1~~wws.~r—v_-~ . v V , V V . t r z I '- l _ u ‘ . | I N , 7 THE ALLOCATION OF PRODUCTION COSTS ’ ”,3 WITH THE USE OF LEARNING CURVES ' Thesis for the Degree of ‘Ph. D. e; MICHIGAN STATE UNIVERSITY WAYNE JOHN MORSE 1971. I I III I II I III III III I III III I I I II III L 1293 100 2 This is to certify that the thesis entitled THE ALLOCATION OF PRODUCTION COSTS WITH THE USE OF LEARNING CURVES presented by WAYNE JOHN MORS E has been accepted towards fulfillment of the requirements for I H»? degree in Eccocwf’l " C" flak Major professor pm u‘i’cfi’WMY IE / We”) 0-169 s LIBRARY . ESMlChlgan State ‘ " University ‘ \ 5,? )y _ 3 Law wits}? .33 gig I m» Q“. a" + 13.x ‘ . I; 1' :3 -‘ {y. ”A... g: :8... . . W I IL (K M 0“ $3935 .. t _,,;-_“Ci} 5! 1,.1:~w-1"3"""‘ I - C LU§ T. 0 2 3993 *9 _ I I rm .- i " «'3; ’3’}! l ABSTRACT THE ALLOCATION OF PRODUCTION COSTS WITH THE USE OF LEARNING CURVES By Wayne John Morse For most firms in most industries the production costs of a product are higher when that product is first introduced than they are after that product has been produced fer a period of time. A graphic representation of the decrease in production costs as total production increases is referred to as a learning curve. This research was devoted to deve10ping a cost allocation model based on the learning curve phenomenon. Current accounting techniques of cost allocation take a segmented view of the production life cycle of a product and charge inventory or the cost of goods sold in each period on the basis of the actual pro- duction costs of that period. The result is a relatively low level of reported income in early periods when production costs are high and a relatively high level of reported income in later periods when production costs are lower. The learning curve (L-C) cost allocation model developed in this research takes the entire production life cycle of a product into con- sideration and attempts to reconcile the timing differences between this period and the normal accounting period. The effect of using the L-C cost allocation model is to decrease the early period production Wayne John Mbrse costs charged to inventory and the cost of goods sold from their current levels, thus raising reported income, and to increase the later period production costs charged to inventory and the cost of goods sold, thus lowering reported income. These changes in reported income are accomplished by adopting production cost standards based on the learning curve phenomenon and using a cost equalization account to insure that, as production takes place, charges to inventory and the cost of goods sold are equal to standard unit costs based on the average cost of all anticipated production. As long as actual production costs proceed in accordance with the learning curve phenomenon, the reported cost of each unit is the same. If actual production costs differ from these pro- jected by the learning curve, a period cost variance is recognized or the model is changed. The primary difference between the L-C cost allocation model and most other cost allocation models is that they are concerned with matching costs to units while the L-C cost allocation model is concerned with matching costs to production ventures. In the development of the model considerable attention was given to the accounting concepts of matching and materiality. The model was evaluated in the light of certain standards of materiality in order to determine the statistical properties of the underlying cost data re- qndlred before the model should be implemented for external reporting. Somme problems which can arise after the model has been implemented were conssidered.and suggested solutions to these problems were presented. Wayne John Morse Finally, the model was applied to an actual production venture and the income statements obtained from its use were compared with income statements deve10ped by the use of normal accounting procedures. It was concluded that the L-C cost allocation model could be a valuable tool in attempting to reconcile the differences between the accounting period and the production life cycle of a product. The L-C cost allocation model is able to allocate production costs over the entire production life cycle of a product while still retaining the accounting concepts of "cost" and "objectivity." The primary impediment to the adoption of the L-C cost allocation model appears to be a lack of detailed production information. However, once a decision has been made to adopt the model, the additional infor- mation could probably be generated with relatively little cost as a part of the normal accounting process. THE ALLOCATION OF PRODUCTION COSTS WITH THE USE OF LEARNING CURVES BY Wayne John Morse A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR.OF PHILOSOPHY Department of Accomting and Financial Administration 1971 ACKNOWLEIBBMBNTS While it would be impossible to acknowledge everyone who has assisted me in this research effort, the following individuals and organizations are singled out because of the significance of their contribution. Dr. James Don Edwards and the Department of Accounting and Financial Administration provided encouragement, financial assistance, and an atmosphere conducive to scholarly research throughout my Ph.D. program. The Earhart Foundation contributed to the rapid and successful completion of my dissertation by providing a fellowship which allowed me to devote my full energies to my research. Mr. Jack Kissinger and Mr. Gerald St. Amand, two of my fellow students at Michigan State, were especially helpful. Their generous help with granatical, mathematical, and computer problems is deeply appreciated. The members of my counittee, Doctors Arens, Simons, and Lemke (chairman) offered encouragement and helpful criticism. My wife, Linda, besides being called upon to decipher my writing and type all drafts of this dissertation managed to remain cheerful, sympathetic, and encouraging during a period of time when I desperately needed such qualities in my spouse. ii If, despite the help of others, any conceptual, mathematical, grammatical, or typing errors exist in the finished product I claim full responsibility for them. iii TABLE OF CONTENTS PAGE LISTOFTABLES............... ..... .. Vii LIST OF FIGURES . .................... ix Chapter I. THE LEARNING CURVE ................. 1 Introduction ................. 1 Theory of Learning mrves. . ......... 4 Early Research ................ 9 Previous Application . . . . . ........ 12 Basic Mathematics. . ............. 15 Limitations of Learning Curves ........ 22 II. LEARNING CURVES AND ACCOUNTING. . . ........ 26 Introduction ................. 26 Significance of L-C for Accounting Reports . . 29 Economic Value and Accounting Income ..... 33 Long-Term Prospective ............. 35 Industries Where L-C Has Greatest Application ................. 38 An Industrial Application. . . . ....... 40 Purpose and Methodology of Research ...... 42 III. THE LEARNING CURVE COST ALLOCATION mDEL ...... 45 The Model. . . . . ......... 45 Example of the L-C Cost Allocation Model . . . 51 Rate of Return Income Model. . . . . ..... 56 IV. MATHEMATICAL RELATIONSHIPS ............. 62 Introduction . . . . ........... 62 Materiality and Confidence Intervals . . . . . 65 Confidence Interval for Specified b Confidence Level .............. 69 Determining n for Desired Confidence Level and Interval. ............. 72 iv Chapter IV. MATHEMATICAL RELATIONSHIPS (can't). . . . . . . . . Relationship Between b and YN Confidence Intervals........... Relationship Between b and "i Confidence Intervals.............. Relationship Between b_ and T1 Confidence Intervals . . . . . . . . . . . . . . . . . . Minimmn R Required to Obtain Desired b Confidence Level and Interval . ....... Smary of Statistical Procedures. . . . . . . V. PROBLEIIB IN APPLICATION . . . . . . ........ Introduction................. StartupTermination.............. Increase in Production Costs ........ . Decrease in Production Costs . ........ ChangesinN............ ..... Essential Modifications .......... . . Conclusion...... ............ VI. APPLICATION.................... Introduction............ ..... TheData........ ......... Actual (Standard) Cost Model . . . . ..... L-C Model Applied to Total Cost Curve ..... L-C Model Applied to Labor Cost Curve ..... VII. CONCLUSION. ................ . . . . Summary. . . .............. Conclusions and Recommendations for Further Research. . . . . . . . ..... . . BIBLIOGRAPHY. . . . . .................. APPENDICES. O O O O O O O O O O O O O 0000000000 APPENDIX A: Programs Used to Implement the L-C Cost Allocation Model. . . . . . . . . . . . . . Al Determination of Parameters With Unit Cost Data . . . . . . A2 Determination of Parameters With Cumulative Average Cost Data . . . . . . . . . A3 Determination of Units Which Can Be Produced With Given Funds or Time . . . . PAGE 76 82 88 93 102 105 105 107 115 121 126 133 140 141 141 142 145 147 154 161 161 165 167 171 I71 172 175 178 APPENDICES PAGE APPENDIXA: (con't)................ A4 lbdel Projected Cost Data . . . . . . . . . 181 APPENDIX B: Programs Used for Statistical Analysis of L-C Cost Allocation Model . . . . . 184 Bl Confidence Interval for 2 Required to Obtain Confidence Intervals for Y . . . . 185 B2 Confidence Intervals for b Require to Obtain Confidence Intervals for U . . . . 187 B3 Confidence Intervals fer b Require to Obtain Confidence Intervals for T1 . . . . 189 B4 Minimum Value of R Required to Obtain Desired Confidence Level fer b_Confidence Interval O O O O O O O O O O O O O O O O O 191 APPENDIX C: Programs Used to Handle Special Problems in Applying the L-C Cost Allocation Model . . . . . . . . . . . 193 C1 Startup Termination . . . . . . ..... . 194 C2 Change in Production Costs ........ . 197 C3 Percent Change in N Required to Change YN by A Given Percentage ...... 200 C4 Essential Modifications . . . . . . . . . . 202 APPENDIX D: Relationship Between b_ Parameter and L-C FOTCOIIt. e e e e e e e e a e e e e 205 vi LIST OF TABLES PAGE l-l Ctmlative Average Production Times-$096 Learning m‘ 0 O O O O O I O O ...... O O O O O O O O 6 1-2 Loganithmic Transformation of A 90% Learning Curve . 17 1-3 Relationship Between Labor Inputs and L-C Percent. . 25 3-1 Present Value of Cash Flows Discounted At 10%. . . . 58 3-2 Computation of Present Value and Interest ...... 58 3-3 Present Value of G.L.U.B. Co. Cash Flows Discounted At 18 1/2*. I O O O O O ....... O O ..... 59 3-4 Computation of G.L.U.B. Company's Present Value and Interest. . . ................. 60 3-5 Rate of Return, L-C Cost, Standard Cost Incomes Compared ................ . ..... 61 4-1 Percent Confidence Interval for 1_3_ Required to Obtain A :I: 5% Interval for YN ........... 80 4-2 Percent Confidence Interval for b_ Required to Obtain A :t 10% Interval for YN ........... 81 4-3 Percent Confidence Interval for 2 Required to Obtain A :I: 596 Interval for U1 ........... 86 4-4 Percent Confidence Interval for 2 Required to Obtain A r 10% Interval for U1. . . . . . ..... 87 4-5 Percent Confidence Interval for 3 Required to Obtain A t 5% Interval for Ti ........... 91 4-6 Percent Confidence Interval for _b_ Required to Obtain A r 10% Interval for Ti ........... 92 4-7 Minimum R Required to Be 80% Confident that _b_ Has A Desired Confidence Interval . ........ 96 vii LIST OF TABLES (can't) PAGE 4-8 Minimum R Required to Be 90% Confident that _b_ Has A Desired Confidence Interval . . . ...... 98 4-9 Minimum R Required to Be 95% Confident that _b_ Has A Desired Confidence Interval . ........ 100 5-1 Percent Change in N Required to Change YN by 25% . . 128 5-2 Percent Change in N Required to Change YN by 110%. . 129 6-1 Data fer Application of L-C Cost Allocation Model. . 144 6-2 Comparison of Total, Labor, and Materials Cost Data. 154 D b_Values Corresponding to L-C Percents 51-100. . . . 207 viii 1-2 1-3 3-1 3-2 5-1 LIST OF FIGURES PAGE Cumulative Average Production Times--90% Learning Curve ................... 7 Logarmithmic Transformation of A 90% Learning Curve ................... 17 Unit Production Time--80% Learning Curve . ..... 23 Diagram of Flow of Costs . . . ........... 47 Cost Curves for Example Company ........... 49 StartupTermination................. 107 Elements of Composite Curve Caused by Essential Modifications . . . . . ......... . . . . . 