applied on both aggregate and individual common stock basis. V b. Moving Average Market Value Method, based upon an average of 5 years. V c. Least Squares Trend Line Method, based upon market values for 5 years. The methods selected will be compared with each other and with the Historical Cost Method, the Current Market Value Method and the Internal Rate of Return Method, IRR. The Historical Cost Method and the Current Market Value Method will be included in the comparisons because of the current interest in them. The IRR Method will be in- cluded because of the theoretical properties of the method. The com- parison will include a study of the performance of each method for each 141 142 of the factors noted above, a study of the effects upon the ordinal ranking of the methods by changing the weights attributed to each factor and a discussion of other factors that may affect the selection of an accounting method. A. COMPARISON ON THE BASIS OF EACH FACTOR Closeness to Market Value Table 28 is a frequency distribution of the annual deviations from market value for the AB Fund. The accounting methods are arranged across the table by their respective C: values. The first four methods listed are: V c. Trend Line Method. III a. 50%‘Write-up Method. III b. Minimization Formula Methods, aggregate and individual. These four form a group with relatively good performances in the mea- sures of closeness to market value. The Cv values range from 0.053 to 0.103. The median deviations from market value for the 23 years tested ranged from 4% to 5%. The number and size of the large deviations were the major differences among the methods. The maximum deviations ranged from 9% to 14% and the number of years over 5% ranged from 7 to 12. The Trend Line Method was significantly better in these latter character- istics than the other three methods. This explains the lower C3 value for the Trend Line Method. There appears to be no significant differ- ence in the performance among the other three methods. The fifth and sixth methods, the Moving Average Method and the 20% Write-up Method, were very close to each other in the measure of closeness to market value but significantly different than the first 143 H J W O O h m Nmo.N HOO.N com.H qu. «mm. mOH. NOH. NOO. mmO. maHm> NO NO I Nm Nm NN Nm.O NN Nq Nm GOHumH>oO OOOH New NHm qu NmN NmN NQH NqH NMH N GOHumH>mU Esemex NHm NmN NNN NHH No Nm Ne Nm Nq COHumH>mO smHOmz I H I N H H H q N NH cmcu mmmH I H N m m OH HH m «H Nm cu NH N H m m O O O m N NOH ou Nm q m m N N m m N NON cu NOH m c m O q NOm ou NON m O N NOq so NOm n q H Now On NOq N H Nom pm>o ponumz vogue: venue: vogue: vogue: Hm3OH>HOCH mumwmcww< vogue: bosom: umou mmH coHum onImuHHB mwmum>< mOOLumz dalmuHc3 mcHH mnHm> umxumz HmoHuoumHm IHomudd< NON wcH>oz mH38pom coHumNHEHcHz NOm Ocmue Scum coHumH>mQ NO mwmucwoumm mHumow 38» we 835% I ozE m < OOOH I mqu mDH<> HmMmmQ mo MU me. am. NN. am. NH. ma. 0H. No. woo. mwameu essaxmz ma. No. 00. mo. mo. so. mo. mmo. moo. magmas :maumz m N I m m a N q mN Ho. Qu 00. m c w NH w NH NH NH mo. Co No. q NH m 0 OH N N N CH. cu mo. o m o I N m m ON. cu 0H. m N H N on. Ou oN. N oq. on On. N Om. cu oq. sogumz condo: vogue: eogamz noeamz Hanna>ancH mamwmumw< eonamz accumz maam> onlmuwuz mafia umou anImuwp3 moonumz wwmpm>< coflum umxumz Non vcouH HmoHuOumH: NON m~35uom coaumNHEHcHz wcfi>oz Iwoouaa< oaoflw aw