ABSTRACT TIME REDUCTION CURVES AS APPLIED T0 CERTIFIED PUBLIC ACCOUNTING FIRMS By Allan Robert Wright Changing economic conditions have affected the demand for auditing services by Certified Public Accounting firms and their ability to supply these services. Thus, audit time control methods assume greater importance, and this thesis proposes time reduction curve analysis as a useful time control technique for C.P.A. firms. The thesis examines the concept of time reduction (learning) curves, basic elements and determinants of time reduction, and past and present applications of the curves. The audit function of public accounting is analyzed and divided into repetitive and non-repetitive aspects. Factors conducive to time reduction are considered and those relevant to auditing are extracted and divided into two categories, individual and organizational. An empirical study of time reduction in public accounting auditing includes analysis of two and three year sequences of audit data from one hundred and two audits by fourteen C.P.A. firms. Time reduction is analyzed by type of client industry, by type of C.P.A. firm (national, regional, local), by specific C.P.A. firms, by detailed audit function (reported on a limited scale), and by eight factors conducive to time reduction. The eight factors, selected on the basis of objective measurability and data availability, were: auditor repetition on a given audit; audit stability; C.P.A. firm size; Allan Robert Wright training program at C.P.A. firm; number of auditors on the audit; years of experience in auditing the client; years of experience auditing the client's industry; and total years of public accounting experience of all auditors assigned. Time reduction for all C.P.A. firms, year two, averaged 2.7% based on year one hours, and in year three, time reduction percentage was 4.62 based on year two hours. A widely varying pattern of time reduction emerged between: local and national C.P.A. firms; different client industries; and individual C.P.A. firms. Differences between national and local firms and among client industries reflected largely, but not entirely, differing degrees of audit stability and of repeti- tion by auditors on given audits. (Stability refers to audit content or difficulty of the audit as compared to the prior year.) Repetitive audit functions generally exhibit more time reduction than non— repetitive ones. Partial correlation and regression analysis of the eight selected factors produced a coefficient of determination of 52% in year two and 61% in year three of the .0001 confidence level. A strong association between time reduction and stability of audits and repetition of auditors was observed. Audit hours by men new to the audit was added as a secondary factor and proved closely associated with time reduction, particularly for national firms who used new men twice as extensively as local firms. Repetition correlated with time reduction particularly for local firms who practiced it more than national firms. The study was limited by lack of detailed data available to a Allan Robert Wright non-member of the C.P.A. firm and by lack of objective measures for such time reduction related factors as: pre-audit client and C.P.A. firm preparation, client cooperation, uninterrupted work time, etc. Evaluation and cost analysis is made of a hypothetical trade- off between minimum time on the first year's audit (through B factor development) and rapid time reduction on subsequent years' audits (through repetition). A tentative program of time control is sug- gested, incorporating time reduction techniques applicable to auditing, formulas for time calculations, forms pertinent to a control system, and the use of a time reduction specialist. TIME REDUCTION CURVES AS APPLIED TO CERTIFIED PUBLIC ACCOUNTING FIRMS By Allan Robert Wright 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 Graduate School of Business Administration 1972 (EDCOpyright by ALLAN ROBERT WRIGHT 1972 ACKNOWLEDGMENT The following peOple deserve my gratitude and warmest appre- ciation for their contributions to the preparation for and completion of the dissertation: Professor Charles J. Gaa, Chairman of my dissertation committee, who provided continuous assistance, encouragement, direction, and meticulous editing of the thesis. Under Dr. Gaa's direction the thesis preparation was a learning experience in professional excellence. I will always be in his debt for the exemplary assistance which I received from him. Professor Gardner M. Jones who suggested my thesis t0pic and who rendered invaluable service in the developmental stages of the thesis, as well as aid and encouragement in many ways. Professor Alvin A. Arens, a member of my dissertation committee, who assisted in key areas of the thesis with valuable suggestions. Professor William H. Schmidt, also a member of my dissertation committee, a Professor of Statistics from the Educational Psychology area, who provided willing and able assistance beyond the normal course of duties in his department. Professor Roland F. Salmonson, who as head of my guidance com— mittee encouraged me to complete my doctoral program and provided me with an excellent background in accounting theory. The staff of the fourteen cooperating C.P.A. firms who gener- ously provided unlimited time in providing valuable suggestions as well as the underlying data for the thesis. Miss Barbara Fausell of the Jackson Community College English ii Department, who gave invaluable editorial assistance and who noted several conclusions without supporting evidence and supporting evi— dence without conclusions. my wife, Virginia, who offered encouragement, support, and assistance in completion of the dissertation. And finally to Jo McKenzie, who typed the original proposal and the final manuscript under considerable time pressure. I am responsible for any errors or omissions in the manuscript. Should these exist, they should not reflect on the excellent quality of the education nor on the extensive personal attention received from the faculty of Michigan State University. iii TABLE OF CONTENTS ACKNOWLEDGMENTS. . . . . . . . . . . . . . . . . . . . LIST OF TABLES . . . . . . . . . . . . . . . . . . LIST OF FIGURES. . . . . . . . . . . . . . . LIST OF APPENDICES . . . . . . . . . . . Chapter I POTENTIAL APPLICATIONS OF TIME REDUCTION CURVES II III IN THE AUDITING FUNCTION OF CERTIFIED PUBLIC ACCOUNTING FIRMS . . . . . . . . . . . . . . The need for time control in public accounting to meet the pressures of change. . . . . . . The problem of controlling time in the auditing area of public accounting. . . . . . . . . . Purpose of the thesis . . . . . . . . . . . Scope and method of the thesis. . . . . . . . . Limitations of the study. . . . . . . . . . Usefulness of the study . . . . . . . . . . . TIME REDUCTION CURVES - PRINCIPLES, CONCEPTS, AND CONTROVEBIES . C C O O C O I O I O O I O O O The basic concept of the time reduction curve . TWO conditions necessary for the operation of the time reduction curve. . . . . . . . Terminology problems. . . . . . . . . . . . . Total time reduction depends on two variables The two types of time reduction curves: cumulative average curve and unit curve. Mathematical characteristics of the cumulative average curve . . . . . . . . . Graphical portrayal of the cumulative average curve. . . . . . . . . . . . . . . . . Mathematical characteristics of the unit curve. Graphical portrayal of an 80% curve . . . . . . Reconciling differences in concept and usefulness of the two curves . . . The most suitable time reduction curve for public accounting. . . . . . . . . . . HISTORICAL RESEARCH - PAST AND PRESENT APPLICATIONS OF TIME REDUCTION CURVES. . . . Pioneer studies . . . . . . . . . . . . . . . . World War II studies. . . . . . . . . . iv Page 10 12 14 20 22 25 26 29 31 33 33 34 Chapter Page A recent study. . . . . . . . . . . . . . . . 35 Industries in.which time reduction curves may be useful . . . . . . . . . . . . 36 Specific purposes for which time reduction curves are used. . . . . . . . . . . . . . . . . . 38 IV THE NATURE OF AUDITING BY CERTIFIED PUBLIC ACCOUNTANTS . . . . . . . . . . . . . . . . . 47 The presence of repetitive aspects in auditing. . . . . . . . . . . . . . . . . . 47 The relation of the repetitive aspects in auditing to a control system . . . . . . . . 50 Presence of non-repetitive aspects in auditing. . . 50 The relation of non—repetitive aspects in auditing to a control system . . . . . . . . . 54 The need to measure the' 'mix" of repetitive and non-repetitive aspects present on the audit. . . . 55 V INDIVIDUAL AND ORGANIZATIONAL FACTORS AFFECTING TIME REDUCTION IN AUDITING . . . . . . . . . . . . . 56 The concept of factors underlying time reduction . . . . . . . . . . . . . . . 56 Individual factors differentiated from organizational factors . . . . . . . . . . . . . . 56 Basic individual factors which seem relevant to time reduction in the public accounting audit function . . . . . . . . . . . . . . . . 57 Basic organizational factors which seem relevant to time reduction in the public accounting audit function . . . . . . . . . . . . 60 Management's role in control of the factors or skills underlying time reduction. . . . . . . . 63 Control of time through isolation and application of time reduction factors. . . . . 65 A philoSOphy of management in public accounting . . 7 66 VI AN EMPIRICAL STUDY OF TIME REDUCTION IN THE AUDIT FUNCTION IN PUBLIC ACCOUNTING FIRMS. . . . . . . . . 69 The purpose of the empirical study. . . . . . . . . 69 The feasibility of the study. . . . . . . . . 70 The scope and method of the empirical study . . . . 73 Limitations of the empirical study. . . . . . . . . 77 VII RESULTS OF THE STUDY OF TIME REDUCTION IN PUBLIC ACCOUNTING FIRMS. . . . . . . . . . . . . . . 81 An empirical analysis of time reduction by Certified Public Accounting firms. . . . . . . . . 81 V Chapter VIII POSSIBLE FUTURE USES OF TIME REDUCTION CURVES Analysis of time reduction by type of client industry . . . . . Analysis of time reduction by type of COP. A. firm. 0 O O O O I O O 0 Analysis of time reduction by individual C. P. A. firm. 0 0 O O O O O O O O O 0 Analysis of time reduction by detailed audit function . . . . . . . . . . . Multiple regression and correlation analysis for eight reduction related variables. Regression and correlation analysis — Year 2 "" Year 3. o o o o o o o a o 0 Summary of the empirical study. . . . BY CERTIFIED PUBLIC ACCOUNTING FIRMS . Evaluation of the "trade-off" between balanced experience and time reduction potential. Determination of year one audit time. Determination of years needed to reduce audit time. . . . . . . . . . Evaluation of the cost of changes in audit content or client firm induced audit extensions . . . . . . . Cost control sheet embodying time improvement analysis . . . . . . . . Use of a specialist in time reduction . Summation . . . . . . . . . . . . . . BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . APPENDIX A APPENDIX 8 APPENDIX C . APPENDIX D APPENDIX E vi Page 82 99 104 121 123 134 140 142 142 157 162 164 166 170 171 178 182 183 184 185 186 LIST OF TABLES Table Page 1 Two Interpretations of Production Time Yield Different Results . . . . . . . . . . . . . . . 15 2 T. P. Wright's Cumulative Average Curve . . . . . . . 17 3 Boeing Company's Unit Average Curve . . . . . . . . . 17 4 Calculation of Daily Allowance. . . . . . . . . . . . 38 5 Schedule of Financial Drain . . . . . . . . . . . . . 41 6 Summary of Time Reduction by Major Type of Industry of Client Firms . . . . . . . . . . . . . 83 7 Summary of Time Reduction by National, Regional and Local Certified Public Accounting Firms . . . . . 89 8 Comparison of Time Reduction by Type Of C. P. A. Firm. 0 O O O O O O O O O O I O O O O O O 99 9 Improvement Ratios in Audit Hours by Type of C.P.A. Firm. . . . . . . . . . . . . . . . . . . . 100 10 Percentage of Audits with Reduced Time. . . . . . . . 101 11 Audit Stability Ratings by Type of C.P.A. Firm. . . . 102 12 Percentage of Audit Time by Auditors Repeating on Successive Audits. . . . . . . . . . . . 103 13 Audit Time Reduction by Type of Client Industry . . . 114 14 Audit Time Reduction by Individual Local C.P.A. Firms. 0 O O O O O O O O O O O O O O O O O O I 116 15 Correlation of Observed and Expected Time Reduction. . . . . . . . . . . . . . . . . . . . 119 16 Percentage of Repeat Hours Calculation. . . . . . . . 120 17 Time Reduction by Detailed Audit Function . . . . . . 121 18 Year 1 - Year 2 Chi-square Values and Probability Levels. . . . . . . . . . . . . . . . . . 125 19 Comparison of Values of Simple Linear Coefficients Needed for Significance for Observed Correlation Coefficients. . . . . . . . . . . . . . . . . . . . . 128 vii Table 20 21 22 23 24 25 Page Year 1 - Year 2 Results of the Correlation and Regression Analysis . . . . . . . . . . . . . . . 129 Year 2 - Year 3 Chi-square Values and Probability Levels. . . . . . . . . . . . . . . . . . 136 Comparison of Values of Simple Linear Coefficients Needed for Significance for Observed Correlation Coefficients. . . . . . . . . . . . . . . . . . . . . 137 Year 2 - Year 3 Results of the Correlation and Regression Analysis . . . . . . . . . . . . . . . 139 Hours Required by Experienced and Inexperienced Men . . . . . . . . . . . . . . . . . . 151 Comparison of Hours and Cost - Inexperienced vs Experienced Auditors. . . . . . . . . . . . . . . . . 155 viii Figure 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 LIST OF FIGURES The Two Types of Curves . . The Three 80% Learning Curves Using Log-Log Paper . Cumulative Average Time Improvement Curve . . . 80% Learning Curve on Arithmetical Graph Paper. 80% Learning Curve on Log-Log Graph Paper . Unit Hour Curve on Full-Logarithmic Grid. Unit Hour Curve on Semi-Logarithmic Grid. Unit Hour Curve on Arithmetic Grid. The Time Reduction Effort in Public Accounting- Response to Aspects Consuming Audit Time. . . . Control of Factors by Management. Time Time Time Time Time Time Time Time Time Time Time Time Time Time Reduction Reduction Reduction Reduction Reduction Reduction Reduction Reduction Reduction Reduction Reduction Reduction Reduction Reduction A11 Audits All National Firms . . . . . Regional Firm. . . . All Local Firms. National Firm 1. . National Firm 2. . . . . . . National Firm 3. National Firm 4. Regional Firm. . . . . . . . Local Firm 1 . . Local Firm 2 . Local Firm 3 . . . . . . . . Local Firm 4 . Local Firm 5 . . . . . . . ix Page 18 19 23 24 24 27 27 28 64 67 95 96 97 98 105 105 106 106 107 108 108 109 109 110 Figure 25 26 27 28 29 30 31 32 33 34 35 36 37 Time Reduction Local Firm 6 . Time Reduction — Local Firm 7 . Time Reduction Time Reduction Relation of Stability and Time Reduction. Local Firm 9 Local Firm 8 . Relation of Number of Men and Time Reduction. Relation of New Men to Time Reduction (National Firms). . Relation of New Men to Time Reduction (Local Firms) . Trade-Off in Audit Time Reduction - Experienced vs Inexperienced Auditors . Time Reduction Curves for Experienced and Inexperienced Men . Effect of Changes in Audit Content on Audit Hours Sample Time Control Sheet . Analysis Form to Accompany Sample Time Control Sheet. Page 110 111 111 112 130 131 132 133 147 153 164 168 169 Appendix LIST OF APPENDIX Selected Comments on Time Reduction Study by Certified Public Accountants . . . Detailed Listing of Comments by CPA Firms Regarding Proposed Time Reduction Analysis for CPA Firm 0 O O I O O O O O O I O O 0 Determination of Slope for an 80% Time Reduction Curve . . . . . . . . . . . Calculation of Yearly Time Requirements Relation of Firm Experience and Time Reduction. . . . . . Relation of Client Industry Experience and Time Reduction. . . . . . . . Relation of Audit Size and Time Reduction . xi Page 182 183 184 185 186 187 188 CHAPTER I POTENTIAL APPLICATIONS OF TIME REDUCTION CURVES IN THE AUDITING FUNCTION OF CERTIFIED PUBLIC ACCOUNTING FIRMS The need for time control in public accounting to meet the pressures of change In recent years, there has been significant change in the envi- ronment in which public accountants operate. Much of this change has been a result of fluctuating economic conditions and their effect on the client firms of the public accountant. These conditions were double-edged in that they affected both the public accountant's staff and the demand for audit services. All such change which brought pressure on the pdblic accountant may be grouped into demand changes and supply changes. The effect of each demonstrated a strong need for audit time control. Demand for public accounting audit services varied markedly over the 1969-1971 period covered by this study. During the 1969 eco— nomic expansion the demand for auditing services was high. Many existing business firms expanded, added subsidiary firms, enlarged their product mix, and added staff. In addition, many firms mechanized their data processing. Concurrently, a continuous enlargement of the governmental sector increased the number of reports required for federal agencies. As a result, the public accounting firms had diffi— Culty in expanding staff size and quality rapidly enough to meet the intmeased demand for audit services. Compounding the problem was the 1 2 competitively higher pay scale of private firms seeking the best accounting graduates. All of these forces, coupled with a mounting inflation and intensified need for cost control, were transmitted into a seemingly explosive demand for public accounting audit services. However, a new set of demand—supply relationships developed during 1970-1971 as the economy entered a recession phase. Existing client's demands declined somewhat in the merger and new product areas and possibly in the computerization area, but new demands arose in the area of routine audit performance. Smaller staffs at many client offices often gave less client assistance in preparing routine schedules (accounts receivable aging analyses, depreciation computations, etc.) and occasionally client staff quality deteriorated as turnover in- creased. There was also a natural client resistance to audit fee increases. Some public accounting firms, facing a stable or slightly declining demand for audit services in 1970-1971, had an abundance of staff which had been employed at relatively high salaries during the 1969 hiring efforts. Logically, the combined effect of these demand and supply changes was recurring pressure for maximum audit productivity. The problem of controlling time in the auditing area of public accounting The auditing time control problem lies mainly in the difficulty of developing time standards for professional and somewhat non- Standardized tasks. Audits range in sc0pe from the fairly routine to the obviously dissimilar annual audit based on changes in volume, Products, personnel, etc., and finally to the audit presenting totally unexpected variables such as a complete breakdown in internal control. Time control is extremely difficult when many variables are involved. .--n o . .xu.a-A .---o . A .uo—ua T‘- (u! ‘ . u , u .ub‘oul. :6... - f'bo. kn: ""n A "‘r. ‘L. kt C ,1 4 _ (I, v 3 Even in fairly routine audits, the professional nature of public accounting causes unexpected time fluctuations. The auditor is con— stantly deepening the scope of the audit as small discrepancies in one audit area call for a more extensive examination of that area and related areas. In a sense, the problem of audit time control is similar to control of research time with rather similar problems in- volved. There is a more routine side to auditing, however, composed _of some recurring tasks, some constant audit standards, and some fairly consistent audit steps, as well as some basic skill require- ments. It is here where time control appears most promising. These aspects may be subjected to time reduction curve analysis as discussed in Chapter IV. Purpose of the thesis The purpose of the thesis is to demonstrate the usefulness of time reduction curves to public accounting in controlling audit time requirements. A tentative program of time control is suggested, incor- porating time reduction techniques deemed applicable to auditing, and forms pertinent to a newly developed control system are presented. chpe and method of the thesis The concept of the time reduction curve is examined including the components of total time reduction, an analysis of two conflicting time reduction theories, and past and present applications of the Curves. (Chapters II and III) The audit function of public accounting is analyzed and divided into repetitive and non-repetitive aspects for use in an empirical study of time reduction in public accounting firms. (Chapter IV) Factors conducive to time reduction are considered; 4 factors relevant to the audit function are extracted and divided into two categories, individual and organizational, for control purposes. (Chapter V) An empirical study of time reduction in the audit function of public accounting was undertaken in 1969—1971, although audit data from 1967 and 1968 was also included in the study. (Chapters VI and VII) Fourteen public accounting firms provided data on audits of the same clients over a two to three year span of audits. The study in— cludes an examination of five separate phases of time reduction: 1. Time reduction as related to type of client firm industry (retailing, manufacturing, etc.). 2. Time reduction as related to type of C.P.A. firm (national, regional, and local). 3. Time reduction as related to specific C.P.A. firms. 4. Time reduction as associated with detailed audit functions (reported on a limited scale). 5. Time reduction as correlated with eight factors related to time reduction. Audit functions such as verification of cash, accounts receiv- able, inventory, etc. were analyzed for the degree of time reduction by audit function. Lack of readily available data limited the scope of this portion of the study. The eight factors, selected on the basis of historical research and discussion with public accounting practitioners, were deemed measur- able. Several other relevant factors were omitted due to difficulties 0f measurement or unavailability of data. The eight selected factors Were: 1. Years of eXperience of auditors. 2. Years of experience of the C.P.A. firm in auditing the particular client firm. 3. Years of experience of the C.P.A. firm in auditing firms in the same industry as the firm being examined. 4. Hours of time spent on the audit by men who had worked the audit in prior years within the period of this study. 5. The degree of audit stability as to level of difficulty, change of sc0pe, etc. 6. The number of men assigned to the audit each year within the period of this study. 7. The size of the C.P.A. firm in number of employees. 8. The presence or absence of a formal training program within the C.P.A. firm. Only tentative conclusions were drawn from the study because of underlying limitations of the study. The need for a continuing time reduction study within the public accounting firm is stressed. Guides for such a study are proposed, as well as the use of a "model" time control sheet. The utilization of a time control specialist is advo— cated, and various time reduction curve applications are suggested. (Chapter VIII) Limitations of the study Certain limitations, which are discussed in depth in Chapter VI, appeared as the study progressed. Centering around the lack of detailed and readily available data for use by a non—member of the pub— lic accounting firm, they eliminated from examination some of the vari— ables which appear to affect time control and time reduction. A further limitation was the lack of objective measures of the presence of some time reduction related factors. Should future studies be initiated by C.P.A. firms, many of these limitations would disappear Since a member of the C.P.A. firm.wou1d have access to a large volume 6 of data and would be able, through experience, to objectively measure the presence or absence of time reduction factors. Specifically, the limitations are: 1. The availability of data in proper form for in depth analysis a. As to detailed audit function time requirements b. As to large number of consecutive years of audits of same client firm c. As to audits on a first, second, and third year basis where the first year represented a new audit 2. The lack of suitable objective measures of certain factors which may well correlate with time reduction, such as: a. Turnover of client personnel b. Degree of pre-audit preparation by client personnel c. Adequacy of pre-audit conference with client d. Ability of client firm personnel e. Condition of records of client firm f. In some cases, underlying causes of change in audit sc0pe g. Presence of uninterrupted audit time during client's audit h. Other factors not lending themselves to objective measurement by an outsider. Usefulness of the study Finally, despite the limitations of this study, some knowledge has been gained of factors which underlie time reduction. This study may well serve as a "stepping stone" to future "in-house” studies. Even if, in some future internal study, all factors explaining time reduction behavior were not measurable or correlative with observed time reduction, much knowledge of the forces affecting audit time could still be gained. From such beginnings, a modern audit time control system can emerge just as industrial and clerical time control systems emerged in the past. CHAPTER II TIME REDUCTION CURVES - PRINCIPLES, CONCEPTS, AND CONTROVERSIES The basic concept of the time reduction curve The idea that time requirements per unit of produced goods could be reduced through repetitive operations has been well known to industry since the advent of the industrial revolution. Time reduc- tion was the factor underlying the specialization in industry which began before the start of the twentieth century and which became in- corporated in the time and motion study work of Frederick W. Taylor, Frank and Lillian Gilbreth, and other pioneers in this area. Prior to World War II, perhaps the most conspicuous illustra- tion of the advantages of repetitive operations could be seen in the production records of the Ford Motor Company. Mechanization, speciali- zation of task, and a standardization (albeit excessive!) of car model led to the following performance: Year Volume of Units Unit Sales Price1 1910 12,292 $950.00 1926 15,000,000 (approx.) 