133 CHAPTER I THE LEARNING CURVE INTRODUCTION: For most firms in most industries the production costs of a product are higher when that product is first introduced than they are after that product has been produced for a period of time. A graphical representation of the decrease in production costs as total production increases has been referred to as a learning curve. This research effort is devoted to developing a cost allocation model based on the learning curve phenomenon. Current accounting techniques of cost allocation take a seg- mented view of the production life cycle of a product and charge inventory or the cost of goods sold in each period on the basis of actual production costs of that period. A standard cost system usually charges the cost of goods sold with any excess of the actual costs of production over the steady state standard costs of produc- tion. The result is a relatively low level of reported income in early periods when production costs are high and a relatively high level of reported income in later periods when production costs are lower. A cost allocation model based on the learning curve phenomenon would take the entire production life cycle of a product into con- sideration and reconcile the timing differences between this period and the normal accounting period. The effect of using such a cost allocation model would be to decrease the early period production costs charged to inventory and the cost of goods sold from their current levels, thus raising reported income, and to increase the later period production costs charged to inventory and the cost of goods sold above their current levels, thus lowering reported income. These changes in reported income are accomplished by adapting pro- duction cost standards based on the learning curve phenomenon and using a cost equalization account to insure that, as production takes place, charges to inventory and the cost of goods sold are equal to standard unit costs based on the average cost of all anticipated production. As long as actual production costs proceed in accordance with the learning curve phenomenon, the reported cost of each unit is the same. If actual costs differ from those projected by the learning curve, a.period cost variance is recognized or the model is changed. The cost allocation model developed in this research will be similar to the one described above. In the remainder of this chapter brief consideration will be given to the historical development, general characteristics, uses, and limitations of learning curves. In Chapter II their significance for accounting will be discussed. Atten- tion will be given to such topics as the deveIOpment of accrual accounting techniques and the matching concept. In Chapter III the basic elements of a cost allocation model based on the learning curve phenomenon will be presented. By way of a hypothetical cor- poration, the accounting reports which would have resulted from the use of this model will be compared with the accounting reports which would have resulted from the use of current accounting techniques of cost allocation or from the use of an economic value concept of income. In Chapter IV the statistical preperties of the model will be studied. Attention will be given to the importance of the accounting concept of'materiality in the determination of minimum levels of statistical accuracy required to implement the model. In subsequent chapters attention will be given to a number of problems which might arise when attempts are made to implement the model. Possible methods of handling these problems will be suggested. Finally, an application of the model will be made to an actual industrial situation. THEORY OF LEARNING CURVES: The total costs of a product are divisible into pre-, actual, and post-production costs. Pro-production costs include research and deveIOpment, and investments in production facilities. Actual production costs consist mainly of direct labor, materials, and vari- able factory overhead. Post-production costs include product modi- fications and after-sales service.1 The theory of learning curves (L-C) concerns itself with actual production costs. More specifically, it deals with the direct labor element of such costs and other actual production costs associated with the incurrence of direct labor. Its foundation lies in the belief that "a worker learns as he works, and the more often he re- peats an Operation the more efficient he becomes, with the result that the direct labor hours per unit (of production) declines."2 Appli- cation does not, however, deal with individual effort as much as with the efforts of the organization as a whole. A number of factors effect the rate of decrease in the time it takes organizations or individuals to perform a task. Among these factors are the following: (1) The human content of an operation. The greater the human 1!. Hartley, "The Learning Curve and Its Application to the Aircraft Industry," Journal of Industrial Economics, (Merch, 1965), p. 122. 2Frank J. Andres, "The Learning Curve as a Production Tool," Harvard Business Review, (January-February, 1954), p. 87. content, the greater the susceptibility of an Operation to improvement.1 (2) The training, experience, and skill of the man on the job and related personnel whose coordinated efferts are required to com- plete a job. (3) The supervisors and staff who coordinate production.v (4) The production rate. Learning will occur most rapidly when the number of units to be produced is large enough so that the production units are Operating at capacity and production is continuous.2 Assuming that a number of these factors operate in a favorable manner to a sufficient extent, the production time required per unit of output will decrease as output increases in accordance with the theory of the learning curve. The most widely adopted model based on learning curve theory states that: "Whenever the total quantity of units produced doubles, the cumulative average cost per unit decline "3 This model is stated in terms of cost. by a constant percentage. The words "time" and "cost" are used interchangeably in L-C literature. This does not mean that cost and time bear a constant relationship to each other, but that learning curves are used to project both pro- duction times and production costs. The fellowing example is presented 1W. B. Hirschman, "Profit Prom.the Learning Curve," Harvard Business Review, (January-February, 1964), p. 134. 2T. B. Sanders and E. E. Blystone, "The Progress Curve--An Aid to Decision Making," N.A.A. Bulletin, (July, 1961), pp. 81-86. 3Raymond B. Jordan, "Learning How to Use the Learning Curve," N.A.A. Bulletin, (January, 1958), p. 27. in terme of cumulative average time. If the total time to produce the first unit was 100 hours, the second unit was 80 hours, and the third and feurth units together were 144 hours, the production process would be said to be fellowing a 90 percent learning curve, when the learning curve refers to cumula- tive average time. The decrease in cumulative average production time is fUrther illustrated in table l-l. TABLE l-l Cumulative Average Production Times-- 90% Learning Curve Cumulative Cumulative Average Hours Additional Per Block Production Per Unit Production Ayggggg Per unit 1 100.0 Hours 1 100.0 Hours 2 90.0 " 1 80.0 " 4 81.0 " 2 72.0 " 8 72.9 " 4 64.8 " 16 65.6 " 8 58.3 " 32 59.0 " 16 52.4 " This decrease in the cumulative average time required to accomplish a given task is the ratio between the cumulative average direct labor hours required at any unit of output and the cumulative average direct labor hours required at twice that output1 thus 1Hartley, p. 123. 90.0 _ 81.0 . 72.9 mm , and so forth. The infermation presented in table 1-1 is frequently presented in a graphic manner as shown in figure 1'10 FIGURE 1-1 Cumulative Average Production Times--90% Learning Curve Y 10 E» 30 £3 so 3E 7% E 40 :§,g zo "1F"1flT"1fiT'—1flT'—7RT"1RT'77RT-_THT"1RT"TRT'1RRT'4( Cumulative Production in Units Table 1-1 and figure 1-1 show that the "economics of learning" are reaped in decreasing amounts. If the production run is long enough "learning" could cease fer all practical purposes, and the cumulative average hours per unit could become almost constant. The relatively steep portion of the learning curve is referred to as the "startup phase," and the relatively flat portion of the learning curve is re- ferred to as the "steady state phase." The percentage used in reference to learning curves is in reality the complement of the rate of learning. For example, with no learning the learning rate is 0 percent, but the learning curve percent is 100. With a 90 percent learning curve there is a 10 percent decrease in mlative average hours between the first and second units of pro- duction. 1 Some authors prefer to use the terms "progress curve," "time 3 or "experience curve"‘ rather reduction curve,"2 "improvement curve," than "learning curve," because of their belief that a pure learning curve should reflect only the rate of the Operator's learning, and not consider other possible causes of the curve's characteristic downward lepe, such as equipment develOpment, better tooling, im- proved materials and the development of management. They feel that their terminology can more accurately reflect the summation of all these factors. The semantically less accurate, but more widely used term, "learning curve," will be used throughout the remainder of this research. Here it will refer to both individual and organizational learning. It is intended to be a broad concept. ISanders and Blystone, p. 81. 2s. A. Billon, Industrial rm Reduction Curves As Tools For Forecasting, (East Fansing, 196D) . 3W. P. Brown, The Improvement Curve, (Wichita, 1955). ‘A. W. Morgan, E aerience Curves Applicable to the Aircraft Industry, (Baltiiore, I552) . EARLY RESEARCH: Although the general concepts underlying learning curve theory have been known for many years it was not until the late 1930's that the rate of decrease in the time required to accomplish a task was observed to be regular enough to be predictable.1 T. P. Wright, of the Curtiss-Wright Corporation, is credited with formalizing the theory of learning curves. After observing aircraft production for some time, he found a consistent decrease in the cumulative average production time as output doubled. By studying previous production records he was able to determine the rate of de- crease in production times for similar kinds of aircraft. Determining the rate of decrease in production time made it possible for him to predict production times and delivery schedules for future aircraft with a high degree of accuracy.2 The Stanford Research Institute undertook a similar study of the majority of aircraft produced during World War II. This study concluded that although the learning curves for different types of aircraft were different in terms of their starting points (i.e., the labor inputs for the first plane of a particular type), the great majority had one characteristic in common-~their rate of improvement.3 1Andres, p. 87. 2Carl Blair, "The Learning Curve Gets and Assist From the Coquter," Mont Review, (August, 1968), pp. 31-32. 3Andres, p. as. 10 A.third study of aircraft production experience, conducted by the British Ministry of Aircraft Production, led to the same con- clusions.1 In 1943, France J. Montgomery reported on a study he made of the construction of liberty ships. "Between December 1941, when the first two ships were delivered, and the end of April, 1943, the average man-hour requirements per vessel delivered was reduced by more than one half. "2 Montgomery was one of the first to realize the potentially wide applicability of the learning curve phenomenon when he concluded that a study of the production figures of a company manufacturing a complex but standardized item would probably reveal a trend similar to that which occurred in the construction of liberty ships.3 In 1960, S. Alexander Billon conducted a study to see if the learning (time reduction) curve occurred in industries where a pre- conceived model of time reduction was not employed to set standards. His study of 54 products in 3 firms concluded that a "definite regular- ity in time reductions was observed in a majority of cases."4 A review of the literature since 1960 does not reveal any serious attempt to question or examine the theoretical foundations upon which 1E. J. Broster, "The Learning Curve for Labor," Business Management, (March, 1968), p. 35. 2P. J. Montgomery, "Increased Productivity in the Construction of Liberty Vessels," Monthly Labor Review, (November, 1943), p. 861. 31bid. 4Billon, pp. 1-2. 11 the learning curve is based. The majority of writers have concerned themselves with a discussion of how to use the learning curve, the purposes for which its use is suitable, and a discussion of the limitations of its use. 12 PREVIOUS APPLICATIONS: The ability of learning curve models to project production costs or times has resulted in their widespread application in the following areas of managerial decision making and evaluation: (1) (2) (3) (4) (5) (6) (7) (3) (9) 1 Setting selling prices. Projecting labor loads in the factory. Determining manpower requirements. Controlling shOp labor. Determining realistic prices for subcontracted items. Examining the training progress of new employees. Deciding whether to "make or buy." Determining break-even points. Planning finances, including cash flows. Item (4) deserves special attention. By its very nature L-C theory refers to human Operations and teamwork within an organization. During the startup phase of production the use of steady state phase performance norms will yield a stream of "unfavorable variances." These variances do not necessarily signal a departure from expectations nor act as a guide for corrective action. The motivational value of these variances is question- able. If the discrepancy between the steady state standard and actual performance is large, and remains so for several 1 For further readings in the area of previous application of learning curves see the bibliographic references to the works of Andres; Baloff G Kennelly; Brenneck; Broadston; and Jordan. 13 months, the "goal" may lose all its motivational value. Aspiration level studies indicate that subjects may re- ject a goal as being unrealistic and unattainable if the differinces between actual and target performance is large. under such circumstances there have been cases where workers in the steel industry reacted by terminating the startup phase at an artifically low productivity level.2 Instead of steady state stand- ards, L-C theory has been used to develop "moving" or "sliding" standards. Another interesting case is that in which management set its steady state standards at too low a level of productivity. Upon reaching shOp standards labor terminated the startup phase.3 There are new four methods of cost projection: (1) Recent experience data. Companies in mass production industries can use historical cost accounting data, modified for known changes to come, in order to produce standard costs. (2) Similar parts data. Standard costs for parts similar to those which have been produced for an extended period of time can be deveIOped in a manner similar to (1) above. (3) Engineering standards and references. When one item or a very small number of items of a complex nature are to be produced, lNicholas Baloff and John Kennelly, "Accounting Implications of Product and Process Start-Ups," Journal of Accounting Research, (Autumn, 1967), p. 141. 