mummy No popesz I exam m < mwcmcu mwmpm>< mmma I quH QAQHV zH mZOHH > O + O NNENNmzv .u N; C ll (‘4 U .K N N H H N N a N N HH NH sH NH maNH OamuN u> N N N O N N N N H H N N s mwaum>m Nea>oz as H H N N O N HH ON ON HN HN HN HN mw:HNO uoxume Oemuuao >H N N N N N N N N N N N N N NNO HmaON>HOeN .aoNamNNeHcHz a s s N H H H H N N N N N NHO muNNmNNNm .eOHamNHeNeHz NHHH N N N a s a N O N NH NH NH NH NNO aasmaHua NON N N N N N O N s s O O O OH NNO a:-maHus NON mHHH NH NH NH NH NH NH N N N N H H N COHumHumuaam magma NCOH NO NHH NH NH NH NH NH sH NH OH N a N N H axe am OmNHHmHUHeH .N m H NHH HN HN HN HN HN HN HN NH OH NH NH NH NH “Nos HNUHuoamH: H NO . N N, O ON O OH O N O N O H N O N O H O NO O NO O HO O NO Ooesmz «angmz QmHHH>HHHmzmm czum m < on mqm , O HueNHm3_ NO + N Nos HN H H H H H H H >H >H >H >H HN m >H >H ON OH OH OH wH NH H NH OH H OH mH OHH mHH mHH mHH mHH H mmHHH mmHHH mmHHH mH E . SH Lilufild> NH NH OHH NHH NHH NHH OHH t. H H H NH NH nHH mHH mmHHH NH HH >H \\o>\ HH OH HwHH \ NmHHH OH O OHH mmHHH NmHHH NmHHH O m NmHHH NwHHH NmHHH NmHHH >H LHH ,o> NnHHH NOHHH NnHHH m N £>I|!|,£>llll.n>l//; NmHHH N, oHH HQHHH HOHHH HLHHH N O ,IONI/l/ >H mHHH NmHHH mmHHa\ NmHHH O m NnHHH NOHHH NLHHH >H ILNIIIIIO>,. mmHHH . o» nHH NOHHH m c HQHHHIIHHHHHIIHOHHH NmHHH NdHHH NNHHH»\\o>I NmHHH NoHHH N.HH n> O m mmHHH mmHHH mmHHH//NLHHH I\o>.lIl.o>\\ o> NLHHH NLHHH HQHHH .L> L> m N o>.I|IIo>,/// >H HOHHWKWNOHHH NLHHH NOHHH c> OHOHHH nHH: mHH mHH OHH N H >H >H Io> Io>\ HQHHHIIHLHHHIIHDHHHIIHLHHH,. £>r -n> eHH OHH NcHH H > > No 0.0N 0.0H . O.m O.N O.H m.O N.O H.O m0.0 N0.0 H0.0 IO xcmm owdmm Ocm>mHom 5 zoom *uSWHWKN QMHHHHHmzum Hm mHm 0 Cost Valuation = .80 Mt - Ht ; Portfolio valuation reserve at time t equals the difference between 80% of Market Value if Bjt > '80 Mt > Ht and Historical Cost value if book value is greater than 80% and V.t > O of Market Value and Market Value J is greater than Historical Cost = 0.0; Otherwise Value AV,t = E,t - I Ei’t; See IIb. and V t above for J J 1&1 J explanationj if Bjt < .80 Mt and V, > O Jt = Vjt - Vj(t-l); OtherWise Compptation of Earningg ‘ t = :’ Dit + See IIb. and V, above for 3 i=1 explanation + o 03 (Bj(t-1) FPSt) , if Bjt < .80 Mt and if Vjt > O I . + E 3Otherwise 3t 151 3‘ 185 11c. MINIMUM YIELD METHOD Computation of Book Value B N :1: + < jt t jt - V. + t‘,V jt j(t-1) jt AV, = E - 1 . Jt jt Z ijt’ jt Vj(t-1); Otherwise Computation of Earningg E.=ID.;ifV. '0 jt .X it jt 1:1 and Y, > .06 Jt = + ‘ ' 06 (Bj(t_1) PPSt), if V > 0 and Y. ; 06 31'. = AV,t + i Ei't; Otherwise . , = _ S PPSt (Pt t) (m/lZ) if V. > 0 Portfolio book value at time t equals book value by the Historical Cost Method plus a valuation reserve Portfolio valuation reserve at time t equals the valuation reserve at time (t—l) plus the change in reserve Change in the reserve for time t is equal to the portfolio earnings less the earnings of the individual stocks by the Historical Cost Method Earnings for time t equal the greater of dividend income or 6% yield on the investment base; provided the total book value is greater than Historical Cost Value Average value of transactions during time t Computation of Book Value ijt ijm it Computation of Earnings (3811). im v i . l (B 11d. + ij(t~1) 'L1 186 EARNINGS METHOD 1) ia Portfolio book value at time t equals the sum of the book value for the individual stocks Book value for stock i at time