270.00 The unit data is expressed in cumulative units produced to date. This sharp reduction in sales price was made despite an increase in the general price level. Therefore, cost reductions, mainly through time reduction, must have been tremendous in order to make this unit sales price possible. 8 With such dramatic results, it was inevitable that the time reduction factor would become a permanent component of cost and pro- duction analyses. The immediate problem then was whether the rate of time reduction could be forecast with any degree of accuracy. If time per unit could be forecast for the first and last units of production of a given order, a powerful tool for estimating and controlling man— power needs, for product pricing, and for a variety of production and control techniques would have been develOped. T. P. Wright's pioneering article, "Factors Affecting the Cost of Airplanes," pub- lished in 1936, stated that this time improvement was indeed quite predictable. His study, reinforced by other studies done by aircraft companies during and following World War II, led Frank J. Andress in a 1954 article to conclude "....that the rate of improvement was regular enough to be predictable."2 Thus, the idea of time per unit reduction through repetitive operations evolved into the basic concept of the time reduction curve that, on repetitive jobs, processes, models, etc., the time required to complete one unit can be expected to decline in a pre- dictable manner. One definition of this phenomenon of time reduction is: "As the quantity to be produced is doubled, the cumulative aver— age hours per unit are reduced by a given percentage."3 Two conditions necessary for the gperation of the time reduction curve The two conditions necessary for the operation of the time reduction curve are the proper combination of labor and machinery, and the condition that repetitive operations are not continued on a massive scale indefinitely. Concerning the combination of labor and 9 machinery, many writers note that the greater the amount of labor com- bined with a given amount of machinery, the steeper will be the time improvement curve, thus showing more rapid time improvement. Delbert Brewer suggests that: With 75% assembly labor, 25% machine labor, have an 80% curve4 " 50% " " 50% " " , " " 85% curve " 25% " " 75% " " , " " 90% curve The above analysis certainly does not suggest that men are more effi- cient than machines; rather, it implies that man is more variable in his output and improves his time per unit with successive units pro- duced. But a machine's output is apt to be relatively stable over a period Of time, while a man's output is apt to increase with succes- sive units run. The fatigue factor must, of course, be reckoned with in a situation where production is accomplished more by men than by machines. The second condition necessary for the Operation Of the time reduction curve is the limitation that repetitive Operations are not continued on a massive scale indefinitely. Time reduction curve graphs Often terminate at the right (volume) edge of the graph with the curve in a downward sloping condition. It would seem, therefore, that time reduction per unit would continue on for all future units produced. Thus eventually, one unit could be produced "labor free" despite the fact that labor was being employed to produce the part! The general consensus is that, in time, the curve becomes flat and shows no further time improvement. The principle involved here is that, if Operations Of a constant repetitive nature are conducted on a massive scale Of production, the time reduction curve will ulti- mately prove to be inoperable or nearly so. This is particularly 10 true when there are no model changes involved. An exception to this time reduction behavior with volume pro- duction.was noted in the Boeing Company study of Gordon W. Link and Don A. Ellis where small time reductions were continuously made despite great experience in producing an airplane. "The fact that it (unit time) continues to decrease was shown by the B-17 contract which was still decreasing after 6,000 planes had been made."5 This exception is probably explained by the fact that small model changes were being made during a production period of several years. Terminolggygproblems One is not apt to find the term "time reduction curve" fre- quently used in current or historical literature dealing with time reduction. An exception to this arises in the case Of the Douglas Aircraft Company which does use the term "time reduction curve." S. Alexander Billon also uses the term in his doctoral dissertation, 6 Industrial Time Reduction Curves A§_Tools For Forecasting. The common name which has been applied to this phenomenon is the "learning curve," but it is questionable whether a predictable time reduction on successive performances of a job can properly be called a "learning curve." Learning is variously defined as instruction, education, or acquired wisdom, knowledge, or skill. On a given job these aspects of learning may be present, but the learning may be by one worker performing the job, by those who supervise and train the workers, or it may simply represent the removal of an organizational, scheduling, or other impediment to maximum productivity. Therefore, learning alone can not describe the phenomenon of time reduction. ll Pragmatically, time improvement may come even more rapidly from improved morale or from incentive pay plans which are not neces- sarily features of increased knowledge of the job. Thus, the term "learning curve" is at once both too narrow and too all inclusive to explain the process which takes place when time per unit of produc— tion is reduced in a predictable manner. The term is too narrow in that elements other than individual knowledge and skill are involved. Increased knowledge and skill Of the supervisors, improved training programs, more efficient scheduling, and other "organizational competence" may be as potent factors making for time reduction as individual "learning." The term is too broad in that learning in the conventional sense of "acquired wisdom, knowledge, or skill" may not actually occur. On production Operations, it may be difficult to contend that the knowledge or wisdom Of the worker has increased, though perhaps his skill has increased. Rather than skill being developed, reduced time on a particular job may be more of a transi- tory thing on the worker's part so that the time reduction actually represents familiarization, rather than an increase, in basic skills. Alternatives to the term "learning curve" have been proposed by many writers. Sanders and Blystone suggest: (The curve could be stated as....) "Progress, rather than learning curve, to include equipment improvement, better materials, and management development."7 Another author, in citing an aircraft study, does not even identify the familiar properties of the curve, but merely calls it the "Curtis 80% Curve,"8 while T. P. Wright's pioneering study referred to many names for the same feature: ..."Manufacturing progress function, cost- quantity relationship, cost curve, improvement curve, performance 12 "9 curve . Likewise, the Boeing Company in World War II used "exper- ience curve" and also "unit experience curve"10 and Frank J. Andress would prefer the term "productivity" rather than learning as produc- tivity implies sustained improvement.11 In view of the many factors present in achieving a predictable time reduction, the term "time reduction curve" evolves as the most descriptive and most accurate term. Total time reduction dgpends on two variables A time reduction curve describes the time required for the first unit of production and for all subsequent units. Thus, total time reduction potential depends upon two variables: 1. Ability to reduce time per unit on all units after the first unit is produced. 2. Time required for the first unit produced. Graphically, the time required per unit is plotted on the vertical or Y axis and the cumulative number of units is plotted on the horizontal or X axis. Time required for the first unit is known as the "Y inter- cept" or the "B factor." The rate Of time improvement on subsequent units is known as "slope." 13 Three different time reduction patterns are portrayed in the graphs below. Cumul. Ave. Cumul. Ave. Hrs. per unit Hrs. per unit Y (a) Y (b) 10 8 X 0 X 0 C 1 P d t' Cumul. Production umu . ro uc 1on (units) (units) Cumul. Ave. Hrs. per unit Y 9 (C) 0 A‘ X Cumul. Production (units) Graph (a) represents a situation in which no time reduction occurs. Graph (b) represents very rapid time reduction, and Graph (c) shows an average time reduction pattern. Although the graphs are based on cumulative average time concepts rather than on unit time concepts, the time behavior would be basically the same under the unit 14 curve concept. The intercepts P, Q, and R show that in case (a), assumed time required for the first unit was 8 hours, for case (b), 10 hours, and for case (c), 9 hours. In planning time reduction for control purposes, intercept, or time required for the first unit, and slope, the ability to reduce time on subsequent units, must both be considered. The two types Of time reduction curves: cumulative average curve and unit curve The two common types of time reduction curves are the cumula- tive average curve and the unit curve. The preceding calculations treat the curve as a measure of reduction in cumulative average hours per unit produced and is most frequently referred tO as the cumulative average curve. It is not a calculation of the actual time of pro— ducing the last unit but a calculation of the average hours required for all units to date. In other words, cumulative average time per unit is simply a division of cumulative production time for all units produced by the number of units produced. The second type of time reduction curve is called the unit curve because it measures the time it takes to produce a given unit. This calculation is a marginal one, i.e., it is the additional time required to produce one more unit. The mathematical differences between these two types was clearly demonstrated by Carl Blair in his excellent comparison which follows: 15 TABLE 1 TWO INTERPRETATIONS OF PRODUCTION TIME YIELD DIFFERENT RESULTS12 (This table is based on an 85% learning curve) Interpretation I Time to produce: Accumulated average time Interpretation II Time to produce: Unit time Cumulative Cumulative Number Unit Cumulative Average Unit Cumulative Average Of Units Hours Hours Hours Hours Hours Hours 1 100.00 100.00 100.00 100.00 100.00 100.00 2 70.00 170.00 85.00 85.00 185.00 92.50 3 61.87 231.87 77.29 77.29 262.29 87.43 4 57.13 289.00 72.25 72.25 334.54 83.64 5 53.85 342.85 68.57 68.57 403.11 80.62 6 51.35 394.20 65.70 65.70 468.81 78.14 7 49.39 443.59 63.37 63.37 532.18 76.03 8 47.69 491.28 61.41 61.41 593.59 74.20 9 46.38 537.66 59.74 59.74 653.33 72.59 10 45.14 582.80 58.28 58.28 711.61 71.16 250 21.00 6850.00 27.40 27.40 8940.00 35.76 500 17.85 11645.00 23.29 23.29 15195.00 30.39 1000 15.17 19800.00 19.80 19.80 25840.00 25.84 Both of the foregoing tables produce an 85% learning curve. Interpretation 1, Accumulated Average Time, is calculated to show the 85% curve as: 1. Cumulative Hours = Cumulative Average Hours per Unit Cumulative Units 2. Cumulative Average Hours per Unit Ratio of last Cumula- throggh last Unit produced _ tive Average Time to Cumulative Average Hours per Unit _ former Cumulative through earlier Units produced Average Units Time 3. Cumulative Average Hours’per Unit between doubled quantities should show a 15% decrease or require 85% as much time for all units to date at the doubled quantity as they did at the lower quantity. 16 For accumulated average time, as production is doubled from one to two units, Average Hours for all Unitsgto date drOp from 100 to 85. As production is doubled from two to four units, average hours for all units drop from 85 (at two units) to 72.25 (at four units). 72.25 hours is 85% of 85 hours. The Unit_§urve calculation, Interpretation 11, produces an 85% curve as: 1. Time for most recenthn 5 produced = Ratio of last Unit Time for earlier Unit produced Time to earlier Unit Time 2. Between doubled quantities, actual time for the doubled quantity should be 85% Of the time required for the lower quantity. As Unit 2 is produced, it requires 85% as much time as Unit 1 (85 hours vs 100 hours). As Unit 4 is produced, it requires 85% as much time as Unit 2 (72.25 hours vs 85 hours). In summation, the Cumulative Average Curve measures the average time Of all units to date. The Unit Curve measures the time of each discrete unit. Thus, "85% Curves" will reflect different actual quantities Of production, as the table on page 15 indicates, due to the different underlying mathematical bases described above. Another example of such differences is Billon's comparison be— tween the original T. P. Wright curve (a cumulative average curve) with the Boeing improvement curve, which is a unit curve or a unit average curve and reflects a 20% improvement between doubled quantities. 17 TABLE 2 T. P. WRIGHT'S CUMULATIVE AVERAGE CURVE Unit Cumulative Cumulative Unit Hours Average Units 1 100 100 100 2 60 80 160 3 50.6 70.2 210.6 4 45.4 64 256 TABLE 3 BOEING COMPANY'S UNIT AVERAGE CURVEl3 Unit Cumulative Cumulative Unit Hours Average Units 1 100 100 100 2 80 90 180 3 70.2 81.33 250.2 4 64 78.55 314.2 — These tables represent 80% learning curves. With T. P. Wright's curve, the cumulative average column is the basis for measure— ment of learning (time reduction). Thus, from 1 to 2 units, time re— quired for all units to date is 80% of the original time requirement for the first unit. Similarly, going from 2 to 4 units, time required for all units to date is 80% of the average time required for 2 units. The Boeing Company's curve, the unit average curve, is their basis for measuring time reduction. Thus, from 1 to 2 units, time required for the second unit is 80% of the original time requirement for the first unit. Similarly, going from 2 to 4 units, time required for the 4th unit is 80% Of the time required for the 2nd unit. Raymond 8. Jordan has illustrated these differences in shape of the cumulative average and unit time curves in the following graph. 18 on oq. om ON OH 5 o ~...aa _ ...-41 mafia: OH :Ofiuooooum O>Huoaaaso WCHN ‘ mg. .33.. 9,33: 530 CH ON on ow on oo 05 Eggs so HE 039 as H 939E ow om .oa arun lad SlflOH aBelaAV earneInmng 19 In Leonard W. Hein's graphing of the 80% learning curve, the curvature in early stages of production contrasts with the straight line behavior in latter stages of production and the additional curve dePicts an "accumulated total time curve."15 1 50 8 M 3; r4 0-: U Q '1‘ 0 o O *‘ a £9 ES g '8 U E .4 o E g a U U E: 9 g E 8 g E o a m H I'xJ o ? A H N 3 ‘2 £3 E: 00 m o E H “‘ \ ES \' \. In N ‘4 -. r ‘ r-I <3 <5 75 15 c, tn (3 S In N .—q % “I amll panetnmnoov 20 Mathematical characteristics of the cumulative average curve Cumulative average curves are often expressed as mathematical declines in cumulative average time per unit. They are not a marginal calculation cost calculation of actual cost Of the last unit produced but, rather, are the average time per unit of all units produced to date. Jordan illustrated this as: Cumulative avera e hours Cumulativegquantity» (per unit) 6 20 units 47.5 50 " 40.0 65 " 38.2 100 " 35.5 He further illustrated an 89% learning percentage as occurring between 50 and 100 units as: Units to date 100 units 35.5 Cumul.Ave.Hrs.Per Unit Units to prior 50 units 40.0 Cumul.Ave.Hrs.Per Unit date = 89% learning curve Jordan's fairly complete mathematical formulation for various learning concepts is shown below. The various headings "cumulative average value of units," "logarithmic description of the curve," ' and "determination of negative exponent,” etc. "degree of learning,‘ are this writer's rather than Jordan's. Formula 1 —n , 1 Yx = KX Cumulative average value of units Yx = cumulative average value of x units K = value (theoretical or otherwise) Of the lst unit n = eXponent representing the slope or constant relationship between cumulative average cost and units produced x = the number of units produced (Here it should be noted that the value of n is negative, proving that cost declines as units produced increases.) 21 Formula 2 1 Logarithmic description of the curve On log-log paper, the curve is represented by the equation YX=(1og K) minus n time log X. Applying Jordan's formula, a 90% learning curve would be derived with logs as X-'152 or X raised to the minus .152 power. Formula 3 20 Degree Of Learning At point 1, Y = KX-n, point 2 = Y' = l<(2X)—-n then degree of learning = Yf= K (2K)"n and learning % = 2"n (The number 2 indicates Y K ( X)"n a doubled quantity.) Formula 4 21 Determination Of negative exponent Learning curve % . 1__, slope n = log of learning % 2n log 2 and for a 90% curve, slope n = log of .90 = 9.95424-10.00000 log of 2 .30103 = .04576 = .15201, the slope for a 90% learning curve. .30103 Frank Andress defines the curve as: Y=KXn (Where Y K , 2 cumulative average man hours for units number of man hours to build the first unit X = number of completed units n = log(% of learning curve/log (2) ) 22 Wayne J. Morse uses the following formula for projection of production time.23 Yégs- *(Where X the cumulative production (measured on the horizontal axis) Y = the cumulative average hours per unit (measured on the vertical axis) a = the cost, or time it takes to produce the first unit (the intercept on the vertical axis represents this produc— tion time) b = a parameter of the model which accounts for its slope *Morse's formula assumes that b will always be sloping downward to the right and that this carries a plus sign. Graphica1_portraya1 of the cumulative average curve The time reduction curve may be plotted on semi—log or log—log paper. 0n semi-log paper, the curve is curvilinear with the slope flattening out as rate Of time reduction finally begins to decrease. 0n log-log paper, however, the curve is quite dramatic in that it be- comes a straight line. The decline in time required becomes a function of the units produced, and the citation Of the relation of time reduc— tion to units produced is a 20% reduction or an 80% learning curve, as heretofore mentioned. The time improvement curve illustrated below, adOpted from Delbert L. Brewer, is in semi—log form. 23 FIGURE 3 CUMULATIVE AVERAGE TIME IMPROVEMENT CURVE Cumulative Average Hours per Unit 1r 1 unit=100 hours 90.- 2 units=90 hours (100x90%) 80- 4 units=81 hours (90x90%) 8 units=72.9 hours (81x90%) l6wunits=65.6 hours (72.9x90%) 3 60- -—-\_\\_‘\*32 units=59 hours 64 units=53.l 3 hours :1: r. 40“ 0 1 is, 1L .H.-FJMMH___1____L "--1_J 10 20 30 40 50 60 Units Brewer's graph describes a 90% curve in that each time cumu— lative production hours double the cumulative average hours per unit is 90% of the former cumulative average hours per unit. The more frequently encountered 80% curve with doubling of cumulative hours to date has been put in log-log form as follows by James A. Broadston. 24 FIGURE 4 ‘ +1-1 J I 1__.- _' TI] 80% LEARNING CURVE 0N ARITHMETICAL GRAPH PAPER I ‘" .- L. _.._._4, J » -1 k \ fi Quantity x . \‘ t‘throduced irreguml J \fifi __ It 1 - l . CUMULATIVE NUMBER OF UNITS PRODUCED Huy— ‘ A. ‘ COST-DIRECT LABOR HOURS/UNITS l._“ J25 FIGURE 5 80% LEARNING CURVE ON LOG-LOG GRAPH PAPER m . E-i H Ei § :2 m Quanli roduced CUMULATIVE NUMBER OF UNITS PRODUCED 25 This graph clearly brings out the behavior of an 80% learning curve. Where 1 unit requires 10 hours, a doubling to 2 units will re- sult in an average hours per unit of 8 hours, a further doubling to 4 units will cause 6.4 hours to be the average hours per unit when 4 are produced, etc. The time reduction or learning behavior thus illustrated is the phenomenon which is probably responsible for the great interest in learning curves, namely, that time reduction follows a straight line pattern on this graph. Jordan therefore articulated this behavior in the form of a principle: "On log—log paper, if the distance between doubled quantities remains constant and the rate of decrease between doUbled quantities remains constant, the resulting plot will be a straight line."27 On log—log paper, equal distances measured hori- zontally or vertically, indicate equal percentage change. Thus, if units produced (measured horizontally) double, and if time required (measured vertically) is constantly 80% of an earlier time, then a straight line relationship must result. Equal horizontal movements bring uniform vertical movements. Obviously then, the straight line behavior of time reduction in log-log form is a useful characteristic which predicates that time reduction can be anticipated, plotted, and used far more easily than if the pattern were curvilinear. Mathematical characteristics of the unit curve Since the unit curve is a marginal calculation of time to pro— duce the last or added unit, it reflects the actual time to produce a given unit. Its tabular analysis, presented on pages 15 and 17, can 26 be amplified by a consideration of its mathematical and graphical characteristics. All of which suggest distinct advantages of this curve for public accounting. The Boeing Company which is a prime developer and exponent of the use of time reduction curves developed the following formula called the "Basic Equation": (1) Y = Cx“n = lepe man hours of ship no. 1 unit no. of any ship beyond 1 = man hours at unit x P451632 ll When the logs of each side of equation (1) are used a formula that can be solved for the slope, N, exists. 28 (2) Log Y = Log C - N Log x The Boeing 80% Curve shows that the actual time to produce the second unit was 80% of the actual time to produce the first unit. The actual time to produce the fourth unit, similarly, was 80% Of the time required to produce the second unit. Ronald Brenneck also expresses for the unit curve a straight line learning curve progression as follows: Y e_§ (Where Y = unit hours at any unit X2 XN K = hours at unit 1 N = slape or learning rate) Brenneck's formula may be convered to the Boeing formula by multiplying each side by XN. Then, YXN = K, and Y = K—XN, so that Log Y = Log K - NLogX as in the Boeing formula. Graphical_portrayal Of an 80% curve The following two pages present an 80% unit curve using the three common types Of graph paper. 27 mafia: muooz «or mason N.os mason om , muses ooa awn: you muse: QHMU UHZmHHmMDU MDom HHZD N MMDUHm 0H.w m N_ o m moans e ----< r1lv‘--n'|llllni.liv.ox.l ’ l1" AWE so. H30 N.On use; cm ‘0‘ may ufiaa Hon musom QHMQ UHZmHHmMDU macs HHZD o mMDUHm 28 FIGURE 8 UNIT HOUR CURVE ON ARITHMETIC GRID Hours per unit 12 100L 80 60 P 100 hours 80 hours .———v——-—-.4-.-——. P‘rw 7 0.2 hours6 40‘ 20--- ‘ l3nfusion concerning the prOperties of the curve. The Link and Ellis 11‘mula for a given percentage Of learning curve based on the cumulative a*‘-’€2rage hours formula while Link and Ellis use the formula for a given I>eI‘centage of learning curve based on the unit curve formula. A few examples will illustrate how easily such differences can reconciled. In industry where there are large production runs, the c: . ur‘ves under either formula will straighten after the first few units 30 have been completed, thus showing that both curves have the same basic slope in their latter stages. On page 18 the lines on the two graphs become parallel after unit 5. Furthermore, in industrial applications the two curves may be interchanged by a set of mathematical formulas as noted briefly here: Jordan shows the relation between the cumulative average curve and the unit curve as: 1 + N For a 90% curve, 1 + (—.152) = .84831 The above formula would convert a cumulative average type of learning curve slope to the slope of a 90% unit time curve. To predict the time required on additional units beyond a given volume of units produced to date, Jordan's following formula could be applied. Formula 5 32 Formula for added quantity F = (1.0 + P) 1+" — P 1.0 F = factor for an additional quantity P = additional quantity as a % of the previous cumulative quantity 1+N = factor for conversion from cumulative average to indi— vidual unit Corroborating this is Andress' explanation that a mathematical formula can be applied to convert cumulative average hours per unit to unit hours when necessary. ‘m u ‘ 31 33 U = (N+1)KXn (Where U man hours for a unit (N+l) conversion factor, and for an 80% curve (N+l) = +0.67807 K = number of man hours to build the first unit X = number of completed units n = log(% of learning curve/log (2) ) Finally Leonard Hein whose accumulated total time curve is graphed on page 19 states the mathematical formula for it as does Frank Andress. . . 34 = cumulative average cost per unit = a constant = units = lepe o u:>-m Hein's curve for total time is useful for purposes of deter— mining total time and labor pay requirements on a volume basis. Frank Andress would derive the curve as: T = KX Where T total man hours to build a pre— determined35 number of units K = a constant X number Of units n slope The most suitable time reduction curve for public accounting To determine which curve is the most relevant for use by the public accountant, it is necessary to sum up the characteristics of the two curves and then ascertain how these fit the time control needs of the pUblic accountant. The cumulative average curve is useful for pricing, budgeting, and other purposes. The estimated average time (or average labor cost) for the last unit to be produced may be multi— plied by all units produced to date to arrive at the total labor time u u’n ~ ...e . . ..L. .. . ...”- Sufi t.‘ -.--. .-g, . . u{‘- ..w t.._. 