2Ibid. 3James D. Broadston, "Learning Curve Wage Incentives," Management Accounting, (August, 1968), p. 18. 14 the use of engineering standards and references is apprOpriate. (4) Learning Curves. Industries whose products are neither mass produced over a long period of time nor produced in single item quantities are most susceptible to the application of learning curve theory for projecting their costs.1 1Marvin L. Taylor, "The Learning Curve--A Basic Cost Projection Tool," N.A.A. Bulletin, (February, 1961), pp. 21-22. 15 BASIC MATHEMATICS: The mathematics of learning curves concems itself with the development of an equation which will fit the type of curve shown in figure 1-1, and certain modifications to that equation. The purpose of this section is to summarize the work of others1 in terms of a canon set of symbols. Let X I cumulative production (measured on the horizontal axis). cllmulative average production time (cost) per unit (measured on the vertical axis). time (cost) required to produce the first unit (vertical axis intercept). 3 used in text. b I exponent which accounts for the lepe of the L-C. b in text. '< I For the first unit of production in table 1-1 and figure l-l: v . 2% . l99.- 100 hours x 1 No matter what value 2 assumes, the value of Xb will always be 1 when X I 1. For the second unit of production a value of 2 must be found so that: Y - a - - 90 i5 7‘ Solving for b_ 90 - 2b - lOO J‘Por a more detailed discussion of the mathematics of learning curves see the bibliOgraphic references to the works of Andres; Baloff S Kennelly; Blair; Broadston, Hein; Jordan; and Springer, Herliky, kill, S Breggs; especially Hein. 16 b . lOO . 2 ‘36“ 1.1111 b log 2 n log 1.1111 3 10 1.1111 3 .04375 , ' b 4357— 3171753 '51” Likewise when X equals 4: 100 Y - a - - 81.0 9'}? 81.0 - 4b - 100 4b - figgu - 1.23457 b log 4 - 10g 1.23457 . lo 1.23457 3 .09152 a b —&r;§T— m '152‘” Similar calculations could be made for the other values of X and Y in table l-l and figure l-l. Using the values of a and b develOped above it is now possible to project values of Y for all values of X. Thus, for a cumulative production of 128 units the cumulative average hours per unit is: Y - i§§7137" 47.8 On the basis of production data for the first few units of output and the basic equation 1-1 ‘r - 5L- (1-1) projections are made to determine future production time (or cost) . It is this ability to project expected values of Y which has been the basis of most L-C applications. The most widely used methods of finding the g and b_ parameters in (1-1) involve the transformation of this exponential function into a linear one by the use of logarithms. Table 1-2 and figure 1-2 show 17 TABLE 1-2 Logarmithmic Transformation of.A 90% Learning Curve Total Units Leg Cumulative Log Average Hours X _2L_ Y _3L_ 1 0.00000 100.0 2.0000 2 0.30103 90.0 1.95424 4 0.60206 81.0 1.90849 8 0.90309 72.9 1.86273 16 1.20412 65.6 1.81690 32 1.50515 59.0 1.77085 FIGURE 1-2 Logarmithmic Transfermation of A 90% Learning Curve Log Y 2.5 PROJECTED 200 E fl 1.5 Ff fin”““------ 1.0 ACTUAL 0.5 Logarithmof Cumulative Average Hours Per Unit 0.0 E0 0.5 1.0 1.5 2.0 7.? IT‘S—5'“. . Logarithm of Total units Produced Leg X 18 how the information contained in table 1-1 and figure l-l can be transformed into a straight line by the use of logarithms. From equation 1-1 the linear relationship shown in figure 1-2 is found as follows: Y - ax’b (1-2) log Y - log a - b log X (1-3) After transforming the X and Y data for the first few units into logarithmic form we can use the familiar formulas for the least squares regression analysis , b . n2(1ogXlogY)-£logXZlogY (1_4) n1:(logX)2 - n(ZlOgX) 2 loan-M -b§_1_°.3£ ’ (1-5) H n in order to determine the parameters of the equation. Applying equations 1-4 and 1-5 to the data in table 1-2 yields a 2 value of .1520 and an a value of 100. The equation for the correlation coefficient, R _ n2(logXlogY) - ZlogXElogY v’n2(logX)2 - (Elogfir - u/n1:(log\()2 - (21am? ' (1-6) can be used to find the amount of change in Y as X varies which is accounted for by the solved values of _a_ and _b_. For the data in table 1-2 all of the change in Y as X varies is accounted for by the solved values of g and 11. Hence, the correlation coefficient is -1. In Chapter IV a considerable amount of space will be devoted to 1Many authors prefer to use equation 1-2 instead of 1-1 to solve for culml tive average production time. They frequently present (1-2) as Y - all and specify that b is negative. 19 determining minimum absolute values of the correlation coefficient required to implement the cost allocation model develOped in this research. Rough estimates of future production times or costs can be obtained by the use of log-log paper. When this procedure is used the absolute values of the initial production data are plotted directly on log-log paper, a straight line is drawn through this data, and anticipated future values are read directly from the log-log paper. Because such a procedure lacks precision it is not used in this research. The General Electric Company's Mark 11 Time Sharing Service has a number of comuter prOgrams available which calculate anticipated values of Y on the basis of data for the first few units of production.1 Because of their cost and lack of availability for modification these programs were not used in this research. A number of computer programs which do meet the specific needs of this research are listed in the Appendices. There are two basic learning curve models, one is primarily concerned with projection of cumulative average time or cost, the other is primarily concerned with projecting unit time or cost. The differ- ences between these two types of learning curves is best explained by way of a brief example. Assume 100 hours are required to manufacture the first unit of a product which has an 80 percent learning curve. A learning curve model 1General Electric, Analysis Usin Learnin Curves, Mark 11 Time Sharim Service, Program Library Users mic, (September, 1968) . 20 based on cumulative average time applies the 80 percent curve to the cumulative average time for producing the units. Therefore, the cumulative average time for manufacturing two units will be 80 hours and the cumulative time for manufacturing two units is 160 hours. Be- cause the first unit took 100 hours to produce, the time for the second must be 60 hours. A learning curve model based on unit time applies the 80 percent curve to the actual time it takes to produce each unit. Thus the production time for the second unit is 80 hours, and the cumulative time for manufacturing the first two units is 180 hours. Cumulative average time is thus 90 hours. The cumulative average time model of learning curve theory is used, unless indicated otherwise, in the remainder of this research. Two more fermulas used in cumulative average time (cost) models can be derived from (l-l). Total production time (cost) to produce the first X units is developed from (1-1) by multiplying (1-1) by X, r - x - a/xb . (1-7) Equation l-7 is simplified as follows: T . a)‘(l-b) r - ax“ (1-8) where: T - total production time (cost) for the first X units; c - (l-b). Uhit production time (cost) required to produce unit X is derived from (1-8): 0 - ax° - s(x-l)c (1-9) 21 u - a(x° - (x-l)°) (1-10) where: U a time (cost) required to produce unit X. The unit time model of learning curve theory solves equation 1-11, below, for 5 and _b_. u-uT (1-11) This is done by transforming (l-ll) into an equation similar to (1-3) and then applying a least squares regression analysis. The formulas for total production time (1-12) and cumulative average pro- duction time (1-13) are: r - I aX'bdx - axl’b - a(”Lb-1) (1-12) 1 "IT- """l"B""'- and N -b aX Y . u: '11— (1-13) X-l where: N a number of units produced. The cumulative average time model of learning curve theory is used in this research because the cumulative average time of all anticipated production is the most important value which must be cal- culated. There may be merit in deveIOping a cost allocation model based on the unit time model of learning curve theory. This is mentioned in the Suggestions for Further Research. 22 LIMITATIONS 0F LEARNING CURVES: The limiting values of a cumulative average learning curve are 100 percent and 50 percent. If no learning occurs, the cumulative average time per unit does not change and the model follows a 100 percent learning curve. Given any level of output the cumulative average time per unit at that level of output is the same as that at any lower level of output. If the learning curve percent were 50, the model would indicate that the second unit took zero time to produce. If the cumulative average time for the first unit were 100 and the second were 0, the cumulative average time would be 50.1 The mathe- matical properties of the learning curve makes a L-C of less than 70 percent difficult to envision.2 The industrial applications of learning curves fall between the limits of single units produced in accordance with special orders and items which have been mass produced for an extended period of time. As previously mentioned, engineering standards and references are employed when cost or production standards are set for a small number of items of a complex nature, and modified recent experience data is employed when cost or production standards are set for a product which has been mass produced for an extended period of time. Figure 1-3, for an 80 percent learning curve, shows that as total output increases the L-C soon reaches a point where the difference 1Leonard W. Hein, The antitative Approach to Managerial Decisions, (Englewood Cliffs, 1537), p. 91. 2Jordan, p. 27. 23 FIGURE 1-3 Unit Production Time--80% Learning Curve 100 80 60 40 Hours Per lbit 20 h 0 1 10 20 30 40 50 60 70 B0 90 100 110 120 130 140 Cumulative Production in Units X in production time between successive units approaches zero. In learning curve terminology, the learning curve is said to have reached a "steady state." Some authors have said learning curve theory is no longer applicable once the steady state is attained because no further decreases in production time (cost) take place.1 Other authors contend that although the reduction in production time still takes place, it takes place over such a relatively large number of units and periods of timerthat it escapes notice.2 In any event, the application of learning curve models to products which have reached the steady state is of little value . 3 1Nicholas Baloff, "The Learning Curve--Some Controversial Issues," Journal of Industrial Economics, (July, 1966). 2Hirschman. 3Jordan , p. 28. 24 Problems which may hinder all attempts to apply learning curve models include small orders, essential modifications, labor turnover,1 strikes, and terminations of the startup phenomenon.2 Increases in wages3 are also a potential problem when the L-C is used to project production costs. This problem is considered in Chapter V. Because the learning curve phenomena pertains to a large extent to improvement.in the human element of productivity, and man's learning to control machines in more efficient ways, the slope of the curve depends to a large extent on the proportion of human and machine labor involved. In manual Operations time reduction is limited only by the dexterity of the human hand. In manufacturing processes composed principally of machine operations much of the reduction in time and cost is limited by the feed and speed of the machine. Jordan feund the relationships shown in table 1-3 between the L-C percent and the prOportions of Operations perfOrmed by human and ammhine labor.4 Table 1-3 indicates that the learning effect is more significant in production processes that have a greater element of human than machine labor, and that a change from one type of labor to another may have a significant effect on the learning curve. For example, a change from.human to machine labor after a number of units are produced might result in a downward shift in the unit production time or cost curve (an essential modification) and a decrease in the L-C percent. lei-aster, p. 35, 2Baloff uu Kennelly, p. 141. 3Hein, p. 113. 4Jordan, p. 28. Relationship 25 TABLE 1-3 Between Labor Inputs and L-C Percent Human Labor 75% 50% 25% Machine Labor 25% 50% 75% L-C Percent 80% 85% 90% CHAPTER II LEARNING CURVES AND ACCOUNTING INTRODUCTION: Before the advent of long lived business enterprise there was no need for the development of complex cost allocation systems to assist in reporting periodic earnings. Under the Italian bookkeeping methods there was no concept of the accounting period. Most business ventures were of short duration, or at least not continuous after a Specific trading objective had been reached. As a result, profit was calculated only upon the completion of the venture. Without the concept of periodic profit, there was no need fer accruals and deferrals.1 Today corporations have indefinite lives, and managers, investors, and creditors desire timely information about changes in the financial condition of businesses. Accounting reports are important in evaluating the past and planning for the future. Out of this need fer timely information to assist in evaluation and planning has come an emphasis on the periodic reporting of business income. Accounting periods of equal length are used because they are "'consistent' and therefbre promote comparability."2 But merely having reporting periods of equal 1Eldon S. Hendriksen, Accounting Theory, (Homewood, 1970), Pp. 25 -26 e 2Maurice Moonitz, "The Basic Postulates of Accounting," AccountingfiBesearch Study No. l, (AICPA, 1961), p. 17. 