t equals the book value at time (t—l) plus purchases plus gains less proceeds from sales Gain equals; (a) gain on sales for shares sold and (b) appreciation recorded for shares owned at the end of the period Cost of sales for all transactions for stock 1 during time t equals the sum of the individual trans- actions at cost A < m Cost of sales for ;(BSh) 11(t-l) A ail (Psh) , 1a transaction m (No. of shares) X (Cost per share) Earnings for corporation (1) appli- cable to the shares held during time t. Appreciation equals (Z. — D. ) it it Portfolio earnings during time t equals the sum of the earnings of the individual stocks Earnings for stocks i during time t equals the dividends plus gain as determined above 187 Illa. PERCENTAGE WRITE-UP METHOD Computation of Book Value B, = H + V, Portfolio book value at time t jt t jt equals book value by the Historical Cost Method plus a valuation reserve V ‘V Portfolio valuation reserve at time 't : V'(t-l) + ” 't J J J t equals the valuation reserve at time (t—l) plus the change in reserve VX = (t-l) t To adjust the valuation reserve J J at time (t—l) for gains during time t AVjt = 0.1 (Mt — (Ht + VX)); Change in valuation reserve equals 10% of the difference between market value and adjusted book value, provided adjusted book value is greater than valuation by the Historical Cost Method if VX > 0.0 ll 0 H M - H ' Otherwise (t t)’ Computation of Earnings E = i E,_ + AV, Earnings for time t equals earnings L . . . = for the indiVidual stocks by the Historical Cost Method plus the change in the valuation reserve Alternative Parameters I AV,t = 0__._2_(Mt - (Ht + VX)); Change in valuation reserve equals J 20% of the difference between if VX / 0.0 market value and adjusted book value AV,t = 0.5 (Mt ~ (Ht + VX)); Change in valuation reserve equals J 50% of the difference between ‘ . k, .1 ". 1. ii VX ) 0.0 mar ct va ue and adjusted book value 188 IIIb. MINIMIZATION FORMULA METHOD - AGGREGATE Computation of Book Value B,t = Ht + V,t Portfolio book value at time t J J equals book value by the Historical Cost Method plus a valuation reserve \fi = B, - H . . . jt jt t Portfolio valuation reserve at time t equals the portfolio book value less portfolio valuation by the Historical Cost Method r R Y B = K _1 ~._2 + (t:l) Book value is a function of the jt 3 M K 2 K current market value and yield t 1 l . for time (t-l). See the compu— tation on the following page for the development of the formula. = +) K1 Bj(t-l) PISt k =I(D +s —P)—B 2 ,2 it it it j(t-1) i=1 2 2 3K1 R = 2 Ll+’ 3 t R1 AVjt = \JC - Vj(t—1) Change in valuation reserve during time t equals the valuation reserve at time t less the valuation reserve at time (t—l) Computation of Earnings E, + AV, Earnings for time t equals the sum of the earnings for the indi- vidual stocks by the Historical Cost Method plus the change in the valuation reserve 189 COMPUTATION OF THE MINIMIZATION FORMULA Use of the Mathematical Model 2 2 2 C = CV + Cv This is the two factor model deve10ped in Chapter IV, giving equal weight to each factor d C2 = 2 C C' + 2 C C' Minimization formula is the deriva- d B v v y y . t tive of the model, set equal to zero = 0.0 C C' = - C C' v v y y Formula for Each Factor L = At — B,t v M t B.t =1-..1. M t -1 .' :— Lv M t C = Y - Y y Jt j(t-l) = ‘ B + FPS th hjt / ( j(t-1) t) = hjt / K1 E - B + I (D + s - ) — B jt _ jt ,: 1t 1t 1t j(t-l) i=1 2 +" Bjt 1‘2 = + K - Y Cy [(15jt K2) / ll j(t-l) C' = l / E y 1 190 Substitution into the Formula 1-3M: - - TU M y M t K t Lt 'L 1 Solving for B't B. 7 TB K -..];+_.1£ g _ ....l_t_+ Mt M 2 1 K 2 K t_ !