1 32 (or labor cost) for all units. This can be the basis for setting prices on a unit basis or for establishing the total budget. The figure for estimated or budgeted total labor cost will become a key figure in financial drain analysis. The total labor hours figure will help establish labor time and manpower requirements. One dis- advantage for the public accountant in using this curve is that the time required per unit is not readily available. The unit curve seems more uniquely suited to the public accountant for his control needs. The public accountant needs to pre— dict as accurately as possible the time required for the "next" unit. This unit represents an upcoming audit. While the average time to perform a series of years' audits may have use in long range fee estimation, the short term requirement of immediate time predict- ability seems more pertinent. This writer agrees with the Boeing Company that the unit curve will point up differences in actual and estimated time more easily than will the cumulative average curve. CHAPTER III HISTORICAL RESEARCH - PAST AND PRESENT APPLICATIONS OF TIME REDUCTION CURVES Pioneer studies Pioneering studies in time reduction curves extend roughly over the forty year period between the publication of Dr. William P. Bryan's study in 1897 and that Of T. P. Wright in 1936. In his study in the area Of telegraph code learning Bryan Observed a quick time reduction in the early stages of learning with a tapering Off of time reduction later on, thereby isolating the process of the time reduc- tion phenomenon.36 Leslie McDill, during his employment with the McCook Field Company at what is presently Wright-Patterson Field, and James R. Crawford of Lockheed Aircraft Company applied the curve to the airframe industry.37 However, the farsighted study by T. P. Wright in 1936 was the remarkable one. While emphasizing the basic theme that "repetitive work and learning curves go together," the study also stated that the curve is applicable to industries other than aircraft, the construction industry being a case in point. Wright also saw the relation of the Curves to group time reduction so long as the group's aim was to ‘wccomplish a common task more efficiently.38 Wright seemed to look tC) the future when he discussed the environment as a factor affecting 39 1Earning. Seemingly he anticipated the role of organization structure, 33 34 interaction theory, and other modern concepts relating to the environ— ment in its effect on productivity. His recognition of group effort paralleled that Of the Western Electric research of Elton W. Mayo and his staff, which also focused on the importance of dealing with the worker as a member of a group in order to obtain group effort maximiza- tion. This latter work published during the same period corroborated Wright's conclusions. World War II studies Two principal studies, the Stanford Research Institute study and the British Ministry Of Aircraft Production study, which covered the major portion of aircraft production in World War II, arrived at the same overall conclusion: All of the different types Of aircraft had a common rate Of improvement on time required per plane.40 In addition the Stanford study develOped the Stanford Curves from all of World War II and post~war airframe production data.41 7Concurring investigations such as the Boeing studies by Link and Ellis and by Smith, Lansing, Brown and Horton and the 1957 Wright-Patterson Air Force Base study confirmed, reinforced, and interpreted the findings of the British and California groups. At Boeing the valuable work of Link and Ellis recorded the time reduction curve over the life Of the B-17 airplane production.42 In the Smith, Lansing, Brown and Horton study, the authors, using the Stanford Curves which described a 70.7% time reduction slope for air- frames, stated that B factors had to be applied to airframe producers to arrive at this 70.7% curve.43 The B factor concept implied that there is some minimum time requirement for producing the first unit. 35 In a Y=aXmb formula for a straight line curve, the (a) would corre- spond to the B factor. This is the starting point for eventual time reduction, and the highest time per unit which should be required. The eventual time per unit (Y) would depend then on original time (a) less the degree of learning Or improvement percentage (b) for any given number of units produced (X). (The b becomes -b in time reduc- tion formulas to show time reduction.) Thus, it was concluded that a high degree Of learning may not necessarily reflect favorably on a firm, but may indicate that the firm was just quite inefficient to begin.with! Finally, at the Wright-Patterson Air Force Base, the study reinforced the need for a constant mix of machine time and human time to predict time reduction percentages.44 A recent study The interesting and relatively recent (1964) study by William F. Wilkerson conclusively established the acceptance Of the time re- duction phenomenon.45 He discussed the use of learning curves from the viewpoint of a government auditor, tracing out the accounting process for firms doing business under government contract. He noted that time reduction in some manufacturing operations has become so predictable that it is sometimes built into the contract price when the government contracts with civilian producers, e.g., if a govern- ment contract should be terminated before the occurrence Of the time reduction built into the contract, the civilian firm would be reim- bursed for the added cost of high cost production. The high cost pro- duction, Of course, refers to operating in the upper segment of the time reduction curve. This contract clause offers strong evidence of 36 the acceptance and predictability of the time reduction curve. Industries in which time reduction curves may be useful Since the most prominent application of time reduction tech- niques has been in the aircraft industry and the extensive Stanford Institute studies of aircraft time reduction have laid the basis for peacetime aircraft procurement by governmental agencies, time reduc- tion is a cornerstone of industry—government airplane contract negoti- ations; but there are many other industries in which time reduction curves are or may be useful. For instance, in Francis J. Montgomery's study Of the production Of the first 1,500 Liberty vessels made in 1943, as production expanded from 2 to 900 ships, the time required per ship dropped by fifty per cent.46 Likewise Billon indicates that 60% Of metal manufacturers surveyed used time reduction curves in forecasting."7 Werner Hirsch reported in the 1952 study of large machine manufacturing that the 80% learning curve between doubled quantities appeared common in this industry also.l'8 Similarly, available articles on current applications of the learning curve, though not abundant, do imply that there is fairly widespread use of the time reduction curve concept in industry today. Nicholas Baloff indicates the extent of current use of the curve: ...the generalized model has provided every efficient descriptions of many product and process start-ups in a variety of highly mechanized forms of manufacture in these United States industries: steel, basic paper products manufacturing, glass container manufacturing, and automated manufacturing of electrical conductor and electronic switching components.49 Frank Andress specifically substantiates by citing several modern applications of time reduction curves in such widespread 37 industries as machine shOps, residential home construction, shipbuild— ing, home appliances, and electronics.50 Rolfe Wyer states that learning curves have been used with great success among refrigerator manufacturers. He presents an example of extreme accuracy in estima- tion Of cost through use of the learning curves. Just after commencing production on a new refrigerator line, he is able, with time reduction curve analysis, to predict the cost of units far into the future, based on estimated units to be produced.51 Lastly, Raymond Jordan in his excellent book on the learning curve discusses an extensive study of learning rates in the gear-making industry, in which a learning rate of 93% is typical.52 One unusual application of the curve came in an industry whose product was not defined but which had a problem of frequent short run Operations. The application was summarized by Frank J. Powers in his article, "Costs Strike Out With Learning Curve Incen- tives."53 This summary is not only interesting but particularly applicable as some of the problems Of short-time reduction periods which were encountered seem similar to those problems encountered by the public accountant. Short run operations normally might not in- clude the repetitive operations to the extent necessary for the curve to Operate to its fullest advantage. Yet, on Operations continued indefinitely, there is a flattening out or plateau effect, Where time improvement is almost imperceptible.54 Apparently, 95% Of these short run jobs are never repeated at the company in this £3tudy. In addition to this, the assembly line contained varying nllmbers of employees, ranging from one to fifteen operators. A table ftromthe study sheds some light on the actual method used by this firm. . v -\d '1 .0 5T“ ‘. .Ps 38 TABLE 4 CALCULATION OF DAILY ALLOWANCE Learning Z Learning Daily Daily Allowanc;55—_ Days Performance Task Per Operator (Hours) 1 60.0 600 40.0% x 8 = 3.20 2 70.5 705 29.5% x 8 = 2.36 3 75.5 755 24.5% x 8 = 1.96 4 80.0 800 20.0% x 8 = 1.60 5 87.0 870 13.0% x 8 = 1.04 6 100.0 1000 0% x 8 = 0 An incentive system was geared to the time reduction curve to solve the problem of learning new Operations quickly. Also, when the group of Operators exceeded three in number, the company added a group familiarization allowance. The length of the learning period is decided by a conference of the related managers. Finally, the company maintains a list Of learning times for all such short run jobs as bench marks for setting times on new jobs.56 Specific purposes for which time reduction curves are used Beyond the general use of time reduction curves for plotting expected time reduction in labor hours per unit, there are some other specific applications of the curves. These applications when examined in detail show that the curves have great flexibility and that their use is limited only by the imagination of the users. 1. Labor turnover problems The time loss from departure of experienced employees is well known to industry. As one reference, "Determining the Cost of Labor Turnover,"57 clearly outlines, if people terminate employment in the declining phases of the time reduction curve, new employees will replace them and start at the "top' of the learning curve. With time 39 reduction curves, however, management can better quantify the actual cost of a worker starting fresh at the upper portion Of the learning curve. Time required per unit will be high as the new "learning" experience must reoccur. Estimating ending inventory Rather than basing an estimated ending inventory on average cost (which may or may not represent a true average cost,) John Gawa suggests that the inventory value be based on the learning curve.58 This process can be quite accurate. When time declines in the very predictable pattern indi- cated by the learning curve, approximate time required for the last unit can be determined. This time may be in ex- cess of the time required to complete this unit on an average basis. (The average time is contemplated over the entire time reduction process and, on unfinished goods, we may be at various stages of time reduction at the end of an accounting period.) Thus, more accurate inventory determination may be facilitated. John Gawa has merely suggested the use of the curves for inventory valuation. The above analysis is largely this writer's, but it rests heavily on a very detailed analysis of the matter by Wayne MOrse who described the actual use of time reduction curves to value inventory by the Boeing Company.59 Financial drain analysis Writing from the excellent vantage point of an employee of the United States Army Audit Agency - an agency which 40 appears to be fully aware Of potentials of the time reduc— tion curve - John Gawa analyzed financial drain.6O In analyzing the feasibility of a bid from an airframe sub- contractor, he discovered the adequacy of a firm's re- sources to meet needed commitments is important. To illus— trate his findings, a detailed schedule reproduced below brings out the dramatic effect that an 80% time reduction curve can have on a firm's costs and profits. It is note- worthy that time reduction behavior represents a unit curve of the type that the Boeing Company appears to favor. The behavior is a true 80% curve with 20% reduc- tion between doubled accumulated units. The calculations following the table are the writer's for the purpose of refreshing the reader with a brief review of the operation of this unit type of time reduction curve. 41 TABLE 5 SCHEDULE OF FINANCIAL DRAIN Direct Direct Profit Cumu- Unit Labor Labor This lative No Hours Cost OHD. Material G & A Unit Profits 1 100.00 $200.00 $200.00 100.00 50.00 —l92.32 -192.32 2 80.00 160.00 160.00 100.00 42.00 —104.32 —296.64 3 70.21 140.42 140.42 100.00 38.08 - 61.24 —357.88 4 64.00 128.00 128.00 100.00 35.60 - 33.92 —391.80 5 59.56 119.12 119.12 100.00 33.82 - 14.38 -406.18 6 56.16 112.32 112.32 100.00 32.46 + .58 —405.60 7 53.45 106.90 106.90 100.00 31.38 + 12.50 ~393.10 8 51.20 102.40 102.40 100.00 30.48 + 22.40 -370.70 9 49.29 98.58 98.58 100.00 29.72 + 30.80 —339.90 10 47.65 95.30 95.30 100.00 29.06 + 38.02 —301.88 11 46.21 92.42 92.42 100.00 28.48 + 44.36 ~257.52 12 44.93 89.86 89.86 100.00 27.97 + 49.99 —207.53 13 43.79 87.58 87.58 100.00 27.52 + 55.00 —152.53 14 42.76 85.52 85.52 100.00 27.10 + 59.54 — 92.99 15 41.82 83.64 83.64 100.00 26.73 + 63.67 - 29.32 16 40.96 81.92 81.92 100.00 26.38 + 69.46 + 40.14 17 40.17 80.34 80.34 100.00 26.07 + 70.93 +111.07 18 39.42 78.84 78.84 100.00 25.77 + 74.23 +185.30 19 38.75 77.50 77.50 100.00 25.50 + 77.18 +262.48 20 38.12 76.24 76.24 100.00 25.35 + 79.95 +342.43 Illustrative calculations: Direct Labor Direct Labor % Hours Unit No. Hours Hourngeduction Reduction 1 100.00 20 2 80.00 20.00 I00 - 16 _ a 4 64.00 16.00 —80'— 20% 8 51.20 12.80 12°80 = 20% 64 10.24 _ a 16 40.96 10.24 5TT20-- 20% Raymond S. Jordan would note that progress payments may be needed to In connection with the preceding schedule of financial drain, 42 aid such a contractor in his early stages of low production and high 61 financial drain. 4. Make or buy decisions The time reduction curve has proved useful when a company is faced with a decision of making a product which it does not usually make or buying the product from another firm. If a company must interrupt production to produce this type of item, a doUble time loss occurs. a. They will be starting at a high point in unit hour requirements for the newly produced item. b. Resuming production, after an interruption to produce the new part, causes them to go to a higher point on the new time reduction curve compared to their prior point on the curve. Frank Andress has considered this make or buy phenomenon in some depth, and he feels that a short run decision may call for a firm to make a particular new item. Long run considerations, however, must include the potential of buying from another contractor to reduce time according to that firm's time reduction curve.62 If another con— tractor has produced this item previously, he will have a low time requirement on initial production of this order, while the firm which is considering building the item will be starting at the higher initial time requirement on its time reduction curve. Andress seems to be referring to the slope of the curve as well as the difference in relative B factors among various firms. Both of these factors affect ability over a given span of units to reduce time required per unit. 43 Clerical time reduction The area Of clerical tbme control has never been empha— sized as much as industrial time control and perhaps this is due to the less repetitive nature of the work. Any studies in this area would thus be relevant to developing a time control system for public accounting. Maurice Kilbridge applied time reduction curves to clerical Operu ations of a generally repetitive nature in his study of a mail order house. Kilbridge was successful in isolating six factors affecting time reduction. When the effects of these factors were evaluated, Kilbridge found a high correlation between presence of a particular factor and time reduction.63 The factors evaluated were: . Skill and dexterity Knowledge of methods, procedures, media or materials Analysis and judgement General complexity Use of office machine or equipment . Length Of cycle mmano‘m Some Of these factors may be relevant to public accounting particularly factors b, c, and d. They were not evaluated in the empirical study of time reduction as it appeared that they should be evaluated by a member of the C.P.A. firm for proper appraisal. The mail order house study, as well as the Powers study on short run Operations,64 indicate that, by establishing a time reduction curve through Observation of actual time reduction behavior, standards can eventually be determined for repetitive tasks. Hindrances to achieving standards 44 can now be costed out and the variance properly assigned. The variance in the Kilbridge study would result from an insufficiency on the task, of those factors promoting time reduction. These first steps toward a more SOphis- ticated cost accounting system may have some usefulness in develOping a time control system for audit time. Checking actual costs against projected costs Whenever actual costs exceed budgeted costs, an analysis is in order. Either the estimate was incorrect or the time control technique was inadequate. In government contract work, departures from projected costs, as originally submitted on a bid, must often be explained in detail to the governmental agency. William Boren suggests that the time reduction curve will be useful in this respect in that causes Of the cost variance may lie in: a. Learning curve percentage was in error. (Perhaps too low a percentage was used. If 85% was used, go to 90% in the future.) b. Unforseen inefficiencies occurred. (Possibly engineering or drawing changes.) Again, an understanding of factors underlying the curve may well help us to understand variances from the anticipated time reduction. Variances are probably seen in changes in underlying factors. Time reduction can be returned to the normal pattern shown by the curve if only these underlying factors are restored to their normal condition. 10. ll. 12. l3. 14. 45 7. Miscellaneous uses of time reduction curves. The following tabulation is an overview of the many uses of time reduction curves and of the authors advo- cating each particular use. Use Setting selling price Projecting labor loads Determining manpower requirements Controlling shop labor Determining realistic prices for shop labor Establishing starting load costs for new products Examining training programs for new employees Facilitating make or buy decisions Saving on inventory stor- age and handling costs, by limiting inventory size to that called for by the learning curve Effecting transfer of excess workers Evaluating cost to com- pany of change orders Determining cost of not completing a given contract Reflecting on efficiency of 2nd and 3rd shift operations Giving goals to workers Authors CitinggParticular Use Brenneck; Brown, Smith, Lansing, Horton Brenneck, Jordan, Andress Wilkerson Wyer Billon 15. 16. 17. 18. 19. 20. 21. 46 Costing of trained worker Billon terminations Evaluating progress and Kilbridge predicting if employees will reach standard Determining effectiveness Of training program Determining learner's " allowance Setting a standard cost " of employee training and Of employee turnover Preparing manning tables " and replacement schedules Setting a standard cost Reimers CHAPTER IV THE NATURE OF AUDITING BY CERTIFIED PUBLIC ACCOUNTANTS The presence of repetitive aspects in auditing As in any performance task, auditing is intrinsically, though perhaps not Obviously, repetitive. Even its operative base, the application Of constant audit standards, is of necessity a repeated activity which validates all the others: audit functions (or tasks), audit steps, basic skill requirements, and organizational demands. In this study, the term "audit functions" refers to the normal exam— ination of each item on a balance sheet. Thus the examination of cash, of accounts receivable, and of inventory are recurring audit functions. "Audit standards" relate to the minimum amount Of testing, validating, confirmation, etc. needed for the public accountant to certify that the accounting records appear satisfactory. The "audit steps" are the actions taken to accomplish each function and these also tend to be repetitive. A partial listing of these functions, in conjunction with their respective audit steps, follows: Cash 1. Bank reconciliations 2. Footing of cash journals 3. Tracing of ledger postings 4. Internal control analysis (partly repetitive) 5. Petty cash examination 47 48 Accounts receivable 1. Confirmation work 2. Verification Of sub-ledger and control account 3. Aging schedule preparation 4. Examination of write-offs as to propriety 5. Tracing of ledger postings Inventories 1. Observation of physical inventory 2. Test checks of physical inventory 3. Examination Of inventory cut-Off procedure 4. Testing extensions and footings of inventory listing 5. Testing cost to market value The reader will recognize this listing of repetitive steps as only partial. Any standard auditing text, such as Montgomery's, would list many, many more of them. A good auditing book would also acknowledge that the audit steps are repetitive only in the sense of setting some minimum norm for examination of a client's records. Beyond this minimum examination, and indeed during that process, aspects of judgment, imagination, and intuition enter the picture. Differences in the client's internal control, in its management competence, and in the firm's objectives all lead to alteration of examination techniques, extent of audit samples, etc. That is, repetitive steps are applied, using the judgment of the public accountant based on his prior experience, training, intelligence, etc. All Of these considerations of how to audit the client may also be tempered by economic considerations of the client and of the pub- lic accounting firm. The one aspect which is repetitive, although variable, and which is most worthy of consideration by public accountants in develOping a control system is the basic skill of the auditor. Minimally this skill contains four characteristics: 49 Attention to detail Mathematical reasoning ability Ability of self-expression Conceptual ability (ability to interrelate events, persons, places, etc.) «l-‘UJNH 0.. The auditor must continuously give close attention to detail. Evidence Of errors in the accounting process or of fraudulent activi— ties is usually obtained from one or two small discrepancies. Mathe- matical reasoning ability is needed to trace out a complex chain of effects stemming from actual or proposed accounting treatments of events in the client firms. An ability in oral and written expression is required during an audit and in presenting the final audit report to the client. Finally, the auditor should possess conceptual ability to relate Observations in one audit area to those in other audit areas, thus determining the overall quality of the client's accounting performance, weak and strong areas, etc. All of the above skills tend to be repetitive from one audit to another. The final repetitive aspect in auditing might be called organizational demands and this is perhaps the most variable Of the repetitive aspects. In each audit there are conferences with client firm members during which any changes in operations from prior years are noted for their effect on the audit. Auditors may have to familiarize themselves with new key employees and with any accounting procedure changes, and they may wish to select specific areas for audit stress. Although these organizational demands may vary in extent from client to client and from year to year with the same client, these organizational demands are repetitive in nature. 50 The relation of the repetitive aspects in auditing to a control system Manifestly, there is a two-fold relationship between repeti- tive aspects in auditing and the control system needed over audit time requirements. The audit functions, including their steps and the basic skill of the auditors, are repetitive aspects which may lend themselves to analysis and control. 1. 1,000 inventory extensions should require a given amount of time, confirmation Of 1,000 accounts receivable might require another given amount of time, etc. The audit function itself would require a certain time which represented the sum of these individual steps. 