26 27 length is not enough. It is generally recognized that reporting the results of business operations on a regular periodic basis is of little value for decision making unless some attempt is made to match costs with revenues. ...because revenue and expense transactions are reported separately, and because the acquisition and payment for goods and services do not usually coincide with the sales and collection processes related to the same product of the enterprise, matching has come to be considered a necessity or at least desirable. The leads and lags in the acquisition and use of, and the payment for, goods and services are assumed to be the reason for accruals or deferrals in order to match the expense with associated revenue. In 1964, the American Accounting Association's Concepts and Standards Research Study Committee defined "Costs" as resources given up or economic sacrifices made.2 The committee stated that costs "are incurred with the anticipation that they will produce revenues in excess of the outlay"3 and that "apprOpriate reporting of costs and revenues should therefore relate costs with revenues in such a way as to disclose most vividly the relationship between efforts and accomplishments."4 In order to accomplish this the committee advocated that costs should be related to revenues within a specific period on the basis of some discernable positive correlation of such 1Hendriksen, p. 183. 2Concepts and Standards Study Committee, "The Matching Concept," The Accounting Review, (April, 1965), p. 368. 31bid. 41bid. 28 costs with the recognized revenues.1 In the case of costs incurred to produce goods intended for future sale, the committee recommends that the specific costs for material and labor be attached to specific units and that these costs be expensed when these units are sold.2 The procedure described above, and the use of steady state standard costs are generally accepted accounting procedures fer matching pro- duction costs with revenues.3 11bid., p. 369. 21bid. 3In this research it is assumed that cost variances are written off to the cost of goods sold in the period incurred. In all of the examples presented in this research it is further assumed that pro- duction equals sales in each period and that there are no beginning or ending inventories. Therefore, in the examples presented in this research, the cost of goods sold is the same regardless of’whether a standard cost system is used or the actual cost of each unit is expensed in the period it is sold. 29 SIGNIFICANCE OF L-C FOR ACCOUNTING REPORTS: The use of either cost allocation (matching) procedure described above may lead to undesirable results when applied to firms whose unit production costs decline over the entire production life cycle of a product, (i.e., whose production costs follow the learning curve or similar phenomenon). The use of either accounting procedure may lead to significantly understated reported earnings in early accounting periods and overstated reported earnings in later periods. The actual cost of units produced in earlier periods will be above and the actual cost of units produced in later periods will be below the average unit cost of all units produced during the product's production life cycle. The accounting procedures described above make the reported earnings of such firms depend on the current stage in a product's production life cycle. The reported rate of return on investment will be highly variable. The dangers of artificial volatility in reported earnings fer investors were mentioned in a recent speech by Sidney Davidson: [Today] There is a widespread view among managers and accountants that the market responds directly to changes in reported earnings per share, that investors...cannot see through the reported earning data to the underlying economic facts which the reports are supposed to depict. A study reported on in 1967 by Hamil and Hodes indicated that companies with a history of highly volatile earnings tend to trade at a much lower price-earnings multiple than other comparable companies whose 1Sidney Davidson, "Accounting and Financial Reporting in the Seventies," The Journal of Accountancy, (December, 1969), p. 30. 30 growth in earnings has been stable around a basic trend.1 Assuming that investors react to increased variability by demanding an increased return, the variability in a firm's reported earnings which is caused by conventional methods of handling startup costs may lead to a lower P/E ratio for the firm's stock than the firm's underlying economic income trend warrants. Sidney Davidson has also commented on the problems which current cost allocation techniques cause management when reported production costs decline over the production life cycle of a product and startup costs are high. It seems unthinkable that a wise decision by management, based on a careful consideration of probable future con- sequences and proceeding precisely according to plan, should have the effect of reducing reported net income. It is scant comfort for management to be told that, if the program continues according to plan, reported net income will ultimately be higher, indeed higher by an amount that com- pensates for the earlier reported losses or understatements of income. Income measures effectiveness, and judgements on managerial effectiveness are made too frequently for managers to take much solace from the thought of compen— sating gains sometime in the future. It is bad enough to think of the danger of being replaced by a new management as a result of troublesome accounting reporting practices, and worse to be told that the successor management will look especially good as the compensatingzeffect for the losses charged against current management. Mr. Davidson concluded that, "If management comes to feel that accounting practices inhibit desirable action, this indeed will present 1Hamil and Hodes, "Factors Influencing Price-Earnings Multiples," Financial Analyst Journal, (January, 1967), p. 90. 2Sidney Davidson, "The Day of Reckoning--Managerial Analysis and Accounting Theory," Journal of Accounting:Research, (Autumn, 1963), pp. 18-19. 31 a day of reckoning fer accounting."1 Despite the impact of startup costs on reported income, and their significance for investors, managers, and accountants, a review of the literature reveals only one article which indicates the potential magnitude of early period (startup) costs and their impact on financial statements, or suggests better methods of accounting for them.2 Only the aircraft industry has made any attempt to systematically account for theme Baloff’and Kennelly have noted that while accountants pay little attention to such costs and generally regard them as insignificant when averaged out over a one year period, scarcely a week goes by that some company is not using such costs as a rationale for disappointing earnings.3 After reviewing write-ups on corporate earnings in the Wall Street Journal for a period of time, Baloff’and Kennelly concluded that such costs are probably significant and "that the effects of start-ups on earnings provide many challenges for accountants."4 In accounting terminology, the problems discussed above center around income recognition and cost allocation. They are caused by the use of reporting periods which do not coincide with either the production life cycle of a firm's products or the life of the firm, In Accounting Research Study No. 1, Maurice Moonitz noted that, "The 11bid., p. 19. 23. n. Wyer, N.A.A. Bulletin, (July, 1958), Section 2. 33a10££ and Kennelly, p. 142. ‘zbid. 32 problem of recognition and allocation is made more difficult because the 'events' often take longer to work themselves out than the reporting periods customarily in vogue."1 In this research effort the "event" is a venture whose duration is the production life cycle of a product. The problem is how to properly match all of the costs and revenues associated with this venture. 1Moonitz, p. 33. 33 ECONOMIC VALUE AND ACCOUNTING INCOME: On a theoretic level it might be argued that the real problem in income measurement is not one of achieving a proper matching of costs and revenues but one of asset valuation. If assets could be preperly valued on the basis of the revenues they are expected to produce then income would consist of interest on these assets and changes caused by new asset acquisitions or investment programs undertaken by management. Persons who would make such statements are arguing for economic income and.economic value as ideals toward which accounting should strive. At this level of reasoning economic income has been defined to be ...the change, over some period of time, in the value of a firm's assets. The total value of a firm's assets at any point in time can be determined by discounting, at some normal rate of return, the expected net cash flows from asset utilization. The total economic income figure which results from a comparison of beginning and ending period asset values can be fragmented into two components: (1) expected income, and (2) unexpected income. The expected income component can be regarded as interest. It is the product of the normal rate of return and the net present value of the assets at the beginning of the period. The unexpected income component of economic income is equal to changes in asset net present value which deveIOpes as a result of changes in expectations regarding 2 future cash flows. Indeed, "Economic income is generally defined as an ideal theoretical concept which is impractical to implement because of the 1Lawrence Revsine, "0n the Correspondence Between Replacement Cost Income and Economic Income," The Accounting Review, (July, 1970), p. 515. 21bid. , p. 516. 34 difficulty in an uncertain world of measuring cash flows."1 Because of the subjectivity associated with the use of economic income and economic value such concepts cannot be used in practice. In this research they are retained as theoretically ideal concepts.2 But, the objective of the cost allocation model which will be developed is not to approximate economic value and economic income, rather, it is to try and get accounting income to move in the same direction as economic income throughout the production life cycle of a product. lKeith Schwayder, "A Critique of Economic Income as An Accounting Concept," Abacus, (August, 1967), p. 28. 2Schwayder attacks economic income as an unsound theoretic model for accounting income measurement because all of the firmls important economic events except cash flow and rates of subjective income are ignored. He argues that economic income places too much emphasis on the future, does not consider the firm's past and current success in dealing with its economic environment, uses a subjective interest rate rather than the interval rate of return, and is limited by the certainty assumption. See Schwayder, pp. 34-35. In the example developed in Chapter III to compare economic income with the income derived from the use of the cost allocation model developed in this research, the inter- val rate of return is used, certainty is assumed, and the past is ignored. 3S LONGJTERMiPROSPECTIVE: What is needed is a better procedure for reporting costs and revenues. The 1964 AAA Concepts and Standards Research Committee felt that the "Appropriate reporting of costs and revenues should. . . relate costs with revenues in such a way as to disclose most vividly the relationships between efforts and accomplishments."1 This researcher feels that attaching actual production costs to units or using steady state standard costs does not accomplish this objective as well as the use of a cost allocation model based on the learning curve phenaaenon. What is needed is a long-term prospective of expenses which takes into consideration the probable decline in pro- duction costs as more units are produced. Thomas R. Prince, in his book, Extension of the Boundries of Accounting Theog, argues for the use of a long-term income prospective in reporting the results of business Operations.2 According to Prince, "the long-term income perspective attempts to anticipate total cost and total revenue and match these two aggregates."3 He notes that "the long-term approach would have more accruals and more deferrals which would result in the leveling out of reported business income."4 1Concepts and Standards Study Comittee, p. 368. Lrhomas R. Prince, Extension of the Boundries of Accounting Theory, (Cincinnati, 1963), p. I36. 31bid. 41bid. 36 The learning curve cost allocation model developed in this research will result in an additional deferred charge being shown on the balance sheet. It will not result in the addition of'any accruals. It is primarily concerned with the allocation of'production costs. It does not pay specific attention to revenue projection. The model will match costs to revenues on the basis of the percentage of total antic- ipated production sold. Attaching costs to specific units is of secondary'importance.1 Unit costs are important only for purposes of variance analysis. During early periods of production the model will call for deferral of a portion of the incurred production costs through charges to the asset account "Improvements in Production Procedures." In later periods as the production life cycle of a product nears its end the account "Improvements in Production Procedures" will be reduced by charges to "Inventory" and "Cost of Goods Sold." The choice of the title "Improvements in Production Procedures" is intended to convey the notion that these production costs are being deferred (capitalized) because of their relationship to the reduction in future production costs made possible by organizational learning through past production experiences. Increases in this account could be related to increases in the value of organizational learning and decreases in this account could be related to the decline in the cost 1The 1964 AAA.Concepts and Standards Study Committee advocated attaching costs to units. The researcher feels that this choice was made on the basis of the alternatives then available to the committee and that cost allocation procedures similar to those developed herein were not among those alternatives. 