_i l B B, l K _J£+_a]£ = + -— _— 2 2 M Mt K1 t K L 2 2 l— Bjt(Kl + Mt ) = _E- - E;- M 2 K 2 Mt K B, = K jt 3 [Mt 191 IV. CURRENT MARKET VALUE METHOD Computation of Book Value Mt = B,t Portfolio book value by the Current J Market Value Method Portfolio book value at time t equals the sum of the book value of the individual stocks , — B jt igl ijt B,, = M Book value of common stock i equals ijt it the market value of common stock 1 E,t = g Ei’t Portfolio earnings during time t J i=1 J equals the sum of the earnings of the individual stocks Eijt = Dit + Gijt Earnings for stock i during time t equals diVidends plus gain G . = (B,, - B, _ ) + Gain for time t equals; (a) Appre— th lJt lj(t l) ciation in the market value of (S, - P. ) stock i plus (b) sales less 1t 1t purchases = - + (Mir Mi(t-1)) it it 192 Va. MARKET VALUE, LESS A RESERVE METHOD Computation of Book Value B 3 Mt + V jt jt Vjt = ( - 0.1 ) Mt; 1f Bjt > H — ' > > Ht Mt, if Mt Ht Bjt 0.0; Otherwise Computation of Earnings I . = . + AV 3t 132:1 ijt jt AV = V - V, jt jt 3(t-1) Alternative Parameters = ( - 0.2 ) Mt; 1f Bjt > Ht Portfolio book value at time t equals book value by the Market Value Method plus a negative valuation reserve Valuation reserve at time t equals 10% of market value at time t; however, not in excess of mar- ket value less historical cost value Earnings for time t equals earnings for the individual stocks by the Market Value Method plus the change in the valuation reserve Change in the portfolio valuation reserve for time t equals the valuation reserve a time t less the valuation reserve at time (t-l) Valuation reserve at time t equals 20% of market value at time t Valuation reserve at time t equals 33% of market value at time t 193 Va. MARKET VALUE, LESS A RESERVE METHOD - MODIFIED Computation of Book Value M + V Bjt t jt V it ’ VJ(t-l) + A jt‘ if V > ( - 0.2) M it ““" ( - 0.2 ) Mt; Otherwise AV, ( - 0.01 ) M - G. ; 3‘ t i=1 if v > ( - 0.2) Mt jt Vjt - Vj(t-l); OtherWise Computation of Earnings t Portfolio book value at time t equals book value by the Market Value Method plus a negative valuation reserve Portfolio valuation reserve at time t equals the valuation reserve at time (t-l) plus the change in the valuation reserve during time t; however the maxi- mum reserve is 20% of Market Value The change in the portfolio valu- ation reserve during time t equals (a) a negative 1% of market value less gain as determined by the Market Value Method; however, the change equals the valuation reserve at time t less the valuation reserve at time (t-l) if the valuation reserve equals 20% of the market value Earnings for time t equals earnings for the individual stocks by the Market Value Method plus the change in the valuation reserve 194 Vb. Computation of Book Value I B = B jt 121 ijt Bijt = (Bsh)it (AVE)it T (AVE)it - l 2 (MPS)it / 5 , t=T-4 L if T-m Z 4 f T = w (Pps), ] +-| (Mps) [ 1m Ltgm itl 3. Otherwise m = w = 4 - (T - m); w 2 1 Computation of Earningg I E = a., jt igl ijt Eijt = Dit + Gijt G11: = (Bijt ” Bij(t-1)) + (Sit - Pit) MOVING AVERAGE METHOD Portfolio book value at time t equals the sum of the book values of the