2. The basic skill of the auditor should be continuously measured and evaluated. If this skill is increasing, as it should over a period of time, then two beneficial results of his increased skill will occur: (a) A decrease in time requirements on repetitive tasks. The decrease can be matched against some average or expected time reduction noted in point 1 above. (b) Improved. ability to cope with unusual situations which contain nonrecurring factors. Thus, the two-fold relationship involves isolation of repetitive aspects for which time standards may be established. It also involves measurement Of the basic skill of the auditor in terms of his perform- ance against these estimated time standards. The time control system must accomplish these tasks of setting standards and measuring performance. Presence of non—repetitive aspects in auditing An audit for a given client can change rather dramatically from year to year for a variety of reasons. However, the observations made in this study or advanced by practitioners isolate only eight causes. These causes, though not necessarily in the order of their 51 importance, are: 1. Scope of audit change or change in the level of difficulty of an audit Internal control changes Personnel changes in the client's Office Special studies for the client Computerization Of accounts and records Environmental changes . Expansion of duties . Economic changes (DNO‘U'IDLON 0 All of these are non-repetitive for any given client and are, therefore, of great importance in any consideration of a control system. Changes in audit scope or level of audit difficulty can result from several underlying factors. Introduction of new products by a firm and the resulting new cost standards, effect on the firm's resources, possible new collection policies, etc. may require a more extensive audit than in prior years. A merger with another firm can also cause an increase in audit scope as now two sets of records must become one with new accounts being created. Property valuations need to be analyzed and, particularly in the year of merger, a more elaborate set of financial statements need to be prepared. A spin-off, resembling a merger in reverse, also calls for a change in the accounts, though one not so time consuming perhaps. Fluctuations in sales volume can result in more accounting transactions and thus require more audit testing to cover a given percentage of business conducted. Centrali- zation or decentralization may cause the basic unit of entity measure- ment to change. Measuring accounting performance at one location and at several locations requires a different set of accounting reports, controls, data gathering facilities, etc. The auditor must respond with an increased or possibly reduced level of examination. Finally, 52 the quality of accounting work at the client's office can vary, in- creasing or decreasing the testing and observation necessary on the auditor's part. Internal control changes markedly affect time requirements in auditing. Any fluctuations in the quality of internal control, for example, undermine the very cornerstone of the auditor's ability to audit on the basis of sampling some transactions for testing and examination while omitting others. Decreases in the apparent degree of internal control can cause an increase in the items sampled and effect the use of more complete and vigorous audit steps. Personnel changes by the client could be qualitative and/or quantitative in nature. In either event, they effect a need for re— familiarization by the auditor, and may affect the quality of the accounting performance of the client, thus changing audit time requirements. A change in personnel can affect audit time as the auditor must evaluate a new employee's performance in some operations which had been considered safe, or relatively so, when an experienced employee was performing the task. If new personnel also entail a re- alignment Of duties, time may also be consumed in contacting different people for data, assistance, etc. Special studies for the client can be exceedingly time con- suming; they may be unique or one-of-a-kind tasks. These can range from the feasibility Of a new product, new plant, or new key account- ing personnel to a registration statement for the Securities and Exchange Commission. Client computerization of accounts and records may either increase or decrease audit time requirements. In the initial years 53 of installation, new audit techniques must be devised and internal control must be reviewed. The "footprints" available for establishing an audit "trail" have now vanished. In later years, audit time at computerized firms may possibly be reduced as the chance of error in processing Of data is diminished. Environmental changes can occur in the realm of increased governmental reporting standards, in changes in accepted accounting principles, and in the auditor's legal liability to the client. The area Of Medicare statements from hospitals is a case in point illus- trating how an increase in required information can expand audit time requirements. Similarly, a firm doing a larger volume of government contract work may find stricter reporting standards necessary than those required for its privately consumed output. Rapidly changing accounting principles call for a more frequent review of these prin- ciples as applied to events occurring on any given audit. A recent development is the increasing number of law suits involving public accounting firms which may necessitate more extensive audits in the future. There can be an expansion of the auditor's duties from such causes as personnel shortages in the client firm. The auditor may have to prepare schedules which the client had previously prepared, such as accounts receivable, aging statements, etc. Personnel changes may even cause the auditor to provide continuing accounting services until key personnel are replaced. This stOp-gap procedure, while very time consuming, may assure maintenance of a quality accounting performance until replacements are Obtained. Economic conditions not only affect the client firm but 54 specifically affect the auditor also. Special cost cutting studies may be called for in recessionary periods, merger analysis in pros- perous periods, etc. Flexibility is necessary in designing an audit to fit the changing needs of the firm as it responds to changes in economic conditions. For example, a decline in the client's economic status and ability to pay for the audit may call for change in audit method. The auditor may seek more client aid in preparation of schedules, analyses, etc. and may also choose to use the "cycling" technique in which some audit areas are stressed in one year and ignored in the next year. The relation of non-repetitive aspects in auditing to a control system An adequate time control system should record the amount of time spent on non-repetitive aspects of the audit. Further, this time should be separated into classes for purposes of billing the client and for evaluating the performance of the public accounting firm. Two classes might be: 1. Audit firm related aspects 2. Client firm related aspects Category (1) would include amount of time required due to in- adequate pre-audit planning, inexperience of the audit staff, lack of knowledge of the industry being audited, etc. These aspects should elicit a thorough review of the entire training process, assignment Of auditors, and pre-audit preparation by the public accounting firm. The review would question whether these particular non-repetitive aSpects could be anticipated, thus minimizing their effect on audit tinmn This review is essential since audit time resulting from 'L. a") (i ba— presence of these aspects is often absorbed by the public accounting firm and is not charged to the client. Category (2) would include audit time required due to such aspects as personnel changes, internal control problems, new product introduction, etc. which appear to result from the client's actions. These aspects are Often the basis for an audit fee increase. There- fore, the careful evaluation of whether or not an item belongs in this category is mandatory for fee justification. Possibly there is a pattern to these aspects such as a hint of internal control problems in the prior audit. Recognition of such a pattern would thus allow the public accounting firm to make a more timely response to similar problems on future audits. The need to measure the "mix" of repetitive and non-repetitive aspects present on the audit Any control system for public accounting should measure the mix of repetitive versus non-repetitive aspects and the expected time reduction in view of the mix present. Since time reduction is asso— ciated with the presence of repetitive aspects and with a minimum of the time consuming non-repetitive aspects, there should be a close correlation of observed time reduction and the presence of a high degree of repetitive aspects. Obviously, if an audit is largely repetitive in nature, time reduction should be expected and, if it does not occur, the public accountant may look to his own internal management for the cause Of this failure to control time. CHAPTER V INDIVIDUAL AND ORGANIZATIONAL FACTORS AFFECTING TIME REDUCTION IN AUDITING The concept of factors underlyig time reduction Time reduction can be facilitated and controlled through an understanding of those factors-forces, skills, conditions, etc.-- These factors are applied to work Which promote time reduction. Situations which contain varying degrees of repetitive and non- The factors are applied in varying degrees in repetitive aspects. Order to control non—repetitive aspects and to exploit the potential of the repetitive aspects, thus promoting maximum time reduction. kldividual factors differentiated from organizational factors From the results of past time reduction studies and from interviews with public accounting practitioners, two categories of One category factors conducive to time reduction seemed to emerge. was composed Of factors which related to characteristics or qualities 0f the individual, such a knowledge, skill, and judgment. The second category was composed of factors which related to organizational techniques, such as scheduling improvements, advance planning, etc. For further discussion and analyses, the factors are referred to as ind1‘71dua1 factors and organizational factors. 56 57 Basic individual factors which seem relevant to fine reduction in the public accounting audit function The research and interviews resulted in a compilation of a list of five main individual factors conducive to time reduction and relevant to the auditing function in public accounting. These are: VIDLA’NH Degree of metal effort required Knowledge, skill, and judgment Experience Training Attitude toward time reduction The degree of mental effort required by the auditor is con— Siderable and variable. He must be alert, intuitive, and able to learn from and to correlate his experiences on various audits. According to James L. Crawford, the Lockheed Aircraft Company officer: - - -The jobs which require the most mental effort improve at the most rap id rate. Work or lack of experience of the Operators." The mental effort may be due either to complexity of the 66 The individual factor of knowledge, skill, and judgment is re(Illired to a considerable degree in auditing. The knowledge required for effective audit performance ranges from an understanding of simple bookkeeping to a comprehension of the implications which a prOposed atIger may have for long run capital structure of the firm. Skill and judgment are required over a similarly wide range, extending from a I:‘Iitl‘lmetical skills to management advisory skills, and from judgment (>i3 the timing of a cash count to a decision on the type of data Del‘tinent for an annual report. Experience must be considered as a prominent factor underlying time reduction. The time reduction curve is based in part upon accumu- lation of experience as more units are produced. Experience brings 58 familiarity to a task and this in turn promotes time reduction. In public accounting, experience could be measured in a variety of con- texts. The number Of years which an auditor spent in public account- ing would be one measure of experience. This measure would usually indicate that the auditor was experienced on all or most of the audit functions, such as cash, inventory, etc. This type of experience might assure a minimum time required to perform each function on a new andit, and thus a new audit might require only familiarization with a flea»? industry, new personnel, and other organizational aspects. A S€3<113cts should normally present less of a problem in the later years of the audit and time reduction should be expected then. The question of which type of experience best correlates with t3jLIIme: reduction in the public accounting audit function is similar to the question Of how time per unit is determined with industrial time re<111ction curves. Time is reduced by applying to the first unit time (called Y intercept, or B factor) a certain rate of time improvement (Slope or -b exponent). Time on the first unit is a reflection of initial skill in production based on accumulated general experience 7a1i~1111 products similar to the new product being considered. This was ‘tflhl‘i Ineaning Of the Stanford studies in applying B or levels of expe- t':Lerice factors to airframe producers to get an average first unit ‘Zflanew Beyond the first unit, speed of familiarization seems to be ‘tll‘i remaining determinant of time improvement. It might be noted that the area Of potential time reduction is limited for a firm which is 111itially very skillful. Perhaps the years spent in public accounting 59 and the intensity of experience in those years, e.g., progression through a series of increasingly difficult audits, may affect initial time required on a new audit. Beyond this point, familiarization with this particular audit may well be the principal cause of time reduc- tion on subsequent years' audits. The experience of an auditor on an individual client's audit would promote this familiarization and should promote time reduction. Each type of experience seems relevant for reducing audit time. In determining the best measure of experience to use (or whether to use both measures) for correlation with time re- dLICtion, consideration must be given to the alternatives of rapid auditor rotation versus allowing substantial repetition of auditors on a given audit. Later in this study, an attempt will be made to Ine—Elsure hypothetically the cost of this trade-off between rotation and specific audit experience. Training represents a further input into time reduction ability as it cuts across factors of mental ability, skill, knowledge, and even judgment. It can even substitute for lack of experience in Some audit phases. Marvin L. Taylor sums up several related factors conducive to time reduction as: "...the man, training, skill, el'ctz’etience."67 Training can serve to reduce time by clarifying proper audit steps, by demonstrating techniques for carrying out each step, by demonstrating ways to test internal control, etc. The auditor can thus be alerted to events which may occur in an audit (within limits) and thus be better prepared to face situations as they arise. Finally, the auditor's attitude toward time reduction may in itself be a factor promoting or retarding time reduction. In industry, attitudes favorable to time reduction have long been encouraged by 60 incentive pay scales, profit sharing, and cost savings sharing plans. Perhaps the latter two plans and/or other techniques may be used in public accounting to foster an attitude favorable to time reduction. Several authors have stressed the importance of developing this desire to reduce time. Winfred B. Hirschman stated: "Furthermore, improve- znents are always possible over time so long as people are encouraged 68 In the same vein, T. P. Wright noted: "...There is to seek them." a Ileed to believe that progress is possible for the learning curve to wcrric."69 Basic organizational factors which seem relevant to Lime reduction in the public accounting audit function From the results of past time reduction studies and from interviews with public accounting practitioners, a list of organiza- ti<>t1al factors conducive to time reduction and relevant to the audit- ing function in public accounting was compiled. The organizational fac tors selected for analysis in this study are: . Uninterrupted audit assignments . Presence of short tasks at well separated intervals . Scheduling improvement . Effective manpower use . Advance planning needs U'IkaNO-J When audits can proceed in an uninterrupted manner, some time retillction benefits occur. The audit group may work as a team, proceed— thlig. step by step to complete the audit. The steps are interrelated Eit“i the lack Of completion Of one step may slow progression on another Eit:‘it> or even impede completion of the entire audit. The time reduc— tion curve Operates best when a task is continuous. If an industrial task is interrupted, refamiliarization is needed upon return to the original task. The fact that an audit is conducted yearly makes for 61 some discontinuity in the task. The most serious break in continuity, however, may occur when the audit is interrupted to shift some or all of the audit personnel to another audit. In industrial terms, this interruption of a task and return to the task produces the phenomenon Of "scallops." Hirschman states that this behavior is represented by a sharp increase in time on a time reduction curve which had previously been sloping downward. He refers to this as a "toeing up" of the Curve.70 The occurrence of interrupted audit time may thus require analysis by the public accountant as to effects on audit time to determine whether the same "toeing up" effect may not exist. If it does exist, then means of prevention of audit interruption must be st‘IE‘essed. Auditing is also typified by relatively short tasks conducted at Well separated intervals. Frank Andress, in describing this situ- ation as it exists in industry, feels that here learning is important and that great time savings are possible. He cites the need for advance planning and for methods analysis in such circumstances. This is the kind of planning which must precede an audit and which faQILlitates time control. Regarding the length of the production run, and perhaps of the audit, an interesting observation was that of Vincent Shroad, Jr., who discussed the possibility of using the time re(itiction curve for "repeat business" to predict time requirements. He believes that a firm should show an unfavorable variance if the order size is less than some standard size order.72 Marvin L. Taylor also felt that lot size and production rate affected time reduction.73 Pet‘haps on some small audits, the combination of audit experience, ab:11;Lt:y, etc. may not be Optimum for time reduction. The relation 62 of audit size in terms of potential time reduction is thus an organi- zational factor which may be worthy of examination. Scheduling improvement can affect time reduction in that effi— cient scheduling can reduce interruptions and thus affect the continuity Of audit assignments as discussed previously. It can also make the most effective use Of manpower as described below. Schedules must be tailored to match the client's need for periodic examination and re- Ports, and to match the public accounting firm's ability to provide prOper audit personnel. Effective use of manpower would include a range of considera- tions from proper training of staff, to assignment Of the correct uthuber of auditors, and finally to Obtaining the proper mix of eXpe— lrj-s’éeuce, knowledge, auditing ability, management ability, etc. among the assigned personnel. Time reduction may well correlate with any or all Of these factors. For example, auditors with background in the industry being audited who possess the technical auditing skills l“Eeded for the audit problems anticipated, e.g., mergers, computeriza- The number I ‘::i—<>Il studies, etc., should be assigned in proper number. of auditors assigned can, itself, present problems in that too many (:‘attl lead to confusion and too few can lead to overwork.of those few. Finally, advance planning seems a fundamental organizational f'aQtor in that problems of improved scheduling, effective manpower use, dealing with short, intermittent tasks, and creating uninterrupted £111(lit assignments all stem from proper advance planning. The public acCounting firm management must thus be skillful in anticipating Q11-ent needs and public accounting firm capacity to satisfy these heeds . 63 Management's role in control of the factors or skills underlying time reduction Public accounting management can assure that maximum indi— vidual or organizational factors are applied to the audit at the proper time, in the prOper amounts, and in correct proportions. In essence, management applies individual and organizational factors in the effort to control the effect (on time) of repetitive and non— repetitive aspects. A hypothetical example may help point out manage— ment's role in time control. Public accounting firm X holds a pre- aUdit conference with client Y, conducted just before the audit date, Without examination of the previous year's working papers. The con— ference is perforce brief and cursory in nature. Thus, neither a Prior year's weakness in internal control nor the fact that the firm is considering making a public Offering of securities is disclosed. mic—1h additional auditing work is therefore entailed, some Of it Of a non-repetitive nature. Staff which is experienced in preparing S.E.C. Statements is not available when needed, or is transferred in from c)‘zt‘ler in-process audits, thus interrupting the continuity of those audits. Much time might have been saved by proper advance planning, SQI'leduling, avoiding Of interrupted work runs, etc. The handling of o‘rr‘ganizational factors by the management of the public accounting firm seems at fault. Despite these errors, individual factors such as experience, training, and the basic skill of the accountant might have provided the flexibility needed to deal with this host of non- reDetitive aspects. Auditors possessing such backgrounds are, ht"Wever, valuable resources of the firm and their use must be judicious and warranted in terms of time reduction needs. 64 A graphical summary of the public accountant's suggested response to all aspects of the audit might appear as follows: FIGURE 9 THE TIME REDUCTION EFFORT IN PUBLIC ACCOUNTING RESPONSE TO ASPECTS CONSUMING AUDIT TIME ASPECTS CONSUMING TIME ON AUDITS REPETITIVE ASPECTS RESPONSES TO FACTORS CONSUMING TIME INDIVIDUAL FACTORS Demands on Skill Of the Auditor Degree of Mental Effort———\ Constant Audit Standards Knowledge, Skill & Judgment And i t Functions Experience And i t Steps Training I ot‘ganizational Demands /ttitude toward Time Reduction NQN—REPETITIVE ASPECTS ORGANIZATIONAL FACTORS Scope of Audit Change Scheduling Improvement————\ Internal Control Change Uninterrupted Work Assignments... m Client Personnel Changes Effective Manpower Use Special Studies Advance Planning Needs Client Computerization \ Short Tasks at Well Separated) E "\ Intervals Ia-":l.ronmental Changes ‘\ / Expansion Of Duties E Q onomic Changes 65 Control Of time through isolation and application of time reduction factors Determination of those specific factors which promote time reduction is not a particularly difficult task. Time reduction literature contains many references to these factors and interviews with management in particular enterprises will help to isolate those factors peculiar to a given enterprise. What is difficult, however, is the isolation of the effects which each factor has upon time reduc- tion, i.e., how much time reduction each factor appears to effect. If this time reduction potential could be determined, then management would achieve maximum time reduction by causing the prOper factors to be applied to a task at the right time, in the right proportion, etc. Deviations from planned time reduction would be explained by a departure from the proper "mix" of these factors. The problem Of isolating time reduction factors is one of statistical correlation. Ideally, each task could be measured for the degree of presence of these factors at one time and the time required for task completion noted. The same observations could be made on a subsequent produced unit (or completed audit). Finally, a composite graph, formula, etc. could be prepared showing the degree of presence of the factors and the degree of time reduction Observed. The next step would be to try to isolate each factor's effect on time reduction by partial regression or correlation analysis. This would present no great problem if all other conditions of the task remained constant. A problem in some enterprises is that these conditions may not stay constant. Auditing is a case in point and certain conditions of the task, repetitive and non—repetitive aspects, are not always 66 constant. Thus, measurement is needed not only of the factors present on a task, but Of the variability of the task itself. The Kilbridge study74 and the one by Frank Powers75 on short run industrial Operations were the only two studies observed which attempted to measure the contribution of various factors to time reduc- tion. In his study of clerical operations in a mail order house, Kilbridge, in consultation with supervisory staff, arrived at these five factors affecting time reduction: "...skill and dexterity; knowledge of methods, procedure, media, or materials; analysis and judgment; use of Office machines; cycle time." Point values were assigned to each factor present on each job and a list of point values per job was prepared. The relation of points to learning time was estimated and an equation was prepared. From the equation and a conversion chart a standard or expected time reduction curve was pre- pared for each job. As jobs were completed, the actual time perform- ance curves and estimated time performance curves were nearly iden- tical. Thus, the importance of each factor present on a job in reducing time on the job had been proven. This is a procedure which may be applicable to public accounting in isolating the factors and measuring their effect on time reduction. A philosgphy of management in public accounting Management in any sphere represents a mixture of two types of skills: management-technical skill and human relations skills. In public accounting, the management-technical skills include technical work and management techniques (budgeting, scheduling, pay systems, etc.) in supervising that work. Human relations skills are, as the 67 name implies, skills used in dealing with peOple. These skills would include understanding, motivation, communication skills, etc. Efforts to control the individual and organizational factors must be made through the use Of these two skills. Relying solely on a-priori reasoning, the factors might be grouped as follows: FIGURE 10 CONTROL OF FACTORS BY MANAGEMENT Factor May be Controllable By Individual and Management-Technical Human Relations Organizational Factors Skills Skills Individual Knowledge, skill,4judgment X Degree Of Mental Effort X Egperience Training, Attitude toward time reduc. xxx Organizational Continuous production vs interrupted runs Short tasks at well separated intervals Schedulingiimprovements Effective use of manpower Advance planning need x xgfix Partially controllable by management Generally controllable by management X XX The underlying rationale for the foregoing chart is based on several assumptions: 1. That individual factors are only slightly con- trollable by public accounting management. 2. That the auditor is a professional person, not generally motivated by charismatic management. 3. That the auditor is a person who responds to challenges to his ability. 4. That the auditor respects and responds to management which 68 is as professional in nature as is the auditor in performing his duties. 