37 avoidance potential of this learning. Improvements in Production Procedures is regarded as a cost equalization account whose use attempts to compensate for the fact that accounting periods are not symmetric with product production life cycles. When a.new'production venture is under consideration management evaluates it as a whole. Management's attention is not focused as much on the production cost or selling price of each individual unit as it is on the total production costs and total sales over the entire venture. Similarly the L-C cost allocation model attempts to allocate costs over the entire production venture. The objective of the model is to avoid the write-off of costs incurred during a period as period expenses. The objective of the model is to consider all of the costs which will be incurred during the production life cycle of a product and match these costs with revenues on the basis of the percentage of total anticipated production sold. 38 INDUSTRIES WHERE L-C HAS GREATEST APPLICATION: As previously mentioned, the original applications of learning curves were in the airframe industry. Other industries to which learning curves have been applied include: steel, electronic products, home appliances, glass, paper, shipbuilding, textiles, and defense.1 In addition to these industries significant potential applications exist in residential home construction and computer assembly. use of the learning curve requires both room for improvement in the method of'production, and an ability and desire to improve. As table 1-3 showed, the traditional area fer improvement in the L-C is labor efficiency, the higher the percentage of labor in the production process, the more rapid the rate at which production times or costs can fill. Another characteristic of industries to which learning curves are applicable is change, be it a change in product or production process. During the startup phase, the L-C phenomenon is most significant. One cannot profitably apply it to evaluate the future of items which have reached the steady state stage of'production. The consolidated earnings statements of large diversified cor- porations are probably not significantly affected by their failure to include the account "Improvements in Production Procedures." For them, new products are always being phased in while others are being phased out. Yet, even fer these corporations, the use of the account "Improve- ments in Production Procedures" could be of value in reporting divisional, 1See the bibliographic references to the works of Baloff, Baloff and Kennelly, and.Jordan. 39 product line, or'project earnings. The learning curve model developed in this research will find its greatest potential application in companies or divisions which are characterized by product innovation and/or rapid improvement in basic production procedures. Ideally these companies or divisions would have product assembly as their basic task. Their production runs would be between 4 and 5,000 units over a one to five year period. These limits are not strict. 40 AN INDUSTRIAL APPLICATION: The only industry which this researcher has feund that gives any recognition to the learning curve phenomena in their published financial statements is the aircraft industry. The following quotation from the 1967 notes to the consolidated financial statements of the Boeing Corporation is typical: Work in process on military fixed-price incentive type contracts is stated at the total of direct costs and overhead applicable thereto, less the estimated average cost of deliveries based on the estimated total cost of the contracts. Work in process on straight fixed price con- tracts is stated in the same manner, except that applicable research, development, administrative and other general ex- penses are charged directly to earnings as incurred.... To the extent that estimated program costs, determined in the above manner, are expected to exceed total sales price, charges are made to current earnings in order to reduce work in progress to estimated realizable value. Boeing's auditors, Touche Ross and Co., give this company an unqualified Opinion.1 Dispite the fact that Boeing's method of handling unit production costs appears to be similar to the method preposed in this research a comparison of the cost allocation model developed in this research with the cost allocation model described in Boeing's 1967 annual report reveals a.number of significant differences. (1) Boeing leaves costs in excess of average unit production costs in "WOrk in Process" and does not separate them from costs in- curred to produce units still in production. The L-C cost allocation model uses a special asset account to show the unusual nature of this ”SOC e 1Boeing Corporation, Annual Report 1967. 41 (2) Boeing does not regard a cost as excessive, and to be written off in the period incurred, unless such a write-off is necessary in order to reduce work in process to estimated realizable value. The L-C cost allocation model requires a write-off of costs as excessive if the production cost of a unit exceeds the expected cost of that unit as determined by the model. In addition, the model recognizes favorable cost variances when unit production costs are less than expected. (3) Boeing only produces after production orders have been re- ceived. Hence, the number of units to be produced is certain. The L-C cost allocation model does not require 100 percent certainty. Table 5-1 shows that there is considerable leeway in the accuracy with which the estimate of the number of units to be produced can be made. (4) Boeing's cost projections are based on the unit curve version of learning curve theory. The L-C cost allocation model, for reasons stated previously, is based on the cumulative average curve version of learning curve theory. 42 PURPOSE AND METHODODOGY OF RESEARCH: The primary Objective of this research is to develop a cost allocation model based on the learning curve phenomenon. Secondary objectives include analyzing the statistical properties of this model in order to determine its limitations, and testing it by actual applica- tion to an industrial situation. The rationale for the primary objective was set forth in the section "Significance of L-C for Accounting Reports" (page 29). It is the researcher's belief that the cost allo- cation model deveIOped in this research results in a better matching of the costs and revenues associated with a production venture than cost allocation models based on traditional standard or actual costing procedures. In addition, under conditions of certainty, the L—C cost allocation model reports changes in accounting income which vary in the same direction as economic income while traditional cost allocation models result in changes in accounting income which vary in the opposite direction of economic income. In connection with this last point a rate of return income model is presented in Chapter III. The income figures reported by a hypothetical corporation with the use of this rate of return income model are compared with the income figures this hypothetical corporation would have reported had it used either current accounting cost allocation techniques or a cost allocation procedure based on the learning curve. A comparison of the three income figures will show that allocating costs on the basis of the learning curve phenomenon results in changes in income in the same direction as those derived by the use of the rate of return income 43 model while allocating costs on the basis of traditional cost allocation models results in changes in income in the opposite direction as those derived by the use of the rate of return model. Such an occurrence is significant if accounting reports are to be used to evaluate managerial effectiveness. In the real world the relationship between cumulative average time (cost) and the number of units produced does not have a correlation of -1. Hence the statistical properties of the learning curve cost allocation model are important in any application of it. Chapter IV takes a close look at these statistical preperties. Procedures are developed to determine whether or not the model can be applied to a particular situation, to determine the number of units which must be produced to define the model parameters before the model can be used, and to analyze production as it takes place to determine if a variance is of such a magnitude that it may indicate a need to change the model or the method with which it is applied. If a variance between an actual and projected cost occurs, and an analysis of the situation reveals a change in any parameter under- lying the L-C cost allocation model, special techniques can be applied to bring the model into line with this new situation. The necessary techniques are presented in Chapter V along with a discussion of some problems which can occur during application of the model. These problems include union production standards, essential modifications in the product or production process, changes in total anticipated production, and changes in hourly production costs. 44 In Chapter VI the model is applied to an actual production situation and comparisons are made between reported production costs derived by the use of the L-C cost allocation model and production costs derived by the use of traditional cost allocation models. The application of learning curves to production problems and accounting procedures would be difficult without the use of the computer. The accuracy of reading data from log-log paper is low. The time consumed in hand or machine calculation is high. The computer programs required to implement the L-C cost allocation model are listed and documented in the appendices. Reference is made to these programs and the related documentation at various points throughout this research. They are written in the BASIC language. The programs in Appendices A.and C have been run on the following machines: CDC 6500, IBM 360, GB 265, PDP 10. Those in Appendices B and B were run on a CDC 6500. Those in Appendices D and P were run on a GB 265. In order to inform the reader of what is involved in the L-C cost allocation model, Chapter III begins with a brief description of the model and an example of how it operates. CHAPTER III THE LEARNING CURVE COST ALLOCATION MODEL THEJMODEL: The learning curve (L-C) cost allocation model projects unit and cumulative average production costs over the entire anticipated production life cycle of a product on the basis of cost data for the first few units of production. USing this data comparisons are made between the projected cost of each unit and the expected average unit cost of all anticipated production. As production takes place any excess of the projected cost of each unit over the expected average cost of all anticipated production is charged to the asset account "Improvements in Production Procedures" and inventory is charged with an amount equal to the expected average unit cost of all anticipated production. Whenever the projected cost of a unit is less than the expected average unit cost of all anticipated production this differ- ence is deducted from the account "Improvements in Production Pro- cedures" and inventory is charged with an amount equal to the expected average unit cost of all anticipated production. As production takes place any differences between actual and.projected unit cost are written off as a period variance unless a change in a.parameter of the model occurs.1 Figure 3-1 compares the flow of costs under a standard 1These changes are discussed in Chapter V. 45 46 cost model and the L-C cost allocation model. Figure 3-2 presents a series of cost curves for the example presented later in this chapter. Line 1 represents the cumulative average unit cost at various output levels. At N, the number of units of anticipated production, line 1 intersects line 2, the expected average unit cost of all anticipated production. Line 3 represents the calculated (projected) cost of each unit. Until point B is reached line 3 exceeds line 2. Until production reaches the output level represented by point B the account "Improvements in Production Pro- cedures" is charged with the difference between lines 3 and 2. After output reaches point B the account "Improvements in Production Pro- cedures" is credited with the differences between lines 2 and 3. At output level N the balance in Improvements in Production Procedures would be zero. In figure 3-2 this is true because area I is equal to area D. The account "Improvements in Production Procedures" could be shown in any one of several places in the Balance Sheet. It could be shown in Current Assets near Work-In-Process in an attempt to indicate its value as an asset which is derived from the organization's ability to reduce future production costs because of its past production experiences. It could be shown in the Fixed Asset section of the balance sheet in an attempt to indicate the fact that the production venture which this asset account is associated with will include several accounting periods. It could also be shown as a Deferred Charge if the cost equalization nature of this account is stressed. Dispite 47 ooh—505 moaned .e 38 Becca .e 2358 was: 332 .o 330 E35 .e munOU H300< .d at quoaeg e1 qeaoaegun \ 0 /g I (__ 52> \\ r mmgmuasS—P‘ mom: I |_. mafia—Fad! n58 @2sz 329‘ 52.63.: has 9252.5 330 me not. no woman at» 950nm 48 .umoo «we: vouoonomm anon genuu< .v .unoo ewe: oeuoononm uo>o :oauosooum moaemaeauee and me once «we: oueue>e oouoonxo mo «macaw .n .eoauomoomm oeuemqowuee and mo «moo «we: onshore ooeoomxo ae>o uuoo awe: mouoonono mo amooxm .N .uoxoa an uo>enoanm .eouaomeouo oouemwouueu use we once awe: oueue>e oeuoomxe no unou awe: oouoonoum .H Ill-III no IIL IIII . muz a + n 940% o .ILIII maooo no hmou H mmmuozngAaxzoz uoa<4 88¢ 332m. a etqeaoaegun Illa-LII mAzu noeama GEE 928595 52mg Egan SEES 83 3835 28 33> accused me 53359.60 ~-n mum man.oao.NN» u nmN.NNm.NN + on.Nmm.oN» N N meo.NNN.oNN n NNo.eNN.N + NNm.nN¢.N N N N ”wN «\H N HmmmmHzH mbam am.wacaw N HmmmMHzH maam *m.wau¢> «\n a m f Pwmmmth thZHmm>zH HmMMMHzH HZMZHmm>zH memmHzH MhthNMIMm .mrmwnwwlbm .mnhmrpnbwm mem.nmN.Nn NNN.mNo.m onN.enN.NN ONN.eNN.e oo.NmN.NN N\N N NoN.NNm.eNN NNN.omN.N NNN.NNo.NN NNN.NNN.N em.veN.NN N N\N N NNNN.mNV » NeNN.eoeu » noNN.moNV a Noo.oemu N N N\N I. hmmzmth mama am.wuu¢> H Bmm¢m92H mag; *m.man¢> «\H kzmzhwm>zH x hzmzhmm>zH Hmmmmhzn hzmzhmm>zH Hammmth UHm ucomoam m.x:ummou .m.