individual common stocks Book value for common stock 1 at time t equals the average value per share multiplied by the number of shares owned at time t Average value per share for common stock 1 equals the sum of the market value per share for 5 years divided by 5; however, if stock 1 was purchased within the five year period ending at time T, average value per share is weighted by the purchase price to sufficiently to bring the total periods summed to 5. Year of purchase Weighting factor, where T is the current date of valuation and m the year of purchase. Portfolio earnings at time t equals the sum of the earnings of the individual common stocks Earnings for common stock 1 during time t equals dividends plus gain recorded Gain equals the change in book value plus the excess of the proceeds from sales over the purchases during time t 195 Vc. TREND LINE METHOD Computation of Book Value = I B Portfolio book value at time t B. .. Jt igl lJt equals the sum of the book values of the individual common stocks W ll (Bsh). (Bps) , Book value for common stock 1 at it ijt . time t equals the number of shares owned at time t multi— plied by the book value per share ijt (Alpha), + 4 (Beta). Book value per share for common It —’ 1t stock 1 at time t equals an initial computed value plus the rate of change multiplied by the number of time periods after the initial value. For a 5 year linear trend line, 4 time periods after the initial time period, zero (893)1jt (Alpha). (AVE), - 2 (Beta). The initial computed value is the 1t it m 1!: average value less the annual rate of change multiplied by the t mean value of the time periods k) ll UIIH "PJUI t (AVE)it See Method Vb. Moving Average Method, for computation of average value per share for common stock i (Beta)it Annual rate of change in the market 10 value per share for common stock 1 by the least squares formula T I (t - (T—4) ) (Mps)jtl; if (T — m) z 4 (WAve), 2 1t t=T-4L .- (t — (T-4)) (Mps)it ; Other— wise l T (c - (T—4)) (PPS), ! + 2 1m; L .; t=m m = Date of purchase Computation of Earningg See Method Vb, Moving Average Method, E = o ijt for computation of earnings jt “M H i 196 Vd. MARKET VALUE WITH VARIABLE ADJUSTMENT METHOD Computation of Book Value B, = M + V, Portfolio book value at time t Jt t Jt equals book value by the Market Value Method plus a valuation reserve V = V + AV. jt j(t-l) Jt; Portfolio valuation reserve at time t equals the valuation reserve . at time (t-l) plus the change if V, < 0.0 jt in reserve; however, the total value of the fund cannot exceed 0.0; Otherwise market value and the reserve cannot be greater than zero AVjt = Ejt - Z Eijt Change in portfolio valuation i=1 reserve for time t is equal to the portfolio earnings less earnings of the individual stocks by the Market Value Method Computation of Earnings E, = Portfolio earnings are a function Jr of yield, actuarial rate of interest (0.04), and the ratio of the valuation reserve to the market value of the portfolio H IA = E EIJC Vj(t"'l) ; 1f th .04 and Vjt = 0 1-1 = . 0 < 9193 (K1) , 1f th _ .04 and vjt < o = I . < < = iglEijt » if -04 _ th — (RATIO + .04) FACTOR = (FACTOR + 5(th - FACTOR))K1; if FACTOR 5 th 5 (FACTOR + .10) = (FACTOR + %(0-10)) Kl ; if th z (FACTOR + .10) RATIO = Vj(t—l) / Mt FACTOR = 0.04 + RATIO K1 = Bj(_l) + (FPS)t I Y = E.. / K Jt 151 ijt l 0.04 = Actuarial rate of interest