5. That some organizational factors as "continuous produc- tion" and "short tasks" are factors of only slight control by public accountants, and must be compensated for by optimum application of other factors. Thus, if the foregoing chart may be accepted, it suggests that management, by practicing prOper techniques, can do much to effect improvements in factors which underlie time reduction. This improve- ment can come from applying management techniques more often than through applying leadership or charismatic skills. CHAPTER VI AN EMPIRICAL STUDY OF TIME REDUCTION IN THE AUDIT FUNCTION IN PUBLIC ACCOUNTING FIRMS The ppgpose Of the empirical study In order to accomplish the purpose of the thesis, which is to demonstrate the usefulness of time reduction curves to public account- ing in controlling audit time requirements, an empirical study was conducted to determine whether there were any patterns of time reduc- tion. If there was much repetition involved in some audits, it might be assumed that a time reduction curve should exist. The more the individual and organizational factors were brought to bear on succes- sive audits, the more time reduction might be observed. Although the study focuses on the behavior of time reduction with the presence of factors bearing on time reduction, there has been so little research in this area that other phases Of time reduction also had to be con- sidered. Accordingly, time reduction was analyzed in four additional contexts: by type of client firm industry (retailing, manufacturing, etc.), by type of public accounting firm (national, regional, and local) by individual C.P.A. firm, and by detailed audit function. The most beneficial result which could emerge from this study would be the discovery of a pattern of time reduction relationships for types of C.P.A. firms, for types of client industries, for individual firms, and for the detailed audit functions. From such relationships 69 70 much can be learned about conditions conducive to time reduction. Equally beneficial would be the discovery of a strong, positive corre— lation of observed time reduction with each of the eight factors ex- amined which are: 1. Years of experience of auditors 2. Years of experience of the C.P.A. firm in auditing the particular client firm 3. Years of experience of the C.P.A. firm in auditing firms in the same industry as the firm being examined 4. Hours of time spent on the audit by men who had worked the audit in prior years within the period of this study 5. The degree Of audit stability as to level of difficulty, change of scope, etc. 6. The number of men assigned to the audit each year within the period Of this study 7. The size Of the C.P.A. firm in number of employees 8. The presence or absence of a formal training program within the C.P.A. firm Such a result would encourage public accounting firms, when possible, to plan, schedule, and staff audits so that the eight factors would be present or considered in pre-audit planning. The minimum result would be increased knowledge of the time reduction process in public accounting and of the problems present in attempting to reduce time. The feasibility of the study TO determine the feasibility of the study and to avoid repeti- tion of any earlier studies by practitioners, a number of Certified Public Accounting firms including the "big eight" were canvassed. These firms responded unanimously that such a study had never been undertaken to their knowledge. In response to the question of feasi- bility, the "big eight" firms were generally not too encouraging about the outcome of such a study as the detailed list of their comments and those received from other public accounting firms in Appendices A and ‘13 u. If N. SUI ‘2: .~E 71 B indicates. Their most common and significant reservations on the feasibility Of the study stemmed from two main causes: client firm variability and public accounting firm staff and assignment vari— ability. The public accounting firm officials consulted felt that there was client firm variability caused by change in audit scope from year to year. They mentioned that public accounting firm staff variability occurred due to their desire to allow the individual auditors to pro- gress professionally through rapid rotation on client engagements. According to the officials interviewed, the individual auditor appar- ently has this same desire for rapid rotation. Obviously, unstable audits performed by varying personnel each year may present so many variables that correlation analysis of factor effect on time reduction may be greatly complicated. All the authoritative and experiential objections to the study are strong and valid objections. They may be shortsighted ones, how- ever, for three incontrovertible reasons. First, it is certainly Obvious that there is a need to measure the cost in added audit time which arises from the client firm variability. As far as possible, time needs to be reduced by proper planning so that maximum audit engagements can be accomplished at minimum time consistent with quality auditing. (Occasionally, a 100% error in estimated and actual audit time was encountered on single audit engagements.) Time reduction curves may show the cost of variability from added time above last year's time or from failure to reduce time below that of last year as the time reduction curve theory implies in repeat operations. Second, the costs and benefits associated with rapid rotation 72 of personnel through various audits does not appear to have been measured in dollar terms. It is an assumption that the nature of the man and the public accounting firm demands this rotation, but public accountants cannot assume a proposition not expressed in money terms when they themselves often criticize such unsupported reasoning by their clients. When the auditor examines propositions of client plant expansion, merger feasibility, make or buy choice, etc., he operates largely on a pragmatic basis, comparing incremental costs and revenues. Until such analysis is attempted, no recommendation should be made by the public accounting firm concerning these propo- sitions. Time reduction curves, if prepared, may help reveal the costs, if any, of staff turnover on audits. Third, in contacting some public accounting firms, the writer perceived a natural resistance of professionals to the idea that a professional's time could be "time studied;" there was a feeling that everything about the work was so non-routine that any attempt to analyze time was a futile effort. This may be true, but until an examination is made to determine the existence of repetitive aspects, or of any other pattern of time reduction, it would seem rather pre— mature tO pass judgment. Several firms, however, were more optimistic in that they felt that time reduction on audits did exist, although they held reservations as to the exact predictability of time reduc- tion from year to year. Those firms which agreed to cooperate in the study felt that any additional knowledge Of audit time control which could be gained would justify the time and effort expended, thereby justifying the minimum objective of this study. 73 The scppe and method of the empirical study Fourteen Certified Public Accounting firms, three national, one regional, and nine local, with locations in three cities of vary- ing size, cooperated in the study. They made available the audit data, covering a two to three year period, for one hundred and two client firms, including large and small firms from eight different industries. The empirical study was composed of five main phases: 1. Time reduction as related to type of client firm industry (retailing, manufacturing, etc.). 2. Time reduction as related to type of C.P.A. firm (national, regional, and local). 3. Time reduction as related to specific C.P.A. firms. 4. Time reduction as associated with detailed audit functions (reported on a limited scale). 5. Time reduction as correlated with eight factors related to time reduction. The first phase of the study concerned the examination of audit data of eight separate client firm industries in an effort to determine whether there was any pattern of time improvement. This evaluation focuses attention on industries which are most and least susceptible to audit time reduction. This knowledge could lead to a further inquiry into the presence of non-repetitive aspects in some industries, loss of time through familiarization with complex industries, etc. The second phase considered time reduction by type of C.P.A. firm: national, regional, and local. Audit time reduction differences may reflect on the type of organization of the firms, on their varying rotation policies, and on other characteristics of the type of C.P.A. firm. 74 The third phase concerned time reduction by individual C.P.A. firms, and preparation of time reduction curves for each public account- ing firm as well as a curve for the total time of all audits Observed. It was felt that this information would be of interest to the par- ticipating firms. The fourth phase consisted of an examination of the detailed audit functions. Cash, accounts receivable, and most of the normal audit functions were examined on a limited basis to determine time reduction behavior by function. This data could prove useful to firms in budgeting time for an audit. If some functions show a consistent decline in time required, this may eventually become the basis for time reduction standards. This study may point out those areas which, by their variability, seem to contain non-repetitive aspects. This knowledge may help in pre-audit conferences, in scheduling, and in manpower assignment to audits. Thus, if inventory observation re— quired more time than the prior year because of a shortage of client personnel trained in taking inventory, training could be initiated by the client that would reduce time on this function, and the public accounting firm would not need to assign additional personnel for inventory. The fifth phase included an examination of those individual and organizational factors noted in Chapter V which appeared to be correlative with time reduction. Unfortunately, some of the factors could not be used by the researcher because he was a person outside of the public accounting firm. Therefore, out of five individual factors promoting time reduction (mental effort; knowledge, skill, and judgment; experience; training; and attitude toward time 75 reduction), only two (experience and training) could be studied on the basis of set criteria. These set criteria were data availability and measurability in an Objective manner. Experience was evaluated in four different contexts: indi- vidual's experience in public accounting; individual's experience on a given audit; the public accounting firm's experience in auditing the firm; and the public accounting firm's experience in auditing the type of industry. Training was also selected for examination and was evaluated solely on the basis of the presence or absence of a formal company training program. The remaining unexamined factors (mental effort; knowledge, skill, and judgment; and attitude toward time reduc- tion) were not examined as these are especially difficult for an out- sider to measure. These factors can and should be examined by public accounting managers to ascertain whether these three powerful forces are being developed in and evaluated in audit personnel. Partial correlation and regression analysis was applied to determine the degree of time reduction associated with each of the four different types of experience. The same procedure was followed for training and time reduction. Of the five organizational factors lised in Chapter V (continu- Ous production vs interrupted work assignments; short tasks at well separated intervals; the need for advance planning; scheduling improve- merit; and effective use of manpower), two factors (advance planning and! effective use of manpower) were selected for examination. These weree selected on the same basis used in the selection Of individual factzors, i.e., data availability and objective measurability. One "1983 ure of the need for advance plannipg was the degree of change in 76 scope and/or in problems encountered in the audit. Two measures of effective use of manpower were examined and these were the number of employees of the public accounting firm and the number of men assigned to the audit. It was felt that the size Of staff may reflect on the number of levels through which an audit must proceed for checking be- fore final completion and thus reflect on time requirements. Advance planning could at least partially reduce the changes in scope of an audit. It is true that all changes in scope may not be anticipated (and thus minimized in their effect on audit time) but possibly some may be anticipated. Measuring the number Of employees in the public accounting firm was felt meaningful since it may reflect the amount of experience which may be drawn upon in unusual situations, and the number of management levels (assuming the larger the firm, the more levels) which must be involved with the audit. It was an attempt to measure the productivity of small vs large firms. The number of men assigned to the audit was construed as a measure similar to that Of direct labor in a manufacturing situation. Through the selection of the two measures of number of men Of men in the firm and number assigned to the audit, a rough measure of the relation Of direct labor and indirect labor could be Obtained. The remaining two organizational factors (continuous production vs interrupted work assignments and short tasks at well separated intervals) were not examined due to lack of available data. Scheduling improvement was not examined as a separate factor but it may be included under the results of effective use of manpower analysis. The factors and their specific aspects which were examined in the study are: 77 Individual Factors Specific Aspect of the Factor Which Is Examined Experience Training 1. Auditor's years of experience in public accounting 2. Auditor's years of experience on this audit in study period 3. Firm's years of experience on this audit 4. Firm's years of experience on client's industry 5. Presence or absence of formal company training program Opganizational Factors Advance planning 6. Audit stability 7 Effective use of manpower . Number of employees in the public accounting firm 8. Number of auditors assigned to the audit The attempt at correlation analysis by factor was a very pro- ductive area of the study and the other four phases were applied mainly to supplement the factor examination and to learn more of general in- fluences on audit time. Limitations of the empirical study The some phases 1. limitations, which forced a contraction in the scOpe of Of this study, were summarized in Chapter I as: The availability of data in prOper form for in depth analysis As to detailed audit function time requirements As to large number of consecutive years of audits of same client firm As to audits on a first, second, and third year basis where the first year represented a new audit The lack of suitable Objective measures of certain factors which may well correlate with time reduction, such as: Turnover of client personnel Degree of pre-audit preparation by client personnel Adequacy of pre-audit conference with client Ability of client firm personnel Condition of records of client firm In some cases, underlying causes of change in audit scope 78 g. Presence of uninterrupted audit time during client's audit h. Other factors not lending themselves to objective measurement by an outsider Most of these limitations would not exist if a study were per- formed by public accounting firm officials who, by their access to detailed and current data, would have an advantage over an outsider making such a study. The limitations centered around the lack of availability of data for in depth analysis and lack Of suitable objec- tive measures of certain factors which may correlate with time reduc— tion. Data availability presented a problem in that some data from the third year of a sequence of audits was still in process at the time of this investigation. To pursue earlier years' audits and thus have a three year sequence caused problems associated with non-current data, such as recalling the experience in public accounting of departed firm members, the scope change from year to year, etc. Also, non- current data caused difficulties in itemizing information on continu— ous production vs interrupted work runs. In addition, a shortage of first year audits of new clients prevented a deep examination Of the rapid time reduction which might be expected in years two and three, due to overcoming some organizational factors (advance planning in particular) associated with new audits. Either a more extensive sample size or a public accounting firm member concentrating on a study of audits over several years may locate more new audits. Lack of suitable Objective measures presented a problem in that it is difficult to place an Objective value on degree of mental effort, on knowledge, skill, and judgment, and on the auditor's 79 attitude toward time reduction. Therefore, individual and organizational factors underlying time reduction which could not be examined were: degree of mental effort; knowledge, skill, and judgment; continuous production vs inter- rupted work assignments; short tasks at well separated intervals; and attitude of the auditor toward time reduction. These all seemed worthy Of examination, but either lack of data or of an objective measuring device nullified evaluation of these factors. Most Of these could possibly be evaluated by members of the public accounting firm. For identical reasons, other elements, advanced by practi- tioners as important in promoting audit time reduction, could not be examined. These factors were: turnover of client personnel; degree of pre-audit preparation by client personnel; adequacy of pre-audit preparation by client personnel; ability of client firm personnel; condition Of records of client firm; and, in some cases, underlying causes of change in audit scope. It is felt that all of these factors would lend themselves quite well to evaluation by a member of the public accounting firm. A further limitation of the study lay in detailed audit func- tion examination. Often records were not maintained in sufficient detail to observe time required per audit function, such as cash, accounts receivable, etc. Often, only audit time per man per day was recorded and not the time spent on each function. Thus, sample size had to be severely restricted in this area. This limitation cannot be overcome until all firms maintain detailed records of time spent on individual audit functions. The final limitation which is related to all the other 80 limitations is the confidential nature of public accounting records. This slowed the study somewhat and consumed an inordinate amount of the public accountant's time. The names of client firms were not and could not be revealed, thus placing some of the data gathering duties upon the public accountant. Furthermore, a potentially productive area of research, that of time worked and not billed to the client, could not be examined. Again, as with so many of the limitations cited above, these problems could be overcome by a public accounting firm member assigned the task of time reduction research. Eventually then, a practical time control system could emerge as developed by the Certified Public Accounting firms. CHAPTER VII RESULTS OF THE STUDY OF TIME REDUCTION IN PUBLIC ACCOUNTING FIRMS An empirical analysis of time reduction by public accounting firms An empirical analysis of time reduction was made in order to explore the nature of time reduction by Certified Public Accounting firms, and to attempt to determine whether any patterns or correlations of time reduction useful in controlling audit time existed. One hun- dred and two audits, conducted by fourteen public accounting firms over a two or three year period for eight client industry groups, were reviewed. One audit, considered to be non-typical because of unusual client growth, was excluded from the study, making a total of one hundred and one audits examined in the non-statistical section of the study. Twelve audits from the one regional firm were excluded from the statistical portion due to incomplete data. Thus, eighty-nine audits were evaluated statistically for a two-year audit sequence and, of these, sixty-five were also examined over a three-year sequence. The empirical study was composed of five phases: 1. Data accumulation and time reduction analysis by type Of client industry (retailing, manufacturing, etc.) 2. Data accumulation and time reduction curve preparation for national, regional, and local C.P.A. firms. 3. Analysis of time reduction by individual C.P.A. firm. 4. Analysis of time reduction by detailed audit function (cash, accounts receivable, etc.) 81 82 5. Regression and correlation analysis for eight time reduction related factors present on audits. The data accumulation for the first four phases of time reduc— tion (by client industry, by type of C.P.A. firm, by individual firm, and by detailed audit function) is supplemental to the statistical analysis in the latter part of this chapter. These phases represent an attempt to probe the nature of time reduction in a non-statistical sense, seeking apparent associations of time reduction with type of client industry, type of C.P.A. firm, individual firm, and detailed audit functions. Thus, it is a preliminary investigation which cul— minates in an examination of specific factors relating to time reduc- tion. SO little research has been done in the area of time reduction in non-industrial situations that it was felt that both a broad and a specific statistical approach were needed. Analyeis of time reduction by type of client industpy Time reduction was analyzed in relation to the type of client industry: retail firms; miscellaneous firms; non-profit associations; schools and colleges; cities, villages, and townships; churches, hos- pitals, and country clubs; manufacturers; and banks and savings and loan associations. Table 6 on the following page portrays time reduc— tion by industry and indicates total overall time reduction on all audits Observed. For year two, time reduction was slightly in excess of 2.7% and for year three, the reduction was 4.6%. This calculation indicates that, on the average, the audits performed in the second year required 2.7% less time than in the first year and 4.6% less time in the third year than in the second year. 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I ..-__NN_--N_pN_NNNN--m. 1,200 ”11 N.‘.7-u_-.~11._11_ 19000 _" "° -> . -..ic.--‘ __ 800~——-- --—N+—MN~N 600-—-“-—~- 400“ 1 20 4 1 2 3 4 :5 6 7 8 9 410 Years 1 Firms 12 Audits 7 - 3 Year Audits (———9 2225 Time 1 1195 2 1135 3 983 5 - 2 Year Audits (-~J X235 Time 1833 2 2362 98 FIGURE 14 TIME REDUCTION — ALL LOCAL FIRMS Hours 10,000 9,000 77777777} 8,000 7,000 6,000 5,000 4,000 1M¢ 3,000 2,000 1,000 1 2 3 4. .5 6 7 8 9 10 Years 9 Firms 61 Audits 43 - 3 Year Audits (——-9 Year Time 1 9686 2 9803 3 9325 18 - 2 Year Audits (*rr) Year Time 3200 2 3084 99 Analysis of time reduction by type of C.P.A. firm Recapping the data from Table 7, the following comparison is made of time reduction by national, regional, and local C.P.A. firms: TABLE 8 COMPARISON OF TIME REDUCTION BY TYPE OF C.P.A. FIRM 3 Year Audits 2 Year Audits % Time % Time CPA Firms NO. of Reduc. (Incr) No. of Reduc. Total Type - NO. Audits Year 2 Year 3 Audits Year 2 Audits National 4 22 6.4 3.1 6 29 .0 28 Regional 1 7 5 .0 13.4 5 28.0 12 Local _9__ i; (1.2) 4.9 _1_8_ 3.6 61 Totals 14 72 29 101 (Does not include unusual audit by national firm which lowers percent- age to .02 for Year 2 and .003 for Year 3.) This schedule must be interpreted with some care. The percent- aages are calculated on varying size bases, for a different number of audits Of dissimilar size by public accounting firms of unlike size. Iflae hours spent on audits by national and local firms are similar, as fréflale 7 shows hours for national firms as: Year 1, 12,752; Year 2, 12 ,096; Year 3, 11,085 and hours for local firms as: Year 1, 12,886; lfeezir 2, 12,887; Year 3, 9,325. If the unusual audit by one national firm is deleted, the national firm has slightly fewer total hours each Year than the local firm. (National Year 1, 11,037; Year 2, 10,000; and Year 3, 8,671 hours.) However, some conclusions on relative per- formance of the three types of C.P.A. firms can be derived from this comparison. On three year audits the rate of time reduction for 100 national firms is declining. The one regional firm appeared to have great time improvement in the third year audits, although this firm had two audits in which time was greatly reduced in the third year while time reduction performance on other audits was not outstanding. The sampling process may have been weak at this point as a representative sample was requested and control over audits available for submission was difficult. The local firms indicate the greatest rate of improve- ment in their time reduction performance. TABLE 9 IMPROVEMENT RATIOS IN AUDIT HOURS BY TYPE OF C.P.A. FIRM 3 Year Audits Improvement Year 2 Year 3 Ratio Reduction % Reduction % Year 3/Year 2 National 6.4 3.1 —48% (Incr) Regional 5.0 13.4 268% Local (1.2)(Incr) 4.9 508%* *Mathematically, this calculation cannot be made since a positive fig- ure divided by a negative figure must produce a negative figure. In a non-mathematical sense, the calculation may be made in that the local firms went from an increase in time to a reduction in time. A trend appears in the above analysis even though so many vari- ables are involved that judgment of causes of this behavior becomes Complex. It may be that the national firms have a lower B factor or earlyyear time reduction potential and this could be part of the cause of? the behavior. If a firm has a high degree of experience and compe— tence, the early years of an audit are performed at a low time require— lmetnt and further improvement decreases over the years. Conversely, less ex13erienced firms may markedly improve a time requirement which was 101 initially high. Comparison of time reduction performance Of the three types Of C.P.A. firms may also be analyzed on the basis of number and percentage of audits showing time improvement. This method equalizes the compari- son by minimizing the advantage of the regional firm with its two large time reductions in the third year as indicated in the following tables: TABLE 10 PERCENTAGE OF AUDITS WITH REDUCED TIME Year 2 - All Audits Time Time NO Reduction % of Total No. Reduced Increased or Increase Audits with of Audits Audits Audits Audits Reduced Time National 29 21 8 73% Regional 12 5 6 l 42% Local 61 31_ 23_ __ 60% Totals 102 63 38 1 Year 3 - All Audits National 23 14 8 1 60% Regional 7 2 4 l 30% Local fig_ 22_ ll. .1 60% Totals 73 41 29 3 Based on the table above, national and local firms did equally well in year three on the percentage of number of audits with reduced time. Each reduced time on 60% of all audits. Apparently local firms were able to exceed national firms in time reduction on a total per- centage Of hours basis (as in Table 8) because national firms had five audits on which year three time increase was over 20% of year two hours. Audit stability again emerges as a factor in the comparison of 102 national and local firm time performances. Unstable audits may be cancelling some of the gains accrued on stable audits thereby reducing the overall time reduction on the total of national firm audits. A comparison of stability ratings of national versus local firm audits is presented in the following table. TABLE 11 AUDIT STABILITY RATINGS BY TYPE OF C.P.A. FIRM Year 2 Category Category Category Category Category 5 4 3 2 1 Total % of % of % of % of % of Audits Audits Audits Audits Audits Audits National 29 7.0% 0% 76.0% 10.3% 13.7% Local 61 4.9% 11.5% 72.1% 3.3% 8.2% Total 90 Year 3 National 23 7.4% 15.8% 55.6% 18.5% 3.7% Local _4; 18.7% 11.8% 65.1% 2.2% 2.2% Total 66 Stability Categories: Substantially fewer problems and/or reduced amount of work Mild reduction in problems and/or required amount of work Substantially the same as in prior years Mild increase in problems and/or required amount of work Substantially increased problems and/or increased amount of work. U‘J-‘UDNH Combining both years in Table 11, it appears that the local firms had a higher percentage of audits in both Category 4 (Mild in- crease in problems and/or required amount of work) and Category 5 (Substantially increased problems and/or increased amount of work). 