=.4.o mo :owueusmmoo vim mane «on an aeuueauemcu paeaoammon owneooo cameos macaw «come can» assume enemas enough «ceaueonee onqee o~oeno>emane eeon.mNN 1 e.na em.eae.- a u.ea nm.eoa.eeaa m.- ae.ncn.~eaa n.n~ ee.eem.ne » e.ea .ea.nmn.ea ~.e .a~.aae.- m.~ .en.oe~H~a e. .eo.aeeu .npmru.nphbmmqnmwn .npmuu . .nhm»u.p»pmmnqewmn .mum»u;pnpmmnqmpnn e.oea ee.eee aha» e.eea ee.eee mam» o.eea eo.eee some e.eea oe.oee Nee» a ez=o=< » azaoza a a2=o2< a ezsaz< nx\on\e ~x\an\~a Nx\on\e ax\anxuc «:35 «venom 5828 so new fiu-nm eueeaeeeum eaeeen oneu Haney - eeaeeeaaea< awake: nacho eeeeeeene< o-e ueeaunsne< u-a seamen a«unez nacho "each oummfiue> uueo puom «coca mo umou modem 153 gross margins reported with the L-C cost allocation model are higher in the first period and lower in subsequent periods than those reported with the actual or standard cost allocation model. If variable costing is used the following points can be made about the L-C cost allocation model: (1) In the absence of large variances or a change in a parameter the L-C cost allocation model will always report a higher gross margin in earlier periods and a lower gross margin in later periods than an actual or standard cost allocation model. (2) In the absence of variances, or changes in a.parameter of the L-C cost allocation model or the sales price, the L-C cost alloca- tion model will report a constant gross margin percent in all periods and a constant percent for the cost of goods sold. (3) If it is only applied to one element of the cost of goods sold the gross margin percent will vary, but the percentage cost to which it is applied will remain constant. In the example presented above the unadjusted cost of goods sold is the same for all periods after the first (which used a slightly different Bc parameter). In this example the cost variance varied from a low of .9 percent of sales in the first period to a high of 10.6 percent of sales in the last. From the information presented in table 6-1 this appears to be caused by the high level of variability in the cost of materials. In the next section, when the L-C cost allocation model is only applied to labor costs, the highest cost variance is 2.5 percent of sales. 154 L-C “JOEL APPLIED TO LABOR COST CURVE: When a separate analysis is made of the materials and labor cost data contained in table 6-1 it soon becomes evident that the L-C cost allocation model could be implemented with greater accuracy to the labor cost Curve than to either the total cost curve or the materials cost curve. Table 6-2 compares Ac, Bc’ L-C percent, and R for each of these curves at 2 values of n. TABLE 6-2 Comparison of Total, Labor, and Materials Cost Data n A Bc L-C8 R c Total Cost Data 5 815.612 .0723382 95.10 -.976392 10 811.186 .071246 95.18 -.98834 Labor Cost Data 5 567.757 .108667 92.74 -.983418 10 581.089 .113462 92.43 -.992478 Material Cost Data 5 265.294 .0220332 94.48 -.823883 10 258.452 .0166742 98.85 -.82267 For the materials cost data the value of R is and remains so low that the L-C cost allocation model should not be implemented for the materials cost alone. When the materials cost data is combined with the labor cost data the resulting total cost data has a sufficiently high R to permit implementation. Taken alone, the labor cost data.has the highest values of R. Hence, it seems advisable to see what the results would be if the L—C cost allocation model is applied to the labor costs alone, with the actual materials costs written off in accordance with a standard or actual cost model. It should be noted that the relationships indicated in table 6-2 will not always occur. That is, a low R for one 155 component of the total cost curve will not always offset a higher R for another component of the total cost curve and lower R for the total cost curve. There may be situations where two or more R values for the component cost curves will result in a higher R value for the total cost curve when the component curves are combined. This would happen if the variances in the component cost data offset each other when combined. If, at the end of 19x1, the L-C cost allocation model is applied to labor cost data alone, a 11 confidence interval of 10.688 percent is required to insure that at N I 5,000 the actual value of YN will not differ from the coqmted value of YN by more than 10 percent. Table 4-7 indicates that an n of 9 is required to be 80 percent confident that YcN will not vary from YN by more than 10 percent.1 Because R for the labor cost curve increases, and a higher R can be obtained, the model is implemented. If the raw data, from which table 6-1 was computed, were available the data for the first 5 months of production could be broken down to increase n without waiting for additional production periods. Using the computer program listed in Appendix A4 , the average cost of all anticipated production is determined to be $236.174, the total cost of the first 671 units is computed to be $187,808.00, and the balance in Improvements in Production Procedures should be $29,332.40 1Additional refinement, which could be obtained by the use of interpolation, would be of little value here because the maximum con- fidence interval for _b_ in tables 4-7, 4-8, and 4-9 is 10 percent. 156 after 671 units are produced. The actual labor cost of the first 671 units is $187,880.00. Using this data the following analysis and journal entry are made for the period ending 12/31/xl: Actual Labor Cost of Units Produced $187,880.00 -Ca1culated Labor Cost of Units Produced 187 808.00 gogt Mace - minggble [Eavgng f.) m Calculated Labor Cost of Units Produced $187,808.00 -Number of Units Produced x Average Labor Unit Cost v 158,475.60 Change in Improvements in Preduction d s 4.2931239. Labor Cost of Goods Sold $158,475.60 Improvements in Production Procedures 29,332.40 Cost Variance - Unfavorable 72.00 Labor Cost Accounts $187,880.00 The income statement for the 6-month period ending 12/31/xl using the L-C cost allocation model to determine labor costs is: Application - Labor Cost Income Statement (L-C) For the 6-Month Period Ending 12/31/x1 AOINICI 8 Sales $402,600.00 100.0 Cost of Goods Sold: Labor $158,475.60 39.3 Materials 157,685.00 . 39.1 Cost variance 72.00* 316,232.60 78.5 Gross Margin Iii-1251110 m 'Unfavorable For the 9-month period ending 4/30/x2 another analysis of cumula- tive production, X, and cumulative average labor cost, Y, at the end of each month is made. This analysis is made to determine Ac, 8 and c9 157 R on the basis of data for the previous 9 months (n I 9). The new values of'Ac, Bc' and R are 580.458, .113253, and -.99lO38. In order to obtain a 110 percent confidence interval for average labor cost at N I 3,202 1 are needed when with an 80 percent confidence interval, 7 units of data R is -.991038. Because this is less than the number of units of data used, the confidence level is higher and the confidence interval is tighter than that previously specified. By the use of the computer program listed in Appendix A4 the data necessary to implement the L-C cost allocation model for labor costs is determined to be: CUMULATIVE UNIT TOTAL AVERAGE ACCOUNT PRODUCTION COST COST COST BALANCE 671 246.298 186362 277.738 30229.7 2019 217.105 494983 245.162 25188.6 2917 208.602 685950 235.156 7203.69 3202 206.76 745062 232.686 -- This new information indicates that the balance in IPP after 671 units had been produced should have been $30,229.70 instead of $29,332.40. The $897.30 difference between $30,229.70 and $29,332.40 is treated as an adjustment to gross profit in the second period. Using the above data, and the actual production costs shown in the income statements 1For Bc I .113253, rounded to the nearest value in table 4-1, .12029, the b_confidence interval for N I 1,000 is 11.469, and the N confidence interval for N I 5,000 is 9.302. Interpolating for I 3,202 11.469 - 9.302 9 9 x (3,202 - 1,000) - 1.192 9.302 + 1.192 I 10.492 rounded to nearest figure in table 4-7, 10.0 percent. 158 prepared by the use of a standard or actual cost allocation model, the following calculations are made for the periods ending 6/30/x2, 12/31/x2, and 6/30/x3: 6/30/x2 12/31/x2 6/30/x3 Actual Cost of Units Produced $304,372.39 $184,433.27 $54,683.16 -Calculated Cost of units Produced 308,621.00 190,967.00 59,112.00 CostCVarianceIUnfavorable Mia) W W W Calculated Cost of Units Produced $308,621.00 $190,967.00 $59,112.00 -Number of Units Produced x Avera e unit Cost 313,662.10 208,951.91 66,315.69 Change n Improvements in Production Procedures -$ 5,041.10 -$ 17,984.91 -$ 7,203.69 L-C Ad ustment 897.30* M --- *Understatement of balance in IPP at end of previous period. The income statements for the 6-month periods ending 12/3l/xl, 6/30/x2, 12/31/x2, and 6/30/x3, using the L-C cost allocation model for the determination of labor costs are presented on the next page. In this set of statements the labor costs in all periods except the first is 39.7 percent of sales. The labor cost for the first period is 39.3 percent of sales. This difference is caused by the determination of'a new Bc parameter for labor costs during the second. The variance between actual and calculated labor costs varies from a low of less than .05 percent of sales to a high of 2.5 percent of sales. This is considerably better than the low of .9 percent of sales and the high of 10.6 percent of sales which occurred when the L-C cost allocation model was applied to total production costs. The difference is caused by excluding the cost of materials from the L-C cost allocation 159 eneeaesea.. oHnuHohmmge Hg”. Ha gig Hg :88: 886 . c. on.amm oeeaueene< u-a 4.4H ea.noa.e~ » m.e~ ~e.eea.eaa» m.- Hm.eoe.~ena e.a~ ee.aen.ee . eeeaeeefie< 0-4 . ouomom cameo: nacho Poul. . E. E. F FE :38 m.~ ..ee.m~e e - N. H ..na. an». e :He. ae~ F.ee «a eeeeaae> eeeu n.54 ee.e~4.ee a. He ee. was. m- m. an. ac. one. saw ma. an eo.mee.ama eaeaeeeex A.en me.mcn.ee » a.en ”5.5mm.ee~a a.mm ec.nee.nan» ».mn ee.mae.wman .eeeaa "snow .eeeo me eeeu e.eea ee.eee4~a~o e.eec eo.eee.enm» e.eoa ee.oee.eee» e.eem ee.eee.~eea mouse a ez=oz< » az=Qz< a azsoz< a szanae nx\en\e ~x\an\na ~x\en\e cx\an\~c acnvcm noeauom cuaozso emu mom Renew aucomeueum emoocu uuou none; 1 conueoaamm< 160 model. Because of the rising materials cost the gross margin percent fell over the production life cycle. The gross margin percents obtained by applying the model to labor costs does not vary by a significant amount from those obtained by applying the model to total costs. The greatest difference is 1.9 percent of sales. The preference for applying the model to labor costs alone has to rest on the reduction of variances, not on the change in gross margin percent. The model had a.higher L-C percent when it was applied to total costs than it had when applied to labor costs because of the variability in materials costs. Tables 4-1 and 4-2 show that the lower the L-C percent the tighter the confidence interval for b_must be. This required an in- crease in the desired confidence interval for b_(from 5 to 10 percent) when the model was applied to labor costs alone. In some situations it may be necessary to apply the model to a group of items which have a higher L-C percent. The increase in R, obtained by applying the model to data which more closely follows the learning curve, might not be enough to offset the higher value of R required to apply the model to the tighter confidence intervals for b_necessitated by low L-C percents. In both situations presented, the L-C cost allocation model re- sulted in a higher gross profit in the first period and a lower gross profit in the last 2 periods than did the use of an actual (or standard) cost allocation model. CHAPTER.VII CONCLUSION SUMMARY: For most firms in most industries the production costs of a product are higher when that product is first introduced than they are after that product has been produced for a period of'time. A graphic representation of the decrease in production costs as total production increases has been referred to as a learning curve. This research effort was devoted to develOping a cost allocation model based on the learning curve phenomenon. Current accounting techniques of cost allocation take a segmented view of the production life cycle of a.product and charge inventory or the cost of goods sold in each period on the basis of actual production costs of that period. ,A standard cost allocation model usually charges