103 For years two and three, local firms indicated 11.5% and 11.8% in Category 4 while national firms rated 0% and 15.8%. Thus, locals had a higher percentage of unstable audits than did national firms, while nationals had a much greater percentage of audits in the two categories of reduced work on successive audits. Therefore, it appears that sta- bility may not be the main factor promoting time reduction differences between national and local firms as stability favors greater national time reduction in year three and this greater reduction did not occur. In order to focus attention on the degree of repetition of auditors on successive audit assignments as a factor promoting time reduction, the following comparison is presented. TABLE 12 PERCENTAGE OF AUDIT TIME BY AUDITORS REPEATING ON SUCCESSIVE AUDITS Year 2 Audits by Audits by National Firms Local Firms Total 1 — 20% Repeat Hours 5 9 14 20 - 40% " " 7 4 11 40 - 60% " " 6 12 18 60 - 80% " " 4 11 15 80 - 100% " " __6 25 §_1_ 28 61 89 Year 3 1 - 20% Repeat Hours 6 1 7 20 - 402 " " 5 2 7 40 - 60% " " 7 0 7 60 - 802 " " 2 11 13 80 - 100% " 7 " -_2 }2_ ‘31 22 43 65 104 As the preceding table indicates, local firms appear to exhibit more repetition of auditors on successive audits than national firms. In year two, local firms showed 48 audits, or 80% of total audits, with repetition rates of 40% or more, i.e., 40% or more of the audit staff repeated from the prior year's audit. In year two, national firms had 16 audits with a 40% or above rate of repetition, which repre- sented 57% of all audits observed. In year three, local firms indi- cated 38 audits, or 90% of total audits, conducted by staff of which 40% or more were repeating from the prior year while national firms indicated 13 audits, or 54% of total audits, were repeated by 40% or more of the audit staff. Since the comparison in Table 7 shows that local firms increased their performance in year three, the higher rate of repetition by local firms reinforces the time reduction theory that repetition is a factor promoting time reduction. Analysis of time reduction by individual C.P.A. firm Time reduction curves for the individual public accounting firms cooperating in this study are graphically portrayed in Figures 15 through 28 on the following pages. Hours 105 FIGURE 15 TIME REDUCTION - NATIONAL FIRM l 10,000. V I 9,000 8,000 7,000 6,000 5,000 4,ooo,r________-_.fi Year Time F--__i 1 3,857 3,000 2 3,504 3 3,292 2,000 1,0001 2 3 z. 5 6 78 910 Years FIGURE 16 Hours TIME REDUCTION - NATIONAL FIRM 2 10,000 , 3 ' 9,000 8,000 7,000 6,000 —~ 'fi 5,000 4,000‘ Year Time 1 5,131 3,000“‘ 2 5,326 3 5,339 2,000 1,000 1 2 3 a. 5 6 7 8 9 10 Years Year Year 1 2 Time 2,729 2,481 2,454 Time 789 635 Hours 10,000 9,000 8,000 7,000 6,000 5,000 4,000 3,000 2,000 1,000 Hours 1,000 900 800' 700 600 500 400 300 200 100 106 FIGURE 17 TIME REDUCTION — NATIONAL FIRM 3 ——_1|-—-—— “p- . i i l 2 3 10 FIGURE 18 TIME REDUCTION - NATIONAL FIRM 4 9 10 Years N r. »-‘---——-‘-~ -'-——1r-.~—:w . .,3 ‘- w _ H J. —r3—-—- firs—1‘1"*/i -w . ~— 5 6 7 8 5110 Years 107 FIGURE 19 TIME REDUCTION - REGIONAL FIRM Hours 5,000 4,500 4,000 3,500 3,000 I 2,500‘ '”*” Year Time 2,000w——" 1 1,195 2 1,135 1,500 3 983 1,000 500 1 2 3 4 5 6 7 8 9 10 Years Year Time 1 1,312 2 1,524 3 1,310 Year Time 1 756 2 699 Hours 108 FIGURE 20 TIME REDUCTION - LOCAL FIRM 1 10,000 9,000 8,000 7,000 6,000 ' 5,000 4,000 3,000 2,000 1,000 1 Hours 1,000 900 800 700 600 500 400 300 200 100 1 A 2 3 4 FIGURE 21 TIME REDUCTION — LOCAL FIRM 2 5 6 7 E3 9 10 Years 4 5 6 7 8 ‘9 10 Years 109 FIGURE 22 TIME REDUCTION - LOCAL FIRM 3 Hours 1,000 r 900[ 800 700 600 500 Year Time 400 1 210 3 260 200‘“ / 100 l 2 3 4 5 6 7' 8 FIGURE 23 Hours TIME REDUCTION - LOCAL FIRM 4 10,000 9 10 Years 9,000 ._._.. .-_....-_.....--. _- “-31-- 8,000 7,000 6,000 5,000 Year Time 4’000 1 1,019 2 1,524 3,000 3 1,098 2,000 1,000 l 2 3 4 5 6 7 E3 9 10 Years Year Time 1 1,002 2 898 3 1,022 Year Time 1 1,217 2 910 3 676 Hours 5,000 4,500 4,000 3,500 3,000 2,500 2,000 110 FIGURE 24 TIME REDUCTION — LOCAL FIRM 5 1,500 1,000!L\/ ' 500 Hours 5,00 2 3 4 5 6 7' 8 910 FIGURE 25 TIME REDUCTION - LOCAL FIRM 6 Years 4,500 4,00 3,507 3,00 2,500 2,00 1,50 1,00 50 1 2 3 4 5 6 7 8 910 Years Year Time 1 1,667 2 1,507 3 1,497 Year Time 1 1,498 2 1,575 3 1,872 111 FIGURE 26 Hours TIME REDUCTION - LOCAL FIRM 7 10,000 9,00 8,00 7,00 6,00 5,0 4,00 I 1,00 ? 2 3 4 5 6 7 235710 FIGURE 27 Years Hours TIME REDUCTION — LOCAL FIRM 8 10,00 9. 8,0 7,0 1 2 3 4 5 6 7 8 9 10 Years Year Time 1 1,761 2 1,671 3 1,590 Hours 10,000 112 FIGURE 28 TIME REDUCTION - LOCAL FIRM 9 ————-__.. - --. 7 A 9,000 8,000 7,000 6,000 5,000 4,000 3,000 2,000 1,000 1 ._-_....-JL_- ,_____T___ .1 ,..- 113 In isolating the reasons for the wide variations in observed time reduction, it appears that time reduction is affected by the type of client being audited. The examination of time reduction by type of industry indicated different rates of time reduction for the various industries, so perhaps the reason for varying time reduction lies in different mixes of client firms. The possibility exists, however, that reduction by client industry may be due to some quality within those particular audit firms who performed the audit rather than being a phenomenon of the audit or client firm. While the variations in time reduction by individual C.P.A. firms are subjected to multiple regression analysis later in this chapter, the variations due to client mix may also be compared in the following manner. In Table 13, the client industries are listed in order of percentage time reduction by industry as based on data from page 86 and they are assigned weights from one through eight so that the highest weights present among audits of a given C.P.A. firm should be conducive to the greatest time reduction. This is due to these C.P.A. firms having a favorable mix of clients from industries which are quite stable. 114 TABLE 13 AUDIT TIME REDUCTION BY TYPE OF CLIENT INDUSTRY Total Observed Rank of Industry Time Observed Time Reduction % Reduction Industry Weight Decrease (Increase) 1 Miscellaneous Firms 8 51.3% 2 Banks, Savings & Loan Assns. 7 41.5% 3 Cities, Villages, Townships 6 27.0% 4 Manufacturing 5 18.7% 5 Schools and Colleges 4 9.3% 6 Retailing 3 7.6% 7 Non-Profit Assns. 2 (22.0%) 8 Churches, Hospitals, Country Clubs 1 (50.2%) Applying these weights to the client industry mix of national firms results in the calculations below. % reduction (increase) is the reduction in hours divided by the prior year's time in hours. No. of Time Reduction Firm 1 Audits Points Miscellaneous 3 x 8 = 24 Manufacturing 3 x 5 = 15 Schools etc. 1 x 4 — 4 Retailing g_ x 3 = .21 9 70 Average time reduction points per audit = 7.7 Time Year 1 -- 3857 Time Year 2 -- 3504 Reduction: 353 % Reduction: 9.1% Time Year 3 -- 3292 Reduction: 212 % Reduction: 6.0% No. of Time Reduction Firm 2 Audits Points Miscellaneous 1 x 8 = 8 Banks etc. 1 x 7 = 7 Manuf ac turing __§ x 5 = _4_Q 10 55 Average time reduction points per audit = 5.5 Time Year 1 -- 5131 Time Year 2 -- 5326 Reduction: (195) % Reduction: (3.8%) Time Year 3 -- 5339 Reduction: (13) % Reduction: ( .2%) 115 TABLE 13~~Continued No. of Firm 3 Audits Miscellaneous 3 Manufacturing .1 4 Average time reduction points per audit Time Year 1 -- 789 Time Year 2 -— 635 Reduction: Time Reduction Points x 8 = 24 x 5 = ._5 29 = 9.8 154 % Reduction: 25% No. of Time Reduction Firm 4 Audits Points Banks etc 1 x 7 = Manufacturing 3 x 5 = 15 Churches etc. .1 x 1 = '_l 5 23 Average time reduction points per audit = 4.6 Time Year 1 -- 2290 Time Year 2 -- 2219 Reduction: 71 % Reduction: 3.1% Time Year 3 -- 2454 Reduction: (235) 2 Reduction: (10.6%) The above data produces the following correlation analysis: Total Audit Average Average Time Reduction % Time Reduction % Time Reduction Firm Year 2 Year 3 Total Total/2 Points 1 10.4% 6.4% 16.8% 8.4 7.7 2 3.8 .002% 3.8 1.9 5.5 3 25.0% 25.0% 25.0 9.8 4 3.1% (10.6%) (7.5%) (3.75) 4.6 Among the four national firms there appears to be a good rela— tionship between time reduction and the type of client industry being audited. The more time reduction points indicating the presence of a favorable client mix, the more time reduction occurred. Applying the same type of analysis to local firms produces Tables 14 and 15. 116 ANN.NHV ANGNV NN.mH m.N NN HH mHmuoH Hquv NG.N .m: .m mans< 086» m Hess 8H osN qu OHN s n N x m .mcmm< uHNoum-coz Ns.N N.N NN N muHe=< 088» N mm mm." 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O I /////// +57. — xt +10% ”‘ ‘ +15% 30% 40% 50% 60% 70% 80% % New Men ° = Year 2 x = Year 3 ———-= Year 2 Trend (4 Firms) (3 Firms) ' = Year 3 Trend 133 FIGURE 32 RELATION OF NEW MEN TO TIME REDUCTION (Local Firms) % Time Reduction (—) or Increase (+) -15% \ —10% ‘ -5Z ‘\\‘\N\3 X. +52 \ Ali 0 L. . +10% 1 I 1 if ,\ t +15% \ 12% 18% 24% 30% 36% 42% 48% Z New . _ Men - Year 2 x = Year 3 -——-= Year 2 Trend (9 Firms) (8 Firms) Year 3 Trend 134 was confirmed in the correlation and regression analyses in the year 1 to year 2 study. Although stability has been assumed to be contained within the audit itself, it may also be controllable, to an extent, by the C.P.A. firm, and thus it is a complex factor to appraise. Perhaps this is the explanation for the earlier observation that national C.P.A. firms seemed to have more stable audits than local firms. This fact, would, of course, affect potential for time reduction. The probability of repetition promoting time reduction accurately was the same for that of stability, 99.9% accurate or having a .l% possibility of error. The correlation coefficient of repetition of -0.432337 was less than that of stability (-0.604080) as noted in Table 20. Thus, a time reduction pat— tern does seem to exist with repetition and the basic time reduction curve may prove applicable to public accounting. Summarizing the year one to year two analysis, it would seem that two separate forces are Operating to reduce audit time; the B factor and slope of the time reduction curve. The B factor would in~ clude the variables of Training, Stability, Years of Experience, Year 1, and Hours by Men, Year 2. The slope would result from repetition. The B factor would relate, then, to the basic ability of the firm to reduce time, irrespective of knowledge gained of the specific client's operation. Repetition would relate to improvement from knowledge of the specific client Operation. Regression and correlation analysis - Year 2 — Year 3 The analysis of year two to year three time reduction included data from 65 audits. In addition to the eight basic factors examined in the year one to year two study, the following five additional factors 135 or variables were included: hours by men repeating on the audit for the third year; hours by mean repeating in the last year from the prior year of a three year audit sequence; men repeating in year three after a one year lapse; number of men on the audit, year three; and years of experience of men on the audit, year three. Key figures developed from this analysis of audits from year two to year three are presented below: Multiple R2 = 0.6074 Standard Deviation = 51.5876 Multiple R = 0.7794 Degrees of Freedom = 13 _ (For Hypothesis) F value 6°0705 Degrees of Freedom = 51 (For Error) Probability level = Less than .0001 The average hours per audit were 288.6 in year 2 and 276.9 in year 3, and the average hours time reduction per audit was 11.7 hours. Thus the overall time reduction rate from year 2 to year 3 was 4.05%. The coefficient of determination of 0.6074 represents an explan- ation of almost 61% Of the time reduction due to the variables present. This is a higher degree of explained time reduction compared to that of the year 1 to year 2 series. Possibly this is due to more repetition being allowed to develOp, with some men repeating on audits for the third consecutive year. This possibility, and the effect of less stability in year 3 will be considered in more depth later in the analysis. At any rate, an explanation of nearly 61% of the time reduc— tion as being associated with the selected variables and at a prob— ability level of .0001 was felt to be a meaningful correlation of all variables with time reduction, year 3. Stepwise regression analysis, chi—squares, and probability levels for the variables are presented in the following table: 136 TABLE 21 YEAR 2 - YEAR 3 CHI-SQUARE VALUES AND PROBABILITY LEVELS Chi-square Probability Variable Value Level Repeat Hours, Year 3 13.4837 0.0003 Stability, Year 3 9.2997 0.0023 Hours by Men, New Year 3 10.0841 0.0015 Years Experience, Year 2 2.6706 0.1023 Years Experience, Year 3 6.3211 0.0120 Firm Experience 0.0111 0.9163 Industrial Experience 0.6183 0.4317 Men, Year 2 0.0470 0.8283 Men, Year 3 0.0001 0.9910 Size 2.8284 0.0927 Training 4.8416 0.0278 Hours by Men in Year 3 Repeat from Year 1 2.8069 0.0939 Hours by Men in Year 3 Repeat from Year 2 2.1278 0.1447 The first three variables were significant in predicting time reduction, repeating the pattern from years 1 to 2. For the first two variables, Repeat Hours, Year 3, and Stability, Year 3, there is an ability to predict time reduction at the .003 and .0023 confidence levels. This predictive ability must be due to an actual correlation between observed time reduction and presence of the variables rather than time reduction being due to other unmeasured variables. Hours by Men, New Year 3 was a slightly better predictor of time reduction than was Stability, predicting time reduction at the .0015 confidence level. Correlation coefficients were computed for each of the vari— ables and the time reduction from year 2 to year 3. These results are presented in Table 22. Repeat Hours, Years 1, 2, and 3 was the only variable significantly correlated with time reduction, having 137 oz NNN. Naoaoo.o- NoHoHaaN .NH oz NNN. NNNNNH.o aNHN .NH oz NNN. NNoNNo.o N aaaN oaz .HH oz NNN. NNNNNN.o N aaaw oaz .NH oz NNN. ooaNNo.o aooaHaaoxN HaHaaaaooH .N oz NNN. OHNNoo.o- aooaHaaoxN aaHN .N oz NNN. oNaoNo.o N aaaN .aooaHaaoxN aaaaN .N oz NNN. HNoaHH.o N aaaN .aooaaaaoxm aaoa» .N oz NNN. NoaNNH.on N aaaw NaHHHHaaN .N oz NNN. NNNNNH.ou N aaa» 3az oaz No aaaoN .3 oz NNN. 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Several possible applications of time reduction curves are suggested and in— clude the following: 1. Evaluation of the "trade-off" between balanced experience and time reduction potential. Discussion includes re- examination of the B factor, combined consideration of SIOpe and B factor, graphical portrayal of trade-off, hypothetical analysis in hours and in cost terms, and limitations of a hypothetical approach. 2. Determination of year one audit time 3. Determination of years needed to reduce audit time 4. Evaluation of cost of changes in audits Evaluation of the "trade—off" between balanced experience and time reduction potential Consistent with the principles of the time reduction curve, it appears that a "trade-off" is possible between a minimum time on first year audits and rapid time reduction on subsequent years' audits. In time reduction curve analysis, the basic ability to perform on a new product, model, etc. is known as the "B" factor. On page 58 it was 142 143 noted that some eventual minimal time to complete a job depends on the time required to produce the first unit (B factor) and the rate of improvement (slope of the curve). The more ability and experience individuals have with similar jobs, the less time will be required for the first performance on a new job. Accordingly, with a low first unit time, less improvement will be possible on successive units as repetition will not bring great time reduction. Conversely, an in- experienced group may require more time to complete the first unit but will effect more time reduction in repeating the task over several time periods. Thus, the public accountant may possibly make a trade-off of experienced men for inexperienced men on the first year of an audit, thereby incurring a minimum audit time for the first year and less time reduction in successive years. Since the B factor is a useful concept for industry in esti- mating time reduction, it could have the same use for public account- ing. For example, in World War 11 aircraft procurement, the govern- ment recognized varying B factors for aircraft manufacturers who pos- essed differing degrees of production experience and competence. Both the government and the manufacturers, knowing the first unit time (B factor) and time reduction potential (slope or degree of learning), could quite accurately predict time requirements over the months or years of a government contract. As the more experienced aircraft firms require less time on the first production run of new aircraft, so the more experienced public accounting firms may require less time on a first year's audit than the less experienced may require. Nicholas Baloff has commented on this variability of B factors from firm to firm and from product to product.76 Furthermore, public accountants 144 might also utilize the B factor and thus have a powerful tool not only for forecasting annual audit time budgets but also for setting fees, for manpower scheduling, etc. Indeed, the B factor itself could be measured by public accounting firms in order to examine its improvement or deterioration, as such knowledge would be useful in overall time reduction. Undoubtedly, their findings would corroborate the Boeing Company's studies which stated: "In other words, the '8 factor' is a mathematical value which shows the skill level of a certain company's organization. How much is the experience of the Green Company worth?"77 Lastly, and particularly applicable to public accounting, are the other specific B factor determinants proposed by Yezdi Bhada in his discus- sion of pre-product planning: "The better the pre-product planning.... the labor time for the first completed unit is likely to be lower than without such extra care."78 Bhada seems almost to be making particular "...Also proper plan- reference to public accounting when he states: ning at the initial stage lessens the scope for improvement during the course of production which results in a flatter function, lying considerably below one which depicts a smaller amount of pre-produc- tion planning."79 Attention focused on the 8 factor in this study as a result of conversations with the public accounting firms in which the desire to develop rapid competence and varied experience was stressed. It appeared that the firms were attempting to develop the B factor by a policy of rapid rotation of personnel on audits. Such rotation was more prevalent in national CPA firms than in the smaller local firms largely because in the national firms the auditors themselves sought rotation in order to have more challenging assignments. The policies 145 followed in assigning auditors may range from a completely new audit team each year to a repetition of all auditors from the prior year engagement. The advantages of a completely new team may lie in the rapid training, flexibility, and challenge presented to the auditor. The disadvantage would be primarily the sacrifice of maximum second, third, and subsequent years' audit time reduction. This reduction would be based on the acquisition of general organizational familiarity with the client. The advantages of repetition of the entire staff from the prior year's audit would lie in the development of organiza- tional familiarity leading to time reduction, in developing client confidence and harmony with the public accounting firm staff, and possibly in a more coordinated team effort by the audit group. The disadvantages of this approach could be the loss of rapid training, flexibility, and challenge for the individual auditors, and also pure boredom from a repetitive task. This boredom could lead either to the plateau of no further time reduction or to possible time increase as incentive for reduction is not created. To exploit the maximum possible advantages of these two ex— treme positions of complete rotation as opposed to complete repetition of staff on an audit, some intermediate assignment policy should be considered. Such a policy was followed by some firms who reassigned some auditors to the same audit but in more responsible positions than in prior years. This policy seems to offer two advantages. There is some continuity on the audit so that knowledge of client procedures, personnel, and a host of organizational factors are handled smoothly. The client does not feel that he is providing a training ground for new auditors. Thus, it would appear that there is a median point 146 between nearly complete rotation and nearly complete repetition. Efforts should be made to determine the approximate degree of repeti— tion and rotation most conducive to time reduction, auditor satisfac- tion, and client satisfaction. To determine the cost of a company policy of rotation versus the cost of great repetition in audits, a mathematical approach could be attempted. A mathematical approach has some weakness due to the difficulty of quantifying such audit assignment goals as client and auditor satisfaction, and a competent and versatile staff capable of handling new and unusual situations. However, if some basic quantification were accomplished, a decision of rotation versus repetition, or an intermediate position between the two extremes, can be made with those non—mathematical variables considered as a last step in the analysis. This is a method long practiced in most business decisions. Quantification will help focus attention on other non-measurable factors. Any analysis undertaken to determine the costs of a trade—off between rotation and repetition should determine B factor changes and subsequent years' time changes. Any loss of potential time reduction of a subsequent audit by not incurring normal time reduction with repetition should be made up in a general gain of the B factor. That is, the rotation policy must result in an enhanced ability to perform first year audits in a minimum amount of audit time. For example, a firm embarking on a policy of rotation after years of allowing substan- tial repetition on audits should observe increased ability to perform new audits rapdily. This improvement must compensate for the decreased time reduction on subsequent years of a client's audit through not having sufficient repetition of the audit force. Graphically the 147 trade-off can be described in the following manner: FIGURE 33 TRADE-OFF IN AUDIT TIME REDUCTION EXPERIENCED vs INEXPERIENCED Total AUDITORS Audit Time X1 2 I Ix N9 Y \ 2 ___—’ 0* - \JY Y3 4 N9-.- _ Y NTY Q - xsys LH.___ 1 2 3 4 5 Years of Audit The trade-off is represented by the vertical distance between curve Xl-XS, audit time for inexperienced men, and Yl—YS, audit time for experienced men. The smaller yearly time reductions by the expe- rienced men are represented by the areas YlO Y2, YZO Y3, Y3O Y4, and 4 5 O Y . The larger time reduction for the inexperienced men is in the areas X1 0 X2, X2 0 X3, X3 0 X4, and X4 0 XE. A minimum time on Y the first year's audit must compensate for the more rapid reduction obtained by inexperienced men. These two alternative policies are described in the following plans. 148 Plan A: Average ability accountants repeating on the same audit. First year time is high with rapid time reduction occurring in successive years. "Learning" or time reduction is due both to individual and organizational causes. Plan B: More competent accountants assigned to responsible audit positions quickly and rotated frequently. First year time is low because of auditor efficiency. "Learning" or time reduction is difficult to describe because of rotation, sometimes annually, but the minimum time on the first year must come from the basic skill of the auditor, an individual cause. Plan B at all points takes less time but time and pay for each type of auditor must be factored in to derive total job cost. Gain in the B factor should insure minimum initial time on new audits as well as the ability to deal with unusual situations more efficiently. The preceding analysis portrays verbally and graphically the tieed for and a method for determining the costs and benefits of a trade-off between the rapid rotation and repetitive policies of auditor assignment. The problem may also be approached in a mathematical con- text. For example, a determination of the time reduction rate needed by experienced men to attain, in a given period, the time per audit attained by inexperienced men may be made by using the following two formulas. The formula for unit time is: y = ax Where y = total time per unit (or per audit) initial time to perform first unit (or audit) number of units (or number of year's audit) = rate of time reduction per unit (or per audit) The rate assumes a negative sign when dealing with time reduction. a X m 149 If the letter I is used to represent time per audit for in- experienced men, then their audit time formula may be stated as: m . . . I = ax (I is substituted for Y, or total time per audit) Similarly, the letter E may be used to represent total time per audit for experienced men, resulting in the following formula: E = alx1 m1 (E is substituted for Y, or total time per audit) To calculate the time reduction rate needed by experienced men, the following assumptions are made: time for the first unit for inexperienced men, 1200 hours; time for experienced men, 1000 hours, and that the term units denotes completed audits. The slope of the curve or rate of learning for experienced men is assumed to be less than the rate of learning for inexperienced men (m1 is less than m). The given period of time, or x, is four years, assuming that in four years the two groups will have identical audit time. Since x equals years of audits performed, and since on the fourth year, time of both groups is identical, at four years: x = x1 = 4 (Number of years of audits by each group of men is identical) Since audit time for the fourth year is identical for both groups of men: I = E Also, since over the four year audit period, both groups attain the same audit time in the fourth year, the slope needed by the experienced group to attain the same audit time in four years as that attained by the inexperienced group is the observed slope for an 80% time reduction curve of the inexperienced group compared to that 150 needed by the experienced group: -.322 1200 x = 1,000 xlml The slope equation may be solved as: 1200(4)“322 = 1,000(4)m1 Log 1200(-.322)(Log 4) Log 1,000 + m Log 4 1 3.0792 (—.322)(0.6021) 3.0000 + m1 (0.6021) .6021m 3.0792 - 3.0000 + (—.322 x 0.6021) 1 .6021m1 = .0792 + (-.322 x .6021) .6021ml = -.ll47 m1 = -.ll47 .6021 m1 = -.190 Thus the slope of the time reduction curve needed for the ex- perienced men in order to equal in four years the time of the inex- perienced men is —.190. This will represent an 87.66% time reduction curve as calculated below. Applying this rate of time reduction or slope to determine the time required by the experienced men, the following result is obtained: -.1 _ Log y = (1,000) + (2 90) Log y = (1,000) + (3 '190) = Log 1,000 + (-.190) Log 2 = Log 1,000 + (.190) Log 3 Log y = Log 1,000 -.190 Log 2 Log y = Log 1,000 —.190 Log 3 3,000 -.l90 x .30103 3,000 -.l90 x .4771 3,000 -.057l957 3,000 -.090649 2.9428 (rounding)(in logs) 2.909351 or 2.90935 876.6 (antilog of 2.9428 812 (antilog of 2.90935 and the second and the third year audit time) year audit time) 15] Applying the same slope to the fourth year would produce 768.4 hours as the time requirement for that year. Calculations would be: Log y = (1,000) + (4—°190) = Log 1,000 + (-.190) Log 4 Log y = Log 1,000 -.190 Log 4 = 3,000 -.l90 x .6021 = 3,000 - .11444 = 2.88556 = 768.4 (antilog of 2.88556 and fourth year audit time) A comparison of the times of the two groups, experienced and inexperienced, yields the following results: TABLE 24 HOURS REQUIRED BY EXPERIENCED AND INEXPERIENCED MEN Experienced Men Inexperienced Men 87.6% Time Reduction Curve 80.0% Time Reduction Curve (Years) Hours required (Years) Hours required Units ‘_per Unit(audit) Units per Unit(audit) 1 1,000.0 1 1,200 2 876.6 2 960 3 812.0 3 842.5 4 768.4 4 768 To express the above two time reduction potentials in a per- centage basis one would follow time reduction curve theory which states that between doubled quantities, a given percentage time reduc- tion will apply. For the inexperienced men, as audit years were doubled, second year's time was 80% of first year's time, and at four 152 years time was 80% of the time needed in the second year. The slope of the inexperienced men is thus an 80% slope, 960/1,200 and 768/960. The slope for the experienced men is 87.66%, derived as 876.6/1,000 and 768.4/876.6. (For the third year values, Appendix D presents calculations for inexperienced men and calculations for experienced men are ShOWD on page 150—151-) Thus, the experienced men need an 87.66% slope to equal the same time per unit in four years which the inexperi- enced men will achieve in four years. If the relative cost of the work force of inexperienced men were compared with that of experienced men, costs of learning can be put on a measurable basis as the comparison in Table 25, given some mix of personnel at various salary levels and performing the same audit for four years, shows. The following graph sums up on log-log paper the results of the two possible time reduction patterns by experienced and inexperi- enced personnel. 153 FIGURE 34 TIME REDUCTION CURVES FOR EXPERIENCED AND INI‘IXI’ERH‘ZNCED MEN Hours 1200- I N" x 80% Curve ‘ 1000* x a x 900‘ 87.66% Curve ‘\ ‘ 800d 7001 600‘ 500‘ 400‘ 300‘ 200. 100 . J 1 1 In the curves above, plotted on log-log paper, the upper or 80% curve represents the time reduction behavior for ineXper— ienced men and the lower or 87.66% curve portrays the time reduction achieved by experienced men. 154 The preceding analysis, however, is not meaningful until the data is converted into cost terms as the following hypothetical ex— ample illustrates. The relative cost of audits by a group of experi- enced auditors is compared to that of a group of less experienced auditors. It may be assumed that the experienced group of auditors would require 1,000 hours for the first year's audit and have an 87.66% time reduction curve and that the inexperienced group would require 1,200 hours for the first year's audit and have an 80% time improvement curve. Thus the difference in time reduction curve slopes would be consistent with the theory that initial time requirements for an experienced group and the degree of time improvement should be less than for an inexperienced group. The assumed composition of the two audit teams and the salary rates per hour are indicated as follows: Experienced Audit Teamg(87.66% Time Reduction Assumed) % of Total Audit Rank or Salary Hourly Hours Assigned Classification Rate 20% Juniors $5.00 40% Semi-seniors 7.00 40% Seniors 10.00 Inexperienced Audit Team (80% Time Reduction Assumed) % of Total Audit Rank or Salary Hourly Hours Assigned Classification Rate 60% Juniors $5.00 20% Semi—seniors 7.00 20% Seniors 10.00 155 TABLE 25 COMPARISON OF HOURS AND COST - INEXPERIENCED vs EXPERIENCED AUDITORS Hours rgquired Audit labor cost Accumu- Total lated Labor Labor Year Junior Semi Senior Total Juniors Semi Seniors Cost Cost 1 200 400 400 1,000 $1,000 $2,800 $ 4,000 $ 7,800 $ 7,800 2 175 351 351 877 875 2,457 3,510 6,842 14,642 3 160 318 318 796 800 2,226 3,180 6,206 20,848 4 154 307 307 768 770 2,149 3,070 5,989 26,837 689 1,376 1,376 3,441 $3,440 $9,632 $13,760 $26,837 Audit team 1 above: Experienced men; 1,000 hours initial time requirement, 87.66% time reduction curve. Hours required Year Junior Semi Senior Total Juniors Audit labor cost Semi Accumuh Total lated Labor Labor Seniors Cost Cost 1 720 240 240 1,200 $ 3,600 $1,680 $2,400 $ 7,680 $ 7,680 2 576 192 192 960 2,880 1,344 1,920 6,144 13,824 3 506 168 168 842 2,530 1,176 1,680 5,386 19,210 4 460 154 154 768 2,300 1,078 1,540 4,918 24,128 2,262 754 754 3,770_§11,310 $5,278 $7,540 $24,128 Audit team 2 above: Inexperienced men, 1,200 hours initial time requirement, 80% time reduction curve. Difference: Experienced Inexperienced men Inex. over Exp. Total Total Total Total Total Total Year Hours Cost Year Hours Cost Year Hours Cost 1 1,000 $ 7,800 1 1,200 $ 7,680 1 200 ($120) 2 877 6,842 2 960 6,144 2 83 ( 698) 3 796 6,206 3 842 5,386 3 46 ( 815) 4 768 5,989 4 768 4,918 4 0 (1,071) 3,441 §2§,837 3,770 $24,128 329 ($2,704) The above is a recapitulation of the respective costs of experienced as opposed to inexperienced men. :l“ ..flt— -7 4 156 The preceding example serves to point out that a computational solution to the problem of trade—off evaluation is possible, that rela— tive costs may be and should be measured to determine the fiscal suc- cess or shortcomings of a rotation policy. There are some qualifica- tions regarding this evaluation, however. The cost reduction is based on a given mix of accountants at various experience levels and at given pay levels. If either the mix of accountants or the various pay scales is changed, then the outcome of the cost comparison is changed. The results of this example tend to favor the use of inexperienced men as total cost was less over the years. However, this cost conclusion must be rigorously qualified since cost reduction is not the only criteria of audit effectiveness. Other considerations, such as improvement of client's accounting procedures, client retention, etc. may be as im- portant or even more important than cost reductions. Through the use of the foregoing computational approach, attention may be focused on ways to measure achievement of this one criteria of audit effective- ness. Through the use of mathematics and linear programming, it should be possible to set up a formula which would provide data on cost reduction possibilities with various mixes of experience and pay scales. Developing such formulas would require thorough knowledge of individual firm member productivity which may be difficult for the public accounting firm to determine. It implies that a junior accountant should be expected to perform a given job in a certain amount of time, a semi-senior in a certain amount of time (assumed to be a lesser time), etc. A problem arises in that a senior accountant would normally handle different audit areas than a junior so that some 157 minimum acceptable mix to allow for needed expertise and experience must be maintained. Beyond this minimum acceptable mix, there should be a possibility for varying the composition of the audit force to allow for special knowledge, skills, etc. to meet the particular de- mands of a given audit. Determination of year one audit time Using the B factor concept, the public accounting firm should be able to determine more accurately the time required for a first year audit. In the aircraft industry, government auditors discovered the B factor, or time required for the first job, and so should a pub- lic accounting firm be able to discover the B factor on an audit. If some aircraft firms, in contacting with the government for airplane production, were expected to have a lower first unit time than other firms, this was evidence of knowledge of B factor by firms. The pub- lic accounting firm, possessing similar knowledge, should be able to reliably estimate first year audit time. To determine the first year audit time the public accounting firm might use one of several methods such as: 1. Taking average time for first years of similar audits. 2. Totaling average time for all component parts of an audit. For example, totaling the average or standard time for accounts receivable, plus the average time for inventory observation, etc. Allowance would have to be made for size of audit, etc. 3. Comparing the time required by another public accounting firm for a prior audit and projecting it back to what 158 the first year's time would be. If method (3) were to be used, selection of the last year's audit time by the successor firm might be appropriate for several rea— sons. Rates charged by the public accounting firm taking over the audit probably cannot deviate greatly from those charged by the prior firm. Often last audit time is more readily available and more rele- vant to current conditions in the client firm than earlier years' audit data. Finally, the last year's audit time may be a present or future target sought by the successor firm. Thus, for the purpose of developing expected first year time, the formula a = ifi-described below will be useful. Time will be projected backward through the use of this formula, i.e., if the prior audit firm had performed the audit for enough years for the majority of time reduction to occur, the successor firm could estimate first year time as follows: (First year time) a = y (Time,prior audit firm required in last year (Successor's slope of time reduction curve) xm(Successor's normal time to reach a minimum time) It is quite probable that the first year time calculations as suggested in methods (1) and (3) will not agree with the time calcu- lated in method (2). Method (2) would represent total audit time de- rived by adding the total standard times of the various audit functions based on normal time reduction occurring after several years. Methods (1) and (3) project time back to year one and include all of the factors causing year one to have high time requirements. These factors would include gaining familiarity with the client firm organization, records, personnel, etc., and such organizational factors as scheduling improvements, advance planning, etc. It is this aspect of auditing 159 which must be isolated in order to determine the added time and cost required for new audits, much of which results from unfamiliarity with the new client. A similar area of considerable interest would be a comparison of first year time by a successor firm with first year time by the prior audit firm. Any observed time difference could re- flect differences in the public accounting firm organization, but it could also reflect changes in client, in audit scope, etc. Eventually the public accounting firm should find that the two main divisions of audit time may be determined as: l. The period required to become familiar with the client firm, or time required for organizational time improve- ments to occur, which seems at least partly related to the B factor. 2. The period required to reduce individual task time requirements, or the time needed for individual learning or time improvement to occur, which seems a function of the x factor (years of experience). Thus, the B factor, or time required for the first audit unit, seems to represent the element of familiarization with a new client firm. The speed of familiarization and time reduction in this divi— sion of audit time may depend upon: 1. The unique nature of the client firm, capability of its personnel, condition of records, etc. 2. The audit firm's experience with the type of firm and industry being audited. 3. The skill and experience of the accountants assigned to the audit. 160 4. The organization of the CPA firm. 5. The pre-audit preparation of the client firm. Determination of the required first year audit time, based on current time data of a prior audit firm, can be accomplished for a succeeding audit firm through the use of the unit time formula y = axm. This calculation may be illustrated in the following hypothetical ex- ample for which these assumptions are made: a public accounting firm with an 80% time reduction rate normally occurring over a four year period engages a new client; the new client's prior public accounting firm had audited the client for a five year period which is its inter- val required for normal time reduction to occur, and finally, that the most recent audit required 640 hours. The calculation would be made as follows: Formulas: Applying the formula: y = axm Let xm = R R = xIn Log R = log xm a =‘y_ xIn Log R = -.322 (.60206) R = -.l9306 Data: R = antilog (-.19306) x = 4 (Years) R = .0641 y = 640 (Present Hours) m = -.322 Then: a = y or a = 640 = 1,000 xm 0.641 hours The first year audit by the successor firm would require approximately 1,000 hours. Some clarification of the assumptions made in the foregoing I?! 161 example are in order. The time reduction pattern of the prior public accounting firm is not known nor need it be for this analysis. Where- as the prior firm reduced time to 640 hours in five years, the suc- ceeding audit firm contemplates four years only to accomplish this task. It is merely important to assume that the majority of time reduction has occurred for the prior audit firm. Questions may be raised when first year time derived in this manner appears to diverge from first year times developed by the other methods. It may be that the prior audit firm had vastly different competence than the succes- sor firm. In this case, an estimate of first year hours would have to be adjusted to coincide more closely with the estimates based on method (1). Data of a prior audit firm's billings may not always be avail— able to the successor firm; however, in some instances, it may be ob- tained when governmental unit or school audit cost is reflected in published or readily available financial reports. A second applica— tion of the above procedure would be in determination of first year time which could be allowed for a particular audit. A public account— ing firm might have a general idea of the number of hours which could be devoted to the audit yearly over a period of time based on staff size, growth policies of the firm, etc. If the firm could handle the audit at 640 hours yearly over the long term, it would be essential to know the first year time in view of current time pressures and current staff available. The formula above would be useful in this context. 162 Determination of,years needed to reduce audit time A determination of the number of years required to reduce audit time to some normal, minimum, or long range time requirement may be useful. This determination can be made through a further applica- tion of time reduction curve analysis based on a prior firm's experi— ence. A public accounting firm may need to know, given the first year time required on an audit, how quickly they can reduce time to some normal, minimum, or long term average time figure in order to promote long range planning needs in the context of staff time require- ments, available personnel, etc. Or, if an audit were taken over from an experienced firm, i.e., one which had performed the audit for several years, the successor firm might wish to know the number of years required to reduce their time to the prior firm's minimum time figure. Again, the assumption is that after several years, signif— icant time reductions will no longer occur. The following hypothetical illustration of this application assumes that the desired audit time is 1,000 hours, after expected time reduction has occurred. It is also assumed that the first year time requirement is 1,500 hours with an 80% time reduction curve. Formulas: Applying the formulas: y = axm Log 1,000 = log (1,500 x"322) -.323 Log y = log (axm) Log 1,000 = log 1,500 + log(x ) L 1 + 1 < m Log 1,000 = log 1,500 + (-.322 log x) °g y ' °g a 0g x ) Log 1,000 - log 1,500 = -.322 log x Log y _ log a = m log x 3 - 3.1761 = -.322 log x - _ .322 log x = 3 - 3.1761 m log x — log y log a l - 3 _ 3 1761 log x = log y - log a 0g x - _ 3&2 m . = _ x = antilog .547 x antilog(lo§_1,000 log a) x = 3.52 years 163 Thus, in 3.52 years, audit time can be reduced to 1,000 hours, given the time improvement rate and the initial time requirement. This implies that less than 1,000 hours will be required in the fourth year. To check the accuracy of the foregoing calculation and to illustrate the mathematical application of the time reduction curve, year by year time reduction should proceed as follows: Year Time rquired Time calculations 1 1,500 hours Given m * —m ax or y = ax (1,500)(2-.322) _ 322 Log 1,500 + log(2 ' ) Log 1,500 + (-.322) log 2 Log 1,500 -.322 log 2 3.1761 - (.322 x .3010) 3.1761 - .0969 antilog of 3.0792 1,200 hours 2 1,200 hours ‘<‘<‘< ll Log Log y Log K‘<'~< 3 1,052.5 hours y (1.500) (3"322) .322 Log Log 1,500 + log(3- ) Log 1,500 + {-.322) log 3 Log 1,500 -.322 log 3 = 3.1761 - (.322 x .4771) y = 3.1761 - .1536 y = antilog of 3.0225 y = 1,052.5 hours ‘4 “ll Log y Log 3.52 1,000 hours Y = (1.500) (3-52-.322) 322 Log y = Log 1,500 + log(3.52_' ) Log 1,500 + (-.322) log 3.52 Log y Log 1,500 -.322 log 3.52 = 3.1761 - (.322 x .5453) Log y = 3.1761 - .1756 y = antilog of 3.005 ,y = 1,000 hours *The formula y = axm is the formula for a straight line. If the m in the formula is positive, a positive sloping (upward sloping from the origin or y axis intercept) will result. If the m is nega- tive, the line is negatively sloping or downward from the point of origin. Since time reduction curves imply less time on subsequent units than on the initial unit, the line is downward sloping and the sign preceding m must be negative. Evaluation of the cost of changes in audit content or 164 client firm induced audit extensions accounting firm in evaluating the cost of changes in audit scope. Time reduction curve analysis may also prove useful to the public When a client firm merges with another firm, makes any significant change in product line, has turnover of key personnel, converts its accounting system to electronic data processing, etc., an interruption of the normal time reduction process results. This interruption has been observed in industry with a change in tooling, design, specifications, etc. and the time reduction curve then "toes up" or develops "scallops." the effect appears as: Graphically, Effect of Changes in Audit Content on Audit Hours Time per unit(hours) or per audit 1201 100 80- 60' 10 slope. basic change in the item being produced. vertical distance from W to V. .U A .\\ \ V. \\\\C m\‘B‘\ “z “\O ‘.£ *1 1 1 I Curve A Original Time Requirements Time per Units Unit 1 100 2 80 3 70 4 64 Curve B Time Requirements After Change Time per Units Unit 2 100 3 80 4 70 Curve A represents the original time reduction curve with an 80% Curve B represents a time reduction curve after tooling or other The toeing up or scallop is the The time in the second year returned to the same level as achieved in the first year (100 hours per unit.) The result of the change is to cause the time reduction curve to start at the 165 beginning, as though no prior experience had occurred. The cause of the increased time seems rooted in a need for refamiliarization with the new process. When audit content changes markedly, or when the audit is extend— ed, a toeing up or scallop effect in audit time may result. There is no assurance that time will return to the time required in a prior audit. Time could well exceed the time required on a prior audit. Thus, a move— ment to point U on the foregoing graph could occur. In an industrial situation, a change in any of the factors affecting speed of familiarization with the product manufacturing process can be quite serious. A movement to curve C on the graph would cause the anticipated minimum time or cost per unit (y in the y = axm formula) to be either postponed to a later unit in process, or possibly cause the firm never to achieve this minimum cost. The government, in contracting for production, is aware of the time reduction behavior in the con— tracted firm, and it is normal process for the government to pay for the added cost caused by the increase in unit time. Public accountants should also be reimbursed for any added time caused by audit content of extension changes. Conceptually, the added fee over the years should be based on the area V W X Y, if the second year audit required the same time as the first year. The total hours contained in this area multiplied by the average charging rate per hour would be the additional fee needed. (This assumes that fees were allowed to drop as time was reduced. In this case, after a change in audit content, fees would have to increase.) Movement in time requirements to a point such as U could cause the public accounting firm confusion in charging policy and also in scheduling manpower needs. When a time 166 reduction should occur, but in fact an increase in time occurs, there is actually a double loss to the firm. Normal time reduction from A to W should be contemplated if the audit is stable, and if all factors pro— moting time reduction are operative on the audit. Thus, the fact that audit time remains constant in year two is one loss, and the fact that audit time increased beyond the year one time is a second loss. Thus, the total additional fee needed over the years is the result of the hours contained in the area U W X Z multiplied by the average charging rate per hour. Cost control sheet embodying time improvement analysis A cost control sheet can serve many purposes for the CPA firm. It can serve as a basis for billing the client and for a comparison of actual versus budgeted time. It can also serve as an aid in determining the behavior of time expended when certain variables are present on the audit. These variables are the factors influencing time reduction, and so the cost control sheet should provide columns for all of the time reduction variables and a scale to rate the degree of presence or ab- sence of these variables on the audit. With more time reduction var- iables present, more time reduction is to be anticipated. Time records examined during this study presented a broad spec— trum of data accumulation from the very basic to the very detailed. Those embodying very basic data were insufficient for time control; those containing very detailed data were time consuming for auditors to compile during the audit. One firm's control sheet represented a good minimum standard for a cost control sheet and was not prohibitive in time required for its compilation. An abbreviated format of this sheet is 167 presented on the following page. The addition of a section for those factors promoting time reduction would increase its potential for time control. Data for two prior years of a firm's audit is presented in detail by audit function. Improvement or lack of improvement in total audit time as well as individual function time is thus made visible. When actual time for individual audit function departs from estimated time, it is possible to accumulate these deviations by function over a large number of audits and thus ability for time estimating could be improved. It should be evident that for functions of a more routine and repetitive nature actual and estimated time would be fairly similar. When actual and estimated time consistently do not agree, these func- tions would appear to be the more non—repetitive functions. Perhaps the most important advantage then of this time control sheet is its tendency to isolate the non-repetitive aspects of the audit, which should lead to an analysis of the causes of the non—repetitive aspects and possible ways of eliminating them in the future. Certainly not all non-repeti- tive aspects can be avoided but those which rest with the audit firm should be minimized wherever possible. The analysis form accompanying the time control sheet might serve as the means for analyzing the non-repetitive area developed from the sample time control sheet. The first step would be a separation of the variance in actual time over estimated time into two components: audit firm related time variances and client related time variances. The audit firm related variances should pertain to time which is absorbed and not charged to the client because of some fault in the firm's audit method. The client billed item would normally cover the client related time variances. Each type of variance would then be analyzed according 168 a MUOum w .Huc< N Ham .2 a oHooaaa .coo .dflHh .:ou .N>=H on muscuh JOJIPnV 169 .uue .vHo .moun mcHHsv Icon .NuHHHanHm>m uuouou ouosvouw .cOHumuoaooo ucoHHooxo pow mun:0Huwaunooo usuHHo mo oouwoo .oao: NH m oumuIImEOHnoum voumHoa uouaaaoo .vouHsvou econ HON m oumanumoHvsum HNHoonm .ouHumo m.ucoHHu um Hoc:0muon oHnmum new m euouumomamno Hocaomaom MEOHpoua Houucoo .ucH .0: new m monaanmomcmnu Hoaucou HmauoocH .ommouosH uwouw New H .oaoom _ noHHmam mo mama new m womanlomoom annm :H owcmzu _ ”:oHuwcmmem coHtatucccc maoHnoam uaaN:ctm momcmnu momamnu emoom m amow ucoHHo woumHom moHvaum Houu uHo3< w wo oouwon yousnaou HmHuoam Hocsomamm Iaou HmcuoucH :H wwcono_ vaccmwhm> mafia. “wumHmm ucwHHU .wcoo uHVDMIoua mp =0Huco>oua EoHpoan mo ooamov pow Aaooo H .usoHHmoxo my H cu m Eouu annaloouoHONcOO uHosm mam .HGOHuamo mHnu some: vmvaHucH on szou zuHHmsv wcHHovonomv Auoomv H Ou AkuHscou ammo AHon HMOHuoHo omHm .ouo .osHu peasanO .uHm .LoOu wchH>oua cH COHumaomoou ucoHHooxmv m souw mummllnl.vaooO Nwmum saHm H.ouo .moxmu .mqusm umnuo co xao: ou oEHu vouoanONGH >uo>v H cu HoEHu vauasuaouchav m scum mummluunlosHu sue: .uchu .vochuu mamanO Now u m\< coco .vochau hamnsoo mam quam :0 cos n No one Q NHlvochuu .00 cos we N Acme nun .axe .mpzxcoz mo .ozv .quam mqu co noon ou uswaoun OUCOHuomxo wcHucsooom UHHnaa muse» HouOuI||.uoaxe ansm Hooch .muao: uHuam Hmuou\mumoz soon no “mom H .wumom uoHua N cH no“ so voxuoa on: see me vwsa0muoa maaoznuuumaso: “momma mo N .anom w.amm» chu 0» aoHaa Ean chu mcHquom mama» aoHNa No awnEJCIllmqusm aoHaa mama» "coHumcmmem H H 1 L . L N a L H _ a a a _ 7 a , IF 1 (V H H L 1 7 _ 7 1 v , . l . 