the cost of goods sold with any excess of the actual costs of production over the standard costs of production. The result is a relatively low level of reported income in early periods when production costs are high and a relatively high level of reported income in later periods when production costs are lower. The L-C cost allocation model developed in this research takes the entire production life cycle of a product into consideration and 161 162 attempts to reconcile the timing differences between this period and the normal accounting period. The effect of using the L-C cost allo- cation model is to decrease the early period production costs charged to inventory and the cost of goods sold from their current levels, thus raising reported income, and to increase the later period production costs charged to inventory and the cost of goods sold, thus lowering reported income. These changes in reported income are accomplished by adopting production cost standards based on the learning curve phenomenon and using a cost equalization account to insure that, as production takes place, charges to inventory and the cost of goods sold are equal to standard unit costs based on the average cost of all anticipated production. As long as actual production costs proceed in accordance with the learning curve phenomenon, the reported cost of each unit is the same. If actual production costs differ from those projected by the learning curve, a period cost variance is recognized or the model is changed. The primary difference between the L-C cost allocation model and most other cost allocation models is that they are concerned with matching costs to units while the L-C cost allocation model is concerned with.matching costs to production ventures on the basis of the per- centage of completion of the production venture. In addition to developing the basic cost allocation model in Chapter III, a discussion of the significance of the model was presented in Chapter 11. Chapter IV reviewed the accounting concept of'materiality and evaluated the L-C cost allocation model in the light of this concept 163 in order to determine certain statistical preperties of cost data required before the model should be implemented for external reporting. Chapter v referred to a number of problems which can arise after the model has been implemented and mentioned some ways of handling these problems. Finally, in Chapter VI, the results of an application of the model to a production venture were presented. The major points considered in Chapter 11 included a brief review of the matching concept. It was noted that despite the accountants' desire to match costs with revenues, current procedures attach costs to units. In industries which do not display the L-C phenomenon such a procedure leads to meaningful results. But, in industries which display the L-C phenomenon such a procedure may lead to artificial variability in reported earnings. It was further pointed out that this artificial variability in reported earnings may in turn lead to a lower P/E ratio for firms displaying the L-C phenomenon than their economic position justifies. It was also noted that because earnings are lower in early periods than in later periods for firms displaying the L-C phenomenon investors are apt to erroneously evaluate the firm and its management when management is undertaking a project which will eventually prove very profitable. It was concluded that a cost allocation model based on the L-C phenomenon could help eliminate these problems by taking a long term prospective of projects undertaken by management. In Chapter Iv, based on a review of the accounting concept of materiality, it was concluded that before the L-C cost allocation model is implemented for external reporting the model should be able to predict 164 the average cost of all anticipated production with a :10 percent confidence interval and an 80 percent confidence level.' Procedures were develOped, and tables presented, to assist in the implementation of the model with the desired degree of accuracy. Chapter V was devoted to a consideration of some of the problems which can occur after the L-C cost allocation model is imple- mented. The problems considered included termination of the learning curve, changes in production cost, changes in the number of'unitsto be produced, and essential modifications in the product or production process. It was noted that the model is fairly insensitive to changes in the number of units to be produced. The general solution to the above problems involved the computation of a new value for the average cost of all anticipated production and an adjustment to the cost equali- zation account, Improvements in Production Procedures. In the application presented in Chapter VI gross margin was used as a surrogate for net income. In this application the L-C cost alloca- tion model achieved its objective of raising gross margin in the first period while lowering it in the last. The L-C cost allocation model was applied to both total costs and labor costs. This was done because of the high level of variability in materials cost. Applying the model to labor costs alone resulted in a significantly lower variance between the costs projected by the model and the actual costs incurred. 165 CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER RESEARCH: The L-C cost allocation model developed in this research could be a valuable tool in attempting to reconcile the differences between the accounting period and the production life cycle of a product. The L-C cost allocation model is able to allocate production costs over the entire production life cycle of a.product while still retaining the accounting concepts of "cost" and "objectivity." The primary impediment to the adoption of the L-C cost allocation model appears to be a.1ack of detailed production information. However, once a decision has been made to adopt the model, the additional infor- mation could probably be generated with relatively little cost as a part of the normal accounting process. This research centered around the cumulative average time learning curve. Developing a cost allocation model based on the unit time learning curve might be of value. This latter version of'the L-C cost allocation model could then be used whenever the correlation coefficient attainable with the unit time curve was higher than the correlation coefficient attainable with the cumulative average time learning curve. In many ways this research is just a beginning step in attempts to incorporate dynamic production cost data into accounting reports. Frequently other curves or equations may relate more closely to the actual change in costs than the learning curve. There are many research topics in this area. "The study of dynamic data should not be constrained 166 by the learning-curve 'theory' specifications."1 The important fact is that dynamic data can be quantified and result in more meaningful accomting reports . J“lesdi K. Bhada, "Dynamic Cost Analysis," Management Accountin, (July, 1970), p. 14. BIBLIOGRAPHY BIBLIOGRAPHY American Accounting Association, Concepts and Standards Study Cosmittee. "The Matching Concept," The Accounting Review, (April, 1965). American Institute of Certified Public Accountants. Accountin fisfiIts 05 Oper- Principles Board ginion No. 9, "Reporting the a ens, ew or : . . Accountin Princi les Board Opinion No. 11, "Accomting for Income Taxes," {New 7075: I967). Andres, Frank J. "The Learning Curve as a Production Tool," Harvard Business Review, (January-February, 1954). Baloff, Nicholas. "The Learning CurvenSome Controversial Issues," Journal of Industrial Economics, (July, 1966). . "Start-ups in Machine-Intense Manufacture," Journal of Industrial Engineering, (January, 1966) . Baloff, Nicholas and Kennelly, John. "Accomting Implications of Product and Process Start-Ups," Journal of Accomting Research, (Autumn, 1967) . Bernstein, Leopold A. "The Concept of Materiality," The Accomting Review, (January, 1967) . Bhada, Yezdi K. "Dynamic Cost Analysis," Wat Accomting, (July, 1970). Bierman, Harold Jr. gics In Cost AccountinLAnd Decisions. New York: McGraw-Hill, l9 . . Financial Accounting Theogz. New York: The MacMillan Company —"1'9’6s . ' Billon, S. Alexander. "Industrial Time Reduction Curves as Tools for Forecasting," \mpublished Ph.D. dissertation, Michigan State miversity, 1960. Blair, Carl. "The Learning Curve Gets an Assist From the Computer," Mangement Review, (August, 1968). 167 168 Boeing Corporation. Annual Report 1967. Seattle, Washington. Brenneck, Ronald. "Learning Curve Techniques for More Profitable Contracts," N.A.A. Bulletin, (July, 1959). . "The Learning Curve for Labor Hem-safer Pricing," N.A.A. B'illetin, (June, 1959). . "Break-even Charts Reflecting Learning," N.A.A. Bulletin, (Canuary, 1965) . Broadston, James 0. "Learning Curve Wage Incentives," Manggggnt Accotmting, (August, 1968). Broster, E. J. "The Learning Curve for Labor," Business Mum, (March, 1968) . Brown, W. F. The Improvement Curve. Wichita, 1955. Croxton, Frederick E., Cowden, Dudley J ., and Klein, Sidney. Mlied General Statistics. 3rd edition. Englewood Cliffs: Prent ce- Davidson, Sidney. "The Day of Reckoning-Magerial Analysis and Accounting Theory," Journal of Accounting Research, (Autumn, 1963) . . "Accounting and Financial Reporting in the Seventies," 1h_e_ Journal of Accountancy, (December, 1969) . General Electric Company. Program Library Users Guide 80 3217(10101-69, Analysis Using Learning Curves, (September, 1968). Grahm, 8., Dodd, 0. L., and Cottle, S. Securit Analysis: Principles and Technique. New York: McGraw-HIII, 1032. Hall, L. H. "Ezqzerience With Experience (hm-ves for Aircraft Design Changes," N.A.A. Bulletin, (December, 1957). Hamil and Hodes. "Factors Influencing Price-Earnings Multiples," Financial Analyst Journal, (January, 1967) . Hartley, K. "The Learning Curve and Its Application to the Aircraft Industry," Journal of Industrial Econuics, (March, 1965). Hein, Leonard W. The thitative Approach to Managerial Decisions. Englewood Cl 3: t ce , nc., . Hendriksen, Eldon 8. Accounting Theogz. Homeweod: Irwin, 1970. Hicks, Ernest L. "Materiality," Journal of Accountgg Research, (Autun, 1964) . 169 Hirschman, W. B. "Profit From the Learning Osrve, " Harvard Business Re___v_i__ew, (January-February, 1964). Jordan, Raymond B. "Learning How to Use the Learning Curve, " N. A___.___A. Bu1___l___etin, (January, 1958). Kenney, J. F. and keeping, E. 5. Mathematics of Statistics, Part One. Princeton: D. Van Nostrand many, 1nc. , 155i. . Mathematics of Statistics, Part Two. Princeton: D. Van Nostrafi Coqany, 1nc. , 1951. Kilbridge, Maurice. "A Model for Industrial Learning Curves," Manage- ment Science, (July, 1962). Mauts R. k. Financial Reportin b Diversified C anies. New York: ’FinanciaI'Efe cutives sear oundation, 15%;, ‘ Montgomery, Frances J. "Increased Productivity in the Construction of Liberty Vessels," Monthly Labor Review, (November, 1943). Moonits, Maurice. "The Basic Postulates of Accounting," Accounting Research Study No. 1, New York: AICPA, 1961. Morgan, A. N. E rience Curves Applicable to the Aircraft Industry. Baltimore, . Prince, Thomas R. Extension of the Bomdries of Accountin Theo . Cincinnati: SouthWestern PEEKang Co. , 1R3. Rapping, Leonard. "Learning (haves and World War II Production Functions," The Review of Economics and Statistics, (February, 1965) . Revsine, Lawrence. "0n the Correspondence Between Replacement Cost Income and Economic Incae," The Accounting Review, (July, 1970). Sanders, B. T. and Blystone, E. E. "The Progress Curve--An Aid to Decision Making," N.A.A. Bulletin, (July,-l961). Schwayder, Keith. "A Critique of Economic Income as an Accounting Concept," Abacus, (August, 1967). Selby, Samuel, Editor. Standard Mathematical Tables. Cleveland: The Chemical Rubber-Cipany, 1965. Springer, C. H., Herliky, R. E., Mall, R. T., and Beggs, R. I. Probabilistic Models, Volume four of the Mathematics for Manage- ment Serfes. Homewood: Richard D. Irwin, Inc., 1968. 170 Taylor, Marvin L. "The Learning Curve--A Basic Cost Projection Tool," N.A.A. Bulletin, (February, 1961). Woolsey, S. M. "Development of Criteria to Guide the Accomtant in Judging Materiality," The Journal of Accountancy, (February, 1954) . Myer, Rolfe. "Leaning Curve Techniques for Direct Labor Management," N.A.A. Bulletin, (July, 1958), Sections one and two. APPENDICES APPENDIX A Programs Used to Implement the L-C Cost Allocation Model APPENDIX A1 Determination of Parameters With unit Cost Data Purpose: To determine Ac, Bcv L-C percent, and R from unit pro- duction time or cost data. Requirements: Consecutive unit production time or cost data beginning with the first unit of production. Input Data Format: As many DATA statements as required beginning with DATA statement number 500. 500 DATA n, 01, 501 DATA u., 02, ... , 502 DATA ... , Uh_1, Uh Output Data Format: ACTUAL VALUE OF A - ul WWWWVMWOFA-k REGRESSION SLOPE COEFFICIENT B - Bc LEARNING CURVE PERCENT - L-ct COEFFICIENT 0F CORRELATION - R COEFFICIENT 0F DETERMINATION - R? Example: For the example presented in Chapter III the input data would be: 500 DATA 5, 10000, 501 DATA 10000, 7500, 6600, 6000, 5700 172 173 The output would be: ACTUAL VALUE OF A I 10000 COMPUTED VALUE OF A I 10045.7 REGRESSION SLOPE COEFFICIENT B I .207572 LEARNING CURVE PERCENT I 86.5994 COEFFICIENT OF CORRELATION - —.99931 COEFFICIENT OF DETERMINATION I .99862 Mathematics: Based on equations 1-2, 1-3, 1-4, 1-5, l-6, and the relationship: B L-C’6 - 100 93%.? R and R2 is for the log-log slope. 