1 1. a l I. 1 a oocouowcou mumchuoou wEHH uHoo< nochau oucoHaomxo maso: ommnfi man34 N omnaomn< umHHHm flw HI qu5<|oum wwmum EaHm wouQDNHONCch .00 cos we N UHvsm Hooch lea No N aoHpm mummy, mocopowwHo maso: manomn awe» oOCMHam> mEHH nwumem EaHm_ wo :oHuHmoamHQ Hmsuod .umm_ muoosm Houuooo oEHH onamm vaqu3< EaHm Nomaaoou< 09 Snow meNHmc< um mmblo 170 to possible causes. While this judgment would be subjective, experi- ence should effect some degree of facility in estimating the causes of time variance. An important by-product of the analysis of audit time behavior would be the rigorous examination of the "anatomy of an audit." In the larger firms, there may emerge a need for an "audit time specia- list" similar to the methods department of an industrial firm. Use of a specialist in time reduction In larger public accounting firms, it might be advantageous to assign a man or a section of the firm to work exclusively on time reduction and time control on audits. This function is performed either formally or informally in national companies at present, however a spec- ialist might use such tools as the analysis form and time control sheet to analyze time variances more carefully. Only by pinpointing the cause of variances can these either be prevented when the fault lies with the public accounting firm, or charged to clients when they have caused the variance. Points may be assigned to the audit as suggested on the time analysis sheet and eventually a pattern of time reduction and points assigned established. Thus, the more points assigned to an audit, the more time reduction the firm should expect. A high point total would indicate the presence of factors required for maximum time reduction such as client cooperation, adequate pre-audit planning, prOper staff assign- ment, uninterrupted work time, etc. If many points were assigned to an audit, and the expected time reduction did not occur, the audit firm time reduction specialist could then seek out other factors related to time reduction which may have been omitted as causes of such reduction. 171 Finally, the points might be correlated with expected time re- duction as follows: 1. Variables deemed conducive to time reduction (or time increase)“10 variables. These would be established by combined staff judgment. 2. Maximum points assigned to all variables, 100 points, or 10 points for each variable. 3. Percentage of time reduction in particular year of an audit 20%. 4. Value of points as effecting time reduction: 20% expected reduction = .2% time reduction potential for 100 points assigned to each point present factors causing re— duction 5. If then, a total of only 30 points were present on an audit, the expected 6% time reduction would be determined as: 30 points of reduction factors present x .2% = 6% Summation Consistent with time reduction curve theory, time reduction in public accounting appears to depend on the B factor and on the slope of the curve. The organizational factors selected for examination are more associated with development of the B factor while the individual factors examined appear to relate to slope of the curve. The two factors most closely correlated with and predictive of time reduction, stability and repetition, appear to be, respectively, B factor and slope components. One factor, hours by new men, was examined as a secondary calculation to account for total hours spent on audits. This factor rated third among all factors examined in its time reduction correlation and predic— tive qualities and would seem to be properly related and included in the B factor. It represented, especially for national firms, an attempt to improve the C.P.A. firm competence to deal with unusual audit problems 172 by rotating men through a series of progressively more responsible posi- tions. Thus, the three most important factors bear out the significance of B factor and slope in reducing audit time. Several other aspects of time reduction curve theory may prove applicable to public accountants. Time reduction curve formulas may be useful for such purposes as estimating: the cost of the trade-off of balanced experience for B factor development vs repetition for slope improvement; the first year audit time; the years needed to reduce audit time; the years needed to reduce audit time; and the cost of audit scope changes. These may all be useful for particular needs but they are dependent on the maintenance of audit time records in proper detail. The eight basic factors examined, as well as the factor of hours by new men, appear to account for 52% of the time reduction in the second years audits and 61% in the third year audits on a total time basis. Obviously all time reduction has not been explained. Furthermore, on an inter-firm comparison in year three of local firms, the three most significant variables do not reliably predict time reduction. While this may be due in part to the small sample size (42 audits for local firms, year three). it is felt that there are other variables affecting time reduction which are not measured in this study. These factors were not evaluated due to limitations of data availability and due to difficulties of objective measurement as discussed in Chapter VI. These factors, as listed in the sample time control sheet and analysis form, could be incorporated into in-house studies where many of the limitations faced in this study would not be encountered. Finally, those difficulties of obtaining data, experienced in this study due to its ex post facto 173 nature, could be solved by the public accountant by advance planning prior to conducting such a study over successive years. In conclusion, it is hOped that this study may provide a "stepping stone" to future "in-house" studies of time reduction in public accounting. It was through such studies that modern industrial and clerical time control systems evolved. FOOTNOTES 1Winfred B. Hirschman, "Profit from the Learning Curve," Harvard Business Review, January—February, 1964, p. 139. Frank J. Andress, "The Learning Curve as a Production Tool." Harvard Business Review, January-February, 1954, p. 87. Ronald Brenneck, "The Learning Curve for Labor Hours for Pricing," N.A.A. Bulletin, June, 1958, p. 77. 4Delbert L. Brewer, "The Use of Graphs in Audit Reports," U.S. Army Audit Agency Bulletin, March, 1964, p. 55. 5Gordon W. Link and Don A. Ellis, The Experience Curve as Used by the Cost Accounting,Dgpartmen£, Boeing Aircraft Company, Boeing Air- Craft Company, 1945, p. 3. 6S. Alexander Billon, Industrial Time Reduction Curves as Tools for Forecasting, Unpublished Doctoral Dissertation, Michigan State Univer- sity, 1960. 7B. T. Sanders and E. E. Blystone, "The Progress Curve, and Aid to Decision Making," N.A.A. Bulletin, July, 1961, p. 82. 8Rolfe Wyer, "Learning Curve Helps Figure Profits, Control Costs," N.A.C.A. Bulletin, December, 1953, p. 490. 9Winfred B. Hirschman, op. cit., p. 128. 10Gordon W. Link and Don A. Ellis, op. cit., p. 2. 11Frank J. Andress, op. cit., p. 88. 12Carl Blair, "The Learning Curve Gets an Assist From the Computer," Management Review, August, 1968, p. 34. 13S. Alexander Billon, op. cit., p. 71-72. 14Raymond S. Jordan, Learning How to Use the Learning Curve, Material Management Institute, Boston: 1965, p. 1-12. 15Leonard W. Hein, The Quantitative Approach to Managerial Deci- sions, Englewood Cliffs, New Jersey: Prentice—Hall, 1967, p. 98. 16Raymond S. Jordan, op. cit., p. 2-2. 17Ibid., p. 2-2. 18Ibid., p. 2-1. 191bid., p. 2-4. 174 175 201bid., p. 2-8. 21Ibid., p. 2-8. 22Frank J. Andress, op. cit., p. 88. 23Wayne J. Morse, The Allocation of Production Costs with the Use of Learning Curves, Unpublished Doctoral Dissertation, Michigan State University, 1971, p. 15. 24Delbert L. Brewer, op. cit., p. 56. 5James A. Broadston, "Learning Curve Wage Incentives," Manage- ment Accounting, N.A.A., August, 1968, p. 16. 26Ibid., p. 17. 27Raymond S. Jordan, op. cit., p. 1-7. 28William F. Brown, Roy W. Smith, William C. Lansing, and Henry G. Horton, Improvement Curve, The Boeing Company, Seattle, washington, 1963, p. 17. 29Ronald Brenneck, op. cit., p. 71. 30Gordon W. Link and Don A. Ellis, op. cit., p. 3. 31Raymond S. Jordan, op. cit., p. 2-10. 32Ibid., p. 2-10. 33Frank J. Andress, op. cit., p. 89. 34Leonard W. Hein, op. cit., p. 107. 35Frank J. Andress, op. cit., p. 89. 36J. M. Blackburd, "The Acquisition of Skill, an Analysis of Learning Curves," Report No's. 67-73, Medical Research Council,,1ndustrial Health Research Board, London, 1936, p. 20-21. 37 S. Alexander Billon, op. cit., p. 23. 38Winfred B. Hirschman, op. cit., p. 128. 39Ibid., p. 129. 40Wayne J. Morse, op. cit., p. 9-10. 41Brown, Smith, Lansing, and Horton, op. cit., p. 60. 42Gordon W. Link and Don A. Ellis, op. cit. 176 3Brown, Smith, Lansing, and Horton, op. cit., p. 60. 44Miguel A. Reguero, "An Economic Study of the Military Airframe Industry," Department of the Air Force, wright-Patterson Air Force Base, Ohio, 1957, p. 213. 45William F. Wilkerson, "Application of Learning Curve Techniques to Audits," U.S. Army Audit Agengy Bulletin, June, 1964, p. 48. 46S. Alexander Billon, op. cit., p. 32. 471618., p. 193. 8Werner Hirsch, "Manufacturing Progress Function," Review of Economics and Statistics, Vol. 34, May, 1952, p. 143. 49Nicholas Baloff, "The Learning Curve--Some Controversial Issues," Journal of Industrial Economics, July, 1966, p. 279. 50Frank J. Andress, op. cit., p. 95-96. 51Rolfe wyer, as quoted in Readings in Cost Accounting, Budgeting, and Control, 3rd Ed., edited by William E. Thomas, Cincinnati, Ohio: South-Western Publishing Company, 1968, p. 630. 52Raymond 8. Jordan, op. cit., p. 1-1. 53Frank Powers, "Costs Strike Out With Learning Curve Incentive." Factory, October, 1961, p. 90. 541bid., p. 91. 55Ibid., p. 91. 56Ibid., p. 91. 57 H. J. Cohen, "Determining the Cost of Labor Turnover," Cost and Management, Canada, March, 1966. 58John Gawa, "Learning Curves and the Auditor," U.S. Army Audit Agency,Bulletin, March, 1964, p. 62. 59Wayne J. Morse, op. cit., p. 40. 60John Gawa, op. cit., p. 62. 61Raymond S. Jordan, op. cit., p. 2—11. 62Frank J. Andress, op. cit., p. 93. 63Maurice D. Kilbridge, "Predetermined Learning Curves for Clerical Operations," Journal of Industrial Engineering, Vol. 10, No. 3, May-June, 1959, p. 207. 177 64Frank Powers, op. cit., p. 90. 65 v H 9 ' ' William b. Boren, Some Applications of the Learning Curve to Government Contracts," N.A.A. Bulletin, October, 1964. 66S. Alexander Billon, op. cit., p. 30. 67Marvin L. Taylor, "The Learning Curve--A Basic Cost Projection Tool," N.A.A. Bulletin, February, 1961, p. 22. 68Winfred B. Hirschman, op. cit., p. 125. 69Winfred B. Hirschman, op. cit., p. 134. 7OIbid., p. 126. 71Frank J. Andress, op. cit., p. 95. 72Vincent J. Shroad, Jr., "Control of Labor Costs Through the Use of Learning Curves," N.A.A. Bulletin, October, 1964, Sec. 1, p. 17-18. 73Marvin L. Taylor, op. cit., p. 22. 74Maurice L. Taylor, op. cit., p. 22. 75Frank Powers, op. cit., p. 91. 76Nicholas Baloff, op. cit., p. 281. 77Brown, Smith, Lansing, and Horton, op. cit., p. 44. 78Yezdi K. Bhada, "Dynamic Cost Analysis," Management Accounting, N.A.A., July, 1970, p. 12. 79Ibid., p. 12. B IBL IOGRAPHY BIBLIOGRAPHY American Institute of Certified Public Accountants. Fee Determination, Costing, and Budgeting for Accounting_Firms, Management of Accounting Practice No. 15, New York, 1962 Andress, Frank J. "The Learning Curve as a Production Tool," Harvard Business Review, January-February, 1954. Baloff, Nicholas. "The Learning Curve--Some Controversial Issues," Journal of Industrial Economics, July, 1966. Bhada, Yezdi. "Dynamic Cost Analysis," Management Accounting, N.A.A., July, 1970. Bhada, Yezdi. Some Implications of the Experience Factor for Managerial Accounting, Unpublished Doctoral Dissertation, University of Florida, 1968. Billon, S. Alexander. Industrial Time Reduction Curves as Tools for Forecasting, Unpublished Doctoral Dissertation, Michigan State University, 1960. Blackburd, J. M. "The Acquisition of Skill, an Analysis of Learning Curves," Report No's. 67-73, Medical Research Council, Industrial Health Research Board, London, 1936. Blair, Carl. "The Learning Curve Gets an Assist from the Computer," Management Review, August, 1968. Blair, R. V. "Thurstone's Method of Studying the Learning Curve,” Paychological Review, 25.81, 1918. Boeing Company, The. Improvement Curves Tables with Stanford Exparience Curve, Industrial Relations Department, The Boeing Company, Seattle, Washington, 1962. Boren, William B. "Some Applications of the Learning Curve to Government Contracts," N.A.A. Bulletin, October, 1964. Brenneck, Ronald. "The Learning Curve for Labor Hours for Pricing," N.A.A. Bulletin, June, 1958. Brenneck, Ronald. "Breakeven Charts Reflecting Learning," N.A.A. Bulletin, January, 1959. Brenneck, Ronald. "Learning Curve Techniques for More Profitable Contracts," N.A.A. Bulletin, July, 1959. Brewer, Delbert L. "The Use of Graphs in Audit Reports,” U.S. Army Audit Agency Bulletin, March, 1964. Broadston, James A. "Learning Curve Wage Incentives," Management Account— ing, N.A.A., August, 1968. 178 179 Brown, William F., Smith, Roy W., Lansing, William C., and Horton, Henry G. Improvement Curve, Industrial Relations Division, The Boeing Company, Seattle, Washington, 1963. Broster, E. J. "The Learning Curve for Labor," Business Management, March, 1968. Cochrane, E. B. "New Concepts of Learning Curve," Journal of Industrial Engineering, Vol. 11, July-August, 1960. Cohen, H. J. "Determining the Cost of Labor Turnover," Cost and Manage- ment, Canada, March, 1966. Conway, R. W. and Schultz, A., Jr. "The Manufacturing Progress Function," Journal of Industrial Engineering, Vol. 10, January-February, 1959. Eisman, Doris. "The Progress Curve," Journal of Operations Research, January-February, 1959. Gawa, John. "The Learning Curve and Its Application to the Aircraft Industry," Journal of Industrial Economics, Vol. XIII, March, 1965. Gawa, John. ”Learning Curves and the Auditor, U.S. Army Audit Agency Bulletin, March, 1964. Hall, L. H. "Experience with Experience Curves for Aircraft Design Changes," N.A.A. Bulletin, December, 1957. Hein, Leonard W. The Quantitative Approach £9 Managerial Decisions, Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1967. Hirsch, Werner. "Manufacturing Progress Function," Review of Economics and Statistics, Vol. 34, May, 1952. Hirschman, Winfred B. "Profit from the Learning Curve," Harvard Business Review, January-February, 1964. Jordan, Raymond 8. "What's Your Progress Curve?" N.A.A. Bulletin, March, 1962. Jordan, Raymond S. "Learning How to Use the Learning Curve," N.A.A. Bulletin, January, 1958. Jordan, Raymond S. Learning How to Use the Learning Curve, Material Management Institute, Boston, 1965. Kilbridge, Maurice D. "Predetermined Learning Curves for Clerical Operations," Journal of Industrial Engineering, Vol. 10, No. 3, May—June, 1959. Koontz, Harold and O'Donnell, Cyril. Principles of Management, 4th Ed., New York: McGraw-Hill, Inc., 1968. 180 Link, Gordon W. and Ellis, Don A. "The Experience Curve as Used by the Cost Accounting Department, Boeing Aircraft Company, Boeing Aircraft Company, 1945. On file in the University of Washing- ton Library. Montgomery, Francis J. "Increased Productivity in the Construction of Liberty Vessels," Monthly Labor Review, November, 1943. Morse, Wayne J. The Allocation of Production Costs with the Use of Learninngurves, Unpublished Doctoral Dissertation, Michigan State University, 1971. Powers, Frank. "Costs Strike Out With Learning Curve Incentive," Factory, October, 1961. Reguero, Miguel A. "An Economic Study of the Military Airframe Industry," Department of the Air Force, Wright-Patterson Air Force Base, Ohio, 1957. Reimers, J. Morgan. "Cost of Production Evaluation through 'Level of Buoyance' Evaluations," N.A.A. Bulletin, September, 1965. Sanders, B. T. and Blystone, E. E. "The Progress Curve, an Aid to Decision Making," N.A.A. Bulletin, July, 1961. Shepard, A. M. and Lewis, D. "Prior Learning as a Factor in Shaping Per— formance Curves," Government Printing Office, Library of Congress Publication, No. 101487 (U.S. Navy Technical Report SCC 938-1-4). Shroad, Vincent J. Jr. "Control of Labor Costs Through the Use of Learning Curves," N.A.A. Bulletin, October, 1964 (Section 1). Siersma, J. N. "Learning Curve, Cost and Management, May, 1960. Smyth, R. C. "How to Figure Learning Time," Factory, Vol. 101, No. 3, March, 1943. Taylor, Marvin L. "The Learning Curve-—A Basic Cost Projection Tool," N.A.A. Bulletin, February, 1961. Thomas, William E. Readings in Cost Accounting, Budgeting, and Control, 3rd Ed., Cincinnati, Ohio: South-Western Publishing Company, 1968. Wilkerson, William F. "Application of Learning Curve Techniques to Audits," U.S. Army Audit Agency Bulletin, June, 1964. Wright, T. P. "Factors Affecting the Cost of Airplanes," Journal of Aeronautical Science, February, 1956. Wyer, Rolfe. "Learning Curve Helps Figure Profits, Control Costs," N.A.C.A. Bulletin, December, 1953. 181 Wyer, Rolfe. "Industrial Accounting With the Learning Curve," California CPA, February, 1956. Wyer, Rolfe. "Learning Curve Techniques for Direct Labor," N.A.A. Bulletin, July, 1958. Zieke, Robert Paul. Progress Curve Analysis in the Aerospace Industry, The Boeing Company, Seattle, Washington, June, 1962. APPENDICES From APPENDIX A Selected Comments on Time Reduction Study by Certified Public Accountants National Firms: From "No appreciable time reduction (on nine audits surveyed) but there is a shifting of work load to more junior members of the firm. The same economic advantage accrues to the firm as though a total time reduction took place." "There are too many variables affecting examinations from one year to the next to make regression analyses provide meaningful results." "It is unusual for an individual to repeat on such phases as bank reconciliations. In firms specializing by industry-as with hotels—there may be found the degree of repetition needed for the study. There may be some repetition by supervisors in charge of field work." "I know there is a definite improvement pattern but apparently no one has tried to measure it or to quantify it in any way." "The principal benefit accrues from the reduction of supervision time rather than the time devoted to the task itself. The reduc- tion in detail checking and rapid advancement of staff accountants would significantly reduce the situations from which to draw conclu- sions." "Study would be useful to practicing accountants but records may not be kept in sufficient detail to give data needed." "HOpefully, experienced men returning to the job will cause time reduction even though he may not serve in the same capacity." Local Firms: "There is too wide a range of competency of client personnel. Con— stant attempts are made for client preparation of detailed analysis and work schedules. There is a constant input of new members to audit engagements as men mature into supervisory positions." (Regarding differences in tax time required) "Complications arise in: Differences in personnel If the same person repeats (on the tax) his time should be im- proved. Varying information on the taxpayer from one year to the next Differences in methods, manual vs computer Differences in interview time required 182 \OCDNO‘U‘I-L‘WNH #1 Pl #4 P‘ P‘ k‘ H‘ 0‘ u: c~ on n: P‘ C) «L‘WNH APPENDIX B Detailed Listing of Comments by CPA Firms Regarding Proposed Time Reduction Analysis for CPA Firms Factors which will cause difficulty Firms Citing in the study this factor Variability of clients by size Variability of clients by type Changes in the type of client's business Changes in client's geographic area Changes in client's corporate structure Personnel turnover in client's office Changes in client's accounting procedures Changes in composition of the audit staff Varying degrees of experience of audit staff Lack of detailed records at CPA firms Confidential nature of the records Records will vary from client to client There is rapid avancement of staff accountants There is a reduction in detailed checking Manpower vs computer processing changes Lack of repetition of men on same tasks Factors which are favorable to the study It is known that there is a reduction in supervisory time Should be time reduction in specialized CPA firms There is certainly a pattern of reduction Indirect time reduction through shifting more work in second and third years to less experienced personnel Men do repeat on audits but not on same phases, should be time reduction through familiarity 183 P‘ H‘ P‘ P‘ n: P4 n: #4 #4 P4 n: h» h‘ P4 P‘ hi APPENDIX C Determination of Slope for an 80% Time Reduction Curve In the formula y = ax“, y is time required per unit after time reduction occurs, a is the initial time required per unit, x is the number of years, and m is the slope or degree of learning or time reduction. The 510pe, m, for an 80% time reduction curve may be calculated as: When x 100 II |'-" ‘< II x = 2, y = 80 x = 4, y = 64 log y = log a + log xm log y = log a + m log x (1) log 100 = log a + m log 1 (2) log 80 = log a + m log 2 Then, (1) log a = log 100 - m log 1 (2) log 80 = log 100 - m log 1 + m log 2 log 80 — log 100 = m log 2 - m log 1 m 10g 2 — m log 1 = log 80 - 10g 100 m (0.30103 - 0.00) = 1.9031 - 2.0000 .30103 m = .0969 m = -0969 .30103 m = -.322 The slope of -.322 may now be used in the formula y = axm to compute unit time requirements. 184 APPENDIX 1) Calculation of Yearly Time Requirements Assume year 1 requires 1,200 hours = a Assume slope or degree of learning is 80% = m (Appendix C shows m value of -.322 for an 80% slope) Assume year of the audit = x 322 m Then, y = ax and y = ax"' For year 1 1,200 hours given For year 2 = axm or y = ax-m ll ‘< y = 1200 (2'-322) log y log 1200 + log (2"322) log 1200 + (-.322) log 2 log y = log 1200 + (-.322 log 2) = 3.0792 + (—.322 x .3010) 3.0792 -.0969 antilog of 2.9823 960 hours log For year 3 = y = 1200 (3"322) log y = log 1200 + log (3"‘322) = log 1200 + (-.322) log 3 log y = log 1200 + {—.322 log 3) = 3.0792 + (—.322 x .4771) log y = 3.0792 - .1536 y = antilog of 2.9256 y = 842.5 hours For year 4: 768 hours by the same method as above ‘4 II 185 APPENDIX E-l FIGURE 38 RELATION OF FIRM EXPERIENCE AND TIME REDUCTION (Curved Lines Represent Decreases in Time Reduction) Trend Over the Years Z Time Reduction (-) or Increase (+) Year 1 - Year 2 -3z , 1» ' Y T i l -24“. \e r 9 ’ I . o\\\\\\\\ O 0 \C -16 \\x ‘ O , o\ ' ’ \ N 0 r '8T'""“ \ \‘ -‘ '\ o ._ \ I . O ' \. a ‘ , O o o A '\ t O I . ‘ . 4 \. +8 I \\\\ \\“~. x +16 ‘ 1 f I +24 ' +32 A ' 0 4 8 12 16 20 24+ Years 186 -32 -24 -16 +8 +16 +24 +32 APPENDIX E—2 FIGURE 39 RELATION OF CLIENT INDUSTRY EXPERIENCE AND TIME REDUCTION % Time Reduction (—) or Increase (+) Year 1 - Year 2 V— ‘f‘ . 'v “An 0‘} Al“ 187 16 20 24+ Years APPENDIX E-3 FIGURE 40 RELATION OF AUDIT SIZE AND TIME REDUCTION (All Audits Grouped as those Requiring 90 to 150, 150 to 210, etc.) Time Reduction Z 30?f‘ 1 It A?” I ; 257 202 ' 15% 10% l 1' . 5 Less 1 350 7 o 810 than 90 so 210 270 330 450 510 570 630 690 5 a. over Yr. 1 Hours 188 ER ”Tllfiififllfilflifllllfillijlfllfi\iflflfllflfiflilfifES