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 174 LISTING OF A1 READ N,A LET C-O LET D-O LET E-O LET F-O LET GaO LET H-O FOR X91 TO N READ U LET C-C+U LET Y-C/X LET D-D+LOG(X) LET E-E+LOG(Y) LET F-F+LOG(X)*LOG(Y) LET G-G+(LOG(X))+2 LET H-H+(LOG(Y))+2 NEXT X LET B-(N’F-D*E)/(N*G-D+2) LET Al-(E/N)-(B‘(D/N)) LET Bs-B LET Al-EXP(A1) LET L1-100*(A1/(2+B))/A1 LET Rp(N*F-D*E)/(SQR(N*G-D+2)*SQR(N*H-E+2)) LET R2=R+2 PRINT "ACTUAL VALUE OF A I" A PRINT "COMPUTED VALUE OF A -" A1 PRINT "REGRESSION SLOPE COEFFICIENT B a" B PRINT "LEARNING CURVE PERCENT 3" Ll PRINT "COEFFICIENT OF CORRELATION -" R PRINT "COEFFICIENT OF DETERMINATION -" R2 9999 END APPENDIX A2 Determination of Parameters With Cumulative Average Cost Data Purpose: To determine Ac, Bc’ L-C percent, and R from cumulative average production time or cost data. Requirements: A sequence of output levels and the cumulative average production time or cost of all output to each of the listed levels. Consecutive data is not required. Input Data Format: As many DATA statements as required beginning with DATA statement number 500. 500 DATA n, x , Y1, 501 DATA x2, i2, ... , 502 DATA ... , Xn_l, Yn_1, In, Yn Output Data Format: COMPUTED VALUE OF A . Ac REGRESSION SLOPE COEFFICIENT B - Bc LEARNING CURVE PERCENT . L-C% COEFFICIENT OF CORRELATION - R COEFFICIENT OF DETERMINATION - R2 Example: For the original application to the total cost curve presented in Chapter VI the input data would be: 500 DATA 5, 56, 640, 151, 557, 501 DATA 347, 531, 499, 524, 671, 515 175 176 The output would be: COMPUTED VALUE OF A I 815.612 REGRESSION SLOPE COEFFICIENT B I .0723382 LEARNING CURVE PERCENT I 95.1095 COEFFICIENT OF CORRELATION I -.976393 COEFFICIENT OF DETERMHNATION I .953343 Mathematics: Based on equations 1-2, 1-3, 1-4, l-S, 1-6, and the Comments: relationship: L-C’6 - 100 9.6%: R and R2 is for the log—log slepe. The essential difference between A1 and A2 is the presence of statements 170 through 200 in A1 which converts unit data into cumulative average data. In A2 the data is already in this form. Similar programs could easily be devised fer other types of data inputs such as total cost data. 100 110 120 130 140 150 160 170 190, 177 LISTING OF A2 READ N LET 0-0 LET E-o LET FIO LET c-O LET n-o FOR IIl TO N READ x,y The remainder of A2 is the same as Al except that lines 180, 200, and 340 are omitted. APPENDIX A3 Determination of Units Which Can Be Produced‘Nith Given FUnds or Time Purpose: To determine the number of units which can be produced within a given time period or with a specified amount of fUnds. Requirements: Values of Ac, Bc, and an estimate of the available time period if Ac is in terms of time. An estimate of the available funds is required if Ac is in terms of money. Input Data Format: One DATA statement is required for line 500. 500 DATA Ac, BC, T where: T I total available time or funds Output Data Format: FOR A B VALUE OF B GIVEN T HOURS OF AVAILABLE PRODUCTION TIME X UNITS CAN BE PRODUCED Mathematics: The total production time of X units of production is represented by equation l-B. T - Axc (1-8) If T, A, and C are known, the equation can be solved for X: X I Antilog((logT-logA)/C) 178 Comments: 179 The major value of this program is to assist in the preparation of pro-forma financial statements. It could also be used in production scheduling and in sensitivity analysis when it is desired to determine how large a change in X will occur when either T, A, or C changes. Remember CIl-B, and B is the eXponential representative of the learning curve percent . 180 LISTING OF A5 100 READ A,B,T 110 LET CIl-B 120 LET XI(LOG(T)-LOG(A))‘(1/C) 130 LET x-Expm 140 PRINT "FOR A B VALUE OF" B, "GIVEN" T "HOURS OF AVAILABLE" 150 PRINT "PRODUCTION TIME" x "INITs CAN BE PRODUCED" 9999 END APPENDIX A4 Model Projected Cost Data Purpose: To make the cost projections and calculations required to implement the L-C cost allocation medal, including the proper balance in Improvements in Production Procedures at various output levels. Requirements: The previously determined values of Ac and Be, an estimate of N, and the output levels, in terms of units, fer which calculations are desired. Input Data Format: As many DATA statements as required beginning with DATA statement number 500. 500 DATA Ac, BC, N, 501 DATA XI, x2, eee , Xi, eee , X", 0 where: Xi I an output level fer which calculations are desired (X1 3 N) Output Data Format: YATNmYN CUMULATIVE UNIT TOTAL AVERAGE ACCOUNT PRODUCTION COST COST COST BALANCE x1 "1 Ti '1 Ti‘xi'YN xN ”N TN YN ’°" 181 182 Example: For the example presented in Chapter III the input data would be: 500 DATA. 10045.7, .207572, 20, 501 DATA 5, 15, 20, O The output would be: Y AT N I 5394.15 CUMULATIVE WIT TOTAL AVERAGE ACCOLNT PRODUCTION COST COST COST BALANCE 5 5828.76 35963.6 7192.72 8992.9 15 4569 . 77 85 891 . 5726 . O7 4978. 83 20 4297. 1 1 107883 . 5394 . 14 0 Mathematics: Based on equations 1-1, 1-8, 1-10, and the following calculation for the account balance: IPPiITi-Xi-YN. 100 110 120 130 140 ISO 160 170 180 190 200 210 220 230 READ A,B,N LET C-I-E LET AI-A/Nna PRINT "Y AT N -", A1 PRINT "CUMULATIVE UNIT PRINT "PRODUCTION COST READ x LET UIA*(X+C-(X-l)+C) LET TIA*X+C LET YIA/X+B PRINT X,U,T,Y,T-X*Al READ x IF x-o THEN 9999 GO TO 170 9999 END 183 LISTING OF A4 TOTAL AVERAGE COST COST ACCOUNT" BALANCE" APPENDIX B Programs Used for Statistical Analysis of L-C Cost Allocation Model APPENDIX 81 Confidence Intervals for b Required to Obtain Confidence Intethls fer Y“ Purpose: To perferm the calculations necessary to develop tables 4-1 and 4-2. Mathematics: Determines El and 82 in equations 4—10 and 4-11 and indicates the percentage intervals (BC-B2)/Bc and (Bl-Bc)/Bc. The equations are solved fer N values of 100; 500; 1,000; 5,000; and 10,000 while Bc varies from the B value corresponding to L-C percents of 70 to 99. Comments: The program listed is for table 4-1. The program is easily modified for other N values. 185 90 100 110 120 130 140 150 160 170 180 190 186 LISTING OF 81 LET N(1)-100 LET N(2)-500 LET N(3)-1000 LET N(4)-5000 LET N(5)-10000 FOR III TO 5 PRINT "NI",N(I) LET Al-LOG(2) FOR x-70 TO 99 LET F-IOO/x LET D-LOG(F) LET BID/Al LET Bl-(LOG(lOO)+B*LOG(N(I)) -LOG(95))/LOG(N(I)) LET BZI(B*LOG(N(I))-LOG(l.OS))/LOG(N(I)) PRINT "BI",B,"BlI",Bl,"BZI",BZ PRINT "(Bl-B) /E-", (El -3) /B ,"(B-BZ) /E-" , (9-32) [B NEXT x PRINT NEXT I 9999 END APPENDIX 32 Confidence Intervals for 2 Required to Obtain Confidence Intervals for U1 Purpose: To perform the calculations necessary to develOp tables 4-3 and 4-4. Mathematics: Obtains approximate values of Cl and C2 in equation 4-13 and converts to terms of El and BZ. B1 and BZ are listed along with the percent intervals (Bl-B¢)/Bc and (BC-82) IBc. The solutions are accurate to 4 decimal places. The solutions are for N values of 100; 500; 1,000; 5,000; and 10,000 while Bc varies from the E values corresponding to L-C percents of 70 to 99. Col-ents: The program listed is for a 10 percent confidence interval. In the BASIC programing language ”is the same as +. 187 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 188 LISTING OF 82 LET X(1)IIOO LET X(2)ISOO LET X(3)IlOOO LET X(4)ISOOO LET X(5)IIOOOO FOR III TO 5 PRINT "XI",X(I) LET AIIOOOO LET A1ILOG(2) FOR NI7O TO 99 LET FIIOO/N LET DILOG(F) LET BID/A1 LET CII-E LET UIA*(X(I)**C-(X(I)-1)"*C LET BlIB+.1 LET ClII-Bl LET U1IA*(X(I)**C1-(X(I)-1)*’C1) IF U1>I.9O*U’THEN 220 LET BlIBl-.OOOI GO TO 170 LET BZIE-.1 LET C2Il-BZ LET U2IA?(X(I)'*C2-(X(I)-1)**C2) IF U2Z THEN 310 LET UIA1*(X1+Cl-(X1-1) +61) LET TIAl'XMCl LET YIAl/XHBl PRINT X1,U,T,Y,T-X1‘Y(N) GO TO 230 FOR XIZ+I TO N LET TIT+U(Z) IF Xl>X THEN 360 LET YIT/X PRINT X,U(Z) ,T,Y,T-(X'Y(N)) NEXT X 00 TO 230 9999 END ClllULATIVE AVERAGE ACCOWT" BALANCE" APPENDIX C2 Change in Production Costs Purpose: To develOp the cost projections required to implement the L-C cost allocation model when there is a change in the cost of the underlying factors of production. Requirements: Values of Al, B, 2, A2, and N. Where: A1 I original estimate of a B I regression slope coefficient 2 I output level at which costs increase A2 I Al increased or decreased by the percentage change in costs N total anticipated production Input Data Format: As many DATA statements as required beginning with DATA statement number 500. 500 DATA Al, B, 2, A2, N, 501 DATA X1, , X" Output Data Format: Same as in Appendix Cl . Example: For the decrease in production costs presented in Chapter V the input data would be: 500 DATA 10045.7, .207572, 11, 8036.56, 20, 501 DATA 5, 11, 15, 20, 0 The output would be: 197 198 VALUE OF Y AT N I 4938.2 CUMMLATIVE UNIT TOTAL CUMULATIVE ACCOUNT PRODUCTION COST COST AVERAEI EALANCE 5 5828.76 35963.6 7192.73 11272.6 11 3909.32 66197.9 6017.99 11877.6 15 3655.81 81170.5 5411.37 7097.49 20 3437.69 98764.1 4938.2 -0- Mathematics: Similar to those in Appendix A4 to Z. From Z on the value of Ac used in computations is changed. The total cost of all anticipated production is: T-(ucz-1)°)+(A2-N°)-(A2(2-1)°) and 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 199 LISTING OF C2 READ A1,8,Z,A2 ,N LET CI1-8 LET T1I(A1*(Z-1)§C)+(A2‘NTC)-(A2*(Z-1)TC) LET Y2IT1/N PRINT "VALUE OF Y AT NI",Y2 PRINT "CIMULATIVE [NIT TOTAL CIMULATIVE PRINT "PRODIETIW COST COST AVERAE READ X1 IF XIIO THEN 9999 IF X1>(Z—1) THEN 250 LET UIA1*(X1+C-X1-1) TC) LET TIA1*X1*C LET VIM/X198 PRINT X1,U,T,Y,T-X1*Y2 GO TO 170 LET TIA1’(Z-1)+C FOR XIZ TO N LET UIA2*(XTC-(X-1)TC) LET TITIU IF X1>X THEN 320 LET TIT/X PRINT X,U,T,V,TIX'Y2 NEXT X 00 TO 170 9999 END ACCDINT" EALANCE” Purpose: APPENDIX C3 Percent Change in N Required to Change YN by A Given Percentage To calculate the values presented in tables 6-1 and 6-2. Mathematics: Computes N1 and N2 in equations 6-6 and 6-7 fer N Comments: values of 100; 500; 1,000; 5,000; and 10,000; when Bc varies from those values corresponding to L-C percents of 70 to 99. Also computes the percentage intervals (N1-N)/N and (N2-N)/N. The program.listed is fer table 6-2. 200 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 $00 501 201 LISTING OF C3 READ M LET AILOG(2) FOR 1-1 TO 11 READ N PRINT N FOR N1-70 TO 99 LET CIlOO/Nl LET DILOG(C) LET BID/A LET XlI (B'LOG(N) -LOG( .90) ) IE LET X2I(B*LOG(N)-LOG(1.10))/B LET X1IEXP(X1) LET X2IEXP(X2) PRINT B,Xl,(Xl-N)/N,X2,(X2-N)/N mnNI PRINT NEXT I DATA 5, DATA 100,500,1000,5000,10000, 9999 END APPENDIX C4 Essential Modifications Purpose: To make the cost projections required to implement the L-C cost allocation model when there are essential modi- fications in the product or production procedures. Requirements: values of Al, Bl, 2, A2, 32, N, and P. A1 and El refer to the original parameters. A2 and B2 are the parameters of the changed portion of the product or pro- duction procedures. 2 is the output level at which the essential modification took place. P is the portion of the original product or production process which has not changed. Input Data Format: As many DATA statements as required beginning with DATA statement 500. Output Data Format: Same as Cl. Example: For the essential modification presented in Chapter V the input data.would be: 500 DATA 10045.7, .207572, 11, 7158.58, .230141, 30, .5, 501 DATA. 5, 10, 11, 15, 30, O 202 The output would be: 203 VALUE OF T AT N I 5912.57 CUMULATIVE UNIT TOTAL CUMULATIVE ACCOUNT PRODUCTION COST COST AVERAGE BALANCE 5 5828.76 35963.6 7192.75 6400.81 10 4989.33 62288.5 6228.85 3162.89 11 9601.9 71890.5 6535.5 6852.23 15 6185.75 98803.3 6586.89 10114.9 30 4753.64 177377. $912.57 -0- Mathematics: Similar to those in Appendix A4 through Z-l. After 2-1 the unit cost is: U'P'A1(XC1-(X-l)51) +A2( (X-2+1)Cz- (10.2)“) 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 204 LISTING OF C4 READ AI,81,Z,A2,82,N,P, LET C1I1-81 LET C2I1-82 LET T1IA1*(Z-1)+C1 FOR XIZ TO N LET T1IT1+P*A1*(XTC1-(X-1)+C1) NEXT X LET T1IT1+A2‘((N-Z+1)+C2) LET Y1IT1/N PRINT "VALUE OF Y AT N I",Y1 PRINT "CUMULATIVE UNIT TOTAL CUMULATIVE PRINT "PRODUCTION COST COST AVERAGE LET TIO READ X1 IF XIIO THEN 9999 IF X1>(Z-1) THEN 310 LET UIA1*(X1+CI-(X1-1)+Cl) LET TIAI'XITCI LET YIAI/XITBI PRINT X1 ,U,T,Y,T-X1*Yl GO TO 230 LET TIA1*(Z-1)+C1 FOR XIZ TO N ACCOINT" BALANCE" LET UIP‘A1*(X+C1-(X-1)+C1)+A2'((X-Z+1)TCZ-(XIZ)+C2) LET TIT+U IF X1>X 00 TO 380 LET YIT/X PRINT X,U,T,Y,T—X*Yl NEXT X 00 TO 250 9999 END APPENDIX D Relationship Between _b_ Parameter and L-C Percent APPENDIX D It was previously determined that a L-Ct of 90 had a 31 value approximately equal to .1520. This was arrived at by solving _b_ in (1-1) when X equaled 2, g equaled 100, and Y equaled 90. Here, when cumulative output doubled from 1 to 2 units, cunlative average time fell from 100 to 90. This same basic relationship can be used to solve for the relationship between any other L-C% and _b_. Solving (1-1) for _b_ in general terms we get: YIac/Xb Y-XbIa XbIa/Y bloom-10mm b. loggaG) 08 If X is set equal to 2, and 1 is set equal to 100, Y then repre- sents the L-C percent and we can solve for _b_. Table D lists the g values corresponding to L-C percents of 51 through 100. The program used to compute the values presented in table 0 is listed on the page following table D. 206 207 TABLE D b Values Corresponding to L—C Percents 51 to 100 L-ct 2_ L-Ct g. 51 0.97145 76 0.59592 52 0.94541 77 0.57707 55 0.91595 78 0.35845 54 0.88896 79 0.54007 55 0.86249 80 0.52192 56 0.85650 81 0.50400 57 0.81096 82 0.28650 58 0.78587 85 0.26881 59 0.76121 84 0.25155 60 0.75696 85 0.25446 61 0.71511 86 0.21759 62- 0.68966 87 0.20091 65 0.66657 88 0.18442 64 0.64585 89 0.16812 65 0.62148 90 0.15200 66 0.59946 91 0.15606 67 0.57776 92 0.12029 68 0.55659 95 0.10469 69 0.55555 94 .0892673 70 0.51457 95 .0740005 71 0.49410 96 .0588957 72 0.47595 97 .0459455 75 0.45405 98 .0291465 74 0.45440 99 .0144996 75 0.41503 100 0.0 10 20 30 4O 50 6O 70 LET AILOG(2) FOR N-51 TO 100 LET CIlOO/N LET DILOG(C) LET BID/A PRINT N,B NEXT N 9999 END 208 LISTING OF PROGRAM FOR D GQN TATE UN V nmnuum iunuugmliflyfflfl“ 12931008 "’Tiijmmwfir